Finite Group Databasebeta

← #34030822

Subgroups — #34030822

Order 18688.

3200 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989656C211yesmaximal, characteristic, complemented
2C2×#41×#64408C211yesmaximal, characteristic, complemented
3#22626461C213yesmaximal, complemented
4#22626458C213yesmaximal, complemented
5#22626456C213yesmaximal, complemented
6#22626447C213yesmaximal, complemented
7#22626446C211yesmaximal, characteristic, complemented
8#22626436C211yesmaximal, characteristic, complemented
9#22626436C211yesmaximal, characteristic, complemented
10#22626423C213yesmaximal, complemented
11#22626419C213yesmaximal, complemented
12#121×#64408C213yesmaximal, complemented
13#22626385C213yesmaximal, complemented
14#22626371C211yesmaximal, characteristic, complemented
15#550×D73C211yesmaximal, characteristic
16#17989656—28no—
17#41×#64408—28no—
18C2×Q8×#64408C2211yescharacteristic
19C2×Q8×#64408C2211yescharacteristic
20C2×Q8×#64408C2211yescharacteristic
21C2×Q8×#64408C2211yescharacteristic
22C2×D4×#64408C2213yes—
23C2×D4×#64408C2213yes—
24C2×D4×#64408C2213yes—
25C2×D4×#64408C2213yes—
26C2×D4×#64408C2216yes—
27C2×#14556670C2213yes—
28C2×#14556670C2213yes—
29C22×C4⋊#64408C2213yes—
30C22×C4×#64408C2213yes—
31#17989539C2213yes—
32#17989539C2213yes—
33#17989539C2216yes—
34#17989539C2213yes—
35#17989539C2213yes—
36#17989538C2213yes—
37#17989538C2213yes—
38#17989537C2213yes—
39#17989537C2213yes—
40#17989537C2216yes—
41#17989536C2211yescharacteristic
42#17989536C2213yes—
43#17989535C2213yes—
44#17989535C2213yes—
45#17989535C2216yes—
46#17989535C2216yes—
47#17989535C2216yes—
48#17989534C2213yes—
49#17989534C2213yes—
50#17989531C2213yes—
51#17989529C2213yes—
52#17989529C2213yes—
53C4⋊C4×#64408C2213yes—
54C4⋊C4×#64408C2213yes—
55C4×C4⋊#64408C2213yes—
56C4×C4⋊#64408C2213yes—
57C22⋊C4×#64408C2216yes—
58C4×C22⋊#64408C2213yes—
59C4×C22⋊#64408C2213yes—
60#17989523C2213yes—
61C2×#41×D73C2211yescharacteristic
62C2×#41×D73C2211yescharacteristic
63#17989259C411yescharacteristic, complemented
64#17989258C413yescomplemented
65#17989257C413yescomplemented
66#17989256C411yescharacteristic, complemented
67#17989256C411yescharacteristic, complemented
68#17989255C413yescomplemented
69#17989255C413yescomplemented
70#127×D73C2213yes—
71#121×D73C2213yes—
72#121×D73C2213yes—
73C4×Q8×D73C2211yescharacteristic
74C4×D4×D73C2213yes—
75#550×C73C411yescharacteristic, complemented
76C23×#64408C2313yes—
77C23×#64408C2313yes—
78C23×#64408C2316yes—
79Q8×#64408—24no—
80Q8×#64408—24no—
81Q8×#64408—24no—
82Q8×#64408D418yescomplemented
83D4×#64408—212no—
84D4×#64408—212no—
85D4×#64408—212no—
86D4×#64408—212no—
87D4×#64408—412no—
88#14556670—212no—
89#14556670—212no—
