Finite Group Databasebeta

← #16070873

Subgroups — #16070873

Order 3328.

1482 conjugacy classes of subgroups.

The subgroup lattice has 1278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123186C211yesmaximal, characteristic
2#13123142C211yesmaximal, characteristic
3#13122760C211yesmaximal, characteristic, complemented
4#13122751C211yesmaximal, characteristic, complemented
5#13122658C211yesmaximal, characteristic, complemented
6#13122657C211yesmaximal, characteristic, complemented
7#13122595C211yesmaximal, characteristic, complemented
8#13122593C211yesmaximal, characteristic, complemented
9#13122429C211yesmaximal, characteristic, complemented
10#13122424C211yesmaximal, characteristic, complemented
11#13122289C211yesmaximal, characteristic, complemented
12#13122285C211yesmaximal, characteristic, complemented
13#13122192C211yesmaximal, characteristic, complemented
14#13122187C211yesmaximal, characteristic, complemented
15#13121708C211yesmaximal, characteristic, complemented
16#13121696C211yesmaximal, characteristic, complemented
17#13121623C211yesmaximal, characteristic, complemented
18#13121614C211yesmaximal, characteristic, complemented
19#13120655C211yesmaximal, characteristic
20#13120655C211yesmaximal, characteristic
21#13119337C211yesmaximal, characteristic
22#13119227C211yesmaximal, characteristic
23#13119223C211yesmaximal, characteristic
24#13119219C211yesmaximal, characteristic
25#13119215C211yesmaximal, characteristic
26#13118976C211yesmaximal, characteristic
27#13118974C211yesmaximal, characteristic
28#13117567C211yesmaximal, characteristic
29#13117564C211yesmaximal, characteristic
30C2×#11718316C211yesmaximal, characteristic
31C13×#2505C211yesmaximal, characteristic
32C22×C4⋊Dic13C2211yescharacteristic
33C22×#6101C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C2×#88144C2211yescharacteristic
36C2×#88143C2211yescharacteristic
37C2×#88143C2211yescharacteristic
38C2×#88142C2211yescharacteristic
39C2×#88132C2211yescharacteristic
40C2×#88132C2211yescharacteristic
41C13×#400C2211yescharacteristic
42C13×#400C2211yescharacteristic
43C13×#400C2211yescharacteristic
44C13×#398C2211yescharacteristic
45C13×#389C2211yescharacteristic
46C13×#387C2211yescharacteristic
47C13×#387C2211yescharacteristic
48C13×#385C2211yescharacteristic
49C13×#385C2211yescharacteristic
50C13×#385C2211yescharacteristic
51C13×#385C2211yescharacteristic
52C13×#382C2211yescharacteristic
53C13×#380C2211yescharacteristic
54C4×C13×C22⋊C4C2211yescharacteristic
55C2×C13×#95C2211yescharacteristic
56#11718873C2211yescharacteristic
57#11718871C2211yescharacteristic
58#11718871C2211yescharacteristic
59#11718871C2211yescharacteristic
60#11718871C2211yescharacteristic
61C4×C22⋊Dic13C2211yescharacteristic
62C2×#88071C2211yescharacteristic
63C2×#88071C2211yescharacteristic
64C2×#88071C2211yescharacteristic
65#11718647C2211yescharacteristic
66#11718647C2211yescharacteristic
67#11718647C2211yescharacteristic
68#11718647C2211yescharacteristic
69#11718646C2211yescharacteristic
70#11718646C2211yescharacteristic
71#11718645C2211yescharacteristic
72#11718645C2211yescharacteristic
73#11718644C2211yescharacteristic
74#11718643C2211yescharacteristic
75#11718643C2211yescharacteristic
76#11718643C2211yescharacteristic
77#11718642C2211yescharacteristic
78#11718642C2211yescharacteristic
79#11718642C2211yescharacteristic
80#11718642C2211yescharacteristic
81#11718642C2211yescharacteristic
82#11718641C2211yescharacteristic
83#11718641C2211yescharacteristic
84#11718641C2211yescharacteristic
85#11718641C2211yescharacteristic
86#11718640C2211yescharacteristic
