Finite Group Databasebeta

← #548×#64408 #34030685

Subgroups — #548×#64408 #34030685

Order 18688.

3232 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×#41×#64408C211yesmaximal, characteristic, complemented
2C22×Q8×#64408C211yesmaximal, characteristic, complemented
3#22626462C213yesmaximal, complemented
4#22626457C213yesmaximal, complemented
5#22626456C213yesmaximal, complemented
6#22626447C213yesmaximal, complemented
7#22626446C211yesmaximal, characteristic, complemented
8#22626436C211yesmaximal, characteristic, complemented
9Q8×C22⋊#64408C211yesmaximal, characteristic, complemented
10#124×#64408C213yesmaximal, complemented
11C22⋊Q8×#64408C213yesmaximal, complemented
12#121×#64408C213yesmaximal, complemented
13C4×Q8×#64408C211yesmaximal, characteristic, complemented
14C4×D4×#64408C213yesmaximal, complemented
15#548×D73C211yesmaximal, characteristic
16#41×#64408—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×#64408C2213yes—
27C2×D4×#64408C2213yes—
28C2×#14556670C2213yes—
29C22×C4⋊#64408C2213yes—
30C22×C4×#64408C2213yes—
31C22×C4×#64408C2213yes—
32(C2×#64408)⋊Q8C2213yes—
33(C2×#64408)⋊Q8C2213yes—
34#17989539C2213yes—
35#17989539C2213yes—
36#17989538C2213yes—
37#17989538C2213yes—
38#17989537C2216yes—
39#17989537C2216yes—
40#17989537C2216yes—
41#17989536C2216yes—
42#17989535C2216yes—
43#17989534C2216yes—
44#17989531C2213yes—
45#17989529C2213yes—
46#17989529C2213yes—
47C4⋊C4×#64408C2213yes—
48C4⋊C4×#64408C2213yes—
49C4⋊C4×#64408C2213yes—
50C4⋊C4×#64408C2213yes—
51C4×C4⋊#64408C2213yes—
52C4×C4⋊#64408C2213yes—
53C22⋊C4×#64408C2211yescharacteristic
54C22⋊C4×#64408C2213yes—
55C22⋊C4×#64408C2213yes—
56C22⋊C4×#64408C2213yes—
57C22⋊C4×#64408C2216yes—
58C4×C22⋊#64408C2213yes—
59C4×C22⋊#64408C2213yes—
60C42×#64408C2213yes—
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×#64408C2313yes—
77C23×#64408C2313yes—
78C23×#64408C2313yes—
79C23×#64408C2311yescharacteristic
80Q8×#64408—212no—
81Q8×#64408—212no—
82Q8×#64408—24no—
83Q8×#64408—24no—
84Q8×#64408—24no—
85Q8×#64408D418yescomplemented
86D4×#64408—212no—
87D4×#64408—212no—
88D4×#64408—212no—
89D4×#64408—212no—
90#14556670—212no—
91C2×C4⋊#64408—212no—
92C2×C4⋊#64408C2313yes—
93C2×C4⋊#64408C2316yes—
94C2×C4⋊#64408C2313yes—
95C2×C4⋊#64408C2313yes—
96C2×C4⋊#64408C2313yes—
97C2×C4⋊#64408C2313yes—
98C2×C4⋊#64408C2313yes—
99C2×C22⋊#64408C2316yes—
100C2×C22⋊#64408C2313yes—
101C2×C22⋊#64408C2313yes—
102C2×C22⋊#64408C2313yes—
103C2×C22⋊#64408C2316yes—
104C2×C22⋊#64408C2311yescharacteristic
105C2×C4×#64408—212no—
106C2×C4×#64408—212no—
