Finite Group Databasebeta

← #33104525

Subgroups — #33104525

Order 18688.

944 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988659C211yesmaximal, characteristic
2#22612376C211yesmaximal, characteristic
3#22610652C211yesmaximal, characteristic, complemented
4#22610649C211yesmaximal, characteristic, complemented
5#22610113C211yesmaximal, characteristic, complemented
6#22610109C211yesmaximal, characteristic, complemented
7#22610109C211yesmaximal, characteristic, complemented
8#22610108C211yesmaximal, characteristic, complemented
9#22610050C211yesmaximal, characteristic, complemented
10#22609913C211yesmaximal, characteristic, complemented
11#22609909C211yesmaximal, characteristic, complemented
12#22609789C211yesmaximal, characteristic, complemented
13#22609627C211yesmaximal, characteristic, complemented
14C2×#17988341C211yesmaximal, characteristic, complemented
15C2×C8×D4×C73C211yesmaximal, characteristic
16C22×#11924012C2211yescharacteristic
17C23×#10596831C2211yescharacteristic
18C2×#14556550C2211yescharacteristic
19C22×C4×Dic73C2211yescharacteristic
20#17988659—24no—
21C2×C4⋊#10596831C2211yescharacteristic
22C2×#14556520C2211yescharacteristic
23C2×#14556520C2211yescharacteristic
24C2×#14556520C2211yescharacteristic
25C2×#14556520C2211yescharacteristic
26C2×#14556520C2211yescharacteristic
27C2×#14556520C2211yescharacteristic
28C2×C22⋊#10596831C2211yescharacteristic
29C2×C22⋊#10596831C2211yescharacteristic
30C2×#14556502C2211yescharacteristic
31#17988480C411yescharacteristic
32#17988480C411yescharacteristic
33#17988473C411yescharacteristic
34#17988473C411yescharacteristic
35#17988467C411yescharacteristic
36#17988467C411yescharacteristic
37#17988462C411yescharacteristic
38#17988462C411yescharacteristic
39C4×C4⋊Dic73C2211yescharacteristic
40C4×C22⋊Dic73C2211yescharacteristic
41C4×C22⋊Dic73C2211yescharacteristic
42#17988433C2211yescharacteristic
43#17988341C2211yescharacteristic
44#17988341C2211yescharacteristic
45#17988341C2211yescharacteristic
46#17988341C2211yescharacteristic
47#17988341C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52#17988341C2211yescharacteristic
53C23×C8×C73C2211yescharacteristic
54C23×C8×C73C2211yescharacteristic
55C2×C4×D4×C73C2211yescharacteristic
56C8×D4×C73—24no—
57C2×C4⋊C8×C73C2211yescharacteristic
58C2×C22⋊C8×C73C2211yescharacteristic
59C2×C22⋊C8×C73C2211yescharacteristic
60C2×C4×C8×C73C2211yescharacteristic
61C23×Dic73C2×C411yescharacteristic
62C23×Dic73C2×C411yescharacteristic
63C2×#11924012—22no—
64C2×#11924012—22no—
65C2×#11924012—41no—
66C22×#10596831—22no—
67C22×#10596831—22no—
68C22×#10596831—41no—
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71C22×#10596831C2311yescharacteristic
72C22×#10596831C2311yescharacteristic
