Finite Group Databasebeta

← #33292152

Subgroups — #33292152

Order 18688.

2570 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989098C211yesmaximal, characteristic, complemented
2#22617966C211yesmaximal, characteristic, complemented
3#22617959C211yesmaximal, characteristic, complemented
4#22617958C211yesmaximal, characteristic, complemented
5#22617953C211yesmaximal, characteristic, complemented
6#22617944C212yesmaximal, complemented
7#22617942C212yesmaximal, complemented
8#22617933C212yesmaximal, complemented
9#22617931C212yesmaximal, complemented
10#22617926C214yesmaximal, complemented
11#22613190C212yesmaximal, complemented
12#22613188C212yesmaximal, complemented
13#22613173C214yesmaximal, complemented
14#22613146C212yesmaximal, complemented
15#22613144C212yesmaximal, complemented
16#22612314C211yesmaximal, characteristic, complemented
17C2×#525×C73C211yesmaximal, characteristic, complemented
18C22×#11924028C2211yescharacteristic
19#17989098—28no—
20C2×#14556574C2212yes—
21C2×#14556570C2211yescharacteristic
22C2×#14556570C2211yescharacteristic
23C2×#14556565C2211yescharacteristic
24C2×#14556565C2211yescharacteristic
25C2×#14556560C2212yes—
26C2×C4×C22⋊D73C2212yes—
27C2×C4×C22⋊D73C2212yes—
28C2×C4×C22⋊D73C2214yescomplemented
29C2×#14556550C2211yescharacteristic
30C2×#14556550C2212yes—
31#17988526C2212yescomplemented
32#17988525C2212yescomplemented
33#17988523C2212yescomplemented
34#17988522C2212yescomplemented
35#17988520C2214yescomplemented
36#17988518C2212yescomplemented
37#17988517C2212yescomplemented
38#17988515C2214yes—
39#17988515C2214yes—
40#17988515C2214yes—
41#17988513C2212yescomplemented
42#17988512C2212yescomplemented
43#17988510C2214yescomplemented
44#17988509C2214yescomplemented
45#17988507C2212yescomplemented
46#17988506C2212yescomplemented
47#17988504C2212yescomplemented
48#17988503C2214yescomplemented
49#17988502C2214yes—
50#17988502C2214yes—
51#17988502C2214yes—
52#17988501C2214yes—
53#17988501C2214yes—
54#17988501C2214yes—
55#17988501C2212yescomplemented
56#17988499C2212yescomplemented
57#17988498C2212yescomplemented
58#17988496C2212yescomplemented
59#17988495C2214yes—
60#17988495C2214yes—
61#17988495C2214yes—
62#17988495C2212yescomplemented
63#17988450C2211yescharacteristic
64#17988450C2211yescharacteristic
65#17988447C2212yes—
66#17988447C2212yes—
67#17988443C2212yes—
68C4×#11924007C2214yescomplemented
69C4×#11924005C2214yescomplemented
70C4×C22⋊Dic73C2212yes—
71C4×C22⋊Dic73C2212yes—
72C4×C22⋊Dic73C2214yescomplemented
73C22×#41×C73C2211yescharacteristic
74C24×C4×C73C2211yescharacteristic
75#525×C73—28no—
