Finite Group Databasebeta

← #34030821

Subgroups — #34030821

Order 18688.

3112 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989656C211yesmaximal, characteristic, complemented
2C22×Q8×#64408C211yesmaximal, characteristic, complemented
3#22626462C213yesmaximal, complemented
4#22626456C213yesmaximal, complemented
5#22626455C213yesmaximal, complemented
6Q8×C4⋊#64408C211yesmaximal, characteristic, complemented
7D4×C4⋊#64408C213yesmaximal, complemented
8#22626436C211yesmaximal, characteristic, complemented
9Q8×C22⋊#64408C211yesmaximal, characteristic, complemented
10#22626421C213yesmaximal, complemented
11#22626418C213yesmaximal, complemented
12#121×#64408C213yesmaximal, complemented
13#22626385C213yesmaximal, complemented
14#22626371C211yesmaximal, characteristic, complemented
15#548×D73C211yesmaximal, characteristic
16#17989656—28no—
17C2×Q8×#64408—28no—
18C2×Q8×#64408C2211yescharacteristic
19C2×Q8×#64408C2213yes—
20C2×Q8×#64408C2211yescharacteristic
21C2×Q8×#64408C2213yes—
22C2×Q8×#64408C2211yescharacteristic
23C2×Q8×#64408C2211yescharacteristic
24C2×D4×#64408C2213yes—
25C2×D4×#64408C2213yes—
26C2×D4×#64408C2216yes—
27C2×#14556670C2213yes—
28C22×C4⋊#64408C2213yes—
29C22×C4⋊#64408C2213yes—
30C22×C4×#64408C2213yes—
31(C2×#64408)⋊Q8C2213yes—
32(C2×#64408)⋊Q8C2213yes—
33#17989539C2213yes—
34#17989539C2213yes—
35#17989538C2213yes—
36#17989538C2216yes—
37#17989538C2213yes—
38#17989537C2213yes—
39#17989537C2213yes—
40#17989537C2216yes—
41#17989537C2216yes—
42#17989536C2213yes—
43#17989536C2213yes—
44#17989535C2213yes—
45#17989535C2213yes—
46#17989534C2211yescharacteristic
47#17989534C2213yes—
48#17989534C2216yes—
49#17989534C2216yes—
50#17989533C2213yes—
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
62C22×Q8×D73C2211yescharacteristic
63#17989249C411yescharacteristic, complemented
64#17989248C411yescharacteristic, complemented
65#17989247C413yescomplemented
66#17989246C413yescomplemented
67#17989245C413yescomplemented
68#17989244C411yescharacteristic, complemented
69#17989243C413yescomplemented
70#124×D73C2213yes—
71C22⋊Q8×D73C2213yes—
72#121×D73C2213yes—
73C4×Q8×D73C2211yescharacteristic
74C4×D4×D73C2213yes—
75#548×C73C411yescharacteristic, complemented
76C23×#64408C2311yescharacteristic
77C23×#64408C2313yes—
78C23×#64408C2316yes—
79Q8×#64408—212no—
80Q8×#64408—212no—
81Q8×#64408—24no—
82Q8×#64408—24no—
83Q8×#64408—24no—
84Q8×#64408D418yescomplemented
85D4×#64408—212no—
86D4×#64408—212no—
87D4×#64408—412no—
88#14556670—212no—
89C2×C4⋊#64408—212no—
90C2×C4⋊#64408—212no—
91C2×C4⋊#64408C2313yes—
92C2×C4⋊#64408C2313yes—
93C2×C4⋊#64408C2313yes—
94C2×C4⋊#64408C2316yes—