73#14556550—41no—
74#14556550—41no—
75C2×C4⋊Dic73C2×C411yescharacteristic
76C2×C4⋊Dic73C2×C411yescharacteristic
77C2×C4⋊Dic73C2×C411yescharacteristic
78C2×C4⋊Dic73C2×C411yescharacteristic
79C2×C22⋊Dic73C2×C411yescharacteristic
80C2×C22⋊Dic73C2×C411yescharacteristic
81C2×C22⋊Dic73C2×C411yescharacteristic
82C2×C22⋊Dic73C2×C411yescharacteristic
83C2×C22⋊Dic73C2×C411yescharacteristic
84C2×C22⋊Dic73C2×C411yescharacteristic
85C2×C4×Dic73—41no—
86C2×C4×Dic73—41no—
87C2×C4×Dic73C2×C411yescharacteristic
88C2×C4×Dic73C2×C411yescharacteristic
89C2×C4×Dic73C2311yescharacteristic
90C2×C4×Dic73C2311yescharacteristic
91C2×C4×Dic73C2311yescharacteristic
92C2×C4×Dic73C2311yescharacteristic
93C4⋊#10596831—22no—
94#14556520—22no—
95#14556520—22no—
96#14556520—41no—
97#14556520—41no—
98#14556520—41no—
99#14556520—41no—
100C22⋊#10596831—22no—
101C22⋊#10596831—22no—
102#14556502—22no—
103#14556498C2×C411yescharacteristic
104#14556498C2×C411yescharacteristic
105#14556498C2×C411yescharacteristic
106#14556498C2×C411yescharacteristic
107#14556498C2×C411yescharacteristic
108#14556498C2×C411yescharacteristic
109#14556498C2×C411yescharacteristic
110#14556498C2×C411yescharacteristic
111#14556498C2×C411yescharacteristic
112#14556498C2×C411yescharacteristic
113C22×D4×C73C2×C411yescharacteristic
114C23×C4×C73C2311yescharacteristic
115C23×C4×C73C2311yescharacteristic
116C22×C8×C73—22no—
117C22×C8×C73—22no—
118C22×C8×C73—22no—
119C22×C8×C73—22no—
120C22×C8×C73—41no—
121C22×C8×C73—41no—
122C22×C8×C73C2311yescharacteristic
123C22×C8×C73C2311yescharacteristic
124C22×C8×C73C2311yescharacteristic
125C22×C8×C73C2311yescharacteristic
126C4×D4×C73D414yes—
127C4×D4×C73Q814yes—
128C2×C4⋊C4×C73C2×C411yescharacteristic
129C2×C22⋊C4×C73C2×C411yescharacteristic
130C2×C22⋊C4×C73C2×C411yescharacteristic
131C2×C42×C73C2311yescharacteristic
132C4⋊C8×C73—22no—
133C22⋊C8×C73—22no—
134C22⋊C8×C73—22no—
135C4×C8×C73—22no—
136C22×Dic73—22no—
137C22×Dic73—22no—
138C22×Dic73—22no—
139C22×Dic73—41no—
140C22×Dic73—41no—
141C22×Dic73—41no—
142C22×Dic73C22×C411yescharacteristic
143C22×Dic73C22×C411yescharacteristic
144C22×Dic73C22×C411yescharacteristic
145C22×Dic73C22×C411yescharacteristic
146C22×Dic73C22×C411yescharacteristic
147C22×Dic73C22×C411yescharacteristic
148C22×Dic73C22×C411yescharacteristic
149C22×Dic73C22×C411yescharacteristic
150#11924012—44no—
151C2×#10596831—21no—
152C2×#10596831—21no—
153C2×#10596831—21no—
154C2×#10596831—21no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—44no—
163C2×#10596831#4112yes—
164C4⋊Dic73—22no—
165C4⋊Dic73—41no—
166C4⋊Dic73—41no—
167C4⋊Dic73—41no—
168C22⋊Dic73—22no—
169C22⋊Dic73—22no—
170C22⋊Dic73—22no—
171C22⋊Dic73—41no—
172C22⋊Dic73—41no—
173C22⋊Dic73—41no—
174C4×Dic73—21no—
