Finite Group Databasebeta

← #30620166

Subgroups — #30620166

Order 15616.

1478 conjugacy classes of subgroups.

The subgroup lattice has 1270 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#435C211yesmaximal, characteristic, complemented
2C2×#16840753C211yesmaximal, characteristic, complemented
3C2×#16840752C211yesmaximal, characteristic, complemented
4#21462335C211yesmaximal, characteristic, complemented
5#21461985C211yesmaximal, characteristic, complemented
6#21461950C211yesmaximal, characteristic, complemented
7#21461834C211yesmaximal, characteristic, complemented
8#21461832C211yesmaximal, characteristic, complemented
9#21461805C211yesmaximal, characteristic, complemented
10#21461804C211yesmaximal, characteristic, complemented
11#21461689C211yesmaximal, characteristic, complemented
12#21461659C211yesmaximal, characteristic, complemented
13#21461659C211yesmaximal, characteristic, complemented
14#21461589C211yesmaximal, characteristic, complemented
15#547×D61C211yesmaximal, characteristic
16C2×D61⋊M16C2211yescharacteristic
17C22×D61⋊C8C2211yescharacteristic
18C2×#14519856C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20#16840794—21no—
21#16840793—21no—
22#16840792—21no—
23#16840791—21no—
24D61⋊(C4⋊C8)C2211yescharacteristic
25#16840753—24no—
26#16840752—24no—
27C2×#14519840C2211yescharacteristic
28C2×#14519840C2211yescharacteristic
29C2×#14519840C2211yescharacteristic
30C2×#14519840C2211yescharacteristic
31C2×#14519840C2211yescharacteristic
32C2×#14519840C2211yescharacteristic
33C2×#14519840C2211yescharacteristic
34C2×#14519840C2211yescharacteristic
35C2×#14519839C2211yescharacteristic
36C2×#14519839C2211yescharacteristic
37C2×#14519839C2211yescharacteristic
38C2×#14519839C2211yescharacteristic
39D61⋊(C22⋊C8)C2211yescharacteristic
40D61⋊(C22⋊C8)C2211yescharacteristic
41#16840721C2211yescharacteristic
42#16840712—21no—
43#16840711—21no—
44#16840710—21no—
45#16840706C2211yescharacteristic
46#16840704C2211yescharacteristic
47#16840704C2211yescharacteristic
48C4×C4⋊#6923C2211yescharacteristic
49C22⋊C4×#6923—21no—
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52#16840635C2211yescharacteristic
53#16840635C2211yescharacteristic
54C2×#41×D61C2211yescharacteristic
55C2×#41×D61C2211yescharacteristic
56#16840417C411yescharacteristic, complemented
57#16840416C411yescharacteristic, complemented
58#16840415C411yescharacteristic, complemented
59#16840414C411yescharacteristic, complemented
60#16840414C411yescharacteristic, complemented
61#16840413—21no—
62#16840412—21no—
63#16840411C411yescharacteristic, complemented
64#16840411C411yescharacteristic, complemented
65#16840410—21no—
66#16840410—21no—
67C4⋊Q8×D61C2211yescharacteristic
68#123×D61—21no—
69#123×D61—21no—
70C22⋊Q8×D61C2211yescharacteristic
71C22⋊Q8×D61C2211yescharacteristic
72#121×D61—21no—
73C4×D4×D61C2211yescharacteristic
74C4×D4×D61C2211yescharacteristic
75C2×C4⋊C4×D61—21no—
76C61×#547C411yescharacteristic, complemented
77C23×#6923—21no—
78C2×#11758213—21no—
79D61⋊M16—22no—
80D61⋊M16—41no—
81C2×#11758217—21no—
82C2×D61⋊C8—22no—
83C2×D61⋊C8—21no—
84C2×D61⋊C8—41no—
85C2×D61⋊C8C2311yescharacteristic
86C2×D61⋊C8C2311yescharacteristic
87C2×D61⋊C8C2311yescharacteristic
88C2×D61⋊C8C2311yescharacteristic
89C22×#92420—21no—
90#14519856—22no—
91#14519856—41no—
92C2×C4⋊#6923—22no—
93C2×C4⋊#6923—21no—
94C2×C4⋊#6923—41no—
95C2×C4⋊#6923C2311yescharacteristic
96C2×C4⋊#6923C2311yescharacteristic
97C2×C4⋊#6923C2311yescharacteristic
98C2×C4⋊#6923C2311yescharacteristic
99C2×C22⋊#6923—21no—
100C2×C22⋊#6923—21no—
101C2×C22⋊#6923—21no—
102C2×C4×#6923—21no—
