Finite Group Databasebeta

← #30553045

Subgroups — #30553045

Order 15616.

1888 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459116C211yesmaximal, characteristic
2#533×D61C211yesmaximal, characteristic, complemented
3#21457211C212yesmaximal, complemented
4#21457205C212yesmaximal, complemented
5#21457195C212yesmaximal, complemented
6#21457190C212yesmaximal, complemented
7#21457161C211yesmaximal, characteristic, complemented
8#21457151C214yesmaximal, complemented
9#21457136C211yesmaximal, characteristic, complemented
10#21457131C211yesmaximal, characteristic, complemented
11#21455633C212yesmaximal, complemented
12#21455625C212yesmaximal, complemented
13#21455446C214yesmaximal, complemented
14#21455303C212yesmaximal, complemented
15#21455292C212yesmaximal, complemented
16C2×#16839784C211yesmaximal, characteristic, complemented
17C61×#3249C211yesmaximal, characteristic, complemented
18C2×#14519809C2214yes—
19C22×#11758189C2212yes—
20#16840319C2211yescharacteristic
21#16840318—21no—
22#16840317C2211yescharacteristic
23#16840317C2211yescharacteristic
24#16840317C2211yescharacteristic
25#16840317C2211yescharacteristic
26#16840316—21no—
27#16840316C2212yes—
28#16840315—21no—
29#16840314—21no—
30#16840314C2212yes—
31#16840313C2211yescharacteristic
32#16840313C2211yescharacteristic
33#16840312C2211yescharacteristic
34C4⋊Q8×D61C2211yescharacteristic
35C4⋊Q8×D61C2211yescharacteristic
36#16840299—21no—
37#16840299C2212yes—
38#16840298—21no—
39#16840298C2212yes—
40#16840297—21no—
41#16840297—21no—
42#125×D61—21no—
43#16840275—21no—
44#16840275C2212yes—
45#16840274—21no—
46C22⋊Q8×D61—21no—
47C22⋊Q8×D61C2212yes—
48C4×#11758226—21no—
49C4×#11758226C2212yes—
50#16840230—21no—
51C4×Q8×D61—21no—
52C4×Q8×D61C2212yes—
53#117×D61—21no—
54C2×C42×D61C2211yescharacteristic
55#16840068C2214yescomplemented
56#16840067C2214yescomplemented
57#16840057C2212yescomplemented
58#16840054C2212yescomplemented
59#16840053C2212yescomplemented
60#16840049C2212yescomplemented
61#16840048C2212yescomplemented
62#16840047C2212yescomplemented
63#16840045C2214yescomplemented
64#16840041C2214yescomplemented
65#16840019C2214yes—
66#16840017C2214yes—
67#16840011C2214yes—
68#16840009C2214yes—
69#16840001C2214yes—
70#16839993C2214yes—
71#16839991C2214yes—
72#16839987C2214yescomplemented
73#16839986C2214yescomplemented
74#16839972C2212yescomplemented
75#16839970C2214yescomplemented
76#16839969C2212yescomplemented
77#16839968C2212yescomplemented
78#16839966C2214yescomplemented
79#16839964C2212yescomplemented
80#16839963C2212yescomplemented
81#16839962C2212yescomplemented
82#16839803C2214yes—
83#16839784C2212yes—
84#16839784C2212yes—
85#16839784C2212yes—
86#16839784C2212yes—
87C2×C4⋊#92418C2211yescharacteristic
88C2×#14519706C2212yes—
89#16839769C2214yes—
90#16839762C2214yes—
91C61×#533C2211yescharacteristic
