Finite Group Databasebeta

← #33085506

Subgroups — #33085506

Order 18688.

1462 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989066C211yesmaximal, characteristic
2C2×#17988612C211yesmaximal, characteristic, complemented
3C2×#17988585C211yesmaximal, characteristic
4C2×#17988580C211yesmaximal, characteristic
5#22612552C211yesmaximal, characteristic, complemented
6#22609947C211yesmaximal, characteristic, complemented
7#22609945C211yesmaximal, characteristic, complemented
8#22609941C211yesmaximal, characteristic, complemented
9#22609939C211yesmaximal, characteristic, complemented
10#22609935C211yesmaximal, characteristic, complemented
11#22609933C211yesmaximal, characteristic, complemented
12#22609929C211yesmaximal, characteristic, complemented
13#22609649C211yesmaximal, characteristic, complemented
14#340×D73C211yesmaximal, characteristic, complemented
15C73×#1802C211yesmaximal, characteristic, complemented
16C22×#11924027C2211yescharacteristic
17C22×#11924011C2211yescharacteristic
18C22×C8×D73C2211yescharacteristic
19#17989066—24no—
20#17989066C418yescomplemented
21C2×C4×Dic146C2211yescharacteristic
22C2×#14556556C2211yescharacteristic
23C2×D4×Dic73C2211yescharacteristic
24C2×C4×C22⋊D73—21no—
25C2×#14556551—21no—
26C2×#14556549C2211yescharacteristic
27C2×#14556548C2211yescharacteristic
28C2×#14556547—21no—
29C22×#11924007—21no—
30C2×C4⋊C4×D73C2211yescharacteristic
31C2×C4⋊C4×D73C2211yescharacteristic
32#17988612—24no—
33C2×C4⋊#10596831C2211yescharacteristic
34C2×#14556520C2211yescharacteristic
35C2×#14556520C2211yescharacteristic
36#17988585—24no—
37#17988580—24no—
38C2×#14556516C2211yescharacteristic
39C2×#14556516C2211yescharacteristic
40C2×#14556514C2211yescharacteristic
41C2×#14556514C2211yescharacteristic
42C2×#14556512C2211yescharacteristic
43C2×#14556512C2211yescharacteristic
44#17988482—21no—
45#17988482—21no—
46#17988458—21no—
47#17988458—21no—
48#17988456C2211yescharacteristic
49#17988453C2211yescharacteristic
50#17988452C2211yescharacteristic
51#17988350C2211yescharacteristic
52#17988350C2211yescharacteristic
53#17988349C2211yescharacteristic
54#17988349C2211yescharacteristic
55#17988349C2211yescharacteristic
56#17988349C2211yescharacteristic
57C2×C4×D4×C73C2211yescharacteristic
58C2×C4⋊C8×C73C2211yescharacteristic
59C2×#102×C73C2211yescharacteristic
60C2×#102×C73C2211yescharacteristic
61#384×C73C2211yescharacteristic
62#340×C73C2211yescharacteristic
63#340×C73C2211yescharacteristic
64C2×#11924027—22no—
65C2×#11924027—22no—
66C2×#11924027—22no—
67C2×#11924027C2×C414yes—
68C2×#11924027D414yes—
69C2×#11924027Q814yes—
70C22×Dic146C2311yescharacteristic
71C22×C22⋊D73—21no—
72C23×Dic73—21no—
73C23×Dic73—21no—
74C22×C4×D73—21no—
75C22×C4×D73—21no—
76C22×C4×D73C2311yescharacteristic
77C2×#11924011—22no—
78C2×#11924011—22no—
79C2×#11924011—22no—
80C22×#10596831C2311yescharacteristic
81C22×#10596831C2311yescharacteristic
