Finite Group Databasebeta

← #33249245

Subgroups — #33249245

Order 18688.

1990 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989118C211yesmaximal, characteristic
2#22613081C212yesmaximal, complemented
3#22613074C212yesmaximal, complemented
4#22613053C212yesmaximal, complemented
5#22613049C212yesmaximal, complemented
6#22612903C212yesmaximal, complemented
7#22612869C212yesmaximal, complemented
8#22612813C212yesmaximal, complemented
9#22612785C212yesmaximal, complemented
10#22612740C212yesmaximal, complemented
11#22612731C212yesmaximal, complemented
12#22612698C211yesmaximal, characteristic
13#22612687C211yesmaximal, characteristic, complemented
14#22612684C211yesmaximal, characteristic, complemented
15#22612580C212yesmaximal, complemented
16#22612557C212yesmaximal, complemented
17#22612325C211yesmaximal, characteristic, complemented
18#22612322C211yesmaximal, characteristic, complemented
19C73×#2333C211yesmaximal, characteristic
20#17989118C4116yescomplemented
21C2×#14556584C2212yes—
22C2×#14556582C2211yescharacteristic
23C2×#14556578C2211yescharacteristic
24C2×#14556572C2212yes—
25C2×#14556570C2211yescharacteristic
26C2×#14556556C2211yescharacteristic
27C2×D4×Dic73C2211yescharacteristic
28C2×D4×Dic73C2212yes—
29C2×#14556547C2212yes—
30C22×C4×Dic73C2211yescharacteristic
31#17988491C2212yes—
32#17988491C2212yes—
33#17988490C2212yes—
34#17988484C2212yes—
35#17988484C2212yes—
36#17988482C2212yes—
37#17988482C2212yes—
38#17988481C2212yes—
39#17988481C2212yes—
40#17988481C2212yes—
41#17988481C2212yes—
42#17988481C2212yes—
43#17988480C2212yes—
44#17988475C2212yes—
45#17988475C2212yes—
46#17988475C2212yes—
47#17988475C2212yes—
48#17988475C2212yes—
49#17988473C2212yes—
50#17988472C2212yes—
51#17988472C2212yes—
52#17988471C2212yes—
53#17988471C2212yes—
54#17988471C2212yes—
55#17988470C2212yes—
56#17988470C2212yes—
57#17988469C2212yes—
58#17988469C2212yes—
59#17988469C2212yes—
60#17988467C2212yes—
61#17988467C2212yes—
62#17988460C2212yes—
63#17988460C2212yes—
64#17988459C2212yes—
65#17988459C2212yes—
66#17988454C2212yes—
67#17988454C2212yes—
68#17988454C2212yes—
69#17988452C2212yes—
70#17988451C2212yes—
71#17988451C2212yes—
72#17988450C2211yescharacteristic
73#17988448C2212yes—
74#17988448C2212yes—
75#17988445C2212yes—
76#17988445C2211yescharacteristic
77#17988445C2212yes—
78#17988445C2211yescharacteristic
79C4⋊C4×Dic73C2212yes—
80C4×#11924007C2212yes—
81C4×#11924007C2211yescharacteristic
82C4×#11924007C2212yes—
83C4×#11924007C2211yescharacteristic
84C4×C4⋊Dic73C2212yes—
85#17988438C2212yes—
86#17988438C2212yes—
87C22⋊C4×Dic73C2212yes—
88C22⋊C4×Dic73C2212yes—
