Finite Group Databasebeta

← #33248693

Subgroups — #33248693

Order 18688.

2024 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989341C211yesmaximal, characteristic
2#22613122C212yesmaximal, complemented
3#22613121C212yesmaximal, complemented
4#22613116C211yesmaximal, characteristic, complemented
5#22613109C212yesmaximal, complemented
6#22613102C211yesmaximal, characteristic
7#22613096C212yesmaximal, complemented
8#22613095C212yesmaximal, complemented
9#22613076C212yesmaximal
10#22612502C212yesmaximal, complemented
11#125×Dic73C211yesmaximal, characteristic, complemented
12#22612486C211yesmaximal, characteristic, complemented
13#22612481C212yesmaximal, complemented
14#22612481C212yesmaximal, complemented
15#22612470C211yesmaximal, characteristic
16#22612465C212yesmaximal, complemented
17#22612461C212yesmaximal, complemented
18#22612452C212yesmaximal
19C73×#2382C211yesmaximal, characteristic, complemented
20#17989341C4116yescomplemented
21C2×#14556590C2212yes—
22C2×#14556586C2212yes—
23C2×#14556586C2212yes—
24C2×#14556583C2211yescharacteristic
25C2×#14556579C2211yescharacteristic
26C2×#14556576C2212yes—
27C2×#14556571C2212yes—
28C2×#14556569C2212yes—
29C2×#14556556C2211yescharacteristic
30C2×#14556556C2212yes—
31C2×#14556553C2211yescharacteristic
32C2×C42×D73C2212yes—
33#17988493C2212yes—
34#17988492C2211yescharacteristic
35#17988491C2212yes—
36#17988491C2212yes—
37#17988491C2212yes—
38#17988488C2211yescharacteristic
39#17988486C2211yescharacteristic
40#17988486C2211yescharacteristic
41#17988485C2212yes—
42#17988484C2212yes—
43#17988483C2211yescharacteristic
44#17988483C2211yescharacteristic
45#17988482C2212yes—
46#17988482C2212yes—
47#17988479C2212yes—
48#17988479C2212yes—
49#17988479C2212yes—
50#17988478C2212yes—
51#17988478C2212yes—
52#17988478C2212yes—
53#17988477C2212yes—
54#17988477C2212yes—
55#17988476C2212yes—
56#17988476C2212yes—
57#17988474C2212yes—
58#17988474C2212yes—
59#17988473C2212yes—
60#17988473C2212yes—
61#17988472C2212yes—
62#17988472C2212yes—
63#17988471C2212yes—
64#17988470C2212yes—
65#17988470C2212yes—
66#17988469C2212yes—
67#17988469C2212yes—
68#17988468C2212yes—
69#17988465C2212yes—
70#17988461C2212yes—
71#17988461C2212yes—
72#17988458C2212yes—
73#17988458C2212yes—
74#17988458C2212yes—
75#17988456C2212yes—
76#17988454C2212yes—
77#17988454C2212yes—
78#17988453C2211yescharacteristic
79#17988449C2212yes—
80#17988446C2212yes—
81#17988444C2212yes—
82C4⋊C4×Dic73C2211yescharacteristic
83C4⋊C4×Dic73C2211yescharacteristic
84C4⋊C4×Dic73C2212yes—
85C4⋊C4×Dic73C2212yes—