92C61×#533C2211yescharacteristic
93C61×#477C2212yescomplemented
94C61×#477C2212yescomplemented
95C61×#467C2214yes—
96C61×#462C2212yescomplemented
97C61×#462C2212yescomplemented
98C2×C4⋊C8×C61C2211yescharacteristic
99C2×#11758226—21no—
100C2×#11758226C2312yes—
101C2×#11758222—21no—
102C2×Q8×D61—21no—
103C2×Q8×D61C2312yes—
104C22×C4×D61D411yescharacteristic
105C22×C4×D61D411yescharacteristic
106C22×C4×D61C2311yescharacteristic
107#14519809—48no—
108C2×#11758202C2314yes—
109C2×#11758190C2314yes—
110C2×#11758201C2314yes—
111C2×#11758189—44no—
112C2×#11758189C2314yes—
113C2×#11758189C2314yes—
114C22×#92418C2312yes—
115#14519777C2311yescharacteristic
116#14519777C2311yescharacteristic
117#14519777C2311yescharacteristic
118#14519776—21no—
119#14519776—21no—
120#14519776—21no—
121#14519776C2312yes—
122#14519775—21no—
123#14519775C2312yes—
124#14519774C2311yescharacteristic
125#14519772—22no—
126#14519772—22no—
127#14519769—21no—
128#14519768—21no—
129#14519768—21no—
130#14519768—21no—
131#14519768C2312yes—
132#14519767—22no—
133#14519767—22no—
134#14519766—21no—
135#14519766C2312yes—
136#14519765—21no—
137#14519762—22no—
138#14519762—22no—
139#14519761—22no—
140#14519757—21no—
141#14519757—21no—
142#14519757—21no—
143#14519757C2312yes—
144#14519756—21no—
145#14519756C2312yes—
146#14519755—22no—
147#14519755—22no—
148#14519754—22no—
149#14519754—22no—
150#14519753—21no—
151#14519753—21no—
152#14519753C2312yes—
153#14519753C2312yes—
154#14519752—21no—
155#14519752—21no—
156#14519752—21no—
157#14519752C2312yes—
158#14519751—21no—
159#14519751C2312yes—
160#14519747—22no—
161Q8×Dic61—21no—
162Q8×Dic61—21no—
163Q8×Dic61C2312yes—
164Q8×Dic61C2312yes—
165C4×Dic122—21no—
166C4×Dic122—22no—
167C4×Dic122—22no—
168C4×Dic122C2312yes—
169#14519742—21no—
170#14519742—22no—
171#14519742—22no—
172#14519742—21no—
173#14519742—21no—
174#14519742C2312yes—
175C4×D244—22no—
176C4×D244—22no—
177C4×D244—21no—
178C4×D244C2312yes—
179#14519739—22no—
180#14519739—22no—
181#14519739—21no—
182#14519739—21no—
183#14519739—21no—
184#14519739C2312yes—
185#14519737—22no—
186#14519737—22no—
187#14519736—21no—
188#14519735—21no—
189#14519735—21no—
190#14519735—21no—
191#14519735—22no—
192#14519735—22no—
193#14519735C2312yes—
194#14519734—22no—
195#14519734—22no—
196#14519733—22no—
197C4⋊C4×D61—21no—
198C4⋊C4×D61—21no—
199C4⋊C4×D61—21no—
200C4⋊C4×D61—22no—
201C4⋊C4×D61—22no—
202C4⋊C4×D61C2312yes—
203C22⋊C4×D61—22no—
204C2×C4×Dic61D411yescharacteristic
205C2×C4×Dic61D411yescharacteristic
206C2×C4×Dic61C2311yescharacteristic
207C42×D61—22no—
208C42×D61—22no—
209C42×D61D411yescharacteristic
210C42×D61D411yescharacteristic
211C42×D61D411yescharacteristic
212C42×D61D411yescharacteristic
213C42×D61C2311yescharacteristic
214C42×D61C2311yescharacteristic
215C42×D61C2311yescharacteristic