89C22⋊C4×Dic73C2212yes—
90C22⋊C4×Dic73C2211yescharacteristic
91C22⋊C4×Dic73C2211yescharacteristic
92C4×C22⋊Dic73C2212yes—
93C4×C22⋊Dic73C2211yescharacteristic
94#17988433C2211yescharacteristic
95#17988433C2211yescharacteristic
96#17988432C2212yes—
97#17988432C2212yes—
98C2×#14556498C2212yes—
99C2×#121×C73C2211yescharacteristic
100#390×C73C2212yes—
101#388×C73C2212yes—
102#387×C73C2212yes—
103#386×C73C2212yes—
104#386×C73C2212yes—
105#381×C73C2211yescharacteristic
106C4×C22⋊C4×C73C2212yes—
107C4×C22⋊C4×C73C2211yescharacteristic
108C22×Dic146C2311yescharacteristic
109C23×Dic73C2312yes—
110C23×Dic73C2312yes—
111C23×Dic73C2311yescharacteristic
112C23×Dic73C2311yescharacteristic
113#14556584C2×C4116yescomplemented
114#14556582C2×C418yescomplemented
115#14556578C2×C418yes—
116#14556572C2×C4116yescomplemented
117#14556570C2×C418yescomplemented
118#14556556C2×C418yescomplemented
119D4×Dic73C2×C418yes—
120D4×Dic73C2×C4116yescomplemented
121#14556547C2×C4116yescomplemented
122C2×C4⋊Dic73C2312yes—
123C2×C4⋊Dic73C2312yes—
124C2×C4⋊Dic73C2311yescharacteristic
125C2×#11924007C2312yes—
126C2×#11924007C2312yes—
127C2×#11924007C2312yes—
128C2×#11924007C2312yes—
129C2×#11924007C2312yes—
130C2×#11924007C2312yes—
131C2×#11924007C2312yes—
132C2×#11924007C2312yes—
133C2×#11924007C2312yes—
134C2×#11924007C2312yes—
135C2×#11924007C2312yes—
136C2×C22⋊Dic73C2312yes—
137C2×C22⋊Dic73C2312yes—
138C2×C22⋊Dic73C2311yescharacteristic
139C2×C22⋊Dic73C2311yescharacteristic
140C2×C22⋊Dic73C2312yes—
141C2×C22⋊Dic73C2312yes—
142C2×C22⋊Dic73C2312yes—
143C2×C22⋊Dic73C2312yes—
144C2×C22⋊Dic73C2312yes—
145C2×C22⋊Dic73C2312yes—
146C2×C4×Dic73C2×C418yescomplemented
147C2×C4×Dic73C2312yes—
148C2×C4×Dic73C2312yes—
149C2×C4×Dic73C2312yes—
150C2×C4×Dic73C2312yes—
151C2×C4×Dic73C2311yescharacteristic
152C2×C4×Dic73C2311yescharacteristic
153C2×C4×Dic73C2312yes—
154C2×C4×Dic73C2312yes—
155C2×C4×Dic73C2312yes—
156C2×C4×Dic73C2311yescharacteristic
157C2×C4×Dic73C2312yes—
158C2×C4×Dic73C2311yescharacteristic
159C2×C4×Dic73C2311yescharacteristic
160C2×C4×Dic73C2311yescharacteristic
161#14556498C2312yes—
162#14556498C2312yes—
163#14556498C2312yes—
164#14556498C2312yes—
165#14556498C2312yes—
166#14556498C2312yes—
167#14556498C2312yes—
168#14556498C2312yes—
169#14556498C2312yes—
170#14556498C2312yes—
171#14556498C2312yes—
172#14556498C2312yes—
173#14556498C2312yes—
174#14556498C2312yes—
175#14556498C2312yes—
176#14556498C2312yes—
177#14556498C2312yes—
178#14556498C2312yes—
179#14556498C2312yes—
180#14556498C2312yes—
181#14556498C2312yes—
182#14556498C2312yes—
183#14556498C2312yes—
184C22×D4×C73C2311yescharacteristic
