Finite Group Databasebeta

← #15883660

Subgroups — #15883660

Order 3328.

1058 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718858C211yesmaximal, characteristic, complemented
2#13123563C211yesmaximal, characteristic, complemented
3C22×#88077C211yesmaximal, characteristic, complemented
4#13123285C211yesmaximal, characteristic, complemented
5#13115730C211yesmaximal, characteristic, complemented
6#13115549C211yesmaximal, characteristic, complemented
7#13115486C211yesmaximal, characteristic, complemented
8#13115280C211yesmaximal, characteristic, complemented
9#13115165C211yesmaximal, characteristic, complemented
10#13115165C211yesmaximal, characteristic, complemented
11#13115113C211yesmaximal, characteristic, complemented
12#13115043C211yesmaximal, characteristic, complemented
13#13114683C211yesmaximal, characteristic, complemented
14#13114600C211yesmaximal, characteristic, complemented
15C13×#3002C211yesmaximal, characteristic
16C22×C13×#41C2211yescharacteristic
17C2×C13×#135C2211yescharacteristic
18C2×C13×#135C2211yescharacteristic
19C13×#525C2211yescharacteristic
20C2×#88202C2211yescharacteristic
21C2×#88202C2211yescharacteristic
22C2×#88202C2211yescharacteristic, complemented
23C22×C4×Dic13C2211yescharacteristic
24C22×#6099C2211yescharacteristic
25C13×#452C411yescharacteristic, complemented
26C13×#452C411yescharacteristic, complemented
27C13×#451C411yescharacteristic, complemented
28C13×#450C411yescharacteristic, complemented
29C13×#449C411yescharacteristic, complemented
30C13×#449C411yescharacteristic, complemented
31C13×#448C411yescharacteristic, complemented
32C13×#447C411yescharacteristic, complemented
33C13×#416C2211yescharacteristic
34C13×#416C2211yescharacteristic
35C2×C13×C22⋊C8C2211yescharacteristic
36C2×#88077—24no—
37C2×#88077C2211yescharacteristic
38C2×#88077C2211yescharacteristic
39C2×#88077C2211yescharacteristic
40C2×#88077C2211yescharacteristic
41C2×#88077C2211yescharacteristic, complemented
42C2×#88077C2211yescharacteristic, complemented
43#11718895—21no—
44#11718895—21no—
45#11718895C2211yescharacteristic
46#11718895C2211yescharacteristic
47#11718895C2211yescharacteristic, complemented
48#11718868—21no—
49#11718868C2211yescharacteristic
50C2×C22⋊#1055—21no—
51C2×C22⋊#1055C2211yescharacteristic
52#11718858—24no—
53C2×#88059C2211yescharacteristic, complemented
54C2×#88059C2211yescharacteristic, complemented
55C2×#88055C2211yescharacteristic, complemented
56C2×#88055C2211yescharacteristic, complemented
57#11718673—21no—
58#11718672—21no—
59#11718672—21no—
60D4×#1055—21no—
61#11718660C2211yescharacteristic, complemented
62#11718658C2211yescharacteristic, complemented
63#11718144C2211yescharacteristic, complemented
64#11718144C2211yescharacteristic, complemented
65#11718142C2211yescharacteristic, complemented
66#11718142C2211yescharacteristic, complemented
67#11718124C2211yescharacteristic, complemented
68#11718124C2211yescharacteristic, complemented
69C2×C13×#41—21no—
70C2×C13×#41—21no—
71C2×C13×#41—22no—
72C2×C13×#41—22no—
73C2×C13×#41—41no—
74C2×C13×#41—41no—
75C2×C13×#41C2×C411yescharacteristic
76C2×C13×#41C2×C411yescharacteristic
77C2×C13×#41C2311yescharacteristic
