Finite Group Databasebeta

← C61×#63005 #29566438

Subgroups — C61×#63005 #29566438

Order 15616.

7024 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3524C214yesmaximal, complemented
2C61×#3524C214yesmaximal, complemented
3C61×#3522C214yesmaximal, complemented
4C61×#3518C214yesmaximal, complemented
5C61×#3516C214yesmaximal, complemented
6C61×#3516C214yesmaximal, complemented
7C61×#3510C216yesmaximal, complemented
8C61×#3502C211yesmaximal, characteristic, complemented
9C61×#3495C216yesmaximal, complemented
10C61×#3494C216yesmaximal, complemented
11C61×#3487C211yesmaximal, characteristic, complemented
12C61×#3486C211yesmaximal, characteristic, complemented
13C61×#3482C214yesmaximal, complemented
14C61×#3480C214yesmaximal, complemented
15C61×#3475C216yesmaximal, complemented
16C2×C61×#548C211yesmaximal, characteristic, complemented
17C4×2−1+4×C61C211yesmaximal, characteristic, complemented
18C61×#3428C211yesmaximal, characteristic, complemented
19C2×C61×#519C211yesmaximal, characteristic, complemented
20C2×2−1+4×C61C2211yescharacteristic
21C22×#41×C61C2211yescharacteristic
22C23×Q8×C61C2211yescharacteristic
23C61×#559C22112yescomplemented
24C61×#559C22112yescomplemented
25Q82×C61C2214yescomplemented
26C61×#557C2214yescomplemented
27C61×#557C2214yescomplemented
28C61×#557C2214yescomplemented
29C61×#556C2216yescomplemented
30C61×#556C22112yescomplemented
31C61×#556C22112yescomplemented
32C61×#556C22112yescomplemented
33C61×#555C2216yescomplemented
34C61×#555C22112yescomplemented
35C61×#554C2216yescomplemented
36C61×#554C22112yescomplemented
37C61×#553C2216yescomplemented
38C61×#553C2216yescomplemented
39C61×#553C22112yescomplemented
40C61×#553C22112yescomplemented
41C61×#552C22112yes—
42C61×#552C2216yescomplemented
43C61×#552C2216yescomplemented
44C61×#552C22112yescomplemented
45C61×#552C22112yescomplemented
46C61×#551C2214yes—
47C61×#551C22112yes—
48C61×#551C22124yes—
49C61×#550C2214yescomplemented
50C61×#550C2214yescomplemented
51D4×Q8×C61C2214yescomplemented
52D4×Q8×C61C2214yescomplemented
53C61×#548C2214yes—
54C61×#548C2214yes—
55C61×#548C2214yes—
56C61×#548C2214yes—
57C61×#548C2214yescomplemented
58C61×#548C2214yescomplemented
59C61×#548C2214yescomplemented
60C61×#548C2214yescomplemented
61C61×#547C2216yescomplemented
62C61×#547C22112yescomplemented
63C61×#546C22112yes—
64C61×#544C2216yes—
65C61×#542C22112yescomplemented
66C61×#542C22112yescomplemented
67C61×#542C22112yescomplemented
68C61×#542C22112yescomplemented
69C61×#541C22112yescomplemented
70C61×#540C22112yescomplemented
71C61×#536C2216yes—
72C61×#535C2216yes—
73C61×#533C2216yes—
74C61×#533C22112yescomplemented
75C61×#532C22112yescomplemented
76C61×#529C22112yescomplemented
77C61×#529C22112yescomplemented
78C61×#529C22112yescomplemented
79C61×#529C22112yescomplemented
80C61×#529C22112yescomplemented
81C61×#529C22112yescomplemented
82C61×#529C22112yescomplemented
83C2×#124×C61C2213yes—
84C61×#525C2216yes—
85C61×#525C2216yes—
86C2×C22⋊Q8×C61C2213yes—
87C2×#121×C61C2213yes—
88C61×#520C2216yes—
89C61×#520C2214yescomplemented
90C61×#520C2214yescomplemented
91C61×#520C2214yescomplemented
92C61×#519C2211yescharacteristic
93C61×#519C2211yescharacteristic
94C61×#519C2216yes—
95C61×#519C2211yescharacteristic
96C61×#519C2214yescomplemented
97C61×#519C2214yescomplemented
98C61×#519C2214yescomplemented
99C61×#518C2216yes—
100C4×#41×C61C2216yes—
101C4×#41×C61C2214yescomplemented
102C4×#41×C61C2214yescomplemented