185C22×D4×C73C2312yes—
186C23×C4×C73C2312yes—
187C23×C4×C73C2311yescharacteristic
188#121×C73C2×C418yes—
189C2×C4⋊C4×C73C2312yes—
190C2×C4⋊C4×C73C2311yescharacteristic
191C2×C22⋊C4×C73C2312yes—
192C2×C22⋊C4×C73C2312yes—
193C2×C22⋊C4×C73C2311yescharacteristic
194C2×C22⋊C4×C73C2311yescharacteristic
195C2×C22⋊C4×C73C2312yes—
196C2×C22⋊C4×C73C2312yes—
197C2×C22⋊C4×C73C2312yes—
198C2×C42×C73C2311yescharacteristic
199C2×C42×C73C2312yes—
200C2×C42×C73C2311yescharacteristic
201#95×C73C2312yes—
202#95×C73C2312yes—
203#95×C73C2312yes—
204#95×C73C2312yes—
205#95×C73C2312yes—
206C2×Dic146—41no—
207C2×Dic146—41no—
208C2×Dic146C22×C414yes—
209C22×Dic73—42no—
210C22×Dic73—42no—
211C22×Dic73—42no—
212C22×Dic73—42no—
213C22×Dic73—42no—
214C22×Dic73—42no—
215C22×Dic73—42no—
216C22×Dic73C22×C414yes—
217C22×Dic73C22×C414yes—
218C22×Dic73C22×C418yes—
219C22×Dic73C2412yes—
220C22×Dic73C2412yes—
221C22×Dic73C2412yes—
222C22×Dic73C2412yes—
223C22×Dic73C2411yescharacteristic
224C22×Dic73C2411yescharacteristic
225C22×Dic73C2412yes—
226C22×Dic73C2411yescharacteristic
227C22×Dic73C2411yescharacteristic
228C22×Dic73C2412yes—
229C4⋊Dic73—42no—
230C4⋊Dic73C22×C414yes—
231C4⋊Dic73C22×C418yes—
232#11924007—42no—
233#11924007—42no—
234#11924007—42no—
235#11924007—42no—
236#11924007—42no—
237#11924007—42no—
238#11924007—42no—
239#11924007—42no—
240#11924007C22×C418yes—
241#11924007C22×C418yes—
242#11924007C22×C418yes—
243C22⋊Dic73—42no—
244C22⋊Dic73—42no—
245C22⋊Dic73—42no—
246C22⋊Dic73—41no—
247C22⋊Dic73—41no—
248C22⋊Dic73—42no—
249C22⋊Dic73C22×C418yes—
250C22⋊Dic73C22×C418yes—
251C22⋊Dic73C22×C418yes—
252C22⋊Dic73C22×C418yes—
253C4×Dic73—42no—
254C4×Dic73—42no—
255C4×Dic73—42no—
256C4×Dic73—42no—
257C4×Dic73—42no—
258C4×Dic73—42no—
259C4×Dic73—41no—
260C4×Dic73—42no—
261C4×Dic73—41no—
262C4×Dic73C22×C414yes—
263C4×Dic73C22×C414yes—
264C4×Dic73C22×C414yes—
265C4×Dic73C22×C414yes—
266C4×Dic73C22×C418yes—
267C24×C73C2411yescharacteristic
268C24×C73C2412yes—
269C2×D4×C73—42no—
270C2×D4×C73—42no—
271C2×D4×C73—41no—
272C2×D4×C73—41no—
273C2×D4×C73C22×C414yes—
274C2×D4×C73C22×C418yes—
275C22×C4×C73—41no—
276C22×C4×C73—41no—
277C22×C4×C73—42no—
278C22×C4×C73—42no—
279C22×C4×C73—42no—
280C22×C4×C73C22×C414yes—
281C22×C4×C73C2412yes—
282C22×C4×C73C2412yes—
283C22×C4×C73C2412yes—
284C22×C4×C73C2412yes—
285C22×C4×C73C2411yescharacteristic
286C22×C4×C73C2411yescharacteristic
287C22×C4×C73C2412yes—
288C4⋊C4×C73—42no—
289C4⋊C4×C73C22×C414yes—
290C22⋊C4×C73—42no—
291C22⋊C4×C73—42no—
292C22⋊C4×C73—42no—
293C22⋊C4×C73—41no—
294C22⋊C4×C73—42no—
295C22⋊C4×C73—41no—
296C22⋊C4×C73C22×C418yes—