87#11718640C2211yescharacteristic
88#11718640C2211yescharacteristic
89#11718640C2211yescharacteristic
90#11718639C2211yescharacteristic
91#11718639C2211yescharacteristic
92#11718639C2211yescharacteristic
93#11718639C2211yescharacteristic
94#11718639C2211yescharacteristic
95#11718637C2211yescharacteristic
96#11718635C2211yescharacteristic
97#11718634C2211yescharacteristic
98#11718634C2211yescharacteristic
99#11718633C2211yescharacteristic
100#11718633C2211yescharacteristic
101#11718611C2211yescharacteristic
102#11718611C2211yescharacteristic
103#11718607C2211yescharacteristic
104#11718607C2211yescharacteristic
105#11718604C2211yescharacteristic
106#11718604C2211yescharacteristic
107#11718604C2211yescharacteristic
108#11718604C2211yescharacteristic
109#11718603C2211yescharacteristic
110#11718603C2211yescharacteristic
111#11718603C2211yescharacteristic
112#11718603C2211yescharacteristic
113C22⋊C4×Dic13C2211yescharacteristic
114C22⋊C4×Dic13C2211yescharacteristic
115#11718598C2211yescharacteristic
116#11718594C2211yescharacteristic
117#11718594C2211yescharacteristic
118#11718594C2211yescharacteristic
119#11718594C2211yescharacteristic
120#11718594C2211yescharacteristic
121#11718590C2211yescharacteristic
122#11718589C2211yescharacteristic
123C13⋊#401C2211yescharacteristic
124C13⋊#401C2211yescharacteristic
125C13⋊#401C2211yescharacteristic
126C13⋊#401C2211yescharacteristic
127#11718322C2211yescharacteristic
128#11718322C2211yescharacteristic
129#11718321C2211yescharacteristic
130#11718321C2211yescharacteristic
131#11718321C2211yescharacteristic
132#11718320C2211yescharacteristic
133#11718320C2211yescharacteristic
134#11718319C2211yescharacteristic
135#11718319C2211yescharacteristic
136#11718319C2211yescharacteristic
137#11718319C2211yescharacteristic
138#11718319C2211yescharacteristic
139#11718319C2211yescharacteristic
140#11718319C2211yescharacteristic
141#11718319C2211yescharacteristic
142#11718319C2211yescharacteristic
143#11718318C2211yescharacteristic
144#11718318C2211yescharacteristic
145#11718318C2211yescharacteristic
146#11718318C2211yescharacteristic
147#11718318C2211yescharacteristic
148#11718318C2211yescharacteristic
149#11718316C2211yescharacteristic
150#11718316C2211yescharacteristic
151#11718316C2211yescharacteristic
152#11718316C2211yescharacteristic
153#11718316C2211yescharacteristic
154#11718316C2211yescharacteristic
155#11718316C2211yescharacteristic
156#11718316C2211yescharacteristic
157#11718316C2211yescharacteristic
158#11718316C2211yescharacteristic
159#11718315C2211yescharacteristic
160#11718315C2211yescharacteristic
161#11718315C2211yescharacteristic
162#11718315C2211yescharacteristic
163#11718315C2211yescharacteristic
164#11718314C2211yescharacteristic
165#11718314C2211yescharacteristic
166#11718314C2211yescharacteristic
167#11718314C2211yescharacteristic
168#11718313C2211yescharacteristic
169#11718313C2211yescharacteristic
170#11718313C2211yescharacteristic
171#11718313C2211yescharacteristic
172#11718312C2211yescharacteristic
173#11718312C2211yescharacteristic
174#11718312C2211yescharacteristic
175#11718311C2211yescharacteristic
176#11718311C2211yescharacteristic
177#11718308C2211yescharacteristic
178#11718308C2211yescharacteristic
179#11718308C2211yescharacteristic
180#11718308C2211yescharacteristic
181#11718308C2211yescharacteristic
182#11718308C2211yescharacteristic
183#11718307C2211yescharacteristic
184#11718307C2211yescharacteristic
185#11718307C2211yescharacteristic
186#11718307C2211yescharacteristic
187C23×C4×C13C2311yescharacteristic
188C23×C4×C13C2311yescharacteristic
189C23×C4×C13C2311yescharacteristic
