Finite Group Databasebeta

← #15829150

Subgroups — #15829150

Order 3328.

944 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719236C211yesmaximal, characteristic
2#13123494C211yesmaximal, characteristic, complemented
3#13113206C211yesmaximal, characteristic, complemented
4#13113203C211yesmaximal, characteristic, complemented
5#13113193C211yesmaximal, characteristic, complemented
6#13113191C211yesmaximal, characteristic, complemented
7#13113185C211yesmaximal, characteristic
8#13113182C211yesmaximal, characteristic
9#13113179C211yesmaximal, characteristic, complemented
10#13113168C211yesmaximal, characteristic, complemented
11#13113165C211yesmaximal, characteristic, complemented
12#13113159C211yesmaximal, characteristic, complemented
13#13113148C211yesmaximal, characteristic, complemented
14C2×#11718061C211yesmaximal, characteristic, complemented
15C13×#2924C211yesmaximal, characteristic, complemented
16C2×C13×#117C2211yescharacteristic
17C2×#88183C2211yescharacteristic
18C22×#6101C2211yescharacteristic
19#11719236—21no—
20#11719236—21no—
21#11719236—21no—
22#11719236—21no—
23#11719236—21no—
24#11719236—21no—
25#11719236—21no—
26#11719236—21no—
27C2×#88152C411yescharacteristic
28C2×#88150C411yescharacteristic
29C2×#88143C411yescharacteristic
30C2×#88143C411yescharacteristic
31C2×#88140C411yescharacteristic
32C2×#88135C411yescharacteristic
33C2×#88132C411yescharacteristic
34C2×#88131C411yescharacteristic
35C2×#88130C2211yescharacteristic
36C2×#88126C2211yescharacteristic
37C2×#88124C2211yescharacteristic
38C2×C4×Dic26C2211yescharacteristic
39C13×#433—21no—
40C13×#433—21no—
41C13×#432C2211yescharacteristic
42C13×#432C2211yescharacteristic
43C13×#431C2211yescharacteristic
44C13×#431C2211yescharacteristic
45C13×#424—21no—
46C13×#407C2211yescharacteristic
47C2×C13×C22⋊C8C2211yescharacteristic
48C13×#405—21no—
49#11718868C2211yescharacteristic
50C2×C22⋊#1055C2211yescharacteristic
51#11718661—21no—
52#11718661—21no—
53#11718660—21no—
54#11718658—21no—
55#11718587C2211yescharacteristic
56#11718587C2211yescharacteristic
57#11718586C2211yescharacteristic
58#11718586C2211yescharacteristic
59#11718061C2211yescharacteristic
60#11718061C2211yescharacteristic
61#11718061C2211yescharacteristic
62#11718061C2211yescharacteristic
63#11718061C2211yescharacteristic
64#11718061C2211yescharacteristic
65#11718061C2211yescharacteristic
66#11718061C2211yescharacteristic
67#11718061C2211yescharacteristic
68#11718061C2211yescharacteristic
69#11718061C2211yescharacteristic
70#11718061C2211yescharacteristic
71#11718060C2211yescharacteristic
72#11718060C2211yescharacteristic
73#11718060C2211yescharacteristic
74#11718060C2211yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C22×C22⋊D13C2×C411yescharacteristic
77C23×Dic13C2×C411yescharacteristic
78C23×Dic13C2×C411yescharacteristic
79C22×C4×D13C2×C411yescharacteristic
80C22×Dic26C2×C411yescharacteristic
81C2×C13×M16—21no—
82C22×C8×C13—21no—
