Finite Group Databasebeta

← #15789403

Subgroups — #15789403

Order 3328.

1522 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718594C211yesmaximal, characteristic, complemented
2C2×#11718871C211yesmaximal, characteristic
3#13113102C211yesmaximal, characteristic, complemented
4#13113096C211yesmaximal, characteristic, complemented
5#13113091C211yesmaximal, characteristic, complemented
6#13113087C211yesmaximal, characteristic, complemented
7#13113083C211yesmaximal, characteristic
8#13113083C211yesmaximal, characteristic
9#13113079C211yesmaximal, characteristic
10#13113079C211yesmaximal, characteristic
11#13113069C211yesmaximal, characteristic, complemented
12#13113069C211yesmaximal, characteristic, complemented
13#13113063C211yesmaximal, characteristic, complemented
14#13113059C211yesmaximal, characteristic
15C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
16C24×C4×C13C2211yescharacteristic
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C42×C13C2211yescharacteristic
20C22×C42×C13C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C4×C13×C22⋊C4—24no—
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32#11718871C418yescomplemented
33C2×#88071C2211yescharacteristic
34C2×#88071C2211yescharacteristic
35C2×#88071C2211yescharacteristic
36C2×#88071C2211yescharacteristic
37C2×#88071C2211yescharacteristic
38C2×#88071C2211yescharacteristic
39C2×#88071C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53#11718594—24no—
54C25×C13C2311yescharacteristic
55C23×C4×C13—22no—
56C23×C4×C13—22no—
57C23×C4×C13—41no—
58C23×C4×C13—41no—
59C23×C4×C13—41no—
60C23×C4×C13—41no—
61C23×C4×C13C2×C414yes—
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C2×C13×C22⋊C4—22no—
77C2×C13×C22⋊C4—22no—
78C2×C13×C22⋊C4—22no—
79C2×C13×C22⋊C4—22no—
80C2×C13×C22⋊C4—22no—
81C2×C13×C22⋊C4—22no—
82C2×C42×C13—22no—
83C2×C42×C13—41no—
84C2×C42×C13—41no—
85C2×C42×C13—41no—
86C2×C42×C13—41no—
87C2×C42×C13D414yes—
88C2×C22⋊Dic13—22no—
89C2×C22⋊Dic13—22no—
90C2×C22⋊Dic13—22no—
91C2×C22⋊Dic13—22no—
92C2×C22⋊Dic13—41no—
93C2×C22⋊Dic13—41no—
94C2×C22⋊Dic13—41no—
95C2×C22⋊Dic13—41no—
96C2×C22⋊Dic13—41no—
97C2×C22⋊Dic13—41no—
98C2×C22⋊Dic13C2×C414yes—
99C2×C22⋊Dic13C2×C414yes—
100C2×#6101—22no—
101C2×#6101—22no—
102C2×#6101—22no—
103C2×#6101—22no—
104C2×#6101—41no—
105C2×#6101—41no—
106C2×#6101—41no—
107C2×#6101—41no—
108C2×#6101—41no—
109C2×#6101—41no—
110C2×#6101C2×C414yes—
111C2×#6101C2×C414yes—
112C13×#95—22no—
113C13×#95—22no—
114#88071—22no—
115#88071—22no—
116#88071—22no—
117#88071—22no—
118#88071—22no—
119#88071—22no—
120#88071—22no—
121#88071—22no—
122#88071—41no—
123#88071—41no—
124#88071—41no—
125#88071—41no—
126#88071—41no—
127#88071—41no—
128#88071—41no—
129#88071—41no—
130#88071—41no—
131#88071—41no—
132#88071C2×C414yes—
133#88071C2×C414yes—
134#14269—131nomaximal, Sylow
135C24×C13—21no—
136C24×C13—21no—
137C24×C13—21no—
138C24×C13—21no—
139C24×C13—21no—
140C24×C13—21no—
141C24×C13—21no—
142C24×C13—21no—
