Finite Group Databasebeta

← C61×#22506 #29525939

Subgroups — C61×#22506 #29525939

Order 15616.

1148 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3475C211yesmaximal, characteristic
2D4×M16×C61C211yesmaximal, characteristic, complemented
3C61×#2290C211yesmaximal, characteristic, complemented
4C61×#1995C211yesmaximal, characteristic, complemented
5C61×#1986C211yesmaximal, characteristic, complemented
6C61×#1897C211yesmaximal, characteristic, complemented
7C61×#1896C211yesmaximal, characteristic, complemented
8C61×#1871C211yesmaximal, characteristic, complemented
9C61×#1871C211yesmaximal, characteristic, complemented
10C61×#1826C211yesmaximal, characteristic, complemented
11C61×#1826C211yesmaximal, characteristic, complemented
12C61×#1806C211yesmaximal, characteristic, complemented
13C61×#1759C211yesmaximal, characteristic, complemented
14C61×#1733C211yesmaximal, characteristic, complemented
15C2×C61×#339C211yesmaximal, characteristic, complemented
16C22×M16×C61C2211yescharacteristic
17C22×M16×C61C2211yescharacteristic
18C61×#556C411yescharacteristic, complemented
19C61×#555C411yescharacteristic, complemented
20C61×#554C411yescharacteristic, complemented
21C61×#553C411yescharacteristic, complemented
22C61×#553C411yescharacteristic, complemented
23C61×#552—21no—
24C61×#552C411yescharacteristic, complemented
25C61×#552C411yescharacteristic, complemented
26C61×#551—21no—
27C61×#551—21no—
28C61×#547C411yescharacteristic, complemented
29C61×#546—21no—
30C61×#533C2211yescharacteristic
31C61×#529—21no—
32C61×#529—21no—
33C61×#529—21no—
34C61×#525C2211yescharacteristic
35C61×#525C2211yescharacteristic
36C4×#41×C61—21no—
37C4×#41×C61C2211yescharacteristic
38C2×C4×D4×C61C2211yescharacteristic
39C2×#117×C61C2211yescharacteristic
40C2×#117×C61C2211yescharacteristic
41C2×#117×C61C2211yescharacteristic
42C22×C42×C61C2211yescharacteristic
43C61×#436—21no—
44C61×#435—21no—
45C61×#435—21no—
46C8×D4×C61—21no—
47C61×#423C2211yescharacteristic
48C2×#104×C61C2211yescharacteristic
49C2×#104×C61C2211yescharacteristic
50C2×#104×C61C2211yescharacteristic
51C2×#104×C61C2211yescharacteristic
52C61×#407C2211yescharacteristic
53C61×#407C2211yescharacteristic
54C4×M16×C61C2211yescharacteristic
55C61×#388—21no—
56C61×#387—21no—
57C61×#386—21no—
58C61×#385—21no—
59C4×C4⋊C4×C61C2211yescharacteristic
60C4×C22⋊C4×C61C2211yescharacteristic
61C4×C22⋊C4×C61C2211yescharacteristic
62C61×#376C2211yescharacteristic
63C61×#339C2211yescharacteristic
64C61×#339C2211yescharacteristic
65C61×#339C2211yescharacteristic
66C61×#339C2211yescharacteristic
67C61×#339C2211yescharacteristic
68C61×#339C2211yescharacteristic
69C61×#339C2211yescharacteristic
70C61×#339C2211yescharacteristic
71C61×#339C2211yescharacteristic
72C61×#339C2211yescharacteristic
73C61×#339C2211yescharacteristic
74C61×#339C2211yescharacteristic
75C2×#41×C61—21no—
76C2×#41×C61C2311yescharacteristic
77C22×D4×C61D411yescharacteristic
78C23×C4×C61—21no—
79C23×C4×C61C2311yescharacteristic
80C23×C4×C61C2311yescharacteristic
81C2×M16×C61—21no—
82C2×M16×C61—21no—
83C2×M16×C61—22no—
84C2×M16×C61—22no—
85C2×M16×C61—41no—
86C2×M16×C61—41no—
87C2×M16×C61C2311yescharacteristic
88C2×M16×C61C2311yescharacteristic
89C2×M16×C61C2311yescharacteristic
90C2×M16×C61C2311yescharacteristic
91C22×C8×C61—21no—
92C22×C8×C61—21no—
93C4⋊Q8×C61C2×C411yescharacteristic, complemented
94C4⋊Q8×C61C2×C411yescharacteristic, complemented
95#126×C61—21no—