90C2×C4⋊#64408—212no—
91C2×C4⋊#64408C2313yes—
92C2×C4⋊#64408C2313yes—
93C2×C4⋊#64408C2311yescharacteristic
94C2×C4⋊#64408C2313yes—
95C2×C4⋊#64408C2313yes—
96C2×C4⋊#64408C2313yes—
97C2×C4⋊#64408C2313yes—
98C2×C4⋊#64408C2313yes—
99C2×C22⋊#64408C2313yes—
100C2×C22⋊#64408C2316yes—
101C2×C22⋊#64408C2313yes—
102C2×C22⋊#64408C2313yes—
103C2×C22⋊#64408C2316yes—
104C2×C22⋊#64408C2313yes—
105C2×C22⋊#64408C2313yes—
106C2×C22⋊#64408C2313yes—
107C2×C22⋊#64408C2316yes—
108C2×C4×#64408—212no—
109C2×C4×#64408C2311yescharacteristic
110C2×C4×#64408C2313yes—
111C2×C4×#64408C2313yes—
112C2×C4×#64408C2313yes—
113C2×C4×#64408C2313yes—
114C2×C4×#64408C2316yes—
115C2×C4×#64408C2313yes—
116(C2×#64408)⋊C4C2311yescharacteristic
117(C2×#64408)⋊C4C2313yes—
118(C2×#64408)⋊C4C2313yes—
119(C2×#64408)⋊C4C2313yes—
120(C2×#64408)⋊C4C2311yescharacteristic
121(C2×#64408)⋊C4C2311yescharacteristic
122(C2×#64408)⋊C4C2313yes—
123(C2×#64408)⋊C4C2313yes—
124(C2×#64408)⋊C4C2316yes—
125(C2×#64408)⋊C4C2311yescharacteristic
126(C2×#64408)⋊C4C2313yes—
127C2×#11924029C2×C411yescharacteristic, complemented
128C2×#11924029C2×C411yescharacteristic, complemented
129C2×#11924028C2×C413yescomplemented
130C2×#11924028C2×C413yescomplemented
131C2×#11924027C2×C413yescomplemented
132C2×#11924027C2×C413yescomplemented
133#41×D73—24no—
134#41×D73—24no—
135#41×D73—24no—
136#41×D73—24no—
137C2×Q8×D73C2311yescharacteristic
138C2×D4×D73C2313yes—
139C2×D4×D73C2313yes—
140C2×D4×D73C2313yes—
141C2×D4×D73C2316yes—
142C22×C4×D73C2313yes—
143C22×C4×D73C2313yes—
144#14556588C2×C413yescomplemented
145#14556587C2×C416yescomplemented
146#14556587C2×C413yescomplemented
147#14556587C2×C413yescomplemented
148#14556587C2×C416yescomplemented
149#14556566C2×C413yescomplemented
150#14556566C2×C413yescomplemented
151#14556565C2×C413yescomplemented
152#14556565C2×C413yescomplemented
153#14556564C2×C416yescomplemented
154#14556564C2×C416yescomplemented
155#14556563C2×C416yescomplemented
156#14556563C2×C416yescomplemented
157#14556562C2×C413yescomplemented
158#14556562C2×C413yescomplemented
159Q8×Dic73C2×C411yescharacteristic, complemented
160C4×Dic146C2×C413yescomplemented
161#14556556C2×C413yescomplemented
162C4×D292C2×C413yescomplemented
163D4×Dic73C2×C413yescomplemented
164#14556553C2×C413yescomplemented
165C4×C22⋊D73C2×C413yescomplemented
166C4×C22⋊D73C2×C413yescomplemented
167#14556551C2×C413yescomplemented
168#14556551C2×C413yescomplemented
169C4⋊C4×D73C2313yes—
170C4⋊C4×D73C2311yescharacteristic
171C22⋊C4×D73C2313yes—
172C22⋊C4×D73C2313yes—
173C42×D73C2313yes—
174C2×#41×C73C2×C411yescharacteristic, complemented
175C2×#41×C73C2×C411yescharacteristic, complemented
176#127×C73C2×C413yescomplemented
