Finite Group Databasebeta

← #15883675

Subgroups — #15883675

Order 3328.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718858C211yesmaximal, characteristic, complemented
2#13123563C211yesmaximal, characteristic, complemented
3C2×#11718897C211yesmaximal, characteristic, complemented
4#13123285C211yesmaximal, characteristic, complemented
5#13115725C211yesmaximal, characteristic, complemented
6#13115549C211yesmaximal, characteristic, complemented
7#13115486C211yesmaximal, characteristic, complemented
8#13115285C211yesmaximal, characteristic, complemented
9#13115165C211yesmaximal, characteristic, complemented
10#13115165C211yesmaximal, characteristic, complemented
11#13115113C211yesmaximal, characteristic, complemented
12#13115043C211yesmaximal, characteristic, complemented
13#13114676C211yesmaximal, characteristic, complemented
14#13114604C211yesmaximal, characteristic, complemented
15C13×#3002C211yesmaximal, characteristic
16C22×C13×#41C2211yescharacteristic
17C2×C13×#135C2211yescharacteristic
18C2×C13×#135C2211yescharacteristic
19C13×#525C2211yescharacteristic
20C2×#88202C2211yescharacteristic
21C2×#88202C2211yescharacteristic
22C2×#88202C2211yescharacteristic, complemented
23C2×#88180C2211yescharacteristic
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
36#11718897—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×C8×Dic13C2211yescharacteristic, 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
85C13×#135—22no—
86C13×#135—22no—
87C13×#135—41no—
88C13×#135—41no—
89C2×C13×Q16C2×C411yescharacteristic
90C2×C13×Q16C2×C411yescharacteristic
91C2×C13×SD16C2×C411yescharacteristic
92C2×C13×SD16C2×C411yescharacteristic
93C2×C13×SD16C2×C411yescharacteristic
94C2×C13×SD16C2×C411yescharacteristic
95C2×C13×D8C2×C411yescharacteristic
96C2×C13×D8C2×C411yescharacteristic
97C22×C8×C13C2311yescharacteristic
98C22×C8×C13C2311yescharacteristic
99C13×#123—21no—
100C13×C22⋊Q8C2×C411yescharacteristic
101C13×C22⋊Q8C2×C411yescharacteristic
102C13×#121C2×C411yescharacteristic
103C13×#121C2×C411yescharacteristic
104C13×#120—21no—
105C4×D4×C13—21no—
106C4×D4×C13—21no—
107C13×#117C2311yescharacteristic
108C2×C22⋊Dic13—21no—
109#88202—22no—
110#88202—22no—
111#88202—22no—
112#88202—41no—
113#88202—41no—
114#88202—41no—
115#88180—22no—
116#88180—41no—
117C2×C4⋊Dic13—21no—
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
137C13×#103C2×C411yescharacteristic
138C13×#103C2×C411yescharacteristic
139C13×#103C2×C411yescharacteristic
140C13×#102C2×C411yescharacteristic
141C13×#102C2×C411yescharacteristic
142C13×#102C2×C411yescharacteristic
143C13×#102C2×C411yescharacteristic
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—
169C8×Dic13—41no—
170C4⋊#1055—21no—
171C4⋊#1055—21no—
172#88043—21no—
173C4×#1055—21no—
174#22887—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—
238C13×Q16—22no—
239C13×Q16—41no—
240C13×SD16—22no—
241C13×SD16—22no—
242C13×SD16—41no—
243C13×SD16—41no—
244C13×D8—22no—
245C13×D8—41no—
246C2×C8×C13—21no—
247C2×C8×C13—21no—
248C2×C8×C13—21no—
249C2×C8×C13—21no—