297C42×C73—41no—
298C42×C73—41no—
299C42×C73—42no—
300C23×C73—21no—
301C23×C73—21no—
302C23×C73—22no—
303C23×C73—22no—
304C23×C73—22no—
305C23×C73—22no—
306C23×C73—22no—
307C23×C73—22no—
308C23×C73—22no—
309C23×C73—22no—
310C23×C73C23×C414yes—
311C23×C73C23×C412yes—
312C23×C73C2511yescharacteristic
313D4×C73—44no—
314D4×C73—48no—
315C2×C4×C73—21no—
316C2×C4×C73—21no—
317C2×C4×C73—22no—
318C2×C4×C73—22no—
319C2×C4×C73—21no—
320C2×C4×C73—21no—
321C2×C4×C73—22no—
322C2×C4×C73—22no—
323C2×C4×C73—22no—
324C2×C4×C73—22no—
325C2×C4×C73—22no—
326C2×C4×C73—22no—
327C2×C4×C73—22no—
328C2×C4×C73—22no—
329C2×C4×C73—22no—
330C2×C4×C73—22no—
331C2×C4×C73—22no—
332C2×C4×C73—22no—
333C2×C4×C73—44no—
334C2×C4×C73—84no—
335C2×C4×C73C23×C412yes—
336C2×C4×C73C23×C414yes—
337C2×C4×C73C23×C412yes—
338C2×Dic73—22no—
339C2×Dic73—22no—
340C2×Dic73—22no—
341C2×Dic73—22no—
342C2×Dic73—22no—
343C2×Dic73—22no—
344C2×Dic73—22no—
345C2×Dic73—22no—
346C2×Dic73—22no—
347C2×Dic73—22no—
348C2×Dic73—22no—
349C2×Dic73—22no—
350C2×Dic73—22no—
351C2×Dic73—22no—
352C2×Dic73—22no—
353C2×Dic73—22no—
354C2×Dic73—22no—
355C2×Dic73—22no—
356C2×Dic73—22no—
357C2×Dic73—22no—
358C2×Dic73—44no—
359C2×Dic73—48no—
360C2×Dic73—44no—
361C2×Dic73—84no—
362C2×Dic73C23×C412yes—
363C2×Dic73C23×C412yes—
364C2×Dic73C23×C412yes—
365C2×Dic73C23×C412yes—
366C2×Dic73C23×C414yes—
367C2×Dic73C23×C414yes—
368Dic146—44no—
369C22×C73—22no—
370C22×C73—22no—
371C22×C73—24no—
372C22×C73—22no—
373C22×C73—24no—
374C22×C73—24no—
375C22×C73—42no—
376C22×C73—42no—
377C22×C73—42no—
378C22×C73—42no—
379C22×C73—42no—
380C22×C73—42no—
381C22×C73C24×C411yescharacteristic
382C22×C73#58511yescharacteristic
383C22×C73#58512yes—
384C22×C73#58511yescharacteristic
385C22×C73#58512yes—
386C4×C73—22no—
387C4×C73—22no—
388C4×C73—24no—
389C4×C73—42no—
390C4×C73—42no—
391C4×C73—42no—
392C4×C73—42no—
393Dic73—24no—
394Dic73—22no—
395Dic73—22no—
396Dic73—22no—
397Dic73—22no—
398Dic73—24no—
399Dic73—42no—
400Dic73—42no—
401Dic73—42no—
402Dic73—42no—
403#34400—731nomaximal, Sylow
404C2×C73—42no—
405C2×C73—44no—
406C2×C73#342811yescharacteristic
407C2×C73#342811yescharacteristic
408C2×C73#342811yescharacteristic
409C2×C73#356612yes—
410C2×C73#356612yes—
411C2×#529—731no—
412#2376—732no—
413#2376—732no—
414#2373—732no—
415#2373—732no—
416#2357—732no—
417#2353—732no—
418#2346—732no—
419#2343—732no—
420#2337—732no—
421#2336—732no—
422#2333—731no—
423#2333D7311yescharacteristic
424#2332—731no—
425#2332—731no—
426#2320—732no—
427#2318—732no—
428#2283—731no—
429#2283—731no—
430C73#3440011yescharacteristic, complemented, Sylow
431#529—7316no—
432C2×#126—732no—
