Finite Group Databasebeta

← #30622589

Subgroups — #30622589

Order 15616.

926 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462346C211yesmaximal, characteristic
2#21462343C211yesmaximal, characteristic, complemented
3#21461910C211yesmaximal, characteristic, complemented
4#21461909C211yesmaximal, characteristic, complemented
5#21461883C211yesmaximal, characteristic, complemented
6#21461880C211yesmaximal, characteristic, complemented
7#21461815C211yesmaximal, characteristic, complemented
8#21461812C211yesmaximal, characteristic, complemented
9#21461806C211yesmaximal, characteristic
10#21461805C211yesmaximal, characteristic, complemented
11#21461590C211yesmaximal, characteristic, complemented
12#103×#6923C211yesmaximal, characteristic, complemented
13#21461559C211yesmaximal, characteristic, complemented
14#21461507C211yesmaximal, characteristic, complemented
15#468×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×D4×#6923C2211yescharacteristic
18C2×#14519856C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20C2×#14519840C2211yescharacteristic
21C2×#14519840C2211yescharacteristic
22C2×#14519839C2211yescharacteristic
23C2×#14519839C2211yescharacteristic
24D61⋊(C22⋊C8)C2211yescharacteristic
25C2×#14519831C2211yescharacteristic
26C2×C8×#6923C2211yescharacteristic
27(C2×#6923)⋊Q8C2211yescharacteristic
28#16840714—21no—
29#16840714C2211yescharacteristic
30#16840713—21no—
31#16840713C2211yescharacteristic
32#16840713C2211yescharacteristic
33#16840712—21no—
34#16840711—21no—
35#16840710—21no—
36#16840709—21no—
37C4⋊C4×#6923C2211yescharacteristic
38C4⋊C4×#6923C2211yescharacteristic
39C22⋊C4×#6923—21no—
40C22⋊C4×#6923—21no—
41C4×C22⋊#6923C2211yescharacteristic
42#16840636C2211yescharacteristic
43#16840636C2211yescharacteristic
44#16840636C2211yescharacteristic
45#16840636C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C2×SD16×D61C2211yescharacteristic
53C2×M16×D61C2211yescharacteristic
54C22⋊Q8×D61C2211yescharacteristic
55#121×D61C2211yescharacteristic
56#16840011C411yescharacteristic, complemented
57#16840010C411yescharacteristic, complemented
58#16840009C411yescharacteristic, complemented
59#16840008C411yescharacteristic, complemented
60#16840007C411yescharacteristic, complemented
61#16840006C411yescharacteristic, complemented
62#16840005C411yescharacteristic, complemented
63#107×D61C2211yescharacteristic
64#103×D61C2211yescharacteristic
65#102×D61C2211yescharacteristic
66C61×#468C411yescharacteristic, complemented
67C23×#6923—21no—
68C23×#6923—21no—
69C2×D61⋊C8C2311yescharacteristic
70C2×D61⋊C8C2311yescharacteristic
71Q8×#6923—22no—
72Q8×#6923—41no—
73D4×#6923—22no—
74D4×#6923—41no—
75#14519856—22no—
76#14519856—41no—
77C2×C4⋊#6923—22no—
78C2×C4⋊#6923—21no—
79C2×C4⋊#6923—21no—
80C2×C4⋊#6923—21no—
81C2×C4⋊#6923—21no—
82C2×C4⋊#6923—41no—
83C2×C4⋊#6923C2311yescharacteristic
84C2×C4⋊#6923C2311yescharacteristic