177#121×C73C2×C413yescomplemented
178#121×C73C2×C413yescomplemented
179C4×Q8×C73C2×C411yescharacteristic, complemented
180C4×D4×C73C2×C413yescomplemented
181C22×#64408—26no—
182C22×#64408—26no—
183C22×#64408—26no—
184C22×#64408—212no—
185C22×#64408—43no—
186C22×#64408—43no—
187C22×#64408—43no—
188C22×#64408—46no—
189C22×#64408—46no—
190C22×#64408C2413yes—
191C22×#64408C2413yes—
192C22×#64408C2411yescharacteristic
193C22×#64408C2413yes—
194C22×#64408C2411yescharacteristic
195C22×#64408C2411yescharacteristic
196C22×#64408C2413yes—
197C22×#64408C2411yescharacteristic
198C4⋊#64408—26no—
199C4⋊#64408—22no—
200C4⋊#64408—26no—
201C4⋊#64408—26no—
202C4⋊#64408—26no—
203C4⋊#64408—26no—
204C4⋊#64408—43no—
205C4⋊#64408C2×D4112yes—
206C22⋊#64408—26no—
207C22⋊#64408—212no—
208C22⋊#64408—26no—
209C22⋊#64408—26no—
210C22⋊#64408—43no—
211C22⋊#64408—46no—
212C22⋊#64408—43no—
213C22⋊#64408—43no—
214C22⋊#64408—46no—
215C4×#64408—22no—
216C4×#64408—26no—
217C4×#64408—26no—
218C4×#64408—26no—
219C4×#64408—26no—
220C4×#64408—46no—
221C4×#64408C2×D4112yes—
222C23×D73C2413yes—
223C23×D73C2413yes—
224#11924029—24no—
225#11924029—24no—
226#11924028—212no—
227#11924028—212no—
228#11924027—212no—
229#11924027—212no—
230C2×Dic146C22×C413yes—
231Q8×D73C2×D414yes—
232Q8×D73#4114yes—
233C2×D292C22×C413yes—
234C2×D292C22×C413yes—
235C2×D292C22×C413yes—
236C2×D292C22×C416yes—
237C2×C22⋊D73C22×C416yes—
238C2×C22⋊D73C22×C416yes—
239C2×C22⋊D73C22×C413yes—
240C2×C22⋊D73C22×C413yes—
241C2×C22⋊D73C22×C416yes—
242C2×C22⋊D73C22×C416yes—
243D4×D73—26no—
244D4×D73—26no—
245D4×D73—26no—
246D4×D73—26no—
247D4×D73—43no—
248D4×D73—43no—
249D4×D73—46no—
250D4×D73—46no—
251C22×Dic73C22×C413yes—
252C22×Dic73C22×C413yes—
253C2×C4×D73—26no—
254C2×C4×D73—26no—
255C2×C4×D73—26no—
256C2×C4×D73—26no—
257C2×C4×D73C22×C413yes—
258C2×C4×D73C22×C413yes—
259C2×C4×D73C22×C413yes—
260C2×C4×D73C22×C413yes—
261C2×C4×D73C2411yescharacteristic
262C2×C4×D73C2413yes—
263C2×C4×D73C2411yescharacteristic
264C2×C4×D73C2411yescharacteristic
265C2×C4×D73C2413yes—
266C4⋊Dic73C22×C411yescharacteristic
267C4⋊Dic73C22×C413yes—
268#11924007C22×C411yescharacteristic
269#11924007C22×C411yescharacteristic
270#11924007C22×C416yes—
271C22⋊Dic73C22×C413yes—
272C22⋊Dic73C22×C413yes—
273#11924005C22×C413yes—
274#11924005C22×C413yes—
275#11924005C22×C413yes—
276#11924005C22×C413yes—
277C4×Dic73C22×C413yes—
278C4×Dic73C22×C413yes—
279C4×Dic73C22×C413yes—
280#41×C73—24no—
281#41×C73—24no—
282C2×Q8×C73C22×C411yescharacteristic
283C2×D4×C73C22×C413yes—
284C2×D4×C73C22×C413yes—
285C2×D4×C73C22×C413yes—
286C2×D4×C73C22×C416yes—
287C22×C4×C73C22×C413yes—
288C22×C4×C73C22×C413yes—
289C4⋊C4×C73C22×C411yescharacteristic
