Finite Group Databasebeta

← #34026538

Subgroups — #34026538

Order 18688.

1100 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989611C211yesmaximal, characteristic, complemented
2C22×C22⋊#10596833C211yesmaximal, characteristic
3#22626005C211yesmaximal, characteristic, complemented
4#22626004C211yesmaximal, characteristic, complemented
5#22626001C211yesmaximal, characteristic, complemented
6#22626000C211yesmaximal, characteristic, complemented
7#22625875C211yesmaximal, characteristic, complemented
8#22625874C211yesmaximal, characteristic, complemented
9#22625824C211yesmaximal, characteristic, complemented
10#22625789C211yesmaximal, characteristic, complemented
11#22625753C211yesmaximal, characteristic
12#22625668C211yesmaximal, characteristic, complemented
13C22⋊C4×#10596833C211yesmaximal, characteristic, complemented
14#22625661C211yesmaximal, characteristic, complemented
15#22612309C211yesmaximal, characteristic
16C23×#10596833C2211yescharacteristic
17C23×#10596833C2211yescharacteristic
18#17989611—24no—
19C2×#14556658C2211yescharacteristic, complemented
20C2×#14556658C2211yescharacteristic, complemented
21C2×C4⋊#10596833C2211yescharacteristic, complemented
22C2×C4⋊#10596833C2211yescharacteristic, complemented
23C2×C22⋊#10596833—24no—
24C2×C22⋊#10596833C2211yescharacteristic
25C2×C22⋊#10596833C2211yescharacteristic
26C2×C22⋊#10596833C2211yescharacteristic
27C2×C22⋊#10596833C2211yescharacteristic
28C2×C22⋊#10596833C2211yescharacteristic
29C2×C22⋊#10596833C2211yescharacteristic
30C2×C22⋊#10596833C2211yescharacteristic
31C2×C22⋊#10596833C2211yescharacteristic
32C2×C22⋊#10596833C2211yescharacteristic
33C2×C22⋊#10596833C2211yescharacteristic
34C2×#14556646C2211yescharacteristic, complemented
35C2×#14556646C2211yescharacteristic, complemented
36C2×C4×#10596833C2211yescharacteristic, complemented
37C2×C4×#10596833C2211yescharacteristic, complemented
38#17989453C2211yescharacteristic, complemented
39#17989453C2211yescharacteristic, complemented
40#17989453C2211yescharacteristic, complemented
41#17989453C2211yescharacteristic, complemented
42#17989453C2211yescharacteristic, complemented
43#17989453C2211yescharacteristic, complemented
44#17989453C2211yescharacteristic, complemented
45#17989453C2211yescharacteristic, complemented
46C24×Dic73C2211yescharacteristic
47C2×#14556547C2211yescharacteristic
48C2×#14556547C2211yescharacteristic
49#17988448C411yescharacteristic
50#17988448C411yescharacteristic
51#17988445C411yescharacteristic
52#17988445C411yescharacteristic
53#17988445C411yescharacteristic
54#17988445C411yescharacteristic
55#17988443C411yescharacteristic
56C22⋊C4×Dic73C2211yescharacteristic
57C22⋊C4×Dic73C2211yescharacteristic
58C22⋊C4×Dic73C2211yescharacteristic
59C22⋊C4×Dic73C2211yescharacteristic
60#379×C73C411yescharacteristic
61C22×#10596833—22no—
62C22×#10596833—22no—
63C22×#10596833—22no—
64C22×#10596833—22no—
65C22×#10596833—41no—
66C22×#10596833—41no—
67C22×#10596833C2311yescharacteristic
68C22×#10596833C2311yescharacteristic
69C22×#10596833C2311yescharacteristic
70C22×#10596833C2311yescharacteristic
