Finite Group Databasebeta

← D61×#3230 #30552057

Subgroups — D61×#3230 #30552057

Order 15616.

2006 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D61C211yesmaximal, characteristic
2C2×C4⋊Q8×D61C211yesmaximal, characteristic
3#21456972C211yesmaximal, characteristic, complemented
4#21456971C212yesmaximal, complemented
5#21456970C211yesmaximal, characteristic, complemented
6#21456969C214yesmaximal, complemented
7#21456968C214yesmaximal, complemented
8#21456967C211yesmaximal, characteristic, complemented
9#21456966C212yesmaximal, complemented
10#500×D61C212yesmaximal, complemented
11#487×D61C212yesmaximal, complemented
12#484×D61C214yesmaximal
13#477×D61C214yesmaximal, complemented
14#431×D61C211yesmaximal, characteristic
15C61×#3230C211yesmaximal, characteristic, complemented
16C22×Q8×D61—21no—
17#16840319C2211yescharacteristic
18#16840318—21no—
19#16840317C2211yescharacteristic
20#16840317C2211yescharacteristic
21#16840316—21no—
22#16840316C2212yes—
23#16840315—21no—
24#16840314—21no—
25#16840314C2212yes—
26C2×#14519777C2211yescharacteristic
27C2×#14519776—21no—
28C2×#14519776C2212yes—
29C2×#14519775—21no—
30C4⋊Q8×D61—21no—
31C4⋊Q8×D61—21no—
32C4⋊Q8×D61—21no—
33C4⋊Q8×D61—21no—
34C4⋊Q8×D61C2212yes—
35C4⋊Q8×D61C2212yes—
36C4⋊Q8×D61C2212yes—
37C4⋊Q8×D61C2212yes—
38C4⋊Q8×D61C2211yescharacteristic
39C4⋊Q8×D61C2211yescharacteristic
40#125×D61—21no—
41C22⋊Q8×D61—21no—
42C22⋊Q8×D61C2212yes—
43C4×Q8×D61—21no—
44C4×Q8×D61C2212yes—
45#117×D61—21no—
46C2×C4⋊C4×D61—21no—
47C2×C4⋊C4×D61C2212yes—
48C2×C42×D61C2211yescharacteristic
49#16840167C2212yescomplemented
50#16840166C2218yescomplemented
51#16840165C2212yescomplemented
52#16840165C2212yescomplemented
53#16840114C2212yescomplemented
54#16840113C2212yescomplemented
55#16840112C2212yescomplemented
56#16840111C2218yescomplemented
57#16840099C2218yes—
58#16840098C2214yes—
59#16840097C2214yes—
60#16840096C2218yes—
61#16840095C2214yes—
62#16840058C2214yescomplemented
63#16840057C2214yescomplemented
64#16840056C2218yescomplemented
65#16840055C2218yescomplemented
66#16840054C2214yescomplemented
67#16839815C2211yescharacteristic
68#16839814C2212yes—
69#16839813C2212yes—
70#16839812C2212yes—
71#107×D61C2218yes—
72C4⋊C8×D61C2212yes—
73#103×D61C2218yes—
74C22⋊C8×D61C2212yes—
75C4×C8×D61C2212yes—
76C61×#533C2211yescharacteristic
77C2×C4⋊Q8×C61C2211yescharacteristic
78C61×#500C2212yescomplemented
79C61×#487C2212yescomplemented
80C61×#484C2214yes—
81C61×#477C2214yescomplemented
82C61×#431C2211yescharacteristic
83C22×Dic122—21no—
84C22×Dic122—22no—
85C2×Q8×D61—21no—
86C2×Q8×D61—22no—
87C2×Q8×D61—22no—
88C2×Q8×D61—22no—
89C2×Q8×D61—22no—
90C2×Q8×D61—48no—
91C2×Q8×D61C2312yes—
92C22×C4×D61—22no—
93C22×C4×D61D411yescharacteristic