290C4⋊C4×C73C22×C413yes—
291C22⋊C4×C73C22×C413yes—
292C22⋊C4×C73C22×C413yes—
293C42×C73C22×C413yes—
294C23×C73C23×C413yes—
295C23×C73C23×C413yes—
296C22×D73—23no—
297C22×D73—23no—
298C22×D73—23no—
299C22×D73—23no—
300C22×D73—23no—
301C22×D73—23no—
302C22×D73—23no—
303C22×D73—23no—
304C22×D73—23no—
305C22×D73—23no—
306C22×D73—23no—
307C22×D73—23no—
308C22×D73C23×C413yes—
309C22×D73C23×C413yes—
310C22×D73C2511yescharacteristic
311C2×#64408—21no—
312C2×#64408—23no—
313C2×#64408—21no—
314C2×#64408—21no—
315C2×#64408—21no—
316C2×#64408—23no—
317C2×#64408—21no—
318C2×#64408—23no—
319C2×#64408—23no—
320C2×#64408—21no—
321C2×#64408—23no—
322C2×#64408—23no—
323C2×#64408—23no—
324C2×#64408—21no—
325C2×#64408—23no—
326C2×#64408—21no—
327C2×#64408—21no—
328C2×#64408—23no—
329C2×#64408—23no—
330C2×#64408—23no—
331C2×#64408—21no—
332C2×#64408—412no—
333C2×#64408—412no—
334C2×#64408—812no—
335C2×#64408C22×D412yes—
336C2×#64408C22×D416yes—
337C2×#64408H(5,𝔽2)12yes—
338Q8×C73C4×D414yescomplemented
339D4×C73—26no—
340D4×C73—26no—
341D4×C73—43no—
342D4×C73—46no—
343C2×C4×C73—26no—
344C2×C4×C73—26no—
345C2×C4×C73C23×C411yescharacteristic
346C2×C4×C73C23×C413yes—
347C2×C4×C73C23×C411yescharacteristic
348C2×C4×C73C23×C411yescharacteristic
349C2×C4×C73C23×C413yes—
350C22⋊D73—212no—
351C22⋊D73—212no—
352C22⋊D73—43no—
353C22⋊D73—43no—
354C22⋊D73—46no—
355C22⋊D73—46no—
356C2×Dic73—26no—
357C2×Dic73—26no—
358C2×Dic73C23×C411yescharacteristic
359C2×Dic73C23×C413yes—
360C2×Dic73C23×C411yescharacteristic
361C2×Dic73C23×C411yescharacteristic
362C2×Dic73C23×C413yes—
363D292—26no—
364D292—26no—
365D292—43no—
366D292—46no—
367C4×D73—21no—
368C4×D73—21no—
369C4×D73—21no—
370C4×D73—21no—
371C4×D73—23no—
372C4×D73—21no—
373C4×D73—21no—
374C4×D73—23no—
375C4×D73—26no—
376C4×D73—26no—
377C4×D73—26no—
378C4×D73—26no—
379C4×D73C22×D416yes—
380C4×D73C2×#4116yes—
381Dic146C4×D4112yescomplemented
382C22×C73—23no—
383C22×C73—23no—
384C22×C73—23no—
385C22×C73—23no—
386C22×C73—23no—
387C22×C73—23no—
388C22×C73C24×C411yescharacteristic
389C2×D73—23no—
390C2×D73—23no—
391C2×D73—23no—
392C2×D73—23no—
393C2×D73—23no—
394C2×D73—23no—
395C2×D73—43no—
396C2×D73—43no—
397C2×D73—43no—
398C2×D73—43no—
399C2×D73—43no—
400C2×D73—43no—
401C2×D73—43no—
402C2×D73—43no—
403C2×D73C23×D411yescharacteristic
404C2×D73C22×#4111yescharacteristic
405C2×D73C2×H(5,𝔽2)11yescharacteristic
406C2×D73#58511yescharacteristic
407C2×D73#58511yescharacteristic
408C2×D73#58511yescharacteristic
409#64408—22no—
410#64408—22no—
411#64408—26no—
412#64408—41no—
413#64408—43no—
414#64408—43no—
415#64408—43no—
416#64408—41no—
417C4×C73—21no—
418C4×C73—21no—
419C4×C73—21no—
420C4×C73—23no—
421C4×C73C2×C4×D416yes—
