Finite Group Databasebeta

← #16036508

Subgroups — #16036508

Order 3328.

1708 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#13123220C211yesmaximal, characteristic, complemented
2#13123217C211yesmaximal, characteristic, complemented
3#13123187C211yesmaximal, characteristic, complemented
4#13123171C211yesmaximal, characteristic, complemented
5#13120890C211yesmaximal, characteristic, complemented
6#13120888C211yesmaximal, characteristic, complemented
7#13120760C211yesmaximal, characteristic
8#13120760C211yesmaximal, characteristic
9#13120277C211yesmaximal, characteristic, complemented
10#13120269C211yesmaximal, characteristic, complemented
11#13120162C211yesmaximal, characteristic, complemented
12#13120154C211yesmaximal, characteristic, complemented
13#13119567C211yesmaximal, characteristic, complemented
14#13119565C211yesmaximal, characteristic, complemented
15#13119351C211yesmaximal, characteristic, complemented
16#13119287C211yesmaximal, characteristic, complemented
17#13119246C211yesmaximal, characteristic, complemented
18#13119132C211yesmaximal, characteristic
19#13118786C211yesmaximal, characteristic
20#13118784C211yesmaximal, characteristic
21#13118674C211yesmaximal, characteristic, complemented
22#13118526C211yesmaximal, characteristic, complemented
23#13118338C211yesmaximal, characteristic, complemented
24#13118264C211yesmaximal, characteristic
25#13117635C211yesmaximal, characteristic, complemented
26#13117587C211yesmaximal, characteristic, complemented
27#13117587C211yesmaximal, characteristic, complemented
28C4×#88150C211yesmaximal, characteristic, complemented
29#13117316C211yesmaximal, characteristic, complemented
30C4×#88147C211yesmaximal, characteristic
31C13×#2336C211yesmaximal, characteristic, complemented
32C2×C13×#125C2211yescharacteristic
33C2×#88150C2211yescharacteristic
34C2×#88150C2211yescharacteristic
35C2×#88150C2211yescharacteristic
36C2×#88150C2211yescharacteristic
37C2×#88147C2211yescharacteristic
38C2×#88147C2211yescharacteristic
39C2×#88143C2211yescharacteristic
40C2×#88142C2211yescharacteristic
41C2×C4×D52C2211yescharacteristic
42C2×#88126C2211yescharacteristic
43C2×#88126C2211yescharacteristic
44C2×C42×D13C2211yescharacteristic
45C2×C42×D13C2211yescharacteristic
46C2×C4×Dic26C2211yescharacteristic
47C13×#389C2211yescharacteristic
48C13×#389C2211yescharacteristic
49C13×#387C2211yescharacteristic
50C13×#387C2211yescharacteristic
51C13×#387C2211yescharacteristic
52C13×#387C2211yescharacteristic
53C13×#387C2211yescharacteristic
54C13×#387C2211yescharacteristic
55C13×#387C2211yescharacteristic
56C13×#387C2211yescharacteristic
57C13×#383C2211yescharacteristic
58C4×C13×C4⋊C4C2211yescharacteristic
59C4×C13×C4⋊C4C2211yescharacteristic
60C4×C13×C4⋊C4C2211yescharacteristic
61#11718655C2211yescharacteristic
62#11718655C2211yescharacteristic
63#11718654C2211yescharacteristic
64#11718654C2211yescharacteristic
65#11718652C2211yescharacteristic
66#11718652C2211yescharacteristic
67#11718651C2211yescharacteristic
68#11718651C2211yescharacteristic
