Finite Group Databasebeta

← #30565884

Subgroups — #30565884

Order 15616.

2156 conjugacy classes of subgroups.

The subgroup lattice has 1226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21460058C211yesmaximal, characteristic, complemented
2#21458072C212yesmaximal, complemented
3#21457990C212yesmaximal, complemented
4#21457795C212yesmaximal, complemented
5#21457669C212yesmaximal, complemented
6D4×#11758201C212yesmaximal, complemented
7#21457419C212yesmaximal, complemented
8#21457315C212yesmaximal, complemented
9#21457300C212yesmaximal, complemented
10#21456880C212yesmaximal, complemented
11#21456665C212yesmaximal, complemented
12#21456621C211yesmaximal, characteristic, complemented
13#21456572C211yesmaximal, characteristic, complemented
14#21456018C212yesmaximal, complemented
15#21455105C212yesmaximal, complemented
16#21455071C211yesmaximal, characteristic, complemented
17C2×#16839907C211yesmaximal, characteristic, complemented
18#21454867C211yesmaximal, characteristic, complemented
19C61×#3489C211yesmaximal, characteristic, complemented
20C2×#14519802C2212yescomplemented
21C2×#14519802C2211yescharacteristic, complemented
22C2×#14519802C2211yescharacteristic, complemented
23C22×#11758201C2212yescomplemented
24C22×#11758201C2211yescharacteristic, complemented
25C22×#11758199C2211yescharacteristic, complemented
26#16840502—22no—
27#16840458C2212yes—
28#16840458C2212yescomplemented
29D4×D244C2212yes—
30D4×D244C2212yescomplemented
31#16840394—22no—
32#16840367C2212yescomplemented
33#16840352—21no—
34#16840352—21no—
35#16840326C2212yescomplemented
36#16840320—21no—
37#16840320—21no—
38C2×#14519751C2211yescharacteristic
39C2×#14519751C2211yescharacteristic
40#16840152C2212yescomplemented
41#16840136C2212yescomplemented
42#16840130C2212yescomplemented
43#16840116C2212yescomplemented
44#16840100C2212yescomplemented
45#16840095C2212yescomplemented
46#16840090C2212yescomplemented
47#16840083C2212yescomplemented
48#16840080C2212yescomplemented
49#16840075C2212yescomplemented
50#16840069C2212yescomplemented
51#16840062C2212yescomplemented
52#16840013C2212yescomplemented
53#16840010C2212yescomplemented
54#16840010C2212yescomplemented
55#16840010C2212yescomplemented
56#16839996C2212yescomplemented
57#16839993C2212yescomplemented
58#16839993C2212yescomplemented
59#16839993C2212yescomplemented
60#16839974C2212yescomplemented
61#16839974C2212yescomplemented
62#16839964C2212yescomplemented
63#16839964C2212yescomplemented
64#16839962C2212yescomplemented
65#16839957C2212yescomplemented
66#16839912C2212yescomplemented
67#16839912C2212yescomplemented
68#16839912C2212yescomplemented
69#16839907C2212yescomplemented
70#16839907C2212yescomplemented
71#16839907C2212yescomplemented
72#16839907C2212yescomplemented
73#16839907C2212yescomplemented
74#16839907C2212yescomplemented
75#16839907C2212yescomplemented
76#16839907C2212yescomplemented
77#16839901C2212yescomplemented
78#16839901C2212yescomplemented
79#16839901C2212yescomplemented
80#16839901C2212yescomplemented
81#16839901C2212yescomplemented
82#16839896C2212yescomplemented
83#16839895C2212yescomplemented
84#16839872C2212yescomplemented
85#16839860C2212yescomplemented
86C4×#11758201C2212yescomplemented
87C4×#11758199C2212yescomplemented
88#16839840C2212yescomplemented
89#16839834C2212yescomplemented
90#16839834C2212yescomplemented
91D4×#92418C2212yescomplemented
92#16839823C2212yescomplemented
93#16839771C2212yescomplemented
94#16839763C2211yescharacteristic, complemented
95#16839763C2211yescharacteristic, complemented
96#16839758C2212yescomplemented
97C2×#14519701C2211yescharacteristic, complemented
98C2×#14519698C2211yescharacteristic, complemented
99#16839729C2212yescomplemented