143C24×C13—21no—
144C24×C13—21no—
145C24×C13—21no—
146C24×C13—21no—
147C24×C13C22×C412yes—
148C24×C13#4112yes—
149C24×C13#4112yes—
150C24×C13C2411yescharacteristic
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
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×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—28no—
186C22×C4×C13—44no—
187C22×C4×C13—44no—
188C22×C4×C13—44no—
189C22×C4×C13—44no—
190C22×C4×C13—44no—
191C22×C4×C13—44no—
192C22×C4×C13C22×C412yes—
193C22×C4×C13C22×C412yes—
194C22×C4×C13C2×D412yes—
195C22×C4×C13C2×D412yes—
196C22×C4×C13C2×D412yes—
197C22×C4×C13#4112yes—
198C22×C4×C13#4112yes—
199C22×C4×C13#4112yes—
200C22×Dic13—21no—
201C22×Dic13—21no—
202C22×Dic13—21no—
203C22×Dic13—21no—
204C22×Dic13—21no—
205C22×Dic13—21no—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—21no—
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C22×Dic13—21no—
218C22×Dic13—21no—
219C22×Dic13—21no—
220C22×Dic13—21no—
221C22×Dic13—21no—
222C22×Dic13—21no—
223C22×Dic13—21no—
224C22×Dic13—21no—
225C22×Dic13—21no—
226C22×Dic13—21no—
227C22×Dic13—21no—
228C22×Dic13—21no—
229C22×Dic13—21no—
230C22×Dic13—21no—
231C22×Dic13—21no—
232C22×Dic13—21no—
233C22×Dic13—21no—
234C22×Dic13—21no—
235C22×Dic13—21no—
236C22×Dic13—21no—
237C22×Dic13—21no—
238C22×Dic13—21no—
239C22×Dic13—21no—
240C22×Dic13—21no—
241C22×Dic13—21no—
242C22×Dic13—21no—
243C22×Dic13—21no—
244C22×Dic13—21no—
245C22×Dic13—21no—
246C22×Dic13—21no—
247C22×Dic13—21no—
248C22×Dic13—21no—
249C22×Dic13—21no—
250C22×Dic13—21no—
251C22×Dic13—21no—
252C22×Dic13C22×C412yes—
253C22×Dic13C22×C412yes—
254C22×Dic13C22×C412yes—
255C22×Dic13C22×C412yes—
256C13×C22⋊C4—28no—
257C13×C22⋊C4—28no—
258C42×C13—44no—
259C42×C13—44no—
260C22⋊Dic13—28no—
261C22⋊Dic13—44no—
262C22⋊Dic13—44no—
263C22⋊Dic13—44no—
264#6101—28no—
265#6101—44no—
266#6101—44no—
267#6101—44no—
268C2×#387—131no—
269C2×#385—131no—
270C2×C4×C22⋊C4D1311yescharacteristic
271#1445—131no—
272#1443—131no—
273#1442—131no—
274#1441—131no—
275#1440—131no—
276#1440—131no—
277#1439—131no—
278#1439—131no—
279#1436—131no—
280#1436—131no—
281#1434—131no—
282C22⋊#95—131no—
283C23×C13—22no—
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—41no—
302C23×C13—41no—
303C23×C13—41no—
304C23×C13—41no—
305C23×C13—41no—
306C23×C13—41no—
307C23×C13—41no—
308C23×C13—41no—
309C23×C13—41no—
310C23×C13—41no—
311C23×C13—41no—
312C23×C13—41no—
313C23×C13—41no—
314C23×C13—41no—
315C23×C13—41no—
316C23×C13—41no—
317C23×C13#11714yes—
318C23×C13C23×C411yescharacteristic
319C23×C13C22×D411yescharacteristic
320C23×C13C2×#4111yescharacteristic
321C23×C13C2×#4111yescharacteristic
322C23×C13C2×#4111yescharacteristic
323C23×C13C2×#4111yescharacteristic
324C23×C13C2×#4111yescharacteristic
325C23×C13H(5,𝔽2)11yescharacteristic
326C23×C13H(5,𝔽2)11yescharacteristic
327C23×C13H(5,𝔽2)11yescharacteristic
328C23×C13H(5,𝔽2)11yescharacteristic
329C23×C13H(5,𝔽2)11yescharacteristic
330C23×C132−1+411yescharacteristic