69#11718650C2211yescharacteristic
70#11718650C2211yescharacteristic
71#11718650C2211yescharacteristic
72#11718650C2211yescharacteristic
73#11718648C2211yescharacteristic
74#11718648C2211yescharacteristic
75#11718647C2211yescharacteristic
76#11718647C2211yescharacteristic
77#11718645C2211yescharacteristic
78#11718645C2211yescharacteristic
79#11718645C2211yescharacteristic
80#11718643C2211yescharacteristic
81#11718642C2211yescharacteristic
82#11718642C2211yescharacteristic
83#11718642C2211yescharacteristic
84#11718642C2211yescharacteristic
85#11718639C2211yescharacteristic
86#11718639C2211yescharacteristic
87#11718639C2211yescharacteristic
88#11718639C2211yescharacteristic
89#11718639C2211yescharacteristic
90#11718639C2211yescharacteristic
91#11718637C2211yescharacteristic
92C4⋊C4×Dic13C2211yescharacteristic
93C4⋊C4×Dic13C2211yescharacteristic
94#11718633C2211yescharacteristic
95#11718633C2211yescharacteristic
96#11718633C2211yescharacteristic
97#11718633C2211yescharacteristic
98#11718633C2211yescharacteristic
99#11718633C2211yescharacteristic
100#11718633C2211yescharacteristic
101#11718601C2211yescharacteristic
102#11718601C2211yescharacteristic
103#11718601C2211yescharacteristic
104#11718601C2211yescharacteristic
105C4×#6103C2211yescharacteristic
106C4×#6103C2211yescharacteristic
107C4×#6103C2211yescharacteristic
108C4×#6103C2211yescharacteristic
109C4×C4⋊Dic13C2211yescharacteristic
110#11718594C2211yescharacteristic
111#11718594C2211yescharacteristic
112#11718594C2211yescharacteristic
113#11718594C2211yescharacteristic
114#11718594C2211yescharacteristic
115C4×#6101C2211yescharacteristic
116C4×#6101C2211yescharacteristic
117C4×#6101C2211yescharacteristic
118C4×#6101C2211yescharacteristic
119C42×Dic13C2211yescharacteristic
120#11718590C2211yescharacteristic
121#11718590C2211yescharacteristic
122#11718589C2211yescharacteristic
123#11718336C2211yescharacteristic
124#11718336C2211yescharacteristic
125#11718336C2211yescharacteristic
126#11718336C2211yescharacteristic
127#11718336C2211yescharacteristic
128#11718336C2211yescharacteristic
129#11718335C2211yescharacteristic
130#11718335C2211yescharacteristic
131#11718335C2211yescharacteristic
132#11718335C2211yescharacteristic
133#11718334C2211yescharacteristic
134#11718334C2211yescharacteristic
135#11718333C2211yescharacteristic
136#11718333C2211yescharacteristic
137#11718331C2211yescharacteristic
138#11718331C2211yescharacteristic
139#11718329C2211yescharacteristic
140#11718329C2211yescharacteristic
141#11718329C2211yescharacteristic
142#11718329C2211yescharacteristic
143#11718328C2211yescharacteristic
144#11718328C2211yescharacteristic
145#11718328C2211yescharacteristic
146#11718328C2211yescharacteristic
147#11718327C2211yescharacteristic
148#11718327C2211yescharacteristic
149#11718327C2211yescharacteristic
150#11718327C2211yescharacteristic
151#11718325C2211yescharacteristic
152#11718325C2211yescharacteristic
153#11718322C2211yescharacteristic
154#11718321C2211yescharacteristic
155#11718320C2211yescharacteristic
156#11718319C2211yescharacteristic