103C4×#41×C61C2214yescomplemented
104C4×#41×C61C22112yescomplemented
105C2×C4×Q8×C61C2211yescharacteristic
106C2×C4×Q8×C61C2214yescomplemented
107C2×C4×Q8×C61C2214yescomplemented
108C2×C4×Q8×C61C2214yescomplemented
109C2×C4×D4×C61C2213yes—
110C2×#117×C61C2216yes—
111C2×#117×C61C2216yes—
1122−1+4×C61—28no—
113C2×#41×C61—28no—
114C2×#41×C61C2316yes—
115C2×#41×C61C2314yes—
116C2×#41×C61C2314yes—
117C2×#41×C61C2314yes—
118C2×#41×C61C23112yes—
119C22×Q8×C61—28no—
120C22×Q8×C61C2313yes—
121C22×Q8×C61C2314yes—
122C22×Q8×C61C2314yes—
123C22×Q8×C61C2314yes—
124C22×Q8×C61C2311yescharacteristic
125C22×D4×C61C2313yes—
126C22×D4×C61C2313yes—
127C23×C4×C61C2313yes—
128C23×C4×C61C2313yes—
129C4⋊Q8×C61C23112yes—
130C4⋊Q8×C61C2316yes—
131C4⋊Q8×C61C2316yes—
132C4⋊Q8×C61C23112yes—
133C4⋊Q8×C61C23112yes—
134#127×C61C23112yes—
135#126×C61C23124yes—
136#126×C61C23124yes—
137#126×C61C23112yes—
138#126×C61C23112yes—
139#126×C61C2314yes—
140#126×C61C23112yes—
141#126×C61C2314yes—
142#126×C61C23112yes—
143#125×C61C2316yes—
144#125×C61C2316yes—
145#125×C61C23112yes—
146#125×C61C23112yes—
147#125×C61C23112yes—
148#125×C61C23112yes—
149#125×C61C23112yes—
150#124×C61C23124yes—
151#124×C61C23112yes—
152#124×C61C23112yes—
153#124×C61C23112yes—
154#124×C61C23112yes—
155#124×C61C23112yes—
156#124×C61C23112yes—
157#124×C61C2314yes—
158#123×C61C23112yes—
159#123×C61C23124yes—
160#123×C61C23124yes—
161#123×C61C23112yes—
162#123×C61C23112yes—
163#123×C61C23112yes—
164#123×C61C2314yes—
165#123×C61C2314yes—
166#123×C61C2314yes—
167#123×C61C23112yes—
168C22⋊Q8×C61C2314yes—
169C22⋊Q8×C61C23112yes—
170C22⋊Q8×C61C2316yes—
171C22⋊Q8×C61C23124yes—
172C22⋊Q8×C61C23112yes—
173C22⋊Q8×C61C23112yes—
174C22⋊Q8×C61C23112yes—
175C22⋊Q8×C61C2316yes—
176C22⋊Q8×C61C23112yes—
177C22⋊Q8×C61C23112yes—
178C22⋊Q8×C61C2316yes—
179C22⋊Q8×C61C23112yes—
180C22⋊Q8×C61C2316yes—
181C22⋊Q8×C61C2314yes—
182#121×C61C23112yes—
183#121×C61C2316yes—
184#121×C61C23112yes—
185#121×C61C23112yes—
186#121×C61C23112yes—
187#121×C61C23112yes—
188#121×C61C23112yes—
189#121×C61C2316yes—
190#121×C61C23112yes—
191#121×C61C2316yes—
192#121×C61C2316yes—
193#120×C61C23112yes—
194#120×C61C2314yes—
195C4×Q8×C61C23112yes—
196C4×Q8×C61C23112yes—
197C4×Q8×C61C23112yes—
198C4×Q8×C61C23112yes—
199C4×Q8×C61C23112yes—
200C4×Q8×C61C23112yes—
201C4×Q8×C61C2314yes—
202C4×Q8×C61C2314yes—
203C4×Q8×C61C2314yes—
204C4×Q8×C61C2314yes—
205C4×Q8×C61C2314yes—
206C4×Q8×C61C2314yes—
207C4×Q8×C61C2316yes—
208C4×Q8×C61C23112yes—
209C4×Q8×C61C23112yes—
210C4×Q8×C61C2316yes—
211C4×Q8×C61C2314yes—
212C4×Q8×C61C2314yes—
213C4×D4×C61C23112yes—
214C4×D4×C61C23112yes—
215C4×D4×C61C23124yes—
216C4×D4×C61C23112yes—
217C4×D4×C61C23112yes—
218C4×D4×C61C23112yes—
219C4×D4×C61C2316yes—
220C4×D4×C61C23112yes—
221C4×D4×C61C23112yes—
222C4×D4×C61C2316yes—
223C4×D4×C61C2316yes—
224C4×D4×C61C2316yes—
225C4×D4×C61C2316yes—
226C4×D4×C61C23112yes—
227C4×D4×C61C23112yes—
228C4×D4×C61C23112yes—
229C4×D4×C61C2314yes—
230C4×D4×C61C2314yes—
231C4×D4×C61C23112yes—
232C4×D4×C61C2316yes—
233C4×D4×C61C23112yes—
234#117×C61C2316yes—
235#117×C61C2316yes—
236#117×C61C23124yes—
237#117×C61C23112yes—
238#117×C61C23112yes—
239#117×C61C23112yes—
240#117×C61C23112yes—
241#117×C61C2314yes—
242#117×C61C2314yes—
243#117×C61C23112yes—
244#117×C61C23112yes—
245#117×C61C2316yes—
246#117×C61C2316yes—
247#117×C61C23112yes—
248#117×C61C2316yes—
249#117×C61C2316yes—
250#117×C61C2316yes—
251C2×C4⋊C4×C61C2313yes—
252C2×C4⋊C4×C61C2316yes—
