Finite Group Databasebeta

← #33251842

Subgroups — #33251842

Order 18688.

2016 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989337C211yesmaximal, characteristic
2#22613098C212yesmaximal, complemented
3#22613081C211yesmaximal, characteristic
4#22613066C211yesmaximal, characteristic
5#22613049C212yesmaximal, complemented
6#22613046C212yesmaximal, complemented
7#22613043C211yesmaximal, characteristic
8#22613036C212yesmaximal, complemented
9#22612985C212yesmaximal, complemented
10#22612931C212yesmaximal, complemented
11#22612707C212yesmaximal, complemented
12#22612704C212yesmaximal, complemented
13#22612681C212yesmaximal, complemented
14#22612674C212yesmaximal, complemented
15#22612670C212yesmaximal, complemented
16#22612596C211yesmaximal, characteristic
17#22612463C212yesmaximal, complemented
18C4×#14556572C211yesmaximal, characteristic
19C73×#2326C211yesmaximal, characteristic
20#17989337C4116yescomplemented
21C2×#14556589C2212yes—
22C2×#14556584C2212yes—
23C2×#14556584C2212yes—
24C2×#14556583C2212yes—
25C2×#14556572C2211yescharacteristic
26C2×#14556572C2211yescharacteristic
27C2×#14556568C2212yes—
28C2×#14556568C2212yes—
29C2×#14556556C2212yes—
30C22×#11924007C2211yescharacteristic
31C22×C4×Dic73C2211yescharacteristic
32#17988494C2212yes—
33#17988493C2212yes—
34#17988491C2212yes—
35#17988491C2212yes—
36#17988484C2212yes—
37#17988483C2212yes—
38#17988483C2212yes—
39#17988482C2212yes—
40#17988482C2212yes—
41#17988482C2212yes—
42#17988482C2212yes—
43#17988482C2212yes—
44#17988481C2212yes—
45#17988481C2212yes—
46#17988481C2212yes—
47#17988481C2212yes—
48#17988480C2212yes—
49#17988480C2212yes—
50#17988475C2212yes—
51#17988475C2212yes—
52#17988474C2212yes—
53#17988472C2212yes—
54#17988472C2212yes—
55#17988471C2212yes—
56#17988471C2212yes—
57#17988471C2212yes—
58#17988470C2212yes—
59#17988470C2212yes—
60#17988469C2212yes—
61#17988469C2212yes—
62#17988469C2212yes—
63#17988468C2212yes—
64#17988468C2212yes—
65#17988468C2212yes—
66#17988468C2212yes—
67#17988468C2212yes—
68#17988467C2211yescharacteristic
69#17988467C2211yescharacteristic
70#17988460C2212yes—
71#17988459C2211yescharacteristic
72#17988459C2212yes—
73#17988459C2211yescharacteristic
74#17988451C2212yes—
75#17988448C2211yescharacteristic
76#17988448C2211yescharacteristic
77#17988445C2212yes—
78C4⋊C4×Dic73C2212yes—
79C4⋊C4×Dic73C2212yes—
80C4⋊C4×Dic73C2212yes—
81C4×#11924007C2212yes—
82C4×#11924007C2212yes—
83C4×#11924007C2212yes—
84C4×#11924007C2212yes—
85#17988438C2212yes—
86#17988438C2212yes—
87#17988438C2212yes—
88C22⋊C4×Dic73C2212yes—
89C22⋊C4×Dic73C2212yes—
90C22⋊C4×Dic73C2212yes—
91C22⋊C4×Dic73C2212yes—
92C4×C22⋊Dic73C2211yescharacteristic
93C4×C22⋊Dic73C2212yes—
94C4×C22⋊Dic73C2211yescharacteristic
95#17988433C2212yes—
96#17988432C2212yes—
97C2×#124×C73C2211yescharacteristic
98C2×C4×Q8×C73C2211yescharacteristic