95C2×C4⋊#64408C2311yescharacteristic
96C2×C4⋊#64408C2313yes—
97C2×C4⋊#64408C2311yescharacteristic
98C2×C4⋊#64408C2316yes—
99C2×C4⋊#64408C2313yes—
100C2×C4⋊#64408C2313yes—
101C2×C22⋊#64408C2313yes—
102C2×C22⋊#64408C2313yes—
103C2×C22⋊#64408C2313yes—
104C2×C22⋊#64408C2311yescharacteristic
105C2×C22⋊#64408C2313yes—
106C2×C22⋊#64408C2316yes—
107C2×C22⋊#64408C2313yes—
108C2×C4×#64408—212no—
109C2×C4×#64408C2313yes—
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)⋊C4C2313yes—
122(C2×#64408)⋊C4C2313yes—
123(C2×#64408)⋊C4C2313yes—
124(C2×#64408)⋊C4C2313yes—
125(C2×#64408)⋊C4C2316yes—
126(C2×#64408)⋊C4C2313yes—
127C2×#11924029C2×C411yescharacteristic, complemented
128C2×#11924028C2×C413yescomplemented
129C2×#11924027C2×C413yescomplemented
130#41×D73—24no—
131#41×D73—24no—
132C22×Dic146C2×C413yescomplemented
133C2×Q8×D73—24no—
134C2×Q8×D73—24no—
135C2×Q8×D73C2×C411yescharacteristic, complemented
136C2×Q8×D73C2×C413yescomplemented
137C2×Q8×D73C2313yes—
138C2×Q8×D73C2311yescharacteristic
139C2×D4×D73C2313yes—
140C2×D4×D73C2313yes—
141C22×C4×D73C2313yes—
142C22×C4×D73C2313yes—
143#14556580C2×C413yescomplemented
144#14556579C2×C413yescomplemented
145#14556578C2×C413yescomplemented
146#14556577C2×C416yescomplemented
147#14556577C2×C416yescomplemented
148#14556571C2×C413yescomplemented
149#14556570C2×C413yescomplemented
150#14556569C2×C416yescomplemented
151#14556568C2×C416yescomplemented
152#14556567C2×C413yescomplemented
153#14556566C2×C413yescomplemented
154#14556565C2×C413yescomplemented
155#14556564C2×C416yescomplemented
156#14556563C2×C416yescomplemented
157#14556562C2×C413yescomplemented
158Q8×Dic73C2×C411yescharacteristic, complemented
159C4×Dic146C2×C413yescomplemented
160#14556556C2×C413yescomplemented
161C4×D292C2×C413yescomplemented
162D4×Dic73C2×C413yescomplemented
163#14556553C2×C413yescomplemented
164C4×C22⋊D73C2×C413yescomplemented
165C4×C22⋊D73C2×C413yescomplemented
166#14556551C2×C413yescomplemented
167#14556551C2×C413yescomplemented
168C4⋊C4×D73C2313yes—
169C4⋊C4×D73C2313yes—
170C22⋊C4×D73C2316yes—
171C22⋊C4×D73C2311yescharacteristic
172C22⋊C4×D73C2313yes—
173C42×D73C2313yes—
174C2×#41×C73C2×C411yescharacteristic, complemented
175C22×Q8×C73C2×C411yescharacteristic, complemented
176#124×C73C2×C413yescomplemented
177C22⋊Q8×C73C2×C413yescomplemented
178#121×C73C2×C413yescomplemented
179C4×Q8×C73C2×C411yescharacteristic, complemented
180C4×D4×C73C2×C413yescomplemented
181C22×#64408—22no—
182C22×#64408—22no—
183C22×#64408—22no—
184C22×#64408—26no—
185C22×#64408—26no—
186C22×#64408—212no—
187C22×#64408—43no—
188C22×#64408—46no—
189C22×#64408—46no—
190C22×#64408C2413yes—