100#16839726C2211yescharacteristic, complemented
101C2×C22⋊#92418C2211yescharacteristic, complemented
102C2×2−1+4×C61C2211yescharacteristic, complemented
103C22×#41×C61C2211yescharacteristic, complemented
104D4×Q8×C61C2212yescomplemented
105C61×#548C2212yescomplemented
106C61×#547—22no—
107C61×#547C2212yescomplemented
108C61×#546—22no—
109C61×#546C2212yescomplemented
110C61×#537—21no—
111C61×#537C2211yescharacteristic, complemented
112C61×#536—21no—
113C61×#536C2211yescharacteristic, complemented
114C61×#525—21no—
115C61×#525C2211yescharacteristic
116C2×C22⋊Q8×C61—21no—
117C2×C22⋊Q8×C61C2211yescharacteristic, complemented
118C61×#520C2211yescharacteristic, complemented
119C22×D244C2311yescharacteristic
120C22×D244C2311yescharacteristic
121C22×D244C2312yes—
122C22×C22⋊D61—21no—
123C22×C22⋊D61—21no—
124C2×D4×D61—22no—
125C2×D4×D61—22no—
126#14519802—44no—
127#14519802—42no—
128#14519802—42no—
129C2×#11758201—42no—
130C2×#11758201—44no—
131C2×#11758201C2312yes—
132C2×#11758201C2312yes—
133C2×#11758201C2312yes—
134C2×#11758201C2312yes—
135C2×#11758201C2312yes—
136C2×#11758201C2312yes—
137C2×#11758201C2312yes—
138C2×#11758201C2312yes—
139C2×#11758199—42no—
140C2×#11758199C2312yes—
141C2×#11758199C2312yes—
142C2×#11758199C2312yes—
143C2×#11758199C2312yes—
144C2×#11758194C2311yescharacteristic
145C2×#11758194C2311yescharacteristic
146C2×#11758194C2312yes—
147C22×#92418C2311yescharacteristic
148C22×#92418C2311yescharacteristic
149C22×#92418C2312yes—
150#14519774C2312yes—
151#14519773—22no—
152#14519772—22no—
153#14519772—22no—
154#14519769C2312yes—
155#14519766—22no—
156#14519762—22no—
157#14519762—22no—
158#14519759—22no—
159#14519759—22no—
160#14519752—22no—
161#14519752—22no—
162#14519751—21no—
163#14519751—21no—
164#14519751—21no—
165#14519751—21no—
166#14519751C2312yes—
167#14519751C2312yes—
168#14519751C2312yes—
169#14519751C2312yes—
170#14519751C2312yes—
171#14519751C2312yes—
172#14519750—22no—
173#14519750—22no—
174#14519749—22no—
175#14519749—22no—
176#14519747—22no—
177#14519747—22no—
178#14519747—22no—
179#14519747—22no—
180#14519745—22no—
181#14519745—22no—
182C4×D244C2312yes—
183C4×D244C2312yes—
184#14519737—22no—
185#14519737—22no—
186#14519736C2312yes—
187C2×C4⋊Dic61C2311yescharacteristic
188C2×C4⋊Dic61C2311yescharacteristic
189C2×#11758198—21no—
190C2×#11758198—21no—
191#14519710C2312yes—
192#14519710C2312yes—
193#14519708C2312yes—
194#14519708C2312yes—
195C4⋊#92418C2312yes—
196C4⋊#92418C2312yes—
197#14519701C2312yes—
198#14519701C2312yes—
199#14519701C2312yes—
200#14519701C2312yes—
201#14519701C2312yes—
202#14519701C2312yes—
203#14519701C2312yes—
204#14519701C2312yes—
205#14519698C2312yes—
206#14519698C2312yes—
207#14519698C2312yes—
208#14519698C2312yes—
209#14519697C2312yes—
210#14519697C2312yes—
211#14519697C2312yes—
212#14519697C2312yes—
213C22⋊#92418C2312yes—
214C22⋊#92418C2312yes—
215C22⋊#92418C2312yes—
216C22⋊#92418C2312yes—
217C22⋊#92418C2312yes—
218C22⋊#92418C2312yes—
219#14519688C2312yes—
220C4×#92418C2312yes—
2212−1+4×C61—42no—
2222−1+4×C61—42no—
223C2×#41×C61—21no—
224C2×#41×C61—22no—
225C2×#41×C61—21no—
226C2×#41×C61—21no—
227C2×#41×C61—42no—
228C2×#41×C61—42no—
229C2×#41×C61C2311yescharacteristic
230C2×#41×C61C2312yes—
231C2×#41×C61C2311yescharacteristic
232C2×#41×C61C2311yescharacteristic
233C2×#41×C61C2311yescharacteristic
234C2×#41×C61C2311yescharacteristic
235C22×Q8×C61—21no—
236C22×Q8×C61C2312yes—
237C22×Q8×C61C2311yescharacteristic
238C22×Q8×C61C2311yescharacteristic
239C22×D4×C61—21no—
240C22×D4×C61C2311yescharacteristic
241C23×C4×C61—21no—
242C23×C4×C61C2311yescharacteristic
243C4⋊Q8×C61—22no—
244C4⋊Q8×C61C2312yes—
245#124×C61—22no—
246#124×C61C2312yes—
247#123×C61—22no—
248#123×C61—22no—