190C23×Dic13C2311yescharacteristic
191C23×Dic13C2311yescharacteristic
192C23×Dic13C2311yescharacteristic
193C23×Dic13C2311yescharacteristic
194C22×Dic26C2311yescharacteristic
195C22×Dic26C2311yescharacteristic
196C2×C13×C4⋊C4C2311yescharacteristic
197C2×C13×C4⋊C4C2311yescharacteristic
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×C22⋊C4C2311yescharacteristic
207C2×C13×C22⋊C4C2311yescharacteristic
208C2×C13×C22⋊C4C2311yescharacteristic
209C2×C13×C22⋊C4C2311yescharacteristic
210C2×C42×C13C2311yescharacteristic
211C2×C42×C13C2311yescharacteristic
212C2×C22⋊Dic13C2311yescharacteristic
213C2×C22⋊Dic13C2311yescharacteristic
214C2×C22⋊Dic13C2311yescharacteristic
215C2×C22⋊Dic13C2311yescharacteristic
216C2×C4⋊Dic13—42no—
217C2×C4⋊Dic13C2311yescharacteristic
218C2×C4⋊Dic13C2311yescharacteristic
219C2×C4⋊Dic13C2311yescharacteristic
220C2×C4⋊Dic13C2311yescharacteristic
221C2×C4⋊Dic13C2311yescharacteristic
222C2×C4⋊Dic13C2311yescharacteristic
223C2×C4⋊Dic13C2311yescharacteristic
224C2×C4⋊Dic13C2311yescharacteristic
225C2×C4⋊Dic13C2311yescharacteristic
226C2×C4⋊Dic13C2311yescharacteristic
227C2×C4⋊Dic13C2311yescharacteristic
228C2×C4⋊Dic13C2311yescharacteristic
229C2×#6101—24no—
230C2×#6101C2311yescharacteristic
231C2×#6101C2311yescharacteristic
232C2×#6101C2311yescharacteristic
233C2×#6101C2311yescharacteristic
234C2×#6101C2311yescharacteristic
235C2×#6101C2311yescharacteristic
236C2×#6101C2311yescharacteristic
237C2×#6101C2311yescharacteristic
238C2×#6101C2311yescharacteristic
239C2×#6101C2311yescharacteristic
240C2×#6101C2311yescharacteristic
241C2×#6101C2311yescharacteristic
242C2×#6101C2311yescharacteristic
243C2×#6101C2311yescharacteristic
244C2×#6101C2311yescharacteristic
245C2×#6101C2311yescharacteristic
246C2×#6101C2311yescharacteristic
247C2×#6101C2311yescharacteristic
248C2×#6101C2311yescharacteristic
249C2×#6101C2311yescharacteristic
250C2×#6101C2311yescharacteristic
251C2×#6101C2311yescharacteristic
252C2×#6101C2311yescharacteristic
253C2×#6101C2311yescharacteristic
254C2×#6101C2311yescharacteristic
255C2×#6101C2311yescharacteristic
256C2×#6101C2311yescharacteristic
257C2×#6101C2311yescharacteristic
258C2×C4×Dic13—42no—
259C2×C4×Dic13C2311yescharacteristic
260C2×C4×Dic13C2311yescharacteristic
261C2×C4×Dic13C2311yescharacteristic
262C2×C4×Dic13C2311yescharacteristic
263C2×C4×Dic13C2311yescharacteristic
264C2×C4×Dic13C2311yescharacteristic
265C2×C4×Dic13C2311yescharacteristic
266C2×C4×Dic13C2311yescharacteristic
267C2×C4×Dic13C2311yescharacteristic
268C2×C4×Dic13C2311yescharacteristic
269#88144—42no—
270#88143—42no—
271#88143—42no—
272#88142—42no—
273#88132—24no—
274#88132—24no—
275C13×#95C2311yescharacteristic
276C13×#95C2311yescharacteristic
277C13×#95C2311yescharacteristic
278C13×#95C2311yescharacteristic
279C13×#95C2311yescharacteristic
280C13×#95C2311yescharacteristic
281C13×#95C2311yescharacteristic
282C13×#95C2311yescharacteristic
283C13×#95C2311yescharacteristic
284C13×#95C2311yescharacteristic
285C13×#95C2311yescharacteristic
286C13×#95C2311yescharacteristic
287C13×#95C2311yescharacteristic
288C13×#95C2311yescharacteristic
289C13×#95C2311yescharacteristic
290C13×#95C2311yescharacteristic
291#88071C2311yescharacteristic
292#88071C2311yescharacteristic
293#88071C2311yescharacteristic
294#88071C2311yescharacteristic
295#88071C2311yescharacteristic
296#88071C2311yescharacteristic
297#88071C2311yescharacteristic
298#88071C2311yescharacteristic
299#88071C2311yescharacteristic
300#88071C2311yescharacteristic
301#88071C2311yescharacteristic
302#88071C2311yescharacteristic
303#88071C2311yescharacteristic