157#11718317C2211yescharacteristic
158#11718317C2211yescharacteristic
159#11718316C2211yescharacteristic
160#11718316C2211yescharacteristic
161#11718315C2211yescharacteristic
162#11718314C2211yescharacteristic
163#11718314C2211yescharacteristic
164#11718314C2211yescharacteristic
165#11718314C2211yescharacteristic
166#11718313C2211yescharacteristic
167#11718313C2211yescharacteristic
168#11718313C2211yescharacteristic
169#11718313C2211yescharacteristic
170#11718312C2211yescharacteristic
171#11718312C2211yescharacteristic
172#11718312C2211yescharacteristic
173#11718311C2211yescharacteristic
174#11718311C2211yescharacteristic
175#11718308C2211yescharacteristic
176#11718308C2211yescharacteristic
177#11718308C2211yescharacteristic
178#11718308C2211yescharacteristic
179#11718307C2211yescharacteristic
180#11718307C2211yescharacteristic
181#11718307C2211yescharacteristic
182#11718307C2211yescharacteristic
183#11718307C2211yescharacteristic
184#11718307C2211yescharacteristic
185#11718307C2211yescharacteristic
186#11718307C2211yescharacteristic
187C22×D52C2311yescharacteristic
188C22×C4×D13C2311yescharacteristic
189C22×C4×D13C2311yescharacteristic
190C22×C4×D13C2311yescharacteristic
191C22×C4×D13C2311yescharacteristic
192C22×C4×D13C2311yescharacteristic
193C22×C4×D13C2311yescharacteristic
194C22×Dic26C2311yescharacteristic
195C22×Dic26C2311yescharacteristic
196C22×Dic26C2311yescharacteristic
197C13×#125—24no—
198C2×C13×C4⋊C4C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
210C2×C42×C13C2311yescharacteristic
211C2×C42×C13C2311yescharacteristic
212C2×C42×C13C2311yescharacteristic
213C2×C42×C13C2311yescharacteristic
214C2×C42×C13C2311yescharacteristic
215C2×C42×C13C2311yescharacteristic
216C2×C42×C13C2311yescharacteristic
217C2×#6103C2311yescharacteristic
218C2×#6103C2311yescharacteristic
219C2×#6103C2311yescharacteristic
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
233C2×#6103C2311yescharacteristic
234C2×#6103C2311yescharacteristic
235C2×#6103C2311yescharacteristic
236C2×#6103C2311yescharacteristic
237C2×#6103C2311yescharacteristic
238C2×#6103C2311yescharacteristic
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×#6101C2311yescharacteristic
248C2×#6101C2311yescharacteristic
249C2×#6101C2311yescharacteristic
250C2×#6101C2311yescharacteristic
251C2×#6101C2311yescharacteristic
252C2×#6101C2311yescharacteristic
253C2×#6101C2311yescharacteristic
254C2×#6101C2311yescharacteristic
255C2×#6101C2311yescharacteristic
256C2×#6101C2311yescharacteristic
257C2×#6101C2311yescharacteristic
258C2×#6101C2311yescharacteristic
259C2×#6101C2311yescharacteristic
260C2×#6101C2311yescharacteristic
261C2×#6101C2311yescharacteristic
262C2×#6101C2311yescharacteristic
263C2×#6101C2311yescharacteristic
264C2×#6101C2311yescharacteristic
265C2×#6101C2311yescharacteristic
266C2×#6101C2311yescharacteristic
267C2×#6101C2311yescharacteristic
268C2×#6101C2311yescharacteristic
269C2×C4×Dic13C2311yescharacteristic
270C2×C4×Dic13C2311yescharacteristic
271C2×C4×Dic13C2311yescharacteristic
272C2×C4×Dic13C2311yescharacteristic