82C2×C8×D73—22no—
83C2×C8×D73—22no—
84C2×C8×D73—22no—
85C4×Dic146—22no—
86C4×Dic146C2×C414yescomplemented
87#14556556—22no—
88#14556556C2×C414yescomplemented
89D4×Dic73—22no—
90D4×Dic73C2×C414yescomplemented
91C4×C22⋊D73—28no—
92#14556551—28no—
93#14556549—22no—
94#14556549—22no—
95#14556548C2×C414yes—
96#14556548D414yes—
97#14556547—28no—
98C2×C4⋊Dic73C2311yescharacteristic
99C2×C4⋊Dic73C2311yescharacteristic
100C2×C4⋊Dic73C2311yescharacteristic
101C2×#11924007—21no—
102C2×#11924007—21no—
103C2×#11924007—28no—
104C2×#11924007—21no—
105C2×#11924007—21no—
106C2×#11924007—21no—
107C2×#11924007—21no—
108C2×#11924007D411yescharacteristic
109C2×#11924007D411yescharacteristic
110C4⋊C4×D73—22no—
111C4⋊C4×D73—22no—
112C4⋊C4×D73—22no—
113C4⋊C4×D73C2×C414yes—
114C2×C22⋊Dic73—21no—
115C2×#11924005—21no—
116C2×#11924005D411yescharacteristic
117C2×#11924005D411yescharacteristic
118C2×C4×Dic73—21no—
119C2×C4×Dic73—21no—
120C2×C4×Dic73—21no—
121C2×C4×Dic73C2311yescharacteristic
122C4⋊#10596831—22no—
123#14556520—22no—
124#14556520—22no—
125#14556516—22no—
126#14556516—22no—
127#14556514—22no—
128#14556514—22no—
129#14556512—22no—
130#14556512—22no—
131#14556498—21no—
132#14556498—21no—
133#14556498—21no—
134#14556498—21no—
135C22×D4×C73C2311yescharacteristic
136C23×C4×C73—21no—
137C22×C8×C73C2311yescharacteristic
138C22×C8×C73C2311yescharacteristic
139C4×D4×C73—22no—
140C4×D4×C73C2×C414yescomplemented
141C2×C4⋊C4×C73—21no—
142C2×C4⋊C4×C73—21no—
143C2×C4⋊C4×C73C2311yescharacteristic
144C2×C4⋊C4×C73C2311yescharacteristic
145C2×C4⋊C4×C73C2311yescharacteristic
146C2×C22⋊C4×C73—21no—
147C2×C42×C73C2311yescharacteristic
148C4⋊C8×C73—22no—
149#102×C73—22no—
150#102×C73—22no—
151C23×D73C2×D411yescharacteristic
152#11924027—28no—
153#11924027—28no—
154#11924027—28no—
155#11924027C4⋊C4116yescomplemented
156C2×Dic146—21no—
157C2×Dic146—21no—
158C2×Dic146—21no—
159C2×Dic146C22×C412yes—
160C2×Dic146C2×D412yes—
161C2×Dic146C2×Q812yes—
162C2×C22⋊D73—24no—
163C2×C22⋊D73—24no—
164C2×C22⋊D73—24no—
165C22×Dic73—21no—
166C22×Dic73—24no—
167C22×Dic73—24no—
168C22×Dic73—24no—
169C22×Dic73—21no—
170C22×Dic73—24no—
171C22×Dic73—21no—
172C22×Dic73—21no—
173C22×Dic73—81no—
174C22×Dic73—81no—
175C22×Dic73C2×D411yescharacteristic
176C22×Dic73C2×D411yescharacteristic
177C22×Dic73C2×D411yescharacteristic
178C2×C4×D73—24no—
179C2×C4×D73—42no—
180C2×C4×D73—81no—
181C2×C4×D73—81no—
182C2×C4×D73—81no—
183C2×C4×D73—81no—
184C2×C4×D73C22×C412yes—
185C2×C4×D73C2×D412yes—
186C2×C4×D73C2×D412yes—
187C2×C4×D73C2×Q812yes—
188C2×C4×D73#4112yes—
189C2×C4×D73#4112yes—
190#11924011—44no—
191C2×#10596831—21no—
192C2×#10596831—21no—
193C2×#10596831—21no—
194C2×#10596831—21no—
195C2×#10596831—21no—
196C2×#10596831—21no—
197C8×D73—44no—
198C4⋊Dic73—21no—
199C4⋊Dic73—21no—
200C4⋊Dic73—21no—
201C4⋊Dic73—21no—
202C4⋊Dic73—21no—
203C4⋊Dic73C22×C412yes—
204#11924007—24no—
205#11924007—24no—
206#11924007—24no—