304#88071C2311yescharacteristic
305#88071C2311yescharacteristic
306#88071C2311yescharacteristic
307#88071C2311yescharacteristic
308#88071C2311yescharacteristic
309#88071C2311yescharacteristic
310#88071C2311yescharacteristic
311#88071C2311yescharacteristic
312#88071C2311yescharacteristic
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#36762—131nomaximal, Sylow
352C24×C13C2411yescharacteristic
353C22×C4×C13—22no—
354C22×C4×C13—22no—
355C22×C4×C13—22no—
356C22×C4×C13—22no—
357C22×C4×C13—41no—
358C22×C4×C13—41no—
359C22×C4×C13—41no—
360C22×C4×C13—41no—
361C22×C4×C13—41no—
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×C4×C13C2411yescharacteristic
376C22×Dic13—22no—
377C22×Dic13—22no—
378C22×Dic13—22no—
379C22×Dic13—22no—
380C22×Dic13—22no—
381C22×Dic13—22no—
382C22×Dic13—41no—
383C22×Dic13—41no—
384C22×Dic13—41no—
385C22×Dic13—41no—
386C22×Dic13—41no—
387C22×Dic13#4114yes—
388C22×Dic13C2411yescharacteristic
389C22×Dic13C2411yescharacteristic
390C22×Dic13C2411yescharacteristic
391C22×Dic13C2411yescharacteristic
392C22×Dic13C2411yescharacteristic
393C22×Dic13C2411yescharacteristic
394C22×Dic13C2411yescharacteristic
395C22×Dic13C2411yescharacteristic
396C22×Dic13C2411yescharacteristic
397C22×Dic13C2411yescharacteristic
398C22×Dic13C2411yescharacteristic
399C22×Dic13C2411yescharacteristic
400C22×Dic13C2411yescharacteristic
401C22×Dic13C2411yescharacteristic
402C22×Dic13C2411yescharacteristic
403C22×Dic13C2411yescharacteristic
404C2×Dic26—22no—
405C2×Dic26—22no—
406C2×Dic26—41no—
407C2×Dic26—41no—
408C2×Dic26—41no—
409C2×Dic26—41no—
410C13×C4⋊C4—22no—
411C13×C4⋊C4—22no—
412C13×C4⋊C4—41no—
413C13×C4⋊C4—41no—
414C13×C4⋊C4—41no—
415C13×C4⋊C4—41no—
416C13×C4⋊C4—41no—
417C13×C4⋊C4—41no—
418C13×C4⋊C4—41no—
419C13×C4⋊C4—41no—
420C13×C22⋊C4—22no—
421C13×C22⋊C4—22no—
422C13×C22⋊C4—22no—
423C13×C22⋊C4—22no—
424C42×C13—41no—
425C42×C13—41no—
426C22⋊Dic13—22no—
427C22⋊Dic13—22no—
428C22⋊Dic13—22no—
429C22⋊Dic13—22no—
430C4⋊Dic13—22no—
431C4⋊Dic13—22no—
432C4⋊Dic13—22no—
433C4⋊Dic13—22no—
434C4⋊Dic13—22no—
435C4⋊Dic13—22no—
436C4⋊Dic13—41no—
437C4⋊Dic13—41no—
438C4⋊Dic13—41no—
439C4⋊Dic13—41no—
440C4⋊Dic13—41no—
441C4⋊Dic13—41no—
442#6101—22no—
443#6101—22no—
444#6101—22no—
445#6101—22no—
446#6101—22no—
447#6101—22no—
448#6101—22no—
449#6101—22no—
450#6101—22no—
451#6101—22no—
452#6101—22no—
453#6101—22no—
454#6101—41no—
455#6101—41no—
456#6101—41no—
457#6101—41no—
458#6101—41no—
459#6101—41no—
460#6101—41no—
461#6101—41no—
462#6101—41no—
463#6101—41no—
464#6101—41no—
465#6101—41no—
466#6101—41no—
467#6101—41no—
468#6101—41no—
469#6101—41no—
470C4×Dic13—22no—
471C4×Dic13—22no—
472C4×Dic13—41no—
473C4×Dic13—41no—
474C4×Dic13—41no—
475C4×Dic13—41no—
476C4×Dic13—41no—
477C4×Dic13—41no—
478C4×Dic13—41no—
479C4×Dic13—41no—
480#2857—131no—
481#2851—131no—
482#2802—131no—
483#2802—131no—
484#2794—131no—
485#2794—131no—
486#2789—131no—
487#2789—131no—
488#2776—131no—
489#2776—131no—
490#2766—131no—
491#2766—131no—
492#2758—131no—
493#2758—131no—
494#2719—131no—
495#2719—131no—
496#2713—131no—
497#2713—131no—
498#2627—131no—
499#2627—131no—
500#2505—131no—
501#2505D1311yescharacteristic
502#2493—131no—
503#2493—131no—
504#2493—131no—
505#2493—131no—
506#2473—131no—
507#2473—131no—
508#2329—131no—
509#2329—131no—
510C2×#387—131no—
511C23×C13—21no—
512C23×C13—21no—
513C23×C13—21no—
514C23×C13—21no—
515C23×C13C2×#4112yes—
516C23×C132−1+412yes—
517C23×C132−1+412yes—
518C23×C13C2511yescharacteristic
519C2×C4×C13—21no—
520C2×C4×C13—21no—
521C2×C4×C13—21no—
522C2×C4×C13—21no—
523C2×C4×C13—21no—
524C2×C4×C13—21no—
525C2×C4×C13—21no—