273C2×C4×Dic13C2311yescharacteristic
274C2×C4×Dic13C2311yescharacteristic
275C2×C4×Dic13C2311yescharacteristic
276C2×C4×Dic13C2311yescharacteristic
277C2×C4×Dic13C2311yescharacteristic
278C2×C4×Dic13C2311yescharacteristic
279C2×C4×Dic13C2311yescharacteristic
280C2×C4×Dic13C2311yescharacteristic
281C2×C4×Dic13C2311yescharacteristic
282C2×C4×Dic13C2311yescharacteristic
283#88150—24no—
284#88150—24no—
285#88150—24no—
286#88150—42no—
287#88147—24no—
288#88147—24no—
289#88143—24no—
290#88142—42no—
291C4×D52—24no—
292#88126—24no—
293#88126—42no—
294C42×D13—42no—
295C42×D13—42no—
296C4×Dic26—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#35039—131nomaximal, Sylow
358C23×D13C2411yescharacteristic
359C23×D13C2411yescharacteristic
360C22×C4×C13C2411yescharacteristic
361C22×C4×C13C2411yescharacteristic
362C22×C4×C13C2411yescharacteristic
363C22×C4×C13C2411yescharacteristic
364C22×C4×C13C2411yescharacteristic
365C22×C4×C13C2411yescharacteristic
366C22×C4×C13C2411yescharacteristic
367C22×C4×C13C2411yescharacteristic
368C22×C4×C13C2411yescharacteristic
369C22×C4×C13C2411yescharacteristic
370C22×C4×C13C2411yescharacteristic
371C22×C4×C13C2411yescharacteristic
372C22×C4×C13C2411yescharacteristic
373C22×C4×C13C2411yescharacteristic
374C22×C4×C13C2411yescharacteristic
375C22×Dic13C2411yescharacteristic
376C22×Dic13C2411yescharacteristic
377C22×Dic13C2411yescharacteristic
378C22×Dic13C2411yescharacteristic
379C22×Dic13C2411yescharacteristic
380C22×Dic13C2411yescharacteristic
381C22×Dic13C2411yescharacteristic
382C22×Dic13C2411yescharacteristic
383C22×Dic13C2411yescharacteristic
384C22×Dic13C2411yescharacteristic
385C22×Dic13C2411yescharacteristic
386C22×Dic13C2411yescharacteristic
387C22×Dic13C2411yescharacteristic
388C22×Dic13C2411yescharacteristic
389C2×D52—22no—
390C2×D52—22no—
391C2×D52—22no—
392C2×C4×D13—22no—
393C2×C4×D13—22no—
394C2×C4×D13—22no—
395C2×C4×D13—22no—
396C2×C4×D13—22no—
397C2×C4×D13—22no—
398C2×C4×D13—22no—
399C2×C4×D13—22no—
400C2×C4×D13—22no—
401C2×C4×D13—22no—
402C2×C4×D13—41no—
403C2×C4×D13—41no—
404C2×C4×D13—41no—
405C2×C4×D13—41no—
406C2×C4×D13—41no—
407C2×C4×D13—41no—
408C2×C4×D13#4114yes—
409C2×C4×D13#4114yes—
410C2×Dic26—22no—
411C2×Dic26—22no—
412C2×Dic26—22no—
413C2×Dic26—22no—
414C2×Dic26—22no—
415C2×Dic26—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—41no—
429C13×C4⋊C4—41no—
430C13×C4⋊C4#4114yes—
431C42×C13—22no—
432C42×C13—22no—
433C42×C13—22no—
434C42×C13—41no—
435C42×C13—41no—
436C42×C13—41no—
437C42×C13—41no—
438#6103—22no—
439#6103—22no—
440#6103—22no—
441#6103—22no—
442#6103—22no—
443#6103—22no—
444#6103—22no—
445#6103—22no—
446#6103—22no—
447#6103—22no—
448#6103—22no—
449#6103—22no—
450#6103—22no—
451#6103—22no—
452#6103—41no—
453#6103—41no—
454#6103—41no—
455#6103—41no—
456#6103—41no—
457#6103—41no—
458#6103—41no—
459#6103—41no—
460C4⋊Dic13—22no—
461C4⋊Dic13—22no—
462C4⋊Dic13—22no—
463C4⋊Dic13—41no—
464C4⋊Dic13—41no—
465C4⋊Dic13—41no—
466C4⋊Dic13—41no—
467C4⋊Dic13—41no—
468#6101—22no—
469#6101—22no—
470#6101—22no—
471#6101—22no—