253C2×C4⋊C4×C61C23112yes—
254C2×C4⋊C4×C61C2316yes—
255C2×C4⋊C4×C61C2313yes—
256C2×C4⋊C4×C61C2316yes—
257C2×C4⋊C4×C61C2316yes—
258C2×C22⋊C4×C61C2314yes—
259C2×C22⋊C4×C61C23112yes—
260C2×C22⋊C4×C61C2311yescharacteristic
261C2×C22⋊C4×C61C2313yes—
262C2×C22⋊C4×C61C2316yes—
263C2×C42×C61C23112yes—
264C2×C42×C61C2313yes—
265C2×C42×C61C23112yes—
266C2×C42×C61C23112yes—
267C24×C61C2411yescharacteristic
268C24×C61C2413yes—
269#41×C61—216no—
270#41×C61—216no—
271#41×C61—216no—
272#41×C61—224no—
273#41×C61—424no—
274C2×Q8×C61—216no—
275C2×Q8×C61—216no—
276C2×Q8×C61—216no—
277C2×Q8×C61—212no—
278C2×Q8×C61#4118yescomplemented
279C2×Q8×C61C24112yes—
280C2×Q8×C61C2416yes—
281C2×Q8×C61C2414yes—
282C2×Q8×C61C24112yes—
283C2×Q8×C61C2414yes—
284C2×D4×C61—212no—
285C2×D4×C61—46no—
286C2×D4×C61C2414yes—
287C2×D4×C61C2414yes—
288C2×D4×C61C2416yes—
289C2×D4×C61C24112yes—
290C2×D4×C61C2416yes—
291C2×D4×C61C2414yes—
292C2×D4×C61C24112yes—
293C2×D4×C61C24112yes—
294C2×D4×C61C2416yes—
295C22×C4×C61—212no—
296C22×C4×C61—212no—
297C22×C4×C61C2414yes—
298C22×C4×C61C2416yes—
299C22×C4×C61C2416yes—
300C22×C4×C61C24112yes—
301C22×C4×C61C2413yes—
302C22×C4×C61C2411yescharacteristic
303C22×C4×C61C2416yes—
304C22×C4×C61C2416yes—
305C22×C4×C61C2411yescharacteristic
306C22×C4×C61C2414yes—
307C22×C4×C61C2414yes—
308C22×C4×C61C2413yes—
309C22×C4×C61C24112yes—
310C22×C4×C61C24112yes—
311C22×C4×C61C24112yes—
312C22×C4×C61C2413yes—
313C4⋊C4×C61C2416yes—
314C4⋊C4×C61C2414yes—
315C4⋊C4×C61C2414yes—
316C4⋊C4×C61C2416yes—
317C4⋊C4×C61C24112yes—
318C4⋊C4×C61C24112yes—
319C4⋊C4×C61C2416yes—
320C4⋊C4×C61C2416yes—
321C4⋊C4×C61C2416yes—
322C4⋊C4×C61C2416yes—
323C4⋊C4×C61C2416yes—
324C4⋊C4×C61C24112yes—
325C4⋊C4×C61C24112yes—
326C4⋊C4×C61C2416yes—
327C4⋊C4×C61C2414yes—
328C4⋊C4×C61C2414yes—
329C4⋊C4×C61C24112yes—
330C4⋊C4×C61C24112yes—
331C4⋊C4×C61C2414yes—
332C4⋊C4×C61C2414yes—
333C4⋊C4×C61C24112yes—
334C4⋊C4×C61C24112yes—
335C4⋊C4×C61C2414yes—
336C4⋊C4×C61C24112yes—
337C4⋊C4×C61C2414yes—
338C22⋊C4×C61C2414yes—
339C22⋊C4×C61C2414yes—
340C22⋊C4×C61C2414yes—
341C22⋊C4×C61C2414yes—
342C22⋊C4×C61C2414yes—
343C22⋊C4×C61C2411yescharacteristic
344C22⋊C4×C61C24112yes—
345C22⋊C4×C61C24112yes—
346C22⋊C4×C61C2416yes—
347C22⋊C4×C61C24124yes—
348C22⋊C4×C61C2411yescharacteristic
349C22⋊C4×C61C2411yescharacteristic
350C22⋊C4×C61C2411yescharacteristic
351C22⋊C4×C61C2416yes—
352C22⋊C4×C61C2414yes—
353C22⋊C4×C61C24112yes—
354C22⋊C4×C61C2414yes—
355C22⋊C4×C61C24112yes—
356C22⋊C4×C61C2414yes—
357C22⋊C4×C61C24112yes—
358C22⋊C4×C61C24112yes—
359C22⋊C4×C61C2414yes—
360C22⋊C4×C61C2414yes—
361C22⋊C4×C61C24112yes—
362C42×C61C2414yes—
363C42×C61C24112yes—
364C42×C61C2414yes—
365C42×C61C2414yes—
366C42×C61C2416yes—
367C42×C61C24112yes—
368C42×C61C24112yes—
369C42×C61C24112yes—
370C42×C61C24112yes—
371C42×C61C2416yes—
372C42×C61C24112yes—
373C23×C61—22no—
374C23×C61—22no—
375C23×C61—26no—
376C23×C61—41no—
377C23×C61—43no—
378C23×C61—43no—
379C23×C61C2511yescharacteristic
380C23×C61C2516yes—
381C23×C61C2514yes—
382C23×C61C2511yescharacteristic
383C23×C61C2511yescharacteristic
384Q8×C61—224no—
385Q8×C61—212no—
386Q8×C61—44no—
387Q8×C61—412no—
388Q8×C61C2×#41116yes—
389D4×C61—28no—
390D4×C61—212no—
391D4×C61—28no—
392D4×C61—224no—
393D4×C61—212no—
394D4×C61—46no—
395D4×C61—44no—
396D4×C61—412no—
397D4×C61—412no—
398C2×C4×C61—22no—
399C2×C4×C61—26no—
400C2×C4×C61—28no—
401C2×C4×C61—212no—
402C2×C4×C61—212no—
403C2×C4×C61—212no—
404C2×C4×C61—212no—