207#11924007—42no—
208#11924007—81no—
209#11924007—81no—
210#11924007C22⋊C414yes—
211#11924007C22⋊C414yes—
212C22⋊Dic73—24no—
213#11924005—42no—
214#11924005C22⋊C414yes—
215#11924005C22⋊C414yes—
216C4×Dic73—24no—
217C4×Dic73—24no—
218C4×Dic73—42no—
219C4×Dic73C22×C412yes—
220C4×Dic73C2×D412yes—
221C24×C73—21no—
222C2×D4×C73—21no—
223C2×D4×C73—21no—
224C2×D4×C73—21no—
225C2×D4×C73C22×C412yes—
226C2×D4×C73C2×D412yes—
227C2×D4×C73C2×Q812yes—
228C22×C4×C73—21no—
229C22×C4×C73—24no—
230C22×C4×C73—21no—
231C22×C4×C73—21no—
232C22×C4×C73—81no—
233C22×C4×C73—81no—
234C22×C4×C73C2×D411yescharacteristic
235C22×C4×C73C2×D411yescharacteristic
236C22×C4×C73C2411yescharacteristic
237C2×C8×C73—21no—
238C2×C8×C73—21no—
239C2×C8×C73—21no—
240C2×C8×C73—21no—
241C2×C8×C73—21no—
242C2×C8×C73—21no—
243C4⋊C4×C73—21no—
244C4⋊C4×C73—21no—
245C4⋊C4×C73—21no—
246C4⋊C4×C73—21no—
247C4⋊C4×C73—21no—
248C4⋊C4×C73—81no—
249C4⋊C4×C73—81no—
250C4⋊C4×C73C22×C412yes—
251C22⋊C4×C73—24no—
252C42×C73C22×C412yes—
253C42×C73C2×D412yes—
254C23×C73—22no—
255C23×C73—22no—
256C23×C73—22no—
257C23×C73—41no—
258C23×C73—41no—
259C23×C73—41no—
260C23×C73—41no—
261C23×C73C22×D411yescharacteristic
262C22×D73—21no—
263C22×D73—21no—
264C22×D73—21no—
265C22×D73—21no—
266C22×D73C2×C22⋊C412yes—
267C22×D73#12112yes—
268C22×D73C22⋊Q812yes—
269D4×C73—22no—
270D4×C73—22no—
271D4×C73—22no—
272D4×C73C2×C4⋊C414yes—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
275C2×C4×C73—21no—
276C2×C4×C73—21no—
277C2×C4×C73—22no—
278C2×C4×C73—41no—
279C2×C4×C73—41no—
280C2×C4×C73—41no—
281C2×C4×C73—41no—
282C2×C4×C73—41no—
283C2×C4×C73—41no—
284C2×C4×C73—41no—
285C2×C4×C73—41no—
286C2×C4×C73—84no—
287C2×C4×C73C2×C22⋊C412yes—
288C2×C4×C73C2×C22⋊C412yes—
289C2×C4×C73C23×C411yescharacteristic
290C2×C4×C73C22×D411yescharacteristic
291C2×C4×C73C22×D411yescharacteristic
292C2×C4×C73C22×Q811yescharacteristic
293C2×C4×C73C2×#4111yescharacteristic
294C2×C4×C73C2×#4111yescharacteristic
295C22⋊D73—216no—
296C2×Dic73—22no—
297C2×Dic73—22no—
298C2×Dic73—22no—
299C2×Dic73—21no—
300C2×Dic73—21no—
301C2×Dic73—21no—
302C2×Dic73—21no—
303C2×Dic73—216no—
304C2×Dic73—22no—
305C2×Dic73—41no—
306C2×Dic73—41no—
307C2×Dic73—41no—
308C2×Dic73—41no—
309C2×Dic73—41no—
310C2×Dic73—41no—
311C2×Dic73—41no—
312C2×Dic73—41no—
313C2×Dic73—84no—
314C2×Dic73C2×C22⋊C412yes—
315C2×Dic73C2×C22⋊C412yes—
316C2×Dic73C2×C22⋊C412yes—
317C2×Dic73#12112yes—
318C2×Dic73C22⋊Q812yes—
319C4×D73—84no—
320C4×D73—84no—
321C4×D73C2×C4⋊C414yes—
322C4×D73#11714yes—
323C4×D73#12114yes—
324C4×D73C22⋊Q814yes—
325Dic146—22no—
326Dic146—22no—
327Dic146—22no—
328Dic146C2×C4⋊C414yes—
329C8×C73—41no—
330C8×C73—41no—
331#10596831—41no—
332#10596831—41no—
333C22×C73—24no—
334C22×C73—42no—
335C22×C73—42no—
336C22×C73—42no—
337C22×C73—42no—
338C22×C73—42no—
339C22×C73—42no—
340C22×C73C22×C22⋊C411yescharacteristic
341C22×C73C2×#12111yescharacteristic
342C22×C73C2×C22⋊Q811yescharacteristic