86C4⋊C4×Dic73C2211yescharacteristic
87C4⋊C4×Dic73C2212yes—
88C4⋊C4×Dic73C2211yescharacteristic
89#17988438C2212yes—
90#17988438C2212yes—
91#17988438C2212yes—
92#17988434C2212yes—
93#17988434C2212yes—
94#17988434C2212yes—
95#17988434C2212yes—
96#17988434C2212yes—
97C42×Dic73C2212yes—
98C42×Dic73C2211yescharacteristic
99C2×#125×C73C2211yescharacteristic
100#389×C73C2212yes—
101#389×C73C2212yes—
102#387×C73C2212yes—
103#387×C73C2212yes—
104#387×C73C2212yes—
105#387×C73C2212yes—
106#382×C73C2211yescharacteristic
107#382×C73C2211yescharacteristic
108C22×Dic146C2311yescharacteristic
109C22×Dic146C2312yes—
110C22×D292C2311yescharacteristic
111C22×C4×D73C2312yes—
112C22×C4×D73C2312yes—
113C22×C4×D73C2312yes—
114#14556590C2×C4116yescomplemented
115#14556586C2×C4116yescomplemented
116#14556586C2×C4116yescomplemented
117#14556583C2×C418yescomplemented
118#14556579C2×C418yes—
119#14556576C2×C4116yes—
120#14556571C2×C4116yescomplemented
121#14556569C2×C4116yescomplemented
122#14556556—44no—
123#14556556—42no—
124#14556553—42no—
125C2×C4⋊Dic73C2312yes—
126C2×C4⋊Dic73C2311yescharacteristic
127C2×C4⋊Dic73C2311yescharacteristic
128C2×C4⋊Dic73C2312yes—
129C2×C4⋊Dic73C2312yes—
130C2×C4⋊Dic73C2311yescharacteristic
131C2×C4⋊Dic73C2311yescharacteristic
132C2×#11924007C2312yes—
133C2×#11924007C2312yes—
134C2×#11924007C2312yes—
135C2×#11924007C2312yes—
136C2×#11924007C2312yes—
137C2×#11924007C2312yes—
138C2×#11924007C2312yes—
139C2×#11924007C2312yes—
140C2×#11924007C2312yes—
141C2×#11924005C2312yes—
142C2×#11924005C2312yes—
143C2×#11924005C2312yes—
144C2×#11924005C2312yes—
145C2×#11924005C2312yes—
146C2×#11924005C2312yes—
147C2×#11924005C2312yes—
148C2×#11924005C2312yes—
149C2×#11924005C2312yes—
150C2×#11924005C2312yes—
151C2×#11924005C2312yes—
152C2×C4×Dic73C2312yes—
153C2×C4×Dic73C2311yescharacteristic
154C2×C4×Dic73C2312yes—
155C2×C4×Dic73C2312yes—
156C2×C4×Dic73C2311yescharacteristic
157C2×C4×Dic73C2311yescharacteristic
158C2×C4×Dic73C2312yes—
159C2×C4×Dic73C2312yes—
160C2×C4×Dic73C2311yescharacteristic
161C2×C4×Dic73C2311yescharacteristic
162C2×C4×Dic73C2312yes—
163C2×C4×Dic73C2312yes—
164C2×C4×Dic73C2311yescharacteristic
165C2×C4×Dic73C2312yes—
166C2×C4×Dic73C2312yes—
167C42×D73—44no—
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—
184#14556498C2312yes—
185#14556498C2312yes—
186#125×C73C2×C418yescomplemented
187C2×C4⋊C4×C73C2311yescharacteristic
188C2×C4⋊C4×C73C2311yescharacteristic
189C2×C4⋊C4×C73C2311yescharacteristic
190C2×C4⋊C4×C73C2311yescharacteristic
191C2×C4⋊C4×C73C2312yes—