422Dic73—21no—
423Dic73—21no—
424Dic73—21no—
425Dic73—23no—
426Dic73C2×C4×D416yes—
427#34295—731nomaximal, Sylow
428C2×C73—43no—
429C2×C73—43no—
430C2×C73C22×C4×D411yescharacteristic
431C2×C73#342811yescharacteristic
432C2×C73C4×H(5,𝔽2)11yescharacteristic
433D73—43no—
434D73—43no—
435D73#348711yescharacteristic
436D73#348811yescharacteristic
437D73#351711yescharacteristic
438D73#352411yescharacteristic
439C2×#550—731no—
440C2×#520—731no—
441C2×C4×#41—731no—
442#2366—733no—
443#2363—733no—
444#2361—733no—
445#2352—733no—
446#2351—731no—
447#2341—731no—
448#2341—731no—
449#2328—733no—
450#2324—733no—
451C4×#121—733no—
452#2290—733no—
453#2276—731no—
454C73#3429511yescharacteristic, complemented, Sylow
455C22×#41—731no—
456C22×#41—731no—
457#550—731no—
458#550—731no—
459#550—733no—
460#550—733no—
461#550—733no—
462#550—731no—
463#550—733no—
464#550#6440811yescharacteristic, complemented
465C2×#127—733no—
466C2×#121—733no—
467C2×#121—733no—
468#520—1468no—
469C4×#41—1468no—
470C2×C4×Q8—731no—
471C2×C4×Q8—731no—
472C2×C4×Q8—731no—
473C2×C4×Q8—731no—
474C2×C4×Q8—731no—
475C2×C4×D4—736no—
476C2×C4×D4—733no—
477C2×C4×D4—733no—
478C2×C4×D4—733no—
479C2×C4×D4—733no—
480C2×C4×D4—733no—
481C2×#117—733no—
482C2×#117—733no—
483C22×C4⋊C4—733no—
484C22×C42—733no—
485#390—733no—
486#390—736no—
487#390—733no—
488#390—733no—
489#390—733no—
490#389—733no—
491#389—733no—
492#388—736no—
493#388—733no—
494#388—733no—
495#387—733no—
496#387—731no—
497#386—736no—
498#386—733no—
499#386—736no—
500#386—736no—
501#386—733no—
502#385—733no—
503#385—733no—
504#382—733no—
505#380—733no—
506#380—733no—
507C4×C4⋊C4—733no—
508C4×C4⋊C4—733no—
509C4×C4⋊C4—733no—
510C4×C4⋊C4—733no—
511C4×C22⋊C4—733no—
512C4×C22⋊C4—733no—
513C4×C22⋊C4—736no—
514#376—733no—
515C2×#41—731no—
516C2×#41—731no—
517C2×#41—733no—
518C2×#41—733no—
519C2×#41—733no—
520C2×#41—733no—
521C2×#41—1464no—
522C2×#41—1464no—
523C2×#41—1464no—
524C2×#41—1464no—
525C2×#41C2×#6440811yescharacteristic, complemented
526C2×#41C2×#6440811yescharacteristic, complemented
527C22×Q8—731no—
528C22×D4—736no—
529C22×D4—733no—
530C22×D4—733no—
531C22×D4—733no—
532C23×C4—736no—
533C23×C4—733no—
534C23×C4—733no—
535C23×C4—733no—
536C23×C4—733no—
537#127—733no—
538#127—733no—
539#127—736no—
540#127—736no—
541#127—733no—
542#127C2×#6440813yescomplemented
543#121—733no—
544#121—733no—
545#121—736no—
546#121—736no—
547#121—733no—
548#121—733no—
549#121—733no—
550#121—733no—
551#121—736no—
552#121—736no—
553#121C2×#6440813yescomplemented
554#121C2×#6440813yescomplemented
555C4×Q8—738no—
556C4×Q8—731no—
557C4×Q8—733no—
558C4×Q8—733no—
559C4×Q8—1464no—
560C4×Q8—1464no—
561C4×Q8—1464no—