103C2×C4×#6923—21no—
104#14519844—21no—
105C4⋊#92420—21no—
106#14519840—22no—
107#14519840—22no—
108#14519840—22no—
109#14519840—22no—
110#14519840—41no—
111#14519840—41no—
112#14519840—41no—
113#14519840—41no—
114#14519839—22no—
115#14519839—22no—
116#14519839—22no—
117#14519839D414yescomplemented
118#14519834—21no—
119#14519834—21no—
120C22⋊#92420—21no—
121C22⋊#92420—21no—
122#14519832—21no—
123#14519832—21no—
124(C2×#6923)⋊C4—21no—
125(C2×#6923)⋊C4—21no—
126(C2×#6923)⋊C4—21no—
127(C2×#6923)⋊C4—21no—
128(C2×#6923)⋊C4—21no—
129C2×#11758226C2×C411yescharacteristic
130C2×#11758226C2×C411yescharacteristic, complemented
131C2×#11758222—21no—
132C2×#11758222—21no—
133C2×#11758222C2×C411yescharacteristic
134C2×#11758222C2×C411yescharacteristic, complemented
135C2×#11758224—21no—
136C2×#11758224—21no—
137C2×#11758224C2×C411yescharacteristic
138C2×#11758224C2×C411yescharacteristic, complemented
139#41×D61—22no—
140#41×D61—22no—
141#41×D61—22no—
142#41×D61—22no—
143#41×D61—41no—
144#41×D61—41no—
145#41×D61—41no—
146#41×D61—41no—
147C2×Q8×D61C2311yescharacteristic
148C2×Q8×D61C2311yescharacteristic
149C2×D4×D61—21no—
150C2×D4×D61—21no—
151C2×D4×D61D411yescharacteristic
152C2×D4×D61C2311yescharacteristic
153C22×C4×D61—21no—
154C22×C4×D61—21no—
155C22×C4×D61—21no—
156C22×C4×D61C2311yescharacteristic
157C22×C4×D61C2311yescharacteristic
158#14519777C2×C411yescharacteristic, complemented
159#14519776—21no—
160#14519776—21no—
161#14519775C2×C411yescharacteristic, complemented
162#14519775C2×C411yescharacteristic, complemented
163#14519762—21no—
164#14519762—21no—
165#14519762—21no—
166#14519762—21no—
167#14519761—21no—
168#14519761—21no—
169#14519760—21no—
170#14519760—21no—
171#14519759—21no—
172#14519759—21no—
173#14519759—21no—
174#14519759—21no—
175#14519758—21no—
176#14519758—21no—
177#14519757C2×C411yescharacteristic
178#14519757C2×C411yescharacteristic, complemented
179#14519756C2×C411yescharacteristic
180#14519756C2×C411yescharacteristic, complemented
181#14519755—21no—
182#14519755—21no—
183#14519754—21no—
184#14519754—21no—
185#14519753C2×C411yescharacteristic
186#14519753C2×C411yescharacteristic, complemented
187#14519752—21no—
188#14519751—21no—
189#14519750—21no—
190#14519750—21no—
191#14519749—21no—
192#14519749—21no—
193#14519748—21no—
194C4×D244C2×C411yescharacteristic
195C4×D244C2×C411yescharacteristic, complemented
196D4×Dic61C2×C411yescharacteristic, complemented
197D4×Dic61D411yescharacteristic
198#14519739C2×C411yescharacteristic, complemented
199#14519739D411yescharacteristic
200C4×C22⋊D61—21no—
201C4×C22⋊D61C2×C411yescharacteristic
202C4×C22⋊D61C2×C411yescharacteristic
203#14519737—21no—
204#14519737D411yescharacteristic
205#14519737D411yescharacteristic
206C2×C4⋊Dic61—21no—
207C2×#11758196—21no—
208C2×#11758196—21no—
209C4⋊C4×D61—21no—
210C4⋊C4×D61—21no—
211C4⋊C4×D61—21no—
212C4⋊C4×D61—21no—
213C4⋊C4×D61—21no—
214C4⋊C4×D61—21no—
215C4⋊C4×D61—21no—
216C4⋊C4×D61—21no—
217C4⋊C4×D61D411yescharacteristic
218C4⋊C4×D61C2311yescharacteristic
219C22⋊C4×D61—21no—
220C22⋊C4×D61—21no—
221C22⋊C4×D61—21no—
222C22⋊C4×D61D411yescharacteristic
223C22⋊C4×D61D411yescharacteristic
224C42×D61C2311yescharacteristic
225C2×#41×C61C2×C411yescharacteristic
226C2×#41×C61C2×C411yescharacteristic, complemented
227C4⋊Q8×C61C2×C411yescharacteristic, complemented
228#123×C61—21no—
229#123×C61—21no—
230C22⋊Q8×C61C2×C411yescharacteristic
231C22⋊Q8×C61C2×C411yescharacteristic, complemented
232#121×C61—21no—
233C4×D4×C61C2×C411yescharacteristic
234C4×D4×C61C2×C411yescharacteristic, complemented
235C2×C4⋊C4×C61—21no—
236C23×D61—21no—