85C2×C4⋊#6923C2311yescharacteristic
86C2×C4⋊#6923C2311yescharacteristic
87C2×C22⋊#6923—21no—
88C2×C22⋊#6923—21no—
89C2×C22⋊#6923—21no—
90C2×C22⋊#6923—21no—
91C2×C22⋊#6923D411yescharacteristic
92C2×C22⋊#6923D411yescharacteristic
93C2×C4×#6923—21no—
94C2×C4×#6923—21no—
95C2×C4×#6923—21no—
96C2×C4×#6923—21no—
97C2×C4×#6923C2311yescharacteristic
98C2×C4×#6923C2311yescharacteristic
99#14519840—22no—
100#14519840—41no—
101#14519839—22no—
102#14519839—41no—
103#14519834—21no—
104C22⋊#92420—21no—
105#14519831—41no—
106C8×#6923—41no—
107(C2×#6923)⋊C4—21no—
108(C2×#6923)⋊C4—21no—
109(C2×#6923)⋊C4—21no—
110(C2×#6923)⋊C4—21no—
111(C2×#6923)⋊C4—21no—
112(C2×#6923)⋊C4—21no—
113(C2×#6923)⋊C4D411yescharacteristic
114(C2×#6923)⋊C4D411yescharacteristic
115C2×Q8×D61C2311yescharacteristic
116C2×D4×D61—21no—
117C2×D4×D61C2311yescharacteristic
118C22×C4×D61C2311yescharacteristic
119C2×#11758190C2×C411yescharacteristic, complemented
120C2×#11758200C2×C411yescharacteristic, complemented
121C2×#11758201C2×C411yescharacteristic, complemented
122SD16×D61—41no—
123SD16×D61—41no—
124C2×#11758194C2×C411yescharacteristic, complemented
125C2×#11758189C2×C411yescharacteristic, complemented
126C2×#11758189C2×C411yescharacteristic, complemented
127M16×D61—41no—
128M16×D61—41no—
129C2×C8×D61C2311yescharacteristic
130C2×C8×D61C2311yescharacteristic
131#14519757C2×C411yescharacteristic, complemented
132#14519756C2×C411yescharacteristic, complemented
133#14519755—21no—
134#14519754—21no—
135#14519753C2×C411yescharacteristic, complemented
136#14519752C2×C411yescharacteristic
137#14519751C2×C411yescharacteristic
138#14519750—21no—
139#14519749—21no—
140#14519748C2×C411yescharacteristic
141C4⋊C4×D61—21no—
142C4⋊C4×D61C2311yescharacteristic
143C4⋊C4×D61C2311yescharacteristic
144C22⋊C4×D61—21no—
145C22⋊C4×D61—21no—
146#14519711C2×C411yescharacteristic, complemented
147#14519710C2×C411yescharacteristic, complemented
148#14519710C2×C411yescharacteristic, complemented
149#14519702C2×C411yescharacteristic, complemented
150#14519701C2×C411yescharacteristic, complemented
151#14519700C2×C411yescharacteristic, complemented
152#14519699C2×C411yescharacteristic, complemented
153#14519698C2×C411yescharacteristic, complemented
154#14519697C2×C411yescharacteristic, complemented
155C2×SD16×C61C2×C411yescharacteristic, complemented
156C2×M16×C61C2×C411yescharacteristic, complemented
157C22⋊Q8×C61C2×C411yescharacteristic, complemented
158#121×C61C2×C411yescharacteristic
159#107×C61C2×C411yescharacteristic, complemented
160#103×C61C2×C411yescharacteristic, complemented
161#102×C61C2×C411yescharacteristic, complemented
162C23×D61—21no—
163C23×D61C2×D411yescharacteristic
164C22×#6923—21no—
165C22×#6923—21no—
166C22×#6923—21no—
167C22×#6923—21no—
168C22×#6923—42no—
169C22×#6923—42no—
170C22×#6923—42no—
171C22×#6923—42no—
172C22×#6923—81no—
173C22×#6923—81no—
174C22×#6923C2×D411yescharacteristic