250C2×C8×C13C22×C411yescharacteristic
251C2×C8×C13C22×C411yescharacteristic
252C2×C8×C13C22×C411yescharacteristic
253C2×C8×C13C22×C411yescharacteristic
254C13×C4⋊C4—21no—
255C13×C4⋊C4—21no—
256C13×C4⋊C4C22×C411yescharacteristic
257C13×C4⋊C4C22×C411yescharacteristic
258C13×C22⋊C4—21no—
259C13×C22⋊C4—21no—
260C13×C22⋊C4—21no—
261C13×C22⋊C4—21no—
262C13×C22⋊C4—21no—
263C42×C13—21no—
264C22⋊Dic13—42no—
265C4⋊Dic13—42no—
266C4×Dic13—21no—
267C4×Dic13—21no—
268C4×Dic13—21no—
269C4×Dic13C2×D412yes—
270#6099—21no—
271#6099—21no—
272#6099—21no—
273#6099—21no—
274#6099—21no—
275#6099—21no—
276#6099—21no—
277#6099—42no—
278#6099—42no—
279#6099—42no—
280#6099—42no—
281#6099C2×D412yes—
282C2×#1055—21no—
283C2×#1055—21no—
284C2×#1055—21no—
285C2×#1055—21no—
286C2×#1055—21no—
287C2×#1055—21no—
288C2×#1055—21no—
289C2×#1055—21no—
290C2×#1055—42no—
291C2×#1055—42no—
292C2×#1055—42no—
293C2×#1055—42no—
294C2×#1055C2×D411yescharacteristic
295C2×#1055C2×D411yescharacteristic
296C2×#1055C2×D411yescharacteristic
297C2×#1055C2×D411yescharacteristic
298#3002D1311yescharacteristic
299C2×#444—131no—
300#2933—131no—
301C2×#421—131no—
302#2880—131no—
303#1974—131no—
304#1938—131no—
305#1929—131no—
306#1897—131no—
307#1876—131no—
308#1876—131no—
309#1866—131no—
310#1855—131no—
311#1764—131no—
312#1750—131no—
313C23×C13—21no—
314C23×C13—21no—
315C23×C13—21no—
316C23×C13—21no—
317C23×C13—21no—
318C23×C13—41no—
319C23×C13—41no—
320C23×C13—42no—
321C23×C13—42no—
322C23×C13—81no—
323C23×C13C4×D411yescharacteristic
324C23×C13C4×D411yescharacteristic
325C23×C13C2×#4111yescharacteristic
326Q8×C13—21no—
327Q8×C13—21no—
328Q8×C13—21no—
329Q8×C13—21no—
330Q8×C13—21no—
331Q8×C13—42no—
332Q8×C13C4×D412yes—
333D4×C13—22no—
334D4×C13—22no—
335D4×C13—21no—
336D4×C13—21no—
337D4×C13—21no—
338D4×C13—21no—
339D4×C13—21no—
340D4×C13—42no—
341D4×C13—42no—
342D4×C13—42no—
343D4×C13—42no—
344D4×C13—41no—
345D4×C13—41no—
346D4×C13—41no—
347D4×C13—41no—
348D4×C13—81no—
349D4×C13C4×D412yes—
350C2×C4×C13—21no—
351C2×C4×C13—21no—
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—22no—
359C2×C4×C13—21no—
360C2×C4×C13—22no—
361C2×C4×C13—21no—
362C2×C4×C13—21no—
363C2×C4×C13—21no—
364C2×C4×C13—21no—
365C2×C4×C13—21no—
366C2×C4×C13—21no—
367C2×C4×C13—42no—
368C2×C4×C13—42no—
369C2×C4×C13—42no—
370C2×C4×C13—41no—
371C2×C4×C13—41no—
372C2×C4×C13—41no—
373C2×C4×C13—41no—
374C2×C4×C13C4×D411yescharacteristic
375C2×C4×C13C4×D411yescharacteristic
376C2×C4×C13C23×C411yescharacteristic
377C2×C4×C13C22×D411yescharacteristic
378C2×C4×C13C22×D411yescharacteristic
379C2×C4×C13C2×#4111yescharacteristic
380C2×C4×C13H(5,𝔽2)11yescharacteristic
381C2×C4×C13H(5,𝔽2)11yescharacteristic
382C2×Dic13—22no—
383C2×Dic13—41no—
384C2×Dic13—41no—
385C2×Dic13—41no—
386C2×Dic13—41no—
387C2×Dic13—41no—
388C8×C13—21no—
389C8×C13—21no—
390C8×C13—21no—
391C8×C13—21no—
392#1055—21no—
393#1055—21no—
394#1055—22no—
395#1055—21no—
396#1055—21no—
397#1055—41no—
398#1055—41no—
399#1055—41no—
400C22×#41C2×D1311yescharacteristic
401C2×#135C2×D1311yescharacteristic
