Finite Group Databasebeta

← #15879878

Subgroups — #15879878

Order 3328.

1018 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718379C211yesmaximal, characteristic, complemented
2#13117327C211yesmaximal, characteristic
3#13115452C211yesmaximal, characteristic, complemented
4#13115445C211yesmaximal, characteristic, complemented
5#13115439C211yesmaximal, characteristic, complemented
6#13115439C211yesmaximal, characteristic, complemented
7#13115019C211yesmaximal, characteristic, complemented
8#13115014C211yesmaximal, characteristic, complemented
9#13114902C211yesmaximal, characteristic, complemented
10#13114818C211yesmaximal, characteristic, complemented
11#13114748C211yesmaximal, characteristic
12#13114617C211yesmaximal, characteristic, complemented
13C8×C22⋊Dic13C211yesmaximal, characteristic, complemented
14#13114604C211yesmaximal, characteristic, complemented
15C2×C13×#408C211yesmaximal, characteristic
16C22×C13×#41C2211yescharacteristic
17C22×C13×M16C2211yescharacteristic
18C23×C8×C13C2211yescharacteristic
19C2×#88180C2211yescharacteristic
20C22×C4×Dic13C2211yescharacteristic
21C13×#408—24no—
22C2×C13×C22⋊C8C2211yescharacteristic
23C2×C13×C22⋊C8C2211yescharacteristic
24C2×C13×C22⋊C8C2211yescharacteristic
25C2×C13×C22⋊C8C2211yescharacteristic
26#11718891C411yescharacteristic
27#11718891C411yescharacteristic
28#11718882C411yescharacteristic
29#11718882C411yescharacteristic
30#11718881C411yescharacteristic
31#11718881C411yescharacteristic
32#11718881C411yescharacteristic
33#11718881C411yescharacteristic
34C4×C22⋊Dic13C2211yescharacteristic
35C4×C22⋊Dic13C2211yescharacteristic
36C4×C22⋊Dic13C2211yescharacteristic
37C4×C22⋊Dic13C2211yescharacteristic
38C2×C22⋊#1055C2211yescharacteristic
39C2×C22⋊#1055C2211yescharacteristic
40C2×C22⋊#1055C2211yescharacteristic
41C2×C22⋊#1055C2211yescharacteristic
42C2×C22⋊#1055C2211yescharacteristic
43C2×C22⋊#1055C2211yescharacteristic
44C2×#88055C2211yescharacteristic
45C2×#88054C2211yescharacteristic
46C2×#88054C2211yescharacteristic
47C2×#88054C2211yescharacteristic
48C2×#88054C2211yescharacteristic
49C2×C8×Dic13C2211yescharacteristic
50C2×C8×Dic13C2211yescharacteristic
51C2×C8×Dic13C2211yescharacteristic
52#11718379—24no—
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718142C2211yescharacteristic
60#11718142C2211yescharacteristic
61C2×C13×#41—22no—
62C2×C13×#41—22no—
63C2×C13×#41—22no—
64C2×C13×#41—22no—
65C2×C13×#41—41no—
66C2×C13×#41—41no—
67C22×Q8×C13C2×C411yescharacteristic
68C22×D4×C13C2×C411yescharacteristic
69C22×D4×C13C2×C411yescharacteristic
70C22×D4×C13C2×C411yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×Dic13C2×C411yescharacteristic
75C23×Dic13C2×C411yescharacteristic