191C22×#64408C2413yes—
192C22×#64408C2411yescharacteristic
193C22×#64408C2411yescharacteristic
194C22×#64408C2413yes—
195C22×#64408C2413yes—
196C22×#64408C2411yescharacteristic
197C22×#64408C2411yescharacteristic
198C4⋊#64408—212no—
199C4⋊#64408—26no—
200C4⋊#64408—22no—
201C4⋊#64408—22no—
202C4⋊#64408—26no—
203C4⋊#64408—26no—
204C4⋊#64408—26no—
205C4⋊#64408—43no—
206C4⋊#64408—46no—
207C4⋊#64408C2×D4112yes—
208C22⋊#64408—26no—
209C22⋊#64408—22no—
210C22⋊#64408—26no—
211C22⋊#64408—26no—
212C22⋊#64408—26no—
213C22⋊#64408—43no—
214C22⋊#64408—46no—
215C4×#64408—26no—
216C4×#64408—26no—
217C4×#64408—26no—
218C4×#64408—26no—
219C4×#64408—26no—
220C4×#64408—46no—
221C4×#64408C2×D4112yes—
222C23×D73C2413yes—
223C23×D73C2411yescharacteristic
224#11924029—24no—
225#11924028—212no—
226#11924027—212no—
227C2×Dic146—212no—
228C2×Dic146C22×C416yes—
229C2×Dic146C22×C413yes—
230C2×Dic146C22×C413yes—
231Q8×D73—24no—
232Q8×D73—26no—
233Q8×D73—26no—
234Q8×D73—212no—
235Q8×D73C2×D414yes—
236Q8×D73#4114yes—
237C2×D292C22×C413yes—
238C2×D292C22×C413yes—
239C2×C22⋊D73C22×C413yes—
240C2×C22⋊D73C22×C413yes—
241C2×C22⋊D73C22×C416yes—
242D4×D73—26no—
243D4×D73—26no—
244D4×D73—26no—
245D4×D73—26no—
246C22×Dic73C22×C413yes—
247C22×Dic73C22×C413yes—
248C2×C4×D73—26no—
249C2×C4×D73—26no—
250C2×C4×D73—26no—
251C2×C4×D73—26no—
252C2×C4×D73C22×C413yes—
253C2×C4×D73C22×C413yes—
254C2×C4×D73C22×C413yes—
255C2×C4×D73C22×C413yes—
256C2×C4×D73C2411yescharacteristic
257C2×C4×D73C2413yes—
258C2×C4×D73C2413yes—
259C2×C4×D73C2411yescharacteristic
260C2×C4×D73C2413yes—
261C4⋊Dic73C22×C413yes—
262C4⋊Dic73C22×C413yes—
263#11924007C22×C413yes—
264#11924007C22×C413yes—
265#11924007C22×C416yes—
266C22⋊Dic73C22×C411yescharacteristic
267C22⋊Dic73C22×C413yes—
268C22⋊Dic73C22×C416yes—
269#11924005C22×C411yescharacteristic
270#11924005C22×C413yes—
271#11924005C22×C411yescharacteristic
272#11924005C22×C413yes—
273#11924005C22×C416yes—
274#11924005C22×C416yes—
275C4×Dic73C22×C413yes—
276C4×Dic73C22×C413yes—
277C4×Dic73C22×C413yes—
278#41×C73—24no—
279C2×Q8×C73—24no—
280C2×Q8×C73C22×C413yes—
281C2×Q8×C73C22×C411yescharacteristic
282C2×D4×C73C22×C413yes—
283C2×D4×C73C22×C413yes—
284C22×C4×C73C22×C413yes—
285C22×C4×C73C22×C413yes—
286C4⋊C4×C73C22×C413yes—
287C4⋊C4×C73C22×C413yes—
288C22⋊C4×C73C22×C411yescharacteristic
289C22⋊C4×C73C22×C413yes—
290C22⋊C4×C73C22×C416yes—
291C42×C73C22×C413yes—
292C23×C73C23×C413yes—
293C23×C73C23×C411yescharacteristic
294C22×D73—21no—
295C22×D73—21no—
296C22×D73—21no—
297C22×D73—21no—
298C22×D73—23no—
299C22×D73—23no—
300C22×D73—23no—
301C22×D73—23no—
302C22×D73—23no—
303C22×D73—23no—
