Finite Group Databasebeta

← #33104069

Subgroups — #33104069

Order 18688.

964 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988659C211yesmaximal, characteristic
2C2×#17988615C211yesmaximal, characteristic, complemented
3C2×#17988613C211yesmaximal, characteristic, complemented
4#22612396C211yesmaximal, characteristic
5#22610654C211yesmaximal, characteristic, complemented
6#22610652C211yesmaximal, characteristic, complemented
7#22610114C211yesmaximal, characteristic, complemented
8#22610113C211yesmaximal, characteristic, complemented
9#22610109C211yesmaximal, characteristic, complemented
10#22610108C211yesmaximal, characteristic, complemented
11#22610082C211yesmaximal, characteristic, complemented
12#22609913C211yesmaximal, characteristic, complemented
13#22609913C211yesmaximal, characteristic, complemented
14#22609785C211yesmaximal, characteristic, complemented
15C2×#435×C73C211yesmaximal, characteristic
16C22×#11924012C2211yescharacteristic
17C23×#10596831C2211yescharacteristic
18C2×#14556550C2211yescharacteristic
19C2×#14556550C2211yescharacteristic
20#17988659—24no—
21#17988615—24no—
22#17988613—24no—
23C2×C4⋊#10596831C2211yescharacteristic
24C2×#14556520C2211yescharacteristic
25C2×#14556520C2211yescharacteristic
26C2×#14556520C2211yescharacteristic
27C2×#14556520C2211yescharacteristic
28C2×#14556520C2211yescharacteristic
29C2×#14556520C2211yescharacteristic
30C2×#14556520C2211yescharacteristic
31C2×#14556520C2211yescharacteristic
32C2×#14556520C2211yescharacteristic
33C2×#14556520C2211yescharacteristic
34C2×C22⋊#10596831C2211yescharacteristic
35C2×C22⋊#10596831C2211yescharacteristic
36C2×#14556502C2211yescharacteristic
37#17988490C411yescharacteristic
38#17988490C411yescharacteristic
39#17988486C411yescharacteristic
40#17988486C411yescharacteristic
41#17988480C411yescharacteristic
42#17988480C411yescharacteristic
43#17988480C411yescharacteristic
44#17988480C411yescharacteristic
45C4×C4⋊Dic73C2211yescharacteristic
46C4×C22⋊Dic73C2211yescharacteristic
47C4×C22⋊Dic73C2211yescharacteristic
48C42×Dic73C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54#17988341C2211yescharacteristic
55C22×M16×C73C2211yescharacteristic
56C23×C8×C73C2211yescharacteristic
57C2×C4×D4×C73C2211yescharacteristic
58#435×C73—24no—
59C2×C4⋊C8×C73C2211yescharacteristic
60C2×C22⋊C8×C73C2211yescharacteristic
61C2×C22⋊C8×C73C2211yescharacteristic
62C2×#97×C73C2211yescharacteristic
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—22no—
74#14556550—22no—
75#14556550—22no—
76#14556550—22no—
77C2×C4⋊Dic73C2×C411yescharacteristic
78C2×C4⋊Dic73C2×C411yescharacteristic
79C2×C4⋊Dic73C2×C411yescharacteristic
80C2×C4⋊Dic73C2×C411yescharacteristic
81C2×C4⋊Dic73C2×C411yescharacteristic
82C2×C4⋊Dic73C2×C411yescharacteristic
83C2×C22⋊Dic73C2×C411yescharacteristic
84C2×C22⋊Dic73C2×C411yescharacteristic
85C2×C22⋊Dic73C2×C411yescharacteristic
86C2×C22⋊Dic73C2×C411yescharacteristic
87C2×C22⋊Dic73C2×C411yescharacteristic
88C2×C22⋊Dic73C2×C411yescharacteristic
89C2×C22⋊Dic73C2×C411yescharacteristic