331C23×C132−1+411yescharacteristic
332C23×C132−1+411yescharacteristic
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—416no—
355C2×C4×C13—41no—
356C2×C4×C13—41no—
357C2×C4×C13—41no—
358C2×C4×C13—41no—
359C2×C4×C13—41no—
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×C13—41no—
367C2×C4×C13—41no—
368C2×C4×C13—41no—
369C2×C4×C13—41no—
370C2×C4×C13—41no—
371C2×C4×C13—41no—
372C2×C4×C13—41no—
373C2×C4×C13—41no—
374C2×C4×C13—41no—
375C2×C4×C13C4×D414yes—
376C2×Dic13—22no—
377C2×Dic13—22no—
378C2×Dic13—22no—
379C2×Dic13—22no—
380C2×Dic13—22no—
381C2×Dic13—22no—
382C2×Dic13—22no—
383C2×Dic13—22no—
384C2×Dic13—22no—
385C2×Dic13—22no—
386C2×Dic13—22no—
387C2×Dic13—22no—
388C2×Dic13—41no—
389C2×Dic13—41no—
390C2×Dic13—41no—
391C2×Dic13—41no—
392C2×Dic13—41no—
393C2×Dic13—41no—
394C2×Dic13—41no—
395C2×Dic13—41no—
396C2×Dic13—41no—
397C2×Dic13—41no—
398C2×Dic13—41no—
399C2×Dic13—41no—
400C2×Dic13—41no—
401C2×Dic13—41no—
402C2×Dic13—41no—
403C2×Dic13—41no—
404C2×Dic13—41no—
405C2×Dic13—41no—
406C2×Dic13—41no—
407C2×Dic13—41no—
408C2×Dic13—41no—
409C2×Dic13—41no—
410C2×Dic13—41no—
411C2×Dic13—41no—
412C2×Dic13—41no—
413C2×Dic13—41no—
414C2×Dic13—41no—
415C2×Dic13—41no—
416C2×Dic13—41no—
417C2×Dic13—41no—
418C2×Dic13—41no—
419C2×Dic13—41no—
420C2×Dic13—41no—
421C2×Dic13—41no—
422C2×Dic13—41no—
423C2×Dic13—41no—
424C2×Dic13—41no—
425C2×Dic13—41no—
426C2×Dic13—41no—
427C2×Dic13—41no—
428C2×Dic13—41no—
429C2×Dic13—41no—
430C2×Dic13—41no—
431C2×Dic13—41no—
432C24×C4C2×D1311yescharacteristic
433C22×C4⋊C4—131no—
434C22×C4⋊C4—131no—
435C22×C4⋊C4—131no—
436C22×C4⋊C4—131no—
437C22×C22⋊C4—131no—
438C22×C22⋊C4—131no—
439C22×C22⋊C4—131no—
440C22×C22⋊C4—131no—
441C22×C22⋊C4C2×D1311yescharacteristic
442C22×C22⋊C4C2×D1311yescharacteristic
443C22×C42C2×D1311yescharacteristic
444C22×C42C2×D1311yescharacteristic
445#387—264no—
446#385—138no—
447C4×C22⋊C4—24no—
448C2×#95—131no—
449C2×#95—131no—
450C2×#95—131no—
451C2×#95—131no—
452C2×#95—131no—
453C2×#95—131no—
454C2×#95—131no—
455C2×#95—131no—
456C2×#95—131no—
457C2×#95—131no—
458C2×#95—131no—
459C2×#95—131no—
460C2×#95—131no—
461C2×#95—131no—
462C2×#95—131no—
463C2×#95—131no—
464C2×#95—131no—
465C2×#95—131no—
466C2×#95—131no—
467C2×#95—131no—
468C2×#95C2×D1311yescharacteristic
469C2×#95C2×D1311yescharacteristic
470C22×C13—24no—
471C22×C13—24no—
472C22×C13—24no—
473C22×C13—42no—
474C22×C13—42no—
475C22×C13—42no—
476C22×C13—42no—
477C22×C13—42no—
478C22×C13—42no—
479C22×C13—42no—
480C22×C13—42no—
481C22×C13—42no—
482C22×C13—42no—
483C22×C13—42no—
484C22×C13—42no—
485C22×C13C2×#11711yescharacteristic
486C22×C13C2×C4×D411yescharacteristic
487C22×C13C4×#4111yescharacteristic
488C22×C13#51811yescharacteristic
489C22×C13#51811yescharacteristic
490C22×C13#51911yescharacteristic
491C22×C13#52011yescharacteristic
492C22×C13#52511yescharacteristic
493C22×C13#52511yescharacteristic
494C22×C13#52911yescharacteristic
495C22×C13#52911yescharacteristic
496C22×C13#53411yescharacteristic