76C2×#123×C73C2212yes—
77C2×C22⋊Q8×C73C2211yescharacteristic
78C2×C22⋊Q8×C73C2211yescharacteristic
79C2×#121×C73C2211yescharacteristic
80C2×#121×C73C2211yescharacteristic
81C2×#120×C73C2212yes—
82C2×C4×D4×C73C2212yes—
83C2×C4×D4×C73C2212yes—
84C2×#117×C73C2211yescharacteristic
85C2×#11924028—24no—
86C2×#11924028—44no—
87C22×Dic146C2311yescharacteristic
88C22×D292C2311yescharacteristic
89C22×C22⋊D73C2312yes—
90C22×C22⋊D73C2312yes—
91C22×C22⋊D73C2312yes—
92C22×C22⋊D73C2314yes—
93C22×C4×D73C2312yes—
94#14556574—28no—
95#14556570—24no—
96#14556570—24no—
97#14556565—24no—
98#14556565—24no—
99#14556560—28no—
100C4×C22⋊D73—28no—
101C4×C22⋊D73—28no—
102C4×C22⋊D73—48no—
103#14556550—24no—
104#14556550—44no—
105C2×C4⋊Dic73C2311yescharacteristic
106C2×C4⋊Dic73C2311yescharacteristic
107C2×C4⋊Dic73C2314yes—
108C2×#11924007C2312yes—
109C2×#11924007C2312yes—
110C2×#11924007C2314yes—
111C2×#11924007C2314yes—
112C2×#11924007C2314yes—
113C2×C22⋊Dic73C2312yes—
114C2×C22⋊Dic73C2312yes—
115C2×C22⋊Dic73C2312yes—
116C2×C22⋊Dic73C2314yes—
117C2×C22⋊Dic73C2314yes—
118C2×C22⋊Dic73C2314yes—
119C2×C22⋊Dic73C2314yes—
120C2×C22⋊Dic73C2312yes—
121C2×C22⋊Dic73C2312yes—
122C2×C22⋊Dic73C2314yes—
123C2×#11924005C2312yes—
124C2×#11924005C2312yes—
125C2×#11924005C2314yes—
126C2×#11924005C2314yes—
127C2×#11924005C2314yes—
128C2×C4×Dic73C2314yes—
129C2×C4×Dic73C2312yes—
130#14556498C2312yes—
131#14556498C2312yes—
132#14556498C2312yes—
133#14556498C2312yes—
134#14556498C2314yes—
135#14556498C2314yes—
136#14556498C2314yes—
137#14556498C2314yes—
138#14556498C2314yes—
139#14556498C2314yes—
140C25×C73C2311yescharacteristic
141C2×#41×C73—24no—
142C2×#41×C73—44no—
143C22×Q8×C73C2311yescharacteristic
144C22×D4×C73C2312yes—
145C22×D4×C73C2312yes—
146C22×D4×C73C2312yes—
147C22×D4×C73C2311yescharacteristic
148C23×C4×C73—44no—
149C23×C4×C73D418yescomplemented
150C23×C4×C73C2312yes—
151C23×C4×C73C2311yescharacteristic
152C23×C4×C73C2311yescharacteristic
153C23×C4×C73C2311yescharacteristic
154C23×C4×C73C2311yescharacteristic
155C23×C4×C73C2311yescharacteristic
156C23×C4×C73C2311yescharacteristic
157#123×C73—28no—
158C22⋊Q8×C73—24no—
159C22⋊Q8×C73—24no—
160#121×C73—24no—
161#121×C73—24no—
162#120×C73—28no—
163C4×D4×C73—28no—
164C4×D4×C73—28no—
165#117×C73—24no—
166C2×C4⋊C4×C73C2311yescharacteristic
167C2×C4⋊C4×C73C2311yescharacteristic
168C2×C4⋊C4×C73C2312yes—
169C2×C4⋊C4×C73C2312yes—
170C2×C22⋊C4×C73C2312yes—
171C2×C22⋊C4×C73C2312yes—
172C2×C22⋊C4×C73C2312yes—
173C2×C22⋊C4×C73C2312yes—
174C2×C22⋊C4×C73C2312yes—
175C2×C42×C73C2312yes—
176C23×D73C2412yes—
177#11924028—416no—
