Finite Group Databasebeta

← #16072644

Subgroups — #16072644

Order 3328.

1610 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123153C211yesmaximal, characteristic
2#13123142C211yesmaximal, characteristic, complemented
3#13122809C211yesmaximal, characteristic, complemented
4#13122790C211yesmaximal, characteristic, complemented
5#13122756C211yesmaximal, characteristic, complemented
6#13122635C211yesmaximal, characteristic, complemented
7#13122621C211yesmaximal, characteristic, complemented
8#13122523C211yesmaximal, characteristic, complemented
9#13122445C211yesmaximal, characteristic, complemented
10#13122430C211yesmaximal, characteristic, complemented
11#13122385C211yesmaximal, characteristic, complemented
12#13122328C211yesmaximal, characteristic, complemented
13#13122299C211yesmaximal, characteristic, complemented
14#13122268C211yesmaximal, characteristic, complemented
15#13121792C211yesmaximal, characteristic, complemented
16#13121729C211yesmaximal, characteristic, complemented
17#13121714C211yesmaximal, characteristic, complemented
18#13121294C211yesmaximal, characteristic, complemented
19#13120653C211yesmaximal, characteristic, complemented
20#13120619C211yesmaximal, characteristic
21#13119274C211yesmaximal, characteristic
22#13119217C211yesmaximal, characteristic, complemented
23#13118976C211yesmaximal, characteristic, complemented
24#13118643C211yesmaximal, characteristic
25#13118514C211yesmaximal, characteristic, complemented
26#13118317C211yesmaximal, characteristic
27#13118243C211yesmaximal, characteristic
28#13117502C211yesmaximal, characteristic
29#13117459C211yesmaximal, characteristic, complemented
30C2×#11718646C211yesmaximal, characteristic, complemented
31C13×#2484C211yesmaximal, characteristic, complemented
32C2×C13×#117C2211yescharacteristic
33C22×C13×C4⋊C4C2211yescharacteristic
34C2×#88183C2211yescharacteristic
35C2×#88183C2211yescharacteristic
36C2×#88180C2211yescharacteristic
37C22×C4⋊Dic13C2211yescharacteristic
38C22×C4⋊Dic13C2211yescharacteristic
39C22×C4⋊Dic13C2211yescharacteristic
40C22×C4×Dic13C2211yescharacteristic
41C2×#88152C2211yescharacteristic
42C2×#88151C2211yescharacteristic
43C2×#88144C2211yescharacteristic
44C2×#88143C2211yescharacteristic
45C2×#88135C2211yescharacteristic
46C2×#88132C2211yescharacteristic
47C13×#400C2211yescharacteristic
48C13×#400C2211yescharacteristic
49C13×#398C2211yescharacteristic
50C13×#398C2211yescharacteristic
51C13×#387C2211yescharacteristic
52C13×#387C2211yescharacteristic
53C13×#387C2211yescharacteristic
54C13×#387C2211yescharacteristic
55C13×#385C2211yescharacteristic
56C13×#385C2211yescharacteristic
57C13×#381C2211yescharacteristic
58C13×#381C2211yescharacteristic
59C13×#381C2211yescharacteristic
60#11718874C2211yescharacteristic
61#11718872C2211yescharacteristic
62#11718871C2211yescharacteristic
63C2×#88071C2211yescharacteristic
64C2×#88071C2211yescharacteristic
65#11718655C2211yescharacteristic
66#11718655C2211yescharacteristic
67#11718655C2211yescharacteristic
68#11718654C2211yescharacteristic
69#11718653C2211yescharacteristic
70#11718651C2211yescharacteristic
71#11718651C2211yescharacteristic
72#11718651C2211yescharacteristic
73#11718647C2211yescharacteristic
74#11718646C2211yescharacteristic
75#11718646C2211yescharacteristic
76#11718646C2211yescharacteristic
77#11718646C2211yescharacteristic
78#11718646C2211yescharacteristic
79#11718646C2211yescharacteristic
80#11718646C2211yescharacteristic
81#11718646C2211yescharacteristic
82#11718646C2211yescharacteristic
83#11718646C2211yescharacteristic
84#11718646C2211yescharacteristic
85#11718646C2211yescharacteristic
86#11718646C2211yescharacteristic
87#11718646C2211yescharacteristic
88#11718645C2211yescharacteristic
89#11718645C2211yescharacteristic
90#11718645C2211yescharacteristic
91#11718644C2211yescharacteristic
92#11718643C2211yescharacteristic
93#11718642C2211yescharacteristic
94#11718642C2211yescharacteristic
95#11718641C2211yescharacteristic
96#11718639C2211yescharacteristic
97#11718639C2211yescharacteristic
98#11718633C2211yescharacteristic
99#11718633C2211yescharacteristic