192C2×C4⋊C4×C73C2312yes—
193C2×C4⋊C4×C73C2311yescharacteristic
194C2×C4⋊C4×C73C2311yescharacteristic
195C2×C4⋊C4×C73C2312yes—
196C2×C4⋊C4×C73C2312yes—
197C2×C42×C73C2312yes—
198C2×C42×C73C2312yes—
199C2×C42×C73C2311yescharacteristic
200#95×C73C2312yes—
201#95×C73C2312yes—
202#95×C73C2312yes—
203#95×C73C2312yes—
204#95×C73C2312yes—
205#95×C73C2312yes—
206#95×C73C2312yes—
207#95×C73C2312yes—
208C23×D73C2412yes—
209C2×Dic146—42no—
210C2×Dic146—41no—
211C2×Dic146—41no—
212C2×Dic146—42no—
213C2×Dic146C22×C418yes—
214C2×Dic146C22×C414yes—
215C2×D292—41no—
216C2×D292—41no—
217C2×D292C22×C414yes—
218C22×Dic73C2411yescharacteristic
219C22×Dic73C2411yescharacteristic
220C22×Dic73C2412yes—
221C22×Dic73C2412yes—
222C22×Dic73C2411yescharacteristic
223C22×Dic73C2412yes—
224C22×Dic73C2412yes—
225C22×Dic73C2412yes—
226C22×Dic73C2411yescharacteristic
227C2×C4×D73—24no—
228C2×C4×D73—24no—
229C2×C4×D73—24no—
230C2×C4×D73—42no—
231C2×C4×D73—42no—
232C2×C4×D73—42no—
233C2×C4×D73—42no—
234C2×C4×D73—42no—
235C2×C4×D73C22×C418yes—
236C4⋊Dic73—41no—
237C4⋊Dic73—42no—
238C4⋊Dic73—42no—
239C4⋊Dic73—41no—
240C4⋊Dic73C22×C414yes—
241C4⋊Dic73C22×C418yes—
242C4⋊Dic73C22×C414yes—
243#11924007—42no—
244#11924007—42no—
245#11924007—42no—
246#11924007—42no—
247#11924007—42no—
248#11924007—42no—
249#11924007C22×C418yes—
250#11924007C22×C418yes—
251#11924007C22×C418yes—
252#11924005—42no—
253#11924005—42no—
254#11924005—42no—
255#11924005—42no—
256#11924005—42no—
257#11924005—42no—
258#11924005C22×C418yes—
259#11924005C22×C418yes—
260#11924005C22×C418yes—
261#11924005C22×C418yes—
262#11924005C22×C418yes—
263C4×Dic73—24no—
264C4×Dic73—24no—
265C4×Dic73—22no—
266C4×Dic73—24no—
267C4×Dic73—24no—
268C4×Dic73—22no—
269C4×Dic73—24no—
270C4×Dic73—22no—
271C4×Dic73—42no—
272C4×Dic73—42no—
273C4×Dic73—42no—
274C4×Dic73—41no—
275C4×Dic73—41no—
276C4×Dic73—41no—
277C4×Dic73C22×C418yes—
278C22×C4×C73C2412yes—
279C22×C4×C73C2412yes—
280C22×C4×C73C2412yes—
281C22×C4×C73C2412yes—
282C22×C4×C73C2411yescharacteristic
283C22×C4×C73C2412yes—
284C22×C4×C73C2411yescharacteristic
285C22×C4×C73C2411yescharacteristic
286C22×C4×C73C2412yes—
287C4⋊C4×C73—42no—
288C4⋊C4×C73—41no—
289C4⋊C4×C73—41no—
290C4⋊C4×C73—41no—
291C4⋊C4×C73—42no—
292C4⋊C4×C73—41no—
293C4⋊C4×C73C22×C414yes—
294C4⋊C4×C73C22×C418yes—
295C4⋊C4×C73C22×C418yes—
296C4⋊C4×C73C22×C414yes—
297C42×C73—42no—
298C42×C73—42no—
299C42×C73C22×C414yes—
300C23×C73C2511yescharacteristic
301C22×D73—22no—
302C22×D73—22no—
303C22×D73—22no—
304C22×D73—22no—
305C22×D73—22no—
306C22×D73—22no—