343C22×C73#57611yescharacteristic
344C22×C73#57711yescharacteristic
345C22×C73#57711yescharacteristic
346C22×C73#57811yescharacteristic
347C2×D73—22no—
348C2×D73—22no—
349C2×D73—22no—
350C2×D73—22no—
351C2×D73—22no—
352C2×D73—22no—
353C2×D73#38014yes—
354C4×C73—22no—
355C4×C73—22no—
356C4×C73—42no—
357C4×C73—81no—
358C4×C73—81no—
359C4×C73C22×C4⋊C411yescharacteristic
360C4×C73C2×#11711yescharacteristic
361C4×C73C2×#12111yescharacteristic
362C4×C73C2×C22⋊Q811yescharacteristic
363Dic73—22no—
364Dic73—22no—
365Dic73—24no—
366Dic73—42no—
367Dic73—81no—
368Dic73—81no—
369Dic73#38014yes—
370#20652—731nomaximal, Sylow
371C2×C73—44no—
372C2×C73C2×#38011yescharacteristic
373C2×C73#289711yescharacteristic
374C2×C73#289811yescharacteristic
375C2×C73#304511yescharacteristic
376C2×C73#304611yescharacteristic
377C2×C73#308311yescharacteristic
378C2×C73#308411yescharacteristic
379D73—24no—
380C2×#520—731no—
381C2×#424—731no—
382C2×#417—731no—
383C2×#416—731no—
384#2317—731no—
385#1805—731no—
386#1805—731no—
387#1804—731no—
388#1804—731no—
389#1803—731no—
390#1803—731no—
391#1802—731no—
392#1802D7311yescharacteristic, complemented
393#1736—731no—
394C2×#340—731no—
395C73#2065211yescharacteristic, complemented, Sylow
396C22×#41—731no—
397C22×M16—731no—
398C23×C8—731no—
399#520—738no—
400#520—1464no—
401C2×C4×Q8—731no—
402C2×C4×Q8—731no—
403C2×C4×D4—731no—
404C2×C4×D4—1461no—
405C2×C4×D4—1461no—
406C2×C4×D4C2×D7311yescharacteristic
407C2×#117—731no—
408C2×#117—731no—
409C2×#117—1461no—
410C22×C4⋊C4—731no—
411C22×C4⋊C4—731no—
412C22×C4⋊C4—1461no—
413#424—1464no—
414C2×C4⋊C8—731no—
415C2×C4⋊C8—731no—
416C2×C4⋊C8—731no—
417C2×C4⋊C8C2×D7311yescharacteristic
418#417—1464no—
419#416—1464no—
420C2×#103—731no—
421C2×#103—731no—
422C2×#103—731no—
423C2×#103—731no—
424C2×#102—731no—
425C2×#102—731no—
426C2×#102C2×D7311yescharacteristic
427C2×#102C2×D7311yescharacteristic
428#389—1461no—
429#389—1461no—
430#385—1461no—
431#385—1461no—
432#384—731no—
433#384C2×D7311yescharacteristic
434#382—731no—
435#382—731no—
436#340—731no—
437#340—731no—
438#340—731no—
439#340—731no—
440#340—731no—
441#340—731no—
442#340C2×D7311yescharacteristic
443#340C2×D7311yescharacteristic
444C2×#41—734no—
445C2×#41—734no—
446C2×#41—734no—
447C2×#41—1462no—
448C2×#41—1462no—
449C2×#41—1462no—
450C22×Q8—731no—
451C22×D4—1461no—
452C22×D4C22×D7311yescharacteristic
453C23×C4—21no—
454C23×C4—731no—
455C23×C4—1461no—
456C23×C4—1461no—
457C23×C4—1461no—
458C23×C4—1461no—
459C2×M16—1462no—
460C2×M16—1462no—
461C2×M16—1462no—
462C22×C8—731no—
463C22×C8—731no—
464C22×C8—1462no—
465C22×C8—1462no—
466C22×C8—1462no—
467C22×C8C22×D7311yescharacteristic
468C22×C8C22×D7311yescharacteristic
469C4×Q8—734no—
470C4×Q8—734no—
471C4×Q8—1462no—
472C4×Q8—1462no—
473C4×D4—22no—
474C4×D4—734no—
475C4×D4—1462no—
476C4×D4—1468no—
477C4×D4—1468no—
478C4×D4C4×D7314yescomplemented
479#117—734no—
480#117—734no—