175C22×#6923C2×D411yescharacteristic
176C22×#6923C2×D411yescharacteristic
177C22×#6923C2×D411yescharacteristic
178C2×Q8×C61C22×C411yescharacteristic
179C2×D4×C61—21no—
180C2×D4×C61C22×C411yescharacteristic
181C22×C4×C61C22×C411yescharacteristic
182C2×C22⋊D61—21no—
183C2×C22⋊D61—21no—
184C2×C22⋊D61—21no—
185C22×Dic61#4111yescharacteristic
186Q8×D61—21no—
187Q8×D61—21no—
188Q8×D61—21no—
189Q8×D61—21no—
190D4×D61—21no—
191D4×D61—21no—
192D4×D61—21no—
193D4×D61—21no—
194D4×D61—81no—
195D4×D61—81no—
196C2×D244—21no—
197C2×D244C22×C411yescharacteristic
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61C22×C411yescharacteristic
206C2×C4×D61C2×D411yescharacteristic
207C2×C4×D61#4111yescharacteristic
208C2×C4×D61C2411yescharacteristic
209C2×Dic122—21no—
210C2×Dic122C22×C411yescharacteristic
211C22⋊#6923—22no—
212C22⋊#6923—41no—
213C22⋊#6923—42no—
214C22⋊#6923—42no—
215C22⋊#6923—42no—
216C22⋊#6923—81no—
217C2×#92420—21no—
218C2×#92420—21no—
219C4⋊#6923—21no—
220C4⋊#6923—21no—
221C4⋊#6923—21no—
222C4⋊#6923—21no—
223C4⋊#6923—21no—
224C4⋊#6923—21no—
225C4⋊#6923—42no—
226C4⋊#6923—42no—
227C4⋊#6923—81no—
228C4⋊#6923—81no—
229C4⋊#6923#4112yes—
230C4⋊#6923#4112yes—
231C4×#6923—21no—
232C4×#6923—21no—
233C4×#6923—21no—
234C4×#6923—21no—
235C4×#6923—42no—
236C4×#6923—42no—
237C4×#6923—81no—
238C4×#6923—81no—
239D61⋊C8—21no—
240D61⋊C8—21no—
241D61⋊C8—21no—
242D61⋊C8—21no—
243SD16×C61—41no—
244M16×C61—41no—
245C2×C8×C61C22×C411yescharacteristic
246C2×C8×C61C22×C411yescharacteristic
247C4⋊C4×C61—21no—
248C4⋊C4×C61C22×C411yescharacteristic
249C4⋊C4×C61C22×C411yescharacteristic
250C22⋊C4×C61—21no—
251C22⋊C4×C61—21no—
252C22⋊Dic61—21no—
253C22⋊Dic61—21no—
254#11758201—41no—
255#11758200—41no—
256#11758198—21no—
257#11758198—21no—
258#11758198—21no—
259#11758198—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61C22×C411yescharacteristic
262C4⋊Dic61C22×C411yescharacteristic
263#11758196—21no—
264#11758196—21no—
265#11758196—21no—
266#11758196—21no—
267#11758194—41no—
268C2×#92418C22×C411yescharacteristic
269C2×#92418C22×C411yescharacteristic
270#11758190—41no—
271#11758189—41no—
272#11758189—41no—
273C8×D61—21no—
274C8×D61—21no—
275C8×D61—21no—
276C8×D61—21no—
277C23×C61—21no—
278C23×C61C4×D411yescharacteristic
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—41no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—41no—
290C22×D61—41no—
291C22×D61—41no—
292C22×D61C4×D411yescharacteristic
293C22×D61C22×D411yescharacteristic
294C2×#6923—21no—
295C2×#6923—21no—
296C2×#6923—21no—
297C2×#6923—21no—
298C2×#6923—21no—
299C2×#6923—22no—
300C2×#6923—22no—
301C2×#6923—21no—
302C2×#6923—21no—
303C2×#6923—21no—
304C2×#6923—21no—
305C2×#6923—21no—
306C2×#6923—21no—
307C2×#6923—41no—
308C2×#6923—41no—
309C2×#6923—41no—
310C2×#6923—41no—
311C2×#6923—41no—
312C2×#6923—41no—
313C2×#6923—41no—
314C2×#6923—41no—
315C2×#6923—41no—