107C2×C4×#64408C2311yescharacteristic
108C2×C4×#64408C2313yes—
109C2×C4×#64408C2313yes—
110C2×C4×#64408C2313yes—
111C2×C4×#64408C2313yes—
112C2×C4×#64408C2313yes—
113C2×C4×#64408C2313yes—
114C2×C4×#64408C2313yes—
115C2×C4×#64408C2313yes—
116C2×C4×#64408C2311yescharacteristic
117C2×C4×#64408C2313yes—
118C2×C4×#64408C2313yes—
119(C2×#64408)⋊C4C2311yescharacteristic
120(C2×#64408)⋊C4C2313yes—
121(C2×#64408)⋊C4C2313yes—
122(C2×#64408)⋊C4C2313yes—
123(C2×#64408)⋊C4C2311yescharacteristic
124(C2×#64408)⋊C4C2313yes—
125(C2×#64408)⋊C4C2316yes—
126(C2×#64408)⋊C4C2316yes—
127(C2×#64408)⋊C4C2316yes—
128C2×#11924029C2×C411yescharacteristic, complemented
129C2×#11924028C2×C413yescomplemented
130C2×#11924027C2×C413yescomplemented
131#41×D73—24no—
132#41×D73—24no—
133C22×Dic146C2×C413yescomplemented
134C2×Q8×D73—24no—
135C2×Q8×D73—24no—
136C2×Q8×D73C2×C411yescharacteristic, complemented
137C2×Q8×D73C2×C413yescomplemented
138C2×Q8×D73C2313yes—
139C2×Q8×D73C2311yescharacteristic
140C2×D4×D73C2313yes—
141C2×D4×D73C2313yes—
142C22×C4×D73C2313yes—
143C22×C4×D73C2313yes—
144#14556580C2×C413yescomplemented
145#14556579C2×C413yescomplemented
146#14556578C2×C413yescomplemented
147#14556577C2×C416yescomplemented
148#14556577C2×C416yescomplemented
149#14556571C2×C413yescomplemented
150#14556570C2×C413yescomplemented
151#14556569C2×C416yescomplemented
152#14556568C2×C416yescomplemented
153#14556567C2×C413yescomplemented
154#14556566C2×C413yescomplemented
155#14556565C2×C413yescomplemented
156#14556564C2×C416yescomplemented
157#14556563C2×C416yescomplemented
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×D73C2313yes—
171C22⋊C4×D73C2311yescharacteristic
172C22⋊C4×D73C2313yes—
173C22⋊C4×D73C2316yes—
174C42×D73C2313yes—
175C2×#41×C73C2×C411yescharacteristic, complemented
176C22×Q8×C73C2×C411yescharacteristic, complemented
177#124×C73C2×C413yescomplemented
178C22⋊Q8×C73C2×C413yescomplemented
179#121×C73C2×C413yescomplemented
180C4×Q8×C73C2×C411yescharacteristic, complemented
181C4×D4×C73C2×C413yescomplemented
182C22×#64408—22no—
183C22×#64408—22no—
184C22×#64408—26no—
185C22×#64408—26no—
186C22×#64408—26no—
187C22×#64408—26no—
188C22×#64408—26no—
189C22×#64408—26no—
190C22×#64408—26no—
191C22×#64408—43no—
192C22×#64408—43no—
193C22×#64408#4114yescomplemented
194C22×#64408C2413yes—
195C22×#64408C2413yes—
196C22×#64408C2413yes—
197C22×#64408C2413yes—
198C22×#64408C2411yescharacteristic
199C22×#64408C2411yescharacteristic
200C22×#64408C2411yescharacteristic
201C22×#64408C2411yescharacteristic
202C4⋊#64408—212no—
203C4⋊#64408—26no—