405C2×C4×C61—224no—
406C2×C4×C61—44no—
407C2×C4×C61—412no—
408C2×C4×C61—44no—
409C2×C4×C61—41no—
410C2×C4×C61—43no—
411C2×C4×C61—412no—
412C2×C4×C61—412no—
413C2×C4×C61C2×#41112yes—
414C2×C4×C61C2514yes—
415C2×C4×C61C2511yescharacteristic
416C2×C4×C61C2511yescharacteristic
417C2×C4×C61C2514yes—
418C2×C4×C61C2511yescharacteristic
419C2×C4×C61C2514yes—
420C2×C4×C61C2514yes—
421C2×C4×C61C2516yes—
422C2×C4×C61C2514yes—
423C2×C4×C61C2514yes—
424C2×C4×C61C2514yes—
425C2×C4×C61C2516yes—
426C2×C4×C61C2511yescharacteristic
427C2×C4×C61C2516yes—
428#63005C6111yesmaximal, characteristic, direct product factor, Sylow
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—21no—
433C22×C61—21no—
434C22×C61—24no—
435C22×C61—26no—
436C22×C61—24no—
437C22×C61—26no—
438C22×C61—21no—
439C22×C61—26no—
440C22×C61—24no—
441C22×C61—21no—
442C22×C61—44no—
443C22×C61—86no—
444C22×C61C22×#4112yes—
445C22×C61#58512yes—
446C22×C61C2611yescharacteristic
447C4×C61—21no—
448C4×C61—21no—
449C4×C61—24no—
450C4×C61—26no—
451C4×C61—24no—
452C4×C61—24no—
453C4×C61—26no—
454C4×C61—24no—
455C4×C61—21no—
456C4×C61—24no—
457C4×C61—24no—
458C4×C61—24no—
459C4×C61—21no—
460C4×C61C22×#41112yes—
461#3524C2×C6114yescomplemented
462#3524C2×C6114yescomplemented
463#3522C2×C6114yescomplemented
464#3518C2×C6114yescomplemented
465#3516C2×C6114yescomplemented
466#3516C2×C6114yescomplemented
467#3510C2×C6116yescomplemented
468#3502C2×C6111yescharacteristic, complemented
469#3495C2×C6116yescomplemented
470#3494C2×C6116yescomplemented
471#3487C2×C6111yescharacteristic, complemented
472#3486C2×C6111yescharacteristic, complemented
473#3482C2×C6114yescomplemented
474#3480C2×C6114yescomplemented
475#3475C2×C6116yescomplemented
476C2×#548C2×C6111yescharacteristic, complemented
477C4×2−1+4C2×C6111yescharacteristic, complemented
478#3428C2×C6111yescharacteristic, complemented
479C2×#519C2×C6111yescharacteristic, complemented
480C2×C61—22no—
481C2×C61—22no—
482C2×C61—44no—
483C2×C61—41no—
484C2×C61—46no—
485C2×C61C23×#4111yescharacteristic
486C2×C61C2×#58511yescharacteristic
487C2×C612−1+611yescharacteristic
488C2×2−1+4C22×C6111yescharacteristic
489C22×#41C22×C6111yescharacteristic
490C23×Q8C22×C6111yescharacteristic
491#559C22×C61112yescomplemented
492#559C22×C61112yescomplemented
493Q82C22×C6114yescomplemented
494#557C22×C6114yescomplemented
495#557C22×C6114yescomplemented
496#557C22×C6114yescomplemented
497#556C22×C6116yescomplemented
498#556C22×C61112yescomplemented
499#556C22×C61112yescomplemented
500#556C22×C61112yescomplemented
501#555C22×C6116yescomplemented
502#555C22×C61112yescomplemented
503#554C22×C6116yescomplemented
504#554C22×C61112yescomplemented
505#553C22×C6116yescomplemented
506#553C22×C6116yescomplemented
507#553C22×C61112yescomplemented
508#553C22×C61112yescomplemented
509#552C22×C61112yes—
510#552C22×C6116yescomplemented
511#552C22×C6116yescomplemented
512#552C22×C61112yescomplemented
513#552C22×C61112yescomplemented
514#551C22×C6114yes—
515#551C22×C61112yes—
516#551C22×C61124yes—
517#550C22×C6114yescomplemented
518#550C22×C6114yescomplemented
519D4×Q8C22×C6114yescomplemented
520D4×Q8C22×C6114yescomplemented
521#548C22×C6114yes—
522#548C22×C6114yes—
523#548C22×C6114yes—
524#548C22×C6114yes—
525#548C22×C6114yescomplemented
526#548C22×C6114yescomplemented
527#548C22×C6114yescomplemented
528#548C22×C6114yescomplemented
529#547C22×C6116yescomplemented
530#547C22×C61112yescomplemented
531#546C22×C61112yes—