178C2×Dic146—22no—
179C2×Dic146—42no—
180C2×D292—22no—
181C2×D292—42no—
182C2×C22⋊D73—24no—
183C2×C22⋊D73—24no—
184C2×C22⋊D73—24no—
185C2×C22⋊D73—44no—
186C2×C22⋊D73—44no—
187C2×C22⋊D73—42no—
188C2×C22⋊D73—44no—
189C2×C22⋊D73—44no—
190C2×C22⋊D73—42no—
191C2×C22⋊D73—44no—
192C22×Dic73C2414yes—
193C22×Dic73C2414yes—
194C22×Dic73C2412yes—
195C22×Dic73C2412yes—
196C22×Dic73C2412yes—
197C2×C4×D73—24no—
198C2×C4×D73—28no—
199C4⋊Dic73—22no—
200C4⋊Dic73—22no—
201C4⋊Dic73—44no—
202#11924007—24no—
203#11924007—24no—
204#11924007—44no—
205#11924007—44no—
206#11924007—44no—
207C22⋊Dic73—24no—
208C22⋊Dic73—24no—
209C22⋊Dic73—24no—
210C22⋊Dic73—44no—
211C22⋊Dic73—44no—
212C22⋊Dic73—44no—
213C22⋊Dic73—44no—
214C22⋊Dic73—42no—
215C22⋊Dic73—42no—
216C22⋊Dic73—44no—
217#11924005—24no—
218#11924005—24no—
219#11924005—44no—
220#11924005—44no—
221#11924005—44no—
222C4×Dic73—24no—
223C4×Dic73—28no—
224C24×C73—42no—
225C24×C73—42no—
226C24×C73—42no—
227C24×C73C2×D414yes—
228C24×C73C2412yes—
229C24×C73C2411yescharacteristic
230C24×C73C2411yescharacteristic
231C24×C73C2411yescharacteristic
232#41×C73—416no—
233C2×Q8×C73—22no—
234C2×Q8×C73—42no—
235C2×D4×C73—24no—
236C2×D4×C73—24no—
237C2×D4×C73—24no—
238C2×D4×C73—22no—
239C2×D4×C73—42no—
240C2×D4×C73—44no—
241C2×D4×C73—42no—
242C2×D4×C73—42no—
243C2×D4×C73—44no—
244C22×C4×C73—24no—
245C22×C4×C73—24no—
246C22×C4×C73—24no—
247C22×C4×C73—24no—
248C22×C4×C73—28no—
249C22×C4×C73—416no—
250C22×C4×C73—42no—
251C22×C4×C73—42no—
252C22×C4×C73—42no—
253C22×C4×C73C2×D414yes—
254C22×C4×C73C2×D414yes—
255C22×C4×C73C2×D414yes—
256C22×C4×C73C2×D414yes—
257C22×C4×C73C2×D414yes—
258C22×C4×C73C2×D414yes—
259C22×C4×C73C2412yes—
260C22×C4×C73C2412yes—
261C22×C4×C73C2412yes—
262C22×C4×C73C2411yescharacteristic
263C22×C4×C73C2411yescharacteristic
264C22×C4×C73C2411yescharacteristic
265C22×C4×C73C2411yescharacteristic
266C4⋊C4×C73—22no—
267C4⋊C4×C73—22no—
268C4⋊C4×C73—24no—
269C4⋊C4×C73—24no—
270C22⋊C4×C73—24no—
271C22⋊C4×C73—24no—
272C22⋊C4×C73—24no—
273C22⋊C4×C73—24no—
274C22⋊C4×C73—24no—
275C42×C73—24no—
276C23×C73—22no—
277C23×C73—22no—
278C23×C73—22no—
279C23×C73—22no—
280C23×C73—22no—
281C23×C73—22no—
282C23×C73—22no—
283C23×C73—22no—
284C23×C73—22no—
285C23×C73—22no—
286C23×C73—24no—
287C23×C73—22no—
288C23×C73—24no—
289C23×C73—22no—
290C23×C73—44no—
291C23×C73—44no—
292C23×C73—44no—
293C23×C73—416no—
294C23×C73C22×D412yes—
295C23×C73C22×D412yes—
296C23×C73C22×D412yes—
297C23×C73C2511yescharacteristic
298C22×D73—22no—
299C22×D73—24no—
300C22×D73—22no—
301C22×D73—24no—
302C22×D73—22no—
303Q8×C73—44no—
304D4×C73—44no—