216C42×D61C2311yescharacteristic
217#14519710C2314yes—
218#14519709C2314yes—
219#14519708C2314yes—
220C4⋊#92418C2312yes—
221C4⋊#92418C2312yes—
222#14519706C2314yes—
223#14519706C2314yes—
224#14519702C2314yes—
225#14519701C2314yes—
226#14519701C2314yes—
227#14519700C2314yes—
228#14519699C2314yes—
229#14519697C2314yes—
230C2×Q16×C61C2314yes—
231C22×C8×C61C2312yes—
232C4⋊Q8×C61C2311yescharacteristic
233C4⋊Q8×C61C2311yescharacteristic
234C4⋊Q8×C61C2311yescharacteristic
235C4⋊Q8×C61C2311yescharacteristic
236#125×C61—21no—
237#125×C61—21no—
238C22⋊Q8×C61—21no—
239C22⋊Q8×C61—21no—
240C22⋊Q8×C61C2312yes—
241C22⋊Q8×C61C2312yes—
242C4×Q8×C61—21no—
243C4×Q8×C61—21no—
244C4×Q8×C61C2312yes—
245C4×Q8×C61C2312yes—
246#117×C61—21no—
247#117×C61—21no—
248C2×C42×C61C2311yescharacteristic
249#107×C61C2314yes—
250C4⋊C8×C61C2312yes—
251C4⋊C8×C61C2312yes—
252#103×C61C2314yes—
253#103×C61C2314yes—
254C23×D61C2×D411yescharacteristic
255C2×Q8×C61—21no—
256C2×Q8×C61—21no—
257C2×Q8×C61C2412yes—
258C2×Q8×C61C2412yes—
259C22×C4×C61C2×D411yescharacteristic
260C22×C4×C61C2×D411yescharacteristic
261C22×C4×C61C2411yescharacteristic
262C2×C22⋊D61—22no—
263C22×Dic61C2×D411yescharacteristic
264C22×Dic61C2×D411yescharacteristic
265C22×Dic61C2×D411yescharacteristic
266#11758226—24no—
267#11758226—24no—
268#11758226—44no—
269Q8×D61—24no—
270Q8×D61—24no—
271Q8×D61—44no—
272#11758222—44no—
273C2×D244—22no—
274C2×D244—22no—
275C2×D244—21no—
276C2×D244—21no—
277C2×D244C2412yes—
278C2×C4×D61—24no—
279C2×C4×D61—22no—
280C2×C4×D61—22no—
281C2×C4×D61—22no—
282C2×C4×D61—22no—
283C2×C4×D61—22no—
284C2×C4×D61—22no—
285C2×C4×D61—22no—
286C2×C4×D61—42no—
287C2×C4×D61C2×D411yescharacteristic
288C2×C4×D61C2×D411yescharacteristic
289C2×C4×D61C2×D411yescharacteristic
290C2×C4×D61C2×D411yescharacteristic
291C2×C4×D61C2×D411yescharacteristic
292C2×C4×D61C2×D411yescharacteristic
293C2×C4×D61C2×D411yescharacteristic
294C2×C4×D61C2×D411yescharacteristic
295C2×C4×D61C2×D411yescharacteristic
296C2×C4×D61C2×D411yescharacteristic
297C2×C4×D61C2411yescharacteristic
298C2×C4×D61C2411yescharacteristic
299C2×Dic122—21no—
300C2×Dic122—21no—
301C2×Dic122—22no—
302C2×Dic122—22no—
303C2×Dic122C2412yes—
304Q16×C61—44no—
305C2×C8×C61—42no—
306C2×C8×C61C2414yes—
307C4⋊C4×C61—21no—
308C4⋊C4×C61—21no—
309C4⋊C4×C61—21no—
310C4⋊C4×C61—21no—
311C4⋊C4×C61—21no—
312C4⋊C4×C61—21no—
313C4⋊C4×C61—22no—
314C4⋊C4×C61—22no—
315C4⋊C4×C61—22no—
316C4⋊C4×C61—22no—
317C4⋊C4×C61C2412yes—
318C4⋊C4×C61C2412yes—
319C22⋊C4×C61—22no—
320C22⋊C4×C61—22no—
321C42×C61—22no—
322C42×C61—22no—
323C42×C61C2×D411yescharacteristic
324C42×C61C2×D411yescharacteristic
325C42×C61C2411yescharacteristic
326C42×C61C2411yescharacteristic
327C22⋊Dic61—22no—
328#11758202—44no—
329#11758201—44no—
330#11758198—22no—
331#11758198—22no—
332#11758198—22no—
333#11758198—22no—