96#126×C61—21no—
97#126×C61—21no—
98#126×C61—21no—
99#126×C61—21no—
100#126×C61—21no—
101#125×C61—21no—
102#125×C61—21no—
103#125×C61—21no—
104#125×C61C2×C411yescharacteristic, complemented
105#125×C61C2×C411yescharacteristic, complemented
106#124×C61—21no—
107#124×C61—21no—
108#124×C61—21no—
109#123×C61—21no—
110#123×C61—21no—
111#123×C61—21no—
112#123×C61—21no—
113#123×C61—21no—
114#123×C61—21no—
115#123×C61—21no—
116#123×C61—21no—
117C22⋊Q8×C61—21no—
118C22⋊Q8×C61—21no—
119C22⋊Q8×C61—21no—
120C22⋊Q8×C61—21no—
121C22⋊Q8×C61—21no—
122C22⋊Q8×C61C2×C411yescharacteristic
123C22⋊Q8×C61C2×C411yescharacteristic
124C22⋊Q8×C61C2×C411yescharacteristic, complemented
125C22⋊Q8×C61C2×C411yescharacteristic, complemented
126#121×C61—21no—
127#121×C61—21no—
128#121×C61—21no—
129#121×C61C2×C411yescharacteristic
130#121×C61C2×C411yescharacteristic
131#121×C61C2×C411yescharacteristic, complemented
132#121×C61C2×C411yescharacteristic, complemented
133#120×C61—21no—
134#120×C61—21no—
135C4×Q8×C61—21no—
136C4×Q8×C61—21no—
137C4×Q8×C61—21no—
138C4×Q8×C61C2×C411yescharacteristic, complemented
139C4×Q8×C61C2×C411yescharacteristic, complemented
140C4×D4×C61—21no—
141C4×D4×C61—21no—
142C4×D4×C61—21no—
143C4×D4×C61—21no—
144C4×D4×C61—21no—
145C4×D4×C61—21no—
146C4×D4×C61—21no—
147C4×D4×C61—21no—
148C4×D4×C61—21no—
149C4×D4×C61C2×C411yescharacteristic
150C4×D4×C61C2×C411yescharacteristic
151C4×D4×C61C2×C411yescharacteristic
152C4×D4×C61C2×C411yescharacteristic
153C4×D4×C61C2×C411yescharacteristic, complemented
154C4×D4×C61C2×C411yescharacteristic, complemented
155C4×D4×C61D411yescharacteristic
156C4×D4×C61D411yescharacteristic
157C4×D4×C61D411yescharacteristic
158C4×D4×C61D411yescharacteristic
159#117×C61—21no—
160#117×C61—21no—
161#117×C61—21no—
162#117×C61—21no—
163#117×C61—21no—
164#117×C61—21no—
165#117×C61—21no—
166#117×C61—21no—
167#117×C61—22no—
168#117×C61—41no—
169#117×C61C2×C411yescharacteristic
170#117×C61C2×C411yescharacteristic
171#117×C61C2×C411yescharacteristic, complemented
172#117×C61C2×C411yescharacteristic, complemented
173#117×C61C2311yescharacteristic
174#117×C61C2311yescharacteristic
175#117×C61C2311yescharacteristic
176C2×C4⋊C4×C61—21no—
177C2×C4⋊C4×C61—21no—
178C2×C4⋊C4×C61C2×C411yescharacteristic
179C2×C4⋊C4×C61C2×C411yescharacteristic
180C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
181C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
182C2×C4⋊C4×C61D411yescharacteristic
183C2×C22⋊C4×C61—21no—
184C2×C22⋊C4×C61—21no—
185C2×C22⋊C4×C61—21no—
186C2×C22⋊C4×C61—21no—
187C2×C22⋊C4×C61—21no—
188C2×C22⋊C4×C61D411yescharacteristic
189C2×C22⋊C4×C61D411yescharacteristic
190C2×C42×C61—21no—
191C2×C42×C61—21no—
192C2×C42×C61—21no—
193C2×C42×C61—22no—
194C2×C42×C61—21no—
195C2×C42×C61—41no—
196C2×C42×C61C2311yescharacteristic
197C2×C42×C61C2311yescharacteristic
198C2×C42×C61C2311yescharacteristic
199C2×C42×C61C2311yescharacteristic
200C2×C42×C61C2311yescharacteristic
201C4⋊C8×C61—21no—
202C4⋊C8×C61—21no—
203#104×C61—22no—
204#104×C61—22no—
205#104×C61—41no—
206#104×C61—41no—
207C22⋊C8×C61—21no—
208C22⋊C8×C61—21no—
209C22⋊C8×C61—21no—
210C22⋊C8×C61—21no—
211#97×C61—21no—
212C4×C8×C61—21no—
213#95×C61—21no—
214#95×C61—21no—
215#95×C61—21no—
216#95×C61—21no—
217#95×C61—21no—
218C24×C61C2×D411yescharacteristic
219C24×C61C2×D411yescharacteristic
220#41×C61—21no—
221#41×C61—21no—
222#41×C61—21no—
223#41×C61—21no—
224#41×C61—44no—