481#117—1462no—
482#117—1462no—
483#117—1468no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—731no—
487C2×C4⋊C4—731no—
488C2×C4⋊C4—731no—
489C2×C4⋊C4—734no—
490C2×C4⋊C4—731no—
491C2×C4⋊C4—731no—
492C2×C4⋊C4—1462no—
493C2×C4⋊C4—1462no—
494C2×C4⋊C4—1462no—
495C2×C4⋊C4—1461no—
496C2×C4⋊C4—1461no—
497C2×C4⋊C4—1461no—
498C2×C4⋊C4—1468no—
499C2×C4⋊C4—1461no—
500C2×C4⋊C4—1461no—
501C2×C4⋊C4—1461no—
502C2×C4⋊C4C22×D7311yescharacteristic
503C2×C4⋊C4C22×D7311yescharacteristic
504C2×C4⋊C4C22×D7311yescharacteristic
505C2×C22⋊C4—21no—
506C2×C22⋊C4—731no—
507C2×C22⋊C4—731no—
508C2×C22⋊C4—1461no—
509C2×C22⋊C4—1461no—
510C2×C42—731no—
511C2×C42—1461no—
512C2×C42—1461no—
513C2×C42—1461no—
514C2×C42C22×D7311yescharacteristic
515C4⋊C8—22no—
516C4⋊C8—1462no—
517C4⋊C8—1462no—
518C4⋊C8—1462no—
519#103—1462no—
520#103—1462no—
521#103—1462no—
522#103—1462no—
523#102—22no—
524#102—22no—
525#102—1462no—
526#102—1462no—
527#95—1461no—
528#95—1461no—
529#95—1461no—
530#95—1461no—
531C24—21no—
532C24—731no—
533#41—7316no—
534#41—1468no—
535#41—1468no—
536#41—1468no—
537C2×Q8—732no—
538C2×Q8—732no—
539C2×Q8—732no—
540C2×Q8—1461no—
541C2×Q8—1461no—
542C2×Q8—1461no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—1464no—
547C2×D4—1464no—
548C2×D4—1464no—
549C2×D4C2×C4×D7312yes—
550C2×D4D4×D7312yes—
551C2×D4Q8×D7312yes—
552C22×C4—21no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—81no—
557C22×C4—81no—
558C22×C4—2922no—
559C22×C4—5841no—
560C22×C4—5841no—
561C22×C4—5841no—
562C22×C4—5841no—
563C22×C4—5841no—
564C22×C4—5841no—
565C22×C4—731no—
566C22×C4—732no—
567C22×C4—732no—
568C22×C4—732no—
569C22×C4—732no—
570C22×C4—732no—
571C22×C4—732no—
572C22×C4—731no—
573C22×C4—731no—
574C22×C4—1464no—
575C22×C4—1461no—
576C22×C4—1461no—
577C22×C4—1461no—
578C22×C4—1464no—
579C22×C4—1464no—
580C22×C4—1464no—
581C22×C4—1464no—
582C22×C4—1461no—
583C22×C4D4×D7311yescharacteristic
584C22×C4D4×D7311yescharacteristic
585C22×C4C23×D7311yescharacteristic
586M16—2924no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—2924no—
594C2×C8—1461no—
595C2×C8—1461no—
596C2×C8—1461no—
597C2×C8—1461no—
598C2×C8—1461no—
599C2×C8—1461no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—81no—
606C4⋊C4—81no—
607C4⋊C4—2922no—
608C4⋊C4—5841no—
609C4⋊C4—5841no—
610C4⋊C4—734no—
611C4⋊C4—734no—
612C4⋊C4—732no—
613C4⋊C4—1464no—
614C4⋊C4—1464no—
615C4⋊C4—1461no—
616C4⋊C4—1461no—
617C4⋊C4—1461no—
618C4⋊C4—1461no—
619C4⋊C4—1464no—
620C4⋊C4—1461no—
621C4⋊C4C2×C4×D7312yes—
622C22⋊C4—24no—
623C22⋊C4—2922no—
624C22⋊C4—734no—
625C22⋊C4—734no—
626C22⋊C4—1464no—
627C42—2922no—
628C42—732no—
629C42—732no—
630C42—1464no—
631C42—1464no—
632C42C2×C4×D7312yes—
633C42D4×D7312yes—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—732no—
642C23—732no—
643C23—732no—
644C23—1461no—
645C23—1461no—
646C23—1461no—
647C23—1461no—
648C23C2×D4×D7311yescharacteristic
649Q8—734no—
650Q8—1462no—
651Q8—1462no—