237C23×D61C2×D411yescharacteristic
238C23×D61C2×D411yescharacteristic
239C22×#6923—21no—
240C22×#6923—21no—
241C22×#6923—21no—
242C22×#6923—21no—
243C22×#6923—42no—
244C22×#6923—42no—
245C22×#6923—81no—
246#41×C61—22no—
247#41×C61—22no—
248#41×C61—41no—
249#41×C61—41no—
250C2×Q8×C61C22×C411yescharacteristic
251C2×Q8×C61C22×C411yescharacteristic
252C2×D4×C61—21no—
253C2×D4×C61—21no—
254C2×D4×C61C22⋊C411yescharacteristic
255C2×D4×C61C22×C411yescharacteristic
256C22×C4×C61—21no—
257C22×C4×C61—21no—
258C22×C4×C61—21no—
259C22×C4×C61C22×C411yescharacteristic
260C22×C4×C61C22×C411yescharacteristic
261C2×C22⋊D61—21no—
262C2×C22⋊D61—21no—
263C2×C22⋊D61—21no—
264C2×C22⋊D61—21no—
265C2×C22⋊D61—21no—
266C2×C22⋊D61C22⋊C411yescharacteristic
267C2×C22⋊D61C22⋊C411yescharacteristic
268C22×Dic61—21no—
269C22×Dic61—21no—
270C22×Dic61—21no—
271C22×Dic61C2×D411yescharacteristic
272C22×Dic61C2×D411yescharacteristic
273#11758226—22no—
274#11758226—22no—
275#11758226—41no—
276#11758226—41no—
277Q8×D61—21no—
278Q8×D61—21no—
279Q8×D61—21no—
280Q8×D61—21no—
281Q8×D61—21no—
282Q8×D61—21no—
283Q8×D61—21no—
284Q8×D61—21no—
285#11758224—22no—
286#11758224—22no—
287#11758224—41no—
288#11758224—41no—
289#11758224—42no—
290#11758224—42no—
291#11758224—42no—
292#11758224—42no—
293D4×D61—21no—
294D4×D61—21no—
295D4×D61—41no—
296D4×D61—41no—
297D4×D61—42no—
298D4×D61—42no—
299D4×D61—42no—
300D4×D61—42no—
301D4×D61C2×D412yes—
302D4×D61#4112yes—
303#11758222—22no—
304#11758222—22no—
305#11758222—41no—
306#11758222—41no—
307#11758222—42no—
308#11758222—42no—
309#11758222—42no—
310#11758222—42no—
311C2×D244—21no—
312C2×D244—21no—
313C2×D244C22⋊C411yescharacteristic
314C2×D244C22×C411yescharacteristic
315C2×C4×D61—21no—
316C2×C4×D61—21no—
317C2×C4×D61—21no—
318C2×C4×D61—21no—
319C2×C4×D61—21no—
320C2×C4×D61—21no—
321C2×C4×D61—21no—
322C2×C4×D61—21no—
323C2×C4×D61—21no—
324C2×C4×D61—21no—
325C2×C4×D61—21no—
326C2×C4×D61—21no—
327C2×C4×D61—21no—
328C2×C4×D61—21no—
329C2×C4×D61—21no—
330C2×C4×D61—21no—
331C2×C4×D61—21no—
332C2×C4×D61—42no—
333C2×C4×D61—42no—
334C2×C4×D61—42no—
335C2×C4×D61—42no—
336C2×C4×D61—42no—
337C2×C4×D61—42no—
338C2×C4×D61C22×C411yescharacteristic
339C2×C4×D61C22×C411yescharacteristic
340C2×C4×D61C2×D411yescharacteristic
341C2×C4×D61C2×D411yescharacteristic
342C2×C4×D61C2×D411yescharacteristic
343C2×C4×D61C2×D411yescharacteristic
344C2×C4×D61C2×D411yescharacteristic
345C2×C4×D61C2×D411yescharacteristic
346C2×C4×D61C2411yescharacteristic
347C2×Dic122—21no—
348C2×Dic122—21no—
349C2×Dic122C22×C411yescharacteristic
350C2×Dic122C22×C411yescharacteristic
351C22⋊#6923—42no—
352C22⋊#6923—42no—
353C22⋊#6923—81no—
354#11758217—42no—
355C2×#92420—21no—
356C2×#92420—21no—
357C2×#92420—21no—
358C2×#92420—21no—
359C2×#92420—42no—
360C4⋊#6923—21no—
361C4⋊#6923—21no—
362C4⋊#6923—21no—
363C4⋊#6923—21no—
364C4⋊#6923—21no—
365C4⋊#6923—21no—
366C4⋊#6923—21no—
367C4⋊#6923—42no—
368C4⋊#6923C2×D412yes—
369C4×#6923—42no—
370C4×#6923—81no—
371#11758213—42no—
372D61⋊C8—21no—
373D61⋊C8—21no—
374D61⋊C8—21no—
375D61⋊C8—21no—
376D61⋊C8—21no—
377D61⋊C8—21no—
378D61⋊C8—21no—
379D61⋊C8—42no—
380D61⋊C8C2×D412yes—
381C4⋊C4×C61—21no—
382C4⋊C4×C61—21no—
383C4⋊C4×C61—21no—
384C4⋊C4×C61—21no—
385C4⋊C4×C61C22⋊C411yescharacteristic
386C4⋊C4×C61C22×C411yescharacteristic
387C22⋊C4×C61—21no—
388C22⋊C4×C61—21no—
389C22⋊C4×C61—21no—
390C22⋊C4×C61C22⋊C411yescharacteristic
391C22⋊C4×C61C22⋊C411yescharacteristic
392C42×C61C22×C411yescharacteristic
393C22⋊Dic61—21no—
394C22⋊Dic61—21no—
395C22⋊Dic61—21no—
396C22⋊Dic61C22⋊C411yescharacteristic
397C22⋊Dic61C22⋊C411yescharacteristic