334#11758198—22no—
335#11758198—22no—
336#11758198—22no—
337#11758198—22no—
338#11758198—22no—
339#11758198—22no—
340C4⋊Dic61—21no—
341C4⋊Dic61—21no—
342C4⋊Dic61—21no—
343C4⋊Dic61—21no—
344C4⋊Dic61—22no—
345C4⋊Dic61—22no—
346C4⋊Dic61—22no—
347C4⋊Dic61—22no—
348C4⋊Dic61C2412yes—
349C4⋊Dic61C2412yes—
350#11758196—22no—
351#11758196—22no—
352#11758196—22no—
353#11758196—22no—
354#11758196—22no—
355#11758196—22no—
356#11758196—22no—
357#11758196—22no—
358#11758196—22no—
359#11758196—22no—
360C4×Dic61—22no—
361C4×Dic61—22no—
362C4×Dic61—22no—
363C4×Dic61—22no—
364C4×Dic61—22no—
365C4×Dic61C2×D411yescharacteristic
366C4×Dic61C2×D411yescharacteristic
367C4×Dic61C2×D411yescharacteristic
368C4×Dic61C2×D411yescharacteristic
369C4×Dic61C2×D411yescharacteristic
370C4×Dic61C2×D411yescharacteristic
371C4×Dic61C2×D411yescharacteristic
372C4×Dic61C2×D411yescharacteristic
373C4×Dic61C2×D411yescharacteristic
374C4×Dic61C2×D411yescharacteristic
375C4×Dic61C2411yescharacteristic
376C4×Dic61C2411yescharacteristic
377C2×#92418—42no—
378C2×#92418C2414yes—
379#11758190—44no—
380#11758189—28no—
381#11758189—44no—
382C23×C61C22×D411yescharacteristic
383C22×D61—22no—
384C22×D61—22no—
385C22×D61—22no—
386C22×D61—41no—
387C22×D61C22×D411yescharacteristic
388C22×D61C22×D411yescharacteristic
389Q8×C61—22no—
390Q8×C61—22no—
391Q8×C61—22no—
392Q8×C61—22no—
393Q8×C61—42no—
394Q8×C61—42no—
395C2×C4×C61—21no—
396C2×C4×C61—21no—
397C2×C4×C61—22no—
398C2×C4×C61—22no—
399C2×C4×C61—22no—
400C2×C4×C61—22no—
401C2×C4×C61—41no—
402C2×C4×C61#13714yescomplemented
403C2×C4×C61C22×D411yescharacteristic
404C2×C4×C61C22×D411yescharacteristic
405C2×C4×C61C22×D411yescharacteristic
406C2×C4×C61C22×D411yescharacteristic
407C2×C4×C61C22×D411yescharacteristic
408C2×C4×C61C2511yescharacteristic
409C22⋊D61—44no—
410C2×Dic61—22no—
411C2×Dic61—22no—
412C2×Dic61—22no—
413C2×Dic61—22no—
414C2×Dic61—22no—
415C2×Dic61—22no—
416C2×Dic61C22×D411yescharacteristic
417C2×Dic61C22×D411yescharacteristic
418C2×Dic61C22×D411yescharacteristic
419C2×Dic61C22×D411yescharacteristic
420C2×Dic61C22×D411yescharacteristic
421C2×Dic61C22×D411yescharacteristic
422D244—22no—
423D244—22no—
424D244—42no—
425D244—44no—
426D244—44no—
427D244—42no—
428C4×D61—22no—
429C4×D61—22no—
430C4×D61—22no—
431C4×D61—22no—
432C4×D61—22no—
433C4×D61—21no—
434C4×D61—21no—
435C4×D61—22no—
436C4×D61—22no—
437C4×D61—22no—
438C4×D61—41no—
439C4×D61—41no—
440C4×D61—44no—
441C4×D61—44no—
442C4×D61—44no—
443C4×D61—44no—
444C4×D61—44no—
445C4×D61H(5,𝔽2)12yes—
446C4×D612−1+412yes—
447Dic122—22no—
448Dic122—22no—
449Dic122—42no—
450Dic122—42no—
451Dic122—44no—
452Dic122—44no—
453C8×C61—24no—
454#92418—24no—
455#60918—611nomaximal, Sylow
456C22×C61—21no—
457C22×C61—21no—
458C22×C61C2×#13712yes—
459C22×C61C23×D411yescharacteristic
460C2×D61—21no—
461C2×D61—21no—