304C22×D73C23×C413yes—
305C22×D73C23×C411yescharacteristic
306C22×D73H(5,𝔽2)12yes—
307C22×D732−1+412yes—
308C22×D73C2511yescharacteristic
309C2×#64408—28no—
310C2×#64408—21no—
311C2×#64408—23no—
312C2×#64408—21no—
313C2×#64408—21no—
314C2×#64408—21no—
315C2×#64408—23no—
316C2×#64408—21no—
317C2×#64408—23no—
318C2×#64408—23no—
319C2×#64408—21no—
320C2×#64408—23no—
321C2×#64408—23no—
322C2×#64408—23no—
323C2×#64408—23no—
324C2×#64408—21no—
325C2×#64408—21no—
326C2×#64408—23no—
327C2×#64408—21no—
328C2×#64408—21no—
329C2×#64408—23no—
330C2×#64408—23no—
331C2×#64408—412no—
332C2×#64408—812no—
333C2×#64408C22×D412yes—
334C2×#64408C22×D416yes—
335C2×#644082−1+412yes—
336Q8×C73—26no—
337Q8×C73C4×D414yescomplemented
338D4×C73—26no—
339D4×C73—26no—
340C2×C4×C73—26no—
341C2×C4×C73—26no—
342C2×C4×C73C23×C411yescharacteristic
343C2×C4×C73C23×C413yes—
344C2×C4×C73C23×C413yes—
345C2×C4×C73C23×C411yescharacteristic
346C2×C4×C73C23×C413yes—
347C22⋊D73—26no—
348C22⋊D73—26no—
349C22⋊D73—212no—
350C2×Dic73—26no—
351C2×Dic73—26no—
352C2×Dic73C23×C411yescharacteristic
353C2×Dic73C23×C413yes—
354C2×Dic73C23×C413yes—
355C2×Dic73C23×C411yescharacteristic
356C2×Dic73C23×C413yes—
357D292—26no—
358D292—26no—
359C4×D73—21no—
360C4×D73—23no—
361C4×D73—21no—
362C4×D73—23no—
363C4×D73—23no—
364C4×D73—23no—
365C4×D73—21no—
366C4×D73—21no—
367C4×D73—26no—
368C4×D73—26no—
369C4×D73—26no—
370C4×D73—26no—
371C4×D73C22×D416yes—
372C4×D73C2×#4116yes—
373Dic146—26no—
374Dic146—212no—
375Dic146C4×D4112yescomplemented
376C22×C73—21no—
377C22×C73—21no—
378C22×C73—23no—
379C22×C73—23no—
380C22×C73—23no—
381C22×C73#52012yescomplemented
382C22×C73C24×C411yescharacteristic
383C2×D73—21no—
384C2×D73—21no—
385C2×D73—22no—
386C2×D73—22no—
387C2×D73—22no—
388C2×D73—22no—
389C2×D73—23no—
390C2×D73—23no—
391C2×D73—23no—
392C2×D73—43no—
393C2×D73—43no—
394C2×D73—43no—
395C2×D73—43no—
396C2×D73#52012yescomplemented
397C2×D73C23×D411yescharacteristic
398C2×D73C22×#4111yescharacteristic
399C2×D73C2×H(5,𝔽2)11yescharacteristic
400C2×D73C2×2−1+411yescharacteristic
401C2×D73C2×2−1+411yescharacteristic
402C2×D73#58511yescharacteristic
403#64408—22no—
404#64408—22no—
405#64408—26no—
406#64408—41no—
407#64408—43no—
408#64408—43no—
409#64408—41no—
410#64408—43no—
411C4×C73—23no—
412C4×C73—21no—
413C4×C73—23no—
414C4×C73—21no—
415C4×C73C2×C4×D416yes—
416Dic73—23no—
417Dic73—21no—
418Dic73—23no—
419Dic73—21no—
420Dic73C2×C4×D416yes—
421#34294—731nomaximal, Sylow
422C2×C73—22no—
423C2×C73—43no—
424C2×C73C22×C4×D411yescharacteristic
425C2×C73C2×#52011yescharacteristic
426C2×C73C4×2−1+411yescharacteristic
427D73—22no—
428D73—43no—