83C13×#117D411yescharacteristic
84C13×#117D411yescharacteristic
85C13×#117D411yescharacteristic
86C13×#117D411yescharacteristic
87C13×#117D411yescharacteristic
88C13×#117D411yescharacteristic
89C13×#117D411yescharacteristic
90C13×#117D411yescharacteristic
91C2×C13×C4⋊C4C2×C411yescharacteristic
92C2×C13×C4⋊C4C2×C411yescharacteristic
93C2×C13×C22⋊C4C2×C411yescharacteristic
94C2×C13×C22⋊C4C2×C411yescharacteristic
95C2×C42×C13C2311yescharacteristic
96C2×C42×C13C2311yescharacteristic
97C2×C22⋊Dic13C2×C411yescharacteristic
98#88183—21no—
99#88183—21no—
100#88183—21no—
101#88183—21no—
102C2×#6103C2×C411yescharacteristic
103C2×#6103C2×C411yescharacteristic
104C2×#6103C2×C411yescharacteristic
105C2×#6103C2×C411yescharacteristic
106C2×#6103C2311yescharacteristic
107C2×C4⋊Dic13C2×C411yescharacteristic
108C2×C4⋊Dic13C2×C411yescharacteristic
109C2×C4⋊Dic13C2×C411yescharacteristic
110C2×#6101—21no—
111C2×#6101—21no—
112C2×#6101—21no—
113C2×#6101—21no—
114C2×#6101C2×C411yescharacteristic
115C2×#6101C2×C411yescharacteristic
116C2×#6101C2×C411yescharacteristic
117C2×#6101C2×C411yescharacteristic
118C2×#6101C2×C411yescharacteristic
119C2×#6101C2×C411yescharacteristic
120C2×#6101C2×C411yescharacteristic
121C2×#6101C2×C411yescharacteristic
122C2×#6101C2311yescharacteristic
123C2×#6101C2311yescharacteristic
124C2×#6101C2311yescharacteristic
125C2×C4×Dic13C2×C411yescharacteristic
126C2×C4×Dic13C2×C411yescharacteristic
127C2×C4×Dic13C2×C411yescharacteristic
128C2×#6099—21no—
129C22×#1055—21no—
130#88152—21no—
131#88152—21no—
132#88152—21no—
133#88152—21no—
134#88150—21no—
135#88150—21no—
136#88150—21no—
137#88150—21no—
138#88143—21no—
139#88143—21no—
140#88143—21no—
141#88143—21no—
142#88143—21no—
143#88143—21no—
144#88143—21no—
145#88143—21no—
146#88140—21no—
147#88140—21no—
148#88140—21no—
149#88140—21no—
150#88135—21no—
151#88135—21no—
152#88135—21no—
153#88135—21no—
154#88132—21no—
155#88132—21no—
156#88132—21no—
157#88132—21no—
158#88131—21no—
159#88131—21no—
160#88131—21no—
161#88131—21no—
162#88130—21no—
163#88130—21no—
164#88130—21no—
165#88130—21no—
166#88126—21no—
167#88126—21no—
168#88126—21no—
169#88126—21no—
170#88124—21no—
171#88124—21no—
172#88124—21no—
173#88124—21no—
174C4×Dic26—21no—
175C4×Dic26—21no—
176C4×Dic26—21no—
177C4×Dic26—21no—
178C13×C4⋊C8—21no—
179C13×C4⋊C8—21no—
180C13×C4⋊C8—21no—
181C13×C4⋊C8—21no—
182C13×C22⋊C8—21no—
183C13×C22⋊C8—21no—
184C13×C22⋊C8C2311yescharacteristic
185C13×C22⋊C8C2311yescharacteristic
186C13×C22⋊C8C2311yescharacteristic
187C13×C22⋊C8C2311yescharacteristic
188C13×#97—21no—
189C13×#97—21no—
190C4×C8×C13—21no—
191C4×C8×C13—21no—
192C22⋊#1055—21no—
193C22⋊#1055—21no—
194C22⋊#1055C2311yescharacteristic
195C22⋊#1055C2311yescharacteristic
196C22⋊#1055C2311yescharacteristic
197C22⋊#1055C2311yescharacteristic
198C4⋊#1055—21no—
199C4⋊#1055—21no—
200C4⋊#1055—21no—
201C4⋊#1055—21no—
202#88043—21no—
203#88043—21no—
204C4×#1055—21no—