532#544C22×C6116yes—
533#542C22×C61112yescomplemented
534#542C22×C61112yescomplemented
535#542C22×C61112yescomplemented
536#542C22×C61112yescomplemented
537#541C22×C61112yescomplemented
538#540C22×C61112yescomplemented
539#536C22×C6116yes—
540#535C22×C6116yes—
541#533C22×C6116yes—
542#533C22×C61112yescomplemented
543#532C22×C61112yescomplemented
544#529C22×C61112yescomplemented
545#529C22×C61112yescomplemented
546#529C22×C61112yescomplemented
547#529C22×C61112yescomplemented
548#529C22×C61112yescomplemented
549#529C22×C61112yescomplemented
550#529C22×C61112yescomplemented
551C2×#124C22×C6113yes—
552#525C22×C6116yes—
553#525C22×C6116yes—
554C2×C22⋊Q8C22×C6113yes—
555C2×#121C22×C6113yes—
556#520C22×C6116yes—
557#520C22×C6114yescomplemented
558#520C22×C6114yescomplemented
559#520C22×C6114yescomplemented
560#519C22×C6111yescharacteristic
561#519C22×C6111yescharacteristic
562#519C22×C6116yes—
563#519C22×C6111yescharacteristic
564#519C22×C6114yescomplemented
565#519C22×C6114yescomplemented
566#519C22×C6114yescomplemented
567#518C22×C6116yes—
568C4×#41C22×C6116yes—
569C4×#41C22×C6114yescomplemented
570C4×#41C22×C6114yescomplemented
571C4×#41C22×C6114yescomplemented
572C4×#41C22×C61112yescomplemented
573C2×C4×Q8C22×C6111yescharacteristic
574C2×C4×Q8C22×C6114yescomplemented
575C2×C4×Q8C22×C6114yescomplemented
576C2×C4×Q8C22×C6114yescomplemented
577C2×C4×D4C22×C6113yes—
578C2×#117C22×C6116yes—
579C2×#117C22×C6116yes—
580C61#6300511yescharacteristic, direct product factor, Sylow
5812−1+4—28no—
582C2×#41—28no—
583C2×#41C23×C6116yes—
584C2×#41C23×C6114yes—
585C2×#41C23×C6114yes—
586C2×#41C23×C6114yes—
587C2×#41C23×C61112yes—
588C22×Q8—28no—
589C22×Q8C23×C6114yes—
590C22×Q8C23×C6114yes—
591C22×Q8C23×C6113yes—
592C22×Q8C23×C6114yes—
593C22×Q8C23×C6111yescharacteristic
594C22×D4C23×C6113yes—
595C22×D4C23×C6113yes—
596C23×C4C23×C6113yes—
597C23×C4C23×C6113yes—
598C4⋊Q8C23×C61112yes—
599C4⋊Q8C23×C6116yes—
600C4⋊Q8C23×C6116yes—
601C4⋊Q8C23×C61112yes—
602C4⋊Q8C23×C61112yes—
603#127C23×C61112yes—
604#126C23×C6114yes—
605#126C23×C61112yes—
606#126C23×C6114yes—
607#126C23×C61112yes—
608#126C23×C61124yes—
609#126C23×C61124yes—
610#126C23×C61112yes—
611#126C23×C61112yes—
612#125C23×C6116yes—
613#125C23×C6116yes—
614#125C23×C61112yes—
615#125C23×C61112yes—
616#125C23×C61112yes—
617#125C23×C61112yes—
618#125C23×C61112yes—
619#124C23×C61112yes—
620#124C23×C61112yes—
621#124C23×C6114yes—
622#124C23×C61112yes—
623#124C23×C61112yes—
624#124C23×C61112yes—
625#124C23×C61112yes—
626#124C23×C61124yes—
627#123C23×C6114yes—
628#123C23×C61112yes—
629#123C23×C61112yes—
630#123C23×C6114yes—
631#123C23×C6114yes—
632#123C23×C61112yes—
633#123C23×C61124yes—
634#123C23×C61124yes—
635#123C23×C61112yes—
636#123C23×C61112yes—
637C22⋊Q8C23×C61112yes—
638C22⋊Q8C23×C61112yes—
639C22⋊Q8C23×C6116yes—
640C22⋊Q8C23×C6116yes—
641C22⋊Q8C23×C6116yes—
642C22⋊Q8C23×C6116yes—
643C22⋊Q8C23×C6114yes—
644C22⋊Q8C23×C61112yes—
645C22⋊Q8C23×C61112yes—
646C22⋊Q8C23×C61112yes—
647C22⋊Q8C23×C61112yes—
648C22⋊Q8C23×C6114yes—
649C22⋊Q8C23×C61112yes—
650C22⋊Q8C23×C61124yes—
651#121C23×C61112yes—
652#121C23×C61112yes—
653#121C23×C6116yes—
654#121C23×C6116yes—
655#121C23×C6116yes—
656#121C23×C6116yes—
657#121C23×C61112yes—
658#121C23×C61112yes—
659#121C23×C61112yes—
660#121C23×C61112yes—
661#121C23×C61112yes—
662#120C23×C6114yes—
663#120C23×C61112yes—
664C4×Q8C23×C6114yes—
665C4×Q8C23×C6114yes—
666C4×Q8C23×C6116yes—
667C4×Q8C23×C6114yes—