175C4×Dic73—21no—
176C4×Dic73—21no—
177C4×Dic73—21no—
178C4×Dic73—21no—
179C4×Dic73—21no—
180C4×Dic73—21no—
181C4×Dic73—21no—
182C4×Dic73—41no—
183C4×Dic73—41no—
184C24×C73C22×C411yescharacteristic
185C24×C73C22×C411yescharacteristic
186C2×D4×C73—22no—
187C2×D4×C73—22no—
188C2×D4×C73C4⋊C414yes—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73—21no—
192C22×C4×C73—21no—
193C22×C4×C73—21no—
194C22×C4×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73C22×C411yescharacteristic
198C22×C4×C73C22×C411yescharacteristic
199C22×C4×C73C22×C411yescharacteristic
200C22×C4×C73C22×C411yescharacteristic
201C22×C4×C73C2×D412yes—
202C22×C4×C73C2×D412yes—
203C22×C4×C73C2×Q812yes—
204C22×C4×C73C2×Q812yes—
205C22×C4×C73C2411yescharacteristic
206C2×C8×C73—21no—
207C2×C8×C73—21no—
208C2×C8×C73—21no—
209C2×C8×C73—21no—
210C2×C8×C73—21no—
211C2×C8×C73—21no—
212C2×C8×C73—21no—
213C2×C8×C73—21no—
214C2×C8×C73—21no—
215C2×C8×C73—21no—
216C2×C8×C73—21no—
217C2×C8×C73—44no—
218C2×C8×C73—44no—
219C2×C8×C73#4112yes—
220C4⋊C4×C73C4⋊C414yes—
221C22⋊C4×C73C4⋊C414yes—
222C22⋊C4×C73C4⋊C414yes—
223C42×C73C2×D412yes—
224C42×C73C2×Q812yes—
225C23×C73—21no—
226C23×C73—21no—
227C23×C73—21no—
228C23×C73—21no—
229C23×C73—21no—
230C23×C73—21no—
231C23×C73—21no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73—21no—
235C23×C73C2×C4⋊C412yes—
236C23×C73C2×C4⋊C412yes—
237C23×C73#13112yes—
238C23×C73#13112yes—
239C23×C73C23×C411yescharacteristic
240D4×C73—28no—
241C2×C4×C73—21no—
242C2×C4×C73—21no—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—21no—
246C2×C4×C73—21no—
247C2×C4×C73—21no—
248C2×C4×C73—21no—
249C2×C4×C73—22no—
250C2×C4×C73—22no—
251C2×C4×C73—22no—
252C2×C4×C73—22no—
253C2×C4×C73—22no—
254C2×C4×C73—22no—
255C2×C4×C73—22no—
256C2×C4×C73—22no—
257C2×C4×C73C2×C4⋊C412yes—
258C2×C4×C73C2×C4⋊C412yes—
259C2×C4×C73C2×C4⋊C412yes—
260C2×C4×C73C2×C4⋊C412yes—
261C2×C4×C73C22×D411yescharacteristic
262C2×C4×C73C22×Q811yescharacteristic
263C2×C4×C73C2×#4111yescharacteristic
264C2×C4×C73C2×#4111yescharacteristic
265C2×C4×C73H(5,𝔽2)11yescharacteristic
266C2×C4×C73H(5,𝔽2)11yescharacteristic
267C2×Dic73—21no—
268C2×Dic73—21no—
269C2×Dic73—21no—
270C2×Dic73—21no—
271C2×Dic73—21no—
272C2×Dic73—21no—
273C2×Dic73—21no—
274C2×Dic73—21no—
275C2×Dic73—21no—
276C2×Dic73—21no—
277C2×Dic73—21no—
278C2×Dic73—21no—
279C2×Dic73—21no—
280C2×Dic73—21no—
281C2×Dic73—21no—
282C2×Dic73—21no—
283C2×Dic73—21no—
284C2×Dic73—21no—
285C2×Dic73—21no—
286C2×Dic73—21no—
287C2×Dic73—21no—
288C2×Dic73—21no—
289C2×Dic73—21no—
290C2×Dic73—44no—
291C2×Dic73—44no—
292C2×Dic73#13112yes—
293C8×C73—22no—
294C8×C73—41no—
295C8×C73—41no—
296C8×C73—41no—
297#10596831—22no—
298#10596831—41no—
299#10596831—41no—
300#10596831—41no—
