Finite Group Databasebeta

← #30548530

Subgroups — #30548530

Order 15616.

2074 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840385C211yesmaximal, characteristic, complemented
2#21459020C211yesmaximal, characteristic, complemented
3#21456091C214yesmaximal, complemented
4#21456084C214yesmaximal, complemented
5#21456051C214yesmaximal, complemented
6#21456006C214yesmaximal, complemented
7#21455759C211yesmaximal, characteristic, complemented
8#21455632C212yesmaximal, complemented
9#21455316C212yesmaximal, complemented
10#21455077C211yesmaximal, characteristic, complemented
11#21455073C211yesmaximal, characteristic
12#21454634C212yesmaximal, complemented
13#21454626C212yesmaximal, complemented
14#21454454C211yesmaximal, characteristic, complemented
15C61×#3095C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C2×#14519808C2212yes—
18C2×#14519805C2212yes—
19#16840385—22no—
20#16840385—22no—
21#16840385C2214yes—
22#16840385C2214yescomplemented
23C2×#14519776C2211yescharacteristic, complemented
24C2×#14519772—21no—
25C2×#14519766C2211yescharacteristic, complemented
26C2×#14519763—21no—
27C2×#14519759—21no—
28C2×#14519757—21no—
29C2×#14519751C2211yescharacteristic
30#16840243C2212yescomplemented
31#16840243C2212yescomplemented
32#16840242—21no—
33#16840242—21no—
34#16840239C2212yescomplemented
35#16840236C2212yescomplemented
36#16840235—21no—
37#16840235—21no—
38C4×#11758222—22no—
39#16840230C2212yes—
40#16840230C2212yes—
41C2×Q8×Dic61C2211yescharacteristic, complemented
42C2×#14519739C2211yescharacteristic, complemented
43C2×#14519736C2211yescharacteristic
44#117×D61—22no—
45#16840086C2214yes—
46#16840080C2212yescomplemented
47#16840075C2212yescomplemented
48#16840056C2214yescomplemented
49#16840051C2214yescomplemented
50#16840046C2214yescomplemented
51#16840041C2214yescomplemented
52#16839987C2214yescomplemented
53#16839987C2214yescomplemented
54#16839980C2214yescomplemented
55#16839980C2214yescomplemented
56#16839922C2214yescomplemented
57#16839917C2212yescomplemented
58#16839912C2212yescomplemented
59#16839909C2214yes—
60#16839903C2212yes—
61#16839898C2212yes—
62#16839873C2214yescomplemented
63#16839866C2214yescomplemented
64#16839865C2214yescomplemented
65#16839861C2214yescomplemented
66#16839854C2214yescomplemented
67#16839849C2214yescomplemented
68#16839847C2214yescomplemented
69#16839844C2214yescomplemented
70#16839820C2214yescomplemented
71#16839820C2214yescomplemented
72#16839805C2212yescomplemented
73#16839785C2212yescomplemented
74#16839766C2212yescomplemented
75#16839764C2212yes—
76#16839761C2212yes—
77#16839726C2211yescharacteristic
78M16×Dic61C2212yescomplemented
79C2×C22⋊Q8×C61C2211yescharacteristic
80C2×#117×C61C2211yescharacteristic
81C61×#485C2214yescomplemented
82C61×#484C2212yescomplemented
83C61×#483C2212yescomplemented
84C61×#428C2212yescomplemented