205C4×#1055—21no—
206#17417—131nomaximal, Sylow
207C24×C13C22×C411yescharacteristic
208C23×D13C22×C411yescharacteristic
209C22×C4×C13—42no—
210C22×C4×C13C22×C411yescharacteristic
211C22×C4×C13C22×C411yescharacteristic
212C22×C4×C13C22×C411yescharacteristic
213C22×C4×C13C22×C411yescharacteristic
214C22×C4×C13C22×C411yescharacteristic
215C22×C4×C13C2×D411yescharacteristic
216C22×C4×C13C2×D411yescharacteristic
217C22×C4×C13C2×D411yescharacteristic
218C22×C4×C13C2×D411yescharacteristic
219C22×C4×C13C2411yescharacteristic
220C2×C22⋊D13—21no—
221C2×C22⋊D13—21no—
222C2×C22⋊D13—42no—
223C22×Dic13—21no—
224C22×Dic13—21no—
225C22×Dic13—21no—
226C22×Dic13—21no—
227C22×Dic13—22no—
228C22×Dic13—41no—
229C22×Dic13—42no—
230C22×Dic13C22×C411yescharacteristic
231C22×Dic13C22×C411yescharacteristic
232C22×Dic13C22×C411yescharacteristic
233C22×Dic13C22×C411yescharacteristic
234C22×Dic13C22×C411yescharacteristic
235C22×Dic13C22×C411yescharacteristic
236C22×Dic13C22×C411yescharacteristic
237C2×C4×D13—21no—
238C2×C4×D13—21no—
239C2×C4×D13—22no—
240C2×C4×D13—41no—
241C2×Dic26—21no—
242C2×Dic26—21no—
243C2×Dic26—22no—
244C2×Dic26—41no—
245C13×M16—42no—
246C2×C8×C13—21no—
247C2×C8×C13—21no—
248C2×C8×C13—21no—
249C2×C8×C13—21no—
250C2×C8×C13—42no—
251C13×C4⋊C4C22⋊C411yescharacteristic
252C13×C4⋊C4C22⋊C411yescharacteristic
253C13×C4⋊C4C22⋊C411yescharacteristic
254C13×C4⋊C4C22⋊C411yescharacteristic
255C13×C4⋊C4C22⋊C411yescharacteristic
256C13×C4⋊C4C22⋊C411yescharacteristic
257C13×C4⋊C4C22⋊C411yescharacteristic
258C13×C4⋊C4C22⋊C411yescharacteristic
259C13×C22⋊C4C22⋊C411yescharacteristic
260C13×C22⋊C4C22⋊C411yescharacteristic
261C13×C22⋊C4C22⋊C411yescharacteristic
262C13×C22⋊C4C22⋊C411yescharacteristic
263C13×C22⋊C4C22⋊C411yescharacteristic
264C13×C22⋊C4C22⋊C411yescharacteristic
265C13×C22⋊C4C22⋊C411yescharacteristic
266C13×C22⋊C4C22⋊C411yescharacteristic
267C42×C13C2×D411yescharacteristic
268C42×C13C2×D411yescharacteristic
269C42×C13C2×D411yescharacteristic
270C42×C13C2×D411yescharacteristic
271C42×C13C2×D411yescharacteristic
272C42×C13C2×D411yescharacteristic
273C42×C13C2×D411yescharacteristic
274C42×C13C2×D411yescharacteristic
275C22⋊Dic13—21no—
276C22⋊Dic13—21no—
277#6103—21no—
278#6103—21no—
279#6103—21no—
280#6103—21no—
281#6103—21no—
282#6103—21no—
283#6103—21no—
284#6103—21no—
285#6103—21no—
286#6103—21no—
287C4⋊Dic13—21no—
288C4⋊Dic13—21no—
289C4⋊Dic13—21no—
290C4⋊Dic13—21no—
291C4⋊Dic13—21no—
292C4⋊Dic13—21no—
293#6101—21no—
294#6101—21no—
295#6101—21no—
296#6101—21no—
297#6101—21no—
298#6101—21no—
299#6101—21no—
300#6101—21no—
301#6101—21no—
302#6101—21no—
303#6101—21no—
304#6101—21no—
305#6101—21no—
306#6101—21no—
307#6101—21no—
308#6101—21no—
309#6101—21no—
310#6101—21no—
311#6101—21no—
312#6101—21no—
313#6101—21no—
314#6101—21no—
315C4×Dic13—21no—
316C4×Dic13—21no—
317C4×Dic13—21no—
318C4×Dic13—21no—
319C4×Dic13—21no—
320C4×Dic13—21no—
321#6099—42no—
322C2×#1055—21no—