204C4⋊#64408—26no—
205C4⋊#64408—26no—
206C4⋊#64408—26no—
207C4⋊#64408—26no—
208C4⋊#64408C2×D4112yes—
209C22⋊#64408—26no—
210C22⋊#64408—212no—
211C22⋊#64408—26no—
212C22⋊#64408—26no—
213C22⋊#64408—46no—
214C22⋊#64408#4114yescomplemented
215C4×#64408—26no—
216C4×#64408—26no—
217C4×#64408—22no—
218C4×#64408—26no—
219C4×#64408—26no—
220C4×#64408—26no—
221C4×#64408—22no—
222C4×#64408—26no—
223C4×#64408—26no—
224C4×#64408—26no—
225C4×#64408—43no—
226C4×#64408C2×D4112yes—
227C23×D73C2413yes—
228C23×D73C2411yescharacteristic
229#11924029—24no—
230#11924028—212no—
231#11924027—212no—
232C2×Dic146—212no—
233C2×Dic146C22×C416yes—
234C2×Dic146C22×C413yes—
235C2×Dic146C22×C413yes—
236Q8×D73—24no—
237Q8×D73—26no—
238Q8×D73—26no—
239Q8×D73—212no—
240Q8×D73C2×D414yes—
241Q8×D73#4114yes—
242C2×D292C22×C413yes—
243C2×D292C22×C413yes—
244C2×C22⋊D73C22×C413yes—
245C2×C22⋊D73C22×C413yes—
246C2×C22⋊D73C22×C416yes—
247D4×D73—26no—
248D4×D73—26no—
249D4×D73—26no—
250D4×D73—26no—
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×D73C2413yes—
264C2×C4×D73C2411yescharacteristic
265C2×C4×D73C2413yes—
266C4⋊Dic73C22×C413yes—
267C4⋊Dic73C22×C413yes—
268#11924007C22×C413yes—
269#11924007C22×C413yes—
270#11924007C22×C416yes—
271C22⋊Dic73C22×C411yescharacteristic
272C22⋊Dic73C22×C413yes—
273C22⋊Dic73C22×C416yes—
274#11924005C22×C411yescharacteristic
275#11924005C22×C413yes—
276#11924005C22×C411yescharacteristic
277#11924005C22×C413yes—
278#11924005C22×C416yes—
279#11924005C22×C416yes—
280C4×Dic73C22×C413yes—
281C4×Dic73C22×C413yes—
282C4×Dic73C22×C413yes—
283#41×C73—24no—
284C2×Q8×C73—24no—
285C2×Q8×C73C22×C413yes—
286C2×Q8×C73C22×C411yescharacteristic
287C2×D4×C73C22×C413yes—
288C2×D4×C73C22×C413yes—
289C22×C4×C73C22×C413yes—
290C22×C4×C73C22×C413yes—
291C4⋊C4×C73C22×C413yes—
292C4⋊C4×C73C22×C413yes—
293C22⋊C4×C73C22×C411yescharacteristic
294C22⋊C4×C73C22×C413yes—
295C22⋊C4×C73C22×C416yes—
296C42×C73C22×C413yes—
297C23×C73C23×C413yes—
298C23×C73C23×C411yescharacteristic
299C22×D73—21no—
300C22×D73—21no—
301C22×D73—21no—
302C22×D73—21no—
303C22×D73—23no—
304C22×D73—23no—
305C22×D73—23no—
306C22×D73—23no—
307C22×D73—23no—
308C22×D73—23no—
309C22×D73C23×C413yes—
310C22×D73C23×C411yescharacteristic
311C22×D73C2×#4112yes—
312C22×D73C2×#4112yes—
313C22×D73C2511yescharacteristic
314C2×#64408—21no—
315C2×#64408—21no—
316C2×#64408—21no—
317C2×#64408—23no—
318C2×#64408—21no—
319C2×#64408—21no—
320C2×#64408—23no—
321C2×#64408—21no—
322C2×#64408—28no—
323C2×#64408—23no—
324C2×#64408—23no—
325C2×#64408—23no—
326C2×#64408—23no—
327C2×#64408—23no—