94C22×C4×D61D411yescharacteristic
95C22×C4×D61C2311yescharacteristic
96C2×C8×D61C2314yes—
97#14519777—21no—
98#14519777—21no—
99#14519777C2311yescharacteristic
100#14519777C2312yes—
101#14519777C2312yes—
102#14519777C2311yescharacteristic
103#14519776—22no—
104#14519776—22no—
105#14519776—22no—
106#14519776—22no—
107#14519776—22no—
108#14519776—22no—
109#14519776—21no—
110#14519776—21no—
111#14519776—21no—
112#14519776C2314yes—
113#14519776C2314yes—
114#14519776C2312yes—
115#14519775—22no—
116#14519775—22no—
117#14519775—22no—
118#14519775—22no—
119#14519775—21no—
120#14519775C2312yes—
121#14519769—21no—
122#14519768—21no—
123#14519768—21no—
124#14519767—22no—
125#14519767—22no—
126#14519757—21no—
127#14519757C2312yes—
128#14519756—21no—
129#14519756C2312yes—
130#14519755—22no—
131#14519755—22no—
132#14519754—22no—
133#14519754—22no—
134#14519753—21no—
135#14519753C2312yes—
136Q8×Dic61—21no—
137Q8×Dic61C2312yes—
138C4×Dic122—21no—
139C4×Dic122—22no—
140C4×Dic122—22no—
141C4×Dic122C2312yes—
142#14519742—21no—
143#14519742—22no—
144#14519742—22no—
145#14519742C2312yes—
146#14519736—21no—
147#14519735—21no—
148#14519735—21no—
149#14519734—22no—
150#14519733—22no—
151C2×C4⋊Dic61—21no—
152C2×C4⋊Dic61C2312yes—
153C2×#11758196—22no—
154C2×#11758196—22no—
155C4⋊C4×D61—22no—
156C4⋊C4×D61—22no—
157C4⋊C4×D61—22no—
158C4⋊C4×D61—22no—
159C4⋊C4×D61—22no—
160C4⋊C4×D61—22no—
161C4⋊C4×D61—21no—
162C4⋊C4×D61—21no—
163C4⋊C4×D61—21no—
164C4⋊C4×D61—22no—
165C4⋊C4×D61—22no—
166C4⋊C4×D61C2314yes—
167C4⋊C4×D61C2314yes—
168C4⋊C4×D61C2312yes—
169C22⋊C4×D61—22no—
170C2×C4×Dic61D411yescharacteristic
171C2×C4×Dic61D411yescharacteristic
172C2×C4×Dic61C2311yescharacteristic
173C42×D61—22no—
174C42×D61D411yescharacteristic
175C42×D61D411yescharacteristic
176C42×D61D411yescharacteristic
177C42×D61D411yescharacteristic
178C42×D61C2311yescharacteristic
179C42×D61C2311yescharacteristic
180C42×D61C2311yescharacteristic
181C42×D61C2311yescharacteristic
182#14519711C2318yes—
183#14519710C2318yes—
184#14519710C2318yes—
185C4⋊#92418C2312yes—
186#14519706C2314yes—
187#14519702C2318yes—
188#14519701C2318yes—
189#14519700C2318yes—
190C22⋊#92418C2312yes—
191#14519689C2314yes—
192C4×#92418C2312yes—
193C8×Dic61C2314yes—
194C22×Q8×C61—21no—
195C4⋊Q8×C61—21no—
196C4⋊Q8×C61—21no—
197C4⋊Q8×C61C2311yescharacteristic
198C4⋊Q8×C61C2312yes—
199C4⋊Q8×C61C2312yes—
200C4⋊Q8×C61C2311yescharacteristic
201#125×C61—21no—
202C22⋊Q8×C61—21no—
203C22⋊Q8×C61C2312yes—
204C4×Q8×C61—21no—
205C4×Q8×C61C2312yes—
206#117×C61—21no—
207C2×C4⋊C4×C61—21no—
208C2×C4⋊C4×C61C2312yes—
209C2×C42×C61C2311yescharacteristic
210#107×C61C2318yes—
211C4⋊C8×C61C2312yes—
212#103×C61C2318yes—
213C22⋊C8×C61C2312yes—
214C4×C8×C61C2312yes—
215C23×D61C2×D411yescharacteristic