249#123×C61—22no—
250#123×C61—22no—
251#123×C61D412yes—
252C22⋊Q8×C61—21no—
253C22⋊Q8×C61—21no—
254C22⋊Q8×C61—21no—
255C22⋊Q8×C61—21no—
256C22⋊Q8×C61—21no—
257C22⋊Q8×C61—22no—
258C22⋊Q8×C61—22no—
259C22⋊Q8×C61—22no—
260C22⋊Q8×C61D411yescharacteristic
261C22⋊Q8×C61D411yescharacteristic
262C22⋊Q8×C61C2312yes—
263C22⋊Q8×C61C2312yes—
264C22⋊Q8×C61C2312yes—
265#121×C61—21no—
266#121×C61—22no—
267#121×C61—22no—
268#121×C61—22no—
269#121×C61—22no—
270#121×C61D411yescharacteristic
271#121×C61D411yescharacteristic
272#121×C61C2312yes—
273#120×C61—22no—
274#120×C61D412yes—
275C4×Q8×C61C2312yes—
276C4×D4×C61—22no—
277C4×D4×C61—22no—
278C4×D4×C61—22no—
279C4×D4×C61C2312yes—
280C4×D4×C61C2312yes—
281C4×D4×C61C2312yes—
282#117×C61—21no—
283#117×C61C2311yescharacteristic
284C2×C4⋊C4×C61—21no—
285C2×C4⋊C4×C61—21no—
286C2×C4⋊C4×C61—22no—
287C2×C4⋊C4×C61C2311yescharacteristic
288C2×C22⋊C4×C61—21no—
289C2×C22⋊C4×C61—22no—
290C24×C61—21no—
291C24×C61C2×D411yescharacteristic
292C23×D61—21no—
293C23×D61—21no—
294C23×D61—22no—
295#41×C61—22no—
296#41×C61—22no—
297#41×C61—22no—
298#41×C61—22no—
299#41×C61—24no—
300#41×C61—41no—
301#41×C61—41no—
302#41×C61—41no—
303#41×C61—41no—
304#41×C61—41no—
305#41×C61—41no—
306#41×C61—42no—
307#41×C61—44no—
308#41×C61—44no—
309#41×C61—44no—
310#41×C61—48no—
311C2×Q8×C61—21no—
312C2×Q8×C61—22no—
313C2×Q8×C61—21no—
314C2×Q8×C61—22no—
315C2×Q8×C61—24no—
316C2×Q8×C61—41no—
317C2×Q8×C61—42no—
318C2×Q8×C61—41no—
319C2×Q8×C61—41no—
320C2×Q8×C61—44no—
321C2×Q8×C61C2×D411yescharacteristic
322C2×Q8×C61C2412yes—
323C2×Q8×C61C2411yescharacteristic
324C2×Q8×C61C2411yescharacteristic
325C2×D4×C61—21no—
326C2×D4×C61—22no—
327C2×D4×C61—22no—
328C2×D4×C61—21no—
329C2×D4×C61—21no—
330C2×D4×C61—21no—
331C2×D4×C61—22no—
332C2×D4×C61—21no—
333C2×D4×C61—41no—
334C2×D4×C61—44no—
335C2×D4×C61C2×D412yes—
336C2×D4×C61C2×D412yes—
337C2×D4×C61C2×D412yes—
338C2×D4×C61C2×D411yescharacteristic
339C2×D4×C61C2411yescharacteristic
340C2×D4×C61C2411yescharacteristic
341C22×C4×C61—21no—
342C22×C4×C61—21no—
343C22×C4×C61—22no—
344C22×C4×C61—21no—
345C22×C4×C61—21no—
346C22×C4×C61—22no—
347C22×C4×C61—21no—
348C22×C4×C61—21no—
349C22×C4×C61—21no—
350C22×C4×C61—22no—
351C22×C4×C61—41no—
352C22×C4×C61—41no—
353C22×C4×C61—44no—
354C22×C4×C61C2×D411yescharacteristic
355C22×C4×C61C2×D411yescharacteristic
356C22×C4×C61C2×D411yescharacteristic
357C22×C4×C61C2412yes—
358C22×C4×C61C2411yescharacteristic
359C22×C4×C61C2411yescharacteristic
360C22×C4×C61C2411yescharacteristic
361C2×C22⋊D61—22no—
362C2×C22⋊D61—22no—
363C2×C22⋊D61—22no—
364C2×C22⋊D61—22no—
365C2×C22⋊D61—22no—
366C2×C22⋊D61—22no—
367C2×C22⋊D61—82no—
368C2×C22⋊D61—82no—
369C22×Dic61—21no—
370C22×Dic61—21no—
371D4×D61—84no—
372D4×D61—84no—
373C2×D244—22no—
374C2×D244—22no—
375C2×D244—21no—
376C2×D244—21no—
377C2×D244—22no—
378C2×D244—41no—
379C2×D244—42no—
380C2×D244—41no—
381C2×D244—42no—
382C2×D244—41no—
383C2×D244—41no—
384C2×D244C2412yes—
385C2×D244C2412yes—
386C2×C4×D61—22no—
387C2×C4×D61—22no—
388C4⋊C4×C61—22no—
389C4⋊C4×C61—21no—
390C4⋊C4×C61—22no—
391C4⋊C4×C61—22no—
392C4⋊C4×C61—22no—
393C4⋊C4×C61—22no—
394C4⋊C4×C61—22no—
395C4⋊C4×C61C2×D411yescharacteristic
396C4⋊C4×C61C2×D412yes—
397C4⋊C4×C61C2×D411yescharacteristic
398C4⋊C4×C61C2×D412yes—
399C4⋊C4×C61C2412yes—
400C22⋊C4×C61—22no—
401C22⋊C4×C61—22no—
402C22⋊C4×C61—22no—
403C22⋊C4×C61—22no—
404C22⋊C4×C61—22no—
405C22⋊C4×C61—22no—
406C22⋊C4×C61—22no—
407C22⋊C4×C61C2×D412yes—
408C22⋊C4×C61C2×D412yes—
409C22⋊C4×C61C2×D412yes—
410C22⋊C4×C61C2×D412yes—
411C22⋊C4×C61C2×D412yes—
412C42×C61—22no—
413C42×C61C2412yes—
414C22⋊Dic61—22no—
415#11758201—24no—
416#11758201—24no—
417#11758201—42no—
418#11758201—42no—
419#11758201—42no—