76C2×C13×M16—22no—
77C2×C13×M16—22no—
78C2×C13×M16—41no—
79C22×C8×C13—22no—
80C22×C8×C13—22no—
81C22×C8×C13—41no—
82C22×C8×C13C2311yescharacteristic
83C22×C8×C13C2311yescharacteristic
84C22×C8×C13C2311yescharacteristic
85C22×C8×C13C2311yescharacteristic
86C2×C22⋊Dic13C2×C411yescharacteristic
87C2×C22⋊Dic13C2×C411yescharacteristic
88C2×C22⋊Dic13C2×C411yescharacteristic
89C2×C22⋊Dic13C2×C411yescharacteristic
90C2×C22⋊Dic13C2×C411yescharacteristic
91C2×C22⋊Dic13C2×C411yescharacteristic
92C2×C22⋊Dic13C2×C411yescharacteristic
93C2×C22⋊Dic13C2×C411yescharacteristic
94C2×C22⋊Dic13C2×C411yescharacteristic
95C2×C22⋊Dic13C2×C411yescharacteristic
96#88180—41no—
97#88180—41no—
98C2×C4⋊Dic13C2×C411yescharacteristic
99C2×C4⋊Dic13C2×C411yescharacteristic
100C2×C4×Dic13—22no—
101C2×C4×Dic13—22no—
102C2×C4×Dic13C2×C411yescharacteristic
103C2×C4×Dic13C2×C411yescharacteristic
104C2×C4×Dic13C2311yescharacteristic
105C2×C4×Dic13C2311yescharacteristic
106C2×C4×Dic13C2311yescharacteristic
107C2×C4×Dic13C2311yescharacteristic
108C22×#1055C2311yescharacteristic
109C22×#1055C2311yescharacteristic
110C22×#1055C2311yescharacteristic
111C22×#1055C2311yescharacteristic
112C13×C22⋊C8—22no—
113C13×C22⋊C8—22no—
114C13×C22⋊C8—22no—
115C13×C22⋊C8D414yes—
116#88071C2×C411yescharacteristic
117#88071C2×C411yescharacteristic
118#88071C2×C411yescharacteristic
119#88071C2×C411yescharacteristic
120#88071C2×C411yescharacteristic
121#88071C2×C411yescharacteristic
122#88071C2×C411yescharacteristic
123#88071C2×C411yescharacteristic
124C22⋊#1055—22no—
125C22⋊#1055—22no—
126C22⋊#1055—22no—
127C22⋊#1055—22no—
128C22⋊#1055—41no—
129C22⋊#1055—41no—
130#88055—41no—
131#88054—22no—
132#88054—22no—
133#88054—41no—
134#88054—41no—
135C8×Dic13—22no—
136C8×Dic13—22no—
137C8×Dic13—41no—
138#22556—131nomaximal, Sylow
139C24×C13C22×C411yescharacteristic
140C24×C13C22×C411yescharacteristic
141C24×C13C22×C411yescharacteristic
142C13×#41—44no—
143C13×#41—44no—
144C13×#41—44no—
145C13×#41—44no—
146C2×Q8×C13—22no—
147C2×Q8×C13—22no—
148C2×Q8×C13—41no—
149C2×D4×C13—22no—
150C2×D4×C13—22no—
151C2×D4×C13—22no—
152C2×D4×C13—22no—
153C2×D4×C13—22no—
154C2×D4×C13—22no—
155C2×D4×C13—41no—
156C2×D4×C13—41no—
157C2×D4×C13—41no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13C22×C411yescharacteristic
173C22×C4×C13C22×C411yescharacteristic
174C22×C4×C13C22×C411yescharacteristic
175C22×C4×C13C2×D412yes—
176C22×C4×C13#4112yes—
177C22×C4×C13#4112yes—
178C22×C4×C13#4112yes—
179C22×C4×C13C2411yescharacteristic
180C22×Dic13—22no—
181C22×Dic13—22no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—41no—
186C22×Dic13C22×C411yescharacteristic
187C22×Dic13C22×C411yescharacteristic
188C22×Dic13C22×C411yescharacteristic