433C2×#125—731no—
434C2×#124—731no—
435C2×#123—732no—
436C2×C22⋊Q8—731no—
437C2×#121C2×D7311yescharacteristic
438C2×C4×Q8—731no—
439C2×C4×D4—731no—
440C2×C4×D4—732no—
441C2×#117—732no—
442C22×C42—731no—
443#391—732no—
444#391—732no—
445#390—732no—
446#390C2×D7312yes—
447#389—732no—
448#389—732no—
449#389—732no—
450#389—732no—
451#388—732no—
452#388—732no—
453#388—732no—
454#388—732no—
455#388—732no—
456#388—732no—
457#388—732no—
458#388—732no—
459#388—732no—
460#388—732no—
461#388—732no—
462#388C2×D7312yes—
463#387—732no—
464#387—732no—
465#387—732no—
466#387—732no—
467#387—732no—
468#387—732no—
469#387—732no—
470#387—732no—
471#387—732no—
472#387—732no—
473#387—732no—
474#387C2×D7312yes—
475#386—732no—
476#386—732no—
477#386C2×D7312yes—
478#386C2×D7312yes—
479#385—732no—
480#385—732no—
481#385—732no—
482#385—732no—
483#383—732no—
484#383—732no—
485#383—732no—
486#382—732no—
487#382—732no—
488#382—732no—
489#381—731no—
490#381—732no—
491#381—732no—
492#381C2×D7311yescharacteristic
493#380—732no—
494#380—732no—
495#380—731no—
496#380—731no—
497C4×C4⋊C4—732no—
498C4×C4⋊C4—732no—
499C4×C4⋊C4—732no—
500C4×C4⋊C4—732no—
501C4×C4⋊C4—731no—
502C4×C4⋊C4—731no—
503C4×C4⋊C4—732no—
504C4×C4⋊C4—732no—
505C4×C22⋊C4—731no—
506C4×C22⋊C4—732no—
507C4×C22⋊C4—732no—
508C4×C22⋊C4—732no—
509C4×C22⋊C4—732no—
510C4×C22⋊C4—731no—
511C4×C22⋊C4—731no—
512C4×C22⋊C4C2×D7311yescharacteristic
513C4×C22⋊C4C2×D7312yes—
514#376—731no—
515#376—731no—
516#376—732no—
517#376—732no—
518C2×#95—732no—
519C22×Q8—731no—
520C22×D4C22×D7312yes—
521C22×D4C22×D7311yescharacteristic
522C23×C4—732no—
523C23×C4—732no—
524C23×C4—731no—
525C23×C4—731no—
526C23×C4C22×D7312yes—
527C23×C4C22×D7311yescharacteristic
528#126—7316no—
529#125—738no—
530#124—738no—
531#123—7316no—
532C22⋊Q8—738no—
533#121C4×D7318yes—
534C4×Q8—738no—
535C4×D4—738no—
536C4×D4—7316no—
537#117—7316no—
538C2×C4⋊C4—732no—
539C2×C4⋊C4—732no—
540C2×C4⋊C4—732no—
541C2×C4⋊C4—732no—
542C2×C4⋊C4—732no—
543C2×C4⋊C4—732no—
544C2×C4⋊C4—732no—
545C2×C4⋊C4—732no—
546C2×C4⋊C4—732no—
547C2×C4⋊C4—732no—
548C2×C4⋊C4—732no—
549C2×C4⋊C4—731no—
550C2×C4⋊C4—732no—
551C2×C4⋊C4—732no—
552C2×C4⋊C4C22×D7312yes—
553C2×C4⋊C4C22×D7311yescharacteristic
554C2×C22⋊C4—731no—
555C2×C22⋊C4—732no—
556C2×C22⋊C4—731no—
557C2×C22⋊C4—732no—
558C2×C22⋊C4—732no—
559C2×C22⋊C4—732no—
560C2×C22⋊C4—732no—
561C2×C22⋊C4—732no—
562C2×C22⋊C4—732no—
563C2×C22⋊C4—732no—
564C2×C22⋊C4C22×D7311yescharacteristic
565C2×C22⋊C4C22×D7311yescharacteristic
566C2×C22⋊C4C22×D7312yes—
567C2×C22⋊C4C22×D7312yes—
568C2×C22⋊C4C22×D7312yes—
569C2×C22⋊C4C22×D7312yes—
570C2×C22⋊C4C22×D7312yes—