562C4×Q8C2×#6440811yescharacteristic, complemented
563C4×D4—29212no—
564C4×D4—733no—
565C4×D4—733no—
566C4×D4—733no—
567C4×D4—733no—
568C4×D4—733no—
569C4×D4—733no—
570C4×D4—733no—
571C4×D4—14612no—
572C4×D4—14612no—
573C4×D4—14612no—
574C4×D4—14612no—
575C4×D4C2×#6440813yescomplemented
576#117—14612no—
577#117—14612no—
578C2×C4⋊C4—733no—
579C2×C4⋊C4—733no—
580C2×C4⋊C4—731no—
581C2×C4⋊C4—733no—
582C2×C4⋊C4—733no—
583C2×C4⋊C4—733no—
584C2×C4⋊C4—731no—
585C2×C4⋊C4—733no—
586C2×C4⋊C4—733no—
587C2×C4⋊C4—733no—
588C2×C4⋊C4—14612no—
589C2×C22⋊C4—736no—
590C2×C22⋊C4—736no—
591C2×C22⋊C4—733no—
592C2×C22⋊C4—733no—
593C2×C22⋊C4—733no—
594C2×C22⋊C4—733no—
595C2×C22⋊C4—733no—
596C2×C22⋊C4—733no—
597C2×C22⋊C4—736no—
598C2×C22⋊C4—733no—
599C2×C22⋊C4—733no—
600C2×C42—736no—
601C2×C42—733no—
602C2×C42—733no—
603C2×C42—733no—
604C2×C42—733no—
605C2×C42—733no—
606C2×C42—733no—
607C2×C42—731no—
608C2×C42—14612no—
609#95—731no—
610#95—733no—
611#95—733no—
612#95—733no—
613#95—733no—
614#95—731no—
615#95—731no—
616#95—733no—
617#95—736no—
618#95—731no—
619#95—733no—
620C24—733no—
621C24—733no—
622#41—24no—
623#41—24no—
624#41—14612no—
625#41—14612no—
626#41—14612no—
627#41—14612no—
628#41—1464no—
629#41—1464no—
630C2×Q8—734no—
631C2×Q8—734no—
632C2×Q8—733no—
633C2×Q8C22×#6440811yescharacteristic
634C2×D4—2926no—
635C2×D4—2926no—
636C2×D4—2923no—
637C2×D4—2923no—
638C2×D4—733no—
639C2×D4—733no—
640C2×D4—736no—
641C2×D4—736no—
642C2×D4—736no—
643C2×D4—736no—
644C2×D4—733no—
645C2×D4—736no—
646C2×D4—733no—
647C2×D4—733no—
648C2×D4—1466no—
649C2×D4—1466no—
650C2×D4—1466no—
651C2×D4—1466no—
652C2×D4C22×#6440813yes—
653C2×D4C22×#6440813yes—
654C2×D4C22×#6440813yes—
655C2×D4C22×#6440816yes—
656C22×C4—2923no—
657C22×C4—2923no—
658C22×C4—2923no—
659C22×C4—2926no—
660C22×C4—2926no—
661C22×C4—733no—
662C22×C4—731no—
663C22×C4—733no—
664C22×C4—731no—
665C22×C4—733no—
666C22×C4—733no—
667C22×C4—733no—
668C22×C4—733no—
669C22×C4—733no—
670C22×C4—733no—
671C22×C4—731no—
672C22×C4—731no—
673C22×C4—733no—
674C22×C4—731no—
675C22×C4—731no—
676C22×C4—733no—
677C22×C4—733no—
678C22×C4—733no—
679C22×C4—731no—
680C22×C4—1466no—
681C22×C4—1466no—
682C22×C4—1466no—
683C22×C4—1466no—
684C22×C4—1466no—
685C22×C4—1466no—
686C22×C4—1466no—
687C22×C4—14612no—
688C22×C4C22×#6440813yes—
689C22×C4C22×#6440813yes—
690C4⋊C4—2923no—
691C4⋊C4—7312no—
692C4⋊C4—731no—
693C4⋊C4—731no—
694C4⋊C4—736no—
695C4⋊C4—731no—
696C4⋊C4—733no—
697C4⋊C4—1466no—
698C4⋊C4—1466no—
699C4⋊C4—1462no—
700C4⋊C4—1466no—
701C4⋊C4—1466no—
702C4⋊C4—1466no—
703C4⋊C4C22×#6440811yescharacteristic
704C4⋊C4C22×#6440813yes—
705C22⋊C4—2923no—
706C22⋊C4—2926no—
707C22⋊C4—2923no—
708C22⋊C4—2923no—
709C22⋊C4—2926no—
710C22⋊C4—733no—