420#11758201—42no—
421#11758201—42no—
422#11758201—42no—
423#11758199—24no—
424#11758199—24no—
425#11758199—42no—
426#11758199—42no—
427#11758198—22no—
428#11758198—22no—
429#11758198—22no—
430#11758198—22no—
431#11758198—22no—
432#11758198—22no—
433#11758198—22no—
434#11758198—22no—
435C4⋊Dic61—21no—
436C4⋊Dic61—21no—
437C4⋊Dic61C2412yes—
438C4⋊Dic61C2412yes—
439#11758196—22no—
440#11758196—22no—
441C4×Dic61—22no—
442#11758194—42no—
443#11758194—41no—
444#11758194—41no—
445C2×#92418—41no—
446C2×#92418—41no—
447C2×#92418—42no—
448C2×#92418C2412yes—
449C2×#92418C2412yes—
450C2×#92418C2412yes—
451C2×#92418C2412yes—
452C23×C61—21no—
453C23×C61—22no—
454C23×C61—21no—
455C23×C61—41no—
456C23×C61—41no—
457C23×C61—42no—
458C23×C61—42no—
459C23×C61—81no—
460C23×C61C22×D412yes—
461C23×C61C22×D411yescharacteristic
462C23×C61C22×D411yescharacteristic
463C23×C61C22×D411yescharacteristic
464C22×D61—22no—
465C22×D61—22no—
466C22×D61—42no—
467C22×D61—42no—
468C22×D61—81no—
469C22×D61—81no—
470C22×D61—82no—
471C22×D61—82no—
472C22×D61—82no—
473C22×D61—81no—
474C22×D61—81no—
475Q8×C61—21no—
476Q8×C61—22no—
477Q8×C61—21no—
478Q8×C61—22no—
479Q8×C61—21no—
480Q8×C61—41no—
481Q8×C61—44no—
482Q8×C61—42no—
483Q8×C61—42no—
484Q8×C61H(5,𝔽2)12yes—
485D4×C61—24no—
486D4×C61—24no—
487D4×C61—21no—
488D4×C61—21no—
489D4×C61—21no—
490D4×C61—42no—
491D4×C61—42no—
492D4×C61—41no—
493D4×C61—42no—
494D4×C61—42no—
495D4×C61—42no—
496D4×C61—44no—
497D4×C61—42no—
498D4×C61—82no—
499D4×C61H(5,𝔽2)12yes—
500C2×C4×C61—24no—
501C2×C4×C61—21no—
502C2×C4×C61—21no—
503C2×C4×C61—21no—
504C2×C4×C61—22no—
505C2×C4×C61—21no—
506C2×C4×C61—21no—
507C2×C4×C61—22no—
508C2×C4×C61—21no—
509C2×C4×C61—21no—
510C2×C4×C61—22no—
511C2×C4×C61—22no—
512C2×C4×C61—21no—
513C2×C4×C61—41no—
514C2×C4×C61—41no—
515C2×C4×C61—41no—
516C2×C4×C61—42no—
517C2×C4×C61—42no—
518C2×C4×C61—42no—
519C2×C4×C61—44no—
520C2×C4×C61—44no—
521C2×C4×C61—42no—
522C2×C4×C61—42no—
523C2×C4×C61—82no—
524C2×C4×C61—81no—
525C2×C4×C61C22×D412yes—
526C2×C4×C61C22×D412yes—
527C2×C4×C61C22×D412yes—
528C2×C4×C61C22×D411yescharacteristic
529C2×C4×C61C22×D411yescharacteristic
530C2×C4×C61C22×D411yescharacteristic
531C2×C4×C61C2511yescharacteristic
532C22⋊D61—44no—
533C22⋊D61—44no—
534C22⋊D61—82no—
535C22⋊D61—82no—
536C22⋊D61—82no—
537C22⋊D61—82no—
538C2×Dic61—22no—
539C2×Dic61—22no—
540C2×Dic61—81no—
541C2×Dic61—81no—
542D244—22no—
543D244—22no—
544D244—22no—
545D244—22no—
546D244—81no—
547D244—81no—
548D244—82no—
549D244—82no—
550D244—82no—
551C4×D61—82no—
552C4×D61—82no—
553#92418—22no—
554#92418—22no—
555#92418—22no—
556#92418—22no—
557#61621—611nomaximal, Sylow
558C22×C61—21no—
559C22×C61—21no—
560C22×C61—21no—
561C22×C61—21no—
562C22×C61—22no—
563C22×C61—21no—
564C22×C61—22no—
565C22×C61—22no—
566C22×C61—21no—
567C22×C61—21no—
568C22×C61—21no—
569C22×C61—22no—
570C22×C61—41no—
571C22×C61—41no—
572C22×C61—41no—
573C22×C61—41no—
574C22×C61—41no—
575C22×C61—82no—
576C22×C61—84no—
577C22×C61#57712yes—
578C22×C61C23×D411yescharacteristic
579C2×D61—42no—
580C2×D61—42no—
581C2×D61—42no—
582C2×D61—42no—
583C2×D61—42no—
584C2×D61—42no—
585C2×D61—162no—
586C2×D61—162no—
587C2×D61—164no—
588C4×C61—22no—
589C4×C61—21no—
590C4×C61—21no—
591C4×C61—22no—
592C4×C61—21no—
593C4×C61—22no—
594C4×C61—22no—
595C4×C61—42no—
596C4×C61—41no—
597C4×C61—42no—
598C4×C61C2×H(5,𝔽2)11yescharacteristic
599C4×C61C2×H(5,𝔽2)11yescharacteristic
600Dic61—42no—
601Dic61—42no—
602#3537—611no—
603#3489D6111yescharacteristic, complemented
604#3326—612no—
605#3320—612no—
606#3307—612no—
607#3297—612no—
608D4×SD16—612no—
609#3272—612no—
610#3265—612no—
611#3264—612no—
612#3221—612no—
613#3198—612no—
614#3193—611no—
615#3187—611no—
616#3119—612no—