307C22×D73C23×C414yes—
308C2×C4×C73—22no—
309C2×C4×C73—21no—
310C2×C4×C73—21no—
311C2×C4×C73—22no—
312C2×C4×C73—21no—
313C2×C4×C73—22no—
314C2×C4×C73—21no—
315C2×C4×C73—21no—
316C2×C4×C73—21no—
317C2×C4×C73—22no—
318C2×C4×C73—22no—
319C2×C4×C73—22no—
320C2×C4×C73—22no—
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×C73C23×C412yes—
331C2×C4×C73C23×C412yes—
332C2×C4×C73C23×C412yes—
333C2×C4×C73C23×C414yes—
334C2×C4×C73C23×C414yes—
335C2×Dic73—22no—
336C2×Dic73—22no—
337C2×Dic73—22no—
338C2×Dic73—22no—
339C2×Dic73—22no—
340C2×Dic73—22no—
341C2×Dic73—22no—
342C2×Dic73—21no—
343C2×Dic73—21no—
344C2×Dic73—21no—
345C2×Dic73—22no—
346C2×Dic73—21no—
347C2×Dic73—21no—
348C2×Dic73—22no—
349C2×Dic73—22no—
350C2×Dic73—21no—
351C2×Dic73—21no—
352C2×Dic73—21no—
353C2×Dic73—21no—
354C2×Dic73—22no—
355C2×Dic73—22no—
356C2×Dic73C23×C414yes—
357C2×Dic73C23×C414yes—
358C2×Dic73C23×C414yes—
359C2×Dic73H(5,𝔽2)12yes—
360C2×Dic732−1+412yes—
361C2×Dic732−1+412yes—
362D292—44no—
363C4×D73—48no—
364C4×D73—48no—
365C4×D73—48no—
366Dic146—44no—
367Dic146—48no—
368C22×C73C24×C411yescharacteristic
369C22×C73C2×H(5,𝔽2)11yescharacteristic
370C22×C73C2×2−1+411yescharacteristic
371C22×C73C2×2−1+411yescharacteristic
372C22×C73#58511yescharacteristic
373C22×C73#58511yescharacteristic
374C22×C73#58511yescharacteristic
375C2×D73—24no—
376C2×D73—24no—
377C2×D73—24no—
378C2×D73—42no—
379C2×D73—42no—
380C2×D73—42no—
381C2×D73—42no—
382C4×C73—24no—
383C4×C73—22no—
384C4×C73—22no—
385C4×C73—24no—
386C4×C73—22no—
387C4×C73—42no—
388C4×C73—42no—
389C4×C73—42no—
390C4×C73—42no—
391Dic73—24no—
392Dic73—24no—
393Dic73—24no—
394Dic73—42no—
395Dic73—41no—
396Dic73—41no—
397Dic73—41no—
398Dic73—42no—
399Dic73#56314yescomplemented
400C4×#563—731nomaximal, Sylow
401C2×C73C4×H(5,𝔽2)11yescharacteristic
402C2×C73C4×2−1+411yescharacteristic
403C2×C73C4×2−1+411yescharacteristic
404C2×C73C2×#56311yescharacteristic
405C2×C73#352911yescharacteristic
406C2×C73#353111yescharacteristic
407C2×C73#353111yescharacteristic
408D73—44no—
409C2×#563—731no—
410#2383—732no—
411#2383—732no—
412#2382—731no—
413#2382D7311yescharacteristic, complemented
414#2381—732no—
415#2379—731no—
416#2378—732no—
417#2378—732no—
418#2376—732no—
419C4×C4⋊Q8—732no—
420C4×#125—731no—
421C4×#125—731no—
422C4×#126—732no—
423C4×#126—732no—
424C4×#124—731no—
425C4×C22⋊Q8—732no—
426C4×C22⋊Q8—732no—
427C4×#123—732no—
428C73C4×#56311yescharacteristic, complemented, Sylow
429#563—7316no—
430C2×C4⋊Q8—732no—
431C2×#126—732no—
432C2×#126—732no—
433C2×#125—731no—