99C2×C4×D4×C73C2211yescharacteristic
100#391×C73C2211yescharacteristic
101#390×C73C2211yescharacteristic
102#388×C73C2212yes—
103#388×C73C2212yes—
104#385×C73C2212yes—
105#385×C73C2212yes—
106#384×C73C2211yescharacteristic
107#376×C73C2211yescharacteristic
108C22×Dic146C2312yes—
109C23×Dic73C2311yescharacteristic
110C23×Dic73C2311yescharacteristic
111C23×Dic73C2311yescharacteristic
112C23×Dic73C2311yescharacteristic
113#14556589C2×C4116yescomplemented
114#14556584C2×C4116yescomplemented
115#14556584C2×C4116yescomplemented
116#14556583C2×C4116yescomplemented
117#14556572C2×C418yes—
118#14556572C2×C418yes—
119#14556568C2×C4116yescomplemented
120#14556568C2×C4116yescomplemented
121#14556556—44no—
122C2×C4⋊Dic73C2312yes—
123C2×C4⋊Dic73C2312yes—
124C2×C4⋊Dic73C2312yes—
125C2×#11924007—42no—
126C2×#11924007C2312yes—
127C2×#11924007C2312yes—
128C2×#11924007C2312yes—
129C2×#11924007C2312yes—
130C2×#11924007C2312yes—
131C2×#11924007C2312yes—
132C2×#11924007C2312yes—
133C2×#11924007C2312yes—
134C2×#11924007C2312yes—
135C2×#11924007C2312yes—
136C2×#11924007C2312yes—
137C2×#11924007C2312yes—
138C2×#11924007C2312yes—
139C2×#11924007C2312yes—
140C2×C22⋊Dic73C2312yes—
141C2×C22⋊Dic73C2311yescharacteristic
142C2×C22⋊Dic73C2311yescharacteristic
143C2×C22⋊Dic73C2312yes—
144C2×C22⋊Dic73C2312yes—
145C2×C22⋊Dic73C2311yescharacteristic
146C2×C22⋊Dic73C2311yescharacteristic
147C2×C22⋊Dic73C2312yes—
148C2×C4×Dic73—42no—
149C2×C4×Dic73C2312yes—
150C2×C4×Dic73C2312yes—
151C2×C4×Dic73C2312yes—
152C2×C4×Dic73C2312yes—
153C2×C4×Dic73C2312yes—
154C2×C4×Dic73C2312yes—
155C2×C4×Dic73C2312yes—
156C2×C4×Dic73C2312yes—
157C2×C4×Dic73C2312yes—
158C2×C4×Dic73C2312yes—
159C2×C4×Dic73C2312yes—
160C2×C4×Dic73C2312yes—
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—
183C22×Q8×C73C2311yescharacteristic
184C22×D4×C73C2311yescharacteristic
185C23×C4×C73C2311yescharacteristic
186C23×C4×C73C2311yescharacteristic
187#124×C73C2×C418yes—
188C4×Q8×C73—42no—
189C4×D4×C73—42no—
190C2×C4⋊C4×C73C2312yes—
191C2×C4⋊C4×C73C2312yes—
192C2×C4⋊C4×C73C2312yes—
193C2×C4⋊C4×C73C2311yescharacteristic
194C2×C4⋊C4×C73C2311yescharacteristic
195C2×C22⋊C4×C73C2312yes—
196C2×C22⋊C4×C73C2312yes—
197C2×C22⋊C4×C73C2311yescharacteristic
198C2×C22⋊C4×C73C2311yescharacteristic
199C2×C22⋊C4×C73C2312yes—
200C2×C22⋊C4×C73C2312yes—
201C2×C42×C73C2311yescharacteristic
202C2×C42×C73C2312yes—
203C2×C42×C73C2311yescharacteristic
204C2×C42×C73C2311yescharacteristic
205#95×C73C2312yes—
206#95×C73C2312yes—
207#95×C73C2312yes—
208#95×C73C2312yes—
209C2×Dic146—42no—
210C2×Dic146—42no—
211C2×Dic146C22×C418yes—
212C22×Dic73—24no—
213C22×Dic73—41no—
214C22×Dic73—41no—
215C22×Dic73—41no—
216C22×Dic73—41no—
217C22×Dic73—41no—
218C22×Dic73—41no—
219C22×Dic73—42no—
220C22×Dic73C22×C414yes—
221C22×Dic73C22×C414yes—
222C22×Dic73C2412yes—