472#6101—22no—
473#6101—22no—
474#6101—22no—
475#6101—22no—
476#6101—22no—
477#6101—22no—
478#6101—22no—
479#6101—22no—
480#6101—22no—
481#6101—22no—
482#6101—22no—
483#6101—22no—
484#6101—22no—
485#6101—41no—
486#6101—41no—
487#6101—41no—
488#6101—41no—
489#6101—41no—
490C4×Dic13—22no—
491C4×Dic13—22no—
492C4×Dic13—22no—
493C4×Dic13—22no—
494C4×Dic13—22no—
495C4×Dic13—22no—
496C4×Dic13—22no—
497C4×Dic13—22no—
498C4×Dic13—22no—
499C4×Dic13—41no—
500C4×Dic13—41no—
501C4×Dic13—41no—
502C4×Dic13—41no—
503C4×Dic13—41no—
504#2864—131no—
505#2863—131no—
506#2857—131no—
507#2855—131no—
508#2652—131no—
509#2652—131no—
510#2638—131no—
511#2638—131no—
512#2588—131no—
513#2588—131no—
514#2577—131no—
515#2577—131no—
516#2523—131no—
517#2523—131no—
518#2506—131no—
519#2499—131no—
520#2495—131no—
521#2485—131no—
522#2460—131no—
523#2460—131no—
524#2451—131no—
525#2439—131no—
526#2421—131no—
527#2415—131no—
528#2336—131no—
529#2336D1311yescharacteristic, complemented
530#2332—131no—
531#2332—131no—
532C4×C22⋊Q8—131no—
533#2296—131no—
534C42×D4—131no—
535C23×C13C2511yescharacteristic
536C22×D13—21no—
537C22×D13—21no—
538C22×D13—21no—
539C22×D13—21no—
540C22×D13—21no—
541C22×D13—21no—
542C22×D13—21no—
543C22×D13—21no—
544C22×D13—21no—
545C22×D13—21no—
546C22×D13—21no—
547C22×D13—21no—
548C22×D13C2×#4112yes—
549C22×D13C2×#4112yes—
550C2×C4×C13—21no—
551C2×C4×C13—21no—
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×C13C2×#4112yes—
591C2×C4×C13C2×#4112yes—
592C2×C4×C13C2×#4112yes—
593C2×C4×C13C2×#4112yes—
594C2×C4×C13C2×#4112yes—
595C2×Dic13—21no—
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×Dic13C2×#4112yes—
633C2×Dic13C2×#4112yes—
634C2×Dic13H(5,𝔽2)12yes—
635C2×Dic132−1+412yes—
636C2×Dic132−1+412yes—
637D52—28no—
638C4×D13—28no—
639C4×D13—44no—
640C4×D13—44no—
641C4×D13—44no—
642C4×D13—44no—
643C4×D13—44no—
644Dic26—44no—
645Dic26—82no—
646Dic26—82no—
647C2×C4⋊Q8—131no—
648C2×#125—131no—
649C2×#125C2×D1311yescharacteristic
650C2×C22⋊Q8—131no—
651C2×C22⋊Q8—131no—
652C2×C22⋊Q8—131no—
653C2×C22⋊Q8—131no—
654C2×C4×Q8—131no—
655C2×C4×D4—131no—
656C2×C4×D4—131no—
657C2×C4×D4—131no—
658C2×#117—131no—
659C2×#117—131no—
660C22×C42—131no—
661C22×C42—131no—
662#400—131no—
663#400—131no—
664#400—131no—
665#400—131no—
666#400—131no—
667#400—131no—
668#398—131no—
669#398—131no—
670#398—131no—
671#398—131no—
672#397—131no—
673#397—131no—
674#397—131no—
675#397—131no—
676#397—131no—
677#397—131no—
678#397—131no—
679#397—131no—
680#397—131no—
681#397—131no—
682#397—131no—
683#397—131no—
684#396—131no—
685#396—131no—
686#395—131no—
687#395—131no—
688#394—131no—
689#394—131no—
690#394—131no—
691#394—131no—
692#393—131no—
693#393—131no—
694#391—131no—
695#391—131no—
696#391—131no—
697#391—131no—
698#391—131no—
699#391—131no—
700#391—131no—
701#391—131no—
702#391—131no—
703#391—131no—
704#389—131no—
705#389—131no—
706#389—131no—
707#389—131no—
708#389—131no—
709#389—131no—
710#389—131no—
711#389—131no—
712#389—131no—
713#389—131no—
714#389—131no—
715#389—131no—
716#389C2×D1311yescharacteristic