225C2×Q8×C61—21no—
226C2×Q8×C61—21no—
227C2×Q8×C61C22×C411yescharacteristic
228C2×D4×C61—21no—
229C2×D4×C61—21no—
230C2×D4×C61—21no—
231C2×D4×C61—21no—
232C2×D4×C61—21no—
233C2×D4×C61—42no—
234C2×D4×C61C22⋊C411yescharacteristic
235C2×D4×C61C22⋊C411yescharacteristic
236C2×D4×C61C22⋊C411yescharacteristic
237C2×D4×C61C22⋊C411yescharacteristic
238C2×D4×C61C22×C411yescharacteristic
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—21no—
247C22×C4×C61—21no—
248C22×C4×C61—21no—
249C22×C4×C61—21no—
250C22×C4×C61—21no—
251C22×C4×C61—21no—
252C22×C4×C61—21no—
253C22×C4×C61—21no—
254C22×C4×C61—21no—
255C22×C4×C61—21no—
256C22×C4×C61—21no—
257C22×C4×C61—21no—
258C22×C4×C61—42no—
259C22×C4×C61—42no—
260C22×C4×C61—42no—
261C22×C4×C61C22×C411yescharacteristic
262C22×C4×C61C22×C411yescharacteristic
263C22×C4×C61C22×C411yescharacteristic
264C22×C4×C61C22×C411yescharacteristic
265C22×C4×C61C2×D411yescharacteristic
266C22×C4×C61C2×D411yescharacteristic
267C22×C4×C61C2×D411yescharacteristic
268C22×C4×C61C2×D411yescharacteristic
269C22×C4×C61C2×D411yescharacteristic
270C22×C4×C61C2×D411yescharacteristic
271C22×C4×C61C2×D411yescharacteristic
272C22×C4×C61C2×D411yescharacteristic
273C22×C4×C61C2411yescharacteristic
274M16×C61—21no—
275M16×C61—21no—
276M16×C61—21no—
277M16×C61—21no—
278M16×C61—21no—
279M16×C61—21no—
280M16×C61—21no—
281M16×C61—42no—
282M16×C61—42no—
283M16×C61#4112yescomplemented
284C2×C8×C61—21no—
285C2×C8×C61—21no—
286C2×C8×C61—21no—
287C2×C8×C61—21no—
288C2×C8×C61—42no—
289C2×C8×C61—42no—
290C4⋊C4×C61—21no—
291C4⋊C4×C61—21no—
292C4⋊C4×C61—21no—
293C4⋊C4×C61—21no—
294C4⋊C4×C61—21no—
295C4⋊C4×C61—21no—
296C4⋊C4×C61—21no—
297C4⋊C4×C61—21no—
298C4⋊C4×C61—21no—
299C4⋊C4×C61—21no—
300C4⋊C4×C61—21no—
301C4⋊C4×C61—21no—
302C4⋊C4×C61—21no—
303C4⋊C4×C61—21no—
304C4⋊C4×C61—21no—
305C4⋊C4×C61—21no—
306C4⋊C4×C61—42no—
307C4⋊C4×C61—42no—
308C4⋊C4×C61C22⋊C411yescharacteristic
309C4⋊C4×C61C22⋊C411yescharacteristic
310C4⋊C4×C61C22⋊C411yescharacteristic
311C4⋊C4×C61C22⋊C411yescharacteristic
312C4⋊C4×C61C22×C411yescharacteristic
313C4⋊C4×C61C22×C411yescharacteristic
314C4⋊C4×C61C22×C411yescharacteristic
315C4⋊C4×C61C22×C411yescharacteristic
316C4⋊C4×C61C22×C411yescharacteristic
317C4⋊C4×C61C22×C411yescharacteristic
318C22⋊C4×C61—21no—
319C22⋊C4×C61—21no—
320C22⋊C4×C61—21no—
321C22⋊C4×C61—21no—
322C22⋊C4×C61—21no—
323C22⋊C4×C61—21no—
324C22⋊C4×C61—21no—
325C22⋊C4×C61—21no—
326C22⋊C4×C61—21no—
327C22⋊C4×C61—21no—
328C22⋊C4×C61—21no—
329C22⋊C4×C61—21no—
330C22⋊C4×C61—21no—
331C22⋊C4×C61—21no—
332C22⋊C4×C61—21no—
333C22⋊C4×C61—21no—
334C22⋊C4×C61—21no—
335C22⋊C4×C61—42no—
336C22⋊C4×C61—42no—
337C22⋊C4×C61—42no—
338C22⋊C4×C61C22⋊C411yescharacteristic
339C22⋊C4×C61C22⋊C411yescharacteristic
340C22⋊C4×C61C22⋊C411yescharacteristic
341C22⋊C4×C61C22⋊C411yescharacteristic
342C22⋊C4×C61C22⋊C411yescharacteristic
343C22⋊C4×C61C22⋊C411yescharacteristic
344C22⋊C4×C61C22⋊C411yescharacteristic
345C22⋊C4×C61C22⋊C411yescharacteristic
346C42×C61—21no—
347C42×C61—21no—
348C42×C61—21no—
349C42×C61—21no—
350C42×C61—21no—
351C42×C61—21no—
352C42×C61—21no—
353C42×C61—21no—
354C42×C61—21no—
355C42×C61—21no—
356C42×C61—21no—
357C42×C61—21no—
358C42×C61—21no—
359C42×C61—21no—
360C42×C61—21no—
361C42×C61—21no—
362C42×C61—42no—
363C42×C61C22×C411yescharacteristic
364C42×C61C22×C411yescharacteristic
365C42×C61C2×D411yescharacteristic
366C42×C61C2×D411yescharacteristic
367C42×C61#4112yescomplemented