316C2×#6923—41no—
317C2×#6923—84no—
318C2×#6923—84no—
319C2×#6923#13712yes—
320Q8×C61—21no—
321Q8×C61—21no—
322D4×C61—21no—
323D4×C61—21no—
324D4×C61—81no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61C4×D411yescharacteristic
331C2×C4×C61C23×C411yescharacteristic
332C22⋊D61—41no—
333C22⋊D61—41no—
334C22⋊D61—81no—
335C22⋊D61—81no—
336C2×Dic61—21no—
337C2×Dic61—21no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—21no—
341C2×Dic61C4×D411yescharacteristic
342C2×Dic61C2×#4111yescharacteristic
343D244—21no—
344D244—21no—
345D244—81no—
346C4×D61—21no—
347C4×D61—21no—
348C4×D61—21no—
349C4×D61—21no—
350C4×D61—21no—
351C4×D61—21no—
352C4×D61—41no—
353C4×D61—41no—
354C4×D61—41no—
355C4×D61—41no—
356C4×D61—41no—
357C4×D61—41no—
358C4×D61C2×#4111yescharacteristic
359C4×D61C2×#4111yescharacteristic
360C4×D61H(5,𝔽2)11yescharacteristic
361C4×D61H(5,𝔽2)11yescharacteristic
362Dic122—21no—
363Dic122—21no—
364Dic122—41no—
365Dic122—41no—
366#92420—41no—
367#92420—41no—
368C8×C61—21no—
369C8×C61—21no—
370#92418—21no—
371#92418—21no—
372#23142—611nomaximal, Sylow
373C22×C61—21no—
374C22×C61—21no—
375C22×C61—21no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61C2×C4×D411yescharacteristic
380C2×D61—21no—
381C2×D61—21no—
382C2×D61—21no—
383C2×D61—41no—
384C2×D61—41no—
385C2×D61—41no—
386C2×D61—41no—
387C2×D61—41no—
388C2×D61—41no—
389C2×D61—41no—
390C2×D61—81no—
391C2×D61—81no—
392C2×D61—81no—
393C2×D61—81no—
394C2×D61#54611yescharacteristic
395C2×D61#54611yescharacteristic
396C2×D61C2×#13711yescharacteristic
397C2×D61#57511yescharacteristic
398C2×D61#57611yescharacteristic
399C2×D61#57711yescharacteristic
400#6923—22no—
401#6923—41no—
402#6923—41no—
403#6923—42no—
404#6923—41no—
405#6923—42no—
406#6923—81no—
407#6923—81no—
408C4×C61—21no—
409C4×C61—41no—
410C4×C61—41no—
411C4×C61—41no—
412C4×C61C4×#4111yescharacteristic
413C4×C61#51811yescharacteristic
414Dic61—21no—
415Dic61—41no—
416Dic61—41no—
417Dic61—41no—
418Dic61#55311yescharacteristic
419Dic61#55311yescharacteristic
420C2×#468—611no—
421#2363—611no—
422#2360—611no—
423#1935—611no—
424#1934—611no—
425#1921—611no—
426#1918—611no—
427#1880—611no—
428#1877—611no—
429#1874—611no—
430#1873—611no—
431#1762—611no—
432C4×#103—611no—
433#1753—611no—
434#1736—611no—
435C2×C61—41no—
436C2×C61—81no—
437C2×C61#236411yescharacteristic
438C2×C61C4×#13711yescharacteristic
439C2×C61#294611yescharacteristic
440D61—41no—
441D61—81no—
442D61#331911yescharacteristic
443D61#332011yescharacteristic
444D61#332311yescharacteristic
445D61#333311yescharacteristic
446C22×SD16—611no—
447C22×M16—611no—
448C2×C22⋊Q8—611no—
449C2×#121—611no—
450C2×C4×Q8—611no—
451C2×C4×D4—611no—
452C2×#117—611no—
453C22×C4⋊C4—611no—
454#468—611no—
455#468—611no—
456#468—611no—
457#468—611no—
458#468—611no—
459#468—611no—
460#468—611no—
461#468#692311yescharacteristic, complemented
462C2×#107—611no—
463C2×#103—611no—
