Finite Group Databasebeta

← #30553015

Subgroups — #30553015

Order 15616.

2168 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459115C211yesmaximal, characteristic, complemented
2C2×#16840312C211yesmaximal, characteristic, complemented
3#21457207C212yesmaximal, complemented
4#21457200C212yesmaximal, complemented
5#21457182C214yesmaximal, complemented
6#21457146C214yesmaximal, complemented
7#21457136C212yesmaximal, complemented
8#21457129C212yesmaximal, complemented
9#21455635C212yesmaximal, complemented
10#21455618C212yesmaximal, complemented
11#21455438C214yesmaximal, complemented
12#21455300C212yesmaximal, complemented
13#21455285C212yesmaximal, complemented
14C2×C61×#423C211yesmaximal, characteristic, complemented
15C22×#11758222—21no—
16C2×#14519805C2214yes—
17#16840319C2211yescharacteristic
18#16840319C2211yescharacteristic, complemented
19#16840319C2211yescharacteristic, complemented
20#16840312—21no—
21#16840312—21no—
22#16840312—21no—
23#16840312—21no—
24#16840312C2212yes—
25#16840312C2212yes—
26#16840312C2212yes—
27#16840312C2212yes—
28#16840312C2211yescharacteristic
29#16840312C2211yescharacteristic, complemented
30#16840312C2211yescharacteristic, complemented
31C2×#14519777C2211yescharacteristic
32C2×#14519774C2211yescharacteristic
33#16840296—21no—
34#16840296—21no—
35#16840296—21no—
36#16840296—21no—
37#16840296C2212yescomplemented
38#16840296C2212yescomplemented
39C2×#14519765—21no—
40#16840273—21no—
41#16840273—21no—
42#16840273C2212yes—
43C2×#14519751—21no—
44C2×#14519751C2212yes—
45C4×#11758222—21no—
46C4×#11758222—21no—
47C4×#11758222C2212yes—
48C2×C4×D244—21no—
49C2×C4×D244C2212yes—
50#16840063C2218yescomplemented
51#16840058C2214yescomplemented
52#16840053C2214yescomplemented
53#16840053C2214yescomplemented
54#16840048C2214yescomplemented
55#16840043C2214yescomplemented
56#16840043C2214yescomplemented
57#16840015C2218yescomplemented
58#16840008C2218yescomplemented
59#16839998C2218yescomplemented
60#16839991C2218yescomplemented
61#16839978C2218yescomplemented
62#16839968C2214yescomplemented
63#16839963C2214yescomplemented
64#16839963C2214yescomplemented
65#16839958C2214yescomplemented
66#16839958C2214yescomplemented
67#16839958C2214yescomplemented
68#16839804C2214yes—
69#16839768C2214yes—
70#16839764C2214yes—
71C22×M16×C61C2212yes—
72C22×C42×C61C2211yescharacteristic
73C61×#423C2212yes—
74C61×#423C2212yes—
75C61×#423C2212yescomplemented
76C61×#423C2212yescomplemented
77C2×C4⋊C8×C61C2212yescomplemented
78C2×C4⋊C8×C61C2212yescomplemented
79C2×#11758222—21no—
80C2×#11758222—21no—
81C2×#11758222—22no—
82C2×#11758222—22no—
83C2×#11758222—22no—
84C2×#11758222—22no—
85C2×#11758222—48no—
86C2×#11758222C2312yes—
87C22×Dic122—21no—
88C22×D244—21no—
89C22×D244—21no—
90C22×D244C2312yes—
91C22×C22⋊D61—22no—
92C22×C4×D61—22no—
93#14519805—48no—
94C2×#11758190C2318yes—
95C2×D488C2318yes—
96#14519777—21no—
97#14519777—21no—
98#14519777C2311yescharacteristic