402C2×#135C2×D1311yescharacteristic
403C2×#131—131no—
404C2×#131—131no—
405C2×#131—131no—
406C22×M16—131no—
407#525C2×D1311yescharacteristic
408C2×#117—131no—
409#452Dic1311yescharacteristic, complemented
410#452Dic1311yescharacteristic, complemented
411#451Dic1311yescharacteristic, complemented
412#450Dic1311yescharacteristic, complemented
413#449Dic1311yescharacteristic, complemented
414#449Dic1311yescharacteristic, complemented
415#448Dic1311yescharacteristic, complemented
416#447Dic1311yescharacteristic, complemented
417#444—264no—
418#436—261no—
419#435—261no—
420#435—261no—
421C8×D4—261no—
422C2×#108—131no—
423C2×#108—131no—
424#424—131no—
425#421—264no—
426C2×#104—131no—
427C2×#104—131no—
428C2×#104—131no—
429C2×#104—131no—
430C2×#104—131no—
431C2×#104—131no—
432#416C2×D1311yescharacteristic
433#416C2×D1311yescharacteristic
434#408—131no—
435#408—131no—
436#408—131no—
437#408—261no—
438#408—261no—
439#407—131no—
440#407—261no—
441C2×C22⋊C8—131no—
442C2×C22⋊C8—261no—
443C2×C22⋊C8C2×D1311yescharacteristic
444#405—131no—
445C2×#97—131no—
446C2×C4×C8—131no—
447#341—131no—
448#341—131no—
449#339—131no—
450#339—131no—
451#336—131no—
452#336—131no—
453C22×C13—21no—
454C22×C13—21no—
455C22×C13—21no—
456C22×C13—21no—
457C22×C13—22no—
458C22×C13—21no—
459C22×C13—21no—
460C22×C13—21no—
461C22×C13—21no—
462C22×C13—41no—
463C22×C13—41no—
464C22×C13—41no—
465C22×C13—41no—
466C22×C13—41no—
467C22×C13—41no—
468C22×C13—41no—
469C22×C13—41no—
470C22×C13—81no—
471C22×C13—81no—
472C22×C13—84no—
473C22×C13C2×C4×D411yescharacteristic
474C22×C13#54611yescharacteristic
475C22×C13#55111yescharacteristic
476C4×C13—21no—
477C4×C13—21no—
478C4×C13—22no—
479C4×C13—41no—
480C4×C13—41no—
481C4×C13—41no—
482C4×C13—41no—
483C4×C13C2×C4×D411yescharacteristic
484C4×C13#51811yescharacteristic
485C4×C13D4211yescharacteristic
486C4×C13#54611yescharacteristic
487Dic13—42no—
488Dic13—81no—
489C2×#41—21no—
490C2×#41—21no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41C2×Dic1311yescharacteristic
496C2×#41C2×Dic1311yescharacteristic
497C2×#41C22×D1311yescharacteristic
498C2×#41C22×D1311yescharacteristic
499C2×#41C22×D1311yescharacteristic
500C22×Q8C2×Dic1311yescharacteristic
501C22×D4—21no—
502C22×D4C2×Dic1311yescharacteristic
503C23×C4—21no—
504C23×C4C22×D1311yescharacteristic
505#135—22no—
506#135—22no—
507#135—41no—
508#135—41no—
509C2×Q16C2×Dic1311yescharacteristic
510C2×Q16C2×Dic1311yescharacteristic
511C2×SD16C2×Dic1311yescharacteristic
512C2×SD16C2×Dic1311yescharacteristic
513C2×SD16C2×Dic1311yescharacteristic
514C2×SD16C2×Dic1311yescharacteristic
515C2×D8C2×Dic1311yescharacteristic
516C2×D8C2×Dic1311yescharacteristic
517#131—262no—
518#131—262no—
519#131—262no—
520#131—521no—
521#131—521no—
522#131—521no—
523C2×M16—131no—
524C2×M16—131no—
525C2×M16—131no—
526C2×M16—131no—
527C2×M16—261no—
528C2×M16—261no—
529C2×M16—261no—
530C2×M16—261no—
531C2×M16—262no—
532C2×M16—521no—
533C22×C8—131no—
534C22×C8—131no—
535C22×C8—261no—
536C22×C8—261no—
537C22×C8—261no—
538C22×C8—261no—
539C22×C8C22×D1311yescharacteristic