398#11758198—21no—
399#11758198—21no—
400#11758198—21no—
401#11758198—21no—
402#11758198—21no—
403#11758198—21no—
404#11758198C22⋊C411yescharacteristic
405#11758198C22⋊C411yescharacteristic
406#11758198C22⋊C411yescharacteristic
407#11758198C22⋊C411yescharacteristic
408C4⋊Dic61—21no—
409C4⋊Dic61—21no—
410C4⋊Dic61—21no—
411C4⋊Dic61—21no—
412C4⋊Dic61C22⋊C411yescharacteristic
413C4⋊Dic61C22×C411yescharacteristic
414#11758196—21no—
415#11758196—21no—
416#11758196—21no—
417#11758196—21no—
418#11758196—21no—
419#11758196—21no—
420#11758196—21no—
421#11758196—21no—
422#11758196—21no—
423#11758196C22⋊C411yescharacteristic
424#11758196C22⋊C411yescharacteristic
425C4×Dic61C22×C411yescharacteristic
426C4×Dic61C2×D411yescharacteristic
427C4×Dic61C2×D411yescharacteristic
428C23×C61—21no—
429C23×C61C2×C22⋊C411yescharacteristic
430C23×C61C2×C22⋊C411yescharacteristic
431C22×D61—21no—
432C22×D61—21no—
433C22×D61—21no—
434C22×D61—22no—
435C22×D61—21no—
436C22×D61—21no—
437C22×D61—22no—
438C22×D61—21no—
439C22×D61—21no—
440C22×D61—21no—
441C22×D61—21no—
442C22×D61—21no—
443C22×D61—21no—
444C22×D61—21no—
445C22×D61—21no—
446C22×D61—41no—
447C22×D61—41no—
448C22×D61—41no—
449C22×D61—41no—
450C22×D61C2×C22⋊C411yescharacteristic
451C22×D61C2×C22⋊C411yescharacteristic
452C22×D61C22×D411yescharacteristic
453C2×#6923—22no—
454C2×#6923—41no—
455C2×#6923—41no—
456C2×#6923—41no—
457C2×#6923—41no—
458C2×#6923—41no—
459C2×#6923—41no—
460C2×#6923—41no—
461C2×#6923—41no—
462C2×#6923—41no—
463C2×#6923—41no—
464C2×#6923—41no—
465C2×#6923—84no—
466Q8×C61—21no—
467Q8×C61—21no—
468Q8×C61—21no—
469Q8×C61—21no—
470D4×C61—21no—
471D4×C61—41no—
472D4×C61—42no—
473D4×C61—42no—
474D4×C61C4×D412yes—
475C2×C4×C61—21no—
476C2×C4×C61—21no—
477C2×C4×C61—21no—
478C2×C4×C61—21no—
479C2×C4×C61—21no—
480C2×C4×C61—21no—
481C2×C4×C61—21no—
482C2×C4×C61—42no—
483C2×C4×C61—42no—
484C2×C4×C61—42no—
485C2×C4×C61C2×C22⋊C411yescharacteristic
486C2×C4×C61C2×C22⋊C411yescharacteristic
487C2×C4×C61C2×C22⋊C411yescharacteristic
488C2×C4×C61C2×C22⋊C411yescharacteristic
489C2×C4×C61C23×C411yescharacteristic
490C22⋊D61—22no—
491C22⋊D61—22no—
492C22⋊D61—41no—
493C22⋊D61—41no—
494C22⋊D61—42no—
495C22⋊D61—42no—
496C22⋊D61—42no—
497C22⋊D61—42no—
498C2×Dic61—21no—
499C2×Dic61—21no—
500C2×Dic61—21no—
501C2×Dic61—21no—
502C2×Dic61—21no—
503C2×Dic61—21no—
504C2×Dic61—21no—
505C2×Dic61—42no—
506C2×Dic61—42no—
507C2×Dic61—42no—
508C2×Dic61C2×C22⋊C411yescharacteristic
509C2×Dic61C2×C22⋊C411yescharacteristic
510C2×Dic61C2×C22⋊C411yescharacteristic
511C2×Dic61C2×C22⋊C411yescharacteristic
512C2×Dic61C22×D411yescharacteristic
513D244—21no—
514D244—41no—
515D244—42no—
516D244—42no—
517D244C4×D412yes—
518C4×D61—21no—
519C4×D61—21no—
520C4×D61—21no—
521C4×D61—21no—
522C4×D61—21no—
523C4×D61—21no—
524C4×D61—21no—
525C4×D61—21no—
526C4×D61—21no—
527C4×D61—21no—
528C4×D61—21no—
529C4×D61—21no—
530C4×D61—21no—
531C4×D61—21no—
532C4×D61—21no—
533C4×D61—21no—
534C4×D61—42no—
535C4×D61—42no—
536C4×D61—42no—
537C4×D61—42no—
538C4×D61—42no—
539C4×D61—42no—
540C4×D61—41no—
541C4×D61—41no—
542C4×D61—41no—
543C4×D61—41no—
544C4×D61—41no—
545C4×D61—41no—
546C4×D61C22×D411yescharacteristic
547C4×D61C2×#4111yescharacteristic
548C4×D61H(5,𝔽2)11yescharacteristic
549C4×D61H(5,𝔽2)11yescharacteristic
550Dic122—21no—
551Dic122—21no—
552Dic122—21no—
553Dic122—21no—
554Dic122—41no—
555Dic122—41no—
556Dic122—41no—
557Dic122—41no—
558#92420—22no—
559#92420—41no—
560#92420—41no—
561#92420—41no—
562#22420—611nomaximal, Sylow
563C22×C61—21no—
564C22×C61—21no—
565C22×C61—22no—
566C22×C61—21no—
567C22×C61—21no—
568C22×C61—21no—