100#11718633C2211yescharacteristic
101#11718619C2211yescharacteristic
102#11718619C2211yescharacteristic
103#11718619C2211yescharacteristic
104#11718611C2211yescharacteristic
105#11718611C2211yescharacteristic
106#11718611C2211yescharacteristic
107#11718611C2211yescharacteristic
108#11718611C2211yescharacteristic
109#11718607C2211yescharacteristic
110#11718607C2211yescharacteristic
111#11718603C2211yescharacteristic
112#11718603C2211yescharacteristic
113#11718603C2211yescharacteristic
114C22⋊C4×Dic13C2211yescharacteristic
115#11718601C2211yescharacteristic
116#11718601C2211yescharacteristic
117#11718597C2211yescharacteristic
118#11718597C2211yescharacteristic
119#11718596C2211yescharacteristic
120#11718596C2211yescharacteristic
121#11718594C2211yescharacteristic
122#11718594C2211yescharacteristic
123#11718338C2211yescharacteristic
124#11718338C2211yescharacteristic
125#11718338C2211yescharacteristic
126#11718336C2211yescharacteristic
127#11718335C2211yescharacteristic
128#11718335C2211yescharacteristic
129#11718335C2211yescharacteristic
130#11718331C2211yescharacteristic
131#11718331C2211yescharacteristic
132#11718331C2211yescharacteristic
133#11718330C2211yescharacteristic
134#11718329C2211yescharacteristic
135#11718329C2211yescharacteristic
136#11718329C2211yescharacteristic
137#11718329C2211yescharacteristic
138#11718325C2211yescharacteristic
139C13⋊#401C2211yescharacteristic
140#11718322C2211yescharacteristic
141#11718322C2211yescharacteristic
142#11718322C2211yescharacteristic
143#11718322C2211yescharacteristic
144#11718322C2211yescharacteristic
145#11718322C2211yescharacteristic
146#11718322C2211yescharacteristic
147#11718321C2211yescharacteristic
148#11718321C2211yescharacteristic
149#11718321C2211yescharacteristic
150#11718321C2211yescharacteristic
151#11718320C2211yescharacteristic
152#11718320C2211yescharacteristic
153#11718320C2211yescharacteristic
154#11718319C2211yescharacteristic
155#11718319C2211yescharacteristic
156#11718318C2211yescharacteristic
157#11718318C2211yescharacteristic
158#11718318C2211yescharacteristic
159#11718318C2211yescharacteristic
160#11718317C2211yescharacteristic
161#11718317C2211yescharacteristic
162#11718317C2211yescharacteristic
163#11718317C2211yescharacteristic
164#11718316C2211yescharacteristic
165#11718316C2211yescharacteristic
166#11718316C2211yescharacteristic
167#11718316C2211yescharacteristic
168#11718316C2211yescharacteristic
169#11718315C2211yescharacteristic
170#11718315C2211yescharacteristic
171#11718315C2211yescharacteristic
172#11718315C2211yescharacteristic
173#11718314C2211yescharacteristic
174#11718314C2211yescharacteristic
175#11718314C2211yescharacteristic
176#11718313C2211yescharacteristic
177#11718313C2211yescharacteristic
178#11718313C2211yescharacteristic
179#11718312C2211yescharacteristic
180#11718312C2211yescharacteristic
181#11718311C2211yescharacteristic
182#11718308C2211yescharacteristic
183#11718308C2211yescharacteristic
184#11718308C2211yescharacteristic
185#11718308C2211yescharacteristic
186#11718307C2211yescharacteristic
187C23×C4×C13C2311yescharacteristic
188C23×C4×C13C2311yescharacteristic
189C23×C4×C13C2311yescharacteristic
190C22×C22⋊D13C2311yescharacteristic
191C23×Dic13C2311yescharacteristic
192C23×Dic13C2311yescharacteristic
193C23×Dic13C2311yescharacteristic
194C23×Dic13C2311yescharacteristic
195C22×C4×D13C2311yescharacteristic
196C22×Dic26C2311yescharacteristic
197C13×#117—24no—
198C2×C13×C4⋊C4—24no—
199C2×C13×C4⋊C4C2311yescharacteristic
200C2×C13×C4⋊C4C2311yescharacteristic
201C2×C13×C4⋊C4C2311yescharacteristic
202C2×C13×C4⋊C4C2311yescharacteristic
203C2×C13×C4⋊C4C2311yescharacteristic
204C2×C13×C4⋊C4C2311yescharacteristic
205C2×C13×C4⋊C4C2311yescharacteristic
206C2×C13×C4⋊C4C2311yescharacteristic
207C2×C13×C4⋊C4C2311yescharacteristic
208C2×C13×C4⋊C4C2311yescharacteristic
209C2×C13×C22⋊C4C2311yescharacteristic
210C2×C13×C22⋊C4C2311yescharacteristic
211C2×C13×C22⋊C4C2311yescharacteristic
212C2×C13×C22⋊C4C2311yescharacteristic
213C2×C42×C13C2311yescharacteristic
214C2×C42×C13C2311yescharacteristic