223C22×Dic73C2412yes—
224C22×Dic73C2412yes—
225C22×Dic73C2412yes—
226C22×Dic73C2412yes—
227C22×Dic73C2412yes—
228C22×Dic73C2412yes—
229C22×Dic73C2412yes—
230C4⋊Dic73—42no—
231C4⋊Dic73C22×C418yes—
232C4⋊Dic73C22×C418yes—
233#11924007—24no—
234#11924007—24no—
235#11924007—42no—
236#11924007—42no—
237#11924007—42no—
238#11924007—42no—
239#11924007—42no—
240#11924007—42no—
241#11924007C22×C418yes—
242#11924007C22×C418yes—
243#11924007C22×C418yes—
244#11924007C22×C418yes—
245#11924007C22×C418yes—
246#11924007C22×C418yes—
247C22⋊Dic73—24no—
248C22⋊Dic73—42no—
249C22⋊Dic73—41no—
250C22⋊Dic73—41no—
251C22⋊Dic73C22×C418yes—
252C22⋊Dic73C22×C418yes—
253C22⋊Dic73C22×C414yes—
254C22⋊Dic73C22×C414yes—
255C4×Dic73—24no—
256C4×Dic73—24no—
257C4×Dic73—24no—
258C4×Dic73—42no—
259C4×Dic73—42no—
260C4×Dic73—42no—
261C4×Dic73—42no—
262C4×Dic73—42no—
263C4×Dic73—42no—
264C4×Dic73—42no—
265C4×Dic73—42no—
266C4×Dic73C22×C418yes—
267C24×C73C2411yescharacteristic
268C24×C73C2411yescharacteristic
269C2×Q8×C73—41no—
270C2×Q8×C73—41no—
271C2×Q8×C73C22×C414yes—
272C2×D4×C73—41no—
273C2×D4×C73—41no—
274C2×D4×C73C22×C414yes—
275C22×C4×C73—22no—
276C22×C4×C73—22no—
277C22×C4×C73—42no—
278C22×C4×C73—42no—
279C22×C4×C73C2412yes—
280C22×C4×C73C2411yescharacteristic
281C22×C4×C73C2411yescharacteristic
282C22×C4×C73C2411yescharacteristic
283C22×C4×C73C2412yes—
284C22×C4×C73C2412yes—
285C22×C4×C73C2412yes—
286C22×C4×C73C2411yescharacteristic
287C22×C4×C73C2411yescharacteristic
288C4⋊C4×C73—24no—
289C4⋊C4×C73—42no—
290C4⋊C4×C73—42no—
291C4⋊C4×C73—41no—
292C4⋊C4×C73—41no—
293C22⋊C4×C73—42no—
294C22⋊C4×C73—42no—
295C22⋊C4×C73—41no—
296C22⋊C4×C73—41no—
297C22⋊C4×C73C22×C418yes—
298C22⋊C4×C73C22×C418yes—
299C42×C73—22no—
300C42×C73—41no—
301C42×C73—42no—
302C42×C73C22×C414yes—
303C23×C73—21no—
304C23×C73—21no—
305C23×C73—22no—
306C23×C73—22no—
307C23×C73—22no—
308C23×C73—22no—
309C23×C73—21no—
310C23×C73—21no—
311C23×C73C23×C412yes—
312C23×C73C23×C412yes—
313C23×C73C2511yescharacteristic
314Q8×C73—44no—
315D4×C73—44no—
316C2×C4×C73—21no—
317C2×C4×C73—22no—
318C2×C4×C73—22no—
319C2×C4×C73—21no—
320C2×C4×C73—22no—
321C2×C4×C73—22no—
322C2×C4×C73—22no—
323C2×C4×C73—21no—
324C2×C4×C73—22no—
325C2×C4×C73—21no—
326C2×C4×C73—21no—
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—22no—
334C2×C4×C73—22no—
335C2×C4×C73—44no—
336C2×C4×C73—82no—
337C2×C4×C73C23×C414yes—
338C2×C4×C73C23×C412yes—
339C2×C4×C73C23×C414yes—
340C2×C4×C73H(5,𝔽2)12yes—
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—22no—
359C2×Dic73—22no—
360C2×Dic73—44no—
361C2×Dic73—44no—
362C2×Dic73—44no—
363C2×Dic73—82no—
364C2×Dic73C23×C414yes—
365C2×Dic73C23×C414yes—
366C2×Dic73C23×C414yes—
367C2×Dic73C23×C414yes—
368C2×Dic732−1+414yes—
369Dic146—48no—
370C22×C73—22no—
371C22×C73—22no—
372C22×C73—24no—
373C22×C73—24no—
374C22×C73—41no—