462C2×D61—21no—
463C2×D61—21no—
464C2×D61—21no—
465C2×D61—44no—
466C2×D61—42no—
467C2×D61—42no—
468C2×D61—42no—
469C2×D61#53712yes—
470C4×C61—21no—
471C4×C61—21no—
472C4×C61—21no—
473C4×C61—42no—
474C4×C61—42no—
475C4×C61—42no—
476C4×C61—42no—
477C4×C61C2×#13712yes—
478C4×C61C2×#13712yes—
479C4×C61C2×H(5,𝔽2)11yescharacteristic
480C4×C61C2×2−1+411yescharacteristic
481Dic61—21no—
482Dic61—21no—
483Dic61—21no—
484Dic61—21no—
485Dic61—42no—
486Dic61—42no—
487Dic61—42no—
488Dic61#53712yes—
489Dic61#57512yes—
490#3444—611no—
491C2×#533—611no—
492#3255—612no—
493#3254—612no—
494#3252—612no—
495#3252—612no—
496#3249—611no—
497#3249D6111yescharacteristic, complemented
498#3248—614no—
499#3246—611no—
500#3246—611no—
501#3079—612no—
502#3078—612no—
503#3056—614no—
504#3039—612no—
505#3037—612no—
506C2×#423—611no—
507C2×C61—22no—
508C2×C61C2×#53711yescharacteristic
509C2×C61C22×#13711yescharacteristic
510C2×C61C2×#57511yescharacteristic
511D61—22no—
512D61—41no—
513D61—82no—
514C2×#137—614no—
515C22×M16—612no—
516#533—611no—
517#533—611no—
518#533—611no—
519#533—611no—
520#533—612no—
521#533—612no—
522#533—611no—
523#533—1221no—
524#533—1221no—
525#533—1221no—
526#533—1221no—
527#533C2×D6111yescharacteristic
528#533C2×D6111yescharacteristic
529#532—611no—
530#532—611no—
531#532—611no—
532C2×C4⋊Q8—611no—
533C2×C4⋊Q8—611no—
534#529—612no—
535#529—612no—
536#529—1221no—
537#529—1221no—
538#529—1221no—
539#529—1221no—
540C2×#125—1221no—
541#525—612no—
542#525—1221no—
543#525—1221no—
544C2×C22⋊Q8—612no—
545C2×C22⋊Q8—1221no—
546C4×#41—612no—
547C4×#41—1221no—
548C4×#41—1221no—
549C2×C4×Q8—612no—
550C2×C4×Q8—1221no—
551C2×#117—1221no—
552C22×C42—611no—
553#479—614no—
554#479—614no—
555#477—612no—
556#477—612no—
557#477C2×D6112yescomplemented
558#477C2×D6112yescomplemented
559#476—612no—
560#476—612no—
561#475—612no—
562#475—612no—
563#475—614no—
564#474—614no—
565#470—614no—
566#470—614no—
567#468—614no—
568#468—614no—
569#467—614no—
570#467C2×D6114yes—
571#465—614no—
572#465—614no—
573#464—614no—
574#464—614no—
575#462—614no—
576#462—612no—
577#462—612no—
578#462C2×D6112yescomplemented
579#462C2×D6112yescomplemented
580#461—612no—
581#461—612no—
582#461—614no—
583#460—612no—
584#460—612no—
585#428—614no—
586#423—612no—
587#423—612no—
588#423—612no—
589#423—612no—
590C2×C4⋊C8—612no—
591C2×C4⋊C8—611no—
592C2×C4⋊C8C2×D6111yescharacteristic
593#419—614no—
594#417—614no—
595C61#6091811yescharacteristic, complemented, Sylow
596C2×#41—612no—
597C2×#41—1221no—
598C2×#41—1221no—
599C22×Q8—612no—
600C22×Q8—1221no—
601C23×C4—611no—
602C23×C4—611no—
603C23×C4—611no—
604#137—2448no—
605C2×Q16—614no—
606C2×Q16C22×D6114yes—
607C2×SD16—614no—
608C2×SD16—614no—
609C2×M16—614no—
610C2×M16—614no—
611C2×M16—2444no—
612C22×C8—612no—
613C22×C8C22×D6112yes—
614C4⋊Q8—612no—
615C4⋊Q8—612no—