434C2×#125C2×D7311yescharacteristic
435C2×#124—731no—
436C2×#123—732no—
437C2×C22⋊Q8—732no—
438C2×C22⋊Q8—732no—
439C2×C4×Q8—731no—
440C2×C4×Q8—732no—
441C2×C4×D4—731no—
442C22×C42—732no—
443#391—731no—
444#391—732no—
445#391—732no—
446#391—732no—
447#391—732no—
448#390—731no—
449#389—731no—
450#389—731no—
451#389—731no—
452#389—731no—
453#389—732no—
454#389—732no—
455#389—732no—
456#389—732no—
457#389C2×D7312yes—
458#389C2×D7312yes—
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#388—732no—
468#388—732no—
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#387C2×D7312yes—
482#387C2×D7312yes—
483#387C2×D7312yes—
484#387C2×D7312yes—
485#386—732no—
486#385—732no—
487#385—732no—
488#385—732no—
489#385—732no—
490#385—732no—
491#384—732no—
492#383—732no—
493#383—732no—
494#382—731no—
495#382C2×D7311yescharacteristic
496#382C2×D7311yescharacteristic
497#381—732no—
498#380—732no—
499#380—732no—
500C4×C4⋊C4—731no—
501C4×C4⋊C4—731no—
502C4×C4⋊C4—732no—
503C4×C4⋊C4—732no—
504C4×C4⋊C4—732no—
505C4×C4⋊C4—731no—
506C4×C4⋊C4—731no—
507C4×C4⋊C4—732no—
508C4×C4⋊C4—732no—
509C4×C4⋊C4—732no—
510C4×C22⋊C4—732no—
511C4×C22⋊C4—732no—
512C4×C22⋊C4—732no—
513C4×C22⋊C4—732no—
514C4×C22⋊C4—732no—
515C43—732no—
516C43—731no—
517C22×Q8—732no—
518C22×Q8—731no—
519C22×D4—731no—
520C23×C4—732no—
521C23×C4—732no—
522C23×C4—732no—
523C4⋊Q8—7316no—
524#126—7316no—
525#126—7316no—
526#125—738no—
527#125C4×D7318yescomplemented
528#124—738no—
529#123—7316no—
530C22⋊Q8—7316no—
531C22⋊Q8—7316no—
532C4×Q8—2924no—
533C4×Q8—2922no—
534C4×D4—2922no—
535C2×C4⋊C4—732no—
536C2×C4⋊C4—732no—
537C2×C4⋊C4—732no—
538C2×C4⋊C4—732no—
539C2×C4⋊C4—732no—
540C2×C4⋊C4—731no—
541C2×C4⋊C4—731no—
542C2×C4⋊C4—732no—
543C2×C4⋊C4—732no—
544C2×C4⋊C4—732no—
545C2×C4⋊C4—731no—
546C2×C4⋊C4—732no—
547C2×C4⋊C4—732no—
548C2×C4⋊C4—732no—
549C2×C4⋊C4—732no—
550C2×C4⋊C4—731no—
551C2×C4⋊C4C22×D7311yescharacteristic
552C2×C4⋊C4C22×D7312yes—
553C2×C4⋊C4C22×D7311yescharacteristic
554C2×C4⋊C4C22×D7311yescharacteristic
555C2×C4⋊C4C22×D7311yescharacteristic
556C2×C4⋊C4C22×D7312yes—
557C2×C4⋊C4C22×D7311yescharacteristic
558C2×C4⋊C4C22×D7312yes—
559C2×C4⋊C4C22×D7312yes—
560C2×C4⋊C4C22×D7311yescharacteristic
561C2×C22⋊C4—732no—
562C2×C22⋊C4—732no—
563C2×C22⋊C4—732no—
564C2×C22⋊C4—732no—
565C2×C22⋊C4—732no—
566C2×C22⋊C4—732no—
567C2×C22⋊C4—732no—
568C2×C22⋊C4—732no—
569C2×C22⋊C4—732no—
570C2×C22⋊C4—732no—
571C2×C22⋊C4—732no—
572C2×C42—2924no—
573C2×C42—731no—
574C2×C42—732no—
575C2×C42—731no—
576C2×C42—731no—
577C2×C42—732no—
578C2×C42—732no—
579C2×C42—732no—