323C2×#1055—21no—
324C2×#1055—21no—
325C2×#1055—21no—
326C2×#1055—42no—
327C2×#552—131no—
328#2924—131no—
329#2924D1311yescharacteristic, complemented
330#1473—131no—
331#1473—131no—
332#1470—131no—
333#1470—131no—
334#1468—131no—
335#1468—131no—
336#1467—131no—
337#1464—131no—
338#1463—131no—
339#1461—131no—
340#1458—131no—
341C2×#324—131no—
342C23×C13—21no—
343C23×C13—21no—
344C23×C13—22no—
345C23×C13—41no—
346C23×C13C2×C22⋊C411yescharacteristic
347C23×C13C2×C22⋊C411yescharacteristic
348C23×C13C23×C411yescharacteristic
349C22×D13—21no—
350C22×D13—21no—
351C22×D13—21no—
352C22×D13—41no—
353C22×D13—41no—
354C2×C4×C13—21no—
355C2×C4×C13—21no—
356C2×C4×C13—21no—
357C2×C4×C13—21no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—41no—
361C2×C4×C13—41no—
362C2×C4×C13—41no—
363C2×C4×C13—41no—
364C2×C4×C13—41no—
365C2×C4×C13—41no—
366C2×C4×C13C2×C22⋊C411yescharacteristic
367C2×C4×C13C2×C22⋊C411yescharacteristic
368C2×C4×C13C2×C22⋊C411yescharacteristic
369C2×C4×C13C2×C22⋊C411yescharacteristic
370C2×C4×C13C2×C22⋊C411yescharacteristic
371C2×C4×C13C2×C22⋊C411yescharacteristic
372C2×C4×C13C2×C22⋊C411yescharacteristic
373C2×C4×C13C2×C22⋊C411yescharacteristic
374C2×C4×C13C2×C22⋊C411yescharacteristic
375C2×C4×C13C2×C22⋊C411yescharacteristic
376C2×C4×C13C22×D411yescharacteristic
377C2×C4×C13C22×D411yescharacteristic
378C22⋊D13—42no—
379C22⋊D13—42no—
380C2×Dic13—21no—
381C2×Dic13—21no—
382C2×Dic13—21no—
383C2×Dic13—21no—
384C2×Dic13—21no—
385C2×Dic13—21no—
386C2×Dic13—21no—
387C2×Dic13—21no—
388C2×Dic13—21no—
389C2×Dic13—21no—
390C2×Dic13—21no—
391C2×Dic13—21no—
392C2×Dic13—42no—
393C2×Dic13—42no—
394C2×Dic13—42no—
395C2×Dic13—42no—
396C2×Dic13—41no—
397C2×Dic13—41no—
398C2×Dic13—41no—
399C2×Dic13—41no—
400C2×Dic13#13112yes—
401C4×D13—42no—
402C4×D13—42no—
403Dic26—42no—
404Dic26—42no—
405C8×C13—41no—
406C8×C13—41no—
407C8×C13—41no—
408C8×C13—41no—
409#1055—41no—
410#1055—41no—
411#1055—41no—
412#1055—41no—
413#552—261no—
414#552—261no—
415#552—261no—
416#552—261no—
417#552—261no—
418#552—261no—
419#552—261no—
420#552—261no—
421C2×#126—131no—
422C2×#126—131no—
423C2×#125—131no—
424C2×#125—131no—
425C2×#125—131no—
426C2×#123—131no—
427C2×#123—131no—
428C2×C22⋊Q8—131no—
429C2×C22⋊Q8—131no—
430C2×C4×Q8—131no—
431C2×C4×D4—131no—
432C2×#117—131no—
433C2×#117—131no—
434C2×#117C2×D1311yescharacteristic
435C22×C4⋊C4—131no—
436#433—21no—
437#433—21no—
438#433—261no—
439#433—261no—
440#432—131no—
441#432—131no—
442#432C2×D1311yescharacteristic
443#432C2×D1311yescharacteristic
444#431—131no—
445#431—131no—
446#431C2×D1311yescharacteristic
447#431C2×D1311yescharacteristic
448#424—21no—
449#424—261no—
450#407—131no—
451#407C2×D1311yescharacteristic
452C2×C22⋊C8—131no—
453C2×C22⋊C8C2×D1311yescharacteristic
454#405—21no—
455#405—261no—
456#324—131no—
457#324—131no—
458#324—131no—
459#324—131no—
460#324—131no—
461#324—131no—
462#324—131no—
463#324—131no—
464#324—131no—
465#324—131no—
466#324—131no—