99#14519777C2311yescharacteristic
100#14519777C2312yes—
101#14519777C2312yes—
102#14519777C2311yescharacteristic
103#14519774—21no—
104#14519774—21no—
105#14519774C2311yescharacteristic
106#14519774C2312yes—
107#14519774C2312yes—
108#14519771—22no—
109#14519771—22no—
110#14519769—21no—
111#14519769—21no—
112#14519769C2312yes—
113#14519765—22no—
114#14519765—22no—
115#14519765—22no—
116#14519765—22no—
117#14519765—21no—
118#14519765—21no—
119#14519765C2312yes—
120#14519760—22no—
121#14519760—22no—
122#14519760—22no—
123#14519756—21no—
124#14519756—21no—
125#14519756—21no—
126#14519756—21no—
127#14519756C2312yes—
128#14519756C2312yes—
129#14519751—22no—
130#14519751—22no—
131#14519751—22no—
132#14519751—22no—
133#14519751—22no—
134#14519751—22no—
135#14519751—21no—
136#14519751—21no—
137#14519751—21no—
138#14519751—21no—
139#14519751C2314yes—
140#14519751C2312yes—
141#14519751C2314yes—
142#14519751C2312yes—
143#14519746—22no—
144C4×Dic122—21no—
145C4×Dic122—21no—
146C4×Dic122—21no—
147C4×Dic122—21no—
148C4×Dic122C2312yes—
149C4×Dic122C2312yes—
150C4×D244—22no—
151C4×D244—22no—
152C4×D244—22no—
153C4×D244—22no—
154C4×D244—22no—
155C4×D244—22no—
156C4×D244—21no—
157C4×D244—21no—
158C4×D244—21no—
159C4×D244—21no—
160C4×D244C2312yes—
161C4×D244C2312yes—
162C4×D244C2314yes—
163C4×D244C2314yes—
164C4×C22⋊D61—22no—
165C4×C22⋊D61—22no—
166C4×C22⋊D61—22no—
167C4×C22⋊D61—22no—
168C4×C22⋊D61—22no—
169C4×C22⋊D61—22no—
170#14519736—21no—
171#14519736—21no—
172#14519736C2312yes—
173#14519734—22no—
174#14519734—22no—
175#14519734—22no—
176C2×C4⋊Dic61—21no—
177C2×C4⋊Dic61C2312yes—
178C2×#11758198—22no—
179C2×#11758198—22no—
180C42×D61—22no—
181#14519711C2318yes—
182#14519709C2318yes—
183#14519702C2318yes—
184#14519699C2318yes—
185#14519699C2318yes—
186#14519699C2318yes—
187C23×C4×C61D411yescharacteristic
188C23×C4×C61D411yescharacteristic
189C23×C4×C61C2311yescharacteristic
190C2×M16×C61—44no—
191C2×M16×C61C2314yes—
192C2×M16×C61C2314yes—
193C22×C8×C61C2314yes—
194C2×C42×C61D411yescharacteristic
195C2×C42×C61D411yescharacteristic
196C2×C42×C61D411yescharacteristic
197C2×C42×C61D411yescharacteristic
198C2×C42×C61D411yescharacteristic
199C2×C42×C61D411yescharacteristic
200C2×C42×C61C2311yescharacteristic
201C2×C42×C61C2311yescharacteristic
202C2×C42×C61C2311yescharacteristic
203C2×C42×C61C2311yescharacteristic
204C2×C42×C61C2311yescharacteristic
205C2×C42×C61C2311yescharacteristic
206C4⋊C8×C61C2314yes—
207C4⋊C8×C61C2314yes—
208C4⋊C8×C61C2314yes—
209C4⋊C8×C61C2314yes—
210C24×C61C2×D411yescharacteristic
211C23×D61—22no—
212C22×C4×C61—24no—
213C22×C4×C61—22no—
214C22×C4×C61—22no—
215C22×C4×C61—42no—
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2×D411yescharacteristic
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2411yescharacteristic
232C22×C4×C61C2411yescharacteristic
233C22×C4×C61C2411yescharacteristic
234C2×C22⋊D61—24no—
235C2×C22⋊D61—24no—
236C2×C22⋊D61—22no—
237C2×C22⋊D61—22no—