497C22×C13#53511yescharacteristic
498C22×C13#53611yescharacteristic
499C22×C13#53711yescharacteristic
500C22×C13#53811yescharacteristic
501C22×C13#53811yescharacteristic
502C22×C13#53811yescharacteristic
503C22×C13#53811yescharacteristic
504C22×C13#53811yescharacteristic
505C22×C13#53911yescharacteristic
506C22×C13#53911yescharacteristic
507C22×C13#53911yescharacteristic
508C22×C13#53911yescharacteristic
509C22×C13#53911yescharacteristic
510C22×C13#53911yescharacteristic
511C22×C13#53911yescharacteristic
512C22×C13#53911yescharacteristic
513C22×C13#53911yescharacteristic
514C22×C13#54011yescharacteristic
515C22×C13#54111yescharacteristic
516C22×C13#54211yescharacteristic
517C22×C13#54211yescharacteristic
518C22×C13#54211yescharacteristic
519C22×C13#54211yescharacteristic
520C4×C13—24no—
521C4×C13—42no—
522C4×C13—42no—
523C4×C13—42no—
524C4×C13—42no—
525C4×C13—42no—
526Dic13—42no—
527Dic13—42no—
528Dic13—42no—
529Dic13—42no—
530Dic13—81no—
531Dic13—81no—
532Dic13—81no—
533Dic13—81no—
534C25C22×D1311yescharacteristic
535C23×C4—22no—
536C23×C4—22no—
537C23×C4—41no—
538C23×C4—41no—
539C23×C4—41no—
540C23×C4—41no—
541C23×C4—131no—
542C23×C4—131no—
543C23×C4—131no—
544C23×C4—131no—
545C23×C4—131no—
546C23×C4—131no—
547C23×C4—131no—
548C23×C4—131no—
549C23×C4C4×D1314yes—
550C23×C4C22×D1311yescharacteristic
551C23×C4C22×D1311yescharacteristic
552C23×C4C22×D1311yescharacteristic
553C23×C4C22×D1311yescharacteristic
554C23×C4C22×D1311yescharacteristic
555C23×C4C22×D1311yescharacteristic
556C2×C4⋊C4—134no—
557C2×C4⋊C4—134no—
558C2×C4⋊C4—262no—
559C2×C4⋊C4—262no—
560C2×C4⋊C4—262no—
561C2×C4⋊C4—262no—
562C2×C4⋊C4—521no—
563C2×C4⋊C4—521no—
564C2×C4⋊C4—521no—
565C2×C4⋊C4—521no—
566C2×C4⋊C4—521no—
567C2×C4⋊C4—521no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—134no—
575C2×C22⋊C4—134no—
576C2×C22⋊C4—262no—
577C2×C22⋊C4—262no—
578C2×C22⋊C4—262no—
579C2×C22⋊C4—262no—
580C2×C22⋊C4—521no—
581C2×C22⋊C4—521no—
582C2×C22⋊C4—521no—
583C2×C22⋊C4—521no—
584C2×C22⋊C4—521no—
585C2×C22⋊C4—521no—
586C2×C42—22no—
587C2×C42—41no—
588C2×C42—41no—
589C2×C42—41no—
590C2×C42—41no—
591C2×C42C22⋊D1314yes—
592#95—22no—
593#95—22no—
594#95—134no—
595#95—134no—
596#95—262no—
597#95—262no—
598#95—262no—
599#95—262no—
600#95—262no—
601#95—262no—
602#95—262no—
603#95—262no—
604#95—521no—
605#95—521no—
606#95—521no—
607#95—521no—
608#95—521no—
609#95—521no—
610#95—521no—
611#95—521no—
612#95—521no—
613#95—521no—
614C2×C13—44no—
615C2×C13#229011yescharacteristic
616C2×C13#231311yescharacteristic
617C2×C13#231811yescharacteristic
618C2×C13#232111yescharacteristic
619C2×C13#232311yescharacteristic
620C2×C13#233211yescharacteristic
621C2×C13#233511yescharacteristic
622C2×C13#263011yescharacteristic
623C2×C13#263311yescharacteristic
624C2×C13#263611yescharacteristic
625C2×C13#263811yescharacteristic
626C2×C13#264911yescharacteristic
627C2×C13#265211yescharacteristic
628C2×C13#265211yescharacteristic
629C2×C13#265311yescharacteristic