215C2×C22⋊Dic13C2311yescharacteristic
216C2×C22⋊Dic13C2311yescharacteristic
217C2×C22⋊Dic13C2311yescharacteristic
218#88183—24no—
219#88183—42no—
220C2×#6103C2311yescharacteristic
221C2×#6103C2311yescharacteristic
222C2×#6103C2311yescharacteristic
223C2×#6103C2311yescharacteristic
224C2×#6103C2311yescharacteristic
225C2×#6103C2311yescharacteristic
226C2×#6103C2311yescharacteristic
227C2×#6103C2311yescharacteristic
228C2×#6103C2311yescharacteristic
229C2×#6103C2311yescharacteristic
230C2×#6103C2311yescharacteristic
231C2×#6103C2311yescharacteristic
232C2×#6103C2311yescharacteristic
233#88180—42no—
234C2×C4⋊Dic13—42no—
235C2×C4⋊Dic13—42no—
236C2×C4⋊Dic13—42no—
237C2×C4⋊Dic13C2311yescharacteristic
238C2×C4⋊Dic13C2311yescharacteristic
239C2×C4⋊Dic13C2311yescharacteristic
240C2×C4⋊Dic13C2311yescharacteristic
241C2×C4⋊Dic13C2311yescharacteristic
242C2×C4⋊Dic13C2311yescharacteristic
243C2×C4⋊Dic13C2311yescharacteristic
244C2×C4⋊Dic13C2311yescharacteristic
245C2×C4⋊Dic13C2311yescharacteristic
246C2×C4⋊Dic13C2311yescharacteristic
247C2×C4⋊Dic13C2311yescharacteristic
248C2×C4⋊Dic13C2311yescharacteristic
249C2×C4⋊Dic13C2311yescharacteristic
250C2×C4⋊Dic13C2311yescharacteristic
251C2×C4⋊Dic13C2311yescharacteristic
252C2×C4⋊Dic13C2311yescharacteristic
253C2×C4⋊Dic13C2311yescharacteristic
254C2×C4⋊Dic13C2311yescharacteristic
255C2×C4⋊Dic13C2311yescharacteristic
256C2×C4⋊Dic13C2311yescharacteristic
257C2×C4⋊Dic13C2311yescharacteristic
258C2×C4⋊Dic13C2311yescharacteristic
259C2×C4⋊Dic13C2311yescharacteristic
260C2×C4⋊Dic13C2311yescharacteristic
261C2×C4⋊Dic13C2311yescharacteristic
262C2×#6101C2311yescharacteristic
263C2×#6101C2311yescharacteristic
264C2×#6101C2311yescharacteristic
265C2×#6101C2311yescharacteristic
266C2×#6101C2311yescharacteristic
267C2×#6101C2311yescharacteristic
268C2×#6101C2311yescharacteristic
269C2×#6101C2311yescharacteristic
270C2×#6101C2311yescharacteristic
271C2×#6101C2311yescharacteristic
272C2×#6101C2311yescharacteristic
273C2×#6101C2311yescharacteristic
274C2×#6101C2311yescharacteristic
275C2×#6101C2311yescharacteristic
276C2×#6101C2311yescharacteristic
277C2×#6101C2311yescharacteristic
278C2×#6101C2311yescharacteristic
279C2×#6101C2311yescharacteristic
280C2×#6101C2311yescharacteristic
281C2×C4×Dic13—42no—
282C2×C4×Dic13C2311yescharacteristic
283C2×C4×Dic13C2311yescharacteristic
284C2×C4×Dic13C2311yescharacteristic
285C2×C4×Dic13C2311yescharacteristic
286C2×C4×Dic13C2311yescharacteristic
287C2×C4×Dic13C2311yescharacteristic
288C2×C4×Dic13C2311yescharacteristic
289C2×C4×Dic13C2311yescharacteristic
290C2×C4×Dic13C2311yescharacteristic
291#88152—42no—
292#88151—42no—
293#88144—42no—
294#88143—42no—
295#88135—42no—
296#88132—42no—
297C13×#95C2311yescharacteristic
298C13×#95C2311yescharacteristic
299C13×#95C2311yescharacteristic
300C13×#95C2311yescharacteristic
301C13×#95C2311yescharacteristic
302C13×#95C2311yescharacteristic
303C13×#95C2311yescharacteristic
304C13×#95C2311yescharacteristic
305C13×#95C2311yescharacteristic
306C13×#95C2311yescharacteristic
307C13×#95C2311yescharacteristic
308C13×#95C2311yescharacteristic
309C13×#95C2311yescharacteristic
310C13×#95C2311yescharacteristic
311C13×#95C2311yescharacteristic
312C13×#95C2311yescharacteristic
313#88071C2311yescharacteristic
314#88071C2311yescharacteristic
315#88071C2311yescharacteristic
316#88071C2311yescharacteristic
317#88071C2311yescharacteristic
318#88071C2311yescharacteristic
319#88071C2311yescharacteristic
320#88071C2311yescharacteristic
321#88071C2311yescharacteristic
322#88071C2311yescharacteristic
323#88071C2311yescharacteristic
324#88071C2311yescharacteristic
325#88071C2311yescharacteristic
326#88071C2311yescharacteristic
327#88071C2311yescharacteristic
328#88071C2311yescharacteristic
329#88071C2311yescharacteristic
330#88071C2311yescharacteristic
331#88071C2311yescharacteristic
332#88071C2311yescharacteristic
333#88071C2311yescharacteristic
334#88071C2311yescharacteristic
335#88071C2311yescharacteristic
336#88071C2311yescharacteristic
337#88071C2311yescharacteristic
338#88071C2311yescharacteristic
339#88071C2311yescharacteristic