238C2×C22⋊D61—22no—
239C2×C22⋊D61—48no—
240C22×Dic61—22no—
241#11758222—24no—
242#11758222—24no—
243#11758222—44no—
244#11758222—48no—
245#11758222—48no—
246#11758222—48no—
247#11758222—44no—
248#11758222—48no—
249C2×D244—24no—
250C2×D244—24no—
251C2×D244—22no—
252C2×D244—22no—
253C2×D244—22no—
254C2×D244—22no—
255C2×D244—22no—
256C2×D244—21no—
257C2×D244—21no—
258C2×D244—44no—
259C2×D244—44no—
260C2×D244C2414yes—
261C2×D244C2412yes—
262C2×C4×D61—24no—
263C2×C4×D61—24no—
264C2×C4×D61—22no—
265C2×C4×D61—22no—
266C2×C4×D61—22no—
267C2×C4×D61—48no—
268C2×Dic122—22no—
269C2×Dic122—22no—
270C2×Dic122—21no—
271C2×Dic122—21no—
272C2×Dic122—44no—
273C2×Dic122C2412yes—
274M16×C61—28no—
275M16×C61—44no—
276C2×C8×C61—44no—
277C2×C8×C61C2418yes—
278C42×C61C2×D411yescharacteristic
279C42×C61C2×D411yescharacteristic
280C42×C61C2×D411yescharacteristic
281C42×C61C2×D411yescharacteristic
282C42×C61C2×D411yescharacteristic
283C42×C61C2×D411yescharacteristic
284C42×C61C2×D411yescharacteristic
285C42×C61C2×D411yescharacteristic
286C42×C61C2×D411yescharacteristic
287C42×C61C2×D411yescharacteristic
288C42×C61C2×D411yescharacteristic
289C42×C61C2×D411yescharacteristic
290C42×C61C2411yescharacteristic
291C42×C61C2411yescharacteristic
292C42×C61C2411yescharacteristic
293C42×C61C2411yescharacteristic
294C22⋊Dic61—22no—
295C22⋊Dic61—22no—
296C22⋊Dic61—22no—
297#11758198—24no—
298#11758198—24no—
299#11758198—24no—
300#11758198—24no—
301#11758198—22no—
302#11758198—22no—
303#11758198—22no—
304#11758198—22no—
305#11758198—22no—
306#11758198—22no—
307C4⋊Dic61—22no—
308C4⋊Dic61—22no—
309C4⋊Dic61—22no—
310C4⋊Dic61—21no—
311C4⋊Dic61—21no—
312C4⋊Dic61—21no—
313C4⋊Dic61—21no—
314C4⋊Dic61C2412yes—
315C4⋊Dic61C2412yes—
316C4⋊Dic61C2414yes—
317#11758196—22no—
318#11758196—22no—
319#11758196—22no—
320#11758196—22no—
321#11758196—22no—
322#11758196—22no—
323C4×Dic61—22no—
324C4×Dic61—22no—
325C4×Dic61—22no—
326D488—48no—
327#11758190—48no—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61—41no—
331C23×C61C22×D411yescharacteristic
332C23×C61C22×D411yescharacteristic
333C23×C61C22×D411yescharacteristic
334C22×D61—22no—
335C22×D61—24no—
336C22×D61—44no—
337C22×D61—44no—
338C22×D61—44no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—21no—
353C2×C4×C61—21no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61AGL(1,ℤ/8)14yescomplemented
358C2×C4×C61C22×D411yescharacteristic
359C2×C4×C61C22×D411yescharacteristic
360C2×C4×C61C22×D411yescharacteristic
361C2×C4×C61C22×D411yescharacteristic
362C2×C4×C61C22×D411yescharacteristic
363C2×C4×C61C22×D411yescharacteristic
364C2×C4×C61C22×D411yescharacteristic
365C2×C4×C61C22×D411yescharacteristic
366C2×C4×C61C22×D411yescharacteristic
367C2×C4×C61C22×D411yescharacteristic
368C2×C4×C61C22×D411yescharacteristic
369C2×C4×C61H(5,𝔽2)12yes—
370C2×C4×C612−1+412yes—
371C2×C4×C61C2511yescharacteristic
372C22⋊D61—48no—
373C22⋊D61—44no—
374C22⋊D61—44no—
375C22⋊D61—48no—
376C22⋊D61—44no—