571C2×C42—732no—
572C2×C42—731no—
573C2×C42—732no—
574C2×C42—731no—
575C2×C42—732no—
576C2×C42—732no—
577C2×C42—732no—
578C2×C42—732no—
579C2×C42—732no—
580C2×C42—738no—
581C2×C42—731no—
582C2×C42—732no—
583C2×C42—731no—
584C2×C42—731no—
585C2×C42—731no—
586C2×C42C22×D7311yescharacteristic
587C2×C42C22×D7311yescharacteristic
588C2×C42C22×D7312yes—
589#95—732no—
590#95—732no—
591#95—732no—
592#95—732no—
593#95—732no—
594#95—732no—
595#95—732no—
596#95—732no—
597#95—732no—
598#95—732no—
599#95—732no—
600#95—732no—
601#95—732no—
602#95—732no—
603#95—732no—
604#95—732no—
605#95—732no—
606#95—732no—
607#95—732no—
608#95—732no—
609#95—732no—
610#95—732no—
611#95—732no—
612#95C22×D7312yes—
613#95C22×D7312yes—
614#95C22×D7312yes—
615#95C22×D7312yes—
616#95C22×D7312yes—
617C24C23×D7311yescharacteristic
618C24C23×D7312yes—
619C2×Q8—2921no—
620C2×Q8—2921no—
621C2×Q8—734no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4C2×C4×D7318yes—
627C2×D4C2×C4×D7314yes—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—2922no—
634C22×C4—2922no—
635C22×C4—2922no—
636C22×C4—2922no—
637C22×C4—2922no—
638C22×C4—2922no—
639C22×C4—2922no—
640C22×C4—734no—
641C22×C4—734no—
642C22×C4—738no—
643C22×C4—731no—
644C22×C4—731no—
645C22×C4—732no—
646C22×C4—731no—
647C22×C4—731no—
648C22×C4—732no—
649C22×C4—732no—
650C22×C4—732no—
651C22×C4—732no—
652C22×C4—732no—
653C22×C4C2×C4×D7314yes—
654C22×C4C23×D7312yes—
655C22×C4C23×D7312yes—
656C22×C4C23×D7312yes—
657C22×C4C23×D7312yes—
658C22×C4C23×D7311yescharacteristic
659C22×C4C23×D7311yescharacteristic
660C22×C4C23×D7312yes—
661C4⋊C4—42no—
662C4⋊C4—2922no—
663C4⋊C4—2922no—
664C4⋊C4—2922no—
665C4⋊C4—2922no—
666C4⋊C4—2922no—
667C4⋊C4—2922no—
668C4⋊C4—2922no—
669C4⋊C4—2922no—
670C4⋊C4—2922no—
671C4⋊C4—738no—
672C4⋊C4—738no—
673C4⋊C4—738no—
674C4⋊C4—734no—
675C4⋊C4—738no—
676C4⋊C4C2×C4×D7314yes—
677C22⋊C4—42no—
678C22⋊C4—41no—
679C22⋊C4—41no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—2922no—
684C22⋊C4—2921no—
685C22⋊C4—2921no—
686C22⋊C4—2922no—
687C22⋊C4—2922no—
688C22⋊C4—2922no—
689C22⋊C4—738no—
690C22⋊C4—738no—
691C22⋊C4—738no—
692C22⋊C4—738no—
693C22⋊C4C2×C4×D7318yes—
694C42—41no—
695C42—41no—
696C42—42no—
697C42—2921no—
698C42—2921no—
699C42—2922no—
700C42—2922no—
701C42—2922no—
702C42—2922no—
703C42—2922no—
704C42—2922no—
705C42—2922no—
706C42—734no—
707C42—734no—
708C42—734no—
709C42—734no—
710C42—738no—
711C23—21no—
712C23—21no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23C22×C4×D7314yes—
722C23C22×C4×D7312yes—
723C23C24×D7311yescharacteristic
724Q8—2924no—
725D4—44no—
726D4—48no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—44no—