668C4×Q8C23×C6114yes—
669C4×Q8C23×C61112yes—
670C4×Q8C23×C61112yes—
671C4×Q8C23×C6114yes—
672C4×Q8C23×C6114yes—
673C4×Q8C23×C61112yes—
674C4×Q8C23×C61112yes—
675C4×Q8C23×C61112yes—
676C4×Q8C23×C6116yes—
677C4×Q8C23×C6114yes—
678C4×Q8C23×C6114yes—
679C4×Q8C23×C61112yes—
680C4×Q8C23×C61112yes—
681C4×Q8C23×C61112yes—
682C4×D4C23×C6116yes—
683C4×D4C23×C6116yes—
684C4×D4C23×C6116yes—
685C4×D4C23×C6116yes—
686C4×D4C23×C6114yes—
687C4×D4C23×C6116yes—
688C4×D4C23×C61112yes—
689C4×D4C23×C6116yes—
690C4×D4C23×C6114yes—
691C4×D4C23×C61112yes—
692C4×D4C23×C61112yes—
693C4×D4C23×C61112yes—
694C4×D4C23×C61112yes—
695C4×D4C23×C61112yes—
696C4×D4C23×C61112yes—
697C4×D4C23×C61112yes—
698C4×D4C23×C61112yes—
699C4×D4C23×C61112yes—
700C4×D4C23×C61112yes—
701C4×D4C23×C61112yes—
702C4×D4C23×C61124yes—
703#117C23×C6114yes—
704#117C23×C6116yes—
705#117C23×C6116yes—
706#117C23×C6116yes—
707#117C23×C6116yes—
708#117C23×C6116yes—
709#117C23×C61112yes—
710#117C23×C61112yes—
711#117C23×C6116yes—
712#117C23×C6116yes—
713#117C23×C61112yes—
714#117C23×C61112yes—
715#117C23×C6114yes—
716#117C23×C61112yes—
717#117C23×C61112yes—
718#117C23×C61112yes—
719#117C23×C61124yes—
720C2×C4⋊C4C23×C6116yes—
721C2×C4⋊C4C23×C6116yes—
722C2×C4⋊C4C23×C6116yes—
723C2×C4⋊C4C23×C6116yes—
724C2×C4⋊C4C23×C6113yes—
725C2×C4⋊C4C23×C6113yes—
726C2×C4⋊C4C23×C61112yes—
727C2×C22⋊C4C23×C6114yes—
728C2×C22⋊C4C23×C61112yes—
729C2×C22⋊C4C23×C6111yescharacteristic
730C2×C22⋊C4C23×C6113yes—
731C2×C22⋊C4C23×C6116yes—
732C2×C42C23×C61112yes—
733C2×C42C23×C61112yes—
734C2×C42C23×C6113yes—
735C2×C42C23×C61112yes—
736C24C24×C6111yescharacteristic
737C24C24×C6113yes—
738#41—216no—
739#41—216no—
740#41—216no—
741#41—224no—
742#41—424no—
743C2×Q8—216no—
744C2×Q8—216no—
745C2×Q8—216no—
746C2×Q8—212no—
747C2×Q8#41×C6118yescomplemented
748C2×Q8C24×C61112yes—
749C2×Q8C24×C6116yes—
750C2×Q8C24×C6114yes—
751C2×Q8C24×C61112yes—
752C2×Q8C24×C6114yes—
753C2×D4—212no—
754C2×D4—46no—
755C2×D4C24×C6114yes—
756C2×D4C24×C6114yes—
757C2×D4C24×C6116yes—
758C2×D4C24×C61112yes—
759C2×D4C24×C6116yes—
760C2×D4C24×C6114yes—
761C2×D4C24×C61112yes—
762C2×D4C24×C61112yes—
763C2×D4C24×C6116yes—
764C22×C4—212no—
765C22×C4—212no—
766C22×C4C24×C6114yes—
767C22×C4C24×C6116yes—
768C22×C4C24×C6116yes—
769C22×C4C24×C61112yes—
770C22×C4C24×C6113yes—
771C22×C4C24×C6111yescharacteristic
772C22×C4C24×C6116yes—
773C22×C4C24×C6116yes—
774C22×C4C24×C6111yescharacteristic
775C22×C4C24×C6114yes—
776C22×C4C24×C6114yes—
777C22×C4C24×C6113yes—
778C22×C4C24×C61112yes—
779C22×C4C24×C61112yes—
780C22×C4C24×C61112yes—
781C22×C4C24×C6113yes—
782C4⋊C4C24×C6116yes—
783C4⋊C4C24×C6114yes—
784C4⋊C4C24×C6114yes—
785C4⋊C4C24×C6116yes—
786C4⋊C4C24×C61112yes—
787C4⋊C4C24×C61112yes—
788C4⋊C4C24×C6116yes—
789C4⋊C4C24×C6116yes—
790C4⋊C4C24×C6116yes—
791C4⋊C4C24×C6116yes—
792C4⋊C4C24×C6116yes—
793C4⋊C4C24×C61112yes—
794C4⋊C4C24×C61112yes—
795C4⋊C4C24×C6116yes—
796C4⋊C4C24×C6114yes—
797C4⋊C4C24×C6114yes—
798C4⋊C4C24×C61112yes—
799C4⋊C4C24×C61112yes—
800C4⋊C4C24×C6114yes—
801C4⋊C4C24×C6114yes—
802C4⋊C4C24×C61112yes—
803C4⋊C4C24×C61112yes—
804C4⋊C4C24×C6114yes—
805C4⋊C4C24×C61112yes—
806C4⋊C4C24×C6114yes—
807C22⋊C4C24×C6114yes—
808C22⋊C4C24×C6114yes—
809C22⋊C4C24×C6114yes—
810C22⋊C4C24×C6114yes—
811C22⋊C4C24×C6114yes—
812C22⋊C4C24×C6111yescharacteristic
813C22⋊C4C24×C61112yes—
814C22⋊C4C24×C61112yes—
815C22⋊C4C24×C6116yes—
816C22⋊C4C24×C61124yes—
817C22⋊C4C24×C6111yescharacteristic
818C22⋊C4C24×C6111yescharacteristic