189C22×Dic13C22×C411yescharacteristic
190C22×Dic13C22×C411yescharacteristic
191C22×Dic13C22×C411yescharacteristic
192C22×Dic13C22×C411yescharacteristic
193C22×Dic13C22×C411yescharacteristic
194C13×M16—44no—
195C2×C8×C13—21no—
196C2×C8×C13—21no—
197C2×C8×C13—21no—
198C2×C8×C13—21no—
199C2×C8×C13—21no—
200C2×C8×C13—21no—
201C2×C8×C13—21no—
202C2×C8×C13—21no—
203C2×C8×C13—21no—
204C2×C8×C13—21no—
205C2×C8×C13—44no—
206C2×C8×C13C2×D412yes—
207C2×C8×C13C2×D412yes—
208C22⋊Dic13—22no—
209C22⋊Dic13—22no—
210C22⋊Dic13—22no—
211C22⋊Dic13—22no—
212C22⋊Dic13—22no—
213C22⋊Dic13—22no—
214C22⋊Dic13—41no—
215C22⋊Dic13—41no—
216C22⋊Dic13—41no—
217C22⋊Dic13—41no—
218C4⋊Dic13—41no—
219C4⋊Dic13—41no—
220C4×Dic13—22no—
221C4×Dic13—22no—
222C4×Dic13—21no—
223C4×Dic13—21no—
224C4×Dic13—21no—
225C4×Dic13—21no—
226C4×Dic13—21no—
227C4×Dic13—21no—
228C4×Dic13—21no—
229C4×Dic13—21no—
230C2×#1055—21no—
231C2×#1055—21no—
232C2×#1055—21no—
233C2×#1055—21no—
234C2×#1055—21no—
235C2×#1055—21no—
236C2×#1055—21no—
237C2×#1055—21no—
238C2×#1055—21no—
239C2×#1055—21no—
240C2×#1055—21no—
241C2×#1055—21no—
242C2×#431—131no—
243C2×#408D1311yescharacteristic
244#2297—131no—
245#1924—131no—
246#1923—131no—
247#1923—131no—
248#1923—131no—
249#1851—131no—
250#1850—131no—
251#1817—131no—
252#1798—131no—
253#1780—131no—
254#1753—131no—
255C8×C22⋊C4—131no—
256#1750—131no—
257C23×C13—21no—
258C23×C13—21no—
259C23×C13—21no—
260C23×C13—21no—
261C23×C13—21no—
262C23×C13—21no—
263C23×C13—21no—
264C23×C13—21no—
265C23×C13—21no—
266C23×C13—21no—
267C23×C13—21no—
268C23×C13—21no—
269C23×C13—21no—
270C23×C13—21no—
271C23×C13—21no—
272C23×C13—21no—
273C23×C13—21no—
274C23×C13—21no—
275C23×C13—21no—
276C23×C13#11712yes—
277C23×C13C4×D412yes—
278C23×C13C23×C411yescharacteristic
279Q8×C13—44no—
280D4×C13—44no—
281D4×C13—44no—
282D4×C13—44no—
283C2×C4×C13—21no—
284C2×C4×C13—21no—
285C2×C4×C13—21no—
286C2×C4×C13—21no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—21no—
296C2×C4×C13—21no—
297C2×C4×C13—21no—
298C2×C4×C13—41no—
299C2×C4×C13—41no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13#11712yes—
303C2×C4×C13C4×D412yes—
304C2×C4×C13C22×D411yescharacteristic
305C2×C4×C13C2×#4111yescharacteristic
306C2×C4×C13C2×#4111yescharacteristic
307C2×C4×C13C2×#4111yescharacteristic
308C2×C4×C13H(5,𝔽2)11yescharacteristic
309C2×C4×C13H(5,𝔽2)11yescharacteristic
310C2×Dic13—28no—
311C2×Dic13—21no—
312C2×Dic13—21no—
313C2×Dic13—21no—
314C2×Dic13—21no—
315C2×Dic13—21no—
316C2×Dic13—21no—
317C2×Dic13—21no—
318C2×Dic13—21no—
319C2×Dic13—21no—
320C2×Dic13—21no—
321C2×Dic13—21no—
322C2×Dic13—21no—
323C2×Dic13—21no—
324C2×Dic13—21no—
325C2×Dic13—21no—
326C2×Dic13—21no—
327C2×Dic13—21no—