90C2×C22⋊Dic73C2×C411yescharacteristic
91C2×C4×Dic73C2×C411yescharacteristic
92C2×C4×Dic73C2×C411yescharacteristic
93C2×C4×Dic73C2×C411yescharacteristic
94C2×C4×Dic73C2×C411yescharacteristic
95C2×C4×Dic73C2311yescharacteristic
96C2×C4×Dic73C2311yescharacteristic
97C2×C4×Dic73C2311yescharacteristic
98C2×C4×Dic73C2311yescharacteristic
99C4⋊#10596831—22no—
100#14556520—22no—
101#14556520—22no—
102#14556520—22no—
103#14556520—22no—
104#14556520—22no—
105#14556520—22no—
106#14556520—22no—
107#14556520—41no—
108#14556520—41no—
109#14556520D414yescomplemented
110C22⋊#10596831—22no—
111C22⋊#10596831—22no—
112#14556502—22no—
113#14556498C2×C411yescharacteristic
114#14556498C2×C411yescharacteristic
115#14556498C2×C411yescharacteristic
116#14556498C2×C411yescharacteristic
117#14556498C2×C411yescharacteristic
118#14556498C2×C411yescharacteristic
119C22×D4×C73C2×C411yescharacteristic
120C23×C4×C73C2311yescharacteristic
121C23×C4×C73C2311yescharacteristic
122C2×M16×C73—22no—
123C2×M16×C73—22no—
124C2×M16×C73—41no—
125C22×C8×C73—22no—
126C22×C8×C73—22no—
127C22×C8×C73—41no—
128C22×C8×C73C2311yescharacteristic
129C22×C8×C73C2311yescharacteristic
130C22×C8×C73C2311yescharacteristic
131C22×C8×C73C2311yescharacteristic
132C4×D4×C73D414yes—
133C4×D4×C73Q814yes—
134C2×C4⋊C4×C73C2×C411yescharacteristic
135C2×C22⋊C4×C73C2×C411yescharacteristic
136C2×C22⋊C4×C73C2×C411yescharacteristic
137C2×C42×C73C2311yescharacteristic
138C4⋊C8×C73—22no—
139C22⋊C8×C73—22no—
140C22⋊C8×C73—22no—
141#97×C73—22no—
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×#10596831C2×D412yes—
164C4⋊Dic73—22no—
165C4⋊Dic73—22no—
166C4⋊Dic73—22no—
167C4⋊Dic73—22no—
168C4⋊Dic73—41no—
169C4⋊Dic73—41no—
170C22⋊Dic73—22no—
171C22⋊Dic73—22no—
172C22⋊Dic73—22no—
173C22⋊Dic73—22no—
174C22⋊Dic73—22no—
175C22⋊Dic73—22no—
176C22⋊Dic73—41no—
177C22⋊Dic73—41no—
178C4×Dic73—21no—
179C4×Dic73—21no—
180C4×Dic73—21no—
181C4×Dic73—21no—
182C4×Dic73—21no—
183C4×Dic73—21no—
184C4×Dic73—22no—
185C4×Dic73—41no—
186C4×Dic73—41no—
187C4×Dic73—41no—
188C4×Dic73C2×D412yes—
189C4×Dic73#4112yes—
190C24×C73C22×C411yescharacteristic
191C24×C73C22×C411yescharacteristic
192C2×D4×C73—41no—
193C2×D4×C73—41no—
194C2×D4×C73C4⋊C414yes—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201C22×C4×C73—21no—
202C22×C4×C73—21no—
203C22×C4×C73C22×C411yescharacteristic
204C22×C4×C73C22×C411yescharacteristic
205C22×C4×C73C22×C411yescharacteristic
206C22×C4×C73C22×C411yescharacteristic
207C22×C4×C73C2×D412yes—
208C22×C4×C73C2×D412yes—
209C22×C4×C73C2×Q812yes—
210C22×C4×C73C2×Q812yes—
211C22×C4×C73C2411yescharacteristic
212M16×C73—44no—
213C2×C8×C73—21no—
214C2×C8×C73—21no—
215C2×C8×C73—21no—
216C2×C8×C73—21no—
217C2×C8×C73—21no—
218C2×C8×C73—21no—
219C2×C8×C73—21no—
220C2×C8×C73—21no—
221C2×C8×C73—21no—
222C2×C8×C73—21no—
223C2×C8×C73—21no—
224C2×C8×C73—44no—
225C2×C8×C73C2×D412yes—
226C4⋊C4×C73C4⋊C414yes—
227C22⋊C4×C73C4⋊C414yes—
228C22⋊C4×C73C4⋊C414yes—
229C42×C73C2×D412yes—
230C42×C73C2×Q812yes—
231C23×C73—21no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73—21no—