540C22×C8C22×D1311yescharacteristic
541#123—21no—
542C22⋊Q8C2×Dic1311yescharacteristic
543C22⋊Q8C2×Dic1311yescharacteristic
544#121C2×Dic1311yescharacteristic
545#121C2×Dic1311yescharacteristic
546#120—21no—
547C4×D4—21no—
548C4×D4—21no—
549#117—262no—
550#117—521no—
551#117C22×D1311yescharacteristic
552C2×C4⋊C4—261no—
553C2×C22⋊C4—261no—
554C2×C42—131no—
555C2×C42—131no—
556#108—262no—
557#108—521no—
558C4⋊C8—261no—
559C4⋊C8—261no—
560#104—134no—
561#104—262no—
562#104—262no—
563#104—262no—
564#104—262no—
565#104—521no—
566#103C2×Dic1311yescharacteristic
567#103C2×Dic1311yescharacteristic
568#103C2×Dic1311yescharacteristic
569#103C2×Dic1311yescharacteristic
570#102C2×Dic1311yescharacteristic
571#102C2×Dic1311yescharacteristic
572#102C2×Dic1311yescharacteristic
573#102C2×Dic1311yescharacteristic
574C22⋊C8—131no—
575C22⋊C8—131no—
576C22⋊C8—131no—
577C22⋊C8—131no—
578C22⋊C8—261no—
579C22⋊C8—261no—
580C22⋊C8—261no—
581C22⋊C8—261no—
582C22⋊C8—261no—
583C22⋊C8—261no—
584C22⋊C8—261no—
585C22⋊C8—261no—
586C22⋊C8C2×Dic1311yescharacteristic
587C22⋊C8C2×Dic1311yescharacteristic
588C22⋊C8C2×Dic1311yescharacteristic
589C22⋊C8C2×Dic1311yescharacteristic
590#97—261no—
591#97—262no—
592C4×C8—261no—
593C4×C8—521no—
594C2×C13—21no—
595C2×C13—21no—
596C2×C13—41no—
597C2×C13—41no—
598C2×C13—42no—
599C2×C13—81no—
600C2×C13—81no—
601C2×C13#235811yescharacteristic
602C2×C13#295511yescharacteristic
603C2×C13#295711yescharacteristic
604C24—21no—
605C24#612911yescharacteristic
606#41—21no—
607#41—21no—
608#41—22no—
609#41—22no—
610#41—21no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—42no—
619#41—42no—
620#41—41no—
621#41—41no—
622#41—42no—
623#41—42no—
624#41D4×D1312yes—
625#41#612912yes—
626C2×Q8—21no—
627C2×Q8—22no—
628C2×Q8—41no—
629C2×Q8C22×Dic1311yescharacteristic
630C2×Q8C22×Dic1311yescharacteristic
631C2×Q8C22×Dic1311yescharacteristic
632C2×D4—21no—
633C2×D4—22no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—41no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4C22×Dic1311yescharacteristic
645C2×D4C22×Dic1311yescharacteristic
646C2×D4C22×Dic1311yescharacteristic
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—261no—
660C22×C4—261no—
661C22×C4D4×D1311yescharacteristic
662C22×C4D4×D1311yescharacteristic
663C22×C4#612911yescharacteristic
664C22×C4C22×Dic1311yescharacteristic
665C22×C4C22×Dic1311yescharacteristic
666C22×C4C23×D1311yescharacteristic
667Q16—22no—
668Q16—41no—
669SD16—22no—
670SD16—22no—
671SD16—41no—
672SD16—41no—
673D8—22no—
674D8—41no—
675M16—132no—
676M16—261no—
677M16—261no—
678M16—261no—
679M16—261no—
680M16—261no—
681M16—261no—
682M16—261no—
683M16—522no—
684M16—522no—
685M16—522no—
686M16—522no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—131no—
692C2×C8—131no—
693C2×C8—131no—
694C2×C8—131no—
695C2×C8—261no—
696C2×C8—261no—
697C2×C8—261no—
698C2×C8—261no—
699C2×C8—261no—
700C2×C8—261no—
701C2×C8—261no—
702C2×C8—261no—
703C2×C8—522no—
704C2×C8—522no—
705C2×C8—522no—
706C2×C8—522no—
707C2×C8C22×Dic1311yescharacteristic
708C2×C8C22×Dic1311yescharacteristic