85C61×#419C2212yescomplemented
86C61×#407C2211yescharacteristic
87C2×#11758222—21no—
88C2×#11758222—21no—
89C2×#11758222—28no—
90C2×#11758222C2312yes—
91C2×#11758222C2312yes—
92C22×Dic122—21no—
93C22×Dic122C2311yescharacteristic
94C22×D244C2311yescharacteristic
95C22×D244C2311yescharacteristic
96C22×C22⋊D61—21no—
97C22×C22⋊D61—21no—
98C22×C4×D61—21no—
99C22×C4×D61—21no—
100#14519808—28no—
101#14519805—28no—
102C2×#11758202C2314yes—
103C2×#11758190C2314yes—
104C2×#11758201C2314yes—
105C2×D488C2314yes—
106C2×#11758194C2312yes—
107#14519776—22no—
108#14519776C2314yes—
109#14519772—24no—
110#14519772—24no—
111#14519766—22no—
112#14519766C2314yes—
113#14519763—24no—
114#14519763—24no—
115#14519759—24no—
116#14519759—24no—
117#14519757—24no—
118#14519757—24no—
119#14519751—21no—
120#14519751—21no—
121#14519751C2312yes—
122#14519751C2312yes—
123Q8×Dic61—22no—
124Q8×Dic61C2314yes—
125C4×Dic122—22no—
126C4×Dic122—22no—
127#14519742C2312yes—
128#14519742C2312yes—
129#14519742C2312yes—
130#14519742C2312yes—
131C4×D244—22no—
132C4×D244—22no—
133#14519739—22no—
134#14519739C2314yes—
135#14519739C2312yes—
136#14519739C2312yes—
137#14519739C2312yes—
138#14519739C2312yes—
139C4×C22⋊D61—22no—
140C4×C22⋊D61—22no—
141C4×C22⋊D61—22no—
142C4×C22⋊D61—22no—
143#14519737—22no—
144#14519737—22no—
145#14519737—22no—
146#14519737—22no—
147#14519736D412yes—
148#14519736D412yes—
149#14519736C2312yes—
150#14519736C2312yes—
151#14519735—22no—
152#14519735—22no—
153#14519734—22no—
154#14519734—22no—
155#14519733—22no—
156#14519733—22no—
157C2×C4⋊Dic61—21no—
158C2×C4⋊Dic61D411yescharacteristic
159C2×C4⋊Dic61D411yescharacteristic
160C2×C4⋊Dic61C2311yescharacteristic
161C2×#11758196—21no—
162C4⋊C4×D61—22no—
163C4⋊C4×D61—22no—
164C2×C22⋊Dic61D411yescharacteristic
165C2×C22⋊Dic61D411yescharacteristic
166C2×#11758198—21no—
167C2×#11758198—21no—
168C2×#11758198—21no—
169C2×#11758198—21no—
170C22⋊C4×D61—22no—
171C22⋊C4×D61—22no—
172C2×C4×Dic61—21no—
173C2×C4×Dic61C2311yescharacteristic
174C2×C4×Dic61C2311yescharacteristic
175C42×D61—22no—
176C42×D61—22no—
177#14519710C2314yes—
178#14519708C2314yes—
179#14519706C2314yes—
180#14519706C2314yes—
181#14519702C2314yes—
182#14519700C2314yes—
183#14519699C2314yes—
184#14519697C2314yes—
185#14519697C2314yes—
186#14519697C2314yes—
187C22⋊#92418C2312yes—
188C22⋊#92418C2312yes—
189#14519687C2314yes—
190C8×Dic61C2314yes—
191C22×Q8×C61C2311yescharacteristic
192C23×C4×C61C2311yescharacteristic
193C2×M16×C61C2312yes—
194C22⋊Q8×C61—21no—
195C22⋊Q8×C61—21no—
196C22⋊Q8×C61C2312yes—
197C22⋊Q8×C61C2312yes—
198#117×C61—21no—
199#117×C61—21no—
200#117×C61C2312yes—
201#117×C61C2312yes—
202C2×C4⋊C4×C61—21no—
203C2×C4⋊C4×C61C2311yescharacteristic
204C2×C4⋊C4×C61C2311yescharacteristic
205C2×C4⋊C4×C61C2311yescharacteristic
206C2×C22⋊C4×C61—21no—
207C2×C22⋊C4×C61—21no—