464C2×#103—611no—
465C2×#103—611no—
466C2×#102—611no—
467C2×#102—611no—
468C2×#102—611no—
469C2×C22⋊C8—611no—
470C2×#97—611no—
471C2×C4×C8—611no—
472#391—611no—
473#390—611no—
474#390—1221no—
475#389—611no—
476#389—611no—
477#389—1221no—
478#388—1221no—
479#387—1221no—
480#386—1221no—
481#385—1221no—
482C4×C4⋊C4—611no—
483C4×C4⋊C4—611no—
484C4×C22⋊C4—611no—
485C4×C22⋊C4—1221no—
486C4×C22⋊C4—1221no—
487#340—611no—
488#340—611no—
489#340—611no—
490#340—611no—
491#340—611no—
492#340—611no—
493#340—611no—
494#340—611no—
495#336—611no—
496#336—611no—
497C61#2314211yescharacteristic, complemented, Sylow
498C22×Q8—611no—
499C22×D4—611no—
500C22×D4—1221no—
501C23×C4—611no—
502C23×C4—1221no—
503C23×C4—1221no—
504C2×SD16—611no—
505C2×SD16—611no—
506C2×SD16—611no—
507C2×SD16—2441no—
508C2×SD16—2441no—
509C2×SD16C2×#692311yescharacteristic, complemented
510C2×M16—611no—
511C2×M16—611no—
512C2×M16—611no—
513C2×M16—2441no—
514C2×M16—2441no—
515C2×M16C2×#692311yescharacteristic, complemented
516C22×C8—611no—
517C22×C8—611no—
518C22×C8—611no—
519C22×C8—611no—
520C22⋊Q8—611no—
521C22⋊Q8—611no—
522C22⋊Q8—611no—
523C22⋊Q8—1221no—
524C22⋊Q8—1221no—
525C22⋊Q8C2×#692311yescharacteristic, complemented
526#121—611no—
527#121—611no—
528#121—611no—
529#121—1221no—
530#121—1221no—
531#121C2×#692311yescharacteristic
532C4×Q8—1222no—
533C4×Q8—2441no—
534C4×D4—1222no—
535C4×D4—2441no—
536#117—1222no—
537#117—2441no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—611no—
540C2×C4⋊C4—611no—
541C2×C4⋊C4—611no—
542C2×C4⋊C4—611no—
543C2×C4⋊C4—611no—
544C2×C4⋊C4—1221no—
545C2×C4⋊C4—1222no—
546C2×C4⋊C4—1221no—
547C2×C4⋊C4—1221no—
548C2×C4⋊C4—1221no—
549C2×C4⋊C4—1221no—
550C2×C4⋊C4—2441no—
551C2×C22⋊C4—611no—
552C2×C22⋊C4—611no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1221no—
556C2×C22⋊C4—1221no—
557C2×C22⋊C4—1221no—
558C2×C22⋊C4—1221no—
559C2×C42—611no—
560C2×C42—611no—
561C2×C42—1221no—
562C2×C42—1221no—
563C2×C42—1221no—
564C2×C42—1221no—
565#107—611no—
566#107—611no—
567#107—611no—
568#107C2×#692311yescharacteristic, complemented
569#103—611no—
570#103—611no—
571#103—611no—
572#103—1222no—
573#103—2441no—
574#103C2×#692311yescharacteristic, complemented
575#102—611no—
576#102—611no—
577#102—611no—
578#102—1222no—
579#102—2441no—
580#102C2×#692311yescharacteristic, complemented
581C22⋊C8—1221no—
582C22⋊C8—1221no—
583#97—2441no—
584C4×C8—2441no—
585#95—611no—
586#95—611no—
587#95—1221no—
588#95—1221no—
589#95—1221no—
590#95—1221no—
591#95—1221no—
592#95—1221no—
593C24—611no—
594C24—1221no—
595C2×Q8—611no—
596C2×Q8—1221no—
597C2×Q8—1221no—
598C2×Q8—1221no—
599C2×Q8—1221no—
600C2×Q8—1221no—
601C2×Q8C22×#692311yescharacteristic
602C2×D4—21no—
603C2×D4—611no—
604C2×D4—1221no—
605C2×D4—1221no—
606C2×D4—1221no—
607C2×D4—1221no—
608C2×D4—1221no—
609C2×D4—1221no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4—4881no—
613C2×D4—4881no—