709C2×C8C22×Dic1311yescharacteristic
710C2×C8C22×Dic1311yescharacteristic
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—522no—
714C4⋊C4C22×Dic1311yescharacteristic
715C4⋊C4C22×Dic1311yescharacteristic
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—522no—
722C42—21no—
723C42—132no—
724C42—261no—
725C42—261no—
726C42—261no—
727C13#2288711yescharacteristic, complemented, Sylow
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—81no—
738C23D4×Dic1311yescharacteristic
739C23D4×Dic1311yescharacteristic
740C23C2×#612911yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—21no—
745Q8—21no—
746Q8—42no—
747Q8D4×Dic1312yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—81no—
764D4D4×Dic1312yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—262no—
790C2×C4—521no—
791C2×C4—521no—
792C2×C4—521no—
793C2×C4—521no—
794C2×C4—521no—
795C2×C4D4×Dic1311yescharacteristic
796C2×C4D4×Dic1311yescharacteristic
797C2×C4C2×D4×D1311yescharacteristic
798C2×C4C2×D4×D1311yescharacteristic
799C2×C4C2×#612911yescharacteristic
800C2×C4#8825111yescharacteristic
801C2×C4#8825111yescharacteristic
802C2×C4C23×Dic1311yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—261no—
808C8—261no—
809C8—262no—
810C8—261no—
811C8—261no—
812C8—521no—
813C8—521no—
814C8—521no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—81no—
833C22—81no—
834C22—84no—
835C22#1171929211yescharacteristic
836C22#1171929611yescharacteristic
837C22C2×D4×Dic1311yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—522no—
846C4—1041no—
847C4#1171929511yescharacteristic
848C4#1171929611yescharacteristic
849C4C2×D4×Dic1311yescharacteristic
850C4#1171950311yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—81no—
858C2#1311782011yescharacteristic
859C2#1312373911yescharacteristic
860C2#1312375311yescharacteristic
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#22887
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. C2×#11718897C2semidirect
4. #13123285C2semidirect
5. #13115725C2semidirect
6. #13115549C2semidirect
7. #13115486C2semidirect
8. #13115285C2semidirect
9. #13115165C2semidirect
10. #13115165C2semidirect
11. #13115113C2semidirect
12. #13115043C2semidirect
13. #13114676C2semidirect
14. #13114604C2semidirect
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×C8×Dic13C22semidirect
61. #11718660C22semidirect
62. #11718658C22semidirect
63. #11718144C22semidirect
64. #11718144C22semidirect
65. #11718142C22semidirect
66. #11718142C22semidirect
67. #11718124C22semidirect
68. #11718124C22semidirect
153. #88077D4semidirect
409. #452Dic13semidirect
410. #452Dic13semidirect
411. #451Dic13semidirect
412. #450Dic13semidirect
413. #449Dic13semidirect
414. #449Dic13semidirect
415. #448Dic13semidirect
416. #447Dic13semidirect
727. C13#22887semidirect

Maximal subgroups

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

subgroupindex
C2×#117188582
#131235632
C2×#117188972
#131232852
#131157252
#131155492
#131154862
#131152852
#131151652
#131151132
#131150432
#131146762
#131146042
C13×#30022
#2288713