216C2×Q8×C61—22no—
217C2×Q8×C61—22no—
218C2×Q8×C61—21no—
219C2×Q8×C61—44no—
220C2×Q8×C61C2412yes—
221C22×C4×C61—22no—
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2411yescharacteristic
225C22×Dic61—22no—
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229Q8×D61—28no—
230Q8×D61—48no—
231Q8×D61—48no—
232Q8×D61—48no—
233Q8×D61—44no—
234Q8×D61—48no—
235C2×C4×D61—24no—
236C2×C4×D61—24no—
237C2×C4×D61—24no—
238C2×C4×D61—24no—
239C2×C4×D61—22no—
240C2×C4×D61—22no—
241C2×C4×D61—48no—
242C2×C4×D61Q1618yes—
243C2×C4×D61C2×D411yescharacteristic
244C2×C4×D61C2×D411yescharacteristic
245C2×C4×D61C2×D411yescharacteristic
246C2×C4×D61C2×D411yescharacteristic
247C2×C4×D61C2×D411yescharacteristic
248C2×C4×D61C2×D411yescharacteristic
249C2×C4×D61C2×D411yescharacteristic
250C2×C4×D61C2×D411yescharacteristic
251C2×C4×D61C2×D411yescharacteristic
252C2×C4×D61C2×D411yescharacteristic
253C2×C4×D61C2411yescharacteristic
254C2×C4×D61C2411yescharacteristic
255C2×Dic122—22no—
256C2×Dic122—22no—
257C2×Dic122—21no—
258C2×Dic122—24no—
259C2×Dic122—24no—
260C2×Dic122—22no—
261C2×Dic122—22no—
262C2×Dic122—48no—
263C2×Dic122—44no—
264C2×Dic122C2412yes—
265C2×C8×C61C2414yes—
266C4⋊C4×C61—22no—
267C4⋊C4×C61—22no—
268C4⋊C4×C61—22no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61—21no—
272C4⋊C4×C61—22no—
273C4⋊C4×C61—22no—
274C4⋊C4×C61C2414yes—
275C4⋊C4×C61C2412yes—
276C22⋊C4×C61—22no—
277C42×C61—22no—
278C42×C61C2×D411yescharacteristic
279C42×C61C2×D411yescharacteristic
280C42×C61C2411yescharacteristic
281C42×C61C2411yescharacteristic
282C22⋊Dic61—22no—
283#11758198—22no—
284#11758198—22no—
285C4⋊Dic61—22no—
286C4⋊Dic61—22no—
287C4⋊Dic61—22no—
288C4⋊Dic61—21no—
289C4⋊Dic61—21no—
290C4⋊Dic61—21no—
291C4⋊Dic61—22no—
292C4⋊Dic61—22no—
293C4⋊Dic61C2414yes—
294C4⋊Dic61C2412yes—
295#11758196—22no—
296#11758196—22no—
297#11758196—24no—
298#11758196—24no—
299#11758196—24no—
300#11758196—24no—
301#11758196—22no—
302#11758196—22no—
303#11758196—22no—
304#11758196—22no—
305#11758196—22no—
306#11758196—22no—
307C4×Dic61—22no—
308C4×Dic61—22no—
309C4×Dic61—22no—
310C4×Dic61C2×D411yescharacteristic
311C4×Dic61C2×D411yescharacteristic
312C4×Dic61C2×D411yescharacteristic
313C4×Dic61C2×D411yescharacteristic
314C4×Dic61C2×D411yescharacteristic
315C4×Dic61C2×D411yescharacteristic
316C4×Dic61C2×D411yescharacteristic
317C4×Dic61C2×D411yescharacteristic
318C4×Dic61C2×D411yescharacteristic
319C4×Dic61C2×D411yescharacteristic
320C4×Dic61C2411yescharacteristic
321C4×Dic61C2411yescharacteristic
322C2×#92418C2414yes—
323C8×D61—28no—
324C23×C61C22×D411yescharacteristic
325C22×D61—22no—
326C22×D61—22no—
327C22×D61C2×Q1614yes—
328C22×D61C22×D411yescharacteristic
329C22×D61C22×D411yescharacteristic