328C2×#64408—23no—
329C2×#64408—23no—
330C2×#64408—23no—
331C2×#64408—23no—
332C2×#64408—412no—
333C2×#64408—412no—
334C2×#64408—412no—
335C2×#64408C22×D416yes—
336C2×#64408C22×D412yes—
337C2×#64408C2×#4112yes—
338C2×#64408C2×#4112yes—
339C2×#64408C2×#4112yes—
340C2×#64408C2×#4112yes—
341C2×#644082−1+412yes—
342Q8×C73—26no—
343Q8×C73C4×D414yescomplemented
344D4×C73—26no—
345D4×C73—26no—
346C2×C4×C73—26no—
347C2×C4×C73—26no—
348C2×C4×C73C23×C411yescharacteristic
349C2×C4×C73C23×C413yes—
350C2×C4×C73C23×C413yes—
351C2×C4×C73C23×C411yescharacteristic
352C2×C4×C73C23×C413yes—
353C22⋊D73—26no—
354C22⋊D73—26no—
355C22⋊D73—212no—
356C2×Dic73—26no—
357C2×Dic73—26no—
358C2×Dic73C23×C411yescharacteristic
359C2×Dic73C23×C413yes—
360C2×Dic73C23×C413yes—
361C2×Dic73C23×C411yescharacteristic
362C2×Dic73C23×C413yes—
363D292—26no—
364D292—26no—
365C4×D73—21no—
366C4×D73—23no—
367C4×D73—21no—
368C4×D73—23no—
369C4×D73—23no—
370C4×D73—23no—
371C4×D73—21no—
372C4×D73—21no—
373C4×D73—26no—
374C4×D73—26no—
375C4×D73—26no—
376C4×D73—26no—
377C4×D73C22×D416yes—
378C4×D73C2×#4116yes—
379Dic146—26no—
380Dic146—212no—
381Dic146C4×D4112yescomplemented
382C22×C73—21no—
383C22×C73—21no—
384C22×C73—23no—
385C22×C73—23no—
386C22×C73—23no—
387C22×C73C4×#4112yescomplemented
388C22×C73C24×C411yescharacteristic
389C2×D73—21no—
390C2×D73—21no—
391C2×D73—22no—
392C2×D73—22no—
393C2×D73—22no—
394C2×D73—22no—
395C2×D73—23no—
396C2×D73—23no—
397C2×D73—23no—
398C2×D73—43no—
399C2×D73—43no—
400C2×D73—43no—
401C2×D73—43no—
402C2×D73C4×#4112yescomplemented
403C2×D73C23×D411yescharacteristic
404C2×D73C22×#4111yescharacteristic
405C2×D73C22×#4111yescharacteristic
406C2×D73C22×#4111yescharacteristic
407C2×D73C2×2−1+411yescharacteristic
408C2×D73#58511yescharacteristic
409#64408—22no—
410#64408—22no—
411#64408—26no—
412#64408—22no—
413#64408—43no—
414#64408—43no—
415#64408—43no—
416#64408#54814yesdirect product factor
417C4×C73—23no—
418C4×C73—21no—
419C4×C73—23no—
420C4×C73—21no—
421C4×C73C2×C4×D416yes—
422Dic73—23no—
423Dic73—21no—
424Dic73—23no—
425Dic73—21no—
426Dic73C2×C4×D416yes—
427C4×#548—731nomaximal, Sylow
428C2×C73—22no—
429C2×C73—43no—
430C2×C73C22×C4×D411yescharacteristic
431C2×C73C2×C4×#4111yescharacteristic
432C2×C73C4×2−1+411yescharacteristic
433D73—22no—
434D73—43no—
435D73C2×#54811yescharacteristic
436D73D4×#4111yescharacteristic
437D73#348011yescharacteristic
438D73#348211yescharacteristic
439C2×#548—731no—
440C2×C4×#41—731no—
441C22×C4×Q8—731no—
442#2367—733no—
443#2362—733no—
444#2361—733no—
445#2352—733no—
446#2351—731no—