340#88071C2311yescharacteristic
341#88071C2311yescharacteristic
342#88071C2311yescharacteristic
343#88071C2311yescharacteristic
344#88071C2311yescharacteristic
345#88071C2311yescharacteristic
346#88071C2311yescharacteristic
347#88071C2311yescharacteristic
348#88071C2311yescharacteristic
349#88071C2311yescharacteristic
350#88071C2311yescharacteristic
351#88071C2311yescharacteristic
352#88071C2311yescharacteristic
353#88071C2311yescharacteristic
354#88071C2311yescharacteristic
355#88071C2311yescharacteristic
356#88071C2311yescharacteristic
357#36824—131nomaximal, Sylow
358C24×C13C2411yescharacteristic
359C23×D13C2411yescharacteristic
360C22×C4×C13—22no—
361C22×C4×C13—22no—
362C22×C4×C13—22no—
363C22×C4×C13—22no—
364C22×C4×C13—22no—
365C22×C4×C13—22no—
366C22×C4×C13—22no—
367C22×C4×C13—22no—
368C22×C4×C13#4114yes—
369C22×C4×C13C2411yescharacteristic
370C22×C4×C13C2411yescharacteristic
371C22×C4×C13C2411yescharacteristic
372C22×C4×C13C2411yescharacteristic
373C22×C4×C13C2411yescharacteristic
374C22×C4×C13C2411yescharacteristic
375C22×C4×C13C2411yescharacteristic
376C22×C4×C13C2411yescharacteristic
377C22×C4×C13C2411yescharacteristic
378C22×C4×C13C2411yescharacteristic
379C22×C4×C13C2411yescharacteristic
380C22×C4×C13C2411yescharacteristic
381C22×C4×C13C2411yescharacteristic
382C22×C4×C13C2411yescharacteristic
383C2×C22⋊D13—22no—
384C2×C22⋊D13—22no—
385C2×C22⋊D13—22no—
386C22×Dic13—22no—
387C22×Dic13—22no—
388C22×Dic13—22no—
389C22×Dic13—22no—
390C22×Dic13—22no—
391C22×Dic13—41no—
392C22×Dic13—41no—
393C22×Dic13—41no—
394C22×Dic13—41no—
395C22×Dic13—41no—
396C22×Dic13—41no—
397C22×Dic13—41no—
398C22×Dic13C2411yescharacteristic
399C22×Dic13C2411yescharacteristic
400C22×Dic13C2411yescharacteristic
401C22×Dic13C2411yescharacteristic
402C22×Dic13C2411yescharacteristic
403C22×Dic13C2411yescharacteristic
404C22×Dic13C2411yescharacteristic
405C22×Dic13C2411yescharacteristic
406C22×Dic13C2411yescharacteristic
407C22×Dic13C2411yescharacteristic
408C22×Dic13C2411yescharacteristic
409C22×Dic13C2411yescharacteristic
410C22×Dic13C2411yescharacteristic
411C22×Dic13C2411yescharacteristic
412C22×Dic13C2411yescharacteristic
413C2×C4×D13—41no—
414C2×C4×D13—41no—
415C2×C4×D13—41no—
416C2×Dic26—41no—
417C2×Dic26—41no—
418C2×Dic26—41no—
419C13×C4⋊C4—22no—
420C13×C4⋊C4—22no—
421C13×C4⋊C4—22no—
422C13×C4⋊C4—22no—
423C13×C4⋊C4—22no—
424C13×C4⋊C4—22no—
425C13×C4⋊C4—22no—
426C13×C4⋊C4—22no—
427C13×C4⋊C4—22no—
428C13×C4⋊C4—22no—
429C13×C22⋊C4—22no—
430C13×C22⋊C4—22no—
431C13×C22⋊C4—22no—
432C13×C22⋊C4—22no—
433C42×C13—22no—
434C42×C13—22no—
435C22⋊Dic13—22no—
436C22⋊Dic13—22no—
437C22⋊Dic13—22no—
438#6103—22no—
439#6103—22no—
440#6103—22no—
441#6103—22no—
442#6103—22no—
443#6103—41no—
444#6103—41no—
445#6103—41no—
446#6103—41no—
447#6103—41no—
448#6103—41no—
449#6103—41no—
450#6103—41no—
451C4⋊Dic13—22no—
452C4⋊Dic13—22no—
453C4⋊Dic13—41no—
454C4⋊Dic13—41no—
455C4⋊Dic13—41no—
456C4⋊Dic13—41no—
457C4⋊Dic13—41no—
458C4⋊Dic13—41no—
459C4⋊Dic13—41no—
460C4⋊Dic13—41no—
461C4⋊Dic13—41no—
462C4⋊Dic13—41no—
463C4⋊Dic13—41no—
464C4⋊Dic13—41no—
465C4⋊Dic13—41no—
466C4⋊Dic13—41no—
467C4⋊Dic13—41no—
468C4⋊Dic13—41no—
469C4⋊Dic13—41no—
470C4⋊Dic13—41no—
471C4⋊Dic13—41no—
472C4⋊Dic13—41no—
473C4⋊Dic13—41no—
474C4⋊Dic13—41no—
475C4⋊Dic13—41no—
476#6101—22no—
477#6101—22no—
478#6101—22no—
479#6101—22no—
480#6101—22no—
481#6101—22no—
482#6101—22no—
483#6101—41no—
484#6101—41no—
485#6101—41no—
486#6101—41no—
487#6101—41no—
488#6101—41no—
489#6101—41no—
490#6101—41no—
491#6101—41no—
492#6101—41no—
493#6101—41no—
494#6101—41no—
495C4×Dic13—22no—
496C4×Dic13—22no—
497C4×Dic13—41no—
498C4×Dic13—41no—
499C4×Dic13—41no—
500C4×Dic13—41no—
501C4×Dic13—41no—
502C4×Dic13—41no—
503C4×Dic13—41no—
504#2852—131no—
505#2851—131no—
506#2807—131no—
507#2805—131no—
508#2802—131no—
509#2792—131no—
510#2791—131no—
511#2783—131no—
512#2777—131no—
513#2776—131no—
514#2773—131no—
515#2769—131no—
516#2767—131no—
517#2765—131no—
518#2726—131no—
519#2721—131no—
520#2720—131no—
521#2689—131no—
522#2627—131no—
523#2623—131no—
524#2498—131no—
525#2493—131no—