717#389C2×D1311yescharacteristic
718#388—131no—
719#388—131no—
720#388—131no—
721#388—131no—
722#388—131no—
723#388—131no—
724#388—131no—
725#388—131no—
726#387—131no—
727#387—131no—
728#387—131no—
729#387—131no—
730#387—131no—
731#387—131no—
732#387—131no—
733#387—131no—
734#387—131no—
735#387—131no—
736#387—131no—
737#387—131no—
738#387—131no—
739#387—131no—
740#387—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#387C2×D1311yescharacteristic
753#387C2×D1311yescharacteristic
754#387C2×D1311yescharacteristic
755#387C2×D1311yescharacteristic
756#387C2×D1311yescharacteristic
757#387C2×D1311yescharacteristic
758#387C2×D1311yescharacteristic
759#387C2×D1311yescharacteristic
760#385—131no—
761#385—131no—
762#385—131no—
763#385—131no—
764#385—131no—
765#385—131no—
766#385—131no—
767#385—131no—
768#384—131no—
769#383—131no—
770#383—131no—
771#383—131no—
772#383C2×D1311yescharacteristic
773#382—131no—
774#382—131no—
775#381—131no—
776#381—131no—
777#380—131no—
778#380—131no—
779#380—131no—
780#380—131no—
781#380—131no—
782#380—131no—
783C4×C4⋊C4—131no—
784C4×C4⋊C4—131no—
785C4×C4⋊C4—131no—
786C4×C4⋊C4—131no—
787C4×C4⋊C4—131no—
788C4×C4⋊C4—131no—
789C4×C4⋊C4—131no—
790C4×C4⋊C4C2×D1311yescharacteristic
791C4×C4⋊C4C2×D1311yescharacteristic
792C4×C4⋊C4C2×D1311yescharacteristic
793C4×C22⋊C4—131no—
794C4×C22⋊C4—131no—
795C4×C22⋊C4—131no—
796C4×C22⋊C4—131no—
797C4×C22⋊C4—131no—
798C4×C22⋊C4—131no—
799C4×C22⋊C4—131no—
800C4×C22⋊C4—131no—
801C43—131no—
802C22×C13C22×#4111yescharacteristic
803C22×C13C22×#4111yescharacteristic
804C22×C13C22×#4111yescharacteristic
805C22×C13C2×H(5,𝔽2)11yescharacteristic
806C22×C13C2×2−1+411yescharacteristic
807C22×C13C2×2−1+411yescharacteristic
808C22×C13#58511yescharacteristic
809C2×D13—22no—
810C2×D13—22no—
811C2×D13—22no—
812C2×D13—22no—
813C2×D13—22no—
814C2×D13—22no—
815C2×D13—41no—
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—22no—
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—
837C4×C13—41no—
838Dic13—22no—
839Dic13—22no—
840Dic13—41no—
841Dic13—41no—
842Dic13—41no—
843Dic13—41no—
844Dic13—41no—
845Dic13—41no—
846Dic13—41no—
847Dic13—41no—
848Dic13—41no—
849Dic13—41no—
850Dic13—41no—
851Dic13#53914yes—
852C22×Q8—131no—
853C22×Q8—131no—
854C22×Q8—131no—
855C22×D4—131no—
856C23×C4—131no—
857C23×C4—131no—
858C23×C4—131no—
859C23×C4—131no—
860C23×C4—131no—
861C23×C4—131no—
862C4⋊Q8—522no—
863#125—24no—
864#125—264no—
865C22⋊Q8—264no—
866C22⋊Q8—264no—
867C22⋊Q8—264no—
868C22⋊Q8—522no—
869C4×Q8—522no—
870C4×D4—264no—
871C4×D4—264no—
872C4×D4—264no—
873#117—264no—
874#117—522no—
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⋊C4C22×D1311yescharacteristic
906C2×C4⋊C4C22×D1311yescharacteristic
907C2×C4⋊C4C22×D1311yescharacteristic
908C2×C4⋊C4C22×D1311yescharacteristic
909C2×C4⋊C4C22×D1311yescharacteristic
910C2×C4⋊C4C22×D1311yescharacteristic
911C2×C4⋊C4C22×D1311yescharacteristic
912C2×C4⋊C4C22×D1311yescharacteristic
913C2×C4⋊C4C22×D1311yescharacteristic
914C2×C4⋊C4C22×D1311yescharacteristic
915C2×C4⋊C4C22×D1311yescharacteristic
916C2×C4⋊C4C22×D1311yescharacteristic