368C23×C61—21no—
369C23×C61—21no—
370C23×C61—22no—
371C23×C61—21no—
372C23×C61—21no—
373C23×C61—21no—
374C23×C61—41no—
375C23×C61—41no—
376C23×C61—41no—
377C23×C61C2×C22⋊C411yescharacteristic
378C23×C61C2×C22⋊C411yescharacteristic
379C23×C61C2×C22⋊C411yescharacteristic
380C23×C61C2×C22⋊C411yescharacteristic
381C23×C61C22×D411yescharacteristic
382Q8×C61—21no—
383Q8×C61—21no—
384Q8×C61—42no—
385Q8×C61—81no—
386D4×C61—22no—
387D4×C61—22no—
388D4×C61—21no—
389D4×C61—21no—
390D4×C61—41no—
391D4×C61—41no—
392D4×C61—42no—
393D4×C61—41no—
394D4×C61—41no—
395D4×C61—42no—
396D4×C61—81no—
397D4×C61—81no—
398C2×C4×C61—21no—
399C2×C4×C61—21no—
400C2×C4×C61—21no—
401C2×C4×C61—21no—
402C2×C4×C61—21no—
403C2×C4×C61—21no—
404C2×C4×C61—21no—
405C2×C4×C61—21no—
406C2×C4×C61—21no—
407C2×C4×C61—21no—
408C2×C4×C61—21no—
409C2×C4×C61—21no—
410C2×C4×C61—21no—
411C2×C4×C61—21no—
412C2×C4×C61—21no—
413C2×C4×C61—21no—
414C2×C4×C61—21no—
415C2×C4×C61—21no—
416C2×C4×C61—21no—
417C2×C4×C61—21no—
418C2×C4×C61—22no—
419C2×C4×C61—21no—
420C2×C4×C61—21no—
421C2×C4×C61—21no—
422C2×C4×C61—21no—
423C2×C4×C61—21no—
424C2×C4×C61—21no—
425C2×C4×C61—21no—
426C2×C4×C61—22no—
427C2×C4×C61—41no—
428C2×C4×C61—41no—
429C2×C4×C61—42no—
430C2×C4×C61—41no—
431C2×C4×C61—41no—
432C2×C4×C61—41no—
433C2×C4×C61—42no—
434C2×C4×C61—48no—
435C2×C4×C61—41no—
436C2×C4×C61—42no—
437C2×C4×C61—41no—
438C2×C4×C61—41no—
439C2×C4×C61—41no—
440C2×C4×C61—41no—
441C2×C4×C61—41no—
442C2×C4×C61—41no—
443C2×C4×C61—41no—
444C2×C4×C61—41no—
445C2×C4×C61—81no—
446C2×C4×C61—81no—
447C2×C4×C61—81no—
448C2×C4×C61C2×C22⋊C411yescharacteristic
449C2×C4×C61C2×C22⋊C411yescharacteristic
450C2×C4×C61C2×C22⋊C411yescharacteristic
451C2×C4×C61C2×C22⋊C411yescharacteristic
452C2×C4×C61C2×C22⋊C411yescharacteristic
453C2×C4×C61C2×C22⋊C411yescharacteristic
454C2×C4×C61C2×C22⋊C411yescharacteristic
455C2×C4×C61C2×C22⋊C411yescharacteristic
456C2×C4×C61C23×C411yescharacteristic
457C2×C4×C61C22×D411yescharacteristic
458C2×C4×C61C2×#4111yescharacteristic
459C2×C4×C61C2×#4111yescharacteristic
460C2×C4×C61H(5,𝔽2)11yescharacteristic
461C2×C4×C612−1+411yescharacteristic
462C8×C61—22no—
463C8×C61—41no—
464C8×C61—41no—
465C8×C61—41no—
466#22506C6111yesmaximal, characteristic, direct product factor, Sylow
467C22×C61—21no—
468C22×C61—21no—
469C22×C61—21no—
470C22×C61—21no—
471C22×C61—21no—
472C22×C61—21no—
473C22×C61—21no—
474C22×C61—21no—
475C22×C61—21no—
476C22×C61—21no—
477C22×C61—21no—
478C22×C61—21no—
479C22×C61—21no—
480C22×C61—42no—
481C22×C61—42no—
482C22×C61—41no—
483C22×C61—41no—
484C22×C61—41no—
485C22×C61—81no—
486C22×C61—81no—
487C22×C61#42112yes—
488C22×C61C22×C22⋊C411yescharacteristic
489C22×C61#54611yescharacteristic
490C22×C61#54711yescharacteristic
491C4×C61—21no—
492C4×C61—21no—
493C4×C61—21no—
494C4×C61—21no—
495C4×C61—21no—
496C4×C61—21no—
497C4×C61—21no—
498C4×C61—21no—
499C4×C61—42no—
500C4×C61—42no—
501C4×C61—41no—
502C4×C61—41no—
503C4×C61—41no—
504C4×C61—41no—
505C4×C61—41no—
506C4×C61—41no—
507C4×C61—41no—
508C4×C61—81no—
509C4×C61—81no—
510C4×C61C4×#4111yescharacteristic
511C4×C61#52011yescharacteristic
512C4×C61#54611yescharacteristic
513C4×C61#54711yescharacteristic
514#3475C2×C6111yescharacteristic
515D4×M16C2×C6111yescharacteristic, complemented
516#2290C2×C6111yescharacteristic, complemented
517#1995C2×C6111yescharacteristic, complemented
518#1986C2×C6111yescharacteristic, complemented