711C22⋊C4—733no—
712C22⋊C4—733no—
713C22⋊C4—733no—
714C22⋊C4—733no—
715C22⋊C4—733no—
716C22⋊C4—1466no—
717C22⋊C4—1466no—
718C22⋊C4—14612no—
719C22⋊C4—1466no—
720C22⋊C4C22×#6440813yes—
721C22⋊C4C22×#6440813yes—
722C42—2926no—
723C42—7312no—
724C42—733no—
725C42—733no—
726C42—733no—
727C42—1462no—
728C42—1466no—
729C42—1466no—
730C42—1466no—
731C42—1466no—
732C42C22×#6440813yes—
733C23—731no—
734C23—733no—
735C23—733no—
736C23—1463no—
737C23—1463no—
738C23—1463no—
739C23—1463no—
740C23—1463no—
741C23—1463no—
742C23—1463no—
743C23—1463no—
744C23—1463no—
745C23—1463no—
746C23—1463no—
747C23—1463no—
748C23C23×#6440813yes—
749C23C23×#6440813yes—
750Q8—7312no—
751Q8D4×#6440814yescomplemented
752D4—26no—
753D4—26no—
754D4—43no—
755D4—46no—
756D4—2923no—
757D4—2926no—
758D4—2923no—
759D4—2923no—
760D4—2926no—
761D4—2926no—
762D4—14612no—
763D4—14612no—
764D4—1466no—
765D4—1466no—
766C2×C4—26no—
767C2×C4—26no—
768C2×C4—29212no—
769C2×C4—29212no—
770C2×C4—58412no—
771C2×C4—733no—
772C2×C4—736no—
773C2×C4—736no—
774C2×C4—732no—
775C2×C4—736no—
776C2×C4—732no—
777C2×C4—731no—
778C2×C4—733no—
779C2×C4—731no—
780C2×C4—731no—
781C2×C4—1466no—
782C2×C4—1466no—
783C2×C4—1463no—
784C2×C4—1461no—
785C2×C4—1463no—
786C2×C4—1461no—
787C2×C4—1461no—
788C2×C4—1461no—
789C2×C4—1461no—
790C2×C4—1461no—
791C2×C4—1463no—
792C2×C4—1461no—
793C2×C4—1461no—
794C2×C4—1463no—
795C2×C4—1463no—
796C2×C4—1463no—
797C2×C4—1461no—
798C2×C4—1463no—
799C2×C4—1461no—
800C2×C4—1461no—
801C2×C4—1463no—
802C2×C4—1463no—
803C2×C4—1463no—
804C2×C4—1463no—
805C2×C4—1461no—
806C2×C4—1466no—
807C2×C4—1466no—
808C2×C4—1463no—
809C2×C4—1461no—
810C2×C4—1461no—
811C2×C4—1461no—
812C2×C4—1461no—
813C2×C4—1463no—
814C2×C4—1466no—
815C2×C4—1466no—
816C2×C4C23×#6440811yescharacteristic
817C2×C4C23×#6440813yes—
818C2×C4C23×#6440811yescharacteristic
819C2×C4C23×#6440811yescharacteristic
820C2×C4C23×#6440813yes—
821C22—23no—
822C22—23no—
823C22—23no—
824C22—23no—
825C22—23no—
826C22—23no—
827C22—2923no—
828C22—2923no—
829C22—2923no—
830C22—2923no—
831C22—2923no—
832C22—2923no—
833C22—2923no—
834C22—2923no—
835C22—731no—
836C22—731no—
837C22—731no—
838C22—731no—
839C22—731no—
840C22—731no—
841C22—1463no—
842C22—1463no—
843C22—1463no—
844C22—1463no—
845C22—1463no—
846C22—1463no—
847C22C24×#6440811yescharacteristic
848C4—21no—
849C4—21no—
850C4—21no—
851C4—23no—
852C4—2923no—
853C4—2923no—
854C4—2921no—
855C4—2923no—
856C4—2921no—
857C4—736no—
858C4—1462no—
859C4—1462no—
860C4—1466no—
861C4—1461no—
862C4—1461no—
863C4—1461no—
864C4—1463no—
865C4C2×D4×#6440816yes—
866C2—43no—
867C2—43no—
868C2—2923no—
869C2—2923no—
870C2—731no—
871C2—731no—
872C2—731no—
873C2—731no—