569C22×C61—21no—
570C22×C61—41no—
571C22×C61—41no—
572C22×C61C22×C22⋊C411yescharacteristic
573C2×D61—21no—
574C2×D61—21no—
575C2×D61—22no—
576C2×D61—21no—
577C2×D61—21no—
578C2×D61—21no—
579C2×D61—21no—
580C2×D61—41no—
581C2×D61—41no—
582C2×D61—41no—
583C2×D61—41no—
584C2×D61—42no—
585C2×D61—41no—
586C2×D61—41no—
587C2×D61—42no—
588C2×D61—41no—
589C2×D61—41no—
590C2×D61—42no—
591C2×D61—41no—
592C2×D61—41no—
593C2×D61—42no—
594C2×D61D4211yescharacteristic
595C2×D61#54611yescharacteristic
596C2×D61#57511yescharacteristic
597C2×D61#57511yescharacteristic
598C2×D61#57711yescharacteristic
599C2×D61#57811yescharacteristic
600#6923—42no—
601#6923—81no—
602#6923—81no—
603#6923—81no—
604C4×C61—21no—
605C4×C61—21no—
606C4×C61—21no—
607C4×C61—21no—
608C4×C61—41no—
609C4×C61—41no—
610C4×C61—41no—
611C4×C61C2×C4×D411yescharacteristic
612C4×C61#51811yescharacteristic
613Dic61—21no—
614Dic61—21no—
615Dic61—21no—
616Dic61—21no—
617Dic61—41no—
618Dic61—41no—
619Dic61—41no—
620Dic61D4211yescharacteristic
621Dic61#54611yescharacteristic
622C2×#547—611no—
623C2×#435—611no—
624C2×#417—611no—
625C2×#416—611no—
626#2352—611no—
627#1981—611no—
628#1960—611no—
629#1894—611no—
630#1892—611no—
631#1873—611no—
632#1872—611no—
633#1804—611no—
634#1788—611no—
635#1788—611no—
636#1762—611no—
637C2×C61—41no—
638C2×C61—41no—
639C2×C61—42no—
640C2×C61D4×C22⋊C411yescharacteristic
641C2×C61#289611yescharacteristic
642C2×C61#289811yescharacteristic
643D61—41no—
644D61—41no—
645D61—42no—
646D61#326711yescharacteristic
647D61#326911yescharacteristic
648D61#330711yescharacteristic
649D61#331511yescharacteristic
650C22×#41—611no—
651C22×#41—611no—
652C22×M16—611no—
653C23×C8—611no—
654#547—611no—
655#547—611no—
656#547—611no—
657#547—611no—
658#547—611no—
659#547—611no—
660#547—611no—
661#547—1221no—
662#547—1221no—
663#547—1221no—
664#547—1221no—
665#547#692311yescharacteristic, complemented
666C2×C4⋊Q8—611no—
667C2×#123—1221no—
668C2×#123—1221no—
669C2×C22⋊Q8—611no—
670C2×C22⋊Q8—611no—
671C2×#121—1221no—
672C2×C4×D4—611no—
673C2×C4×D4—611no—
674C2×#117—611no—
675C22×C4⋊C4—611no—
676C22×C4⋊C4—1221no—
677#435—1221no—
678#435—1221no—
679#435—1221no—
680#435—1221no—
681C2×C4⋊C8—611no—
682#417—1224no—
683#416—1224no—
684C2×#103—611no—
685C2×#103—611no—
686C2×#103—611no—
687C2×#103—611no—
688C2×#103—611no—
689C2×#103—611no—
690C2×#103—611no—
691C2×#103—611no—
692C2×#102—611no—
693C2×#102—611no—
694C2×#102—611no—
695C2×#102—611no—
696C2×C22⋊C8—611no—
697C2×C22⋊C8—611no—
698C2×#97—611no—
699#388—1221no—
700#387—1221no—
701#386—1221no—
702#382—611no—
703#380—611no—
704#380—611no—
705C4×C4⋊C4—611no—
706C4×C22⋊C4—1221no—
707#340—611no—
708#340—611no—
709#340—611no—
710#340—611no—
711C61#2242011yescharacteristic, complemented, Sylow
712C2×#41—611no—
713C2×#41—611no—
714C2×#41—611no—
715C2×#41—611no—
716C2×#41—611no—
717C2×#41—611no—
718C2×#41—1221no—
719C2×#41—1221no—
720C2×#41—1221no—
721C2×#41—1221no—
722C2×#41—1222no—
723C2×#41—1222no—
724C2×#41—1222no—
725C2×#41—1222no—
726C2×#41—2441no—
727C2×#41—2441no—
728C2×#41—2441no—
729C2×#41—2441no—
730C2×#41C2×#692311yescharacteristic
731C2×#41C2×#692311yescharacteristic, complemented
732C22×Q8—611no—
733C22×Q8—611no—
734C22×D4—611no—
735C22×D4—611no—
736C22×D4—1221no—
737C22×D4—1221no—
738C23×C4—611no—
739C23×C4—611no—
740C23×C4—1221no—
741C23×C4—1221no—
742C23×C4—1221no—
743C23×C4—1221no—
744C2×M16—1222no—
745C2×M16—1221no—
746C2×M16—1221no—
747C2×M16—2441no—
748C22×C8—611no—
749C22×C8—611no—
750C22×C8—611no—
751C22×C8—611no—
752C22×C8—1222no—
753C22×C8—1221no—
754C22×C8—1221no—
755C22×C8—2441no—