617#3010—612no—
618#3006—611no—
619C2×#449—611no—
620#2976—611no—
621C2×C61—22no—
622C2×C61—42no—
623C2×C61—41no—
624C2×C61—41no—
625C2×C61—42no—
626C2×C61—81no—
627C2×C61#348411yescharacteristic
628C2×C61C2×#57711yescharacteristic
629C2×C61#358511yescharacteristic
630D61—82no—
631D61—82no—
632C2×2−1+4C2×D6111yescharacteristic, complemented
633C22×#41C2×D6111yescharacteristic, complemented
634C2×AGL(1,ℤ/8)—611no—
635C2×AGL(1,ℤ/8)—611no—
636C2×AGL(1,ℤ/8)—612no—
637C22×SD16—611no—
638C22×SD16—612no—
639C22×D8—611no—
640#560—1222no—
641#553—612no—
642#553—612no—
643D4×Q8C2×D6112yescomplemented
644#548C2×D6112yescomplemented
645#547—22no—
646#547C2×D6112yescomplemented
647#546—22no—
648#546C2×D6112yescomplemented
649D42—612no—
650D42—612no—
651D42—1222no—
652#540—612no—
653#538—1221no—
654#538—1221no—
655#537—21no—
656#537C2×D6111yescharacteristic, complemented
657#536—21no—
658#536C2×D6111yescharacteristic, complemented
659#535—612no—
660#534—1221no—
661#534—1221no—
662#525—21no—
663#525C2×D6111yescharacteristic
664C2×C22⋊Q8—21no—
665C2×C22⋊Q8C2×D6111yescharacteristic, complemented
666C2×#121—611no—
667C2×#121—611no—
668#520C2×D6111yescharacteristic, complemented
669#496—612no—
670#492—612no—
671#491—612no—
672#488—612no—
673#485—612no—
674#484—612no—
675#483—612no—
676#482—612no—
677#481—612no—
678#480—612no—
679#479—612no—
680#478—612no—
681#469—612no—
682#468—612no—
683#468—612no—
684#468—612no—
685#466—612no—
686#465—612no—
687#465—612no—
688#465—612no—
689#463—612no—
690#463—612no—
691#461—612no—
692#461—612no—
693#460—612no—
694#459—612no—
695#450—612no—
696#450—612no—
697#450—612no—
698#449—612no—
699#449—612no—
700#449—612no—
701#449—612no—
702#449—612no—
703#449—612no—
704#449—612no—
705#449—612no—
706#448—612no—
707#448—612no—
708#448—612no—
709#448—612no—
710#448—612no—
711#447—612no—
712#447—612no—
713#442—612no—
714#440—612no—
715C4×SD16—612no—
716C4×D8—612no—
717#436—612no—
718#435—612no—
719#435—612no—
720C8×D4—612no—
721#433—612no—
722#419—612no—
723#417—611no—
724#417—611no—
725#416—612no—
726C2×#103—611no—
727C2×#102—611no—
728#408—612no—
729#407—611no—
730C2×C22⋊C8—611no—
731C61#6162111yescharacteristic, complemented, Sylow
7322−1+4—42no—
7332−1+4—42no—
734C2×#41—21no—
735C2×#41—22no—
736C2×#41—21no—
737C2×#41—21no—
738C2×#41—42no—
739C2×#41—42no—
740C2×#41C22×D6111yescharacteristic
741C2×#41C22×D6112yes—
742C2×#41C22×D6111yescharacteristic
743C2×#41C22×D6111yescharacteristic
744C2×#41C22×D6111yescharacteristic
745C2×#41C22×D6111yescharacteristic
746C22×Q8—21no—
747C22×Q8C22×D6112yes—
748C22×Q8C22×D6111yescharacteristic
749C22×Q8C22×D6111yescharacteristic
750C22×D4—21no—
751C22×D4—611no—
752C22×D4—611no—
753C22×D4—612no—
754C22×D4—1221no—
755C22×D4—1221no—
756C22×D4—1222no—
757C22×D4—1222no—
758C22×D4C22×D6111yescharacteristic
759C23×C4—21no—
760C23×C4C22×D6111yescharacteristic
761AGL(1,ℤ/8)—2444no—
762AGL(1,ℤ/8)—2442no—
763AGL(1,ℤ/8)—2442no—
764C2×SD16—612no—
765C2×SD16—612no—
766C2×SD16—612no—
767C2×SD16—612no—
768C2×SD16—612no—
769C2×SD16—612no—
770C2×SD16—612no—
771C2×SD16—612no—
772C2×SD16—2442no—
773C2×SD16—2444no—
774C2×D8—612no—
775C2×D8—612no—
776C2×D8—612no—
777C2×D8—612no—
778C2×D8—2442no—
779C2×M16—611no—
780C2×M16—611no—
781C2×M16—612no—
782C22×C8—611no—
783C22×C8—611no—
784C22×C8—612no—
785C4⋊Q8—22no—
786C4⋊Q8C22×D6112yes—
787#127—612no—
788#127—1222no—
789#126—1222no—
790#126—1222no—
791#125—612no—
792#124—22no—
793#124—1222no—
794#124C22×D6112yes—
795#123—22no—
796#123—22no—
797#123—22no—
798#123—22no—
799#123—1222no—
800#123—1222no—
801#123—1222no—
802#123—1222no—
803#123C22⋊D6112yes—
804C22⋊Q8—21no—
805C22⋊Q8—21no—
806C22⋊Q8—21no—
807C22⋊Q8—21no—
808C22⋊Q8—22no—
809C22⋊Q8—21no—