526C2×C4×C13—21no—
527C2×C4×C13—21no—
528C2×C4×C13—21no—
529C2×C4×C13—21no—
530C2×C4×C13—21no—
531C2×C4×C13—21no—
532C2×C4×C13—21no—
533C2×C4×C13—21no—
534C2×C4×C13—21no—
535C2×C4×C13—21no—
536C2×C4×C13—21no—
537C2×C4×C13—21no—
538C2×C4×C13—21no—
539C2×C4×C13—21no—
540C2×C4×C13—21no—
541C2×C4×C13—21no—
542C2×C4×C13—21no—
543C2×C4×C13—21no—
544C2×C4×C13—21no—
545C2×C4×C13—21no—
546C2×C4×C13—21no—
547C2×C4×C13—21no—
548C2×C4×C13—21no—
549C2×C4×C13—21no—
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—44no—
561C2×C4×C13—44no—
562C2×C4×C13—82no—
563C2×C4×C132−1+412yes—
564C2×Dic13—21no—
565C2×Dic13—21no—
566C2×Dic13—21no—
567C2×Dic13—21no—
568C2×Dic13—21no—
569C2×Dic13—21no—
570C2×Dic13—21no—
571C2×Dic13—21no—
572C2×Dic13—21no—
573C2×Dic13—21no—
574C2×Dic13—21no—
575C2×Dic13—21no—
576C2×Dic13—21no—
577C2×Dic13—21no—
578C2×Dic13—21no—
579C2×Dic13—21no—
580C2×Dic13—21no—
581C2×Dic13—21no—
582C2×Dic13—21no—
583C2×Dic13—21no—
584C2×Dic13—21no—
585C2×Dic13—21no—
586C2×Dic13—21no—
587C2×Dic13—21no—
588C2×Dic13—21no—
589C2×Dic13—21no—
590C2×Dic13—21no—
591C2×Dic13—21no—
592C2×Dic13—21no—
593C2×Dic13—21no—
594C2×Dic13—21no—
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—44no—
610C2×Dic13—44no—
611C2×Dic13—44no—
612C2×Dic13—82no—
613C2×Dic13C2×#4112yes—
614C2×Dic13C2×#4112yes—
615C2×Dic13H(5,𝔽2)12yes—
616Dic26—82no—
617Dic26—82no—
618C2×C4⋊Q8—131no—
619C2×#125—131no—
620C2×#125—131no—
621C2×#125—131no—
622C2×C22⋊Q8—131no—
623C2×C22⋊Q8—131no—
624C22×C4⋊C4—131no—
625C22×C4⋊C4—131no—
626C22×C42—131no—
627#401—131no—
628#401—131no—
629#401—131no—
630#401—131no—
631#400—131no—
632#400—131no—
633#400—131no—
634#400—131no—
635#400—131no—
636#400—131no—
637#400—131no—
638#400—131no—
639#400—131no—
640#400—131no—
641#400—131no—
642#400—131no—
643#400—131no—
644#400—131no—
645#400—131no—
646#400—131no—
647#400—131no—
648#400—131no—
649#400—131no—
650#400—131no—
651#400—131no—
652#400C2×D1311yescharacteristic
653#400C2×D1311yescharacteristic
654#400C2×D1311yescharacteristic
655#398—131no—
656#398—131no—
657#398—131no—
658#398—131no—
659#398—131no—
660#398—131no—
661#398—131no—
662#398—131no—
663#398—131no—
664#398—131no—
665#398—131no—
666#398—131no—
667#398—131no—
668#398—131no—
669#398—131no—
670#398C2×D1311yescharacteristic
671#395—131no—
672#395—131no—
673#395—131no—
674#395—131no—
675#391—131no—
676#391—131no—
677#391—131no—
678#391—131no—
679#391—131no—
680#391—131no—
681#389—131no—
682#389—131no—
683#389—131no—
684#389—131no—
685#389—131no—
686#389—131no—
687#389—131no—
688#389—131no—
689#389—131no—
690#389—131no—
691#389—131no—
692#389—131no—
693#389—131no—
694#389C2×D1311yescharacteristic
695#387—131no—
696#387—131no—
697#387—131no—
698#387—131no—
699#387—131no—
700#387—131no—
701#387—131no—
702#387—131no—
703#387—131no—
704#387—131no—
705#387—131no—
706#387—131no—
707#387—131no—
708#387—131no—
709#387—131no—
710#387—131no—
711#387—131no—
712#387—131no—
713#387—131no—
714#387—131no—
715#387—131no—
716#387—131no—
717#387—131no—
718#387—131no—
719#387—131no—
720#387—131no—
721#387—131no—
722#387—131no—
723#387—131no—
724#387—131no—
725#387—131no—
726#387—131no—
727#387—131no—
728#387—131no—
729#387—131no—
730#387—131no—
731#387—131no—
732#387—131no—
733#387C2×D1311yescharacteristic
734#387C2×D1311yescharacteristic
735#385—131no—
736#385—131no—
737#385—131no—
738#385—131no—
739#385—131no—
740#385—131no—
741#385—131no—
742#385—131no—
743#385C2×D1311yescharacteristic
744#385C2×D1311yescharacteristic
745#385C2×D1311yescharacteristic
746#385C2×D1311yescharacteristic
747#384—131no—
748#383—131no—
749#383—131no—
750#383—131no—