208C2×C42×C61—21no—
209#107×C61C2314yes—
210#106×C61C2314yes—
211#103×C61C2314yes—
212#103×C61C2314yes—
213C22⋊C8×C61C2312yes—
214C22⋊C8×C61C2312yes—
215C24×C61C2×D411yescharacteristic
216C23×D61—21no—
217C23×D61—21no—
218C2×Q8×C61—21no—
219C2×Q8×C61—24no—
220C2×Q8×C61C2412yes—
221C22×C4×C61—24no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2411yescharacteristic
230C22×C4×C61C2411yescharacteristic
231C22×C4×C61C2411yescharacteristic
232C2×C22⋊D61—28no—
233C2×C22⋊D61—22no—
234C2×C22⋊D61—22no—
235C2×C22⋊D61—22no—
236C2×C22⋊D61—22no—
237C2×C22⋊D61—82no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61C2×D411yescharacteristic
241C22×Dic61C2×D411yescharacteristic
242C22×Dic61C2×D411yescharacteristic
243C22×Dic61C2×D411yescharacteristic
244#11758222—28no—
245#11758222—28no—
246#11758222—24no—
247#11758222—24no—
248#11758222—24no—
249#11758222#4118yes—
250C2×D244—21no—
251C2×D244—24no—
252C2×D244—24no—
253C2×D244—21no—
254C2×D244C2412yes—
255C2×D244C2412yes—
256C2×C4×D61—28no—
257C2×C4×D61—22no—
258C2×C4×D61—22no—
259C2×C4×D61—24no—
260C2×C4×D61—22no—
261C2×C4×D61—22no—
262C2×C4×D61—22no—
263C2×C4×D61—22no—
264C2×C4×D61—82no—
265C2×Dic122—21no—
266C2×Dic122—24no—
267C2×Dic122—24no—
268C2×Dic122—82no—
269C2×Dic122C2412yes—
270M16×C61—24no—
271C2×C8×C61C2414yes—
272C4⋊C4×C61—22no—
273C4⋊C4×C61—22no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61—21no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61C2412yes—
278C4⋊C4×C61C2412yes—
279C4⋊C4×C61C2412yes—
280C22⋊C4×C61—22no—
281C22⋊C4×C61—22no—
282C22⋊C4×C61—22no—
283C22⋊C4×C61—22no—
284C42×C61—22no—
285C42×C61—22no—
286C22⋊Dic61C2×D412yes—
287C22⋊Dic61C2×D412yes—
288C22⋊Dic61C2×D412yes—
289C22⋊Dic61C2×D412yes—
290#11758202—28no—
291#11758201—28no—
292#11758198—22no—
293#11758198—22no—
294#11758198—22no—
295#11758198—22no—
296#11758198—22no—
297#11758198—22no—
298#11758198—24no—
299#11758198—24no—
300#11758198—24no—
301C4⋊Dic61—21no—
302C4⋊Dic61—24no—
303C4⋊Dic61C2×D412yes—
304C4⋊Dic61C2×D412yes—
305C4⋊Dic61C2×D412yes—
306C4⋊Dic61C2×D412yes—
307C4⋊Dic61C2412yes—
308#11758196—22no—
309#11758196—22no—
310#11758196—22no—
311#11758196—22no—
312#11758196—24no—
313C4×Dic61—22no—
314C4×Dic61—22no—
315C4×Dic61—22no—
316C4×Dic61—22no—
317C4×Dic61—24no—
318C4×Dic61C2×D412yes—
319C4×Dic61C2×D412yes—
320C4×Dic61C2412yes—
321C4×Dic61C2412yes—
322#11758194—24no—
323C2×#92418C2414yes—
324D488—28no—
325#11758190—28no—
326C23×C61—22no—
327C23×C61—41no—
328C23×C61—41no—
329C23×C61C22×D411yescharacteristic
330C23×C61C22×D411yescharacteristic
331C23×C61C22×D411yescharacteristic
332C22×D61—22no—
333C22×D61—24no—
334C22×D61—22no—
335C22×D61—42no—
336C22×D61—42no—
337C22×D61—42no—
338C22×D61—81no—
339C22×D61—81no—
340Q8×C61—24no—
341Q8×C61—42no—
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—22no—
351C2×C4×C61—42no—
352C2×C4×C61—42no—