78C2×C13×#41C2311yescharacteristic
79C2×C13×#41C2311yescharacteristic
80C22×Q8×C13C2×C411yescharacteristic
81C22×D4×C13—21no—
82C22×D4×C13C2×C411yescharacteristic
83C23×C4×C13—21no—
84C23×C4×C13C2311yescharacteristic
85C23×Dic13—21no—
86C13×#135—22no—
87C13×#135—22no—
88C13×#135—41no—
89C13×#135—41no—
90C2×C13×Q16C2×C411yescharacteristic, complemented
91C2×C13×Q16C2×C411yescharacteristic, complemented
92C2×C13×SD16C2×C411yescharacteristic, complemented
93C2×C13×SD16C2×C411yescharacteristic, complemented
94C2×C13×SD16C2×C411yescharacteristic, complemented
95C2×C13×SD16C2×C411yescharacteristic, complemented
96C2×C13×D8C2×C411yescharacteristic, complemented
97C2×C13×D8C2×C411yescharacteristic, complemented
98C22×C8×C13C2311yescharacteristic
99C22×C8×C13C2311yescharacteristic
100C13×#123—21no—
101C13×C22⋊Q8C2×C411yescharacteristic
102C13×C22⋊Q8C2×C411yescharacteristic
103C13×#121C2×C411yescharacteristic
104C13×#121C2×C411yescharacteristic
105C13×#120—21no—
106C4×D4×C13—21no—
107C4×D4×C13—21no—
108C13×#117C2311yescharacteristic
109#88202—22no—
110#88202—22no—
111#88202—22no—
112#88202—41no—
113#88202—41no—
114#88202—41no—
115C2×C4×Dic13—22no—
116C2×C4×Dic13—21no—
117C2×C4×Dic13—41no—
118C2×C4×Dic13C2311yescharacteristic
119C2×C4×Dic13C2311yescharacteristic
120C2×#6099—21no—
121C2×#6099—21no—
122C2×#6099—21no—
123C2×#6099—21no—
124C2×#6099—22no—
125C2×#6099—41no—
126C2×#6099C2311yescharacteristic
127C2×#6099C2311yescharacteristic
128C2×#6099C2311yescharacteristic
129C2×#6099C2311yescharacteristic
130C22×#1055—21no—
131C22×#1055—21no—
132C22×#1055—21no—
133C22×#1055—21no—
134C22×#1055C2311yescharacteristic
135C22×#1055C2311yescharacteristic
136C13×#103C2×C411yescharacteristic, complemented
137C13×#103C2×C411yescharacteristic, complemented
138C13×#103C2×C411yescharacteristic, complemented
139C13×#103C2×C411yescharacteristic, complemented
140C13×#102C2×C411yescharacteristic, complemented
141C13×#102C2×C411yescharacteristic, complemented
142C13×#102C2×C411yescharacteristic, complemented
143C13×#102C2×C411yescharacteristic, complemented
144C13×C22⋊C8C2×C411yescharacteristic
145C13×C22⋊C8C2×C411yescharacteristic
146C13×C22⋊C8C2×C411yescharacteristic
147C13×C22⋊C8C2×C411yescharacteristic
148#88077—22no—
149#88077—22no—
150#88077—22no—
151#88077—22no—
152#88077—41no—
153#88077D414yescomplemented
154C22⋊#1055—21no—
155C22⋊#1055—21no—
156C22⋊#1055—21no—
157C22⋊#1055—21no—
158C22⋊#1055—21no—
159C22⋊#1055—21no—
160C22⋊#1055—21no—
161C22⋊#1055—21no—
162C22⋊#1055D411yescharacteristic
163C22⋊#1055D411yescharacteristic
164C22⋊#1055D411yescharacteristic
165C22⋊#1055D411yescharacteristic
166#88059—22no—
167#88059—41no—
168#88055—22no—
169#88055—41no—
170C4⋊#1055—21no—
171C4⋊#1055—21no—
172#88043—21no—
173C4×#1055—21no—
174#22886—131nomaximal, Sylow
175C24×C13—21no—
176C24×C13#4111yescharacteristic
177C13×#41—21no—
178C13×#41—21no—
179C13×#41—22no—
180C13×#41—22no—
181C13×#41—21no—
182C13×#41—21no—
183C13×#41—21no—
184C13×#41—21no—
185C13×#41—21no—
186C13×#41—21no—
187C13×#41—21no—
188C13×#41—21no—
189C13×#41—42no—
190C13×#41—42no—
191C13×#41—41no—
192C13×#41—41no—
193C13×#41—42no—
194C13×#41—42no—
195C13×#41C2×D412yes—