330Q8×C61—24no—
331Q8×C61—44no—
332Q8×C61—44no—
333Q8×C61—42no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—24no—
339C2×C4×C61—44no—
340C2×C4×C61C2×Q1614yes—
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C22×D411yescharacteristic
344C2×C4×C61C22×D411yescharacteristic
345C2×C4×C61C22×D411yescharacteristic
346C2×C4×C61C2511yescharacteristic
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—24no—
352C2×Dic61—44no—
353C2×Dic61C2×Q1614yes—
354C2×Dic61C22×D411yescharacteristic
355C2×Dic61C22×D411yescharacteristic
356C2×Dic61C22×D411yescharacteristic
357C2×Dic61C22×D411yescharacteristic
358C2×Dic61C22×D411yescharacteristic
359C2×Dic61C22×D411yescharacteristic
360C4×D61—22no—
361C4×D61—22no—
362C4×D61—22no—
363C4×D61—22no—
364C4×D61—22no—
365C4×D61—22no—
366C4×D61—48no—
367C4×D61—44no—
368C4×D61—48no—
369C4×D61—44no—
370C4×D61C2×Q1614yes—
371C4×D61C2×Q1614yes—
372C4×D61C2×Q1614yes—
373C4×D61C2×Q1614yes—
374C4×D61AGL(1,ℤ/8)14yes—
375C4×D612−1+414yes—
376Dic122—24no—
377Dic122—48no—
378Dic122—44no—
379Dic122—44no—
380Dic122—42no—
381Dic122—44no—
382Dic122—48no—
383Dic122—44no—
384C8×C61—24no—
385#92418—24no—
386C2×#3230—611nomaximal, Sylow
387C22×C61—21no—
388C22×C61—21no—
389C22×C61C22×Q1612yes—
390C22×C61C23×D411yescharacteristic
391C2×D61—21no—
392C2×D61—21no—
393C2×D61—28no—
394C2×D61#53612yes—
395C2×D61C22×Q1612yes—
396C2×D61C22×Q1612yes—
397C2×D61C2×AGL(1,ℤ/8)12yes—
398C4×C61—21no—
399C4×C61—21no—
400C4×C61—42no—
401C4×C61—44no—
402C4×C61—42no—
403C4×C61C22×Q1612yes—
404C4×C61C22×Q1612yes—
405C4×C61C2×AGL(1,ℤ/8)12yes—
406C4×C61C2×2−1+412yes—
407Dic61—21no—
408Dic61—21no—
409Dic61—42no—
410Dic61—44no—
411Dic61—42no—
412Dic61#53612yes—
413Dic61C22×Q1612yes—
414Dic61C22×Q1612yes—
415Dic61C2×AGL(1,ℤ/8)12yes—
416C2×#533—611no—
417C22×C4⋊Q8—611no—
418#3230—612no—
419#3230—612no—
420#3230—614no—
421#3230—614no—
422#3230—611no—
423#3230—611no—
424#3230—611no—
425#3230D6111yescharacteristic, direct product factor
426C2×#500—612no—
427C2×#487—612no—
428C2×#484—614no—
429C2×#477—614no—
430C2×#431—611no—
431C2×C61—22no—
432C2×C61C2×#53611yescharacteristic
433C2×C61C23×Q1611yescharacteristic
434C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
435D61—22no—
436D61#323014yesdirect product factor
437C23×Q8—1221no—
438#533—611no—
439#533—611no—
440#533—612no—
441#533—612no—
442#533—611no—
443#533—1221no—
444#533—1221no—
445#533—1221no—
446#533—1221no—
447#533C2×D6111yescharacteristic
448C2×C4⋊Q8—612no—
449C2×C4⋊Q8—612no—
450C2×C4⋊Q8—611no—
451C2×C4⋊Q8—612no—
452C2×C4⋊Q8—612no—
453C2×C4⋊Q8—612no—
454C2×C4⋊Q8—611no—
455C2×C4⋊Q8—611no—
456C2×C4⋊Q8—1221no—
457C2×C4⋊Q8—1221no—
458C2×C4⋊Q8—1221no—
459C2×C4⋊Q8—1221no—
460C2×C4⋊Q8—1221no—
461C2×C4⋊Q8—1221no—
462C2×C4⋊Q8C2×D6111yescharacteristic