751#383—131no—
752#382—131no—
753#382—131no—
754#382C2×D1311yescharacteristic
755#381—131no—
756#381—131no—
757#381—131no—
758#381—131no—
759#380—131no—
760#380—131no—
761#380—131no—
762#380—131no—
763#380—131no—
764#380C2×D1311yescharacteristic
765C4×C22⋊C4—131no—
766C4×C22⋊C4—131no—
767C4×C22⋊C4—131no—
768C4×C22⋊C4C2×D1311yescharacteristic
769C2×#95—131no—
770C2×#95—131no—
771C2×#95—131no—
772C2×#95C2×D1311yescharacteristic
773C22×C13—22no—
774C22×C13—22no—
775C22×C13—22no—
776C22×C13—22no—
777C22×C13—22no—
778C22×C13—22no—
779C22×C13#54114yes—
780C22×C13C22×#4111yescharacteristic
781C22×C13C2×H(5,𝔽2)11yescharacteristic
782C22×C13C2×2−1+411yescharacteristic
783C22×C13C2×2−1+411yescharacteristic
784C22×C13C2×2−1+411yescharacteristic
785C22×C13#58511yescharacteristic
786C22×C13#58511yescharacteristic
787C4×C13—22no—
788C4×C13—41no—
789C4×C13—41no—
790C4×C13—41no—
791C4×C13—41no—
792C4×C13—41no—
793C4×C13—41no—
794C4×C13—41no—
795C4×C13—41no—
796C4×C13—41no—
797C4×C13—41no—
798C4×C13—41no—
799C4×C13—41no—
800C4×C13—41no—
801Dic13—22no—
802Dic13—22no—
803Dic13—22no—
804Dic13—41no—
805Dic13—41no—
806Dic13—41no—
807Dic13—41no—
808Dic13—41no—
809Dic13—41no—
810Dic13—41no—
811Dic13—41no—
812Dic13—41no—
813Dic13—41no—
814Dic13—41no—
815Dic13—41no—
816Dic13—41no—
817C22×Q8—131no—
818C22×Q8—131no—
819C23×C4—131no—
820C23×C4—131no—
821C23×C4—131no—
822C23×C4—131no—
823C23×C4C22×D1311yescharacteristic
824C23×C4C22×D1311yescharacteristic
825C23×C4C22×D1311yescharacteristic
826C4⋊Q8—522no—
827#125—522no—
828#125—522no—
829#125—522no—
830C22⋊Q8—264no—
831C22⋊Q8—264no—
832C2×C4⋊C4—131no—
833C2×C4⋊C4—131no—
834C2×C4⋊C4—131no—
835C2×C4⋊C4—131no—
836C2×C4⋊C4—131no—
837C2×C4⋊C4—131no—
838C2×C4⋊C4—131no—
839C2×C4⋊C4—131no—
840C2×C4⋊C4—131no—
841C2×C4⋊C4—131no—
842C2×C4⋊C4—131no—
843C2×C4⋊C4—131no—
844C2×C4⋊C4—131no—
845C2×C4⋊C4—131no—
846C2×C4⋊C4—131no—
847C2×C4⋊C4—131no—
848C2×C4⋊C4—131no—
849C2×C4⋊C4—131no—
850C2×C4⋊C4—131no—
851C2×C4⋊C4—131no—
852C2×C4⋊C4—131no—
853C2×C4⋊C4—131no—
854C2×C4⋊C4—131no—
855C2×C4⋊C4—131no—
856C2×C4⋊C4—131no—
857C2×C4⋊C4—131no—
858C2×C4⋊C4—131no—
859C2×C4⋊C4—131no—
860C2×C4⋊C4—131no—
861C2×C4⋊C4—131no—
862C2×C4⋊C4—131no—
863C2×C4⋊C4—131no—
864C2×C4⋊C4—131no—
865C2×C4⋊C4—131no—
866C2×C4⋊C4—131no—
867C2×C4⋊C4—131no—
868C2×C4⋊C4—131no—
869C2×C4⋊C4—131no—
870C2×C4⋊C4—131no—
871C2×C4⋊C4—131no—
872C2×C4⋊C4—264no—
873C2×C4⋊C4—522no—
874C2×C4⋊C4C22×D1311yescharacteristic
875C2×C4⋊C4C22×D1311yescharacteristic
876C2×C4⋊C4C22×D1311yescharacteristic
877C2×C4⋊C4C22×D1311yescharacteristic
878C2×C4⋊C4C22×D1311yescharacteristic
879C2×C4⋊C4C22×D1311yescharacteristic
880C2×C4⋊C4C22×D1311yescharacteristic
881C2×C4⋊C4C22×D1311yescharacteristic
882C2×C4⋊C4C22×D1311yescharacteristic
883C2×C4⋊C4C22×D1311yescharacteristic
884C2×C22⋊C4—131no—
885C2×C22⋊C4—131no—
886C2×C22⋊C4—131no—
887C2×C22⋊C4—131no—
888C2×C22⋊C4C22×D1311yescharacteristic
889C2×C22⋊C4C22×D1311yescharacteristic
890C2×C22⋊C4C22×D1311yescharacteristic
891C2×C22⋊C4C22×D1311yescharacteristic
892C2×C42—131no—
893C2×C42—131no—
894C2×C42—131no—
895C2×C42—131no—
896C2×C42—131no—
897C2×C42—131no—
898C2×C42—131no—
899C2×C42—131no—
900C2×C42—131no—
901C2×C42—131no—
902C2×C42—522no—
903C2×C42C22×D1311yescharacteristic
904C2×C42C22×D1311yescharacteristic
905#95—131no—
906#95—131no—
907#95—131no—
908#95—131no—
909#95—131no—
910#95—131no—
911#95—131no—
912#95—131no—
913#95—131no—
914#95—131no—
915#95—131no—
916#95—131no—
917#95—131no—
918#95—131no—
919#95—131no—
920#95—131no—
921#95—131no—
922#95—131no—
923#95—131no—
924#95—131no—
925#95—131no—
926#95—131no—
927#95—131no—
928#95—131no—