429D73#348611yescharacteristic
430D73#348811yescharacteristic
431D73#351611yescharacteristic
432D73#352211yescharacteristic
433C2×#548—731no—
434C2×#520—731no—
435C22×C4×Q8—731no—
436#2367—733no—
437#2361—733no—
438#2360—733no—
439Q8×C4⋊C4—731no—
440D4×C4⋊C4—733no—
441#2341—731no—
442Q8×C22⋊C4—731no—
443#2326—733no—
444#2323—733no—
445C4×#121—733no—
446#2290—733no—
447#2276—731no—
448C73#3429411yescharacteristic, complemented, Sylow
449C22×#41—731no—
450C23×Q8—731no—
451#548—731no—
452#548—731no—
453#548—733no—
454#548—733no—
455#548—733no—
456#548—731no—
457#548—733no—
458#548#6440811yescharacteristic, complemented
459C2×#124—733no—
460C2×C22⋊Q8—733no—
461C2×#121—733no—
462#520—1468no—
463C2×C4×Q8—731no—
464C2×C4×Q8—731no—
465C2×C4×Q8—733no—
466C2×C4×Q8—731no—
467C2×C4×Q8—731no—
468C2×C4×Q8—731no—
469C2×C4×Q8—733no—
470C2×C4×Q8—1468no—
471C2×C4×D4—736no—
472C2×C4×D4—733no—
473C2×C4×D4—733no—
474C2×C4×D4—733no—
475C2×#117—733no—
476C22×C4⋊C4—733no—
477C22×C4⋊C4—733no—
478C22×C42—733no—
479#391—733no—
480#391—733no—
481#390—733no—
482#390—733no—
483#389—736no—
484#389—733no—
485#389—733no—
486#388—736no—
487#388—736no—
488#388—733no—
489#388—733no—
490#387—733no—
491#387—733no—
492#386—733no—
493#386—733no—
494#385—736no—
495#385—736no—
496#385—733no—
497#385—731no—
498#384—733no—
499#380—733no—
500#380—733no—
501C4×C4⋊C4—733no—
502C4×C4⋊C4—733no—
503C4×C4⋊C4—733no—
504C4×C4⋊C4—733no—
505C4×C22⋊C4—733no—
506C4×C22⋊C4—733no—
507C4×C22⋊C4—736no—
508#376—733no—
509C2×#41—731no—
510C2×#41—733no—
511C2×#41—733no—
512C2×#41—1464no—
513C2×#41—1464no—
514C2×#41C2×#6440811yescharacteristic, complemented
515C22×Q8—731no—
516C22×Q8—733no—
517C22×Q8—733no—
518C22×Q8—731no—
519C22×Q8—733no—
520C22×Q8—1464no—
521C22×Q8—1464no—
522C22×Q8C2×#6440811yescharacteristic, complemented
523C22×D4—733no—
524C22×D4—733no—
525C23×C4—736no—
526C23×C4—733no—
527C23×C4—733no—
528C23×C4—733no—
529C23×C4—731no—
530#124—733no—
531#124—733no—
532#124—736no—
533#124—736no—
534#124—733no—
535#124C2×#6440813yescomplemented
536C22⋊Q8—733no—
537C22⋊Q8—733no—
538C22⋊Q8—736no—
539C22⋊Q8—733no—
540C22⋊Q8—736no—
541C22⋊Q8C2×#6440813yescomplemented
542#121—733no—
543#121—736no—
544#121—733no—
545#121—733no—
546#121—736no—
547#121C2×#6440813yescomplemented
548C4×Q8—738no—
549C4×Q8—731no—
550C4×Q8—733no—
551C4×Q8—733no—
552C4×Q8—14612no—
553C4×Q8—14612no—
554C4×Q8—1464no—
555C4×Q8—1464no—
556C4×Q8—1464no—
557C4×Q8C2×#6440811yescharacteristic, complemented
558C4×D4—29212no—
559C4×D4—733no—
560C4×D4—733no—
561C4×D4—733no—
562C4×D4—733no—
563C4×D4—733no—
564C4×D4—733no—
565C4×D4—733no—
566C4×D4—14612no—
567C4×D4—14612no—