447#2341—731no—
448Q8×C22⋊C4—731no—
449C4×#124—733no—
450C4×C22⋊Q8—733no—
451C4×#121—733no—
452C42×Q8—731no—
453C42×D4—733no—
454C73C4×#54811yescharacteristic, complemented, Sylow
455C22×#41—731no—
456C23×Q8—731no—
457#548—731no—
458#548—731no—
459#548—733no—
460#548—733no—
461#548—733no—
462#548—731no—
463#548—733no—
464#548#6440811yescharacteristic, direct product factor
465C2×#124—733no—
466C2×C22⋊Q8—733no—
467C2×#121—733no—
468C4×#41—1468no—
469C2×C4×Q8—731no—
470C2×C4×Q8—731no—
471C2×C4×Q8—731no—
472C2×C4×Q8—731no—
473C2×C4×Q8—731no—
474C2×C4×Q8—733no—
475C2×C4×Q8—733no—
476C2×C4×Q8—1468no—
477C2×C4×D4—733no—
478C2×C4×D4—733no—
479C2×C4×D4—733no—
480C2×C4×D4—733no—
481C2×C4×D4—733no—
482C2×#117—733no—
483C22×C4⋊C4—733no—
484C22×C42—733no—
485C22×C42—733no—
486#391—733no—
487#391—733no—
488#390—733no—
489#390—733no—
490#389—733no—
491#389—733no—
492#388—736no—
493#388—736no—
494#388—736no—
495#387—736no—
496#386—736no—
497#385—736no—
498#382—733no—
499#380—733no—
500#380—733no—
501C4×C4⋊C4—733no—
502C4×C4⋊C4—733no—
503C4×C4⋊C4—733no—
504C4×C4⋊C4—733no—
505C4×C4⋊C4—733no—
506C4×C4⋊C4—733no—
507C4×C22⋊C4—733no—
508C4×C22⋊C4—733no—
509C4×C22⋊C4—733no—
510C4×C22⋊C4—733no—
511C4×C22⋊C4—731no—
512C4×C22⋊C4—733no—
513C4×C22⋊C4—736no—
514C43—733no—
515C2×#41—731no—
516C2×#41—733no—
517C2×#41—733no—
518C2×#41—1464no—
519C2×#41—1464no—
520C2×#41C2×#6440811yescharacteristic, complemented
521C22×Q8—731no—
522C22×Q8—733no—
523C22×Q8—733no—
524C22×Q8—731no—
525C22×Q8—733no—
526C22×Q8—1464no—
527C22×Q8—1464no—
528C22×Q8C2×#6440811yescharacteristic, complemented
529C22×D4—733no—
530C22×D4—733no—
531C23×C4—733no—
532C23×C4—733no—
533C23×C4—731no—
534C23×C4—733no—
535C23×C4—733no—
536C23×C4—733no—
537#124—733no—
538#124—733no—
539#124—736no—
540#124—736no—
541#124—733no—
542#124C2×#6440813yescomplemented
543C22⋊Q8—733no—
544C22⋊Q8—733no—
545C22⋊Q8—736no—
546C22⋊Q8—733no—
547C22⋊Q8—736no—
548C22⋊Q8C2×#6440813yescomplemented
549#121—733no—
550#121—736no—
551#121—733no—
552#121—733no—
553#121—736no—
554#121C2×#6440813yescomplemented
555C4×Q8—738no—
556C4×Q8—731no—
557C4×Q8—733no—
558C4×Q8—733no—
559C4×Q8—14612no—
560C4×Q8—14612no—
561C4×Q8—1464no—
562C4×Q8—1464no—
563C4×Q8—1464no—
564C4×Q8C2×#6440811yescharacteristic, complemented
565C4×D4—733no—
566C4×D4—733no—
567C4×D4—733no—
568C4×D4—733no—
569C4×D4—733no—
570C4×D4—733no—
571C4×D4—733no—
572C4×D4—14612no—
573C4×D4—14612no—
574C4×D4—14612no—
575C4×D4—14612no—
576C4×D4C2×#6440813yescomplemented
577#117—14612no—
578C2×C4⋊C4—733no—
579C2×C4⋊C4—733no—