328C2×Dic13—21no—
329C2×Dic13—21no—
330C2×Dic13—21no—
331C2×Dic13—21no—
332C2×Dic13—44no—
333C2×Dic13#13112yes—
334C2×Dic13#13112yes—
335C2×Dic13#13112yes—
336C8×C13—22no—
337C8×C13—22no—
338C8×C13—41no—
339C8×C13—41no—
340#1055—41no—
341#1055—41no—
342#1055—41no—
343#1055—41no—
344C22×#41C2×D1311yescharacteristic
345C22×M16C2×D1311yescharacteristic
346C23×C8C2×D1311yescharacteristic
347C2×#117—131no—
348C22×C42—131no—
349#431—264no—
350C2×C4⋊C8—131no—
351C2×C4⋊C8—131no—
352C2×C4⋊C8—131no—
353C2×C4⋊C8—131no—
354#408—24no—
355C2×C22⋊C8—131no—
356C2×C22⋊C8—131no—
357C2×C22⋊C8—131no—
358C2×C22⋊C8—131no—
359C2×C22⋊C8—131no—
360C2×C22⋊C8—131no—
361C2×C22⋊C8C2×D1311yescharacteristic
362C2×C22⋊C8C2×D1311yescharacteristic
363C2×C22⋊C8C2×D1311yescharacteristic
364C2×C22⋊C8C2×D1311yescharacteristic
365C2×#97—131no—
366C2×C4×C8—131no—
367C2×C4×C8—131no—
368C2×C4×C8—131no—
369#391—131no—
370#391—131no—
371#390—131no—
372#390—131no—
373#386—131no—
374#386—131no—
375#386—131no—
376#386—131no—
377C4×C22⋊C4—131no—
378C4×C22⋊C4—131no—
379C4×C22⋊C4—131no—
380C4×C22⋊C4—131no—
381#336—131no—
382#336—131no—
383#336—131no—
384#336—131no—
385#336—131no—
386#336—131no—
387#336—131no—
388#336—131no—
389C22×C13—22no—
390C22×C13—22no—
391C22×C13—22no—
392C22×C13—22no—
393C22×C13—22no—
394C22×C13—22no—
395C22×C13—41no—
396C22×C13—41no—
397C22×C13—41no—
398C22×C13—41no—
399C22×C13—41no—
400C22×C13—41no—
401C22×C13—41no—
402C22×C13—41no—
403C22×C13—41no—
404C22×C13—41no—
405C22×C13—41no—
406C22×C13—41no—
407C22×C13—41no—
408C22×C13—41no—
409C22×C13—41no—
410C22×C13C2×#11711yescharacteristic
411C22×C13C2×C4×D411yescharacteristic
412C22×C13#51811yescharacteristic
413C22×C13C2×#13111yescharacteristic
414C22×C13C2×#13111yescharacteristic
415C22×C13C2×#13111yescharacteristic
416C22×C13#56811yescharacteristic
417C4×C13—22no—
418C4×C13—22no—
419C4×C13—41no—
420C4×C13#54611yescharacteristic
421C4×C13#54611yescharacteristic
422C4×C13#55111yescharacteristic
423C4×C13#55111yescharacteristic
424Dic13—22no—
425Dic13—22no—
426Dic13—22no—
427Dic13—41no—
428Dic13—41no—
429Dic13—41no—
430Dic13—41no—
431Dic13—41no—
432C2×#41—22no—
433C2×#41—22no—
434C2×#41—22no—
435C2×#41—22no—
436C2×#41—41no—
437C2×#41—41no—
438C22×Q8C4×D1311yescharacteristic
439C22×D4C4×D1311yescharacteristic
440C22×D4C4×D1311yescharacteristic
441C22×D4C4×D1311yescharacteristic
442C23×C4—131no—
443C23×C4—131no—
444C23×C4C22×D1311yescharacteristic
445C23×C4C22×D1311yescharacteristic
446C23×C4C22×D1311yescharacteristic
447C2×M16—22no—
448C2×M16—22no—
449C2×M16—41no—
450C22×C8—22no—
451C22×C8—22no—
452C22×C8—41no—
453C22×C8—131no—
454C22×C8—131no—
455C22×C8—131no—
456C22×C8—131no—
457C22×C8C22×D1311yescharacteristic