917C2×C22⋊C4—131no—
918C2×C22⋊C4—131no—
919C2×C22⋊C4—131no—
920C2×C22⋊C4—131no—
921C2×C22⋊C4—131no—
922C2×C22⋊C4—131no—
923C2×C22⋊C4—131no—
924C2×C22⋊C4—131no—
925C2×C22⋊C4—131no—
926C2×C22⋊C4—131no—
927C2×C22⋊C4—131no—
928C2×C22⋊C4—131no—
929C2×C22⋊C4—131no—
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×C42—131no—
940C2×C42—131no—
941C2×C42—131no—
942C2×C42—131no—
943C2×C42—131no—
944C2×C42—131no—
945C2×C42—131no—
946C2×C42—131no—
947C2×C42—131no—
948C2×C42—131no—
949C2×C42—131no—
950C2×C42—131no—
951C2×C42—131no—
952C2×C42—131no—
953C2×C42—522no—
954C2×C42—522no—
955C2×C42C22×D1311yescharacteristic
956C2×C42C22×D1311yescharacteristic
957C2×C42C22×D1311yescharacteristic
958C2×C42C22×D1311yescharacteristic
959C2×C42C22×D1311yescharacteristic
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#344411yescharacteristic
1023C2×C13C2×#53911yescharacteristic
1024C2×C13#346111yescharacteristic
1025C2×C13#350511yescharacteristic
1026C2×C13#350911yescharacteristic
1027C2×C13#351811yescharacteristic
1028C2×C13#352011yescharacteristic
1029D13—42no—
1030D13—42no—
1031C24—131no—
1032C24—131no—
1033C2×Q8—262no—
1034C2×Q8—262no—
1035C2×Q8—262no—
1036C2×Q8—262no—
1037C2×Q8—262no—
1038C2×Q8—521no—
1039C2×Q8—521no—
1040C2×Q8—521no—
1041C2×Q8—521no—
1042C2×D4—262no—
1043C2×D4—262no—
1044C2×D4—262no—
1045C22×C4—131no—
1046C22×C4—131no—
1047C22×C4—131no—
1048C22×C4—134no—
1049C22×C4—134no—
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—262no—
1062C22×C4—262no—
1063C22×C4—262no—
1064C22×C4—262no—
1065C22×C4—262no—
1066C22×C4—262no—
1067C22×C4—262no—
1068C22×C4—262no—
1069C22×C4—262no—
1070C22×C4—262no—
1071C22×C4—521no—
1072C22×C4—521no—
1073C22×C4—521no—
1074C22×C4—521no—
1075C22×C4—521no—
1076C22×C4—521no—
1077C22×C4C23×D1311yescharacteristic
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—41no—
1102C4⋊C4—41no—
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—262no—
1112C4⋊C4—262no—
1113C4⋊C4—262no—
1114C4⋊C4—262no—
1115C4⋊C4—262no—
1116C4⋊C4—262no—
1117C4⋊C4—262no—
1118C4⋊C4—262no—
1119C4⋊C4—262no—
1120C4⋊C4—262no—
1121C4⋊C4—262no—
1122C4⋊C4—262no—
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#612714yes—
1134C22⋊C4—262no—
1135C22⋊C4—262no—
1136C22⋊C4—262no—
1137C22⋊C4—262no—
1138C22⋊C4—262no—
1139C22⋊C4—262no—
1140C22⋊C4—262no—
1141C22⋊C4—262no—
1142C22⋊C4—262no—
1143C22⋊C4—262no—
1144C22⋊C4—262no—
1145C22⋊C4—262no—
1146C22⋊C4—262no—
1147C22⋊C4—262no—
1148C22⋊C4—521no—
1149C22⋊C4—521no—
1150C22⋊C4—521no—
1151C22⋊C4—521no—
1152C22⋊C4—521no—
1153C22⋊C4—521no—
1154C22⋊C4—521no—
1155C22⋊C4—521no—
1156C42—22no—
1157C42—22no—
1158C42—22no—
1159C42—41no—
1160C42—41no—
1161C42—41no—
1162C42—41no—
1163C42—262no—
1164C42—262no—
1165C42—262no—
1166C42—262no—
1167C42—262no—
1168C42—262no—
1169C42—262no—
1170C42—262no—
1171C42—262no—
1172C42—521no—
1173C42—521no—
1174C42—521no—
1175C42—521no—
1176C42—521no—
1177C13#3503911yescharacteristic, complemented, Sylow
1178C23—132no—
1179C23—132no—
1180C23—261no—
1181C23—261no—
1182C23—261no—
1183C23—261no—
1184C23—261no—