746C2×C4—84no—
747C2×C4—2924no—
748C2×C4—2924no—
749C2×C4—2928no—
750C2×C4—5844no—
751C2×C4—732no—
752C2×C4—732no—
753C2×C4—732no—
754C2×C4—732no—
755C2×C4—734no—
756C2×C4—734no—
757C2×C4—1462no—
758C2×C4—1462no—
759C2×C4—1462no—
760C2×C4—1462no—
761C2×C4—1462no—
762C2×C4—1462no—
763C2×C4—1462no—
764C2×C4—1462no—
765C2×C4—1462no—
766C2×C4—1462no—
767C2×C4—1462no—
768C2×C4—1462no—
769C2×C4—1462no—
770C2×C4—1462no—
771C2×C4—1462no—
772C2×C4—1462no—
773C2×C4—1462no—
774C2×C4—1462no—
775C2×C4—1462no—
776C2×C4—1462no—
777C2×C4C22×C4×D7312yes—
778C2×C4C22×C4×D7312yes—
779C2×C4C22×C4×D7314yes—
780C22—22no—
781C22—22no—
782C22—24no—
783C22—24no—
784C22—22no—
785C22—24no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22C23×C4×D7311yescharacteristic
793C22#1798942211yescharacteristic
794C22#1798942212yes—
795C22#1798942211yescharacteristic
796C22#1798942312yes—
797C4—22no—
798C4—22no—
799C4—24no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—2922no—
805C4—2922no—
806C4—2922no—
807C4—2922no—
808C4—1462no—
809C4—1462no—
810C4—1464no—
811C4—1462no—
812C4—1462no—
813C4—1464no—
814C2—42no—
815C2—44no—
816C2#2262312911yescharacteristic
817C2#2262312911yescharacteristic
818C2#2262313011yescharacteristic
819C2#2262459512yes—
820C2#2262460312yes—
subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
FittingC73×#2333C2
socle, cosocleC23×C73C25
prime radicalC2×#121×C73C22
hypercenter#2333D73
hypocenterC73#34400
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2333

Complements

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

NH ≅ G/Ntype
2. #22613081C2semidirect
3. #22613074C2semidirect
4. #22613053C2semidirect
5. #22613049C2semidirect
6. #22612903C2semidirect
7. #22612869C2semidirect
8. #22612813C2semidirect
9. #22612785C2semidirect
10. #22612740C2semidirect
11. #22612731C2semidirect
13. #22612687C2semidirect
14. #22612684C2semidirect
15. #22612580C2semidirect
16. #22612557C2semidirect
17. #22612325C2semidirect
18. #22612322C2semidirect
20. #17989118C4semidirect
113. #14556584C2×C4semidirect
114. #14556582C2×C4semidirect
116. #14556572C2×C4semidirect
117. #14556570C2×C4semidirect
118. #14556556C2×C4semidirect
120. D4×Dic73C2×C4semidirect
121. #14556547C2×C4semidirect
146. C2×C4×Dic73C2×C4semidirect
430. C73#34400semidirect

Maximal subgroups

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

subgroupindex
C2×#179891182
#226130812
#226130742
#226130532
#226130492
#226129032
#226128692
#226128132
#226127852
#226127402
#226127312
#226126982
#226126872
#226126842
#226125802
#226125572
#226123252
#226123222
C73×#23332
#3440073