301C22×C73—22no—
302C22×C73—22no—
303C22×C73—22no—
304C22×C73—22no—
305C22×C73—22no—
306C22×C73—22no—
307C22×C73—22no—
308C22×C73—22no—
309C22×C73—22no—
310C22×C73—41no—
311C22×C73—41no—
312C22×C73—41no—
313C22×C73—41no—
314C22×C73#42414yes—
315C22×C73C22×C4⋊C411yescharacteristic
316C22×C73C4×#4111yescharacteristic
317C22×C73#51811yescharacteristic
318C22×C73C2×#13111yescharacteristic
319C22×C73C2×#13111yescharacteristic
320C22×C73C2×#13111yescharacteristic
321C22×C73#56811yescharacteristic
322C4×C73—22no—
323C4×C73—22no—
324C4×C73—22no—
325C4×C73—22no—
326C4×C73#54611yescharacteristic
327C4×C73#54611yescharacteristic
328C4×C73#55411yescharacteristic
329C4×C73#55411yescharacteristic
330Dic73—22no—
331Dic73—41no—
332Dic73—41no—
333Dic73—41no—
334Dic73—41no—
335Dic73—41no—
336Dic73—41no—
337Dic73—41no—
338#22697—731nomaximal, Sylow
339C2×C73—24no—
340C2×C73—42no—
341C2×C73#234911yescharacteristic
342C2×C73C2×#42411yescharacteristic
343C2×C73#290611yescharacteristic
344C2×C73#296611yescharacteristic
345C2×C73#296811yescharacteristic
346C2×C73#297611yescharacteristic
347C2×C73#297711yescharacteristic
348C2×#435—731no—
349C2×C8×D4D7311yescharacteristic
350#2290—731no—
351#1940—731no—
352#1939—731no—
353#1851—731no—
354#1850—731no—
355#1850—731no—
356#1850—731no—
357#1832—731no—
358#1798—731no—
359#1797—731no—
360#1768—731no—
361#1729—731no—
362C2×#336—731no—
363C73#2269711yescharacteristic, complemented, Sylow
364C22×M16—731no—
365C23×C8—731no—
366C23×C8C2×D7311yescharacteristic
367C23×C8C2×D7311yescharacteristic
368C2×C4×D4C2×D7311yescharacteristic
369C2×#117—731no—
370C22×C42—731no—
371#435—1464no—
372C8×D4—24no—
373C2×C4⋊C8—731no—
374C2×C4⋊C8—731no—
375C2×C4⋊C8—731no—
376C2×C4⋊C8—731no—
377C2×C4⋊C8—731no—
378C2×C4⋊C8—731no—
379C2×C4⋊C8—731no—
380C2×C4⋊C8C2×D7311yescharacteristic
381C2×C22⋊C8—731no—
382C2×C22⋊C8—731no—
383C2×C22⋊C8C2×D7311yescharacteristic
384C2×C22⋊C8C2×D7311yescharacteristic
385C2×#97—731no—
386C2×C4×C8C2×D7311yescharacteristic
387#388—731no—
388#388—731no—
389#387—731no—
390#387—731no—
391#386—731no—
392#386—731no—
393#385—731no—
394#385—731no—
395C4×C4⋊C4—731no—
396C4×C22⋊C4—731no—
397C4×C22⋊C4—731no—
398#376—731no—
399#336—731no—
400#336—731no—
401#336—731no—
402#336—731no—
403#336—731no—
404#336—731no—
405#336—731no—
406#336—731no—
407#336—731no—
408#336—731no—
409C22×D4C4×D7311yescharacteristic
410C23×C4—731no—
411C23×C4—731no—
412C23×C4C22×D7311yescharacteristic
413C23×C4C22×D7311yescharacteristic
414C2×M16—2921no—
415C2×M16—1462no—
416C2×M16—1462no—
417C22×C8—22no—
418C22×C8—22no—
419C22×C8—22no—
420C22×C8—22no—
421C22×C8—41no—
422C22×C8—41no—
423C22×C8—2921no—
424C22×C8—731no—
425C22×C8—731no—
426C22×C8—731no—
427C22×C8—731no—
428C22×C8—1462no—