568C4×D4C2×#6440813yescomplemented
569#117—14612no—
570C2×C4⋊C4—736no—
571C2×C4⋊C4—733no—
572C2×C4⋊C4—733no—
573C2×C4⋊C4—733no—
574C2×C4⋊C4—733no—
575C2×C4⋊C4—733no—
576C2×C4⋊C4—733no—
577C2×C4⋊C4—733no—
578C2×C4⋊C4—736no—
579C2×C4⋊C4—731no—
580C2×C4⋊C4—733no—
581C2×C4⋊C4—731no—
582C2×C4⋊C4—14612no—
583C2×C4⋊C4—14612no—
584C2×C22⋊C4—736no—
585C2×C22⋊C4—733no—
586C2×C22⋊C4—731no—
587C2×C22⋊C4—733no—
588C2×C22⋊C4—736no—
589C2×C22⋊C4—733no—
590C2×C22⋊C4—733no—
591C2×C22⋊C4—733no—
592C2×C22⋊C4—731no—
593C2×C22⋊C4—733no—
594C2×C42—736no—
595C2×C42—733no—
596C2×C42—733no—
597C2×C42—733no—
598C2×C42—733no—
599C2×C42—733no—
600C2×C42—733no—
601C2×C42—733no—
602C2×C42—14612no—
603#95—731no—
604#95—733no—
605#95—733no—
606#95—733no—
607#95—731no—
608#95—733no—
609#95—733no—
610#95—736no—
611#95—733no—
612#95—733no—
613#95—733no—
614C24—731no—
615C24—733no—
616#41—24no—
617#41—14612no—
618#41—14612no—
619#41—1464no—
620C2×Q8—24no—
621C2×Q8—734no—
622C2×Q8—734no—
623C2×Q8—733no—
624C2×Q8—736no—
625C2×Q8—733no—
626C2×Q8—14612no—
627C2×Q8—1466no—
628C2×Q8—1466no—
629C2×Q8—14612no—
630C2×Q8—1464no—
631C2×Q8C22×#6440813yes—
632C2×Q8C22×#6440811yescharacteristic
633C2×D4—733no—
634C2×D4—733no—
635C2×D4—736no—
636C2×D4—733no—
637C2×D4—733no—
638C2×D4—1466no—
639C2×D4—1466no—
640C2×D4—1466no—
641C2×D4—1466no—
642C2×D4C22×#6440813yes—
643C2×D4C22×#6440813yes—
644C22×C4—2923no—
645C22×C4—2926no—
646C22×C4—2926no—
647C22×C4—733no—
648C22×C4—731no—
649C22×C4—731no—
650C22×C4—733no—
651C22×C4—733no—
652C22×C4—733no—
653C22×C4—733no—
654C22×C4—733no—
655C22×C4—733no—
656C22×C4—733no—
657C22×C4—731no—
658C22×C4—733no—
659C22×C4—733no—
660C22×C4—731no—
661C22×C4—731no—
662C22×C4—733no—
663C22×C4—731no—
664C22×C4—733no—
665C22×C4—733no—
666C22×C4—1466no—
667C22×C4—1466no—
668C22×C4—1466no—
669C22×C4—1466no—
670C22×C4—1466no—
671C22×C4—1466no—
672C22×C4—14612no—
673C22×C4—1462no—
674C22×C4—1462no—
675C22×C4—1462no—
676C22×C4C22×#6440813yes—
677C22×C4C22×#6440813yes—
678C4⋊C4—2923no—
679C4⋊C4—2926no—
680C4⋊C4—7312no—
681C4⋊C4—733no—
682C4⋊C4—733no—
683C4⋊C4—736no—
684C4⋊C4—733no—
685C4⋊C4—733no—
686C4⋊C4—1462no—
687C4⋊C4—1466no—
688C4⋊C4—1466no—
689C4⋊C4—1466no—
690C4⋊C4—14612no—
691C4⋊C4—1462no—
692C4⋊C4—1466no—
693C4⋊C4C22×#6440813yes—
694C4⋊C4C22×#6440813yes—
695C22⋊C4—2923no—
696C22⋊C4—2926no—
697C22⋊C4—731no—
698C22⋊C4—733no—
699C22⋊C4—736no—
700C22⋊C4—731no—
701C22⋊C4—731no—
702C22⋊C4—733no—
703C22⋊C4—733no—
704C22⋊C4—736no—
705C22⋊C4—736no—
706C22⋊C4—1466no—
707C22⋊C4—1466no—
708C22⋊C4—1466no—
709C22⋊C4—1462no—
710C22⋊C4—1466no—
711C22⋊C4C22×#6440811yescharacteristic
712C22⋊C4C22×#6440813yes—