377C2×Dic61—22no—
378C2×Dic61—22no—
379C2×Dic61—22no—
380C2×Dic61—24no—
381C2×Dic61—44no—
382D244—24no—
383D244—22no—
384D244—24no—
385D244—22no—
386D244—44no—
387D244—44no—
388D244—42no—
389D244—44no—
390D244—44no—
391D244—42no—
392D244—44no—
393C4×D61—48no—
394C4×D61—44no—
395C4×D61—48no—
396C4×D61—44no—
397C4×D61—44no—
398Dic122—22no—
399Dic122—22no—
400Dic122—44no—
401Dic122—42no—
402Dic122—44no—
403Dic122—42no—
404C8×C61—28no—
405#60916—611nomaximal, Sylow
406C22×C61—21no—
407C22×C61—21no—
408C22×C61—21no—
409C22×C61—21no—
410C22×C61—21no—
411C22×C61—21no—
412C22×C61—21no—
413C22×C61—44no—
414C22×C61#53712yes—
415C22×C61C2×AGL(1,ℤ/8)12yes—
416C22×C61C23×D411yescharacteristic
417C2×D61—42no—
418C2×D61—44no—
419C2×D61—44no—
420C2×D61—42no—
421C2×D61—42no—
422C2×D61—44no—
423C2×D61—88no—
424C4×C61—21no—
425C4×C61—21no—
426C4×C61—21no—
427C4×C61—21no—
428C4×C61—21no—
429C4×C61—21no—
430C4×C61—21no—
431C4×C61#53712yes—
432C4×C61C2×AGL(1,ℤ/8)12yes—
433C4×C61C2×AGL(1,ℤ/8)12yes—
434C4×C61#57512yes—
435C4×C61C2×H(5,𝔽2)11yescharacteristic
436C4×C61C2×2−1+411yescharacteristic
437Dic61—42no—
438Dic61—44no—
439Dic61—42no—
440Dic61—42no—
441#3444—611no—
442C2×#532—611no—
443#3254—612no—
444#3253—612no—
445#3251—614no—
446#3247—614no—
447#3246—612no—
448#3245—612no—
449#3079—612no—
450#3077—612no—
451#3055—614no—
452#3038—612no—
453#3036—612no—
454C2×#423D6111yescharacteristic, complemented
455C2×C61—22no—
456C2×C61—22no—
457C2×C61—41no—
458C2×C61C2×#53711yescharacteristic
459C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
460C2×C61C2×#57511yescharacteristic
461D61—82no—
462D61—84no—
463C22×#41—1221no—
464C2×AGL(1,ℤ/8)—614no—
465C22×M16C2×D6112yes—
466#533—611no—
467#533—611no—
468#533—611no—
469#532—612no—
470#532—612no—
471#532—612no—
472#532—612no—
473#532—611no—
474#532—611no—
475#532—611no—
476#532—1221no—
477#532—1221no—
478#532—1221no—
479#532—1221no—
480C2×C4⋊Q8—611no—
481C2×#127—611no—
482#529—612no—
483#529—612no—
484#529—1221no—
485#529—1221no—
486#529—1221no—
487#529—1221no—
488C2×#124—1221no—
489#525—612no—
490#525—1221no—
491#525—1221no—
492C2×#121—612no—
493C2×#121—1221no—
494C4×#41—612no—
495C4×#41—1221no—
496C4×#41—1221no—
497C2×C4×D4—612no—
498C2×C4×D4—1221no—
499C22×C42C2×D6111yescharacteristic
500#478—618no—
501#477—614no—
502#476—614no—
503#476—614no—
504#475—614no—
505#474—614no—
506#474—614no—
507#469—618no—
508#468—618no—
509#466—618no—
510#465—618no—
511#463—618no—
512#461—614no—
513#460—614no—
514#460—614no—
515#459—614no—
516#459—614no—
517#459—614no—
518#428—614no—
519#423C2×D6112yes—
520#423C2×D6112yes—
521#423C2×D6112yescomplemented
522#423C2×D6112yescomplemented
523C2×C4⋊C8C2×D6112yescomplemented
524C2×C4⋊C8C2×D6112yescomplemented
525#418—614no—
526#417—614no—
527C61#6091611yescharacteristic, complemented, Sylow
528C2×#41—612no—
529C2×#41—1221no—
530C2×#41—1221no—
531C2×#41—1222no—
532C2×#41—1222no—
533C2×#41—1222no—
534C2×#41—1222no—
535C2×#41—2448no—