240C23×C73—21no—
241C23×C73—21no—
242C23×C73—21no—
243C23×C73C2×C4⋊C412yes—
244C23×C73C2×C4⋊C412yes—
245C23×C73C23×C411yescharacteristic
246D4×C73—44no—
247C2×C4×C73—21no—
248C2×C4×C73—21no—
249C2×C4×C73—21no—
250C2×C4×C73—21no—
251C2×C4×C73—21no—
252C2×C4×C73—21no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—22no—
256C2×C4×C73—22no—
257C2×C4×C73—22no—
258C2×C4×C73—22no—
259C2×C4×C73—22no—
260C2×C4×C73—22no—
261C2×C4×C73—22no—
262C2×C4×C73—22no—
263C2×C4×C73C2×C4⋊C412yes—
264C2×C4×C73C2×C4⋊C412yes—
265C2×C4×C73C2×C4⋊C412yes—
266C2×C4×C73C2×C4⋊C412yes—
267C2×C4×C73C22×D411yescharacteristic
268C2×C4×C73C22×D411yescharacteristic
269C2×C4×C73C22×Q811yescharacteristic
270C2×C4×C73C2×#4111yescharacteristic
271C2×C4×C73H(5,𝔽2)11yescharacteristic
272C2×C4×C732−1+411yescharacteristic
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—21no—
291C2×Dic73—21no—
292C2×Dic73—21no—
293C2×Dic73—21no—
294C2×Dic73C4×D412yes—
295C2×Dic73C4×D412yes—
296C2×Dic73#13112yes—
297C8×C73—22no—
298C8×C73—41no—
299C8×C73—41no—
300C8×C73—41no—
301#10596831—22no—
302#10596831—41no—
303#10596831—41no—
304#10596831—41no—
305C22×C73—22no—
306C22×C73—22no—
307C22×C73—22no—
308C22×C73—22no—
309C22×C73—22no—
310C22×C73—22no—
311C22×C73—41no—
312C22×C73—41no—
313C22×C73—41no—
314C22×C73—41no—
315C22×C73—41no—
316C22×C73—41no—
317C22×C73—41no—
318C22×C73—41no—
319C22×C73C22×C4⋊C411yescharacteristic
320C22×C73C2×C4×D411yescharacteristic
321C22×C73#52011yescharacteristic
322C22×C73C2×#13111yescharacteristic
323C22×C73#56811yescharacteristic
324C22×C73#56811yescharacteristic
325C22×C73#56811yescharacteristic
326C4×C73—22no—
327C4×C73—22no—
328C4×C73—22no—
329C4×C73—22no—
330C4×C73D4211yescharacteristic
331C4×C73#54711yescharacteristic
332C4×C73D4×Q811yescharacteristic
333C4×C73#55411yescharacteristic
334Dic73—22no—
335Dic73—22no—
336Dic73—22no—
337Dic73—41no—
338Dic73—41no—
339Dic73—41no—
340Dic73—41no—
341Dic73—41no—
342#22652—731nomaximal, Sylow
343C2×C73—42no—
344C2×C73—42no—
345C2×C73D4×C4⋊C411yescharacteristic
346C2×C73#290511yescharacteristic
347C2×C73#290611yescharacteristic
348C2×C73#293211yescharacteristic
349C2×C73#293511yescharacteristic
350C2×C73#299211yescharacteristic
351C2×C73#299511yescharacteristic
352C2×#435—731no—
353C2×#435D7311yescharacteristic
354C2×#424—731no—
355C2×#424—731no—
356#2293—731no—
357#1940—731no—
358#1940—731no—
359#1851—731no—
360#1851—731no—
361#1850—731no—
362#1850—731no—
363#1842—731no—
364#1798—731no—
365#1798—731no—
366#1767—731no—
367C73#2265211yescharacteristic, complemented, Sylow
368C22×M16—731no—
369C22×M16C2×D7311yescharacteristic
370C23×C8—731no—
371C23×C8C2×D7311yescharacteristic
372C2×C4×D4C2×D7311yescharacteristic
373C2×#117—731no—
374C2×#117—731no—
375#435—24no—
376#435—1464no—
377#424—1464no—
378#424—1464no—
379C2×C4⋊C8—731no—
380C2×C4⋊C8—731no—
381C2×C4⋊C8—731no—
382C2×C4⋊C8—731no—
383C2×C4⋊C8—731no—
384C2×C4⋊C8—731no—
385C2×C4⋊C8—731no—
386C2×C4⋊C8—731no—
387C2×C4⋊C8—731no—
388C2×C4⋊C8—731no—
389C2×C4⋊C8—731no—
390C2×C4⋊C8C2×D7311yescharacteristic