519#1897C2×C6111yescharacteristic, complemented
520#1896C2×C6111yescharacteristic, complemented
521#1871C2×C6111yescharacteristic, complemented
522#1871C2×C6111yescharacteristic, complemented
523#1826C2×C6111yescharacteristic, complemented
524#1826C2×C6111yescharacteristic, complemented
525#1806C2×C6111yescharacteristic, complemented
526#1759C2×C6111yescharacteristic, complemented
527#1733C2×C6111yescharacteristic, complemented
528C2×#339C2×C6111yescharacteristic, complemented
529C2×C61—21no—
530C2×C61—21no—
531C2×C61—22no—
532C2×C61—41no—
533C2×C61—41no—
534C2×C61—41no—
535C2×C61—81no—
536C2×C61#233911yescharacteristic
537C2×C61C2×#42111yescharacteristic
538C2×C61#290111yescharacteristic
539C22×M16C22×C6111yescharacteristic
540C22×M16C22×C6111yescharacteristic
541#556C4×C6111yescharacteristic, complemented
542#555C4×C6111yescharacteristic, complemented
543#554C4×C6111yescharacteristic, complemented
544#553C4×C6111yescharacteristic, complemented
545#553C4×C6111yescharacteristic, complemented
546#552—21no—
547#552C4×C6111yescharacteristic, complemented
548#552C4×C6111yescharacteristic, complemented
549#551—21no—
550#551—21no—
551#547C4×C6111yescharacteristic, complemented
552#546—21no—
553#533C22×C6111yescharacteristic
554#529—21no—
555#529—21no—
556#529—21no—
557#525C22×C6111yescharacteristic
558#525C22×C6111yescharacteristic
559C4×#41—21no—
560C4×#41C22×C6111yescharacteristic
561C2×C4×D4C22×C6111yescharacteristic
562C2×#117C22×C6111yescharacteristic
563C2×#117C22×C6111yescharacteristic
564C2×#117C22×C6111yescharacteristic
565C22×C42C22×C6111yescharacteristic
566#436—21no—
567#435—21no—
568#435—21no—
569C8×D4—21no—
570#423C22×C6111yescharacteristic
571C2×#104C22×C6111yescharacteristic
572C2×#104C22×C6111yescharacteristic
573C2×#104C22×C6111yescharacteristic
574C2×#104C22×C6111yescharacteristic
575#407C22×C6111yescharacteristic
576#407C22×C6111yescharacteristic
577C4×M16C22×C6111yescharacteristic
578#388—21no—
579#387—21no—
580#386—21no—
581#385—21no—
582C4×C4⋊C4C22×C6111yescharacteristic
583C4×C22⋊C4C22×C6111yescharacteristic
584C4×C22⋊C4C22×C6111yescharacteristic
585#376C22×C6111yescharacteristic
586#339C22×C6111yescharacteristic
587#339C22×C6111yescharacteristic
588#339C22×C6111yescharacteristic
589#339C22×C6111yescharacteristic
590#339C22×C6111yescharacteristic
591#339C22×C6111yescharacteristic
592#339C22×C6111yescharacteristic
593#339C22×C6111yescharacteristic
594#339C22×C6111yescharacteristic
595#339C22×C6111yescharacteristic
596#339C22×C6111yescharacteristic
597#339C22×C6111yescharacteristic
598C61#2250611yescharacteristic, direct product factor, Sylow
599C2×#41—21no—
600C2×#41C23×C6111yescharacteristic
601C22×D4D4×C6111yescharacteristic
602C23×C4—21no—
603C23×C4C23×C6111yescharacteristic
604C23×C4C23×C6111yescharacteristic
605C2×M16—21no—
606C2×M16—21no—
607C2×M16—22no—
608C2×M16—22no—
609C2×M16—41no—
610C2×M16—41no—
611C2×M16C23×C6111yescharacteristic
612C2×M16C23×C6111yescharacteristic
613C2×M16C23×C6111yescharacteristic
614C2×M16C23×C6111yescharacteristic
615C22×C8—21no—
616C22×C8—21no—
617C4⋊Q8C2×C4×C6111yescharacteristic, complemented
618C4⋊Q8C2×C4×C6111yescharacteristic, complemented
619#126—21no—
620#126—21no—
621#126—21no—
622#126—21no—
623#126—21no—
624#126—21no—
625#125—21no—
626#125—21no—
627#125—21no—
628#125C2×C4×C6111yescharacteristic, complemented
629#125C2×C4×C6111yescharacteristic, complemented
630#124—21no—
631#124—21no—
632#124—21no—