819C22⋊C4C24×C6111yescharacteristic
820C22⋊C4C24×C6116yes—
821C22⋊C4C24×C6114yes—
822C22⋊C4C24×C61112yes—
823C22⋊C4C24×C6114yes—
824C22⋊C4C24×C61112yes—
825C22⋊C4C24×C6114yes—
826C22⋊C4C24×C61112yes—
827C22⋊C4C24×C61112yes—
828C22⋊C4C24×C6114yes—
829C22⋊C4C24×C6114yes—
830C22⋊C4C24×C61112yes—
831C42C24×C6114yes—
832C42C24×C61112yes—
833C42C24×C6114yes—
834C42C24×C6114yes—
835C42C24×C6116yes—
836C42C24×C61112yes—
837C42C24×C61112yes—
838C42C24×C61112yes—
839C42C24×C61112yes—
840C42C24×C6116yes—
841C42C24×C61112yes—
842C23—22no—
843C23—22no—
844C23—26no—
845C23—41no—
846C23—43no—
847C23—43no—
848C23C25×C6111yescharacteristic
849C23C25×C6116yes—
850C23C25×C6114yes—
851C23C25×C6111yescharacteristic
852C23C25×C6111yescharacteristic
853Q8—224no—
854Q8—212no—
855Q8—44no—
856Q8—412no—
857Q8C2×#41×C61116yes—
858D4—28no—
859D4—212no—
860D4—28no—
861D4—224no—
862D4—212no—
863D4—46no—
864D4—44no—
865D4—412no—
866D4—412no—
867C2×C4—22no—
868C2×C4—26no—
869C2×C4—28no—
870C2×C4—212no—
871C2×C4—212no—
872C2×C4—212no—
873C2×C4—212no—
874C2×C4—224no—
875C2×C4—44no—
876C2×C4—412no—
877C2×C4—44no—
878C2×C4—41no—
879C2×C4—43no—
880C2×C4—412no—
881C2×C4—412no—
882C2×C4C2×#41×C61112yes—
883C2×C4C25×C6114yes—
884C2×C4C25×C6111yescharacteristic
885C2×C4C25×C6111yescharacteristic
886C2×C4C25×C6114yes—
887C2×C4C25×C6111yescharacteristic
888C2×C4C25×C6114yes—
889C2×C4C25×C6114yes—
890C2×C4C25×C6116yes—
891C2×C4C25×C6114yes—
892C2×C4C25×C6114yes—
893C2×C4C25×C6114yes—
894C2×C4C25×C6116yes—
895C2×C4C25×C6111yescharacteristic
896C2×C4C25×C6116yes—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—24no—
903C22—26no—
904C22—24no—
905C22—26no—
906C22—21no—
907C22—26no—
908C22—24no—
909C22—21no—
910C22—44no—
911C22—86no—
912C22C22×#41×C6112yes—
913C22C61×#58512yes—
914C22C26×C6111yescharacteristic
915C4—21no—
916C4—21no—
917C4—24no—
918C4—26no—
919C4—24no—
920C4—24no—
921C4—26no—
922C4—24no—
923C4—21no—
924C4—24no—
925C4—24no—
926C4—24no—
927C4—21no—
928C4C22×#41×C61112yes—
929C2—22no—
930C2—22no—
931C2—41no—
932C2—46no—
933C2—44no—
934C2C23×#41×C6111yescharacteristic
935C2C2×C61×#58511yescharacteristic
936C2C61×2−1+611yescharacteristic
subgroupG/H
center, socleC22×C61C26
commutator, Frattini, cosocleC22C26×C61
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3524C2semidirect
2. C61×#3524C2semidirect
3. C61×#3522C2semidirect
4. C61×#3518C2semidirect
5. C61×#3516C2semidirect
6. C61×#3516C2semidirect
7. C61×#3510C2semidirect
8. C61×#3502C2semidirect
9. C61×#3495C2semidirect
10. C61×#3494C2semidirect
11. C61×#3487C2semidirect
12. C61×#3486C2semidirect
13. C61×#3482C2semidirect
14. C61×#3480C2semidirect
15. C61×#3475C2semidirect
16. C2×C61×#548C2semidirect
17. C4×2−1+4×C61C2semidirect
18. C61×#3428C2semidirect
19. C2×C61×#519C2semidirect
23. C61×#559C22semidirect
24. C61×#559C22semidirect
25. Q82×C61C22semidirect
26. C61×#557C22semidirect
27. C61×#557C22semidirect
28. C61×#557C22semidirect
29. C61×#556C22semidirect
30. C61×#556C22semidirect
31. C61×#556C22semidirect
32. C61×#556C22semidirect
33. C61×#555C22semidirect
34. C61×#555C22semidirect
35. C61×#554C22semidirect
36. C61×#554C22semidirect
37. C61×#553C22semidirect
38. C61×#553C22semidirect
39. C61×#553C22semidirect
40. C61×#553C22semidirect
42. C61×#552C22semidirect
43. C61×#552C22semidirect
44. C61×#552C22semidirect
45. C61×#552C22semidirect
49. C61×#550C22semidirect
50. C61×#550C22semidirect
51. D4×Q8×C61C22semidirect
52. D4×Q8×C61C22semidirect