467#324—131no—
468#323—131no—
469#323—131no—
470#323—131no—
471#323—131no—
472C22×C13—21no—
473C22×C13—21no—
474C22×C13—21no—
475C22×C13—21no—
476C22×C13—21no—
477C22×C13—21no—
478C22×C13—21no—
479C22×C13—42no—
480C22×C13—42no—
481C22×C13#41012yes—
482C22×C13C22×C22⋊C411yescharacteristic
483C22×C13C2×#13111yescharacteristic
484C22×C13#56811yescharacteristic
485C2×D13—41no—
486C2×D13—41no—
487C2×D13—41no—
488C2×D13—81no—
489C2×D13—81no—
490C4×C13—21no—
491C4×C13—21no—
492C4×C13—21no—
493C4×C13—21no—
494C4×C13—21no—
495C4×C13—21no—
496C4×C13—21no—
497C4×C13—21no—
498C4×C13—21no—
499C4×C13—21no—
500C4×C13—21no—
501C4×C13—21no—
502Dic13—22no—
503Dic13—41no—
504Dic13—41no—
505Dic13—41no—
506Dic13—41no—
507Dic13—41no—
508Dic13—41no—
509C22×Q8—131no—
510C22×D4—131no—
511C23×C4—131no—
512C23×C4—131no—
513C23×C4—131no—
514C23×C4C22×D1311yescharacteristic
515C2×M16—21no—
516C2×M16—261no—
517C22×C8—21no—
518C22×C8—261no—
519#126—261no—
520#126—261no—
521#126—261no—
522#126—261no—
523#126—261no—
524#126—261no—
525#126—261no—
526#126—261no—
527#125—261no—
528#125—261no—
529#125—261no—
530#125—261no—
531#125—261no—
532#125—261no—
533#125—261no—
534#125—261no—
535#125—261no—
536#125—261no—
537#125—261no—
538#125—261no—
539#123—261no—
540#123—261no—
541#123—261no—
542#123—261no—
543#123—261no—
544#123—261no—
545#123—261no—
546#123—261no—
547C22⋊Q8—261no—
548C22⋊Q8—261no—
549C22⋊Q8—261no—
550C22⋊Q8—261no—
551C22⋊Q8—261no—
552C22⋊Q8—261no—
553C22⋊Q8—261no—
554C22⋊Q8—261no—
555C4×Q8—261no—
556C4×Q8—261no—
557C4×Q8—261no—
558C4×Q8—261no—
559C4×D4—261no—
560C4×D4—261no—
561C4×D4—261no—
562C4×D4—261no—
563#117—261no—
564#117—261no—
565#117—261no—
566#117—261no—
567#117—261no—
568#117—261no—
569#117—261no—
570#117—261no—
571#117D5211yescharacteristic
572#117D5211yescharacteristic
573#117D5211yescharacteristic
574#117D5211yescharacteristic
575#117C22⋊D1311yescharacteristic
576#117C22⋊D1311yescharacteristic
577#117C22⋊D1311yescharacteristic
578#117C22⋊D1311yescharacteristic
579C2×C4⋊C4—131no—
580C2×C4⋊C4—131no—
581C2×C4⋊C4—131no—
582C2×C4⋊C4—131no—
583C2×C4⋊C4—131no—
584C2×C4⋊C4—131no—
585C2×C4⋊C4—131no—
586C2×C4⋊C4—131no—
587C2×C4⋊C4—131no—
588C2×C4⋊C4—131no—
589C2×C4⋊C4—131no—
590C2×C4⋊C4—131no—
591C2×C4⋊C4—131no—
592C2×C4⋊C4—131no—
593C2×C4⋊C4—261no—
594C2×C4⋊C4—261no—
595C2×C4⋊C4—261no—
596C2×C4⋊C4—261no—
597C2×C4⋊C4C4×D1311yescharacteristic
598C2×C4⋊C4C4×D1311yescharacteristic
599C2×C22⋊C4—131no—
600C2×C22⋊C4—131no—
601C2×C22⋊C4—131no—
602C2×C22⋊C4—131no—
603C2×C22⋊C4—131no—
604C2×C22⋊C4—131no—
605C2×C22⋊C4C4×D1311yescharacteristic
606C2×C22⋊C4C4×D1311yescharacteristic
607C2×C42—131no—
608C2×C42—131no—
609C2×C42—131no—
610C2×C42C22×D1311yescharacteristic
611C2×C42C22×D1311yescharacteristic
612C4⋊C8—21no—
613C4⋊C8—21no—
614C4⋊C8—21no—
615C4⋊C8—21no—
616C4⋊C8—261no—
617C4⋊C8—261no—
618C4⋊C8—261no—
619C4⋊C8—261no—
620C22⋊C8—21no—
621C22⋊C8—21no—
622C22⋊C8—131no—
623C22⋊C8—131no—