810C22⋊Q8—22no—
811C22⋊Q8—22no—
812C22⋊Q8C22⋊D6111yescharacteristic
813C22⋊Q8C22⋊D6111yescharacteristic
814C22⋊Q8C22×D6112yes—
815C22⋊Q8C22×D6112yes—
816C22⋊Q8C22×D6112yes—
817#121—21no—
818#121—22no—
819#121—22no—
820#121—22no—
821#121—22no—
822#121—612no—
823#121—612no—
824#121—612no—
825#121—612no—
826#121—612no—
827#121—612no—
828#121—1222no—
829#121—1222no—
830#121—1221no—
831#121—1221no—
832#121—1221no—
833#121—1221no—
834#121—1222no—
835#121—1222no—
836#121—1222no—
837#121—1222no—
838#121C22⋊D6111yescharacteristic
839#121C22⋊D6111yescharacteristic
840#121C22×D6112yes—
841#120—22no—
842#120—1222no—
843#120—1222no—
844#120—1222no—
845#120—1222no—
846#120—1222no—
847#120—1222no—
848#120C22⋊D6112yes—
849C4×Q8C22×D6112yes—
850C4×D4—22no—
851C4×D4—22no—
852C4×D4—22no—
853C4×D4—612no—
854C4×D4—612no—
855C4×D4—1222no—
856C4×D4—1222no—
857C4×D4C22×D6112yes—
858C4×D4C22×D6112yes—
859C4×D4C22×D6112yes—
860#117—21no—
861#117—612no—
862#117C22×D6111yescharacteristic
863C2×C4⋊C4—21no—
864C2×C4⋊C4—21no—
865C2×C4⋊C4—22no—
866C2×C4⋊C4—611no—
867C2×C4⋊C4—611no—
868C2×C4⋊C4C22×D6111yescharacteristic
869C2×C22⋊C4—21no—
870C2×C22⋊C4—22no—
871C2×C22⋊C4—1221no—
872C2×C22⋊C4—1221no—
873#107—612no—
874#107—612no—
875#106—612no—
876#106—612no—
877C4⋊C8—612no—
878C4⋊C8—612no—
879#103—612no—
880#103—612no—
881#103—612no—
882#103—612no—
883#103—612no—
884#103—612no—
885#103—612no—
886#103—612no—
887#102—612no—
888#102—612no—
889#102—612no—
890#102—612no—
891#102—612no—
892#102—612no—
893#102—612no—
894#102—612no—
895C22⋊C8—612no—
896C22⋊C8—612no—
897C22⋊C8—612no—
898C22⋊C8—612no—
899C22⋊C8—612no—
900C22⋊C8—612no—
901#97—612no—
902C4×C8—612no—
903C24—21no—
904C24—1222no—
905C24—1221no—
906C24—1221no—
907C24C2×C22⋊D6111yescharacteristic
908#41—22no—
909#41—22no—
910#41—22no—
911#41—22no—
912#41—24no—
913#41—41no—
914#41—41no—
915#41—41no—
916#41—41no—
917#41—41no—
918#41—41no—
919#41—42no—
920#41—44no—
921#41—44no—
922#41—44no—
923#41—48no—
924C2×Q8—21no—
925C2×Q8—22no—
926C2×Q8—21no—
927C2×Q8—22no—
928C2×Q8—24no—
929C2×Q8—41no—
930C2×Q8—42no—
931C2×Q8—41no—
932C2×Q8—41no—
933C2×Q8—44no—
934C2×Q8C2×C22⋊D6111yescharacteristic
935C2×Q8C23×D6112yes—
936C2×Q8C23×D6111yescharacteristic
937C2×Q8C23×D6111yescharacteristic
938C2×D4—21no—
939C2×D4—22no—
940C2×D4—22no—
941C2×D4—21no—
942C2×D4—21no—
943C2×D4—21no—
944C2×D4—22no—
945C2×D4—21no—
946C2×D4—41no—
947C2×D4—44no—
948C2×D4—612no—
949C2×D4—612no—
950C2×D4—1222no—
951C2×D4—1222no—
952C2×D4—1222no—
953C2×D4—1222no—
954C2×D4—1222no—
955C2×D4—1222no—
956C2×D4—1221no—
957C2×D4—1221no—
958C2×D4—1222no—
959C2×D4—1222no—
960C2×D4—1222no—
961C2×D4—4884no—
962C2×D4—4884no—
963C2×D4—4882no—
964C2×D4—4882no—
965C2×D4—2441no—
966C2×D4—2441no—
967C2×D4—2442no—
968C2×D4—2441no—
969C2×D4—2441no—
970C2×D4—2442no—
971C2×D4C2×C22⋊D6112yes—
972C2×D4C2×C22⋊D6112yes—
973C2×D4C2×C22⋊D6111yescharacteristic
974C2×D4C2×C22⋊D6112yes—
975C2×D4C23×D6111yescharacteristic
976C2×D4C23×D6111yescharacteristic
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—22no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—22no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—22no—
987C22×C4—41no—
988C22×C4—41no—
989C22×C4—44no—
990C22×C4—1221no—
991C22×C4—1221no—
992C22×C4—1222no—
993C22×C4—1222no—
994C22×C4C2×C22⋊D6111yescharacteristic
995C22×C4C2×C22⋊D6111yescharacteristic
996C22×C4C2×C22⋊D6111yescharacteristic
997C22×C4C23×D6111yescharacteristic
998C22×C4C23×D6111yescharacteristic
999C22×C4C23×D6111yescharacteristic
1000C22×C4C23×D6112yes—
1001SD16—1224no—
1002SD16—1224no—
1003SD16—2442no—
1004SD16—2442no—
1005SD16—2442no—
1006SD16—2442no—
1007SD16—2442no—
1008SD16—2442no—
1009D8—1224no—
1010D8—1224no—
1011D8—2442no—
1012D8—2442no—