756C4⋊Q8—611no—
757C4⋊Q8—611no—
758C4⋊Q8—611no—
759C4⋊Q8—1221no—
760C4⋊Q8—1221no—
761C4⋊Q8C2×#692311yescharacteristic, complemented
762#123—21no—
763#123—21no—
764#123—1221no—
765#123—1221no—
766#123—1221no—
767#123—1221no—
768#123—1221no—
769#123—1221no—
770#123—1221no—
771#123—1221no—
772#123—1221no—
773#123—1221no—
774#123—1221no—
775#123—1221no—
776#123—1221no—
777#123—1221no—
778C22⋊Q8—611no—
779C22⋊Q8—611no—
780C22⋊Q8—611no—
781C22⋊Q8—611no—
782C22⋊Q8—611no—
783C22⋊Q8—611no—
784C22⋊Q8—1221no—
785C22⋊Q8—1221no—
786C22⋊Q8—1221no—
787C22⋊Q8—1221no—
788C22⋊Q8C2×#692311yescharacteristic
789C22⋊Q8C2×#692311yescharacteristic, complemented
790#121—21no—
791#121—1221no—
792#121—1221no—
793#121—1221no—
794#121—1221no—
795#121—1221no—
796#121—1221no—
797#121—1221no—
798C4×D4—611no—
799C4×D4—611no—
800C4×D4—611no—
801C4×D4—611no—
802C4×D4—611no—
803C4×D4—611no—
804C4×D4—611no—
805C4×D4—611no—
806C4×D4—611no—
807C4×D4—611no—
808C4×D4—1221no—
809C4×D4—1221no—
810C4×D4C2×#692311yescharacteristic
811C4×D4C2×#692311yescharacteristic, complemented
812#117—1222no—
813#117—2441no—
814C2×C4⋊C4—21no—
815C2×C4⋊C4—611no—
816C2×C4⋊C4—611no—
817C2×C4⋊C4—611no—
818C2×C4⋊C4—611no—
819C2×C4⋊C4—611no—
820C2×C4⋊C4—611no—
821C2×C4⋊C4—1221no—
822C2×C4⋊C4—1221no—
823C2×C4⋊C4—1221no—
824C2×C4⋊C4—1221no—
825C2×C4⋊C4—1221no—
826C2×C4⋊C4—1221no—
827C2×C4⋊C4—1221no—
828C2×C4⋊C4—1221no—
829C2×C4⋊C4—1221no—
830C2×C4⋊C4—1221no—
831C2×C4⋊C4—1222no—
832C2×C4⋊C4—1221no—
833C2×C4⋊C4—1221no—
834C2×C4⋊C4—2441no—
835C2×C22⋊C4—611no—
836C2×C22⋊C4—611no—
837C2×C22⋊C4—1221no—
838C2×C22⋊C4—1221no—
839C2×C22⋊C4—1221no—
840C2×C22⋊C4—1221no—
841C2×C22⋊C4—1221no—
842C2×C22⋊C4—1221no—
843C2×C42—611no—
844C2×C42—1221no—
845C2×C42—1221no—
846C4⋊C8—1221no—
847C4⋊C8—1221no—
848#103—1222no—
849#103—1222no—
850#103—1222no—
851#103—1222no—
852#103—2441no—
853#103—2441no—
854#103—2441no—
855#103—2441no—
856#102—614no—
857#102—1222no—
858#102—1222no—
859#102—1222no—
860C22⋊C8—1221no—
861C22⋊C8—1221no—
862C22⋊C8—1221no—
863C22⋊C8—1221no—
864#97—1221no—
865#97—1221no—
866#95—1221no—
867#95—1221no—
868#95—1221no—
869#95—1221no—
870#95—1221no—
871C24—611no—
872C24—611no—
873C24—1221no—
874#41—22no—
875#41—22no—
876#41—41no—
877#41—41no—
878#41—1222no—
879#41—1222no—
880#41—1222no—
881#41—1222no—
882#41—1222no—
883#41—1222no—
884#41—2441no—
885#41—2441no—
886#41—2442no—
887#41—2442no—
888#41—2442no—
889#41—2442no—
890#41—2441no—
891#41—2441no—
892#41—2442no—
893#41—2442no—
894#41—2442no—
895#41—2442no—
896#41—2441no—
897#41—2441no—
898C2×Q8—611no—
899C2×Q8—611no—
900C2×Q8—1221no—
901C2×Q8—1221no—
902C2×Q8—1221no—
903C2×Q8—1221no—
904C2×Q8—1221no—
905C2×Q8—1221no—
906C2×Q8—1221no—
907C2×Q8—1221no—
908C2×Q8—1221no—
909C2×Q8—1221no—
910C2×Q8C22×#692311yescharacteristic
911C2×Q8C22×#692311yescharacteristic
912C2×D4—21no—
913C2×D4—21no—
914C2×D4—612no—
915C2×D4—612no—
916C2×D4—611no—
917C2×D4—611no—
918C2×D4—611no—
919C2×D4—611no—
920C2×D4—1221no—
921C2×D4—1221no—
922C2×D4—1221no—
923C2×D4—1221no—
924C2×D4—1221no—
925C2×D4—1221no—
926C2×D4—1221no—
927C2×D4—1221no—
928C2×D4—1221no—
929C2×D4—2441no—
930C2×D4—2441no—
931C2×D4—2442no—
932C2×D4—2442no—
933C2×D4—2442no—
934C2×D4—2442no—
935C2×D4C22⋊#692311yescharacteristic
936C2×D4C22×#692311yescharacteristic
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—611no—
941C22×C4—611no—
942C22×C4—611no—
943C22×C4—611no—
944C22×C4—611no—
945C22×C4—611no—
946C22×C4—611no—
947C22×C4—611no—
948C22×C4—611no—
949C22×C4—611no—
950C22×C4—611no—
951C22×C4—1221no—
952C22×C4—1221no—
953C22×C4—1221no—
954C22×C4—1221no—
955C22×C4—1221no—
956C22×C4—1221no—