526#2484D1311yescharacteristic, complemented
527#2473—131no—
528#2449—131no—
529#2438—131no—
530#2419—131no—
531#2413—131no—
532#2322—131no—
533#2317—131no—
534C2×#389—131no—
535C23×C13—21no—
536C23×C13—21no—
537C23×C13—21no—
538C23×C13—21no—
539C23×C13C2×#4112yes—
540C23×C13H(5,𝔽2)12yes—
541C23×C132−1+412yes—
542C23×C13C2511yescharacteristic
543C22×D13—21no—
544C22×D13—21no—
545C22×D13—21no—
546C22×D13—21no—
547C22×D13—21no—
548C22×D13—21no—
549C22×D13—21no—
550C2×C4×C13—28no—
551C2×C4×C13—28no—
552C2×C4×C13—21no—
553C2×C4×C13—21no—
554C2×C4×C13—21no—
555C2×C4×C13—21no—
556C2×C4×C13—21no—
557C2×C4×C13—21no—
558C2×C4×C13—21no—
559C2×C4×C13—21no—
560C2×C4×C13—21no—
561C2×C4×C13—21no—
562C2×C4×C13—21no—
563C2×C4×C13—21no—
564C2×C4×C13—21no—
565C2×C4×C13—21no—
566C2×C4×C13—21no—
567C2×C4×C13—21no—
568C2×C4×C13—21no—
569C2×C4×C13—21no—
570C2×C4×C13—21no—
571C2×C4×C13—21no—
572C2×C4×C13—21no—
573C2×C4×C13—21no—
574C2×C4×C13—21no—
575C2×C4×C13—21no—
576C2×C4×C13—21no—
577C2×C4×C13—21no—
578C2×C4×C13—21no—
579C2×C4×C13—21no—
580C2×C4×C13—21no—
581C2×C4×C13—21no—
582C2×C4×C13—21no—
583C2×C4×C13—21no—
584C2×C4×C13—21no—
585C2×C4×C13—21no—
586C2×C4×C13—21no—
587C2×C4×C13—21no—
588C2×C4×C13—21no—
589C2×C4×C13—21no—
590C2×C4×C13—44no—
591C2×C4×C13C2×#4112yes—
592C2×C4×C13C2×#4112yes—
593C2×C4×C13H(5,𝔽2)12yes—
594C2×C4×C132−1+412yes—
595C22⋊D13—44no—
596C2×Dic13—21no—
597C2×Dic13—21no—
598C2×Dic13—21no—
599C2×Dic13—21no—
600C2×Dic13—21no—
601C2×Dic13—21no—
602C2×Dic13—21no—
603C2×Dic13—21no—
604C2×Dic13—21no—
605C2×Dic13—21no—
606C2×Dic13—21no—
607C2×Dic13—21no—
608C2×Dic13—21no—
609C2×Dic13—21no—
610C2×Dic13—21no—
611C2×Dic13—21no—
612C2×Dic13—21no—
613C2×Dic13—21no—
614C2×Dic13—21no—
615C2×Dic13—21no—
616C2×Dic13—21no—
617C2×Dic13—21no—
618C2×Dic13—21no—
619C2×Dic13—21no—
620C2×Dic13—21no—
621C2×Dic13—21no—
622C2×Dic13—21no—
623C2×Dic13—21no—
624C2×Dic13—21no—
625C2×Dic13—21no—
626C2×Dic13—21no—
627C2×Dic13—21no—
628C2×Dic13—21no—
629C2×Dic13—21no—
630C2×Dic13—21no—
631C2×Dic13—21no—
632C2×Dic13—21no—
633C2×Dic13—21no—
634C2×Dic13—21no—
635C2×Dic13—21no—
636C2×Dic13—21no—
637C2×Dic13—21no—
638C2×Dic13—21no—
639C2×Dic13—21no—
640C2×Dic13—44no—
641C2×Dic13—44no—
642C2×Dic13—82no—
643C2×Dic13—82no—
644C2×Dic132−1+412yes—
645C4×D13—82no—
646Dic26—82no—
647C2×#126—131no—
648C2×#125—131no—
649C2×#125—131no—
650C2×#123—131no—
651C2×#123—131no—
652C2×C22⋊Q8—131no—
653C2×C22⋊Q8—131no—
654C2×C4×D4—131no—
655C2×#117—131no—
656C2×#117C2×D1311yescharacteristic
657C22×C4⋊C4—131no—
658C22×C4⋊C4—131no—
659C22×C4⋊C4—131no—
660C22×C4⋊C4C2×D1311yescharacteristic
661C22×C42—131no—
662#401—131no—
663#400—131no—
664#400—131no—
665#400—131no—
666#400—131no—
667#400—131no—
668#400—131no—
669#400—131no—
670#400—131no—
671#400—131no—
672#400—131no—
673#400—131no—
674#400C2×D1311yescharacteristic
675#400C2×D1311yescharacteristic
676#399—131no—
677#399—131no—
678#399—131no—
679#399—131no—
680#398—131no—
681#398—131no—
682#398—131no—
683#398—131no—
684#398—131no—
685#398—131no—
686#398—131no—
687#398—131no—
688#398—131no—
689#398—131no—
690#398—131no—
691#398—131no—
692#398—131no—
693#398—131no—
694#398—131no—
695#398—131no—
696#398C2×D1311yescharacteristic
697#398C2×D1311yescharacteristic
698#397—131no—
699#397—131no—
700#397—131no—
701#397—131no—
702#397—131no—
703#396—131no—
704#396—131no—
705#396—131no—
706#395—131no—
707#395—131no—
708#395—131no—
709#395—131no—
710#391—131no—
711#389—131no—
712#389—131no—
713#389—131no—
714#389—131no—
715#389—131no—
716#389—131no—
717#389—131no—
718#389—131no—
719#389—131no—
720#389—131no—
721#389—131no—
722#389—131no—
723#389—131no—
724#389—131no—
725#389—131no—
726#389—131no—
727#389—131no—
728#389—131no—
729#389—131no—
730#389—131no—
731#389—131no—
732#388—131no—
733#388—131no—
734#388—131no—
735#388—131no—
736#388—131no—
737#388—131no—
738#388—131no—
739#388—131no—
740#388—131no—
741#387—131no—
742#387—131no—
743#387—131no—
744#387—131no—
745#387—131no—
746#387—131no—
747#387—131no—
748#387—131no—
749#387—131no—
750#387—131no—
751#387—131no—
752#387—131no—
753#387—131no—
754#387—131no—
755#387—131no—