375C22×C73—41no—
376C22×C73—41no—
377C22×C73—41no—
378C22×C73—42no—
379C22×C73—42no—
380C22×C73C24×C411yescharacteristic
381C22×C73C2×H(5,𝔽2)11yescharacteristic
382C22×C73C2×2−1+412yes—
383C22×C73#58512yes—
384C22×C73#58511yescharacteristic
385C4×C73—24no—
386C4×C73—22no—
387C4×C73—24no—
388C4×C73—22no—
389C4×C73—42no—
390C4×C73—41no—
391C4×C73—41no—
392C4×C73—41no—
393C4×C73—42no—
394Dic73—24no—
395Dic73—24no—
396Dic73—24no—
397Dic73—24no—
398Dic73—24no—
399Dic73—42no—
400Dic73—42no—
401Dic73—42no—
402#34514—731nomaximal, Sylow
403C2×C73—42no—
404C2×C73—42no—
405C2×C73C4×H(5,𝔽2)11yescharacteristic
406C2×C73C4×2−1+412yes—
407C2×C73#353311yescharacteristic
408C2×C73#353811yescharacteristic
409C2×C73#356512yes—
410C2×#563—731no—
411#2378—732no—
412#2376—731no—
413#2374—731no—
414#2373—732no—
415#2373—732no—
416#2372—731no—
417#2371—732no—
418#2365—732no—
419#2360—732no—
420#2334—732no—
421#2334—732no—
422#2332—732no—
423#2331—732no—
424#2330—732no—
425#2326D7311yescharacteristic
426#2322—731no—
427C4×C22⋊Q8—732no—
428C4×#123—731no—
429C73#3451411yescharacteristic, complemented, Sylow
430#563—7316no—
431C2×C4⋊Q8—732no—
432C2×#126—732no—
433C2×#126—732no—
434C2×#125—732no—
435C2×#124C2×D7311yescharacteristic
436C2×#123—731no—
437C2×#123—731no—
438C2×C22⋊Q8—732no—
439C2×C22⋊Q8—732no—
440C2×C4×Q8—732no—
441C2×C4×Q8C2×D7311yescharacteristic
442C2×C4×D4C2×D7311yescharacteristic
443C22×C4⋊C4—731no—
444C22×C42—731no—
445#391—732no—
446#391—732no—
447#391—732no—
448#391—732no—
449#391C2×D7311yescharacteristic
450#390C2×D7311yescharacteristic
451#389—732no—
452#389—732no—
453#389—732no—
454#389—732no—
455#389—732no—
456#389—732no—
457#389—732no—
458#389—732no—
459#388—732no—
460#388—732no—
461#388—732no—
462#388—732no—
463#388—732no—
464#388—732no—
465#388—732no—
466#388—732no—
467#388C2×D7312yes—
468#388C2×D7312yes—
469#387—732no—
470#387—732no—
471#387—732no—
472#387—732no—
473#387—732no—
474#387—732no—
475#387—732no—
476#387—732no—
477#387—732no—
478#387—732no—
479#387—732no—
480#387—732no—
481#387—732no—
482#387—732no—
483#387—732no—
484#387—732no—
485#386—731no—
486#386—731no—
487#385—732no—
488#385—731no—
489#385—732no—
490#385—731no—
491#385C2×D7312yes—
492#385C2×D7312yes—
493#384C2×D7311yescharacteristic
494#382—732no—
495#381—731no—
496#381—731no—
497#380—732no—
498C4×C4⋊C4—732no—
499C4×C4⋊C4—732no—
500C4×C4⋊C4—732no—
501C4×C4⋊C4—732no—
502C4×C4⋊C4—732no—
503C4×C4⋊C4—732no—
504C4×C4⋊C4—732no—
505C4×C4⋊C4—732no—
506C4×C4⋊C4—732no—
507C4×C4⋊C4—732no—
508C4×C22⋊C4—731no—
509C4×C22⋊C4—731no—
510C4×C22⋊C4—732no—
511C4×C22⋊C4—732no—
512C4×C22⋊C4—732no—
513C4×C22⋊C4—732no—
514C4×C22⋊C4—732no—
515#376—732no—
516#376—732no—
517#376C2×D7311yescharacteristic
518C22×Q8—732no—
519C22×Q8C22×D7311yescharacteristic
520C22×D4C22×D7311yescharacteristic
521C23×C4—731no—
522C23×C4—731no—