458C22×C8C22×D1311yescharacteristic
459C22×C8C22×D1311yescharacteristic
460C22×C8C22×D1311yescharacteristic
461#117—521no—
462#117—521no—
463C2×C4⋊C4—131no—
464C2×C4⋊C4—131no—
465C2×C22⋊C4—131no—
466C2×C22⋊C4—131no—
467C2×C22⋊C4—131no—
468C2×C22⋊C4—131no—
469C2×C22⋊C4—131no—
470C2×C22⋊C4—131no—
471C2×C22⋊C4—131no—
472C2×C22⋊C4—131no—
473C2×C22⋊C4—131no—
474C2×C22⋊C4—131no—
475C2×C42—131no—
476C2×C42—131no—
477C2×C42—131no—
478C2×C42—131no—
479C2×C42—131no—
480C2×C42—131no—
481C2×C42—262no—
482C2×C42—262no—
483C4⋊C8—262no—
484C4⋊C8—262no—
485C4⋊C8—521no—
486C4⋊C8—521no—
487C22⋊C8—22no—
488C22⋊C8—22no—
489C22⋊C8—22no—
490C22⋊C8—262no—
491C22⋊C8—262no—
492C22⋊C8—262no—
493C22⋊C8—262no—
494C22⋊C8—521no—
495C22⋊C8—521no—
496C22⋊C8C22⋊D1314yes—
497#97—521no—
498C4×C8—262no—
499C4×C8—262no—
500C4×C8—521no—
501#95—131no—
502#95—131no—
503#95—131no—
504#95—131no—
505#95—131no—
506#95—131no—
507#95—131no—
508#95—131no—
509C2×C13—42no—
510C2×C13—42no—
511C2×C13—81no—
512C2×C13#234211yescharacteristic
513C2×C13#292211yescharacteristic
514C2×C13#292511yescharacteristic
515C2×C13#292911yescharacteristic
516C2×C13#293311yescharacteristic
517C2×C13#297911yescharacteristic
518C2×C13#298111yescharacteristic
519C24C2×C4×D1311yescharacteristic
520C24C2×C4×D1311yescharacteristic
521C24C2×C4×D1311yescharacteristic
522#41—44no—
523#41—44no—
524#41—44no—
525#41—44no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—41no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—41no—
536C2×D4—41no—
537C2×D4—41no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—131no—
553C22×C4—131no—
554C22×C4—131no—
555C22×C4—131no—
556C22×C4—131no—
557C22×C4—131no—
558C22×C4—131no—
559C22×C4—131no—
560C22×C4—262no—
561C22×C4—262no—
562C22×C4—262no—
563C22×C4—262no—
564C22×C4—262no—
565C22×C4—521no—
566C22×C4C2×C4×D1311yescharacteristic
567C22×C4C2×C4×D1311yescharacteristic
568C22×C4C2×C4×D1311yescharacteristic
569C22×C4#612712yes—
570C22×C4#612912yes—
571C22×C4#612912yes—
572C22×C4C2×C22⋊D1312yes—
573C22×C4C23×D1311yescharacteristic
574M16—44no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—44no—
586C2×C8—261no—
587C2×C8—261no—
588C2×C8—261no—
589C2×C8—261no—
590C2×C8—261no—
591C2×C8—261no—
592C2×C8—261no—
593C2×C8—261no—
594C2×C8—261no—
595C2×C8—261no—
596C2×C8—261no—
597C2×C8—261no—
598C2×C8C2×C22⋊D1312yes—
599C2×C8C2×C22⋊D1312yes—
600C4⋊C4—521no—
601C4⋊C4—521no—
602C22⋊C4—262no—
603C22⋊C4—262no—
604C22⋊C4—262no—
605C22⋊C4—262no—
606C22⋊C4—262no—
607C22⋊C4—262no—
608C22⋊C4—521no—
609C22⋊C4—521no—
610C22⋊C4—521no—
611C22⋊C4—521no—
612C42—262no—
613C42—262no—
614C42—261no—
615C42—261no—
616C42—261no—
617C42—261no—
618C42—261no—
619C42—261no—
620C42—261no—
621C42—261no—