756#387—131no—
757#387—131no—
758#387—131no—
759#387—131no—
760#387—131no—
761#387—131no—
762#387C2×D1311yescharacteristic
763#387C2×D1311yescharacteristic
764#387C2×D1311yescharacteristic
765#387C2×D1311yescharacteristic
766#386—131no—
767#386—131no—
768#386—131no—
769#386—131no—
770#385—131no—
771#385—131no—
772#385—131no—
773#385—131no—
774#385—131no—
775#385—131no—
776#385—131no—
777#385—131no—
778#385—131no—
779#385—131no—
780#385—131no—
781#385—131no—
782#385C2×D1311yescharacteristic
783#385C2×D1311yescharacteristic
784#384—131no—
785#384—131no—
786#383—131no—
787#383—131no—
788#382—131no—
789#382—131no—
790#382—131no—
791#381—131no—
792#381—131no—
793#381C2×D1311yescharacteristic
794#381C2×D1311yescharacteristic
795#381C2×D1311yescharacteristic
796#380—131no—
797#380—131no—
798#380—131no—
799C4×C22⋊C4—131no—
800C2×#95—131no—
801C2×#95—131no—
802C22×C13—22no—
803C22×C13—22no—
804C22×C13—22no—
805C22×C13—22no—
806C22×C13—22no—
807C22×C13—22no—
808C22×C13#53914yes—
809C22×C13C22×#4111yescharacteristic
810C22×C13C2×H(5,𝔽2)11yescharacteristic
811C22×C13C2×H(5,𝔽2)11yescharacteristic
812C22×C13C2×2−1+411yescharacteristic
813C22×C13C2×2−1+411yescharacteristic
814C22×C13C2×2−1+411yescharacteristic
815C22×C13#58511yescharacteristic
816C2×D13—41no—
817C2×D13—41no—
818C2×D13—41no—
819C2×D13—41no—
820C2×D13—41no—
821C2×D13—41no—
822C2×D13—41no—
823C4×C13—22no—
824C4×C13—22no—
825C4×C13—22no—
826C4×C13—22no—
827C4×C13—41no—
828C4×C13—41no—
829C4×C13—41no—
830C4×C13—41no—
831C4×C13—41no—
832C4×C13—41no—
833C4×C13—41no—
834C4×C13—41no—
835C4×C13—41no—
836C4×C13—41no—
837Dic13—22no—
838Dic13—41no—
839Dic13—41no—
840Dic13—41no—
841Dic13—41no—
842Dic13—41no—
843Dic13—41no—
844Dic13—41no—
845Dic13—41no—
846Dic13—41no—
847Dic13—41no—
848Dic13—41no—
849Dic13—41no—
850Dic13—41no—
851Dic13—41no—
852C22×Q8—131no—
853C22×D4—131no—
854C23×C4—131no—
855C23×C4—131no—
856C23×C4—131no—
857C23×C4—131no—
858C23×C4—131no—
859C23×C4C22×D1311yescharacteristic
860C23×C4C22×D1311yescharacteristic
861C23×C4C22×D1311yescharacteristic
862#126—522no—
863#125—522no—
864#125—522no—
865#123—264no—
866#123—522no—
867C22⋊Q8—522no—
868C22⋊Q8—522no—
869C4×D4—522no—
870#117—24no—
871#117—522no—
872C2×C4⋊C4—24no—
873C2×C4⋊C4—131no—
874C2×C4⋊C4—131no—
875C2×C4⋊C4—131no—
876C2×C4⋊C4—131no—
877C2×C4⋊C4—131no—
878C2×C4⋊C4—131no—
879C2×C4⋊C4—131no—
880C2×C4⋊C4—131no—
881C2×C4⋊C4—131no—
882C2×C4⋊C4—131no—
883C2×C4⋊C4—131no—
884C2×C4⋊C4—131no—
885C2×C4⋊C4—131no—
886C2×C4⋊C4—131no—
887C2×C4⋊C4—131no—
888C2×C4⋊C4—131no—
889C2×C4⋊C4—131no—
890C2×C4⋊C4—131no—
891C2×C4⋊C4—131no—
892C2×C4⋊C4—131no—
893C2×C4⋊C4—131no—
894C2×C4⋊C4—131no—
895C2×C4⋊C4—131no—
896C2×C4⋊C4—131no—
897C2×C4⋊C4—131no—
898C2×C4⋊C4—131no—
899C2×C4⋊C4—131no—
900C2×C4⋊C4—131no—
901C2×C4⋊C4—131no—
902C2×C4⋊C4—131no—
903C2×C4⋊C4—131no—
904C2×C4⋊C4—131no—
905C2×C4⋊C4—131no—
906C2×C4⋊C4—131no—
907C2×C4⋊C4—131no—
908C2×C4⋊C4—131no—
909C2×C4⋊C4—131no—
910C2×C4⋊C4—131no—
911C2×C4⋊C4—131no—
912C2×C4⋊C4—131no—
913C2×C4⋊C4—131no—
914C2×C4⋊C4—131no—
915C2×C4⋊C4—131no—
916C2×C4⋊C4—131no—
917C2×C4⋊C4—522no—
918C2×C4⋊C4—522no—
919C2×C4⋊C4—522no—
920C2×C4⋊C4C22×D1311yescharacteristic
921C2×C4⋊C4C22×D1311yescharacteristic
922C2×C4⋊C4C22×D1311yescharacteristic
923C2×C4⋊C4C22×D1311yescharacteristic
924C2×C4⋊C4C22×D1311yescharacteristic
925C2×C4⋊C4C22×D1311yescharacteristic
926C2×C4⋊C4C22×D1311yescharacteristic
927C2×C4⋊C4C22×D1311yescharacteristic
928C2×C4⋊C4C22×D1311yescharacteristic
929C2×C4⋊C4C22×D1311yescharacteristic
930C2×C22⋊C4—131no—
931C2×C22⋊C4—131no—
932C2×C22⋊C4—131no—
933C2×C22⋊C4—131no—
934C2×C22⋊C4—131no—
935C2×C22⋊C4—131no—
936C2×C22⋊C4—131no—
937C2×C22⋊C4—131no—
938C2×C22⋊C4—131no—
939C2×C22⋊C4—131no—
940C2×C22⋊C4—131no—
941C2×C22⋊C4—131no—
942C2×C22⋊C4—131no—
943C2×C22⋊C4—131no—
944C2×C22⋊C4—131no—
945C2×C22⋊C4—131no—
946C2×C22⋊C4C22×D1311yescharacteristic
947C2×C22⋊C4C22×D1311yescharacteristic
948C2×C22⋊C4C22×D1311yescharacteristic
949C2×C22⋊C4C22×D1311yescharacteristic
950C2×C42—131no—
951C2×C42—131no—
952C2×C42—131no—
953C2×C42—131no—
954C2×C42—131no—
955C2×C42—131no—
956C2×C42—131no—