353C2×C4×C61—81no—
354C2×C4×C61—81no—
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C22×D411yescharacteristic
357C2×C4×C61C22×D411yescharacteristic
358C2×C4×C61C2×#4114yes—
359C2×C4×C61C2511yescharacteristic
360C22⋊D61—28no—
361C22⋊D61—28no—
362C22⋊D61—82no—
363C22⋊D61—82no—
364C2×Dic61—24no—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—42no—
372C2×Dic61C22×D412yes—
373C2×Dic61C22×D412yes—
374C2×Dic61C22×D412yes—
375C2×Dic61C22×D412yes—
376D244—24no—
377D244—22no—
378D244—24no—
379D244—42no—
380D244C2×#4114yes—
381C4×D61—28no—
382C4×D61—28no—
383C4×D61—82no—
384C4×D61—82no—
385C4×D61—82no—
386C4×D61—82no—
387C4×D61—84no—
388Dic122—24no—
389Dic122—22no—
390Dic122—84no—
391Dic122C2×#4114yes—
392C8×C61—24no—
393#92418—24no—
394#60567—611nomaximal, Sylow
395C22×C61—21no—
396C22×C61—21no—
397C22×C61—21no—
398C22×C61—21no—
399C22×C61—21no—
400C22×C61—21no—
401C22×C61—21no—
402C22×C61—21no—
403C22×C61—82no—
404C22×C61#52512yes—
405C22×C61C23×D411yescharacteristic
406C2×D61—24no—
407C2×D61—42no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—42no—
412C2×D61—84no—
413C2×D61—84no—
414C4×C61—21no—
415C4×C61—21no—
416C4×C61—42no—
417C4×C61—42no—
418C4×C61—42no—
419C4×C61—42no—
420C4×C61#52512yes—
421C4×C61C22×#4112yes—
422Dic61—22no—
423Dic61—22no—
424Dic61—22no—
425Dic61—22no—
426Dic61—24no—
427Dic61—42no—
428C2×#542—611no—
429#3428—611no—
430#3125—614no—
431#3124—614no—
432#3121—614no—
433#3118—614no—
434#3095D6111yescharacteristic, complemented
435#3094—611no—
436#3079—612no—
437#3040—612no—
438#3007—611no—
439#3006—611no—
440C4×#137—612no—
441C4×AGL(1,ℤ/8)—612no—
442#2921—611no—
443C2×C61—22no—
444C2×C61—41no—
445C2×C61—41no—
446C2×C61C2×#52511yescharacteristic
447C2×C61#358511yescharacteristic
448C2×C61#358611yescharacteristic
449D61—44no—
450D61—82no—
451C22×#41—611no—
452C2×#137—612no—
453C2×AGL(1,ℤ/8)—612no—
454#542—614no—
455#542—614no—
456#542—1222no—
457#542—1222no—
458C2×C4⋊Q8—611no—
459C2×#126—1221no—
460C2×#124—611no—
461C2×#124—1221no—
462C2×#123—1221no—
463C2×C22⋊Q8—1221no—
464C2×C22⋊Q8C2×D6111yescharacteristic
465C2×#121—611no—
466#520—612no—
467#520—612no—
468#520—1221no—
469#520—1221no—
470#519—612no—
471#518—612no—
472#518—1221no—
473#518—1221no—
474C4×#41—612no—
475C4×#41—612no—
476C4×#41—1222no—
477C2×C4×Q8—611no—
478C2×C4×D4—611no—
479C2×#117—611no—
480C2×#117—1222no—
481C2×#117C2×D6111yescharacteristic
482#485C2×D6114yescomplemented
483#484C2×D6112yescomplemented
484#483C2×D6112yescomplemented
485#482—614no—
486#481—612no—
487#480—612no—
488#477—614no—
489#476—614no—
490#475—614no—
491#474—614no—
492#464—614no—
493#464—614no—
494#463—614no—
495#463—614no—
496#452—614no—
497#451—612no—
498#450—612no—
499#449—614no—
500#448—612no—
501#447—612no—
502#442—614no—
503#441—614no—
504#440—614no—
505#440—614no—
506C4×Q16—614no—
507C4×SD16—614no—