71C22×#10596833C2311yescharacteristic
72C22×#10596833C2311yescharacteristic
73C22×#10596833C2311yescharacteristic
74C22×#10596833C2311yescharacteristic
75#14556658—22no—
76#14556658—41no—
77C4⋊#10596833—22no—
78C4⋊#10596833—41no—
79C22⋊#10596833—22no—
80C22⋊#10596833—22no—
81C22⋊#10596833—22no—
82C22⋊#10596833—22no—
83C22⋊#10596833—22no—
84C22⋊#10596833—22no—
85C22⋊#10596833—22no—
86C22⋊#10596833—41no—
87C22⋊#10596833—41no—
88C22⋊#10596833D414yes—
89#14556646—22no—
90#14556646—41no—
91C4×#10596833—22no—
92C4×#10596833—41no—
93C23×Dic73—22no—
94C23×Dic73—22no—
95C23×Dic73—22no—
96C23×Dic73—22no—
97C23×Dic73—41no—
98C23×Dic73—41no—
99C23×Dic73C2×C411yescharacteristic
100C23×Dic73C2×C411yescharacteristic
101C23×Dic73C2×C411yescharacteristic
102C23×Dic73C2311yescharacteristic
103C23×Dic73C2311yescharacteristic
104C23×Dic73C2311yescharacteristic
105#14556547—22no—
106#14556547—22no—
107#14556547—41no—
108#14556547—41no—
109C2×#11924007C2×C411yescharacteristic
110C2×#11924007C2×C411yescharacteristic
111C2×#11924007C2×C411yescharacteristic
112C2×#11924007C2×C411yescharacteristic
113C2×C22⋊Dic73C2×C411yescharacteristic
114C2×C22⋊Dic73C2×C411yescharacteristic
115C2×C22⋊Dic73C2×C411yescharacteristic
116C2×C22⋊Dic73C2×C411yescharacteristic
117C2×C22⋊Dic73C2×C411yescharacteristic
118C2×C22⋊Dic73C2×C411yescharacteristic
119C2×C4×Dic73C2311yescharacteristic
120C2×C4×Dic73C2311yescharacteristic
121C2×C4×Dic73C2311yescharacteristic
122C2×C4×Dic73C2311yescharacteristic
123#14556498C2×C411yescharacteristic
124#14556498C2×C411yescharacteristic
125#14556498C2×C411yescharacteristic
126#14556498C2×C411yescharacteristic
127#14556498C2×C411yescharacteristic
128#14556498C2×C411yescharacteristic
129#14556498C2×C411yescharacteristic
130#14556498C2×C411yescharacteristic
131C25×C73C2×C411yescharacteristic
132C2×C22⋊C4×C73C2×C411yescharacteristic
133C2×C22⋊C4×C73C2×C411yescharacteristic
134C2×C22⋊C4×C73C2×C411yescharacteristic
135C2×C22⋊C4×C73C2×C411yescharacteristic
136C2×C22⋊C4×C73C2×C411yescharacteristic
137C2×C22⋊C4×C73C2×C411yescharacteristic
138C2×#10596833—21no—
139C2×#10596833—21no—
140C2×#10596833—21no—
141C2×#10596833—21no—
142C2×#10596833—21no—
143C2×#10596833—21no—
144C2×#10596833—21no—
145C2×#10596833—21no—
146C2×#10596833—21no—
147C2×#10596833—21no—
148C2×#10596833—21no—
149C2×#10596833—21no—
150C2×#10596833—21no—
151C2×#10596833—21no—
152C2×#10596833—21no—
153C2×#10596833—21no—
154C2×#10596833—21no—
155C2×#10596833—21no—
156C2×#10596833—21no—
157C2×#10596833—21no—
158C2×#10596833—21no—
159C2×#10596833—21no—
160C2×#10596833—44no—
161C2×#10596833—44no—
162C2×#10596833C2×D412yes—
163C2×#10596833C2×D412yes—
164C22×Dic73—21no—
165C22×Dic73—21no—
166C22×Dic73—21no—
167C22×Dic73—21no—
168C22×Dic73—21no—
169C22×Dic73—21no—
170C22×Dic73—21no—
171C22×Dic73—21no—
172C22×Dic73—22no—
173C22×Dic73—22no—
174C22×Dic73—22no—
175C22×Dic73—22no—
176C22×Dic73—22no—
177C22×Dic73—22no—
178C22×Dic73—21no—
179C22×Dic73—21no—
180C22×Dic73—21no—
181C22×Dic73—21no—
182C22×Dic73—21no—
183C22×Dic73—21no—
184C22×Dic73—41no—