391C2×C22⋊C8—731no—
392C2×C22⋊C8—731no—
393C2×C22⋊C8C2×D7311yescharacteristic
394C2×C22⋊C8C2×D7311yescharacteristic
395C2×#97—731no—
396C2×#97C2×D7311yescharacteristic
397#390—731no—
398#390—731no—
399#389—731no—
400#389—731no—
401#388—731no—
402#388—731no—
403#388—731no—
404#388—731no—
405C4×C4⋊C4—731no—
406C4×C22⋊C4—731no—
407C4×C22⋊C4—731no—
408C43—731no—
409#336—731no—
410#336—731no—
411#336—731no—
412#336—731no—
413#336—731no—
414#336—731no—
415C22×D4C4×D7311yescharacteristic
416C23×C4C22×D7311yescharacteristic
417C23×C4C22×D7311yescharacteristic
418C2×M16—22no—
419C2×M16—22no—
420C2×M16—41no—
421C2×M16—2921no—
422C2×M16—1462no—
423C2×M16—1462no—
424C22×C8—22no—
425C22×C8—22no—
426C22×C8—41no—
427C22×C8—2921no—
428C22×C8—731no—
429C22×C8—731no—
430C22×C8—731no—
431C22×C8—731no—
432C22×C8—1462no—
433C22×C8—1462no—
434C22×C8C22×D7311yescharacteristic
435C22×C8C22×D7311yescharacteristic
436C22×C8C22×D7311yescharacteristic
437C22×C8C22×D7311yescharacteristic
438C4×D4Dic14614yes—
439C4×D4C22⋊D7314yes—
440#117—1462no—
441#117—1462no—
442#117—1462no—
443#117—1462no—
444C2×C4⋊C4—731no—
445C2×C4⋊C4—731no—
446C2×C4⋊C4—731no—
447C2×C4⋊C4—731no—
448C2×C4⋊C4—731no—
449C2×C4⋊C4—731no—
450C2×C4⋊C4C4×D7311yescharacteristic
451C2×C22⋊C4—731no—
452C2×C22⋊C4—731no—
453C2×C22⋊C4—731no—
454C2×C22⋊C4—731no—
455C2×C22⋊C4—731no—
456C2×C22⋊C4—731no—
457C2×C22⋊C4—731no—
458C2×C22⋊C4—731no—
459C2×C22⋊C4C4×D7311yescharacteristic
460C2×C22⋊C4C4×D7311yescharacteristic
461C2×C42—731no—
462C2×C42—731no—
463C2×C42—731no—
464C2×C42—731no—
465C2×C42—731no—
466C2×C42—731no—
467C2×C42—731no—
468C2×C42—731no—
469C2×C42C22×D7311yescharacteristic
470C4⋊C8—22no—
471C4⋊C8—2921no—
472C4⋊C8—2921no—
473C4⋊C8—734no—
474C4⋊C8—1462no—
475C4⋊C8—1462no—
476C4⋊C8—1462no—
477C4⋊C8—1462no—
478C4⋊C8—1462no—
479C4⋊C8—1462no—
480C4⋊C8—1462no—
481C4⋊C8—1462no—
482C22⋊C8—22no—
483C22⋊C8—22no—
484C22⋊C8—1462no—
485C22⋊C8—1462no—
486#97—22no—
487#97—1462no—
488#95—731no—
489#95—731no—
490#95—731no—
491#95—731no—
492#95—731no—
493#95—731no—
494C24C2×C4×D7311yescharacteristic
495C24C2×C4×D7311yescharacteristic
496C2×D4—41no—
497C2×D4—41no—
498C2×D4#1192400714yes—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—731no—
508C22×C4—731no—
509C22×C4—731no—
510C22×C4—731no—
511C22×C4—731no—
512C22×C4—731no—
513C22×C4—731no—
514C22×C4—731no—
515C22×C4C2×C4×D7311yescharacteristic
516C22×C4C2×C4×D7311yescharacteristic
517C22×C4C2×C4×D7311yescharacteristic
518C22×C4C2×C4×D7311yescharacteristic
519C22×C4C2×C22⋊D7312yes—
520C22×C4C2×C22⋊D7312yes—
521C22×C4C2×Dic14612yes—
522C22×C4C2×Dic14612yes—
523C22×C4C23×D7311yescharacteristic
524M16—44no—
525M16—2924no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—44no—
538C2×C8—2924no—
539C2×C8—732no—
540C2×C8—1461no—
541C2×C8—1461no—
542C2×C8—1461no—
543C2×C8—1461no—
544C2×C8—1461no—
545C2×C8—1461no—
546C2×C8—1461no—
547C2×C8—1461no—
548C2×C8—1461no—
549C2×C8—1461no—
550C2×C8—1461no—
551C2×C8D4×D7312yes—
552C4⋊C4—2921no—
553C4⋊C4—2921no—
554C4⋊C4—1462no—
555C4⋊C4—1462no—