580C2×C4⋊C4—733no—
581C2×C4⋊C4—733no—
582C2×C4⋊C4—736no—
583C2×C4⋊C4—733no—
584C2×C4⋊C4—733no—
585C2×C4⋊C4—733no—
586C2×C4⋊C4—733no—
587C2×C4⋊C4—14612no—
588C2×C22⋊C4—736no—
589C2×C22⋊C4—731no—
590C2×C22⋊C4—731no—
591C2×C22⋊C4—733no—
592C2×C22⋊C4—736no—
593C2×C22⋊C4—736no—
594C2×C22⋊C4—733no—
595C2×C22⋊C4—733no—
596C2×C22⋊C4—733no—
597C2×C42—733no—
598C2×C42—733no—
599C2×C42—733no—
600C2×C42—733no—
601C2×C42—733no—
602C2×C42—733no—
603C2×C42—733no—
604C2×C42—733no—
605C2×C42—733no—
606C2×C42—733no—
607C2×C42—733no—
608C2×C42—731no—
609C2×C42—731no—
610C2×C42—14612no—
611C2×C42—14612no—
612#95—731no—
613#95—731no—
614#95—733no—
615#95—733no—
616#95—733no—
617#95—733no—
618#95—736no—
619#95—736no—
620#95—736no—
621C24—731no—
622C24—733no—
623#41—24no—
624#41—14612no—
625#41—14612no—
626#41—1464no—
627C2×Q8—24no—
628C2×Q8—734no—
629C2×Q8—734no—
630C2×Q8—733no—
631C2×Q8—736no—
632C2×Q8—733no—
633C2×Q8—14612no—
634C2×Q8—1466no—
635C2×Q8—1466no—
636C2×Q8—14612no—
637C2×Q8—1464no—
638C2×Q8C22×#6440813yes—
639C2×Q8C22×#6440811yescharacteristic
640C2×D4—733no—
641C2×D4—733no—
642C2×D4—736no—
643C2×D4—733no—
644C2×D4—733no—
645C2×D4—1466no—
646C2×D4—1466no—
647C2×D4—1466no—
648C2×D4—1466no—
649C2×D4C22×#6440813yes—
650C2×D4C22×#6440813yes—
651C22×C4—2923no—
652C22×C4—2923no—
653C22×C4—731no—
654C22×C4—733no—
655C22×C4—734no—
656C22×C4—731no—
657C22×C4—731no—
658C22×C4—731no—
659C22×C4—733no—
660C22×C4—733no—
661C22×C4—733no—
662C22×C4—733no—
663C22×C4—733no—
664C22×C4—733no—
665C22×C4—733no—
666C22×C4—731no—
667C22×C4—731no—
668C22×C4—733no—
669C22×C4—733no—
670C22×C4—733no—
671C22×C4—733no—
672C22×C4—733no—
673C22×C4—1466no—
674C22×C4—1466no—
675C22×C4—1466no—
676C22×C4—1466no—
677C22×C4—1466no—
678C22×C4—1466no—
679C22×C4—1466no—
680C22×C4—1466no—
681C22×C4—1466no—
682C22×C4—1466no—
683C22×C4—1466no—
684C22×C4—1462no—
685C22×C4—1462no—
686C22×C4C22×#6440813yes—
687C22×C4C22×#6440813yes—
688C4⋊C4—7312no—
689C4⋊C4—733no—
690C4⋊C4—733no—
691C4⋊C4—736no—
692C4⋊C4—733no—
693C4⋊C4—733no—
694C4⋊C4—1466no—
695C4⋊C4—14612no—
696C4⋊C4—1466no—
697C4⋊C4—1466no—
698C4⋊C4—1466no—
699C4⋊C4—1466no—
700C4⋊C4C22×#6440813yes—
701C4⋊C4C22×#6440813yes—
702C22⋊C4—2926no—
703C22⋊C4—734no—
704C22⋊C4—731no—
705C22⋊C4—733no—
706C22⋊C4—736no—
707C22⋊C4—731no—
708C22⋊C4—731no—
709C22⋊C4—733no—
710C22⋊C4—733no—
711C22⋊C4—736no—
712C22⋊C4—736no—
713C22⋊C4—14612no—
714C22⋊C4—1466no—
715C22⋊C4—1466no—
716C22⋊C4—1466no—
717C22⋊C4C22×#6440811yescharacteristic
718C22⋊C4C22×#6440813yes—
719C22⋊C4C22×#6440816yes—
720C42—2923no—
721C42—7312no—