508C4×SD16—614no—
509C4×D8—614no—
510#433—614no—
511#433—614no—
512#428—612no—
513#428C2×D6112yescomplemented
514#423—612no—
515#419C2×D6112yescomplemented
516#418—612no—
517#417—612no—
518#417—612no—
519#407—611no—
520#407C2×D6111yescharacteristic
521C4×M16—612no—
522C61#6056711yescharacteristic, complemented, Sylow
523C2×#41—612no—
524C2×#41—612no—
525C2×#41—1228no—
526C2×#41—1221no—
527C2×#41—1221no—
528C22×Q8—611no—
529C22×Q8—1221no—
530C22×Q8C22×D6111yescharacteristic
531C22×D4—611no—
532C22×D4—611no—
533C22×D4—1221no—
534C22×D4—1221no—
535C23×C4—1221no—
536C23×C4—1221no—
537C23×C4C22×D6111yescharacteristic
538#137—1228no—
539AGL(1,ℤ/8)—1228no—
540C2×Q16—614no—
541C2×SD16—614no—
542C2×SD16—614no—
543C2×D8—614no—
544C2×M16—612no—
545C2×M16C22×D6112yes—
546C4⋊Q8—614no—
547C4⋊Q8—1222no—
548#126—1224no—
549#126—1224no—
550#124—614no—
551#124—1222no—
552#124—1224no—
553#124—1224no—
554#123—1224no—
555#123—1224no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8—1224no—
559C22⋊Q8—1224no—
560C22⋊Q8C22×D6112yes—
561C22⋊Q8C22×D6112yes—
562#121—612no—
563#121—612no—
564#121—1221no—
565#121—1221no—
566C4×Q8—614no—
567C4×Q8—612no—
568C4×Q8—612no—
569C4×Q8—612no—
570C4×Q8—612no—
571C4×Q8—1222no—
572C4×Q8—1222no—
573C4×Q8—1222no—
574C4×D4—614no—
575C4×D4—612no—
576C4×D4—612no—
577C4×D4—612no—
578C4×D4—612no—
579C4×D4—1222no—
580C4×D4—1222no—
581C4×D4—1222no—
582C4×D4—1222no—
583C4×D4—1222no—
584C4×D4—1222no—
585C4×D4—1222no—
586C4×D4—1222no—
587C4×D4—1222no—
588C4×D4—1222no—
589C4×D4—1222no—
590#117—21no—
591#117—21no—
592#117—612no—
593#117—612no—
594#117—612no—
595#117—612no—
596#117—1222no—
597#117—1222no—
598#117—1222no—
599#117—1222no—
600#117—1222no—
601#117—1222no—
602#117C22×D6112yes—
603#117C22×D6112yes—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—611no—
606C2×C4⋊C4—611no—
607C2×C4⋊C4—611no—
608C2×C4⋊C4—1222no—
609C2×C4⋊C4—1222no—
610C2×C4⋊C4—1221no—
611C2×C4⋊C4—1221no—
612C2×C4⋊C4C22×D6111yescharacteristic
613C2×C4⋊C4C22×D6111yescharacteristic
614C2×C4⋊C4C22×D6111yescharacteristic
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—611no—
618C2×C22⋊C4—611no—
619C2×C22⋊C4—1222no—
620C2×C22⋊C4—1222no—
621C2×C22⋊C4—1221no—
622C2×C22⋊C4—1221no—
623C2×C22⋊C4—1221no—
624C2×C22⋊C4—1221no—
625C2×C42—21no—
626C2×C42—611no—
627C2×C42—611no—
628C2×C42—1222no—
629C2×C42—1222no—
630C2×C42—1221no—
631#107—614no—
632#107C22×D6114yes—
633#106—614no—
634#106C22×D6114yes—
635C4⋊C8—614no—
636C4⋊C8—614no—
637#103—614no—
638#103—614no—
639#103C22×D6114yes—
640#103C22×D6114yes—
641#102—614no—
642#102—614no—
643#102—614no—
644#102—614no—
645C22⋊C8—612no—
646C22⋊C8—612no—
647C22⋊C8C22×D6112yes—
648C22⋊C8C22×D6112yes—
649#97—614no—
650C4×C8—614no—
651C24—1221no—
652C24—1221no—
653C24D4×D6111yescharacteristic
654#41—618no—
655#41—1224no—
656#41—1224no—
657#41—1228no—