305D4×C73—48no—
306D4×C73—48no—
307D4×C73—48no—
308C2×C4×C73—22no—
309C2×C4×C73—22no—
310C2×C4×C73—22no—
311C2×C4×C73—28no—
312C2×C4×C73—28no—
313C2×C4×C73—28no—
314C2×C4×C73—22no—
315C2×C4×C73—22no—
316C2×C4×C73—22no—
317C2×C4×C73—24no—
318C2×C4×C73—22no—
319C2×C4×C73—24no—
320C2×C4×C73—22no—
321C2×C4×C73—44no—
322C2×C4×C73—44no—
323C2×C4×C73—44no—
324C2×C4×C73—48no—
325C2×C4×C73C22×D412yes—
326C2×C4×C73C22×D412yes—
327C2×C4×C73C22×D412yes—
328C2×C4×C73C22×D412yes—
329C2×C4×C73H(5,𝔽2)14yes—
330C22⋊D73—48no—
331C22⋊D73—48no—
332C22⋊D73—48no—
333C22⋊D73—416no—
334C2×Dic73—22no—
335C2×Dic73—22no—
336C2×Dic73—22no—
337C2×Dic73—24no—
338C2×Dic73—24no—
339C2×Dic73—24no—
340C2×Dic73—24no—
341C2×Dic73—24no—
342C2×Dic73—24no—
343C2×Dic73—22no—
344C2×Dic73—24no—
345C2×Dic73—24no—
346C2×Dic73—22no—
347D292—44no—
348C4×D73—48no—
349Dic146—44no—
350C22×C73—22no—
351C22×C73—22no—
352C22×C73—22no—
353C22×C73—22no—
354C22×C73—22no—
355C22×C73—22no—
356C22×C73—22no—
357C22×C73—22no—
358C22×C73—22no—
359C22×C73—416no—
360C22×C73—44no—
361C22×C73—44no—
362C22×C73—44no—
363C22×C73—42no—
364C22×C73—42no—
365C22×C73—42no—
366C22×C73—44no—
367C22×C73—44no—
368C22×C73C23×D411yescharacteristic
369C22×C73C2×H(5,𝔽2)12yes—
370C22×C73#58512yes—
371C22×C73#58512yes—
372C2×D73—42no—
373C2×D73—42no—
374C2×D73—42no—
375C2×D73—44no—
376C2×D73—44no—
377C4×C73—22no—
378C4×C73—22no—
379C4×C73—22no—
380C4×C73—42no—
381C4×C73—42no—
382C4×C73—42no—
383C4×C73#53414yes—
384Dic73—42no—
385Dic73—42no—
386Dic73—42no—
387Dic73—44no—
388Dic73—44no—
389#36652—731nomaximal, Sylow
390C2×C73—42no—
391C2×C73—42no—
392C2×C73—42no—
393C2×C73—82no—
394C2×C73C2×#53411yescharacteristic
395C2×C73#344911yescharacteristic
396C2×C73#344911yescharacteristic
397C2×C73#352914yes—
398D73—82no—
399C2×#525—731no—
400C2×#525D7311yescharacteristic, complemented
401#2817—731no—
402#2816—731no—
403#2816—731no—
404#2815—731no—
405#2814—732no—
406#2814—732no—
407#2813—732no—
408#2813—732no—
409#2812—734no—
410#2395—732no—
411#2395—732no—
412#2392—734no—
413#2388—732no—
414#2388—732no—
415#2280—731no—
416C73#3665211yescharacteristic, complemented, Sylow
417C22×#41—731no—
418C22×#41C2×D7311yescharacteristic
419C24×C4C2×D7311yescharacteristic
420#525—28no—
421#525—1468no—
422C2×#123—732no—
423C2×#123C2×D7312yes—
424C2×C22⋊Q8—731no—
425C2×C22⋊Q8—731no—
426C2×C22⋊Q8C2×D7311yescharacteristic
427C2×C22⋊Q8C2×D7311yescharacteristic
428C2×#121—731no—
429C2×#121—731no—
430C2×#121C2×D7311yescharacteristic
431C2×#121C2×D7311yescharacteristic
432C2×#120—732no—
433C2×#120C2×D7312yes—
434C2×C4×D4—734no—