185C22×Dic73—41no—
186C22×Dic73—41no—
187C22×Dic73—44no—
188C22×Dic73—44no—
189C22×Dic73—44no—
190C22×Dic73—44no—
191C22×Dic73C22×C411yescharacteristic
192C22×Dic73C22×C411yescharacteristic
193C22×Dic73C22×C411yescharacteristic
194C22×Dic73C22×C411yescharacteristic
195C22×Dic73C22×C411yescharacteristic
196C22×Dic73C22×C411yescharacteristic
197C22×Dic73C22×C411yescharacteristic
198C22×Dic73C2×D412yes—
199C22×Dic73#4112yes—
200C22×Dic73#4112yes—
201C22×Dic73#4112yes—
202C22×Dic73C2411yescharacteristic
203#11924007—22no—
204#11924007—22no—
205#11924007—41no—
206#11924007—41no—
207C22⋊Dic73—22no—
208C22⋊Dic73—22no—
209C22⋊Dic73—22no—
210C22⋊Dic73—22no—
211C22⋊Dic73—41no—
212C22⋊Dic73—41no—
213C4×Dic73—21no—
214C4×Dic73—21no—
215C4×Dic73—21no—
216C4×Dic73—21no—
217C4×Dic73—21no—
218C4×Dic73—21no—
219C4×Dic73—21no—
220C4×Dic73—21no—
221C24×C73—22no—
222C24×C73—22no—
223C24×C73—22no—
224C24×C73—22no—
225C24×C73—22no—
226C24×C73—41no—
227C24×C73—41no—
228C24×C73C22×C411yescharacteristic
229C24×C73C22×C411yescharacteristic
230C24×C73C22×C411yescharacteristic
231C22×C4×C73C22×C411yescharacteristic
232C22×C4×C73C22×C411yescharacteristic
233C22×C4×C73C22×C411yescharacteristic
234C22×C4×C73C22×C411yescharacteristic
235C22⋊C4×C73—22no—
236C22⋊C4×C73—22no—
237C22⋊C4×C73—22no—
238C22⋊C4×C73—22no—
239C22⋊C4×C73—41no—
240C22⋊C4×C73—41no—
241C23×C73—21no—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—28no—
246C23×C73—21no—
247C23×C73—21no—
248C23×C73—21no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73—21no—
252C23×C73—21no—
253C23×C73—21no—
254C23×C73—21no—
255C23×C73—21no—
256C23×C73—21no—
257C23×C73—21no—
258C23×C73—44no—
259C23×C73—44no—
260C23×C73—44no—
261C23×C73—44no—
262C23×C73—44no—
263C23×C73—44no—
264C23×C73#11712yes—
265C23×C73C4×D412yes—
266C23×C73#13112yes—
267C23×C73#13112yes—
268C23×C73#13112yes—
269C23×C73C23×C411yescharacteristic
270C2×C4×C73—21no—
271C2×C4×C73—21no—
272C2×C4×C73—21no—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
275C2×C4×C73—21no—
276C2×C4×C73—21no—
277C2×C4×C73—21no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
280C2×C4×C73—21no—
281C2×C4×C73—21no—
282C2×Dic73—21no—
283C2×Dic73—21no—
284C2×Dic73—21no—
285C2×Dic73—21no—
286C2×Dic73—22no—
287C2×Dic73—22no—
288C2×Dic73—22no—
289C2×Dic73—22no—
290C2×Dic73—22no—
291C2×Dic73—22no—
292C2×Dic73—22no—
293C2×Dic73—22no—
294C2×Dic73—21no—
295C2×Dic73—21no—
296C2×Dic73—21no—
297C2×Dic73—21no—
298C2×Dic73—21no—
299C2×Dic73—21no—
300C2×Dic73—21no—
301C2×Dic73—21no—
302C2×Dic73—21no—
303C2×Dic73—21no—
304C2×Dic73—21no—
305C2×Dic73—21no—
306C2×Dic73—21no—
307C2×Dic73—21no—
308C2×Dic73—21no—
309C2×Dic73—44no—
310C2×Dic73—44no—
311C2×Dic73—44no—
312C2×Dic73—41no—
313C2×Dic73—41no—
314C2×Dic73—41no—
315C2×Dic73—41no—
316C2×Dic73#11712yes—
317C2×Dic73C4×D412yes—
318C2×Dic73C22×D411yescharacteristic
319C2×Dic73C2×#4111yescharacteristic
320C2×Dic73C2×#4111yescharacteristic
321C2×Dic73C2×#4111yescharacteristic
322C2×Dic73H(5,𝔽2)11yescharacteristic
323C2×Dic73H(5,𝔽2)11yescharacteristic
324#10596833—22no—
325#10596833—22no—