1013M16—2442no—
1014M16—2441no—
1015M16—2441no—
1016C2×C8—612no—
1017C2×C8—612no—
1018C2×C8—612no—
1019C2×C8—612no—
1020C2×C8—2441no—
1021C2×C8—2441no—
1022C2×C8—2442no—
1023C4⋊C4—22no—
1024C4⋊C4—21no—
1025C4⋊C4—22no—
1026C4⋊C4—22no—
1027C4⋊C4—22no—
1028C4⋊C4—22no—
1029C4⋊C4—22no—
1030C4⋊C4—612no—
1031C4⋊C4—612no—
1032C4⋊C4—1221no—
1033C4⋊C4—1221no—
1034C4⋊C4—1222no—
1035C4⋊C4—1222no—
1036C4⋊C4C2×C22⋊D6111yescharacteristic
1037C4⋊C4C2×C22⋊D6112yes—
1038C4⋊C4C2×C22⋊D6111yescharacteristic
1039C4⋊C4C2×C22⋊D6112yes—
1040C4⋊C4C23×D6112yes—
1041C22⋊C4—22no—
1042C22⋊C4—22no—
1043C22⋊C4—22no—
1044C22⋊C4—22no—
1045C22⋊C4—22no—
1046C22⋊C4—22no—
1047C22⋊C4—22no—
1048C22⋊C4—1222no—
1049C22⋊C4—1222no—
1050C22⋊C4—1222no—
1051C22⋊C4—1222no—
1052C22⋊C4—1222no—
1053C22⋊C4—1222no—
1054C22⋊C4—1222no—
1055C22⋊C4—1222no—
1056C22⋊C4—1222no—
1057C22⋊C4C2×C22⋊D6112yes—
1058C22⋊C4C2×C22⋊D6112yes—
1059C22⋊C4C2×C22⋊D6112yes—
1060C22⋊C4C2×C22⋊D6112yes—
1061C22⋊C4C2×C22⋊D6112yes—
1062C42—22no—
1063C42—1222no—
1064C42C23×D6112yes—
1065C23—21no—
1066C23—22no—
1067C23—21no—
1068C23—41no—
1069C23—41no—
1070C23—42no—
1071C23—42no—
1072C23—81no—
1073C23—1222no—
1074C23—1222no—
1075C23—4881no—
1076C23—4881no—
1077C23—4882no—
1078C23—4882no—
1079C23—4881no—
1080C23—4882no—
1081C23—4881no—
1082C23—2442no—
1083C23—2442no—
1084C23C22×C22⋊D6111yescharacteristic
1085C23C22×C22⋊D6112yes—
1086C23C22×C22⋊D6111yescharacteristic
1087C23C22×C22⋊D6111yescharacteristic
1088Q8—21no—
1089Q8—22no—
1090Q8—21no—
1091Q8—22no—
1092Q8—21no—
1093Q8—41no—
1094Q8—44no—
1095Q8—42no—
1096Q8—42no—
1097Q8#1451982212yes—
1098D4—24no—
1099D4—24no—
1100D4—21no—
1101D4—21no—
1102D4—21no—
1103D4—42no—
1104D4—41no—
1105D4—42no—
1106D4—42no—
1107D4—42no—
1108D4—42no—
1109D4—44no—
1110D4—42no—
1111D4—82no—
1112D4—1222no—
1113D4—1222no—
1114D4—1222no—
1115D4—1222no—
1116D4—4882no—
1117D4—4882no—
1118D4—4881no—
1119D4—4881no—
1120D4—4882no—
1121D4—4882no—
1122D4—4882no—
1123D4—4882no—
1124D4—4882no—
1125D4—2444no—
1126D4—2444no—
1127D4#1451982212yes—
1128C2×C4—24no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—22no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—22no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—21no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—44no—
1148C2×C4—44no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—82no—
1152C2×C4—81no—
1153C2×C4—1222no—
1154C2×C4—1222no—
1155C2×C4—4882no—
1156C2×C4—4882no—
1157C2×C4—4881no—
1158C2×C4—4881no—
1159C2×C4C22×C22⋊D6112yes—
1160C2×C4C22×C22⋊D6112yes—
1161C2×C4C22×C22⋊D6112yes—
1162C2×C4C22×C22⋊D6111yescharacteristic
1163C2×C4C22×C22⋊D6111yescharacteristic
1164C2×C4C22×C22⋊D6111yescharacteristic
1165C2×C4C24×D6111yescharacteristic
1166C8—1222no—
1167C8—1222no—
1168C8—1222no—
1169C8—1222no—
1170C22—21no—
1171C22—21no—
1172C22—21no—
1173C22—22no—
1174C22—21no—
1175C22—21no—
1176C22—21no—
1177C22—22no—
1178C22—21no—
1179C22—22no—
1180C22—22no—
1181C22—21no—
1182C22—41no—
1183C22—41no—
1184C22—41no—
1185C22—41no—
1186C22—41no—
1187C22—82no—
1188C22—84no—
1189C22—9762no—
1190C22—9764no—
1191C22—9762no—
1192C22—2442no—
1193C22—2442no—
1194C22—2442no—
1195C22—2442no—
1196C22—2442no—
1197C22—2442no—
1198C22#1684057012yes—
1199C22C23×C22⋊D6111yescharacteristic
1200C4—22no—
1201C4—22no—
1202C4—21no—
1203C4—22no—
1204C4—21no—
1205C4—21no—
1206C4—22no—
1207C4—42no—
1208C4—41no—
1209C4—42no—
1210C4—2442no—
1211C4—2442no—
1212C4C2×#1451982211yescharacteristic
1213C4C2×#1451982211yescharacteristic
1214C2—22no—
1215C2—41no—
1216C2—41no—
1217C2—42no—
1218C2—42no—
1219C2—81no—
1220C2—4882no—
1221C2—4882no—
1222C2#2145945411yescharacteristic
1223C2C2×#1684057011yescharacteristic
1224C2#2146059811yescharacteristic