652Q8—1462no—
653D4—22no—
654D4—22no—
655D4—22no—
656D4—14616no—
657D4C4⋊C4×D7314yes—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—84no—
672C2×C4—2921no—
673C2×C4—2921no—
674C2×C4—2921no—
675C2×C4—2921no—
676C2×C4—2921no—
677C2×C4—2921no—
678C2×C4—2921no—
679C2×C4—2921no—
680C2×C4—5844no—
681C2×C4—5844no—
682C2×C4—5844no—
683C2×C4—732no—
684C2×C4—732no—
685C2×C4—732no—
686C2×C4—734no—
687C2×C4—734no—
688C2×C4—734no—
689C2×C4—734no—
690C2×C4—732no—
691C2×C4—732no—
692C2×C4—1462no—
693C2×C4—14616no—
694C2×C4—1461no—
695C2×C4—1461no—
696C2×C4—1461no—
697C2×C4—1461no—
698C2×C4—1462no—
699C2×C4—1462no—
700C2×C4—1462no—
701C2×C4C22⋊C4×D7312yes—
702C2×C4C22⋊C4×D7312yes—
703C2×C4C22×C4×D7311yescharacteristic
704C2×C4C2×D4×D7311yescharacteristic
705C2×C4C2×D4×D7311yescharacteristic
706C2×C4C2×Q8×D7311yescharacteristic
707C2×C4#41×D7311yescharacteristic
708C2×C4#41×D7311yescharacteristic
709C8—41no—
710C8—41no—
711C8—2921no—
712C8—2921no—
713C22—24no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—734no—
721C22—1462no—
722C22—1462no—
723C22—1462no—
724C22—1462no—
725C22—1462no—
726C22—1462no—
727C22C2×C22⋊C4×D7311yescharacteristic
728C22#121×D7311yescharacteristic
729C22C22⋊Q8×D7311yescharacteristic
730C22#1798938811yescharacteristic
731C22#1798939311yescharacteristic
732C22#1798939711yescharacteristic
733C22#1798940311yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—81no—
738C4—81no—
739C4—2922no—
740C4—5841no—
741C4—5841no—
742C4—734no—
743C4—1464no—
744C4—1462no—
745C4—1462no—
746C4C2×C4⋊C4×D7311yescharacteristic
747C4#117×D7311yescharacteristic
748C4#121×D7311yescharacteristic
749C4C22⋊Q8×D7311yescharacteristic
750C2—44no—
751C2—1464no—
752C2#380×D7311yescharacteristic
753C2#2261845211yescharacteristic
754C2#2261846211yescharacteristic
755C2#2261946511yescharacteristic
756C2#2261947611yescharacteristic
757C2#2261977711yescharacteristic
758C2#2261978811yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1802C2
socleC23×C73C22×D4
prime radicalC22×#11924027C22
cosocleC22×C4×C73C24
hypercenter#1802D73
hypocenterC73#20652
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. C2×#17988612C2semidirect
5. #22612552C2semidirect
6. #22609947C2semidirect
7. #22609945C2semidirect
8. #22609941C2semidirect
9. #22609939C2semidirect
10. #22609935C2semidirect
11. #22609933C2semidirect
12. #22609929C2semidirect
13. #22609649C2semidirect
14. #340×D73C2semidirect
15. C73×#1802C2semidirect
20. #17989066C4semidirect
86. C4×Dic146C2×C4semidirect
88. #14556556C2×C4semidirect
90. D4×Dic73C2×C4semidirect
140. C4×D4×C73C2×C4semidirect
155. #11924027C4⋊C4semidirect
392. #1802D73semidirect
395. C73#20652semidirect
478. C4×D4C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179890662
C2×#179886122
C2×#179885852
C2×#179885802
#226125522
#226099472
#226099452
#226099412
#226099392
#226099352
#226099332
#226099292
#226096492
#340×D732
C73×#18022
#2065273