536C22×Q8—1221no—
537C22×D4—612no—
538C22×D4—1222no—
539C22×D4—1221no—
540C22×D4—1221no—
541C23×C4—1222no—
542C23×C4D24411yescharacteristic
543C23×C4D24411yescharacteristic
544C23×C4C22×D6111yescharacteristic
545AGL(1,ℤ/8)—2448no—
546C2×SD16—618no—
547C2×D8—618no—
548C2×M16—44no—
549C2×M16C22×D6114yes—
550C2×M16C22×D6114yes—
551C22×C8C22×D6114yes—
552C4⋊Q8—612no—
553C4⋊Q8—612no—
554C4⋊Q8—611no—
555C4⋊Q8—611no—
556C4⋊Q8—611no—
557C4⋊Q8—1221no—
558C4⋊Q8—1221no—
559#127—612no—
560#127—612no—
561#127—611no—
562#127—1221no—
563#127—1221no—
564#126—1222no—
565#126—1222no—
566#125—612no—
567#125—1221no—
568#125—1221no—
569#124—612no—
570#124—1222no—
571#124—1222no—
572#124—1222no—
573#124—1222no—
574#124—1221no—
575#124—1221no—
576#123—1222no—
577#123—1222no—
578#123—1222no—
579C22⋊Q8—612no—
580C22⋊Q8—612no—
581C22⋊Q8—1221no—
582C22⋊Q8—1221no—
583C22⋊Q8—1221no—
584C22⋊Q8—1221no—
585#121—614no—
586#121—614no—
587#121—612no—
588#121—612no—
589#121—1222no—
590#121—1222no—
591#121—1222no—
592#121—1222no—
593#121—1222no—
594#121—1222no—
595#121—1221no—
596#121—1221no—
597#121—1221no—
598#121—1221no—
599#120—1222no—
600C4×Q8—612no—
601C4×Q8—612no—
602C4×Q8—1221no—
603C4×Q8—1221no—
604C4×Q8—1221no—
605C4×Q8—1221no—
606C4×D4—614no—
607C4×D4—614no—
608C4×D4—612no—
609C4×D4—612no—
610C4×D4—1222no—
611C4×D4—1222no—
612C4×D4—1222no—
613C4×D4—1222no—
614C4×D4—1222no—
615C4×D4—1222no—
616C4×D4—1222no—
617C4×D4—1222no—
618C4×D4—1222no—
619C4×D4—1222no—
620C4×D4—1222no—
621C4×D4—1222no—
622C4×D4—1221no—
623C4×D4—1221no—
624C4×D4—1221no—
625C4×D4—1221no—
626#117—612no—
627#117—1221no—
628#117—1221no—
629#117—1222no—
630#117—1222no—
631#117—1222no—
632C2×C4⋊C4—612no—
633C2×C4⋊C4—1221no—
634C2×C22⋊C4—1222no—
635C2×C22⋊C4—1222no—
636C2×C42—1222no—
637C2×C42D24411yescharacteristic
638C2×C42D24411yescharacteristic
639C2×C42D24411yescharacteristic
640C2×C42D24411yescharacteristic
641C2×C42D24411yescharacteristic
642C2×C42D24411yescharacteristic
643C2×C42C22×D6111yescharacteristic
644C2×C42C22×D6111yescharacteristic
645C2×C42C22×D6111yescharacteristic
646C2×C42C22×D6111yescharacteristic
647C2×C42C22×D6111yescharacteristic
648C2×C42C22×D6111yescharacteristic
649#107—618no—
650#106—618no—
651C4⋊C8C22×D6114yes—
652C4⋊C8C22×D6114yes—
653C4⋊C8C22×D6114yes—
654C4⋊C8C22×D6114yes—
655#103—618no—
656#102—618no—
657#102—618no—
658#102—618no—
659C24—1222no—
660C24C2×D24411yescharacteristic
661#41—1224no—
662#41—1224no—
663#41—2448no—
664#41—2448no—
665#41—2448no—
666#41—2444no—
667#41—2448no—
668#41—2444no—
669C2×Q8—612no—
670C2×Q8—1221no—
671C2×Q8—1221no—
672C2×Q8—1222no—
673C2×Q8—1222no—
674C2×Q8—2444no—
675C2×D4—612no—
676C2×D4—614no—
677C2×D4—1222no—
678C2×D4—1222no—
679C2×D4—1222no—
680C2×D4—1224no—
681C2×D4—1224no—
682C2×D4—1221no—
683C2×D4—1221no—
684C2×D4—1222no—
685C2×D4—1222no—
686C2×D4—1222no—
687C2×D4—1222no—
688C2×D4—1222no—
689C2×D4—1224no—
690C2×D4—1224no—
691C2×D4—2444no—
692C2×D4—2444no—