957C22×C4—1221no—
958C22×C4—1221no—
959C22×C4—1221no—
960C22×C4—1221no—
961C22×C4—1221no—
962C22×C4—1221no—
963C22×C4—1221no—
964C22×C4—1221no—
965C22×C4—1221no—
966C22×C4—1221no—
967C22×C4—1221no—
968C22×C4—1221no—
969C22×C4—1221no—
970C22×C4—1221no—
971C22×C4—1221no—
972C22×C4—1221no—
973C22×C4—1221no—
974C22×C4—1221no—
975C22×C4—4881no—
976C22×C4—2442no—
977C22×C4—2442no—
978C22×C4—2442no—
979C22×C4—2442no—
980C22×C4—2442no—
981C22×C4—2442no—
982C22×C4—2442no—
983C22×C4—2442no—
984C22×C4C22×#692311yescharacteristic
985C22×C4C22×#692311yescharacteristic
986M16—2442no—
987M16—2442no—
988C2×C8—612no—
989C2×C8—1221no—
990C2×C8—1221no—
991C2×C8—1221no—
992C2×C8—1221no—
993C2×C8—1221no—
994C2×C8—1221no—
995C2×C8—1221no—
996C2×C8—1221no—
997C2×C8—1221no—
998C2×C8—1221no—
999C2×C8—1221no—
1000C2×C8—2442no—
1001C2×C8—2442no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—611no—
1007C4⋊C4—611no—
1008C4⋊C4—611no—
1009C4⋊C4—612no—
1010C4⋊C4—611no—
1011C4⋊C4—1221no—
1012C4⋊C4—1221no—
1013C4⋊C4—1221no—
1014C4⋊C4—1221no—
1015C4⋊C4—1221no—
1016C4⋊C4—1221no—
1017C4⋊C4—1221no—
1018C4⋊C4—1221no—
1019C4⋊C4—1221no—
1020C4⋊C4—1221no—
1021C4⋊C4—1221no—
1022C4⋊C4—1221no—
1023C4⋊C4—1221no—
1024C4⋊C4—1221no—
1025C4⋊C4—1221no—
1026C4⋊C4—1221no—
1027C4⋊C4—1221no—
1028C4⋊C4—1221no—
1029C4⋊C4—1221no—
1030C4⋊C4—1221no—
1031C4⋊C4—2442no—
1032C4⋊C4C22⋊#692311yescharacteristic
1033C4⋊C4C22×#692311yescharacteristic
1034C22⋊C4—21no—
1035C22⋊C4—21no—
1036C22⋊C4—21no—
1037C22⋊C4—611no—
1038C22⋊C4—611no—
1039C22⋊C4—611no—
1040C22⋊C4—611no—
1041C22⋊C4—611no—
1042C22⋊C4—611no—
1043C22⋊C4—1221no—
1044C22⋊C4—1221no—
1045C22⋊C4—1221no—
1046C22⋊C4—1221no—
1047C22⋊C4—1221no—
1048C22⋊C4—1221no—
1049C22⋊C4—1221no—
1050C22⋊C4—1221no—
1051C22⋊C4—1221no—
1052C22⋊C4—4881no—
1053C22⋊C4—2442no—
1054C22⋊C4—2442no—
1055C22⋊C4C22⋊#692311yescharacteristic
1056C22⋊C4C22⋊#692311yescharacteristic
1057C42—611no—
1058C42—611no—
1059C42—611no—
1060C42—4881no—
1061C42—2442no—
1062C42C22×#692311yescharacteristic
1063C23—21no—
1064C23—611no—
1065C23—611no—
1066C23—611no—
1067C23—1221no—
1068C23—1221no—
1069C23—1221no—
1070C23—1221no—
1071C23—1221no—
1072C23—1221no—
1073C23—1221no—
1074C23—1222no—
1075C23—1222no—
1076C23—1221no—
1077C23—1221no—
1078C23—1221no—
1079C23—1221no—
1080C23—1221no—
1081C23—1221no—
1082C23—2441no—
1083C23—2441no—
1084C23—2441no—
1085C23—2441no—
1086C23C2×C22⋊#692311yescharacteristic
1087C23C2×C22⋊#692311yescharacteristic
1088Q8—21no—
1089Q8—21no—
1090Q8—21no—
1091Q8—21no—
1092Q8—1221no—
1093Q8—1221no—
1094Q8—1221no—
1095Q8—1221no—
1096Q8—2441no—
1097Q8—2441no—
1098Q8—2441no—
1099Q8—2441no—
1100D4—21no—
1101D4—41no—
1102D4—42no—
1103D4—42no—
1104D4—612no—
1105D4—1222no—
1106D4—1222no—
1107D4—1221no—
1108D4—2441no—
1109D4—2442no—
1110D4—2442no—
1111D4—2441no—
1112D4—2441no—
1113D4—2442no—
1114D4—2442no—
1115D4—2442no—
1116D4—2442no—
1117D4D4×#692312yes—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—42no—
1126C2×C4—42no—
1127C2×C4—42no—
1128C2×C4—611no—
1129C2×C4—611no—
1130C2×C4—611no—
1131C2×C4—611no—
1132C2×C4—611no—
1133C2×C4—611no—
1134C2×C4—611no—
1135C2×C4—611no—
1136C2×C4—611no—
1137C2×C4—1221no—
1138C2×C4—1221no—
1139C2×C4—1221no—
1140C2×C4—1221no—
1141C2×C4—1221no—
1142C2×C4—1221no—
1143C2×C4—1221no—
1144C2×C4—1221no—
1145C2×C4—1221no—
1146C2×C4—1221no—
1147C2×C4—1221no—
1148C2×C4—1221no—
1149C2×C4—1221no—
1150C2×C4—1221no—
1151C2×C4—1221no—
1152C2×C4—1221no—
1153C2×C4—1221no—
1154C2×C4—1221no—
1155C2×C4—1221no—
1156C2×C4—1221no—
1157C2×C4—1222no—
1158C2×C4—1221no—
1159C2×C4—1221no—
1160C2×C4—1221no—
1161C2×C4—4884no—