658#41—1228no—
659#41—1224no—
660C2×Q8—21no—
661C2×Q8—24no—
662C2×Q8—612no—
663C2×Q8—1224no—
664C2×Q8—1224no—
665C2×Q8—1221no—
666C2×Q8—4882no—
667C2×Q8C23×D6112yes—
668C2×D4—612no—
669C2×D4—612no—
670C2×D4—1224no—
671C2×D4—1228no—
672C2×D4—1222no—
673C2×D4—1222no—
674C2×D4—1222no—
675C2×D4—1222no—
676C2×D4—1221no—
677C2×D4—1221no—
678C2×D4—1224no—
679C2×D4—4882no—
680C22×C4—24no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—611no—
686C22×C4—611no—
687C22×C4—611no—
688C22×C4—611no—
689C22×C4—1222no—
690C22×C4—1222no—
691C22×C4—1222no—
692C22×C4—1222no—
693C22×C4—1224no—
694C22×C4—1228no—
695C22×C4—1221no—
696C22×C4—1222no—
697C22×C4—1222no—
698C22×C4—1221no—
699C22×C4—4882no—
700C22×C4D4×D6111yescharacteristic
701C22×C4D4×D6111yescharacteristic
702C22×C4D4×D6111yescharacteristic
703C22×C4C23×D6111yescharacteristic
704C22×C4C23×D6111yescharacteristic
705C22×C4C23×D6111yescharacteristic
706Q16—1228no—
707SD16—1228no—
708SD16—1228no—
709D8—1228no—
710M16—24no—
711M16—1224no—
712C2×C8—614no—
713C2×C8C23×D6114yes—
714C4⋊C4—22no—
715C4⋊C4—22no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—612no—
720C4⋊C4—612no—
721C4⋊C4—612no—
722C4⋊C4—612no—
723C4⋊C4—612no—
724C4⋊C4—1222no—
725C4⋊C4—1222no—
726C4⋊C4—1222no—
727C4⋊C4—1222no—
728C4⋊C4—1224no—
729C4⋊C4—1224no—
730C4⋊C4—1221no—
731C4⋊C4C23×D6112yes—
732C4⋊C4C23×D6112yes—
733C4⋊C4C23×D6112yes—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—612no—
739C22⋊C4—612no—
740C22⋊C4—612no—
741C22⋊C4—612no—
742C22⋊C4—1222no—
743C22⋊C4—1222no—
744C22⋊C4—1222no—
745C22⋊C4—1222no—
746C22⋊C4—1224no—
747C22⋊C4—1224no—
748C22⋊C4—1224no—
749C22⋊C4—1222no—
750C22⋊C4—1222no—
751C42—22no—
752C42—22no—
753C42—612no—
754C42—612no—
755C42—612no—
756C42—612no—
757C42—1222no—
758C42—1222no—
759C42—1222no—
760C42—1222no—
761C42—1224no—
762C23—22no—
763C23—41no—
764C23—41no—
765C23—1224no—
766C23—1222no—
767C23—1222no—
768C23—4881no—
769C23—4881no—
770C23—2442no—
771C23—2442no—
772C23—2442no—
773C23C2×D4×D6111yescharacteristic
774C23C2×D4×D6111yescharacteristic
775C23C2×D4×D6111yescharacteristic
776Q8—24no—
777Q8—42no—
778Q8—614no—
779Q8—1224no—
780Q8—1222no—
781Q8—4884no—
782D4—614no—
783D4—1224no—
784D4—1228no—
785D4—1228no—
786D4—1222no—
787D4—1224no—
788D4—4882no—
789D4—4882no—
790D4—2442no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—81no—
803C2×C4—81no—
804C2×C4—612no—
805C2×C4—612no—
806C2×C4—612no—
807C2×C4—612no—
808C2×C4—1228no—
809C2×C4—1224no—
810C2×C4—1222no—
811C2×C4—1228no—
812C2×C4—1222no—
813C2×C4—4882no—
814C2×C4—4882no—
815C2×C4—4882no—
816C2×C4—4882no—
817C2×C4—4884no—
818C2×C4—2441no—
819C2×C4—2441no—
820C2×C4—2441no—
821C2×C4—2441no—
822C2×C4—2442no—
823C2×C4C2×D4×D6111yescharacteristic
824C2×C4C2×D4×D6111yescharacteristic
825C2×C4C2×D4×D6111yescharacteristic
826C2×C4#41×D6114yes—
827C2×C4C24×D6111yescharacteristic