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24C2×C4×D1312yes—
643C24#612712yes—
644C24#612712yes—
645C24C23×D1311yescharacteristic
646C22×C4—21no—
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—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—28no—
681C22×C4—44no—
682C22×C4—44no—
683C22×C4—44no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—44no—
687C22×C4—132no—
688C22×C4—132no—
689C22×C4—132no—
690C22×C4—132no—
691C22×C4—261no—
692C22×C4—261no—
693C22×C4—261no—
694C22×C4—261no—
695C22×C4—261no—
696C22×C4—261no—
697C22×C4—261no—
698C22×C4—261no—
699C22×C4—261no—
700C22×C4—261no—
701C22×C4—261no—
702C22×C4—261no—
703C22×C4—261no—
704C22×C4—261no—
705C22×C4—261no—
706C22×C4—261no—
707C22×C4—261no—
708C22×C4—261no—
709C22×C4—261no—
710C22×C4—261no—
711C22×C4—261no—
712C22×C4—261no—
713C22×C4—261no—
714C22×C4—261no—
715C22×C4—261no—
716C22×C4—261no—
717C22×C4—261no—
718C22×C4—261no—
719C22×C4—261no—
720C22×C4—261no—
721C22×C4—261no—
722C22×C4—261no—
723C22×C4—261no—
724C22×C4—261no—
725C22×C4—261no—
726C22×C4—261no—
727C22×C4—261no—
728C22×C4—261no—
729C22×C4—261no—
730C22×C4—261no—
731C22×C4—261no—
732C22×C4—261no—
733C22×C4—261no—
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×C4C2×C4×D1312yes—
744C22×C4C2×C4×D1312yes—
745C22×C4#612712yes—
746C22×C4#612712yes—
747C22×C4#612712yes—
748C22×C4C2×C22⋊D1312yes—
749C22×C4C2×C22⋊D1312yes—
750C22×C4C2×C22⋊D1312yes—
751C4⋊C4—268no—
752C4⋊C4—524no—
753C4⋊C4—524no—
754C4⋊C4—524no—
755C22⋊C4—28no—
756C22⋊C4—28no—
757C22⋊C4—268no—
758C22⋊C4—524no—
759C22⋊C4—524no—
760C22⋊C4—524no—
761C42—44no—
762C42—44no—
763C13#1426911yescharacteristic, complemented, Sylow
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23#8812614yes—
799C23C22×C4×D1311yescharacteristic
800C23C2×#612711yescharacteristic
801C23C2×#612711yescharacteristic
802C23C2×#612711yescharacteristic
803C23C2×#612711yescharacteristic
804C23C2×#612711yescharacteristic
805C23#8825111yescharacteristic
806C23#8825111yescharacteristic
807C23#8825111yescharacteristic
808C23#8825111yescharacteristic
809C23#8825611yescharacteristic
810C23#8825711yescharacteristic
811C23#8825711yescharacteristic
812C23#8825711yescharacteristic
813C23C22×C22⋊D1311yescharacteristic
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—416no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—262no—
857C2×C4—262no—
858C2×C4—262no—
859C2×C4—262no—
860C2×C4—262no—
861C2×C4—262no—
862C2×C4—262no—
863C2×C4—262no—
864C2×C4—262no—
865C2×C4—262no—
866C2×C4—262no—
867C2×C4—262no—
868C2×C4—521no—
869C2×C4—521no—
870C2×C4—521no—
871C2×C4—521no—
872C2×C4—521no—
873C2×C4—521no—
874C2×C4—521no—
875C2×C4—521no—
876C2×C4—521no—
877C2×C4—521no—
878C2×C4—521no—
879C2×C4—521no—
880C2×C4—521no—
881C2×C4—521no—
882C2×C4—521no—
883C2×C4—521no—
884C2×C4—521no—
885C2×C4—521no—
886C2×C4—521no—
887C2×C4—521no—
888C2×C4—521no—
889C2×C4—521no—
890C2×C4—521no—
891C2×C4—521no—
892C2×C4—521no—
893C2×C4—521no—
894C2×C4—521no—