624C22⋊C8—131no—
625C22⋊C8—131no—
626C22⋊C8—261no—
627C22⋊C8—261no—
628C22⋊C8C22×D1311yescharacteristic
629C22⋊C8C22×D1311yescharacteristic
630C22⋊C8C22×D1311yescharacteristic
631C22⋊C8C22×D1311yescharacteristic
632#97—21no—
633#97—21no—
634#97—261no—
635#97—261no—
636C4×C8—21no—
637C4×C8—21no—
638C4×C8—261no—
639C4×C8—261no—
640C2×C13—21no—
641C2×C13—21no—
642C2×C13—22no—
643C2×C13—41no—
644C2×C13#288011yescharacteristic
645C2×C13C2×#41011yescharacteristic
646C2×C13#288911yescharacteristic
647D13—81no—
648C24—131no—
649C24C2×C4×D1311yescharacteristic
650C2×Q8—262no—
651C2×Q8—261no—
652C2×Q8—261no—
653C2×Q8—521no—
654C2×D4—261no—
655C2×D4—261no—
656C2×D4—522no—
657C22×C4—42no—
658C22×C4—131no—
659C22×C4—131no—
660C22×C4—131no—
661C22×C4—131no—
662C22×C4—131no—
663C22×C4—131no—
664C22×C4—131no—
665C22×C4—262no—
666C22×C4—262no—
667C22×C4—261no—
668C22×C4—261no—
669C22×C4—261no—
670C22×C4—261no—
671C22×C4—261no—
672C22×C4—261no—
673C22×C4—521no—
674C22×C4—521no—
675C22×C4—522no—
676C22×C4C2×C4×D1311yescharacteristic
677C22×C4C2×C4×D1311yescharacteristic
678C22×C4C2×C4×D1311yescharacteristic
679C22×C4C2×C4×D1311yescharacteristic
680C22×C4C2×C4×D1311yescharacteristic
681C22×C4C2×D5211yescharacteristic
682C22×C4C2×D5211yescharacteristic
683C22×C4C2×C22⋊D1311yescharacteristic
684C22×C4C2×C22⋊D1311yescharacteristic
685C22×C4C23×D1311yescharacteristic
686M16—42no—
687M16—522no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—42no—
693C2×C8—261no—
694C2×C8—261no—
695C2×C8—261no—
696C2×C8—261no—
697C2×C8—522no—
698C4⋊C4—261no—
699C4⋊C4—261no—
700C4⋊C4—261no—
701C4⋊C4—261no—
702C4⋊C4—261no—
703C4⋊C4—261no—
704C4⋊C4—261no—
705C4⋊C4—261no—
706C4⋊C4—261no—
707C4⋊C4—261no—
708C4⋊C4—261no—
709C4⋊C4—261no—
710C4⋊C4—261no—
711C4⋊C4—261no—
712C4⋊C4—261no—
713C4⋊C4—261no—
714C4⋊C4—261no—
715C4⋊C4—261no—
716C4⋊C4—261no—
717C4⋊C4—261no—
718C4⋊C4—261no—
719C4⋊C4—261no—
720C4⋊C4—261no—
721C4⋊C4—261no—
722C4⋊C4—261no—
723C4⋊C4—261no—
724C4⋊C4—261no—
725C4⋊C4—261no—
726C4⋊C4#610311yescharacteristic
727C4⋊C4#610311yescharacteristic
728C4⋊C4#610311yescharacteristic
729C4⋊C4#610311yescharacteristic
730C4⋊C4#610311yescharacteristic
731C4⋊C4#610311yescharacteristic
732C4⋊C4#610311yescharacteristic
733C4⋊C4#610311yescharacteristic
734C22⋊C4—261no—
735C22⋊C4—261no—
736C22⋊C4—261no—
737C22⋊C4—261no—
738C22⋊C4—261no—
739C22⋊C4—261no—
740C22⋊C4—261no—
741C22⋊C4—261no—
742C22⋊C4—261no—
743C22⋊C4—261no—
744C22⋊C4—261no—
745C22⋊C4—261no—
746C22⋊C4#610311yescharacteristic
747C22⋊C4#610311yescharacteristic
748C22⋊C4#610311yescharacteristic
749C22⋊C4#610311yescharacteristic
750C22⋊C4#610311yescharacteristic
751C22⋊C4#610311yescharacteristic
752C22⋊C4#610311yescharacteristic
753C22⋊C4#610311yescharacteristic
754C42—261no—
755C42—261no—
756C42—261no—
757C42—261no—
758C42—261no—
759C42—261no—
760C42C2×D5211yescharacteristic
761C42C2×D5211yescharacteristic
762C42C2×D5211yescharacteristic