713C22⋊C4C22×#6440816yes—
714C42—2926no—
715C42—7312no—
716C42—733no—
717C42—733no—
718C42—733no—
719C42—1466no—
720C42—1466no—
721C42—1466no—
722C42—1466no—
723C42—1466no—
724C42C22×#6440813yes—
725C23—731no—
726C23—732no—
727C23—732no—
728C23—731no—
729C23—733no—
730C23—1463no—
731C23—1463no—
732C23—1463no—
733C23—1463no—
734C23—1463no—
735C23—1463no—
736C23—1461no—
737C23—1461no—
738C23—1461no—
739C23—1461no—
740C23C23×#6440813yes—
741C23C23×#6440811yescharacteristic
742Q8—26no—
743Q8—7312no—
744Q8—14612no—
745Q8—1466no—
746Q8D4×#6440814yescomplemented
747D4—26no—
748D4—26no—
749D4—1466no—
750D4—14612no—
751D4—1466no—
752D4—1466no—
753D4—1466no—
754C2×C4—26no—
755C2×C4—26no—
756C2×C4—29212no—
757C2×C4—58412no—
758C2×C4—733no—
759C2×C4—736no—
760C2×C4—736no—
761C2×C4—732no—
762C2×C4—736no—
763C2×C4—732no—
764C2×C4—731no—
765C2×C4—733no—
766C2×C4—733no—
767C2×C4—731no—
768C2×C4—1466no—
769C2×C4—1466no—
770C2×C4—1463no—
771C2×C4—1463no—
772C2×C4—1461no—
773C2×C4—1461no—
774C2×C4—1461no—
775C2×C4—1461no—
776C2×C4—1463no—
777C2×C4—1463no—
778C2×C4—1463no—
779C2×C4—1461no—
780C2×C4—1461no—
781C2×C4—1463no—
782C2×C4—1463no—
783C2×C4—1463no—
784C2×C4—1461no—
785C2×C4—1463no—
786C2×C4—1463no—
787C2×C4—1463no—
788C2×C4—1461no—
789C2×C4—1461no—
790C2×C4—1463no—
791C2×C4—1463no—
792C2×C4—1461no—
793C2×C4—1466no—
794C2×C4—1466no—
795C2×C4—1463no—
796C2×C4—1461no—
797C2×C4—1463no—
798C2×C4—1461no—
799C2×C4—1461no—
800C2×C4—1461no—
801C2×C4—1468no—
802C2×C4—1466no—
803C2×C4—1466no—
804C2×C4C23×#6440811yescharacteristic
805C2×C4C23×#6440813yes—
806C2×C4C23×#6440813yes—
807C2×C4C23×#6440811yescharacteristic
808C2×C4C23×#6440813yes—
809C22—21no—
810C22—21no—
811C22—23no—
812C22—23no—
813C22—23no—
814C22—2923no—
815C22—2923no—
816C22—2923no—
817C22—2923no—
818C22—731no—
819C22—731no—
820C22—731no—
821C22—731no—
822C22—731no—
823C22—731no—
824C22—732no—
825C22—1462no—
826C22—1462no—
827C22—1462no—
828C22—1462no—
829C22—1463no—
830C22—1463no—
831C22—1463no—
832C22—1461no—
833C22—1461no—
834C22#1798965612yescomplemented
835C22C24×#6440811yescharacteristic
836C4—21no—
837C4—23no—
838C4—23no—
839C4—21no—
840C4—2923no—
841C4—2923no—
842C4—2923no—
843C4—2921no—
844C4—2921no—
845C4—736no—
846C4—1466no—
847C4—1462no—
848C4—1462no—
849C4—1461no—
850C4—1463no—
851C4—1463no—
852C4—1461no—
853C4C2×D4×#6440816yes—
854C2—22no—
855C2—43no—
856C2—2923no—
857C2—731no—
858C2—731no—
859C2—731no—
860C2—731no—
861C2—1462no—
862C2C22×D4×#6440811yescharacteristic
863C2C2×#1798965611yescharacteristic
864C22−1+4×#6440811yescharacteristic
subgroupG/H
center, FrattiniC22C24×#64408
commutator, socleC22×C73C24×C4