523C23×C4—731no—
524C23×C4—731no—
525C23×C4C22×D7311yescharacteristic
526C23×C4C22×D7311yescharacteristic
527C4⋊Q8—7316no—
528#126—7316no—
529#126—7316no—
530#125—7316no—
531#124C4×D7318yes—
532#123—738no—
533#123—738no—
534C22⋊Q8—7316no—
535C22⋊Q8—7316no—
536C4×Q8—42no—
537C4×Q8—2924no—
538C4×D4—42no—
539C2×C4⋊C4—2922no—
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—732no—
550C2×C4⋊C4—732no—
551C2×C4⋊C4—732no—
552C2×C4⋊C4—732no—
553C2×C4⋊C4—732no—
554C2×C4⋊C4—732no—
555C2×C4⋊C4—732no—
556C2×C4⋊C4—732no—
557C2×C4⋊C4C22×D7312yes—
558C2×C4⋊C4C22×D7311yescharacteristic
559C2×C4⋊C4C22×D7311yescharacteristic
560C2×C4⋊C4C22×D7312yes—
561C2×C4⋊C4C22×D7312yes—
562C2×C22⋊C4—732no—
563C2×C22⋊C4—731no—
564C2×C22⋊C4—731no—
565C2×C22⋊C4—732no—
566C2×C22⋊C4—732no—
567C2×C22⋊C4—731no—
568C2×C22⋊C4—731no—
569C2×C22⋊C4—732no—
570C2×C22⋊C4C22×D7311yescharacteristic
571C2×C22⋊C4C22×D7311yescharacteristic
572C2×C22⋊C4C22×D7312yes—
573C2×C22⋊C4C22×D7312yes—
574C2×C22⋊C4C22×D7312yes—
575C2×C22⋊C4C22×D7312yes—
576C2×C42—2922no—
577C2×C42—732no—
578C2×C42—732no—
579C2×C42—732no—
580C2×C42—732no—
581C2×C42—732no—
582C2×C42—732no—
583C2×C42—732no—
584C2×C42—732no—
585C2×C42—732no—
586C2×C42—732no—
587C2×C42—732no—
588C2×C42—732no—
589C2×C42C22×D7311yescharacteristic
590C2×C42C22×D7312yes—
591C2×C42C22×D7311yescharacteristic
592C2×C42C22×D7311yescharacteristic
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#95—732no—
613#95—732no—
614#95—732no—
615#95C22×D7312yes—
616#95C22×D7312yes—
617#95C22×D7312yes—
618#95C22×D7312yes—
619C24C23×D7311yescharacteristic
620C24C23×D7311yescharacteristic
621C2×Q8—41no—
622C2×Q8—41no—
623C2×Q8—2922no—
624C2×Q8—2922no—
625C2×Q8—738no—
626C2×Q8C2×C4×D7314yes—
627C2×D4—41no—
628C2×D4—41no—
629C2×D4C2×C4×D7314yes—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—2921no—
635C22×C4—2921no—
636C22×C4—2921no—
637C22×C4—2921no—
638C22×C4—2921no—
639C22×C4—2921no—
640C22×C4—2922no—
641C22×C4—734no—
642C22×C4—734no—
643C22×C4—732no—
644C22×C4—732no—
645C22×C4—732no—
646C22×C4—732no—
647C22×C4—732no—
648C22×C4—732no—
649C22×C4—732no—
650C22×C4—732no—
651C22×C4—1464no—
652C22×C4C23×D7311yescharacteristic
653C22×C4C23×D7312yes—
654C22×C4C23×D7311yescharacteristic
655C22×C4C23×D7311yescharacteristic
656C22×C4C23×D7312yes—
657C22×C4C23×D7311yescharacteristic
658C22×C4C23×D7312yes—
659C22×C4C23×D7312yes—
660C22×C4C23×D7311yescharacteristic
661C4⋊C4—24no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—41no—
665C4⋊C4—41no—
666C4⋊C4—2922no—
667C4⋊C4—2922no—
668C4⋊C4—2922no—
669C4⋊C4—2922no—
670C4⋊C4—2922no—
671C4⋊C4—2922no—
672C4⋊C4—2922no—
673C4⋊C4—738no—
674C4⋊C4—738no—
675C4⋊C4—738no—
676C4⋊C4—738no—
677C4⋊C4—738no—
678C4⋊C4—738no—
679C4⋊C4—738no—
680C4⋊C4—738no—
681C4⋊C4—1464no—
682C4⋊C4—1464no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C22⋊C4—2922no—