463C2×#125—1221no—
464C2×C22⋊Q8—612no—
465C2×C22⋊Q8—1221no—
466C2×C4×Q8—612no—
467C2×C4×Q8—1221no—
468C2×#117—1221no—
469C22×C4⋊C4—612no—
470C22×C4⋊C4—1221no—
471C22×C42—611no—
472#500—612no—
473#500—612no—
474#500—618no—
475#500—612no—
476#500C2×D6112yescomplemented
477#487—612no—
478#487—612no—
479#487—618no—
480#487—612no—
481#487C2×D6112yescomplemented
482#484—614no—
483#484—614no—
484#484—618no—
485#484—618no—
486#484—614no—
487#484C2×D6114yes—
488#477—614no—
489#477—614no—
490#477—618no—
491#477—614no—
492#477—618no—
493#477C2×D6114yescomplemented
494#431—611no—
495#431—612no—
496#431—612no—
497#431—612no—
498#431C2×D6111yescharacteristic
499C2×#107—618no—
500C2×C4⋊C8—612no—
501C2×#103—618no—
502C2×C22⋊C8—612no—
503C2×C4×C8—612no—
504C61C2×#323011yescharacteristic, complemented, Sylow
505C22×Q8—21no—
506C22×Q8—612no—
507C22×Q8—1222no—
508C22×Q8—1221no—
509C22×Q8—1222no—
510C22×Q8—1222no—
511C22×Q8—1222no—
512C22×Q8—1222no—
513C22×Q8—1221no—
514C22×Q8—2448no—
515C23×C4—611no—
516C23×C4—611no—
517C23×C4—611no—
518C23×C4—1222no—
519C22×C8—614no—
520C4⋊Q8—21no—
521C4⋊Q8—21no—
522C4⋊Q8—614no—
523C4⋊Q8—614no—
524C4⋊Q8—612no—
525C4⋊Q8—612no—
526C4⋊Q8—612no—
527C4⋊Q8—612no—
528C4⋊Q8—611no—
529C4⋊Q8—611no—
530C4⋊Q8—1222no—
531C4⋊Q8—1222no—
532C4⋊Q8—1222no—
533C4⋊Q8—1222no—
534C4⋊Q8—1222no—
535C4⋊Q8—1222no—
536C4⋊Q8—1221no—
537C4⋊Q8—1221no—
538C4⋊Q8—1221no—
539C4⋊Q8—1222no—
540C4⋊Q8—1222no—
541C4⋊Q8—1222no—
542C4⋊Q8—1222no—
543C4⋊Q8—1221no—
544C4⋊Q8—1221no—
545C4⋊Q8—1221no—
546C4⋊Q8C22×D6111yescharacteristic
547C4⋊Q8C22×D6112yes—
548C4⋊Q8C22×D6112yes—
549C4⋊Q8C22×D6111yescharacteristic
550#125—21no—
551#125—1222no—
552#125—1222no—
553#125—1221no—
554#125—1221no—
555#125—1221no—
556C22⋊Q8—21no—
557C22⋊Q8—612no—
558C22⋊Q8—612no—
559C22⋊Q8—612no—
560C22⋊Q8—1222no—
561C22⋊Q8—1222no—
562C22⋊Q8—1222no—
563C22⋊Q8—1222no—
564C22⋊Q8—1221no—
565C22⋊Q8—1221no—
566C22⋊Q8—1221no—
567C22⋊Q8C22×D6112yes—
568C4×Q8—21no—
569C4×Q8—612no—
570C4×Q8—612no—
571C4×Q8—612no—
572C4×Q8—1222no—
573C4×Q8—1222no—
574C4×Q8—1222no—
575C4×Q8—1221no—
576C4×Q8—1222no—
577C4×Q8—1221no—
578C4×Q8—1221no—
579C4×Q8C22×D6112yes—
580#117—21no—
581#117—1222no—
582#117—1222no—
583#117—1221no—
584#117—1221no—
585#117—1221no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—612no—
588C2×C4⋊C4—614no—
589C2×C4⋊C4—614no—
590C2×C4⋊C4—612no—
591C2×C4⋊C4—1222no—
592C2×C4⋊C4—1222no—
593C2×C4⋊C4—1222no—
594C2×C4⋊C4—1222no—
595C2×C4⋊C4—1222no—
596C2×C4⋊C4—1222no—
597C2×C4⋊C4—1221no—
598C2×C4⋊C4—1221no—
599C2×C4⋊C4—1222no—
600C2×C4⋊C4—1222no—
601C2×C4⋊C4—1221no—
602C2×C4⋊C4—1222no—
603C2×C4⋊C4—1222no—
604C2×C4⋊C4—1221no—
605C2×C4⋊C4C22×D6112yes—
606C2×C22⋊C4—1222no—
607C2×C42—611no—
608C2×C42—611no—