929#95—131no—
930#95—131no—
931#95—131no—
932#95—131no—
933#95—131no—
934#95—131no—
935#95—131no—
936#95—131no—
937#95—131no—
938#95—131no—
939#95—131no—
940#95—131no—
941#95—131no—
942#95—131no—
943#95—131no—
944#95—131no—
945#95—131no—
946#95—131no—
947#95—131no—
948#95—131no—
949#95—131no—
950#95—131no—
951#95—131no—
952#95—131no—
953#95—131no—
954#95—131no—
955#95—131no—
956#95—131no—
957#95—131no—
958#95—131no—
959#95—131no—
960#95—131no—
961#95—131no—
962#95—131no—
963#95—131no—
964#95—131no—
965#95C22×D1311yescharacteristic
966#95C22×D1311yescharacteristic
967#95C22×D1311yescharacteristic
968#95C22×D1311yescharacteristic
969#95C22×D1311yescharacteristic
970#95C22×D1311yescharacteristic
971#95C22×D1311yescharacteristic
972#95C22×D1311yescharacteristic
973#95C22×D1311yescharacteristic
974#95C22×D1311yescharacteristic
975#95C22×D1311yescharacteristic
976#95C22×D1311yescharacteristic
977#95C22×D1311yescharacteristic
978#95C22×D1311yescharacteristic
979#95C22×D1311yescharacteristic
980#95C22×D1311yescharacteristic
981C2×C13—24no—
982C2×C13C2×#54111yescharacteristic
983C2×C13#350511yescharacteristic
984C2×C13#350711yescharacteristic
985C2×C13#353511yescharacteristic
986C2×C13#353811yescharacteristic
987C2×C13#356311yescharacteristic
988C2×C13#356411yescharacteristic
989C24C23×D1311yescharacteristic
990C2×Q8—262no—
991C2×Q8—262no—
992C2×Q8—521no—
993C2×Q8—521no—
994C2×Q8—521no—
995C2×Q8—521no—
996C22×C4—22no—
997C22×C4—22no—
998C22×C4—22no—
999C22×C4—22no—
1000C22×C4—41no—
1001C22×C4—41no—
1002C22×C4—41no—
1003C22×C4—41no—
1004C22×C4—41no—
1005C22×C4—131no—
1006C22×C4—131no—
1007C22×C4—131no—
1008C22×C4—134no—
1009C22×C4—131no—
1010C22×C4—131no—
1011C22×C4—131no—
1012C22×C4—131no—
1013C22×C4—131no—
1014C22×C4—131no—
1015C22×C4—131no—
1016C22×C4—131no—
1017C22×C4—131no—
1018C22×C4—131no—
1019C22×C4—131no—
1020C22×C4—131no—
1021C22×C4—131no—
1022C22×C4—262no—
1023C22×C4—262no—
1024C22×C4—262no—
1025C22×C4—262no—
1026C22×C4—262no—
1027C22×C4—262no—
1028C22×C4—521no—
1029C22×C4—521no—
1030C22×C4—521no—
1031C22×C4—521no—
1032C22×C4—521no—
1033C22×C4C23×D1311yescharacteristic
1034C22×C4C23×D1311yescharacteristic
1035C22×C4C23×D1311yescharacteristic
1036C22×C4C23×D1311yescharacteristic
1037C22×C4C23×D1311yescharacteristic
1038C22×C4C23×D1311yescharacteristic
1039C22×C4C23×D1311yescharacteristic
1040C22×C4C23×D1311yescharacteristic
1041C22×C4C23×D1311yescharacteristic
1042C22×C4C23×D1311yescharacteristic
1043C22×C4C23×D1311yescharacteristic
1044C22×C4C23×D1311yescharacteristic
1045C22×C4C23×D1311yescharacteristic
1046C22×C4C23×D1311yescharacteristic
1047C4⋊C4—22no—
1048C4⋊C4—22no—
1049C4⋊C4—41no—
1050C4⋊C4—41no—
1051C4⋊C4—41no—
1052C4⋊C4—41no—
1053C4⋊C4—41no—
1054C4⋊C4—41no—
1055C4⋊C4—41no—
1056C4⋊C4—41no—
1057C4⋊C4—262no—
1058C4⋊C4—262no—
1059C4⋊C4—262no—
1060C4⋊C4—262no—
1061C4⋊C4—262no—
1062C4⋊C4—262no—
1063C4⋊C4—262no—
1064C4⋊C4—262no—
1065C4⋊C4—262no—
1066C4⋊C4—262no—
1067C4⋊C4—262no—
1068C4⋊C4—262no—
1069C4⋊C4—262no—
1070C4⋊C4—262no—
1071C4⋊C4—262no—
1072C4⋊C4—262no—
1073C4⋊C4—262no—
1074C4⋊C4—262no—
1075C4⋊C4—521no—
1076C4⋊C4—521no—
1077C4⋊C4—521no—
1078C4⋊C4—521no—
1079C4⋊C4—521no—
1080C4⋊C4—521no—
1081C4⋊C4—521no—
1082C4⋊C4—521no—
1083C4⋊C4—521no—
1084C4⋊C4—521no—
1085C4⋊C4—521no—
1086C4⋊C4—521no—
1087C4⋊C4—521no—
1088C4⋊C4—521no—
1089C4⋊C4—521no—
1090C4⋊C4—521no—
1091C4⋊C4—521no—
1092C4⋊C4—521no—
1093C4⋊C4—521no—
1094C4⋊C4—521no—
1095C4⋊C4—521no—
1096C4⋊C4—521no—
1097C22⋊C4—22no—
1098C22⋊C4—22no—
1099C22⋊C4—22no—
1100C22⋊C4—22no—
1101C22⋊C4—262no—
1102C22⋊C4—262no—
1103C22⋊C4—262no—
1104C22⋊C4—262no—
1105C42—41no—