688C22⋊C4—2921no—
689C22⋊C4—2921no—
690C22⋊C4—738no—
691C22⋊C4—738no—
692C22⋊C4—734no—
693C22⋊C4—734no—
694C22⋊C4—1464no—
695C22⋊C4C2×C4×D7318yes—
696C22⋊C4C2×C4×D7318yes—
697C42—22no—
698C42—41no—
699C42—42no—
700C42—2922no—
701C42—2922no—
702C42—2922no—
703C42—2922no—
704C42—2922no—
705C42—2922no—
706C42—2922no—
707C42—2922no—
708C42—738no—
709C42—1464no—
710C42—1464no—
711C42—1464no—
712C42C2×C4×D7314yes—
713C23—21no—
714C23—21no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—21no—
720C23—21no—
721C23C22×C4×D7312yes—
722C23C22×C4×D7312yes—
723C23C24×D7311yescharacteristic
724Q8—44no—
725Q8—2928no—
726D4—44no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—44no—
747C2×C4—82no—
748C2×C4—2924no—
749C2×C4—2924no—
750C2×C4—2924no—
751C2×C4—5842no—
752C2×C4—734no—
753C2×C4—734no—
754C2×C4—734no—
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×C4C22×C4×D7314yes—
777C2×C4C22×C4×D7314yes—
778C2×C4C22×C4×D7312yes—
779C2×C4#1455663612yes—
780C22—22no—
781C22—22no—
782C22—24no—
783C22—24no—
784C22—42no—
785C22—42no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22C23×C4×D7311yescharacteristic
791C22C2×#1455663611yescharacteristic
792C222−1+4×D7312yes—
793C22#1798942212yes—
794C22#1798942311yescharacteristic
795C4—22no—
796C4—22no—
797C4—24no—
798C4—24no—
799C4—42no—
800C4—41no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—2922no—
805C4—2922no—
806C4—2922no—
807C4—1464no—
808C4—1464no—
809C4—1464no—
810C4—1464no—
811C4—1464no—
812C2—42no—
813C2—42no—
814C2C4×#1455663611yescharacteristic
815C2#2262314212yes—
816C2#2262410411yescharacteristic
817C2#2262417411yescharacteristic
818C2#2262456712yes—
subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
FittingC73×#2326C2
socle, cosocleC23×C73C25
prime radicalC22×D4×C73C23
hypercenter#2326D73
hypocenterC73#34514
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2326

Complements

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

NH ≅ G/Ntype
2. #22613098C2semidirect
5. #22613049C2semidirect
6. #22613046C2semidirect
8. #22613036C2semidirect
9. #22612985C2semidirect
10. #22612931C2semidirect
11. #22612707C2semidirect
12. #22612704C2semidirect
13. #22612681C2semidirect
14. #22612674C2semidirect
15. #22612670C2semidirect
17. #22612463C2semidirect
20. #17989337C4semidirect
113. #14556589C2×C4semidirect
114. #14556584C2×C4semidirect
115. #14556584C2×C4semidirect
116. #14556583C2×C4semidirect
119. #14556568C2×C4semidirect
120. #14556568C2×C4semidirect
429. C73#34514semidirect

Maximal subgroups

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

subgroupindex
C2×#179893372
#226130982
#226130812
#226130662
#226130492
#226130462
#226130432
#226130362
#226129852
#226129312
#226127072
#226127042
#226126812
#226126742
#226126702
#226125962
#226124632
C4×#145565722
C73×#23262
#3451473