614C2×D4C22×#692311yescharacteristic
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—611no—
623C22×C4—611no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—4881no—
636C22×C4—4881no—
637C22×C4—2442no—
638C22×C4—2442no—
639C22×C4—2442no—
640C22×C4—2442no—
641C22×C4C22×#692311yescharacteristic
642SD16—41no—
643SD16—2441no—
644SD16—2441no—
645SD16—2441no—
646M16—41no—
647M16—2441no—
648M16—2441no—
649M16—2441no—
650C2×C8—611no—
651C2×C8—611no—
652C2×C8—1221no—
653C2×C8—1221no—
654C2×C8—1221no—
655C2×C8—1221no—
656C2×C8—1221no—
657C2×C8—1221no—
658C2×C8—1221no—
659C2×C8—1221no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8C22×#692311yescharacteristic
663C2×C8C22×#692311yescharacteristic
664C4⋊C4—21no—
665C4⋊C4—612no—
666C4⋊C4—612no—
667C4⋊C4—611no—
668C4⋊C4—611no—
669C4⋊C4—1221no—
670C4⋊C4—1221no—
671C4⋊C4—1221no—
672C4⋊C4—1221no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4—1221no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—1221no—
680C4⋊C4—4881no—
681C4⋊C4—4881no—
682C4⋊C4—2442no—
683C4⋊C4—2442no—
684C4⋊C4C22×#692311yescharacteristic
685C4⋊C4C22×#692311yescharacteristic
686C22⋊C4—21no—
687C22⋊C4—21no—
688C22⋊C4—1221no—
689C22⋊C4—1221no—
690C22⋊C4—1221no—
691C22⋊C4—1221no—
692C22⋊C4—1222no—
693C22⋊C4—1221no—
694C22⋊C4—1221no—
695C22⋊C4—4881no—
696C22⋊C4—2442no—
697C22⋊C4—2441no—
698C22⋊C4—2442no—
699C22⋊C4—2442no—
700C42—1221no—
701C42—1221no—
702C42—1221no—
703C42—1221no—
704C42—4881no—
705C42—4881no—
706C42—2442no—
707C42—2442no—
708C23—21no—
709C23—611no—
710C23—611no—
711C23—1221no—
712C23—1221no—
713C23—1221no—
714C23—1221no—
715C23—1221no—
716C23—1221no—
717C23—1221no—
718C23—2441no—
719C23—2441no—
720C23—2441no—
721C23—2441no—
722C23—2441no—
723C23—2441no—
724C23D4×#692311yescharacteristic
725Q8—21no—
726Q8—21no—
727Q8—1221no—
728Q8—1221no—
729Q8—2441no—
730Q8—2441no—
731D4—21no—
732D4—21no—
733D4—81no—
734D4—1221no—
735D4—1221no—
736D4—4881no—
737D4—4881no—
738D4—4881no—
739D4—2441no—
740D4—2441no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—611no—
747C2×C4—611no—
748C2×C4—611no—
749C2×C4—611no—
750C2×C4—611no—
751C2×C4—612no—
752C2×C4—611no—
753C2×C4—1221no—
754C2×C4—1221no—
755C2×C4—1221no—
756C2×C4—1221no—
757C2×C4—1221no—
758C2×C4—1221no—
759C2×C4—1221no—
760C2×C4—1221no—
761C2×C4—1221no—
762C2×C4—1221no—
763C2×C4—1221no—
764C2×C4—1221no—
765C2×C4—1221no—
766C2×C4—1221no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1221no—
770C2×C4—1221no—
771C2×C4—1221no—
772C2×C4—1221no—
773C2×C4—1221no—
774C2×C4—1221no—
775C2×C4—1221no—
776C2×C4—1221no—
777C2×C4—4884no—
778C2×C4—4884no—
779C2×C4—2441no—
780C2×C4—2441no—
781C2×C4—2441no—
782C2×C4—2441no—
783C2×C4—2441no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4—2441no—
790C2×C4—2441no—
791C2×C4—2441no—
792C2×C4—2441no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4D4×#692311yescharacteristic
796C2×C4C23×#692311yescharacteristic