1106C42—41no—
1107C42—262no—
1108C42—262no—
1109C42—521no—
1110C42—521no—
1111C42—521no—
1112C42—521no—
1113C42—521no—
1114C42—521no—
1115C42—521no—
1116C42—521no—
1117C13#3676211yescharacteristic, complemented, Sylow
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23#8825412yes—
1123C23#41×D1312yes—
1124C23#8825712yes—
1125C23C24×D1311yescharacteristic
1126Q8—1042no—
1127Q8—1042no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—44no—
1170C2×C4—44no—
1171C2×C4—82no—
1172C2×C4—132no—
1173C2×C4—132no—
1174C2×C4—132no—
1175C2×C4—261no—
1176C2×C4—261no—
1177C2×C4—261no—
1178C2×C4—261no—
1179C2×C4—261no—
1180C2×C4—261no—
1181C2×C4—261no—
1182C2×C4—261no—
1183C2×C4—261no—
1184C2×C4—261no—
1185C2×C4—261no—
1186C2×C4—261no—
1187C2×C4—261no—
1188C2×C4—261no—
1189C2×C4—261no—
1190C2×C4—261no—
1191C2×C4—261no—
1192C2×C4—261no—
1193C2×C4—261no—
1194C2×C4—261no—
1195C2×C4—261no—
1196C2×C4—261no—
1197C2×C4—261no—
1198C2×C4—261no—
1199C2×C4—261no—
1200C2×C4—261no—
1201C2×C4—261no—
1202C2×C4—261no—
1203C2×C4—261no—
1204C2×C4—261no—
1205C2×C4—261no—
1206C2×C4—261no—
1207C2×C4—261no—
1208C2×C4—261no—
1209C2×C4—261no—
1210C2×C4—261no—
1211C2×C4—261no—
1212C2×C4—261no—
1213C2×C4—261no—
1214C2×C4—261no—
1215C2×C4—261no—
1216C2×C4—261no—
1217C2×C4—261no—
1218C2×C4—261no—
1219C2×C4—261no—
1220C2×C4—524no—
1221C2×C4—524no—
1222C2×C4—524no—
1223C2×C4—1042no—
1224C2×C4#8825712yes—
1225C22—22no—
1226C22—22no—
1227C22—22no—
1228C22—22no—
1229C22—22no—
1230C22—22no—
1231C22#1171940114yes—
1232C22C2×#8825411yescharacteristic
1233C22C2×#41×D1311yescharacteristic
1234C22C2×#8825711yescharacteristic
1235C22C2×#8825711yescharacteristic
1236C22#1171964811yescharacteristic
1237C22D13×H(5,𝔽2)11yescharacteristic
1238C22#1171965011yescharacteristic
1239C4—22no—
1240C4—41no—
1241C4—41no—
1242C4—41no—
1243C4—41no—
1244C4—41no—
1245C4—41no—
1246C4—41no—
1247C4—41no—
1248C4—41no—
1249C4—41no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—262no—
1254C4—262no—
1255C4—262no—
1256C4—521no—
1257C4—521no—
1258C4—521no—
1259C4—521no—
1260C4—521no—
1261C4—521no—
1262C4—521no—
1263C4—521no—
1264C4—521no—
1265C4—521no—
1266C4—521no—
1267C4—521no—
1268C4—521no—
1269C2—24no—
1270C2C2×#1171940111yescharacteristic
1271C2#1312867411yescharacteristic
1272C2#1312869211yescharacteristic
1273C2#1312904011yescharacteristic
1274C2#1312907611yescharacteristic
1275C2#1312944011yescharacteristic
1276C2#1312944811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutator, socle, cosocleC23×C13C25
FittingC13×#2505C2
prime radicalC24×C13C24
hypercenter#2505D13
hypocenterC13#36762
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2505

Complements

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

NH ≅ G/Ntype
3. #13122760C2semidirect
4. #13122751C2semidirect
5. #13122658C2semidirect
6. #13122657C2semidirect
7. #13122595C2semidirect
8. #13122593C2semidirect
9. #13122429C2semidirect
10. #13122424C2semidirect
11. #13122289C2semidirect
12. #13122285C2semidirect
13. #13122192C2semidirect
14. #13122187C2semidirect
15. #13121708C2semidirect
16. #13121696C2semidirect
17. #13121623C2semidirect
18. #13121614C2semidirect
1117. C13#36762semidirect

Maximal subgroups

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

subgroupindex
#131231862
#131231422
#131227602
#131227512
#131226582
#131226572
#131225952
#131225932
#131224292
#131224242
#131222892
#131222852
#131221922
#131221872
#131217082
#131216962
#131216232
#131216142
#131206552
#131193372
#131192272
#131192232
#131192192
#131192152
#131189762
#131189742
#131175672
#131175642
C2×#117183162
C13×#25052
#3676213