622C13#2255611yescharacteristic, complemented, Sylow
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23#8813112yes—
643C23C4×C22⋊D1312yes—
644C23C22×C4×D1311yescharacteristic
645Q8—44no—
646D4—44no—
647D4—44no—
648D4—44no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—132no—
669C2×C4—132no—
670C2×C4—132no—
671C2×C4—268no—
672C2×C4—261no—
673C2×C4—261no—
674C2×C4—261no—
675C2×C4—261no—
676C2×C4—261no—
677C2×C4—261no—
678C2×C4—261no—
679C2×C4—261no—
680C2×C4—261no—
681C2×C4—261no—
682C2×C4—261no—
683C2×C4—261no—
684C2×C4—261no—
685C2×C4—261no—
686C2×C4—261no—
687C2×C4—261no—
688C2×C4—261no—
689C2×C4—261no—
690C2×C4—261no—
691C2×C4—261no—
692C2×C4—261no—
693C2×C4—524no—
694C2×C4#8813112yes—
695C2×C4C4×C22⋊D1312yes—
696C2×C4C2×#612711yescharacteristic
697C2×C4C2×#612911yescharacteristic
698C2×C4C2×#612911yescharacteristic
699C2×C4#8825111yescharacteristic
700C2×C4#8825111yescharacteristic
701C2×C4C22×C22⋊D1311yescharacteristic
702C8—22no—
703C8—22no—
704C8—41no—
705C8—41no—
706C8—521no—
707C8—521no—
708C8—521no—
709C8—521no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22C2×#8813111yescharacteristic
732C22#1171919111yescharacteristic
733C22D13×#13111yescharacteristic
734C22D13×#13111yescharacteristic
735C22D13×#13111yescharacteristic
736C22#1171945511yescharacteristic
737C22C2×C4×C22⋊D1311yescharacteristic
738C4—22no—
739C4—22no—
740C4—41no—
741C4—262no—
742C4—262no—
743C4—262no—
744C4—521no—
745C4—521no—
746C4—521no—
747C4—521no—
748C4—521no—
749C4#1171920011yescharacteristic
750C4#1171920011yescharacteristic
751C4#1171951111yescharacteristic
752C4#1171951111yescharacteristic
753C2—42no—
754C2—42no—
755C2—81no—
756C2#1311768111yescharacteristic
757C2#1312347611yescharacteristic
758C2#1312349811yescharacteristic
759C2#1312352811yescharacteristic
760C2#1312355811yescharacteristic
761C2#1312390011yescharacteristic
762C2#1312390911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC2×C13×#408C2
prime radicalC22×C13×#41C22
cosocleC22×C4×C13C24
hypercenterC2×#408D13
hypocenterC13#22556
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
1. C2×#11718379C2semidirect
3. #13115452C2semidirect
4. #13115445C2semidirect
5. #13115439C2semidirect
6. #13115439C2semidirect
7. #13115019C2semidirect
8. #13115014C2semidirect
9. #13114902C2semidirect
10. #13114818C2semidirect
12. #13114617C2semidirect
13. C8×C22⋊Dic13C2semidirect
14. #13114604C2semidirect
622. C13#22556semidirect

Maximal subgroups

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

subgroupindex
C2×#117183792
#131173272
#131154522
#131154452
#131154392
#131150192
#131150142
#131149022
#131148182
#131147482
#131146172
C8×C22⋊Dic132
#131146042
C2×C13×#4082
#2255613