196C13×#41#4112yes—
197C2×Q8×C13—21no—
198C2×Q8×C13—22no—
199C2×Q8×C13—41no—
200C2×Q8×C13C22×C411yescharacteristic
201C2×Q8×C13C22×C411yescharacteristic
202C2×Q8×C13C22×C411yescharacteristic
203C2×D4×C13—21no—
204C2×D4×C13—22no—
205C2×D4×C13—21no—
206C2×D4×C13—21no—
207C2×D4×C13—21no—
208C2×D4×C13—21no—
209C2×D4×C13—21no—
210C2×D4×C13—21no—
211C2×D4×C13—21no—
212C2×D4×C13—41no—
213C2×D4×C13—42no—
214C2×D4×C13—42no—
215C2×D4×C13C22×C411yescharacteristic
216C2×D4×C13C22×C411yescharacteristic
217C2×D4×C13C22×C411yescharacteristic
218C22×C4×C13—21no—
219C22×C4×C13—21no—
220C22×C4×C13—21no—
221C22×C4×C13—21no—
222C22×C4×C13—21no—
223C22×C4×C13—21no—
224C22×C4×C13—21no—
225C22×C4×C13—21no—
226C22×C4×C13—21no—
227C22×C4×C13—21no—
228C22×C4×C13—42no—
229C22×C4×C13—42no—
230C22×C4×C13C22×C411yescharacteristic
231C22×C4×C13C22×C411yescharacteristic
232C22×C4×C13C2×D411yescharacteristic
233C22×C4×C13C2×D411yescharacteristic
234C22×C4×C13#4111yescharacteristic
235C22×C4×C13C2411yescharacteristic
236C22×Dic13—21no—
237C22×Dic13—21no—
238C22×Dic13—42no—
239C22×Dic13—42no—
240C22×Dic13—42no—
241C13×Q16—22no—
242C13×Q16—41no—
243C13×SD16—22no—
244C13×SD16—22no—
245C13×SD16—41no—
246C13×SD16—41no—
247C13×D8—22no—
248C13×D8—41no—
249C2×C8×C13—21no—
250C2×C8×C13—21no—
251C2×C8×C13—21no—
252C2×C8×C13—21no—
253C2×C8×C13C22×C411yescharacteristic
254C2×C8×C13C22×C411yescharacteristic
255C2×C8×C13C22×C411yescharacteristic
256C2×C8×C13C22×C411yescharacteristic
257C13×C4⋊C4—21no—
258C13×C4⋊C4—21no—
259C13×C4⋊C4C22×C411yescharacteristic
260C13×C4⋊C4C22×C411yescharacteristic
261C13×C22⋊C4—21no—
262C13×C22⋊C4—21no—
263C13×C22⋊C4—21no—
264C13×C22⋊C4—21no—
265C13×C22⋊C4—21no—
266C42×C13—21no—
267C4×Dic13—21no—
268C4×Dic13—21no—
269C4×Dic13—21no—
270C4×Dic13—42no—
271C4×Dic13C2×D412yes—
272#6099—21no—
273#6099—21no—
274#6099—21no—
275#6099—21no—
276#6099—21no—
277#6099—21no—
278#6099—21no—
279#6099—42no—
280#6099—42no—
281#6099—42no—
282#6099—42no—
283#6099C2×D412yes—
284C2×#1055—21no—
285C2×#1055—21no—
286C2×#1055—21no—
287C2×#1055—21no—
288C2×#1055—21no—
289C2×#1055—21no—
290C2×#1055—21no—
291C2×#1055—21no—
292C2×#1055—42no—
293C2×#1055—42no—
294C2×#1055—42no—
295C2×#1055—42no—
296C2×#1055C2×D411yescharacteristic
297C2×#1055C2×D411yescharacteristic
298C2×#1055C2×D411yescharacteristic
299C2×#1055C2×D411yescharacteristic
300#3002D1311yescharacteristic
301C2×#444—131no—
302#2933—131no—
303C22×#104—131no—
304#2880—131no—
305#1975—131no—
306#1938—131no—
307#1929—131no—
308#1896—131no—
309#1876—131no—
310#1876—131no—
311#1866—131no—
312#1855—131no—
313#1765—131no—
314#1749—131no—
315C23×C13—21no—
316C23×C13—21no—
317C23×C13—21no—
318C23×C13—22no—
319C23×C13—21no—
320C23×C13—21no—
321C23×C13—41no—
322C23×C13—42no—
323C23×C13—42no—
324C23×C13—81no—
325C23×C13C4×D411yescharacteristic
326C23×C13C4×D411yescharacteristic
327C23×C13C2×#4111yescharacteristic
328Q8×C13—21no—
329Q8×C13—21no—
330Q8×C13—21no—
331Q8×C13—21no—
332Q8×C13—21no—
333Q8×C13—42no—
334Q8×C13C4×D412yes—
335D4×C13—22no—
336D4×C13—22no—
337D4×C13—21no—
338D4×C13—21no—
339D4×C13—21no—
340D4×C13—21no—
341D4×C13—21no—
342D4×C13—42no—
343D4×C13—42no—
344D4×C13—42no—