435C2×C4×D4—732no—
436C2×C4×D4—732no—
437C2×C4×D4C2×D7312yes—
438C2×C4×D4C2×D7312yes—
439C2×#117—732no—
440C2×#117—731no—
441C2×#117C2×D7311yescharacteristic
442#400—732no—
443#400—732no—
444#399—732no—
445#399—732no—
446#398—732no—
447#398—732no—
448#398—734no—
449#397—732no—
450#397—734no—
451#397—732no—
452#397—734no—
453#397—734no—
454#396—734no—
455#396—734no—
456#395—732no—
457#395—732no—
458#394—732no—
459#394—734no—
460#394—734no—
461#394—734no—
462#394—732no—
463#394—734no—
464#394—734no—
465#394—734no—
466#394—734no—
467#393—732no—
468#393—732no—
469#392—734no—
470#392—734no—
471#392—732no—
472#392—734no—
473#392—732no—
474#381—731no—
475#381—731no—
476#380—732no—
477#380—732no—
478#379—732no—
479C4×C4⋊C4—734no—
480C4×C22⋊C4—732no—
481C4×C22⋊C4—732no—
482C4×C22⋊C4—734no—
483C4×C22⋊C4—734no—
484C25C22×D7311yescharacteristic
485C2×#41—24no—
486C2×#41—44no—
487C2×#41—2924no—
488C2×#41—1464no—
489C22×Q8—731no—
490C22×Q8C22×D7311yescharacteristic
491C22×D4—734no—
492C22×D4—732no—
493C22×D4—732no—
494C22×D4—732no—
495C22×D4—731no—
496C22×D4C22×D7312yes—
497C22×D4C22×D7312yes—
498C22×D4C22×D7312yes—
499C22×D4C22×D7311yescharacteristic
500C23×C4—44no—
501C23×C4—732no—
502C23×C4C22⋊D7318yescomplemented
503C23×C4C22×D7312yes—
504C23×C4C22×D7311yescharacteristic
505C23×C4C22×D7311yescharacteristic
506C23×C4C22×D7311yescharacteristic
507C23×C4C22×D7311yescharacteristic
508C23×C4C22×D7311yescharacteristic
509C23×C4C22×D7311yescharacteristic
510#123—28no—
511#123—1468no—
512C22⋊Q8—24no—
513C22⋊Q8—24no—
514C22⋊Q8—1464no—
515C22⋊Q8—1464no—
516#121—24no—
517#121—24no—
518#121—1464no—
519#121—1464no—
520#120—28no—
521#120—1468no—
522C4×D4—28no—
523C4×D4—28no—
524C4×D4—2928no—
525C4×D4—1468no—
526C4×D4—1468no—
527#117—24no—
528#117—2924no—
529#117—1464no—
530C2×C4⋊C4—734no—
531C2×C4⋊C4—734no—
532C2×C4⋊C4—734no—
533C2×C4⋊C4—734no—
534C2×C4⋊C4—731no—
535C2×C4⋊C4—731no—
536C2×C4⋊C4—732no—
537C2×C4⋊C4—732no—
538C2×C4⋊C4C22×D7311yescharacteristic
539C2×C4⋊C4C22×D7311yescharacteristic
540C2×C4⋊C4C22×D7312yes—
541C2×C4⋊C4C22×D7312yes—
542C2×C22⋊C4—732no—
543C2×C22⋊C4—732no—
544C2×C22⋊C4—734no—
545C2×C22⋊C4—734no—
546C2×C22⋊C4—734no—
547C2×C22⋊C4—734no—
548C2×C22⋊C4—734no—
549C2×C22⋊C4—734no—
550C2×C22⋊C4—734no—
551C2×C22⋊C4—734no—
552C2×C22⋊C4—732no—
553C2×C22⋊C4—732no—
554C2×C22⋊C4—732no—
555C2×C22⋊C4—732no—
556C2×C22⋊C4—732no—
557C2×C22⋊C4C22×D7312yes—
558C2×C22⋊C4C22×D7312yes—
559C2×C22⋊C4C22×D7312yes—
560C2×C22⋊C4C22×D7312yes—
561C2×C22⋊C4C22×D7312yes—
562C2×C42—732no—
563C2×C42—734no—
564C2×C42C22×D7312yes—
565#95—732no—
566#95—732no—
567#95—732no—