429C22×C8—1462no—
430C22×C8C22×D7311yescharacteristic
431C22×C8C22×D7311yescharacteristic
432C22×C8C22×D7311yescharacteristic
433C22×C8C22×D7311yescharacteristic
434C4×D4Dic14614yes—
435C4×D4C22⋊D7314yes—
436#117—2921no—
437#117—2921no—
438C2×C4⋊C4—731no—
439C2×C4⋊C4—731no—
440C2×C4⋊C4—731no—
441C2×C4⋊C4—731no—
442C2×C4⋊C4C4×D7311yescharacteristic
443C2×C22⋊C4—731no—
444C2×C22⋊C4—731no—
445C2×C22⋊C4—731no—
446C2×C22⋊C4—731no—
447C2×C22⋊C4—731no—
448C2×C22⋊C4—731no—
449C2×C22⋊C4C4×D7311yescharacteristic
450C2×C22⋊C4C4×D7311yescharacteristic
451C2×C42—2921no—
452C2×C42—2921no—
453C2×C42—731no—
454C2×C42—731no—
455C2×C42—731no—
456C2×C42—731no—
457C2×C42—731no—
458C2×C42—731no—
459C2×C42C22×D7311yescharacteristic
460C4⋊C8—22no—
461C4⋊C8—2921no—
462C4⋊C8—2921no—
463C4⋊C8—2921no—
464C4⋊C8—2921no—
465C4⋊C8—1462no—
466C4⋊C8—1462no—
467C4⋊C8—1462no—
468C22⋊C8—22no—
469C22⋊C8—22no—
470C22⋊C8—1462no—
471C22⋊C8—1462no—
472#97—1462no—
473C4×C8—22no—
474#95—731no—
475#95—731no—
476#95—731no—
477#95—731no—
478#95—731no—
479#95—731no—
480#95—731no—
481#95—731no—
482#95—731no—
483#95—731no—
484C24C2×C4×D7311yescharacteristic
485C24C2×C4×D7311yescharacteristic
486C2×D4—22no—
487C2×D4—22no—
488C2×D4#1192400714yes—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—2921no—
498C22×C4—2921no—
499C22×C4—2921no—
500C22×C4—731no—
501C22×C4—731no—
502C22×C4—731no—
503C22×C4—731no—
504C22×C4—731no—
505C22×C4—731no—
506C22×C4—731no—
507C22×C4—731no—
508C22×C4—1462no—
509C22×C4—1462no—
510C22×C4—1462no—
511C22×C4C2×C4×D7311yescharacteristic
512C22×C4C2×C4×D7311yescharacteristic
513C22×C4C2×C4×D7311yescharacteristic
514C22×C4C2×C4×D7311yescharacteristic
515C22×C4C2×C22⋊D7312yes—
516C22×C4C2×C22⋊D7312yes—
517C22×C4C2×Dic14612yes—
518C22×C4C2×Dic14612yes—
519C22×C4C23×D7311yescharacteristic
520M16—2924no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—44no—
533C2×C8—44no—
534C2×C8—2924no—
535C2×C8—732no—
536C2×C8—1461no—
537C2×C8—1461no—
538C2×C8—1461no—
539C2×C8—1461no—
540C2×C8—1461no—
541C2×C8—1461no—
542C2×C8—1461no—
543C2×C8—1461no—
544C2×C8—1461no—
545C2×C8—1461no—
546C2×C8—1461no—
547C2×C8#1192402712yes—
548C4⋊C4—2921no—
549C4⋊C4—2921no—
550C4⋊C4—2921no—
551C4⋊C4—1462no—
552C4⋊C4#1192400714yes—
553C22⋊C4—2921no—
554C22⋊C4—2921no—
555C22⋊C4—2921no—
556C22⋊C4—1462no—
557C22⋊C4—1462no—
558C22⋊C4—1462no—
559C22⋊C4#1192400714yes—
560C22⋊C4#1192400714yes—
561C42—2921no—
562C42—2921no—
563C42—1461no—
564C42—1461no—
565C42—1461no—
566C42—1461no—
567C42—1461no—
568C42—1461no—
569C42—1461no—
570C42—1461no—
571C42C2×C22⋊D7312yes—
572C42C2×Dic14612yes—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23C2×#1192400712yes—
584C23C2×#1192400712yes—
585C23#1455659712yes—
586C23#1455659712yes—