828C8—24no—
829C8—1224no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—82no—
839C22—1224no—
840C22—4884no—
841C22—4884no—
842C22—2442no—
843C22—2442no—
844C22—2442no—
845C22—2442no—
846C22—2442no—
847C22#1684027012yes—
848C22C22×D4×D6111yescharacteristic
849C4—21no—
850C4—21no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—1224no—
856C4—1222no—
857C4—1222no—
858C4—1222no—
859C4—1222no—
860C4—2442no—
861C4#1684027012yes—
862C4C2×#41×D6112yes—
863C2—22no—
864C2—41no—
865C2—41no—
866C2—4882no—
867C2—2444no—
868C2C2×#1684027011yescharacteristic
869C2#2146059611yescharacteristic
870C2#2146060211yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3095C2
socleC22×C61C23×D4
prime radical#21455073C2
hypercenter#3095D61
hypocenterC61#60567
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3095

Complements

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

NH ≅ G/Ntype
1. C2×#16840385C2semidirect
2. #21459020C2semidirect
3. #21456091C2semidirect
4. #21456084C2semidirect
5. #21456051C2semidirect
6. #21456006C2semidirect
7. #21455759C2semidirect
8. #21455632C2semidirect
9. #21455316C2semidirect
10. #21455077C2semidirect
12. #21454634C2semidirect
13. #21454626C2semidirect
14. #21454454C2semidirect
15. C61×#3095C2semidirect
22. #16840385C22semidirect
23. C2×#14519776C22semidirect
25. C2×#14519766C22semidirect
30. #16840243C22semidirect
31. #16840243C22semidirect
34. #16840239C22semidirect
35. #16840236C22semidirect
41. C2×Q8×Dic61C22semidirect
42. C2×#14519739C22semidirect
46. #16840080C22semidirect
47. #16840075C22semidirect
48. #16840056C22semidirect
49. #16840051C22semidirect
50. #16840046C22semidirect
51. #16840041C22semidirect
52. #16839987C22semidirect
53. #16839987C22semidirect
54. #16839980C22semidirect
55. #16839980C22semidirect
56. #16839922C22semidirect
57. #16839917C22semidirect
58. #16839912C22semidirect
62. #16839873C22semidirect
63. #16839866C22semidirect
64. #16839865C22semidirect
65. #16839861C22semidirect
66. #16839854C22semidirect
67. #16839849C22semidirect
68. #16839847C22semidirect
69. #16839844C22semidirect
70. #16839820C22semidirect
71. #16839820C22semidirect
72. #16839805C22semidirect
73. #16839785C22semidirect
74. #16839766C22semidirect
78. M16×Dic61C22semidirect
81. C61×#485C22semidirect
82. C61×#484C22semidirect
83. C61×#483C22semidirect
84. C61×#428C22semidirect
85. C61×#419C22semidirect
434. #3095D61semidirect
482. #485C2×D61semidirect
483. #484C2×D61semidirect
484. #483C2×D61semidirect
513. #428C2×D61semidirect
515. #419C2×D61semidirect
522. C61#60567semidirect

Maximal subgroups

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

subgroupindex
C2×#168403852
#214590202
#214560912
#214560842
#214560512
#214560062
#214557592
#214556322
#214553162
#214550772
#214550732
#214546342
#214546262
#214544542
C61×#30952
#6056761