580C2×C42—731no—
581C2×C42—732no—
582C2×C42—732no—
583C2×C42—732no—
584C2×C42—732no—
585C2×C42—732no—
586C2×C42—731no—
587C2×C42—731no—
588C2×C42C22×D7312yes—
589C2×C42C22×D7312yes—
590C2×C42C22×D7311yescharacteristic
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#95C22×D7312yes—
610#95C22×D7312yes—
611#95C22×D7312yes—
612#95C22×D7312yes—
613#95C22×D7312yes—
614#95C22×D7312yes—
615#95C22×D7312yes—
616#95C22×D7312yes—
617C24—732no—
618C2×Q8—2922no—
619C2×Q8—2921no—
620C2×Q8—2921no—
621C2×Q8—2922no—
622C2×Q8—738no—
623C2×Q8—734no—
624C2×D4—2921no—
625C2×D4—2921no—
626C2×D4—734no—
627C22×C4—2922no—
628C22×C4—2922no—
629C22×C4—2922no—
630C22×C4—2922no—
631C22×C4—2922no—
632C22×C4—738no—
633C22×C4—731no—
634C22×C4—732no—
635C22×C4—732no—
636C22×C4—732no—
637C22×C4—731no—
638C22×C4—731no—
639C22×C4—732no—
640C22×C4—732no—
641C22×C4—731no—
642C22×C4—1464no—
643C22×C4—1464no—
644C22×C4—1464no—
645C22×C4C23×D7312yes—
646C22×C4C23×D7312yes—
647C22×C4C23×D7312yes—
648C22×C4C23×D7312yes—
649C22×C4C23×D7312yes—
650C22×C4C23×D7311yescharacteristic
651C22×C4C23×D7311yescharacteristic
652C22×C4C23×D7312yes—
653C22×C4C23×D7311yescharacteristic
654C4⋊C4—42no—
655C4⋊C4—41no—
656C4⋊C4—41no—
657C4⋊C4—41no—
658C4⋊C4—42no—
659C4⋊C4—41no—
660C4⋊C4—2922no—
661C4⋊C4—2922no—
662C4⋊C4—2922no—
663C4⋊C4—2922no—
664C4⋊C4—2922no—
665C4⋊C4—2922no—
666C4⋊C4—2922no—
667C4⋊C4—2921no—
668C4⋊C4—2921no—
669C4⋊C4—2922no—
670C4⋊C4—738no—
671C4⋊C4—738no—
672C4⋊C4—738no—
673C4⋊C4—734no—
674C4⋊C4—738no—
675C4⋊C4—734no—
676C4⋊C4C2×C4×D7314yes—
677C4⋊C4C2×C4×D7318yes—
678C4⋊C4C2×C4×D7318yes—
679C4⋊C4C2×C4×D7314yes—
680C22⋊C4—2922no—
681C22⋊C4—2922no—
682C22⋊C4—2922no—
683C22⋊C4—2922no—
684C22⋊C4—2922no—
685C22⋊C4—2922no—
686C22⋊C4—738no—
687C22⋊C4—738no—
688C22⋊C4—738no—
689C22⋊C4—738no—
690C22⋊C4—738no—
691C42—42no—
692C42—42no—
693C42—2922no—
694C42—2921no—
695C42—2921no—
696C42—2921no—
697C42—2922no—
698C42—2922no—
699C42—738no—
700C42—1464no—
701C42—1464no—
702C42—1462no—
703C42—1464no—
704C42—1462no—
705C42—1464no—
706C42—1462no—
707C42—1464no—
708C42C2×C4×D7314yes—
709C23—734no—
710C23—1462no—
711C23—1462no—
712C23—1462no—
713C23—1462no—
714C23—1462no—
715C23—1462no—
716C23C24×D7311yescharacteristic
717Q8—2928no—
718Q8—2924no—
719D4—2924no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
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—2928no—
743C2×C4—2928no—
744C2×C4—2928no—
745C2×C4—732no—
746C2×C4—732no—
747C2×C4—732no—
748C2×C4—734no—
749C2×C4—734no—
750C2×C4—734no—
751C2×C4—1462no—
752C2×C4—1461no—