895C2×C4—521no—
896C2×C4—521no—
897C2×C4—521no—
898C2×C4—521no—
899C2×C4—521no—
900C2×C4—521no—
901C2×C4—521no—
902C2×C4—521no—
903C2×C4—521no—
904C2×C4—521no—
905C2×C4—521no—
906C2×C4—521no—
907C2×C4—521no—
908C2×C4—521no—
909C2×C4—521no—
910C2×C4—521no—
911C2×C4—521no—
912C2×C4C4×C22⋊D1314yes—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22C2×#8812611yescharacteristic
929C22C4×#612711yescharacteristic
930C22#1171918411yescharacteristic
931C22#1171918411yescharacteristic
932C22#1171919111yescharacteristic
933C22#1171919111yescharacteristic
934C22#1171919911yescharacteristic
935C22#1171919911yescharacteristic
936C22#1171922111yescharacteristic
937C22#1171922311yescharacteristic
938C22#1171922811yescharacteristic
939C22#1171923911yescharacteristic
940C22#1171926511yescharacteristic
941C22#1171926511yescharacteristic
942C22#1171926511yescharacteristic
943C22#1171926611yescharacteristic
944C22#1171926611yescharacteristic
945C22#1171926611yescharacteristic
946C22#1171926711yescharacteristic
947C22#1171926911yescharacteristic
948C22#1171926911yescharacteristic
949C22#1171926911yescharacteristic
950C22#1171926911yescharacteristic
951C22#1171926911yescharacteristic
952C22#1171926911yescharacteristic
953C22#1171926911yescharacteristic
954C22#1171926911yescharacteristic
955C22#1171926911yescharacteristic
956C22C2×C4×C22⋊D1311yescharacteristic
957C22#1171949611yescharacteristic
958C22#1171949611yescharacteristic
959C22#1171950911yescharacteristic
960C22#1171951011yescharacteristic
961C22#1171953011yescharacteristic
962C22#1171953811yescharacteristic
963C4—24no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—522no—
970C4—522no—
971C4—522no—
972C4—522no—
973C4—1041no—
974C4—1041no—
975C4—1041no—
976C4—1041no—
977C2—44no—
978C2#1311727911yescharacteristic
979C2#1311743611yescharacteristic
980C2#1311746311yescharacteristic
981C2#1311749411yescharacteristic
982C2#1311751811yescharacteristic
983C2#1311759211yescharacteristic
984C2#1311762611yescharacteristic
985C2#1312067311yescharacteristic
986C2#1312070411yescharacteristic
987C2#1312073111yescharacteristic
988C2#1312075311yescharacteristic
989C2#1312083311yescharacteristic
990C2#1312087811yescharacteristic
991C2#1312087811yescharacteristic
992C2#1312089311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C4×C13×C22⋊C4C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×C4×C22⋊C4D13
hypocenterC13#14269
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11718594C2semidirect
3. #13113102C2semidirect
4. #13113096C2semidirect
5. #13113091C2semidirect
6. #13113087C2semidirect
11. #13113069C2semidirect
12. #13113069C2semidirect
13. #13113063C2semidirect
32. #11718871C4semidirect
763. C13#14269semidirect

Maximal subgroups

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

subgroupindex
C2×#117185942
C2×#117188712
#131131022
#131130962
#131130912
#131130872
#131130832
#131130792
#131130692
#131130632
#131130592
C2×C4×C13×C22⋊C42
#1426913