609C2×C42—611no—
610C2×C42—611no—
611C2×C42—611no—
612C2×C42—611no—
613C2×C42—611no—
614C2×C42—611no—
615C2×C42—611no—
616C2×C42—611no—
617C2×C42—611no—
618C2×C42—1222no—
619C2×C42C22×D6111yescharacteristic
620#107—618no—
621#107—618no—
622#107—618no—
623#107C22×D6118yes—
624C4⋊C8—614no—
625C4⋊C8—612no—
626C4⋊C8C22×D6112yes—
627#103—618no—
628#103—618no—
629#103—618no—
630#103C22×D6118yes—
631C22⋊C8—612no—
632C22⋊C8—614no—
633C22⋊C8C22×D6112yes—
634C4×C8—614no—
635C4×C8—612no—
636C4×C8C22×D6112yes—
637C24—611no—
638C2×Q8—21no—
639C2×Q8—22no—
640C2×Q8—22no—
641C2×Q8—44no—
642C2×Q8—612no—
643C2×Q8—1222no—
644C2×Q8—1222no—
645C2×Q8—1224no—
646C2×Q8—1224no—
647C2×Q8—1228no—
648C2×Q8—1221no—
649C2×Q8—1222no—
650C2×Q8—1222no—
651C2×Q8—2444no—
652C2×Q8—2448no—
653C2×Q8—2448no—
654C2×Q8—2444no—
655C2×Q8—2448no—
656C2×Q8—2448no—
657C2×Q8—2448no—
658C2×Q8C23×D6112yes—
659C22×C4—22no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—611no—
664C22×C4—611no—
665C22×C4—611no—
666C22×C4—611no—
667C22×C4—618no—
668C22×C4—611no—
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—611no—
672C22×C4—611no—
673C22×C4—611no—
674C22×C4—611no—
675C22×C4—611no—
676C22×C4—1224no—
677C22×C4—1224no—
678C22×C4—1222no—
679C22×C4—1222no—
680C22×C4—1224no—
681C22×C4—1224no—
682C22×C4—1222no—
683C22×C4—2448no—
684C22×C4D4×D6111yescharacteristic
685C22×C4D4×D6111yescharacteristic
686C22×C4C23×D6111yescharacteristic
687C2×C8—614no—
688C2×C8—1228no—
689C2×C8C23×D6114yes—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—614no—
699C4⋊C4—612no—
700C4⋊C4—1224no—
701C4⋊C4—1224no—
702C4⋊C4—1222no—
703C4⋊C4—1224no—
704C4⋊C4—1224no—
705C4⋊C4—1222no—
706C4⋊C4—1222no—
707C4⋊C4—1222no—
708C4⋊C4—1222no—
709C4⋊C4—1222no—
710C4⋊C4—1222no—
711C4⋊C4—1222no—
712C4⋊C4—1222no—
713C4⋊C4—1222no—
714C4⋊C4—1222no—
715C4⋊C4—1222no—
716C4⋊C4—1222no—
717C4⋊C4—1221no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4C23×D6114yes—
721C4⋊C4C23×D6112yes—
722C22⋊C4—22no—
723C22⋊C4—1222no—
724C22⋊C4—1222no—
725C22⋊C4—1222no—
726C42—22no—
727C42—611no—
728C42—611no—
729C42—611no—
730C42—611no—
731C42—611no—
732C42—611no—
733C42—611no—
734C42—611no—
735C42—611no—
736C42—611no—
737C42—611no—
738C42—611no—
739C42—1222no—
740C42—1222no—
741C42—1222no—
742C42D4×D6111yescharacteristic
743C42D4×D6111yescharacteristic
744C42C23×D6111yescharacteristic
745C42C23×D6111yescharacteristic
746C23—611no—
747C23—614no—
748C23—611no—
749C23—1222no—
750C23—1222no—
751C23C2×D4×D6111yescharacteristic
752Q8—24no—
753Q8—44no—
754Q8—44no—
755Q8—42no—
756Q8—1224no—
757Q8—2444no—
758Q8—2444no—
759Q8—2444no—
760Q8—2448no—
761Q8—2448no—
762Q8—2442no—
763Q8—2444no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—24no—
769C2×C4—44no—
770C2×C4—614no—