556C4⋊C4—1462no—
557C4⋊C4—1462no—
558C4⋊C4#1192400714yes—
559C22⋊C4—2921no—
560C22⋊C4—2921no—
561C22⋊C4—1462no—
562C22⋊C4—1462no—
563C22⋊C4—1462no—
564C22⋊C4—1462no—
565C22⋊C4—1462no—
566C22⋊C4—1462no—
567C22⋊C4#1192400714yes—
568C22⋊C4#1192400714yes—
569C42—2921no—
570C42—2921no—
571C42—2921no—
572C42—732no—
573C42—732no—
574C42—1462no—
575C42—1461no—
576C42—1461no—
577C42—1461no—
578C42—1461no—
579C42—1461no—
580C42—1461no—
581C42C2×C22⋊D7312yes—
582C42C2×Dic14612yes—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23C2×#1192400712yes—
596C23C2×#1192400712yes—
597C23C22×C4×D7311yescharacteristic
598D4—44no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—732no—
616C2×C4—732no—
617C2×C4—732no—
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×C4—1461no—
632C2×C4—1461no—
633C2×C4—1461no—
634C2×C4—1461no—
635C2×C4—1461no—
636C2×C4—1461no—
637C2×C4—1461no—
638C2×C4—1461no—
639C2×C4C2×#1192400712yes—
640C2×C4C2×#1192400712yes—
641C2×C4C2×#1192400712yes—
642C2×C4C2×#1192400712yes—
643C2×C4C2×D4×D7311yescharacteristic
644C2×C4C22×C22⋊D7311yescharacteristic
645C2×C4C22×Dic14611yescharacteristic
646C2×C4#41×D7311yescharacteristic
647C2×C4#1455663611yescharacteristic
648C2×C4#1455663811yescharacteristic
649C8—22no—
650C8—41no—
651C8—41no—
652C8—41no—
653C8—2921no—
654C8—2921no—
655C8—2921no—
656C8—1462no—
657C22—22no—
658C22—22no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22C22×#1192400711yescharacteristic
672C22C4×D4×D7311yescharacteristic
673C22#1798906611yescharacteristic
674C22#131×D7311yescharacteristic
675C22#1798935211yescharacteristic
676C22#1798935311yescharacteristic
677C22#1798935311yescharacteristic
678C4—22no—
679C4—22no—
680C4—22no—
681C4—22no—
682C4—2921no—
683C4—2921no—
684C4—2921no—
685C4—2921no—
686C4—2921no—
687C4—1462no—
688C4—1462no—
689C4—1462no—
690C4D4×C22⋊D7311yescharacteristic
691C4#1798923611yescharacteristic
692C4D4×Dic14611yescharacteristic
693C4#1798929611yescharacteristic
694C2—42no—
695C2—42no—
696C2D4×#1192400711yescharacteristic
697C2#2261849411yescharacteristic
698C2#2261849711yescharacteristic
699C2#2261864511yescharacteristic
700C2#2261867211yescharacteristic
701C2#2261906611yescharacteristic
702C2#2261909711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC2×#435×C73C2
prime radicalC22×D4×C73C2×C4
cosocleC22×C4×C73C24
hypercenterC2×#435D73
hypocenterC73#22652
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×#17988615C2semidirect
3. C2×#17988613C2semidirect
5. #22610654C2semidirect
6. #22610652C2semidirect
7. #22610114C2semidirect
8. #22610113C2semidirect
9. #22610109C2semidirect
10. #22610108C2semidirect
11. #22610082C2semidirect
12. #22609913C2semidirect
13. #22609913C2semidirect
14. #22609785C2semidirect
109. #14556520D4semidirect
367. C73#22652semidirect

Maximal subgroups

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

subgroupindex
C2×#179886592
C2×#179886152
C2×#179886132
#226123962
#226106542
#226106522
#226101142
#226101132
#226101092
#226101082
#226100822
#226099132
#226097852
C2×#435×C732
#2265273