568#95—732no—
569#95—734no—
570#95—734no—
571#95—734no—
572#95—734no—
573#95—734no—
574#95—734no—
575C24—42no—
576C24—42no—
577C24—42no—
578C24—732no—
579C24C2×C22⋊D7314yes—
580C24C23×D7312yes—
581C24C23×D7311yescharacteristic
582C24C23×D7311yescharacteristic
583C24C23×D7311yescharacteristic
584#41—416no—
585#41—29216no—
586C2×Q8—22no—
587C2×Q8—42no—
588C2×Q8—2922no—
589C2×Q8—1462no—
590C2×D4—24no—
591C2×D4—24no—
592C2×D4—24no—
593C2×D4—22no—
594C2×D4—42no—
595C2×D4—44no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—44no—
599C2×D4—2922no—
600C2×D4—2924no—
601C2×D4—2922no—
602C2×D4—2924no—
603C2×D4—2924no—
604C2×D4—2924no—
605C2×D4—2922no—
606C2×D4—2924no—
607C2×D4—1464no—
608C2×D4—1464no—
609C2×D4—1464no—
610C2×D4—1462no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—24no—
614C22×C4—24no—
615C22×C4—28no—
616C22×C4—416no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—734no—
621C22×C4—734no—
622C22×C4—732no—
623C22×C4—732no—
624C22×C4—732no—
625C22×C4—1464no—
626C22×C4—1468no—
627C22×C4C2×C22⋊D7314yes—
628C22×C4C2×C22⋊D7314yes—
629C22×C4C2×C22⋊D7314yes—
630C22×C4C2×C22⋊D7314yes—
631C22×C4C2×C22⋊D7314yes—
632C22×C4C2×C22⋊D7314yes—
633C22×C4C23×D7312yes—
634C22×C4C23×D7312yes—
635C22×C4C23×D7312yes—
636C22×C4C23×D7311yescharacteristic
637C22×C4C23×D7311yescharacteristic
638C22×C4C23×D7311yescharacteristic
639C22×C4C23×D7311yescharacteristic
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—2924no—
645C4⋊C4—2924no—
646C4⋊C4—2924no—
647C4⋊C4—2924no—
648C4⋊C4—1464no—
649C4⋊C4—1464no—
650C4⋊C4—1462no—
651C4⋊C4—1462no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—2924no—
658C22⋊C4—2924no—
659C22⋊C4—2924no—
660C22⋊C4—2924no—
661C22⋊C4—2924no—
662C22⋊C4—2924no—
663C22⋊C4—2924no—
664C22⋊C4—2922no—
665C22⋊C4—2922no—
666C22⋊C4—2924no—
667C22⋊C4—1464no—
668C22⋊C4—1464no—
669C22⋊C4—1464no—
670C22⋊C4—1464no—
671C22⋊C4—1464no—
672C42—24no—
673C42—1464no—
674C42—1468no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—24no—
686C23—22no—
687C23—24no—
688C23—22no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—416no—
693C23—1462no—
694C23—1464no—
695C23—1462no—
696C23—1464no—
697C23—1462no—
698C23C22×C22⋊D7312yes—
699C23C22×C22⋊D7312yes—
700C23C22×C22⋊D7312yes—
701C23C24×D7311yescharacteristic
702Q8—44no—
703Q8—2924no—
704D4—44no—
705D4—48no—
706D4—48no—
707D4—48no—
708D4—2924no—
709D4—2928no—
710D4—2928no—
711D4—2928no—
712D4—29216no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—48no—
730C2×C4—2928no—
731C2×C4—1462no—
732C2×C4—1462no—
733C2×C4—1462no—
734C2×C4—1464no—
735C2×C4—1464no—
736C2×C4—1464no—