587C23C22×C4×D7311yescharacteristic
588D4—28no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—2924no—
606C2×C4—2924no—
607C2×C4—732no—
608C2×C4—1461no—
609C2×C4—1461no—
610C2×C4—1461no—
611C2×C4—1461no—
612C2×C4—1461no—
613C2×C4—1461no—
614C2×C4—1461no—
615C2×C4—1461no—
616C2×C4—1461no—
617C2×C4—1461no—
618C2×C4—1461no—
619C2×C4—1461no—
620C2×C4—1461no—
621C2×C4—1461no—
622C2×C4—1461no—
623C2×C4—1461no—
624C2×C4—1461no—
625C2×C4—1461no—
626C2×C4—1461no—
627C2×C4—1461no—
628C2×C4—1461no—
629C2×C4—1461no—
630C2×C4—1461no—
631C2×C4C2×#1192400712yes—
632C2×C4C2×#1192400712yes—
633C2×C4C2×#1192400712yes—
634C2×C4C2×#1192400712yes—
635C2×C4C22×C22⋊D7311yescharacteristic
636C2×C4C22×Dic14611yescharacteristic
637C2×C4#41×D7311yescharacteristic
638C2×C4C2×#1192402711yescharacteristic
639C2×C4#1455663611yescharacteristic
640C2×C4#1455663711yescharacteristic
641C8—22no—
642C8—41no—
643C8—41no—
644C8—41no—
645C8—2921no—
646C8—2921no—
647C8—2921no—
648C8—1462no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—22no—
657C22—22no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22#1798861314yes—
663C22C22×#1192400711yescharacteristic
664C22C4×#1192402711yescharacteristic
665C22#1798905911yescharacteristic
666C22#131×D7311yescharacteristic
667C22C2×#1455659711yescharacteristic
668C22C2×#1455659711yescharacteristic
669C22#1798935211yescharacteristic
670C4—22no—
671C4—22no—
672C4—22no—
673C4—22no—
674C4—2921no—
675C4—2921no—
676C4—2921no—
677C4—2921no—
678C4—2921no—
679C4—2921no—
680C4—2921no—
681C4—1462no—
682C4#1798922511yescharacteristic
683C4#1798923111yescharacteristic
684C4#1798929411yescharacteristic
685C4#1798929611yescharacteristic
686C2—24no—
687C2—42no—
688C2#2261283611yescharacteristic
689C2C2×#1798861311yescharacteristic
690C2#2261849711yescharacteristic
691C2#2261889911yescharacteristic
692C2#2261891911yescharacteristic
693C2#2261897311yescharacteristic
694C2#2261898411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC2×C8×D4×C73C2
prime radicalC22×D4×C73C2×C4
cosocleC22×C4×C73C24
hypercenterC2×C8×D4D73
hypocenterC73#22697
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
3. #22610652C2semidirect
4. #22610649C2semidirect
5. #22610113C2semidirect
6. #22610109C2semidirect
7. #22610109C2semidirect
8. #22610108C2semidirect
9. #22610050C2semidirect
10. #22609913C2semidirect
11. #22609909C2semidirect
12. #22609789C2semidirect
13. #22609627C2semidirect
14. C2×#17988341C2semidirect
363. C73#22697semidirect

Maximal subgroups

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

subgroupindex
C2×#179886592
#226123762
#226106522
#226106492
#226101132
#226101092
#226101082
#226100502
#226099132
#226099092
#226097892
#226096272
C2×#179883412
C2×C8×D4×C732
#2269773