1162C2×C4—2442no—
1163C2×C4—2442no—
1164C2×C4—2442no—
1165C2×C4—2442no—
1166C2×C4—2442no—
1167C2×C4—2442no—
1168C2×C4—2441no—
1169C2×C4—2441no—
1170C2×C4—2441no—
1171C2×C4—2441no—
1172C2×C4—2441no—
1173C2×C4—2441no—
1174C2×C4—2442no—
1175C2×C4—2442no—
1176C2×C4—2442no—
1177C2×C4—2441no—
1178C2×C4—2441no—
1179C2×C4—2441no—
1180C2×C4—2441no—
1181C2×C4—2441no—
1182C2×C4—2441no—
1183C2×C4—2441no—
1184C2×C4—2441no—
1185C2×C4—2441no—
1186C2×C4—2441no—
1187C2×C4—2441no—
1188C2×C4C2×C22⋊#692311yescharacteristic
1189C2×C4C2×C22⋊#692311yescharacteristic
1190C2×C4C2×C22⋊#692311yescharacteristic
1191C2×C4C2×C22⋊#692311yescharacteristic
1192C2×C4C23×#692311yescharacteristic
1193C8—1222no—
1194C8—2441no—
1195C8—2441no—
1196C8—2441no—
1197C22—21no—
1198C22—21no—
1199C22—22no—
1200C22—21no—
1201C22—21no—
1202C22—21no—
1203C22—21no—
1204C22—41no—
1205C22—41no—
1206C22—611no—
1207C22—611no—
1208C22—611no—
1209C22—611no—
1210C22—611no—
1211C22—611no—
1212C22—1221no—
1213C22—1221no—
1214C22—1222no—
1215C22—1221no—
1216C22—1221no—
1217C22—1221no—
1218C22—1221no—
1219C22—2441no—
1220C22—2441no—
1221C22—2441no—
1222C22—2441no—
1223C22—2441no—
1224C22—2441no—
1225C22—2441no—
1226C22—2441no—
1227C22—2442no—
1228C22—2442no—
1229C22—2442no—
1230C22—2442no—
1231C22—2441no—
1232C22—2441no—
1233C22C22×C22⋊#692311yescharacteristic
1234C4—21no—
1235C4—21no—
1236C4—21no—
1237C4—21no—
1238C4—41no—
1239C4—41no—
1240C4—41no—
1241C4—611no—
1242C4—611no—
1243C4—1221no—
1244C4—1221no—
1245C4—1221no—
1246C4—1221no—
1247C4—4881no—
1248C4—4881no—
1249C4—4881no—
1250C4—2442no—
1251C4—2441no—
1252C4—2441no—
1253C4—2441no—
1254C4C2×D4×#692311yescharacteristic
1255C4#1684082911yescharacteristic
1256C2—41no—
1257C2—41no—
1258C2—42no—
1259C2—611no—
1260C2—611no—
1261C2—611no—
1262C2—611no—
1263C2—2441no—
1264C2—2441no—
1265C2—2442no—
1266C2D4×C22⋊#692311yescharacteristic
1267C2#2146243911yescharacteristic
1268C2#2146244111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#547C4
socleC22×C61C22×C22⋊C4
prime radical#547×D61C2
cosocleC2×C4×D61C24
hypercenter#547#6923
hypocenterC61#22420
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. D61⋊#435C2semidirect
2. C2×#16840753C2semidirect
3. C2×#16840752C2semidirect
4. #21462335C2semidirect
5. #21461985C2semidirect
6. #21461950C2semidirect
7. #21461834C2semidirect
8. #21461832C2semidirect
9. #21461805C2semidirect
10. #21461804C2semidirect
11. #21461689C2semidirect
12. #21461659C2semidirect
13. #21461659C2semidirect
14. #21461589C2semidirect
56. #16840417C4semidirect
57. #16840416C4semidirect
58. #16840415C4semidirect
59. #16840414C4semidirect
60. #16840414C4semidirect
63. #16840411C4semidirect
64. #16840411C4semidirect
76. C61×#547C4semidirect
117. #14519839D4semidirect
130. C2×#11758226C2×C4semidirect
134. C2×#11758222C2×C4semidirect
138. C2×#11758224C2×C4semidirect
158. #14519777C2×C4semidirect
161. #14519775C2×C4semidirect
162. #14519775C2×C4semidirect
178. #14519757C2×C4semidirect
180. #14519756C2×C4semidirect
186. #14519753C2×C4semidirect
195. C4×D244C2×C4semidirect
196. D4×Dic61C2×C4semidirect
198. #14519739C2×C4semidirect
226. C2×#41×C61C2×C4semidirect
227. C4⋊Q8×C61C2×C4semidirect
231. C22⋊Q8×C61C2×C4semidirect
234. C4×D4×C61C2×C4semidirect
665. #547#6923semidirect
711. C61#22420semidirect
731. C2×#41C2×#6923semidirect
761. C4⋊Q8C2×#6923semidirect
789. C22⋊Q8C2×#6923semidirect
811. C4×D4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4352
C2×#168407532
C2×#168407522
#214623352
#214619852
#214619502
#214618342
#214618322
#214618052
#214618042
#214616892
#214616592
#214615892
#547×D612
#2242061