1185C23—261no—
1186C23—261no—
1187C23—261no—
1188C23—261no—
1189C23—261no—
1190C23—261no—
1191C23—261no—
1192C23C24×D1311yescharacteristic
1193Q8—524no—
1194Q8—1042no—
1195Q8—1042no—
1196D4—268no—
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—21no—
1236C2×C4—21no—
1237C2×C4—132no—
1238C2×C4—132no—
1239C2×C4—132no—
1240C2×C4—132no—
1241C2×C4—132no—
1242C2×C4—268no—
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—524no—
1281C2×C4—524no—
1282C2×C4—524no—
1283C2×C4—524no—
1284C2×C4—524no—
1285C2×C4C2×#612712yes—
1286C2×C4C2×#612712yes—
1287C2×C4C2×#612712yes—
1288C2×C4#41×D1312yes—
1289C2×C4#41×D1312yes—
1290C22—262no—
1291C22—262no—
1292C22—262no—
1293C22—262no—
1294C22—262no—
1295C22—262no—
1296C22—521no—
1297C22—521no—
1298C22—521no—
1299C22—521no—
1300C22—521no—
1301C22—521no—
1302C22—521no—
1303C22—521no—
1304C22C22×#612711yescharacteristic
1305C22C2×#41×D1311yescharacteristic
1306C22C2×#41×D1311yescharacteristic
1307C22D13×H(5,𝔽2)11yescharacteristic
1308C22D13×2−1+411yescharacteristic
1309C22D13×2−1+411yescharacteristic
1310C22#1171965211yescharacteristic
1311C4—22no—
1312C4—22no—
1313C4—22no—
1314C4—22no—
1315C4—22no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—134no—
1327C4—262no—
1328C4—262no—
1329C4—521no—
1330C4—521no—
1331C4—521no—
1332C4—521no—
1333C4—521no—
1334C4—521no—
1335C4—521no—
1336C4—521no—
1337C4—521no—
1338C4—521no—
1339C4—521no—
1340C2—522no—
1341C2—522no—
1342C2#1312812911yescharacteristic
1343C2D13×#53911yescharacteristic
1344C2#1312826811yescharacteristic
1345C2#1312866811yescharacteristic
1346C2#1312871811yescharacteristic
1347C2#1312884711yescharacteristic
1348C2#1312887511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutator, socle, cosocleC23×C13C25
FittingC13×#2336C2
prime radicalC22×D52C23
hypercenter#2336D13
hypocenterC13#35039
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2336

Complements

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

NH ≅ G/Ntype
1. #13123220C2semidirect
2. #13123217C2semidirect
3. #13123187C2semidirect
4. #13123171C2semidirect
5. #13120890C2semidirect
6. #13120888C2semidirect
9. #13120277C2semidirect
10. #13120269C2semidirect
11. #13120162C2semidirect
12. #13120154C2semidirect
13. #13119567C2semidirect
14. #13119565C2semidirect
15. #13119351C2semidirect
16. #13119287C2semidirect
17. #13119246C2semidirect
21. #13118674C2semidirect
22. #13118526C2semidirect
23. #13118338C2semidirect
25. #13117635C2semidirect
26. #13117587C2semidirect
27. #13117587C2semidirect
28. C4×#88150C2semidirect
29. #13117316C2semidirect
31. C13×#2336C2semidirect
529. #2336D13semidirect
1177. C13#35039semidirect

Maximal subgroups

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

subgroupindex
#131232202
#131232172
#131231872
#131231712
#131208902
#131208882
#131207602
#131202772
#131202692
#131201622
#131201542
#131195672
#131195652
#131193512
#131192872
#131192462
#131191322
#131187862
#131187842
#131186742
#131185262
#131183382
#131182642
#131176352
#131175872
C4×#881502
#131173162
C4×#881472
C13×#23362
#3503913