693C2×D4—2448no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—24no—
697C22×C4—42no—
698C22×C4—1222no—
699C22×C4—1222no—
700C22×C4—1222no—
701C22×C4—1222no—
702C22×C4—1224no—
703C22×C4—1224no—
704C22×C4—2448no—
705C22×C4C2×D24411yescharacteristic
706C22×C4C2×D24411yescharacteristic
707C22×C4C2×D24411yescharacteristic
708C22×C4C2×D24411yescharacteristic
709C22×C4C2×D24411yescharacteristic
710C22×C4C2×D24411yescharacteristic
711C22×C4C2×D24411yescharacteristic
712C22×C4C2×D24411yescharacteristic
713C22×C4C2×D24411yescharacteristic
714C22×C4C2×D24411yescharacteristic
715C22×C4C2×D24411yescharacteristic
716C22×C4C2×D24411yescharacteristic
717C22×C4C2×D24411yescharacteristic
718C22×C4C2×D24411yescharacteristic
719C22×C4C2×D24411yescharacteristic
720C22×C4C23×D6111yescharacteristic
721C22×C4C23×D6111yescharacteristic
722C22×C4C23×D6111yescharacteristic
723SD16—2448no—
724D8—2448no—
725M16—28no—
726M16—44no—
727C2×C8—44no—
728C2×C8C23×D6118yes—
729C4⋊C4—612no—
730C4⋊C4—612no—
731C4⋊C4—614no—
732C4⋊C4—1222no—
733C4⋊C4—1222no—
734C4⋊C4—1222no—
735C4⋊C4—1222no—
736C4⋊C4—1222no—
737C4⋊C4—1222no—
738C4⋊C4—1222no—
739C4⋊C4—1222no—
740C4⋊C4—1222no—
741C4⋊C4—1221no—
742C4⋊C4—1221no—
743C4⋊C4—1221no—
744C4⋊C4—1221no—
745C22⋊C4—1222no—
746C22⋊C4—1222no—
747C22⋊C4—1222no—
748C22⋊C4—1224no—
749C22⋊C4—1224no—
750C22⋊C4—1224no—
751C22⋊C4—1224no—
752C22⋊C4—1222no—
753C22⋊C4—1222no—
754C22⋊C4—1222no—
755C22⋊C4—1222no—
756C22⋊C4—1222no—
757C22⋊C4—1222no—
758C42—1222no—
759C42—1222no—
760C42—1222no—
761C42C2×D24411yescharacteristic
762C42C2×D24411yescharacteristic
763C42C2×D24411yescharacteristic
764C42C2×D24411yescharacteristic
765C42C2×D24411yescharacteristic
766C42C2×D24411yescharacteristic
767C42C2×D24411yescharacteristic
768C42C2×D24411yescharacteristic
769C42C2×D24411yescharacteristic
770C42C2×D24411yescharacteristic
771C42C2×D24411yescharacteristic
772C42C2×D24411yescharacteristic
773C42C23×D6111yescharacteristic
774C42C23×D6111yescharacteristic
775C42C23×D6111yescharacteristic
776C42C23×D6111yescharacteristic
777C23—22no—
778C23—22no—
779C23—41no—
780C23—1222no—
781C23—1224no—
782C23—2444no—
783C23—2444no—
784C23—2444no—
785C23C22×D24411yescharacteristic
786C23C22×D24411yescharacteristic
787C23C22×D24411yescharacteristic
788Q8—1222no—
789Q8—1222no—
790Q8—2444no—
791Q8—2442no—
792Q8—2444no—
793Q8—2442no—
794D4—1222no—
795D4—1224no—
796D4—1224no—
797D4—1222no—
798D4—2444no—
799D4—2444no—
800D4—2442no—
801D4—2448no—
802D4—2444no—
803D4—2448no—
804D4—2444no—
805D4—2444no—
806D4—2444no—
807D4—2442no—
808D4—2444no—
809D4—2444no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—1222no—
829C2×C4—1222no—
830C2×C4—1222no—
831C2×C4—1224no—
832C2×C4—2448no—
833C2×C4—2444no—
834C2×C4—2448no—
835C2×C4—2444no—
836C2×C4—2444no—
837C2×C4—2444no—
838C2×C4#1451980514yescomplemented
839C2×C4C22×D24411yescharacteristic
840C2×C4C22×D24411yescharacteristic
841C2×C4C22×D24411yescharacteristic
842C2×C4C22×D24411yescharacteristic