616C4⋊Q8—611no—
617C4⋊Q8—611no—
618C4⋊Q8—611no—
619C4⋊Q8—1221no—
620C4⋊Q8—1221no—
621C4⋊Q8—1221no—
622C4⋊Q8—1221no—
623C4⋊Q8C22×D6111yescharacteristic
624C4⋊Q8C22×D6111yescharacteristic
625C4⋊Q8C22×D6111yescharacteristic
626C4⋊Q8C22×D6111yescharacteristic
627#127—611no—
628#126—1222no—
629#126—1222no—
630#125—21no—
631#125—21no—
632#125—612no—
633#125—1222no—
634#125—1222no—
635#125—1221no—
636#125—1221no—
637#125—1221no—
638#125—1221no—
639#124—612no—
640#124—1221no—
641#124—1221no—
642#123—1222no—
643#123—1222no—
644#123—1222no—
645C22⋊Q8—21no—
646C22⋊Q8—21no—
647C22⋊Q8—612no—
648C22⋊Q8—612no—
649C22⋊Q8—612no—
650C22⋊Q8—612no—
651C22⋊Q8—1222no—
652C22⋊Q8—1222no—
653C22⋊Q8—1222no—
654C22⋊Q8—1222no—
655C22⋊Q8—1221no—
656C22⋊Q8—1221no—
657C22⋊Q8—1221no—
658C22⋊Q8—1221no—
659C22⋊Q8—1221no—
660C22⋊Q8—1221no—
661C22⋊Q8C22×D6112yes—
662C22⋊Q8C22×D6112yes—
663#121—612no—
664#121—612no—
665#121—1221no—
666#121—1221no—
667#121—1221no—
668#121—1221no—
669#120—1222no—
670C4×Q8—21no—
671C4×Q8—21no—
672C4×Q8—612no—
673C4×Q8—612no—
674C4×Q8—612no—
675C4×Q8—612no—
676C4×Q8—1222no—
677C4×Q8—1222no—
678C4×Q8—1222no—
679C4×Q8—1222no—
680C4×Q8—1221no—
681C4×Q8—1221no—
682C4×Q8—1221no—
683C4×Q8—1221no—
684C4×Q8—1221no—
685C4×Q8—1221no—
686C4×Q8C22×D6112yes—
687C4×Q8C22×D6112yes—
688C4×D4—612no—
689C4×D4—612no—
690C4×D4—1222no—
691C4×D4—1222no—
692C4×D4—1221no—
693C4×D4—1221no—
694C4×D4—1221no—
695C4×D4—1222no—
696C4×D4—1222no—
697C4×D4—1222no—
698C4×D4—1222no—
699C4×D4—1221no—
700#117—21no—
701#117—21no—
702#117—612no—
703#117—1222no—
704#117—1222no—
705#117—1222no—
706#117—1222no—
707#117—1222no—
708#117—1221no—
709#117—1221no—
710#117—1221no—
711#117—1221no—
712C2×C4⋊C4—612no—
713C2×C4⋊C4—1221no—
714C2×C4⋊C4—1221no—
715C2×C4⋊C4—1222no—
716C2×C4⋊C4—1222no—
717C2×C4⋊C4—1221no—
718C2×C22⋊C4—1222no—
719C2×C42—611no—
720C2×C42—611no—
721C2×C42—611no—
722C2×C42—611no—
723C2×C42—611no—
724C2×C42—611no—
725C2×C42—611no—
726C2×C42—611no—
727C2×C42—611no—
728C2×C42—611no—
729C2×C42—611no—
730C2×C42—1222no—
731C2×C42—1222no—
732C2×C42C22×D6111yescharacteristic
733#107—614no—
734#107C22×D6114yes—
735#106—614no—
736#106—614no—
737C4⋊C8—614no—
738C4⋊C8—614no—
739C4⋊C8—612no—
740C4⋊C8—612no—
741C4⋊C8C22×D6112yes—
742C4⋊C8C22×D6112yes—
743#103—614no—
744#103—614no—
745#103—614no—
746#103—614no—
747#103C22×D6114yes—
748#103C22×D6114yes—
749#102—614no—
750#102—614no—
751C24—611no—
752#41—1224no—
753#41—1224no—
754#41—2444no—
755#41—2444no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—612no—
759C2×Q8—1222no—
760C2×Q8—1222no—
761C2×Q8—1224no—
762C2×Q8—1224no—
763C2×Q8—1221no—
764C2×Q8—1221no—
765C2×Q8—2444no—
766C2×Q8C23×D6112yes—
767C2×Q8C23×D6112yes—
768C2×D4—612no—
769C2×D4—1222no—
770C2×D4—1222no—
771C2×D4—1222no—
772C2×D4—1221no—
773C2×D4—1221no—
774C22×C4—611no—
775C22×C4—611no—