326#10596833—41no—
327#10596833—41no—
328#10596833—41no—
329#10596833—41no—
330#10596833—41no—
331#10596833—41no—
332C22×C73—22no—
333C22×C73—22no—
334C22×C73—22no—
335C22×C73—22no—
336C22×C73—22no—
337C22×C73—22no—
338C22×C73—22no—
339C22×C73—22no—
340C22×C73—22no—
341C22×C73—22no—
342C22×C73—22no—
343C22×C73—22no—
344C22×C73—416no—
345C22×C73—41no—
346C22×C73—41no—
347C22×C73—41no—
348C22×C73—41no—
349C22×C73—41no—
350C22×C73—41no—
351C22×C73—41no—
352C22×C73—41no—
353C22×C73#43314yescomplemented
354C22×C73C2×#11711yescharacteristic
355C22×C73C2×C4×D411yescharacteristic
356C22×C73#51811yescharacteristic
357C22×C73C2×#13111yescharacteristic
358C22×C73C2×#13111yescharacteristic
359C22×C73C2×#13111yescharacteristic
360C22×C73#56811yescharacteristic
361C4×C73—41no—
362C4×C73—41no—
363C4×C73—41no—
364C4×C73—41no—
365Dic73—22no—
366Dic73—22no—
367Dic73—41no—
368Dic73—41no—
369Dic73—41no—
370Dic73—41no—
371Dic73—41no—
372Dic73#54611yescharacteristic
373Dic73#54611yescharacteristic
374Dic73#55111yescharacteristic
375Dic73#55111yescharacteristic
376#22558—731nomaximal, Sylow
377C2×C73—24no—
378C2×C73—42no—
379C2×C73—42no—
380C2×C73#234211yescharacteristic
381C2×C73C2×#43311yescharacteristic
382C2×C73#292411yescharacteristic
383C2×C73#292911yescharacteristic
384C2×C73#293311yescharacteristic
385C2×C73#297611yescharacteristic
386C2×C73#297711yescharacteristic
387C2×#433—731no—
388C22×C22⋊C8—731no—
389#2280—731no—
390#1924—731no—
391#1924—731no—
392#1923—731no—
393#1923—731no—
394#1850—731no—
395#1850—731no—
396#1818—731no—
397#1798—731no—
398#1779—731no—
399#1752—731no—
400C8×C22⋊C4—731no—
401#1750—731no—
402C73#2255811yescharacteristic, complemented, Sylow
403C24×C4—731no—
404C23×C8—731no—
405C23×C8—731no—
406C2×#117—731no—
407C2×#117—731no—
408#433—1464no—
409C2×C4⋊C8—731no—
410C2×C4⋊C8—731no—
411C2×C4⋊C8—731no—
412C2×C4⋊C8—731no—
413C2×C22⋊C8—731no—
414C2×C22⋊C8—731no—
415C2×C22⋊C8—731no—
416C2×C22⋊C8—731no—
417C2×C22⋊C8—731no—
418C2×C22⋊C8—731no—
419C2×C22⋊C8—731no—
420C2×C22⋊C8—731no—
421C2×C22⋊C8—731no—
422C2×C22⋊C8—731no—
423C2×C22⋊C8—1464no—
424C2×#97—731no—
425C2×#97—731no—
426C2×C4×C8—731no—
427C2×C4×C8—731no—
428#381—731no—
429#381—731no—
430#380—731no—
431#380—731no—
432#380—731no—
433#380—731no—
434#379—731no—
435#379#6440811yescharacteristic
436C4×C22⋊C4—731no—
437C4×C22⋊C4—731no—
438C4×C22⋊C4—731no—
439C4×C22⋊C4—731no—
440#336—731no—
441#336—731no—
442#336—731no—
443#336—731no—
444#336—731no—
445#336—731no—
446#336—731no—
447#336—731no—
448C25C2×#6440811yescharacteristic
449C23×C4—2921no—
450C23×C4—2921no—
451C23×C4—731no—
452C23×C4—731no—
453C23×C4—731no—
454C23×C4—731no—
455C23×C4—731no—
456C23×C4—731no—
457C23×C4—1462no—
458C23×C4—1462no—
459C23×C4—1462no—
460C23×C4—1462no—
461C22×C8—2921no—
462C22×C8—2921no—
463C22×C8—731no—
464C22×C8—731no—
465C22×C8—731no—
466C22×C8—731no—
467C22×C8—731no—
468C22×C8—731no—
469C22×C8—731no—
470C22×C8—731no—
471C22×C8—1462no—
472C22×C8—1462no—
473C22×C8—1462no—
474C22×C8—1462no—
475#117—2921no—
476#117—2921no—
477#117—1462no—
478#117—1462no—
479C2×C4⋊C4—731no—