722C42—733no—
723C42—733no—
724C42—733no—
725C42—1462no—
726C42—1462no—
727C42—1466no—
728C42—1466no—
729C42—1466no—
730C42—1466no—
731C42—1466no—
732C42—1466no—
733C42—1466no—
734C42—1466no—
735C42C22×#6440813yes—
736C23—731no—
737C23—732no—
738C23—732no—
739C23—731no—
740C23—733no—
741C23—1463no—
742C23—1463no—
743C23—1463no—
744C23—1463no—
745C23—1463no—
746C23—1463no—
747C23—1461no—
748C23—1461no—
749C23—1461no—
750C23—1461no—
751C23C23×#6440813yes—
752C23C23×#6440811yescharacteristic
753Q8—26no—
754Q8—7312no—
755Q8—14612no—
756Q8—1466no—
757Q8D4×#6440814yescomplemented
758D4—26no—
759D4—26no—
760D4—1466no—
761D4—14612no—
762D4—1466no—
763D4—1466no—
764D4—1466no—
765C2×C4—26no—
766C2×C4—26no—
767C2×C4—29212no—
768C2×C4—29212no—
769C2×C4—29212no—
770C2×C4—732no—
771C2×C4—732no—
772C2×C4—732no—
773C2×C4—733no—
774C2×C4—736no—
775C2×C4—736no—
776C2×C4—736no—
777C2×C4—732no—
778C2×C4—732no—
779C2×C4—732no—
780C2×C4—731no—
781C2×C4—733no—
782C2×C4—733no—
783C2×C4—731no—
784C2×C4—1466no—
785C2×C4—1466no—
786C2×C4—1461no—
787C2×C4—1461no—
788C2×C4—1463no—
789C2×C4—1463no—
790C2×C4—1463no—
791C2×C4—1461no—
792C2×C4—1461no—
793C2×C4—1463no—
794C2×C4—1463no—
795C2×C4—1463no—
796C2×C4—1463no—
797C2×C4—1463no—
798C2×C4—1463no—
799C2×C4—1463no—
800C2×C4—1463no—
801C2×C4—1463no—
802C2×C4—1463no—
803C2×C4—1466no—
804C2×C4—1466no—
805C2×C4—1468no—
806C2×C4—1463no—
807C2×C4—1461no—
808C2×C4—1461no—
809C2×C4—1461no—
810C2×C4—1463no—
811C2×C4—1461no—
812C2×C4—1461no—
813C2×C4—1461no—
814C2×C4—1466no—
815C2×C4—1466no—
816C2×C4C23×#6440811yescharacteristic
817C2×C4C23×#6440813yes—
818C2×C4C23×#6440813yes—
819C2×C4C23×#6440811yescharacteristic
820C2×C4C23×#6440813yes—
821C22—21no—
822C22—21no—
823C22—23no—
824C22—23no—
825C22—23no—
826C22—2923no—
827C22—2923no—
828C22—2923no—
829C22—2923no—
830C22—731no—
831C22—731no—
832C22—731no—
833C22—731no—
834C22—731no—
835C22—731no—
836C22—732no—
837C22—1462no—
838C22—1462no—
839C22—1462no—
840C22—1462no—
841C22—1463no—
842C22—1463no—
843C22—1463no—
844C22—1461no—
845C22—1461no—
846C22#41×#6440812yescomplemented
847C22C24×#6440811yescharacteristic
848C4—21no—
849C4—23no—
850C4—23no—
851C4—21no—
852C4—2923no—
853C4—2923no—
854C4—2923no—
855C4—734no—
856C4—736no—
857C4—1462no—
858C4—1466no—
859C4—1462no—
860C4—1462no—
861C4—1461no—
862C4—1463no—
863C4—1463no—
864C4—1461no—
865C4C2×D4×#6440816yes—
866C2—22no—
867C2—43no—
868C2—2923no—
869C2—731no—
870C2—731no—
871C2—731no—
872C2—731no—
873C2—1462no—
874C2C22×D4×#6440811yescharacteristic
875C2C2×#41×#6440811yescharacteristic