874C2C22×D4×#6440811yescharacteristic
875C2#2262691111yescharacteristic
876C2H(5,𝔽2)×#6440811yescharacteristic
subgroupG/H
center, FrattiniC22C24×#64408
commutator, socleC22×C73C24×C4
Fitting#550×C73C4
prime radical#550×D73C2
cosocleC22×D73C25
hypercenter#550#64408
hypocenterC73#34295
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#17989656C2semidirect
2. C2×#41×#64408C2semidirect
3. #22626461C2semidirect
4. #22626458C2semidirect
5. #22626456C2semidirect
6. #22626447C2semidirect
7. #22626446C2semidirect
8. #22626436C2semidirect
9. #22626436C2semidirect
10. #22626423C2semidirect
11. #22626419C2semidirect
12. #121×#64408C2semidirect
13. #22626385C2semidirect
14. #22626371C2semidirect
63. #17989259C4semidirect
64. #17989258C4semidirect
65. #17989257C4semidirect
66. #17989256C4semidirect
67. #17989256C4semidirect
68. #17989255C4semidirect
69. #17989255C4semidirect
75. #550×C73C4semidirect
82. Q8×#64408D4semidirect
127. C2×#11924029C2×C4semidirect
128. C2×#11924029C2×C4semidirect
129. C2×#11924028C2×C4semidirect
130. C2×#11924028C2×C4semidirect
131. C2×#11924027C2×C4semidirect
132. C2×#11924027C2×C4semidirect
144. #14556588C2×C4semidirect
145. #14556587C2×C4semidirect
146. #14556587C2×C4semidirect
147. #14556587C2×C4semidirect
148. #14556587C2×C4semidirect
149. #14556566C2×C4semidirect
150. #14556566C2×C4semidirect
151. #14556565C2×C4semidirect
152. #14556565C2×C4semidirect
153. #14556564C2×C4semidirect
154. #14556564C2×C4semidirect
155. #14556563C2×C4semidirect
156. #14556563C2×C4semidirect
157. #14556562C2×C4semidirect
158. #14556562C2×C4semidirect
159. Q8×Dic73C2×C4semidirect
160. C4×Dic146C2×C4semidirect
161. #14556556C2×C4semidirect
162. C4×D292C2×C4semidirect
163. D4×Dic73C2×C4semidirect
164. #14556553C2×C4semidirect
165. C4×C22⋊D73C2×C4semidirect
166. C4×C22⋊D73C2×C4semidirect
167. #14556551C2×C4semidirect
168. #14556551C2×C4semidirect
174. C2×#41×C73C2×C4semidirect
175. C2×#41×C73C2×C4semidirect
176. #127×C73C2×C4semidirect
177. #121×C73C2×C4semidirect
178. #121×C73C2×C4semidirect
179. C4×Q8×C73C2×C4semidirect
180. C4×D4×C73C2×C4semidirect
338. Q8×C73C4×D4semidirect
381. Dic146C4×D4semidirect
454. C73#34295semidirect
464. #550#64408semidirect
525. C2×#41C2×#64408semidirect
526. C2×#41C2×#64408semidirect
542. #127C2×#64408semidirect
553. #121C2×#64408semidirect
554. #121C2×#64408semidirect
562. C4×Q8C2×#64408semidirect
575. C4×D4C2×#64408semidirect
751. Q8D4×#64408semidirect

Maximal subgroups

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

subgroupindex
C2×#179896562
C2×#41×#644082
#226264612
#226264582
#226264562
#226264472
#226264462
#226264362
#226264232
#226264192
#121×#644082
#226263852
#226263712
#550×D732
#3429573