633#123—21no—
634#123—21no—
635#123—21no—
636#123—21no—
637#123—21no—
638#123—21no—
639#123—21no—
640#123—21no—
641C22⋊Q8—21no—
642C22⋊Q8—21no—
643C22⋊Q8—21no—
644C22⋊Q8—21no—
645C22⋊Q8—21no—
646C22⋊Q8C2×C4×C6111yescharacteristic
647C22⋊Q8C2×C4×C6111yescharacteristic
648C22⋊Q8C2×C4×C6111yescharacteristic, complemented
649C22⋊Q8C2×C4×C6111yescharacteristic, complemented
650#121—21no—
651#121—21no—
652#121—21no—
653#121C2×C4×C6111yescharacteristic
654#121C2×C4×C6111yescharacteristic
655#121C2×C4×C6111yescharacteristic, complemented
656#121C2×C4×C6111yescharacteristic, complemented
657#120—21no—
658#120—21no—
659C4×Q8—21no—
660C4×Q8—21no—
661C4×Q8—21no—
662C4×Q8C2×C4×C6111yescharacteristic, complemented
663C4×Q8C2×C4×C6111yescharacteristic, complemented
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669C4×D4—21no—
670C4×D4—21no—
671C4×D4—21no—
672C4×D4—21no—
673C4×D4C2×C4×C6111yescharacteristic
674C4×D4C2×C4×C6111yescharacteristic
675C4×D4C2×C4×C6111yescharacteristic
676C4×D4C2×C4×C6111yescharacteristic
677C4×D4C2×C4×C6111yescharacteristic, complemented
678C4×D4C2×C4×C6111yescharacteristic, complemented
679C4×D4D4×C6111yescharacteristic
680C4×D4D4×C6111yescharacteristic
681C4×D4D4×C6111yescharacteristic
682C4×D4D4×C6111yescharacteristic
683#117—21no—
684#117—21no—
685#117—21no—
686#117—21no—
687#117—21no—
688#117—21no—
689#117—21no—
690#117—21no—
691#117—22no—
692#117—41no—
693#117C2×C4×C6111yescharacteristic
694#117C2×C4×C6111yescharacteristic
695#117C2×C4×C6111yescharacteristic, complemented
696#117C2×C4×C6111yescharacteristic, complemented
697#117C23×C6111yescharacteristic
698#117C23×C6111yescharacteristic
699#117C23×C6111yescharacteristic
700C2×C4⋊C4—21no—
701C2×C4⋊C4—21no—
702C2×C4⋊C4C2×C4×C6111yescharacteristic
703C2×C4⋊C4C2×C4×C6111yescharacteristic
704C2×C4⋊C4C2×C4×C6111yescharacteristic, complemented
705C2×C4⋊C4C2×C4×C6111yescharacteristic, complemented
706C2×C4⋊C4D4×C6111yescharacteristic
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4D4×C6111yescharacteristic
713C2×C22⋊C4D4×C6111yescharacteristic
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—22no—
718C2×C42—21no—
719C2×C42—41no—
720C2×C42C23×C6111yescharacteristic
721C2×C42C23×C6111yescharacteristic
722C2×C42C23×C6111yescharacteristic
723C2×C42C23×C6111yescharacteristic
724C2×C42C23×C6111yescharacteristic
725C4⋊C8—21no—
726C4⋊C8—21no—
727#104—22no—
728#104—22no—
729#104—41no—
730#104—41no—
731C22⋊C8—21no—
732C22⋊C8—21no—
733C22⋊C8—21no—
734C22⋊C8—21no—
735#97—21no—
736C4×C8—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742C24C2×D4×C6111yescharacteristic
743C24C2×D4×C6111yescharacteristic
744#41—21no—
745#41—21no—
746#41—21no—
747#41—21no—
748#41—44no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8C22×C4×C6111yescharacteristic
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—42no—
758C2×D4C22⋊C4×C6111yescharacteristic
759C2×D4C22⋊C4×C6111yescharacteristic
760C2×D4C22⋊C4×C6111yescharacteristic
761C2×D4C22⋊C4×C6111yescharacteristic
762C2×D4C22×C4×C6111yescharacteristic
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4C22×C4×C6111yescharacteristic
786C22×C4C22×C4×C6111yescharacteristic
787C22×C4C22×C4×C6111yescharacteristic
788C22×C4C22×C4×C6111yescharacteristic
789C22×C4C2×D4×C6111yescharacteristic
790C22×C4C2×D4×C6111yescharacteristic
791C22×C4C2×D4×C6111yescharacteristic
792C22×C4C2×D4×C6111yescharacteristic
793C22×C4C2×D4×C6111yescharacteristic