753C2×C4—1461no—
754C2×C4—1461no—
755C2×C4—1462no—
756C2×C4—1461no—
757C2×C4—1461no—
758C2×C4—1462no—
759C2×C4—1461no—
760C2×C4—1462no—
761C2×C4—1462no—
762C2×C4—1461no—
763C2×C4—1461no—
764C2×C4—1461no—
765C2×C4—1462no—
766C2×C4—1462no—
767C2×C4—1462no—
768C2×C4—1462no—
769C2×C4—1462no—
770C2×C4—1462no—
771C2×C4—1462no—
772C2×C4C22×C4×D7314yes—
773C2×C4C22×C4×D7312yes—
774C2×C4C22×C4×D7312yes—
775C2×C4C22×C4×D7312yes—
776C2×C4C22×C4×D7314yes—
777C22—2922no—
778C22—2922no—
779C22—2922no—
780C22—2922no—
781C22—1464no—
782C22—1464no—
783C22—1464no—
784C22C23×C4×D7311yescharacteristic
785C22H(5,𝔽2)×D7311yescharacteristic
786C222−1+4×D7311yescharacteristic
787C222−1+4×D7311yescharacteristic
788C22#1798942211yescharacteristic
789C22#1798942411yescharacteristic
790C22#1798942411yescharacteristic
791C4—24no—
792C4—22no—
793C4—22no—
794C4—24no—
795C4—22no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—42no—
800C4—2922no—
801C4—2921no—
802C4—2921no—
803C4—2921no—
804C4—2922no—
805C4—734no—
806C4—1464no—
807C4—1464no—
808C4—1464no—
809C2—2924no—
810C2#2262313711yescharacteristic
811C2#2262314011yescharacteristic
812C2#2262314211yescharacteristic
813C2#563×D7311yescharacteristic
814C2#2262406811yescharacteristic
815C2#2262407711yescharacteristic
816C2#2262407911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
FittingC73×#2382C2
socle, cosocleC23×C73C25
prime radicalC22×D292C23
hypercenter#2382D73
hypocenterC73C4×#563
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2382

Complements

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

NH ≅ G/Ntype
2. #22613122C2semidirect
3. #22613121C2semidirect
4. #22613116C2semidirect
5. #22613109C2semidirect
7. #22613096C2semidirect
8. #22613095C2semidirect
10. #22612502C2semidirect
11. #125×Dic73C2semidirect
12. #22612486C2semidirect
13. #22612481C2semidirect
14. #22612481C2semidirect
16. #22612465C2semidirect
17. #22612461C2semidirect
19. C73×#2382C2semidirect
20. #17989341C4semidirect
114. #14556590C2×C4semidirect
115. #14556586C2×C4semidirect
116. #14556586C2×C4semidirect
117. #14556583C2×C4semidirect
120. #14556571C2×C4semidirect
121. #14556569C2×C4semidirect
186. #125×C73C2×C4semidirect
399. Dic73#563semidirect
413. #2382D73semidirect
428. C73C4×#563semidirect
527. #125C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179893412
#226131222
#226131212
#226131162
#226131092
#226131022
#226130962
#226130952
#226130762
#226125022
#125×Dic732
#226124862
#226124812
#226124702
#226124652
#226124612
#226124522
C73×#23822
C4×#56373