345D4×C13—41no—
346D4×C13—41no—
347D4×C13—41no—
348D4×C13—41no—
349D4×C13—42no—
350D4×C13—81no—
351D4×C13C4×D412yes—
352C2×C4×C13—21no—
353C2×C4×C13—21no—
354C2×C4×C13—21no—
355C2×C4×C13—21no—
356C2×C4×C13—21no—
357C2×C4×C13—21no—
358C2×C4×C13—21no—
359C2×C4×C13—21no—
360C2×C4×C13—22no—
361C2×C4×C13—21no—
362C2×C4×C13—22no—
363C2×C4×C13—21no—
364C2×C4×C13—21no—
365C2×C4×C13—21no—
366C2×C4×C13—21no—
367C2×C4×C13—21no—
368C2×C4×C13—21no—
369C2×C4×C13—42no—
370C2×C4×C13—42no—
371C2×C4×C13—42no—
372C2×C4×C13—41no—
373C2×C4×C13—41no—
374C2×C4×C13—41no—
375C2×C4×C13—41no—
376C2×C4×C13C4×D411yescharacteristic
377C2×C4×C13C4×D411yescharacteristic
378C2×C4×C13C23×C411yescharacteristic
379C2×C4×C13C22×D411yescharacteristic
380C2×C4×C13C22×D411yescharacteristic
381C2×C4×C13C2×#4111yescharacteristic
382C2×C4×C13H(5,𝔽2)11yescharacteristic
383C2×C4×C13H(5,𝔽2)11yescharacteristic
384C2×Dic13—22no—
385C2×Dic13—22no—
386C2×Dic13—41no—
387C2×Dic13—41no—
388C2×Dic13—41no—
389C2×Dic13—48no—
390C2×Dic13—41no—
391C8×C13—21no—
392C8×C13—21no—
393C8×C13—21no—
394C8×C13—21no—
395#1055—21no—
396#1055—21no—
397#1055—22no—
398#1055—21no—
399#1055—21no—
400#1055—41no—
401#1055—41no—
402#1055—41no—
403C22×#41C2×D1311yescharacteristic
404C2×#135C2×D1311yescharacteristic
405C2×#135C2×D1311yescharacteristic
406C2×#131—131no—
407C2×#131—131no—
408C2×#131—131no—
409C22×M16—131no—
410#525C2×D1311yescharacteristic
411C22×C42—131no—
412#452Dic1311yescharacteristic, complemented
413#452Dic1311yescharacteristic, complemented
414#451Dic1311yescharacteristic, complemented
415#450Dic1311yescharacteristic, complemented
416#449Dic1311yescharacteristic, complemented
417#449Dic1311yescharacteristic, complemented
418#448Dic1311yescharacteristic, complemented
419#447Dic1311yescharacteristic, complemented
420#444—264no—
421#436—261no—
422#435—261no—
423#435—261no—
424C8×D4—261no—
425C2×#108—131no—
426C2×#108—131no—
427#424—131no—
428C2×#104—131no—
429C2×#104—131no—
430C2×#104—131no—
431C2×#104—131no—
432C2×#104—131no—
433C2×#104—131no—
434C2×#104—264no—
435#416C2×D1311yescharacteristic
436#416C2×D1311yescharacteristic
437#408—131no—
438#408—131no—
439#408—131no—
440#408—261no—
441#408—261no—
442#407—131no—
443#407—261no—
444C2×C22⋊C8—131no—
445C2×C22⋊C8—261no—
446C2×C22⋊C8C2×D1311yescharacteristic
447#405—131no—
448C2×#97—131no—
449C2×#97—131no—
450#341—131no—
451#341—131no—
452#339—131no—
453#339—131no—
454#336—131no—
455#336—131no—
456C22×C13—21no—
457C22×C13—21no—
458C22×C13—21no—
459C22×C13—21no—
460C22×C13—21no—
461C22×C13—22no—
462C22×C13—21no—
463C22×C13—21no—
464C22×C13—42no—
465C22×C13—42no—
466C22×C13—41no—
467C22×C13—41no—
468C22×C13—41no—
469C22×C13—41no—
470C22×C13—41no—
471C22×C13—41no—
472C22×C13—41no—
473C22×C13—41no—
474C22×C13—84no—
475C22×C13#44412yescomplemented
476C22×C13C2×C4×D411yescharacteristic
477C22×C13#54611yescharacteristic
478C22×C13#55111yescharacteristic
479C4×C13—21no—
480C4×C13—21no—
481C4×C13—22no—
482C4×C13—41no—
483C4×C13—41no—
484C4×C13—41no—
485C4×C13—41no—
486C4×C13C2×C4×D411yescharacteristic
487C4×C13#51811yescharacteristic
488C4×C13D4211yescharacteristic
489C4×C13#54611yescharacteristic
490Dic13—42no—