Fitting#548×C73C4
prime radical#548×D73C2
cosocleC22×D73C25
hypercenter#548#64408
hypocenterC73#34294
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#17989656C2semidirect
2. C22×Q8×#64408C2semidirect
3. #22626462C2semidirect
4. #22626456C2semidirect
5. #22626455C2semidirect
6. Q8×C4⋊#64408C2semidirect
7. D4×C4⋊#64408C2semidirect
8. #22626436C2semidirect
9. Q8×C22⋊#64408C2semidirect
10. #22626421C2semidirect
11. #22626418C2semidirect
12. #121×#64408C2semidirect
13. #22626385C2semidirect
14. #22626371C2semidirect
63. #17989249C4semidirect
64. #17989248C4semidirect
65. #17989247C4semidirect
66. #17989246C4semidirect
67. #17989245C4semidirect
68. #17989244C4semidirect
69. #17989243C4semidirect
75. #548×C73C4semidirect
84. Q8×#64408D4semidirect
127. C2×#11924029C2×C4semidirect
128. C2×#11924028C2×C4semidirect
129. C2×#11924027C2×C4semidirect
132. C22×Dic146C2×C4semidirect
135. C2×Q8×D73C2×C4semidirect
136. C2×Q8×D73C2×C4semidirect
143. #14556580C2×C4semidirect
144. #14556579C2×C4semidirect
145. #14556578C2×C4semidirect
146. #14556577C2×C4semidirect
147. #14556577C2×C4semidirect
148. #14556571C2×C4semidirect
149. #14556570C2×C4semidirect
150. #14556569C2×C4semidirect
151. #14556568C2×C4semidirect
152. #14556567C2×C4semidirect
153. #14556566C2×C4semidirect
154. #14556565C2×C4semidirect
155. #14556564C2×C4semidirect
156. #14556563C2×C4semidirect
157. #14556562C2×C4semidirect
158. Q8×Dic73C2×C4semidirect
159. C4×Dic146C2×C4semidirect
160. #14556556C2×C4semidirect
161. C4×D292C2×C4semidirect
162. D4×Dic73C2×C4semidirect
163. #14556553C2×C4semidirect
164. C4×C22⋊D73C2×C4semidirect
165. C4×C22⋊D73C2×C4semidirect
166. #14556551C2×C4semidirect
167. #14556551C2×C4semidirect
174. C2×#41×C73C2×C4semidirect
175. C22×Q8×C73C2×C4semidirect
176. #124×C73C2×C4semidirect
177. C22⋊Q8×C73C2×C4semidirect
178. #121×C73C2×C4semidirect
179. C4×Q8×C73C2×C4semidirect
180. C4×D4×C73C2×C4semidirect
337. Q8×C73C4×D4semidirect
375. Dic146C4×D4semidirect
381. C22×C73#520semidirect
396. C2×D73#520semidirect
448. C73#34294semidirect
458. #548#64408semidirect
514. C2×#41C2×#64408semidirect
522. C22×Q8C2×#64408semidirect
535. #124C2×#64408semidirect
541. C22⋊Q8C2×#64408semidirect
547. #121C2×#64408semidirect
557. C4×Q8C2×#64408semidirect
568. C4×D4C2×#64408semidirect
746. Q8D4×#64408semidirect
834. C22#17989656semidirect

Maximal subgroups

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

subgroupindex
C2×#179896562
C22×Q8×#644082
#226264622
#226264562
#226264552
Q8×C4⋊#644082
D4×C4⋊#644082
#226264362
Q8×C22⋊#644082
#226264212
#226264182
#121×#644082
#226263852
#226263712
#548×D732
#3429473