480C2×C4⋊C4—731no—
481C2×C4⋊C4—731no—
482C2×C4⋊C4—731no—
483C2×C22⋊C4—731no—
484C2×C22⋊C4—731no—
485C2×C22⋊C4—731no—
486C2×C22⋊C4—731no—
487C2×C22⋊C4—731no—
488C2×C22⋊C4—731no—
489C2×C22⋊C4C2×#6440811yescharacteristic
490C2×C22⋊C4C2×#6440811yescharacteristic
491C2×C22⋊C4C2×#6440811yescharacteristic
492C2×C22⋊C4C2×#6440811yescharacteristic
493C2×C22⋊C4C2×#6440811yescharacteristic
494C2×C22⋊C4C2×#6440811yescharacteristic
495C2×C42—731no—
496C2×C42—731no—
497C2×C42—731no—
498C2×C42—731no—
499C4⋊C8—2921no—
500C4⋊C8—2921no—
501C4⋊C8—1462no—
502C4⋊C8—1462no—
503C22⋊C8—2921no—
504C22⋊C8—2921no—
505C22⋊C8—734no—
506C22⋊C8—1462no—
507C22⋊C8—1462no—
508C22⋊C8—1462no—
509C22⋊C8—1462no—
510C22⋊C8—1462no—
511C22⋊C8—1462no—
512C22⋊C8—1462no—
513#97—2921no—
514#97—1462no—
515C4×C8—2921no—
516C4×C8—1462no—
517#95—731no—
518#95—731no—
519#95—731no—
520#95—731no—
521#95—731no—
522#95—731no—
523#95—731no—
524#95—731no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—41no—
531C24—41no—
532C24C22×#6440811yescharacteristic
533C24C22×#6440811yescharacteristic
534C24C22×#6440811yescharacteristic
535C22×C4—2921no—
536C22×C4—2921no—
537C22×C4—2921no—
538C22×C4—2924no—
539C22×C4—2924no—
540C22×C4—2924no—
541C22×C4—2924no—
542C22×C4—731no—
543C22×C4—731no—
544C22×C4—731no—
545C22×C4—732no—
546C22×C4—732no—
547C22×C4—732no—
548C22×C4—732no—
549C22×C4—731no—
550C22×C4—731no—
551C22×C4—731no—
552C22×C4—731no—
553C22×C4—731no—
554C22×C4—1461no—
555C22×C4—1461no—
556C22×C4—1461no—
557C22×C4—1461no—
558C22×C4—1461no—
559C22×C4—1461no—
560C22×C4—1462no—
561C22×C4—1462no—
562C22×C4—1462no—
563C22×C4—1462no—
564C22×C4—1462no—
565C22×C4—1462no—
566C22×C4—1461no—
567C22×C4—1461no—
568C22×C4—1461no—
569C22×C4—1461no—
570C22×C4—1461no—
571C22×C4—1461no—
572C22×C4—1461no—
573C22×C4—1461no—
574C22×C4C22×#6440811yescharacteristic
575C22×C4C22×#6440811yescharacteristic
576C22×C4C22×#6440811yescharacteristic
577C22×C4C22×#6440811yescharacteristic
578C2×C8—2924no—
579C2×C8—2924no—
580C2×C8—732no—
581C2×C8—732no—
582C2×C8—1461no—
583C2×C8—1461no—
584C2×C8—1461no—
585C2×C8—1461no—
586C2×C8—1461no—
587C2×C8—1461no—
588C2×C8—1461no—
589C2×C8—1461no—
590C2×C8—1461no—
591C2×C8—1461no—
592C2×C8—1461no—
593C2×C8—1461no—
594C2×C8—1461no—
595C2×C8—1461no—
596C2×C8—1461no—
597C2×C8—1461no—
598C2×C8—1461no—
599C2×C8—1461no—
600C2×C8—1461no—
601C2×C8—1461no—
602C2×C8—1461no—
603C2×C8—1461no—
604C4⋊C4—2921no—
605C4⋊C4—2921no—
606C4⋊C4—1462no—
607C4⋊C4—1462no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—41no—
613C22⋊C4—41no—
614C22⋊C4—2921no—
615C22⋊C4—2921no—
616C22⋊C4—1462no—
617C22⋊C4—1462no—
618C22⋊C4—1462no—
619C22⋊C4—1462no—
620C42—1461no—
621C42—1461no—
622C42—1461no—
623C42—1461no—
624C42—1461no—
625C42—1461no—
626C42—1461no—
627C42—1461no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—28no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23#1455667012yes—
652C23D4×#6440812yes—
653C23#1455667812yes—
654C23#1455667812yes—
655C23#1455667812yes—
656C23C23×#6440811yescharacteristic
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—2921no—