776C22×C4—611no—
777C22×C4—611no—
778C22×C4—611no—
779C22×C4—611no—
780C22×C4—611no—
781C22×C4—611no—
782C22×C4—611no—
783C22×C4—611no—
784C22×C4—611no—
785C22×C4—611no—
786C22×C4—611no—
787C22×C4—611no—
788C22×C4—611no—
789C22×C4—1222no—
790C22×C4—1222no—
791C22×C4—1222no—
792C22×C4—1222no—
793C22×C4—1222no—
794C22×C4—1222no—
795C22×C4—1224no—
796C22×C4—1222no—
797C22×C4—2442no—
798C22×C4D4×D6111yescharacteristic
799C22×C4D4×D6111yescharacteristic
800C22×C4C23×D6111yescharacteristic
801Q16—44no—
802Q16—2444no—
803SD16—2444no—
804SD16—2444no—
805M16—1228no—
806M16—2444no—
807C2×C8—42no—
808C2×C8—614no—
809C2×C8—2442no—
810C2×C8C23×D6114yes—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—22no—
815C4⋊C4—22no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—22no—
820C4⋊C4—22no—
821C4⋊C4—612no—
822C4⋊C4—612no—
823C4⋊C4—1222no—
824C4⋊C4—1222no—
825C4⋊C4—1222no—
826C4⋊C4—1222no—
827C4⋊C4—1222no—
828C4⋊C4—1222no—
829C4⋊C4—1222no—
830C4⋊C4—1222no—
831C4⋊C4—1222no—
832C4⋊C4—1222no—
833C4⋊C4—1222no—
834C4⋊C4—1222no—
835C4⋊C4—1222no—
836C4⋊C4—1222no—
837C4⋊C4—1221no—
838C4⋊C4—1221no—
839C4⋊C4—1221no—
840C4⋊C4—1221no—
841C4⋊C4C23×D6112yes—
842C4⋊C4C23×D6112yes—
843C22⋊C4—22no—
844C22⋊C4—22no—
845C22⋊C4—1222no—
846C22⋊C4—1222no—
847C22⋊C4—1222no—
848C22⋊C4—1222no—
849C22⋊C4—1222no—
850C22⋊C4—1222no—
851C22⋊C4—1222no—
852C22⋊C4—1222no—
853C22⋊C4—1222no—
854C22⋊C4—1222no—
855C22⋊C4—1222no—
856C42—22no—
857C42—22no—
858C42—611no—
859C42—611no—
860C42—611no—
861C42—611no—
862C42—611no—
863C42—611no—
864C42—611no—
865C42—611no—
866C42—611no—
867C42—611no—
868C42—611no—
869C42—611no—
870C42—1222no—
871C42—1222no—
872C42—1222no—
873C42—1222no—
874C42—1222no—
875C42D4×D6111yescharacteristic
876C42D4×D6111yescharacteristic
877C42C23×D6111yescharacteristic
878C42C23×D6111yescharacteristic
879C23—611no—
880C23—611no—
881C23—1222no—
882C23—1222no—
883C23—1222no—
884C23—2441no—
885C23C2×D4×D6111yescharacteristic
886Q8—22no—
887Q8—22no—
888Q8—22no—
889Q8—22no—
890Q8—42no—
891Q8—42no—
892Q8—1222no—
893Q8—1222no—
894Q8—2442no—
895Q8—2444no—
896Q8—2444no—
897Q8—2442no—
898D4—1222no—
899D4—1222no—
900D4—2442no—
901D4—2444no—
902D4—2444no—
903D4—2444no—
904D4—2442no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—41no—
912C2×C4—611no—
913C2×C4—611no—
914C2×C4—612no—
915C2×C4—612no—
916C2×C4—611no—
917C2×C4—611no—
918C2×C4—611no—
919C2×C4—611no—
920C2×C4—1222no—
921C2×C4—1222no—
922C2×C4—1222no—
923C2×C4—1222no—
924C2×C4—1222no—
925C2×C4—1222no—
926C2×C4—1222no—
927C2×C4—1222no—
928C2×C4—1222no—
929C2×C4—1222no—
930C2×C4—1222no—
931C2×C4—1221no—
932C2×C4—1221no—
933C2×C4—1222no—
934C2×C4—1222no—
935C2×C4—1222no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4—2444no—
939C2×C4—2444no—
940C2×C4—2444no—
941C2×C4—2444no—
942C2×C4—2444no—
943C2×C4#1451980914yescomplemented