737C2×C4—1464no—
738C2×C4—1464no—
739C2×C4—1462no—
740C2×C4—1464no—
741C2×C4—1464no—
742C2×C4—1464no—
743C2×C4—1462no—
744C2×C4C22×C22⋊D7312yes—
745C2×C4C22×C22⋊D7312yes—
746C2×C4C22×C22⋊D7312yes—
747C2×C4C22×C22⋊D7312yes—
748C2×C4#1455663614yes—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—416no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—42no—
763C22—42no—
764C22—44no—
765C22—44no—
766C22—42no—
767C22—2922no—
768C22—2922no—
769C22—2924no—
770C22—2924no—
771C22—2922no—
772C22C23×C22⋊D7311yescharacteristic
773C22C2×#1455663612yes—
774C22#1798942312yes—
775C22#1798942312yes—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—2922no—
783C4—2922no—
784C4—2924no—
785C4—2924no—
786C4—2922no—
787C4#1798914614yes—
788C2—42no—
789C2—42no—
790C2—42no—
791C2—82no—
792C2—5842no—
793C2C2×#1798914611yescharacteristic
794C2#2262326011yescharacteristic
795C2#2262326011yescharacteristic
796C2#2262406914yes—
subgroupG/H
centerC22×C4C23×D73
commutator, socle, cosocleC23×C73C25
FrattiniC23C24×D73
FittingC2×#525×C73C2
hypercenterC2×#525D73
hypocenterC73#36652
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#17989098C2semidirect
2. #22617966C2semidirect
3. #22617959C2semidirect
4. #22617958C2semidirect
5. #22617953C2semidirect
6. #22617944C2semidirect
7. #22617942C2semidirect
8. #22617933C2semidirect
9. #22617931C2semidirect
10. #22617926C2semidirect
11. #22613190C2semidirect
12. #22613188C2semidirect
13. #22613173C2semidirect
14. #22613146C2semidirect
15. #22613144C2semidirect
16. #22612314C2semidirect
17. C2×#525×C73C2semidirect
28. C2×C4×C22⋊D73C22semidirect
31. #17988526C22semidirect
32. #17988525C22semidirect
33. #17988523C22semidirect
34. #17988522C22semidirect
35. #17988520C22semidirect
36. #17988518C22semidirect
37. #17988517C22semidirect
41. #17988513C22semidirect
42. #17988512C22semidirect
43. #17988510C22semidirect
44. #17988509C22semidirect
45. #17988507C22semidirect
46. #17988506C22semidirect
47. #17988504C22semidirect
48. #17988503C22semidirect
55. #17988501C22semidirect
56. #17988499C22semidirect
57. #17988498C22semidirect
58. #17988496C22semidirect
62. #17988495C22semidirect
68. C4×#11924007C22semidirect
69. C4×#11924005C22semidirect
72. C4×C22⋊Dic73C22semidirect
149. C23×C4×C73D4semidirect
400. C2×#525D73semidirect
416. C73#36652semidirect
502. C23×C4C22⋊D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179890982
#226179662
#226179592
#226179582
#226179532
#226179442
#226179422
#226179332
#226179312
#226179262
#226131902
#226131882
#226131732
#226131462
#226131442
#226123142
C2×#525×C732
#3665273