670C2×C4—2921no—
671C2×C4—2921no—
672C2×C4—2921no—
673C2×C4—2924no—
674C2×C4—2924no—
675C2×C4—2924no—
676C2×C4—731no—
677C2×C4—731no—
678C2×C4—731no—
679C2×C4—731no—
680C2×C4—731no—
681C2×C4—731no—
682C2×C4—732no—
683C2×C4—732no—
684C2×C4—1461no—
685C2×C4—1461no—
686C2×C4—1461no—
687C2×C4—1461no—
688C2×C4—1461no—
689C2×C4—1461no—
690C2×C4—1461no—
691C2×C4—1461no—
692C2×C4—1461no—
693C2×C4—1461no—
694C2×C4—1461no—
695C2×C4—1461no—
696C2×C4—1461no—
697C2×C4—1461no—
698C2×C4—1461no—
699C2×C4—1462no—
700C2×C4—1462no—
701C2×C4—1462no—
702C2×C4—1462no—
703C2×C4—1462no—
704C2×C4—1462no—
705C2×C4—1462no—
706C2×C4—1462no—
707C2×C4—1461no—
708C2×C4—1461no—
709C2×C4—1461no—
710C2×C4—1461no—
711C8—2921no—
712C8—2921no—
713C8—2921no—
714C8—2921no—
715C8—2921no—
716C8—2921no—
717C8—1462no—
718C8—1462no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—416no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22#1798961114yescomplemented
741C22C2×#1455667011yescharacteristic
742C22C2×D4×#6440811yescharacteristic
743C22#1798965411yescharacteristic
744C22C2×#1455667811yescharacteristic
745C22C2×#1455667811yescharacteristic
746C22C2×#1455667811yescharacteristic
747C22#1798966511yescharacteristic
748C4—41no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—2921no—
753C4—2921no—
754C4—2921no—
755C4—2921no—
756C4—2921no—
757C4—731no—
758C4—731no—
759C4—731no—
760C4—731no—
761C4—1462no—
762C4—1462no—
763C2—24no—
764C2—42no—
765C2—42no—
766C2#2262643711yescharacteristic
767C2C2×#1798961111yescharacteristic
768C2#2262662011yescharacteristic
769C2#2262664611yescharacteristic
770C2#2262666311yescharacteristic
771C2#2262679711yescharacteristic
772C2#2262680311yescharacteristic
subgroupG/H
center, FrattiniC23C23×#64408
commutator, socleC23×C73C23×C4
Fitting#379×C73C4
prime radicalC25×C73C2×C4
cosocleC22×Dic73C24
hypercenter#379#64408
hypocenterC73#22558
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#17989611C2semidirect
3. #22626005C2semidirect
4. #22626004C2semidirect
5. #22626001C2semidirect
6. #22626000C2semidirect
7. #22625875C2semidirect
8. #22625874C2semidirect
9. #22625824C2semidirect
10. #22625789C2semidirect
12. #22625668C2semidirect
13. C22⋊C4×#10596833C2semidirect
14. #22625661C2semidirect
19. C2×#14556658C22semidirect
20. C2×#14556658C22semidirect
21. C2×C4⋊#10596833C22semidirect
22. C2×C4⋊#10596833C22semidirect
34. C2×#14556646C22semidirect
35. C2×#14556646C22semidirect
36. C2×C4×#10596833C22semidirect
37. C2×C4×#10596833C22semidirect
38. #17989453C22semidirect
39. #17989453C22semidirect
40. #17989453C22semidirect
41. #17989453C22semidirect
42. #17989453C22semidirect
43. #17989453C22semidirect
44. #17989453C22semidirect
45. #17989453C22semidirect
353. C22×C73#433semidirect
402. C73#22558semidirect
740. C22#17989611semidirect

Maximal subgroups

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

subgroupindex
C2×#179896112
C22×C22⋊#105968332
#226260052
#226260042
#226260012
#226260002
#226258752
#226258742
#226258242
#226257892
#226257532
#226256682
C22⋊C4×#105968332
#226256612
#226123092
#2255873