491Dic13—42no—
492C2×#41—21no—
493C2×#41—21no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41C2×Dic1311yescharacteristic
499C2×#41C2×Dic1311yescharacteristic
500C2×#41C22×D1311yescharacteristic
501C2×#41C22×D1311yescharacteristic
502C2×#41C22×D1311yescharacteristic
503C22×Q8C2×Dic1311yescharacteristic
504C22×D4—21no—
505C22×D4C2×Dic1311yescharacteristic
506C23×C4—21no—
507C23×C4—261no—
508C23×C4C22×D1311yescharacteristic
509#135—22no—
510#135—22no—
511#135—41no—
512#135—41no—
513C2×Q16C2×Dic1311yescharacteristic, complemented
514C2×Q16C2×Dic1311yescharacteristic, complemented
515C2×SD16C2×Dic1311yescharacteristic, complemented
516C2×SD16C2×Dic1311yescharacteristic, complemented
517C2×SD16C2×Dic1311yescharacteristic, complemented
518C2×SD16C2×Dic1311yescharacteristic, complemented
519C2×D8C2×Dic1311yescharacteristic, complemented
520C2×D8C2×Dic1311yescharacteristic, complemented
521#131—262no—
522#131—262no—
523#131—262no—
524#131—521no—
525#131—521no—
526#131—521no—
527C2×M16—131no—
528C2×M16—131no—
529C2×M16—131no—
530C2×M16—131no—
531C2×M16—261no—
532C2×M16—261no—
533C2×M16—261no—
534C2×M16—261no—
535C2×M16—262no—
536C2×M16—521no—
537C22×C8—131no—
538C22×C8—131no—
539C22×C8—261no—
540C22×C8—261no—
541C22×C8—261no—
542C22×C8—261no—
543C22×C8C22×D1311yescharacteristic
544C22×C8C22×D1311yescharacteristic
545#123—21no—
546C22⋊Q8C2×Dic1311yescharacteristic
547C22⋊Q8C2×Dic1311yescharacteristic
548#121C2×Dic1311yescharacteristic
549#121C2×Dic1311yescharacteristic
550#120—21no—
551C4×D4—21no—
552C4×D4—21no—
553#117C22×D1311yescharacteristic
554C2×C42—131no—
555C2×C42—131no—
556C2×C42—262no—
557C2×C42—261no—
558C2×C42—521no—
559#108—262no—
560#108—521no—
561C4⋊C8—261no—
562C4⋊C8—261no—
563#104—134no—
564#104—262no—
565#104—262no—
566#104—262no—
567#104—262no—
568#104—521no—
569#103C2×Dic1311yescharacteristic, complemented
570#103C2×Dic1311yescharacteristic, complemented
571#103C2×Dic1311yescharacteristic, complemented
572#103C2×Dic1311yescharacteristic, complemented
573#102C2×Dic1311yescharacteristic, complemented
574#102C2×Dic1311yescharacteristic, complemented
575#102C2×Dic1311yescharacteristic, complemented
576#102C2×Dic1311yescharacteristic, complemented
577C22⋊C8—131no—
578C22⋊C8—131no—
579C22⋊C8—131no—
580C22⋊C8—131no—
581C22⋊C8—261no—
582C22⋊C8—261no—
583C22⋊C8—261no—
584C22⋊C8—261no—
585C22⋊C8—261no—
586C22⋊C8—261no—
587C22⋊C8—261no—
588C22⋊C8—261no—
589C22⋊C8C2×Dic1311yescharacteristic
590C22⋊C8C2×Dic1311yescharacteristic
591C22⋊C8C2×Dic1311yescharacteristic
592C22⋊C8C2×Dic1311yescharacteristic
593#97—261no—
594#97—262no—
595#97—521no—
596C4×C8—261no—
597C2×C13—21no—
598C2×C13—22no—
599C2×C13—21no—
600C2×C13—41no—
601C2×C13—42no—
602C2×C13—81no—
603C2×C13—81no—
604C2×C13#235811yescharacteristic
605C2×C13C2×#44411yescharacteristic
606C2×C13#295611yescharacteristic
607C24—21no—
608C24#612911yescharacteristic
609#41—21no—
610#41—21no—
611#41—22no—
612#41—22no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—21no—
620#41—21no—
621#41—42no—
622#41—42no—
623#41—41no—
624#41—41no—
625#41—42no—
626#41—42no—
627#41D4×D1312yes—
628#41#612912yes—
629C2×Q8—21no—
630C2×Q8—22no—
631C2×Q8—41no—