794C22×C4C2×D4×C6111yescharacteristic
795C22×C4C2×D4×C6111yescharacteristic
796C22×C4C2×D4×C6111yescharacteristic
797C22×C4C24×C6111yescharacteristic
798M16—21no—
799M16—21no—
800M16—21no—
801M16—21no—
802M16—21no—
803M16—21no—
804M16—21no—
805M16—42no—
806M16—42no—
807M16#41×C6112yescomplemented
808C2×C8—21no—
809C2×C8—21no—
810C2×C8—21no—
811C2×C8—21no—
812C2×C8—42no—
813C2×C8—42no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—42no—
831C4⋊C4—42no—
832C4⋊C4C22⋊C4×C6111yescharacteristic
833C4⋊C4C22⋊C4×C6111yescharacteristic
834C4⋊C4C22⋊C4×C6111yescharacteristic
835C4⋊C4C22⋊C4×C6111yescharacteristic
836C4⋊C4C22×C4×C6111yescharacteristic
837C4⋊C4C22×C4×C6111yescharacteristic
838C4⋊C4C22×C4×C6111yescharacteristic
839C4⋊C4C22×C4×C6111yescharacteristic
840C4⋊C4C22×C4×C6111yescharacteristic
841C4⋊C4C22×C4×C6111yescharacteristic
842C22⋊C4—21no—
843C22⋊C4—21no—
844C22⋊C4—21no—
845C22⋊C4—21no—
846C22⋊C4—21no—
847C22⋊C4—21no—
848C22⋊C4—21no—
849C22⋊C4—21no—
850C22⋊C4—21no—
851C22⋊C4—21no—
852C22⋊C4—21no—
853C22⋊C4—21no—
854C22⋊C4—21no—
855C22⋊C4—21no—
856C22⋊C4—21no—
857C22⋊C4—21no—
858C22⋊C4—21no—
859C22⋊C4—42no—
860C22⋊C4—42no—
861C22⋊C4—42no—
862C22⋊C4C22⋊C4×C6111yescharacteristic
863C22⋊C4C22⋊C4×C6111yescharacteristic
864C22⋊C4C22⋊C4×C6111yescharacteristic
865C22⋊C4C22⋊C4×C6111yescharacteristic
866C22⋊C4C22⋊C4×C6111yescharacteristic
867C22⋊C4C22⋊C4×C6111yescharacteristic
868C22⋊C4C22⋊C4×C6111yescharacteristic
869C22⋊C4C22⋊C4×C6111yescharacteristic
870C42—21no—
871C42—21no—
872C42—21no—
873C42—21no—
874C42—21no—
875C42—21no—
876C42—21no—
877C42—21no—
878C42—21no—
879C42—21no—
880C42—21no—
881C42—21no—
882C42—21no—
883C42—21no—
884C42—21no—
885C42—21no—
886C42—42no—
887C42C22×C4×C6111yescharacteristic
888C42C22×C4×C6111yescharacteristic
889C42C2×D4×C6111yescharacteristic
890C42C2×D4×C6111yescharacteristic
891C42#41×C6112yescomplemented
892C23—21no—
893C23—21no—
894C23—22no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23C2×C22⋊C4×C6111yescharacteristic
902C23C2×C22⋊C4×C6111yescharacteristic
903C23C2×C22⋊C4×C6111yescharacteristic
904C23C2×C22⋊C4×C6111yescharacteristic
905C23C22×D4×C6111yescharacteristic
906Q8—21no—
907Q8—21no—
908Q8—42no—
909Q8—81no—
910D4—22no—
911D4—22no—
912D4—21no—
913D4—21no—
914D4—41no—
915D4—41no—
916D4—42no—
917D4—41no—
918D4—41no—
919D4—42no—
920D4—81no—
921D4—81no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—42no—
958C2×C4—48no—
959C2×C4—41no—
960C2×C4—42no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—81no—
970C2×C4—81no—
971C2×C4—81no—
972C2×C4C2×C22⋊C4×C6111yescharacteristic
973C2×C4C2×C22⋊C4×C6111yescharacteristic
974C2×C4C2×C22⋊C4×C6111yescharacteristic
975C2×C4C2×C22⋊C4×C6111yescharacteristic
976C2×C4C2×C22⋊C4×C6111yescharacteristic
977C2×C4C2×C22⋊C4×C6111yescharacteristic
978C2×C4C2×C22⋊C4×C6111yescharacteristic
979C2×C4C2×C22⋊C4×C6111yescharacteristic
980C2×C4C23×C4×C6111yescharacteristic
981C2×C4C22×D4×C6111yescharacteristic
982C2×C4C2×#41×C6111yescharacteristic
983C2×C4C2×#41×C6111yescharacteristic
984C2×C4H(5,𝔽2)×C6111yescharacteristic
985C2×C42−1+4×C6111yescharacteristic
986C8—22no—
987C8—41no—
988C8—41no—
989C8—41no—
990C22—21no—
991C22—21no—
992C22—21no—
993C22—21no—
994C22—21no—
995C22—21no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—42no—
1004C22—42no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—81no—
1009C22—81no—
1010C22C61×#42112yes—