876C22−1+4×#6440811yescharacteristic
subgroupG/H
center, FrattiniC22C24×#64408
commutator, socleC22×C73C24×C4
Fitting#548×C73C4
prime radical#548×D73C2
cosocleC22×D73C25
hypercenter#548#64408
hypocenterC73C4×#548
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#41×#64408C2semidirect
2. C22×Q8×#64408C2semidirect
3. #22626462C2semidirect
4. #22626457C2semidirect
5. #22626456C2semidirect
6. #22626447C2semidirect
7. #22626446C2semidirect
8. #22626436C2semidirect
9. Q8×C22⋊#64408C2semidirect
10. #124×#64408C2semidirect
11. C22⋊Q8×#64408C2semidirect
12. #121×#64408C2semidirect
13. C4×Q8×#64408C2semidirect
14. C4×D4×#64408C2semidirect
63. #17989249C4semidirect
64. #17989248C4semidirect
65. #17989247C4semidirect
66. #17989246C4semidirect
67. #17989245C4semidirect
68. #17989244C4semidirect
69. #17989243C4semidirect
75. #548×C73C4semidirect
85. Q8×#64408D4semidirect
128. C2×#11924029C2×C4semidirect
129. C2×#11924028C2×C4semidirect
130. C2×#11924027C2×C4semidirect
133. C22×Dic146C2×C4semidirect
136. C2×Q8×D73C2×C4semidirect
137. C2×Q8×D73C2×C4semidirect
144. #14556580C2×C4semidirect
145. #14556579C2×C4semidirect
146. #14556578C2×C4semidirect
147. #14556577C2×C4semidirect
148. #14556577C2×C4semidirect
149. #14556571C2×C4semidirect
150. #14556570C2×C4semidirect
151. #14556569C2×C4semidirect
152. #14556568C2×C4semidirect
153. #14556567C2×C4semidirect
154. #14556566C2×C4semidirect
155. #14556565C2×C4semidirect
156. #14556564C2×C4semidirect
157. #14556563C2×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
175. C2×#41×C73C2×C4semidirect
176. C22×Q8×C73C2×C4semidirect
177. #124×C73C2×C4semidirect
178. C22⋊Q8×C73C2×C4semidirect
179. #121×C73C2×C4semidirect
180. C4×Q8×C73C2×C4semidirect
181. C4×D4×C73C2×C4semidirect
193. C22×#64408#41semidirect
214. C22⋊#64408#41semidirect
343. Q8×C73C4×D4semidirect
381. Dic146C4×D4semidirect
387. C22×C73C4×#41semidirect
402. C2×D73C4×#41semidirect
416. #64408#548direct (N × H)
454. C73C4×#548semidirect
464. #548#64408direct (N × H)
520. C2×#41C2×#64408semidirect
528. C22×Q8C2×#64408semidirect
542. #124C2×#64408semidirect
548. C22⋊Q8C2×#64408semidirect
554. #121C2×#64408semidirect
564. C4×Q8C2×#64408semidirect
576. C4×D4C2×#64408semidirect
757. Q8D4×#64408semidirect
846. C22#41×#64408semidirect

Maximal subgroups

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

subgroupindex
C2×#41×#644082
C22×Q8×#644082
#226264622
#226264572
#226264562
#226264472
#226264462
#226264362
Q8×C22⋊#644082
#124×#644082
C22⋊Q8×#644082
#121×#644082
C4×Q8×#644082
C4×D4×#644082
#548×D732
C4×#54873