763C42C2×D5211yescharacteristic
764C42C2×C22⋊D1311yescharacteristic
765C42C2×C22⋊D1311yescharacteristic
766C42C2×C22⋊D1311yescharacteristic
767C42C2×C22⋊D1311yescharacteristic
768C13#1741711yescharacteristic, complemented, Sylow
769C23—22no—
770C23—21no—
771C23—21no—
772C23—41no—
773C23—261no—
774C23—261no—
775C23—261no—
776C23—521no—
777C23—521no—
778C23C2×#610311yescharacteristic
779C23C2×#610311yescharacteristic
780C23C22×C4×D1311yescharacteristic
781Q8—522no—
782Q8—522no—
783D4—522no—
784D4—522no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—132no—
798C2×C4—261no—
799C2×C4—261no—
800C2×C4—261no—
801C2×C4—261no—
802C2×C4—261no—
803C2×C4—261no—
804C2×C4—261no—
805C2×C4—261no—
806C2×C4—261no—
807C2×C4—261no—
808C2×C4—261no—
809C2×C4—261no—
810C2×C4—522no—
811C2×C4—522no—
812C2×C4—522no—
813C2×C4—522no—
814C2×C4—522no—
815C2×C4—522no—
816C2×C4—521no—
817C2×C4—521no—
818C2×C4—521no—
819C2×C4—521no—
820C2×C4C2×#610311yescharacteristic
821C2×C4C2×#610311yescharacteristic
822C2×C4C2×#610311yescharacteristic
823C2×C4C2×#610311yescharacteristic
824C2×C4C2×#610311yescharacteristic
825C2×C4C2×#610311yescharacteristic
826C2×C4C2×#610311yescharacteristic
827C2×C4C2×#610311yescharacteristic
828C2×C4C2×#610311yescharacteristic
829C2×C4C2×#610311yescharacteristic
830C2×C4C22×D5211yescharacteristic
831C2×C4C22×C22⋊D1311yescharacteristic
832C8—41no—
833C8—41no—
834C8—41no—
835C8—41no—
836C8—521no—
837C8—521no—
838C8—521no—
839C8—521no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—42no—
848C22—42no—
849C22—521no—
850C22—521no—
851C22—521no—
852C22—1041no—
853C22—1041no—
854C22#1171866712yes—
855C22D13×#13111yescharacteristic
856C22#1171945511yescharacteristic
857C22C22×#610311yescharacteristic
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—262no—
871C4—521no—
872C4—521no—
873C4—521no—
874C4—521no—
875C4—521no—
876C4—521no—
877C2—21no—
878C2—21no—
879C2—22no—
880C2—41no—
881C2—1041no—
882C2#1312328311yescharacteristic
883C2C2×#1171866711yescharacteristic
884C2#1312331811yescharacteristic
subgroupG/H
centerC22C22×#6103
commutatorC23×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2924C2
socleC22×C13C22×C22⋊C4
prime radicalC22×C22⋊D13C2×C4
cosocleC22×C4×C13C24
hypercenter#2924D13
hypocenterC13#17417
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #13123494C2semidirect
3. #13113206C2semidirect
4. #13113203C2semidirect
5. #13113193C2semidirect
6. #13113191C2semidirect
9. #13113179C2semidirect
10. #13113168C2semidirect
11. #13113165C2semidirect
12. #13113159C2semidirect
13. #13113148C2semidirect
14. C2×#11718061C2semidirect
15. C13×#2924C2semidirect
329. #2924D13semidirect
768. C13#17417semidirect

Maximal subgroups

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

subgroupindex
C2×#117192362
#131234942
#131132062
#131132032
#131131932
#131131912
#131131852
#131131822
#131131792
#131131682
#131131652
#131131592
#131131482
C2×#117180612
C13×#29242
#1741713