632C2×Q8C22×Dic1311yescharacteristic
633C2×Q8C22×Dic1311yescharacteristic
634C2×Q8C22×Dic1311yescharacteristic
635C2×D4—21no—
636C2×D4—22no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—41no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4C22×Dic1311yescharacteristic
648C2×D4C22×Dic1311yescharacteristic
649C2×D4C22×Dic1311yescharacteristic
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—261no—
663C22×C4—261no—
664C22×C4—522no—
665C22×C4—522no—
666C22×C4—522no—
667C22×C4D4×D1311yescharacteristic
668C22×C4D4×D1311yescharacteristic
669C22×C4#612911yescharacteristic
670C22×C4C22×Dic1311yescharacteristic
671C22×C4C22×Dic1311yescharacteristic
672C22×C4C23×D1311yescharacteristic
673Q16—22no—
674Q16—41no—
675SD16—22no—
676SD16—22no—
677SD16—41no—
678SD16—41no—
679D8—22no—
680D8—41no—
681M16—132no—
682M16—261no—
683M16—261no—
684M16—261no—
685M16—261no—
686M16—261no—
687M16—261no—
688M16—261no—
689M16—522no—
690M16—522no—
691M16—522no—
692M16—522no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—131no—
698C2×C8—131no—
699C2×C8—131no—
700C2×C8—131no—
701C2×C8—261no—
702C2×C8—261no—
703C2×C8—261no—
704C2×C8—261no—
705C2×C8—261no—
706C2×C8—261no—
707C2×C8—261no—
708C2×C8—261no—
709C2×C8—522no—
710C2×C8—522no—
711C2×C8—522no—
712C2×C8—522no—
713C2×C8C22×Dic1311yescharacteristic
714C2×C8C22×Dic1311yescharacteristic
715C2×C8C22×Dic1311yescharacteristic
716C2×C8C22×Dic1311yescharacteristic
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4C22×Dic1311yescharacteristic
720C4⋊C4C22×Dic1311yescharacteristic
721C22⋊C4—21no—
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C42—21no—
727C42—132no—
728C42—261no—
729C42—261no—
730C42—261no—
731C42—522no—
732C13#2288611yescharacteristic, complemented, Sylow
733C23—21no—
734C23—21no—
735C23—21no—
736C23—22no—
737C23—21no—
738C23—21no—
739C23—41no—
740C23—42no—
741C23—42no—
742C23—81no—
743C23D4×Dic1311yescharacteristic
744C23D4×Dic1311yescharacteristic
745C23C2×#612911yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—21no—
751Q8—42no—
752Q8D4×Dic1312yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—21no—
759D4—21no—
760D4—42no—
761D4—42no—
762D4—42no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—42no—
768D4—81no—
769D4D4×Dic1312yes—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—262no—
795C2×C4—262no—
796C2×C4—521no—
797C2×C4—521no—
798C2×C4—521no—
799C2×C4—528no—
800C2×C4—521no—
801C2×C4D4×Dic1311yescharacteristic
802C2×C4D4×Dic1311yescharacteristic
803C2×C4C2×D4×D1311yescharacteristic
804C2×C4C2×D4×D1311yescharacteristic
805C2×C4C2×#612911yescharacteristic
806C2×C4#8825111yescharacteristic
807C2×C4#8825111yescharacteristic
808C2×C4C23×Dic1311yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—261no—
814C8—261no—
815C8—262no—
816C8—261no—
817C8—261no—
818C8—521no—
819C8—521no—
820C8—521no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—22no—
827C22—21no—
828C22—21no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—84no—
840C22#1171885812yescomplemented
841C22#1171929211yescharacteristic
842C22#1171929611yescharacteristic
843C22C2×D4×Dic1311yescharacteristic
844C4—21no—
845C4—21no—