57. C61×#548C22semidirect
58. C61×#548C22semidirect
59. C61×#548C22semidirect
60. C61×#548C22semidirect
61. C61×#547C22semidirect
62. C61×#547C22semidirect
65. C61×#542C22semidirect
66. C61×#542C22semidirect
67. C61×#542C22semidirect
68. C61×#542C22semidirect
69. C61×#541C22semidirect
70. C61×#540C22semidirect
74. C61×#533C22semidirect
75. C61×#532C22semidirect
76. C61×#529C22semidirect
77. C61×#529C22semidirect
78. C61×#529C22semidirect
79. C61×#529C22semidirect
80. C61×#529C22semidirect
81. C61×#529C22semidirect
82. C61×#529C22semidirect
89. C61×#520C22semidirect
90. C61×#520C22semidirect
91. C61×#520C22semidirect
96. C61×#519C22semidirect
97. C61×#519C22semidirect
98. C61×#519C22semidirect
101. C4×#41×C61C22semidirect
102. C4×#41×C61C22semidirect
103. C4×#41×C61C22semidirect
104. C4×#41×C61C22semidirect
106. C2×C4×Q8×C61C22semidirect
107. C2×C4×Q8×C61C22semidirect
108. C2×C4×Q8×C61C22semidirect
278. C2×Q8×C61#41semidirect
428. #63005C61direct (N × H)
461. #3524C2×C61semidirect
462. #3524C2×C61semidirect
463. #3522C2×C61semidirect
464. #3518C2×C61semidirect
465. #3516C2×C61semidirect
466. #3516C2×C61semidirect
467. #3510C2×C61semidirect
468. #3502C2×C61semidirect
469. #3495C2×C61semidirect
470. #3494C2×C61semidirect
471. #3487C2×C61semidirect
472. #3486C2×C61semidirect
473. #3482C2×C61semidirect
474. #3480C2×C61semidirect
475. #3475C2×C61semidirect
476. C2×#548C2×C61semidirect
477. C4×2−1+4C2×C61semidirect
478. #3428C2×C61semidirect
479. C2×#519C2×C61semidirect
491. #559C22×C61semidirect
492. #559C22×C61semidirect
493. Q82C22×C61semidirect
494. #557C22×C61semidirect
495. #557C22×C61semidirect
496. #557C22×C61semidirect
497. #556C22×C61semidirect
498. #556C22×C61semidirect
499. #556C22×C61semidirect
500. #556C22×C61semidirect
501. #555C22×C61semidirect
502. #555C22×C61semidirect
503. #554C22×C61semidirect
504. #554C22×C61semidirect
505. #553C22×C61semidirect
506. #553C22×C61semidirect
507. #553C22×C61semidirect
508. #553C22×C61semidirect
510. #552C22×C61semidirect
511. #552C22×C61semidirect
512. #552C22×C61semidirect
513. #552C22×C61semidirect
517. #550C22×C61semidirect
518. #550C22×C61semidirect
519. D4×Q8C22×C61semidirect
520. D4×Q8C22×C61semidirect
525. #548C22×C61semidirect
526. #548C22×C61semidirect
527. #548C22×C61semidirect
528. #548C22×C61semidirect
529. #547C22×C61semidirect
530. #547C22×C61semidirect
533. #542C22×C61semidirect
534. #542C22×C61semidirect
535. #542C22×C61semidirect
536. #542C22×C61semidirect
537. #541C22×C61semidirect
538. #540C22×C61semidirect
542. #533C22×C61semidirect
543. #532C22×C61semidirect
544. #529C22×C61semidirect
545. #529C22×C61semidirect
546. #529C22×C61semidirect
547. #529C22×C61semidirect
548. #529C22×C61semidirect
549. #529C22×C61semidirect
550. #529C22×C61semidirect
557. #520C22×C61semidirect
558. #520C22×C61semidirect
559. #520C22×C61semidirect
564. #519C22×C61semidirect
565. #519C22×C61semidirect
566. #519C22×C61semidirect
569. C4×#41C22×C61semidirect
570. C4×#41C22×C61semidirect
571. C4×#41C22×C61semidirect
572. C4×#41C22×C61semidirect
574. C2×C4×Q8C22×C61semidirect
575. C2×C4×Q8C22×C61semidirect
576. C2×C4×Q8C22×C61semidirect
580. C61#63005direct (N × H)
747. C2×Q8#41×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#35242
C61×#35222
C61×#35182
C61×#35162
C61×#35102
C61×#35022
C61×#34952
C61×#34942
C61×#34872
C61×#34862
C61×#34822
C61×#34802
C61×#34752
C2×C61×#5482
C4×2−1+4×C612
C61×#34282
C2×C61×#5192
#6300561