1011C22C22×C22⋊C4×C6111yescharacteristic
1012C22C61×#54611yescharacteristic
1013C22C61×#54711yescharacteristic
1014C4—21no—
1015C4—21no—
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—21no—
1021C4—21no—
1022C4—42no—
1023C4—42no—
1024C4—41no—
1025C4—41no—
1026C4—41no—
1027C4—41no—
1028C4—41no—
1029C4—41no—
1030C4—41no—
1031C4—81no—
1032C4—81no—
1033C4C4×#41×C6111yescharacteristic
1034C4C61×#52011yescharacteristic
1035C4C61×#54611yescharacteristic
1036C4C61×#54711yescharacteristic
1037C2—21no—
1038C2—21no—
1039C2—22no—
1040C2—41no—
1041C2—41no—
1042C2—41no—
1043C2—81no—
1044C2C61×#233911yescharacteristic
1045C2C2×C61×#42111yescharacteristic
1046C2C61×#290111yescharacteristic
subgroupG/H
centerC2×C4×C61C22×D4
commutatorC2×C4C23×C4×C61
Frattini, cosocleC22×C4C24×C61
socleC22×C61C22×C22⋊C4
prime radicalC61×#3475C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C61 ◁ C2×C4×D4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. D4×M16×C61C2semidirect
3. C61×#2290C2semidirect
4. C61×#1995C2semidirect
5. C61×#1986C2semidirect
6. C61×#1897C2semidirect
7. C61×#1896C2semidirect
8. C61×#1871C2semidirect
9. C61×#1871C2semidirect
10. C61×#1826C2semidirect
11. C61×#1826C2semidirect
12. C61×#1806C2semidirect
13. C61×#1759C2semidirect
14. C61×#1733C2semidirect
15. C2×C61×#339C2semidirect
18. C61×#556C4semidirect
19. C61×#555C4semidirect
20. C61×#554C4semidirect
21. C61×#553C4semidirect
22. C61×#553C4semidirect
24. C61×#552C4semidirect
25. C61×#552C4semidirect
28. C61×#547C4semidirect
93. C4⋊Q8×C61C2×C4semidirect
94. C4⋊Q8×C61C2×C4semidirect
104. #125×C61C2×C4semidirect
105. #125×C61C2×C4semidirect
124. C22⋊Q8×C61C2×C4semidirect
125. C22⋊Q8×C61C2×C4semidirect
131. #121×C61C2×C4semidirect
132. #121×C61C2×C4semidirect
138. C4×Q8×C61C2×C4semidirect
139. C4×Q8×C61C2×C4semidirect
153. C4×D4×C61C2×C4semidirect
154. C4×D4×C61C2×C4semidirect
171. #117×C61C2×C4semidirect
172. #117×C61C2×C4semidirect
180. C2×C4⋊C4×C61C2×C4semidirect
181. C2×C4⋊C4×C61C2×C4semidirect
283. M16×C61#41semidirect
367. C42×C61#41semidirect
466. #22506C61direct (N × H)
515. D4×M16C2×C61semidirect
516. #2290C2×C61semidirect
517. #1995C2×C61semidirect
518. #1986C2×C61semidirect
519. #1897C2×C61semidirect
520. #1896C2×C61semidirect
521. #1871C2×C61semidirect
522. #1871C2×C61semidirect
523. #1826C2×C61semidirect
524. #1826C2×C61semidirect
525. #1806C2×C61semidirect
526. #1759C2×C61semidirect
527. #1733C2×C61semidirect
528. C2×#339C2×C61semidirect
541. #556C4×C61semidirect
542. #555C4×C61semidirect
543. #554C4×C61semidirect
544. #553C4×C61semidirect
545. #553C4×C61semidirect
547. #552C4×C61semidirect
548. #552C4×C61semidirect
551. #547C4×C61semidirect
598. C61#22506direct (N × H)
617. C4⋊Q8C2×C4×C61semidirect
618. C4⋊Q8C2×C4×C61semidirect
628. #125C2×C4×C61semidirect
629. #125C2×C4×C61semidirect
648. C22⋊Q8C2×C4×C61semidirect
649. C22⋊Q8C2×C4×C61semidirect
655. #121C2×C4×C61semidirect
656. #121C2×C4×C61semidirect
662. C4×Q8C2×C4×C61semidirect
663. C4×Q8C2×C4×C61semidirect
677. C4×D4C2×C4×C61semidirect
678. C4×D4C2×C4×C61semidirect
695. #117C2×C4×C61semidirect
696. #117C2×C4×C61semidirect
704. C2×C4⋊C4C2×C4×C61semidirect
705. C2×C4⋊C4C2×C4×C61semidirect
807. M16#41×C61semidirect
891. C42#41×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#34752
D4×M16×C612
C61×#22902
C61×#19952
C61×#19862
C61×#18972
C61×#18962
C61×#18712
C61×#18262
C61×#18062
C61×#17592
C61×#17332
C2×C61×#3392
#2250661