846C4—22no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—522no—
852C4—522no—
853C4#1171929511yescharacteristic
854C4#1171929611yescharacteristic
855C4C2×D4×Dic1311yescharacteristic
856C4#1171950311yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—42no—
862C2—81no—
863C2—81no—
864C2#1311782011yescharacteristic
865C2C2×#1171885811yescharacteristic
866C2#1312374611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
Fitting, prime radicalC13×#3002C2
socleC22×C13C2×C4×D4
cosocleC22×C4×C13C24
hypercenter#3002D13
hypocenterC13#22886
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3002

Complements

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

NH ≅ G/Ntype
1. C2×#11718858C2semidirect
2. #13123563C2semidirect
3. C22×#88077C2semidirect
4. #13123285C2semidirect
5. #13115730C2semidirect
6. #13115549C2semidirect
7. #13115486C2semidirect
8. #13115280C2semidirect
9. #13115165C2semidirect
10. #13115165C2semidirect
11. #13115113C2semidirect
12. #13115043C2semidirect
13. #13114683C2semidirect
14. #13114600C2semidirect
22. C2×#88202C22semidirect
25. C13×#452C4semidirect
26. C13×#452C4semidirect
27. C13×#451C4semidirect
28. C13×#450C4semidirect
29. C13×#449C4semidirect
30. C13×#449C4semidirect
31. C13×#448C4semidirect
32. C13×#447C4semidirect
41. C2×#88077C22semidirect
42. C2×#88077C22semidirect
47. #11718895C22semidirect
53. C2×#88059C22semidirect
54. C2×#88059C22semidirect
55. C2×#88055C22semidirect
56. C2×#88055C22semidirect
61. #11718660C22semidirect
62. #11718658C22semidirect
63. #11718144C22semidirect
64. #11718144C22semidirect
65. #11718142C22semidirect
66. #11718142C22semidirect
67. #11718124C22semidirect
68. #11718124C22semidirect
90. C2×C13×Q16C2×C4semidirect
91. C2×C13×Q16C2×C4semidirect
92. C2×C13×SD16C2×C4semidirect
93. C2×C13×SD16C2×C4semidirect
94. C2×C13×SD16C2×C4semidirect
95. C2×C13×SD16C2×C4semidirect
96. C2×C13×D8C2×C4semidirect
97. C2×C13×D8C2×C4semidirect
136. C13×#103C2×C4semidirect
137. C13×#103C2×C4semidirect
138. C13×#103C2×C4semidirect
139. C13×#103C2×C4semidirect
140. C13×#102C2×C4semidirect
141. C13×#102C2×C4semidirect
142. C13×#102C2×C4semidirect
143. C13×#102C2×C4semidirect
153. #88077D4semidirect
412. #452Dic13semidirect
413. #452Dic13semidirect
414. #451Dic13semidirect
415. #450Dic13semidirect
416. #449Dic13semidirect
417. #449Dic13semidirect
418. #448Dic13semidirect
419. #447Dic13semidirect
475. C22×C13#444semidirect
513. C2×Q16C2×Dic13semidirect
514. C2×Q16C2×Dic13semidirect
515. C2×SD16C2×Dic13semidirect
516. C2×SD16C2×Dic13semidirect
517. C2×SD16C2×Dic13semidirect
518. C2×SD16C2×Dic13semidirect
519. C2×D8C2×Dic13semidirect
520. C2×D8C2×Dic13semidirect
569. #103C2×Dic13semidirect
570. #103C2×Dic13semidirect
571. #103C2×Dic13semidirect
572. #103C2×Dic13semidirect
573. #102C2×Dic13semidirect
574. #102C2×Dic13semidirect
575. #102C2×Dic13semidirect
576. #102C2×Dic13semidirect
732. C13#22886semidirect
840. C22#11718858semidirect

Maximal subgroups

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

subgroupindex
C2×#117188582
#131235632
C22×#880772
#131232852
#131157302
#131155492
#131154862
#131152802
#131151652
#131151132
#131150432
#131146832
#131146002
C13×#30022
#2288613