957C2×C42—131no—
958C2×C42—131no—
959C2×C42—522no—
960C2×C42C22×D1311yescharacteristic
961C2×C42C22×D1311yescharacteristic
962#95—131no—
963#95—131no—
964#95—131no—
965#95—131no—
966#95—131no—
967#95—131no—
968#95—131no—
969#95—131no—
970#95—131no—
971#95—131no—
972#95—131no—
973#95—131no—
974#95—131no—
975#95—131no—
976#95—131no—
977#95—131no—
978#95—131no—
979#95—131no—
980#95—131no—
981#95—131no—
982#95—131no—
983#95—131no—
984#95—131no—
985#95—131no—
986#95—131no—
987#95—131no—
988#95—131no—
989#95—131no—
990#95—131no—
991#95—131no—
992#95—131no—
993#95—131no—
994#95—131no—
995#95—131no—
996#95—131no—
997#95—131no—
998#95—131no—
999#95—131no—
1000#95—131no—
1001#95—131no—
1002#95—131no—
1003#95—131no—
1004#95—131no—
1005#95—131no—
1006#95C22×D1311yescharacteristic
1007#95C22×D1311yescharacteristic
1008#95C22×D1311yescharacteristic
1009#95C22×D1311yescharacteristic
1010#95C22×D1311yescharacteristic
1011#95C22×D1311yescharacteristic
1012#95C22×D1311yescharacteristic
1013#95C22×D1311yescharacteristic
1014#95C22×D1311yescharacteristic
1015#95C22×D1311yescharacteristic
1016#95C22×D1311yescharacteristic
1017#95C22×D1311yescharacteristic
1018#95C22×D1311yescharacteristic
1019#95C22×D1311yescharacteristic
1020#95C22×D1311yescharacteristic
1021#95C22×D1311yescharacteristic
1022C2×C13—24no—
1023C2×C13C2×#53911yescharacteristic
1024C2×C13#349211yescharacteristic
1025C2×C13#350711yescharacteristic
1026C2×C13#353811yescharacteristic
1027C2×C13#354211yescharacteristic
1028C2×C13#354411yescharacteristic
1029C2×C13#356311yescharacteristic
1030D13—81no—
1031C24—131no—
1032C24C23×D1311yescharacteristic
1033C2×Q8—521no—
1034C2×Q8—521no—
1035C2×Q8—521no—
1036C2×D4—262no—
1037C2×D4—262no—
1038C2×D4—262no—
1039C22×C4—22no—
1040C22×C4—22no—
1041C22×C4—22no—
1042C22×C4—22no—
1043C22×C4—22no—
1044C22×C4—22no—
1045C22×C4—22no—
1046C22×C4—22no—
1047C22×C4—131no—
1048C22×C4—131no—
1049C22×C4—131no—
1050C22×C4—131no—
1051C22×C4—131no—
1052C22×C4—131no—
1053C22×C4—131no—
1054C22×C4—131no—
1055C22×C4—131no—
1056C22×C4—131no—
1057C22×C4—131no—
1058C22×C4—131no—
1059C22×C4—131no—
1060C22×C4—131no—
1061C22×C4—131no—
1062C22×C4—262no—
1063C22×C4—262no—
1064C22×C4—262no—
1065C22×C4—262no—
1066C22×C4—262no—
1067C22×C4—521no—
1068C22×C4—521no—
1069C22×C4—521no—
1070C22×C4—521no—
1071C22×C4—521no—
1072C22×C4—521no—
1073C22×C4—521no—
1074C22×C4—521no—
1075C22×C4—521no—
1076C22×C4—521no—
1077C22×C4#612914yes—
1078C22×C4C23×D1311yescharacteristic
1079C22×C4C23×D1311yescharacteristic
1080C22×C4C23×D1311yescharacteristic
1081C22×C4C23×D1311yescharacteristic
1082C22×C4C23×D1311yescharacteristic
1083C22×C4C23×D1311yescharacteristic
1084C22×C4C23×D1311yescharacteristic
1085C22×C4C23×D1311yescharacteristic
1086C22×C4C23×D1311yescharacteristic
1087C22×C4C23×D1311yescharacteristic
1088C22×C4C23×D1311yescharacteristic
1089C22×C4C23×D1311yescharacteristic
1090C22×C4C23×D1311yescharacteristic
1091C22×C4C23×D1311yescharacteristic
1092C4⋊C4—22no—
1093C4⋊C4—22no—
1094C4⋊C4—22no—
1095C4⋊C4—22no—
1096C4⋊C4—22no—
1097C4⋊C4—22no—
1098C4⋊C4—22no—
1099C4⋊C4—22no—
1100C4⋊C4—22no—
1101C4⋊C4—22no—
1102C4⋊C4—262no—
1103C4⋊C4—262no—
1104C4⋊C4—262no—
1105C4⋊C4—262no—
1106C4⋊C4—262no—
1107C4⋊C4—262no—
1108C4⋊C4—262no—
1109C4⋊C4—262no—
1110C4⋊C4—262no—
1111C4⋊C4—521no—
1112C4⋊C4—521no—
1113C4⋊C4—521no—
1114C4⋊C4—521no—
1115C4⋊C4—521no—
1116C4⋊C4—521no—
1117C4⋊C4—521no—
1118C4⋊C4—521no—
1119C4⋊C4—521no—
1120C4⋊C4—521no—
1121C4⋊C4—521no—
1122C4⋊C4—521no—
1123C4⋊C4—521no—
1124C4⋊C4—521no—
1125C4⋊C4—521no—
1126C4⋊C4—521no—
1127C4⋊C4—521no—
1128C4⋊C4—521no—
1129C4⋊C4—521no—
1130C4⋊C4—521no—
1131C4⋊C4—521no—
1132C4⋊C4—521no—
1133C4⋊C4—521no—
1134C4⋊C4—521no—
1135C4⋊C4—521no—
1136C4⋊C4—521no—
1137C4⋊C4—521no—
1138C4⋊C4—521no—
1139C4⋊C4—521no—
1140C4⋊C4—521no—
1141C4⋊C4—521no—
1142C4⋊C4—521no—
1143C4⋊C4—521no—
1144C4⋊C4—521no—
1145C4⋊C4—521no—
1146C22⋊C4—22no—
1147C22⋊C4—22no—
1148C22⋊C4—22no—
1149C22⋊C4—22no—
1150C22⋊C4—262no—
1151C22⋊C4—262no—
1152C22⋊C4—262no—
1153C22⋊C4—262no—
1154C22⋊C4—262no—
1155C22⋊C4—262no—
1156C22⋊C4—262no—
1157C22⋊C4—262no—
1158C22⋊C4—521no—