843C2×C4C22×D24411yescharacteristic
844C2×C4C22×D24411yescharacteristic
845C2×C4C22×D24411yescharacteristic
846C2×C4C22×D24411yescharacteristic
847C2×C4C22×D24411yescharacteristic
848C2×C4C22×D24411yescharacteristic
849C2×C4C22×D24411yescharacteristic
850C2×C4#1451982212yes—
851C2×C4#1451982512yes—
852C2×C4C24×D6111yescharacteristic
853C8—28no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—44no—
862C22—4888no—
863C22—2444no—
864C22—2442no—
865C22—2442no—
866C22—2444no—
867C22—2442no—
868C22—2444no—
869C22#1684034312yes—
870C22C2×#1451980512yes—
871C22C23×D24411yescharacteristic
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—2444no—
880C4—2442no—
881C4—2442no—
882C4—2442no—
883C4#1684034312yes—
884C4C2×#1451980512yes—
885C4C2×#1451980512yes—
886C4#1684056212yes—
887C4C2×#1451982211yescharacteristic
888C4C2×#1451982511yescharacteristic
889C2—22no—
890C2—22no—
891C2—41no—
892C2—4884no—
893C2—4882no—
894C2C2×#1684034311yescharacteristic
895C2C22×#1451980511yescharacteristic
896C2C2×#1684056211yescharacteristic
subgroupG/H
centerC22C23×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#423C2
socleC22×C61C23×D4
hypercenterC2×#423D61
hypocenterC61#60916
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#423

Complements

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

NH ≅ G/Ntype
1. #21459115C2semidirect
2. C2×#16840312C2semidirect
3. #21457207C2semidirect
4. #21457200C2semidirect
5. #21457182C2semidirect
6. #21457146C2semidirect
7. #21457136C2semidirect
8. #21457129C2semidirect
9. #21455635C2semidirect
10. #21455618C2semidirect
11. #21455438C2semidirect
12. #21455300C2semidirect
13. #21455285C2semidirect
14. C2×C61×#423C2semidirect
18. #16840319C22semidirect
19. #16840319C22semidirect
29. #16840312C22semidirect
30. #16840312C22semidirect
37. #16840296C22semidirect
38. #16840296C22semidirect
50. #16840063C22semidirect
51. #16840058C22semidirect
52. #16840053C22semidirect
53. #16840053C22semidirect
54. #16840048C22semidirect
55. #16840043C22semidirect
56. #16840043C22semidirect
57. #16840015C22semidirect
58. #16840008C22semidirect
59. #16839998C22semidirect
60. #16839991C22semidirect
61. #16839978C22semidirect
62. #16839968C22semidirect
63. #16839963C22semidirect
64. #16839963C22semidirect
65. #16839958C22semidirect
66. #16839958C22semidirect
67. #16839958C22semidirect
75. C61×#423C22semidirect
76. C61×#423C22semidirect
77. C2×C4⋊C8×C61C22semidirect
78. C2×C4⋊C8×C61C22semidirect
357. C2×C4×C61AGL(1,ℤ/8)semidirect
454. C2×#423D61semidirect
521. #423C2×D61semidirect
522. #423C2×D61semidirect
523. C2×C4⋊C8C2×D61semidirect
524. C2×C4⋊C8C2×D61semidirect
527. C61#60916semidirect
838. C2×C4#14519805semidirect

Maximal subgroups

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

subgroupindex
#214591152
C2×#168403122
#214572072
#214572002
#214571822
#214571462
#214571362
#214571292
#214556352
#214556182
#214554382
#214553002
#214552852
C2×C61×#4232
#6091661