944C2×C4C2×D4×D6111yescharacteristic
945C2×C4C2×D4×D6111yescharacteristic
946C2×C4C2×D4×D6111yescharacteristic
947C2×C4C2×D4×D6111yescharacteristic
948C2×C4C2×D4×D6111yescharacteristic
949C2×C4C24×D6111yescharacteristic
950C8—24no—
951C8—1224no—
952C22—21no—
953C22—21no—
954C22—612no—
955C22—1221no—
956C22—1221no—
957C22—1221no—
958C22—1221no—
959C22—1221no—
960C22—2444no—
961C22—2442no—
962C22—2442no—
963C22—2442no—
964C22C2×#1451980912yes—
965C22C22×D4×D6111yescharacteristic
966C4—21no—
967C4—21no—
968C4—21no—
969C4—42no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—612no—
974C4—612no—
975C4—1221no—
976C4—1221no—
977C4—1221no—
978C4—1221no—
979C4—2442no—
980C4—2442no—
981C4—2442no—
982C4C2×#1451980912yes—
983C4C2×#1451980912yes—
984C4H(5,𝔽2)×D6111yescharacteristic
985C42−1+4×D6111yescharacteristic
986C2—22no—
987C2—1222no—
988C2—4882no—
989C2—2441no—
990C2#537×D6111yescharacteristic
991C2C22×#1451980911yescharacteristic
992C2#575×D6111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3249C2
socleC22×C61C23×D4
prime radical#21459116C2
hypercenter#3249D61
hypocenterC61#60918
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3249

Complements

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

NH ≅ G/Ntype
2. #533×D61C2semidirect
3. #21457211C2semidirect
4. #21457205C2semidirect
5. #21457195C2semidirect
6. #21457190C2semidirect
7. #21457161C2semidirect
8. #21457151C2semidirect
9. #21457136C2semidirect
10. #21457131C2semidirect
11. #21455633C2semidirect
12. #21455625C2semidirect
13. #21455446C2semidirect
14. #21455303C2semidirect
15. #21455292C2semidirect
16. C2×#16839784C2semidirect
17. C61×#3249C2semidirect
55. #16840068C22semidirect
56. #16840067C22semidirect
57. #16840057C22semidirect
58. #16840054C22semidirect
59. #16840053C22semidirect
60. #16840049C22semidirect
61. #16840048C22semidirect
62. #16840047C22semidirect
63. #16840045C22semidirect
64. #16840041C22semidirect
72. #16839987C22semidirect
73. #16839986C22semidirect
74. #16839972C22semidirect
75. #16839970C22semidirect
76. #16839969C22semidirect
77. #16839968C22semidirect
78. #16839966C22semidirect
79. #16839964C22semidirect
80. #16839963C22semidirect
81. #16839962C22semidirect
93. C61×#477C22semidirect
94. C61×#477C22semidirect
96. C61×#462C22semidirect
97. C61×#462C22semidirect
402. C2×C4×C61#137semidirect
497. #3249D61semidirect
557. #477C2×D61semidirect
558. #477C2×D61semidirect
578. #462C2×D61semidirect
579. #462C2×D61semidirect
595. C61#60918semidirect
943. C2×C4#14519809semidirect

Maximal subgroups

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

subgroupindex
#214591162
#533×D612
#214572112
#214572052
#214571952
#214571902
#214571612
#214571512
#214571362
#214571312
#214556332
#214556252
#214554462
#214553032
#214552922
C2×#168397842
C61×#32492
#6091861