1159C22⋊C4—521no—
1160C22⋊C4—521no—
1161C22⋊C4—521no—
1162C22⋊C4—521no—
1163C22⋊C4—521no—
1164C22⋊C4—521no—
1165C22⋊C4—521no—
1166C42—22no—
1167C42—22no—
1168C42—262no—
1169C42—262no—
1170C42—521no—
1171C42—521no—
1172C42—521no—
1173C42—521no—
1174C42—521no—
1175C42—521no—
1176C42—521no—
1177C13#3682411yescharacteristic, complemented, Sylow
1178C23—21no—
1179C23—21no—
1180C23—21no—
1181C23—21no—
1182C23—261no—
1183C23—261no—
1184C23—261no—
1185C23—261no—
1186C23—261no—
1187C23—261no—
1188C23—261no—
1189C23C2×#612912yes—
1190C23#8825612yes—
1191C23#8825712yes—
1192C23C24×D1311yescharacteristic
1193Q8—1042no—
1194D4—524no—
1195C2×C4—28no—
1196C2×C4—28no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—44no—
1236C2×C4—132no—
1237C2×C4—261no—
1238C2×C4—261no—
1239C2×C4—261no—
1240C2×C4—261no—
1241C2×C4—261no—
1242C2×C4—261no—
1243C2×C4—261no—
1244C2×C4—261no—
1245C2×C4—261no—
1246C2×C4—261no—
1247C2×C4—261no—
1248C2×C4—261no—
1249C2×C4—261no—
1250C2×C4—261no—
1251C2×C4—261no—
1252C2×C4—261no—
1253C2×C4—261no—
1254C2×C4—261no—
1255C2×C4—261no—
1256C2×C4—261no—
1257C2×C4—261no—
1258C2×C4—261no—
1259C2×C4—261no—
1260C2×C4—261no—
1261C2×C4—261no—
1262C2×C4—261no—
1263C2×C4—261no—
1264C2×C4—261no—
1265C2×C4—261no—
1266C2×C4—261no—
1267C2×C4—261no—
1268C2×C4—261no—
1269C2×C4—261no—
1270C2×C4—261no—
1271C2×C4—261no—
1272C2×C4—261no—
1273C2×C4—261no—
1274C2×C4—261no—
1275C2×C4—261no—
1276C2×C4—261no—
1277C2×C4—261no—
1278C2×C4—261no—
1279C2×C4—261no—
1280C2×C4—261no—
1281C2×C4—524no—
1282C2×C4—524no—
1283C2×C4—1042no—
1284C2×C4—1042no—
1285C2×C4—1042no—
1286C2×C4C2×#612912yes—
1287C2×C4C2×#612912yes—
1288C2×C4#8825612yes—
1289C2×C4#8825712yes—
1290C22—22no—
1291C22—22no—
1292C22—22no—
1293C22—22no—
1294C22—22no—
1295C22—22no—
1296C22—521no—
1297C22—521no—
1298C22—521no—
1299C22—521no—
1300C22—521no—
1301C22—521no—
1302C22—521no—
1303C22#1171937014yes—
1304C22C22×#612911yescharacteristic
1305C22C2×#8825611yescharacteristic
1306C22C2×#8825611yescharacteristic
1307C22C2×#8825711yescharacteristic
1308C22C2×#8825711yescharacteristic
1309C22D13×2−1+411yescharacteristic
1310C22#1171965211yescharacteristic
1311C4—22no—
1312C4—22no—
1313C4—22no—
1314C4—22no—
1315C4—41no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—41no—
1325C4—262no—
1326C4—521no—
1327C4—521no—
1328C4—521no—
1329C4—521no—
1330C4—521no—
1331C4—521no—
1332C4—521no—
1333C4—521no—
1334C4—521no—
1335C4—521no—
1336C4—521no—
1337C4—521no—
1338C4—521no—
1339C4—521no—
1340C2—24no—
1341C2—1041no—
1342C2C2×#1171937011yescharacteristic
1343C2#1312854211yescharacteristic
1344C2#1312870011yescharacteristic
1345C2#1312908211yescharacteristic
1346C2#1312914611yescharacteristic
1347C2#1312917811yescharacteristic
1348C2#1312943711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutator, socle, cosocleC23×C13C25
FittingC13×#2484C2
prime radicalC22×C22⋊D13C23
hypercenter#2484D13
hypocenterC13#36824
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2484

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #13123142C2semidirect
3. #13122809C2semidirect
4. #13122790C2semidirect
5. #13122756C2semidirect
6. #13122635C2semidirect
7. #13122621C2semidirect
8. #13122523C2semidirect
9. #13122445C2semidirect
10. #13122430C2semidirect
11. #13122385C2semidirect
12. #13122328C2semidirect
13. #13122299C2semidirect
14. #13122268C2semidirect
15. #13121792C2semidirect
16. #13121729C2semidirect
17. #13121714C2semidirect
18. #13121294C2semidirect
19. #13120653C2semidirect
22. #13119217C2semidirect
23. #13118976C2semidirect
25. #13118514C2semidirect
29. #13117459C2semidirect
30. C2×#11718646C2semidirect
31. C13×#2484C2semidirect
526. #2484D13semidirect
1177. C13#36824semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131231532
#131231422
#131228092
#131227902
#131227562
#131226352
#131226212
#131225232
#131224452
#131224302
#131223852
#131223282
#131222992
#131222682
#131217922
#131217292
#131217142
#131212942
#131206532
#131206192
#131192742
#131192172
#131189762
#131186432
#131185142
#131183172
#131182432
#131175022
#131174592
C2×#117186462
C13×#24842
#3682413