797C8—21no—
798C8—21no—
799C8—1221no—
800C8—1221no—
801C8—2441no—
802C8—2441no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—611no—
810C22—611no—
811C22—611no—
812C22—611no—
813C22—611no—
814C22—611no—
815C22—1221no—
816C22—1221no—
817C22—1221no—
818C22—4881no—
819C22—4881no—
820C22—4881no—
821C22—4881no—
822C22—2441no—
823C22—2441no—
824C22—2441no—
825C22—2441no—
826C22—2441no—
827C22—2441no—
828C22—2441no—
829C22C2×D4×#692311yescharacteristic
830C4—21no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4—611no—
835C4—611no—
836C4—1222no—
837C4—1221no—
838C4—4881no—
839C4—4881no—
840C4—2441no—
841C4—2441no—
842C4—2441no—
843C4—2442no—
844C4—2442no—
845C4—2441no—
846C4—2441no—
847C4—2441no—
848C4#41×#692311yescharacteristic
849C4#1684082911yescharacteristic
850C2—41no—
851C2—81no—
852C2—611no—
853C2—611no—
854C2—611no—
855C2—611no—
856C2—4881no—
857C2—2441no—
858C2#2146234711yescharacteristic
859C2#137×#692311yescharacteristic
860C2#2146257611yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#468C4
socleC22×C61C2×C4×D4
prime radical#121×D61C22
cosocleC2×C4×D61C24
hypercenter#468#6923
hypocenterC61#23142
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
2. #21462343C2semidirect
3. #21461910C2semidirect
4. #21461909C2semidirect
5. #21461883C2semidirect
6. #21461880C2semidirect
7. #21461815C2semidirect
8. #21461812C2semidirect
10. #21461805C2semidirect
11. #21461590C2semidirect
12. #103×#6923C2semidirect
13. #21461559C2semidirect
14. #21461507C2semidirect
56. #16840011C4semidirect
57. #16840010C4semidirect
58. #16840009C4semidirect
59. #16840008C4semidirect
60. #16840007C4semidirect
61. #16840006C4semidirect
62. #16840005C4semidirect
66. C61×#468C4semidirect
119. C2×#11758190C2×C4semidirect
120. C2×#11758200C2×C4semidirect
121. C2×#11758201C2×C4semidirect
124. C2×#11758194C2×C4semidirect
125. C2×#11758189C2×C4semidirect
126. C2×#11758189C2×C4semidirect
131. #14519757C2×C4semidirect
132. #14519756C2×C4semidirect
135. #14519753C2×C4semidirect
146. #14519711C2×C4semidirect
147. #14519710C2×C4semidirect
148. #14519710C2×C4semidirect
149. #14519702C2×C4semidirect
150. #14519701C2×C4semidirect
151. #14519700C2×C4semidirect
152. #14519699C2×C4semidirect
153. #14519698C2×C4semidirect
154. #14519697C2×C4semidirect
155. C2×SD16×C61C2×C4semidirect
156. C2×M16×C61C2×C4semidirect
157. C22⋊Q8×C61C2×C4semidirect
159. #107×C61C2×C4semidirect
160. #103×C61C2×C4semidirect
161. #102×C61C2×C4semidirect
461. #468#6923semidirect
497. C61#23142semidirect
509. C2×SD16C2×#6923semidirect
515. C2×M16C2×#6923semidirect
525. C22⋊Q8C2×#6923semidirect
568. #107C2×#6923semidirect
574. #103C2×#6923semidirect
580. #102C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623462
#214623432
#214619102
#214619092
#214618832
#214618802
#214618152
#214618122
#214618062
#214618052
#214615902
#103×#69232
#214615592
#214615072
#468×D612
#2314261