771C2×C4—611no—
772C2×C4—611no—
773C2×C4—611no—
774C2×C4—611no—
775C2×C4—614no—
776C2×C4—614no—
777C2×C4—614no—
778C2×C4—614no—
779C2×C4—614no—
780C2×C4—614no—
781C2×C4—611no—
782C2×C4—611no—
783C2×C4—1222no—
784C2×C4—1222no—
785C2×C4—1222no—
786C2×C4—1222no—
787C2×C4—1222no—
788C2×C4—1222no—
789C2×C4—1222no—
790C2×C4—1222no—
791C2×C4—1222no—
792C2×C4—1222no—
793C2×C4—1224no—
794C2×C4—2448no—
795C2×C4—2444no—
796C2×C4—2444no—
797C2×C4—2448no—
798C2×C4—2444no—
799C2×C4Q16×D6114yes—
800C2×C4C2×D4×D6111yescharacteristic
801C2×C4C2×D4×D6111yescharacteristic
802C2×C4C2×D4×D6111yescharacteristic
803C2×C4C2×D4×D6111yescharacteristic
804C2×C4C2×D4×D6111yescharacteristic
805C2×C4C24×D6111yescharacteristic
806C8—24no—
807C8—1224no—
808C22—21no—
809C22—21no—
810C22—612no—
811C22—612no—
812C22—612no—
813C22—612no—
814C22—1228no—
815C22—1221no—
816C22—1221no—
817C22C2×Q16×D6112yes—
818C22C22×D4×D6111yescharacteristic
819C4—21no—
820C4—21no—
821C4—44no—
822C4—42no—
823C4—42no—
824C4—612no—
825C4—612no—
826C4—612no—
827C4—612no—
828C4—1221no—
829C4—1221no—
830C4—2444no—
831C4—2442no—
832C4—2442no—
833C4C2×Q16×D6112yes—
834C4C2×Q16×D6112yes—
835C4AGL(1,ℤ/8)×D6112yes—
836C42−1+4×D6112yes—
837C2—22no—
838C2—614no—
839C2—1222no—
840C2#536×D6111yescharacteristic
841C2C22×Q16×D6111yescharacteristic
842C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3230C2
socleC22×C61C23×D4
prime radicalC23×D61C2×D4
hypercenter#3230D61
hypocenterC61C2×#3230
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3230

Complements

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

NH ≅ G/Ntype
3. #21456972C2semidirect
4. #21456971C2semidirect
5. #21456970C2semidirect
6. #21456969C2semidirect
7. #21456968C2semidirect
8. #21456967C2semidirect
9. #21456966C2semidirect
10. #500×D61C2semidirect
11. #487×D61C2semidirect
13. #477×D61C2semidirect
15. C61×#3230C2semidirect
49. #16840167C22semidirect
50. #16840166C22semidirect
51. #16840165C22semidirect
52. #16840165C22semidirect
53. #16840114C22semidirect
54. #16840113C22semidirect
55. #16840112C22semidirect
56. #16840111C22semidirect
62. #16840058C22semidirect
63. #16840057C22semidirect
64. #16840056C22semidirect
65. #16840055C22semidirect
66. #16840054C22semidirect
78. C61×#500C22semidirect
79. C61×#487C22semidirect
81. C61×#477C22semidirect
425. #3230D61direct (N × H)
436. D61#3230direct (N × H)
476. #500C2×D61semidirect
481. #487C2×D61semidirect
493. #477C2×D61semidirect
504. C61C2×#3230semidirect

Maximal subgroups

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

subgroupindex
#533×D612
C2×C4⋊Q8×D612
#214569722
#214569712
#214569702
#214569692
#214569682
#214569672
#214569662
#500×D612
#487×D612
#484×D612
#477×D612
#431×D612
C61×#32302
C2×#323061