subgroupG/H
centerC22C23×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3489C2
socleC22×C61C23×D4
hypercenter#3489D61
hypocenterC61#61621
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #525 ◁ #3489

Complements

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

NH ≅ G/Ntype
1. #21460058C2semidirect
2. #21458072C2semidirect
3. #21457990C2semidirect
4. #21457795C2semidirect
5. #21457669C2semidirect
6. D4×#11758201C2semidirect
7. #21457419C2semidirect
8. #21457315C2semidirect
9. #21457300C2semidirect
10. #21456880C2semidirect
11. #21456665C2semidirect
12. #21456621C2semidirect
13. #21456572C2semidirect
14. #21456018C2semidirect
15. #21455105C2semidirect
16. #21455071C2semidirect
17. C2×#16839907C2semidirect
18. #21454867C2semidirect
19. C61×#3489C2semidirect
20. C2×#14519802C22semidirect
21. C2×#14519802C22semidirect
22. C2×#14519802C22semidirect
23. C22×#11758201C22semidirect
24. C22×#11758201C22semidirect
25. C22×#11758199C22semidirect
28. #16840458C22semidirect
30. D4×D244C22semidirect
32. #16840367C22semidirect
35. #16840326C22semidirect
40. #16840152C22semidirect
41. #16840136C22semidirect
42. #16840130C22semidirect
43. #16840116C22semidirect
44. #16840100C22semidirect
45. #16840095C22semidirect
46. #16840090C22semidirect
47. #16840083C22semidirect
48. #16840080C22semidirect
49. #16840075C22semidirect
50. #16840069C22semidirect
51. #16840062C22semidirect
52. #16840013C22semidirect
53. #16840010C22semidirect
54. #16840010C22semidirect
55. #16840010C22semidirect
56. #16839996C22semidirect
57. #16839993C22semidirect
58. #16839993C22semidirect
59. #16839993C22semidirect
60. #16839974C22semidirect
61. #16839974C22semidirect
62. #16839964C22semidirect
63. #16839964C22semidirect
64. #16839962C22semidirect
65. #16839957C22semidirect
66. #16839912C22semidirect
67. #16839912C22semidirect
68. #16839912C22semidirect
69. #16839907C22semidirect
70. #16839907C22semidirect
71. #16839907C22semidirect
72. #16839907C22semidirect
73. #16839907C22semidirect
74. #16839907C22semidirect
75. #16839907C22semidirect
76. #16839907C22semidirect
77. #16839901C22semidirect
78. #16839901C22semidirect
79. #16839901C22semidirect
80. #16839901C22semidirect
81. #16839901C22semidirect
82. #16839896C22semidirect
83. #16839895C22semidirect
84. #16839872C22semidirect
85. #16839860C22semidirect
86. C4×#11758201C22semidirect
87. C4×#11758199C22semidirect
88. #16839840C22semidirect
89. #16839834C22semidirect
90. #16839834C22semidirect
91. D4×#92418C22semidirect
92. #16839823C22semidirect
93. #16839771C22semidirect
94. #16839763C22semidirect
95. #16839763C22semidirect
96. #16839758C22semidirect
97. C2×#14519701C22semidirect
98. C2×#14519698C22semidirect
99. #16839729C22semidirect
100. #16839726C22semidirect
101. C2×C22⋊#92418C22semidirect
102. C2×2−1+4×C61C22semidirect
103. C22×#41×C61C22semidirect
104. D4×Q8×C61C22semidirect
105. C61×#548C22semidirect
107. C61×#547C22semidirect
109. C61×#546C22semidirect
111. C61×#537C22semidirect
113. C61×#536C22semidirect
117. C2×C22⋊Q8×C61C22semidirect
118. C61×#520C22semidirect
603. #3489D61semidirect
632. C2×2−1+4C2×D61semidirect
633. C22×#41C2×D61semidirect
643. D4×Q8C2×D61semidirect
644. #548C2×D61semidirect
646. #547C2×D61semidirect
648. #546C2×D61semidirect
656. #537C2×D61semidirect
658. #536C2×D61semidirect
665. C2×C22⋊Q8C2×D61semidirect
668. #520C2×D61semidirect
731. C61#61621semidirect

Maximal subgroups

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

subgroupindex
#214600582
#214580722
#214579902
#214577952
#214576692
D4×#117582012
#214574192
#214573152
#214573002
#214568802
#214566652
#214566212
#214565722
#214560182
#214551052
#214550712
C2×#168399072
#214548672
C61×#34892
#6162161