Finite Group Databasebeta

← C61×#63046 #29566479

Subgroups — C61×#63046 #29566479

Order 15616.

6790 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3568C216yesmaximal, complemented
2C61×#3561C216yesmaximal, complemented
3C61×#3558C216yesmaximal, complemented
4C61×#3545C213yesmaximal, complemented
5C61×#3545C216yesmaximal, complemented
6C61×#3540C2112yesmaximal, complemented
7C61×#3532C216yesmaximal, complemented
8C61×#3529C212yesmaximal, complemented
9C2×C61×H(3,𝔽4)C211yesmaximal, characteristic, complemented
10C61×#3514C216yesmaximal, complemented
11C61×#3510C213yesmaximal, complemented
12C61×#3490C216yesmaximal, complemented
13C61×#563C2216yescomplemented
14C61×#563C2213yescomplemented
15C61×#563C2216yescomplemented
16C61×#562C2216yescomplemented
17C61×#562C2216yescomplemented
18C61×#562C2216yescomplemented
19C61×H(3,𝔽4)C2213yescomplemented
20C61×H(3,𝔽4)C2216yescomplemented
21C61×H(3,𝔽4)C2211yescharacteristic, complemented
22C61×H(3,𝔽4)C2216yescomplemented
23C61×H(3,𝔽4)C2216yescomplemented
24C61×H(3,𝔽4)C2213yescomplemented
25C61×#560C22112yescomplemented
26C61×#560C2216yescomplemented
27C61×#559C22112yescomplemented
28C61×#559C2216yescomplemented
29C61×#556C22112yescomplemented
30C61×#556C2216yescomplemented
31C61×#556C22112yescomplemented
32C61×#555C22112yescomplemented
33C61×#555C2216yescomplemented
34C61×#551C22112yescomplemented
35C61×#551C22112yescomplemented
36C61×#551C22112yescomplemented
37C61×#551C22112yescomplemented
38C61×#551C2216yescomplemented
39C61×#551C22112yescomplemented
40C61×#551C2216yescomplemented
41C61×#551C22112yescomplemented
42D4×Q8×C61C2216yescomplemented
43C61×#548C2212yescomplemented
44C61×#548C22112yescomplemented
45C61×#548C2216yescomplemented
46C61×#546C22112yescomplemented
47C61×#546C2216yescomplemented
48C61×#546C22112yescomplemented
49C61×#546C22112yescomplemented
50C61×#546C22112yescomplemented
51C61×#546C22112yescomplemented
52C61×#546C2216yescomplemented
53D42×C61C2216yescomplemented
54D42×C61C2216yescomplemented
55C61×#543C2216yescomplemented
56C61×#542C2216yescomplemented
57C61×#542C22112yescomplemented
58C61×#542C2216yescomplemented
59C61×#542C22112yescomplemented
60C61×#542C22112yescomplemented
61C61×#542C22112yescomplemented
62C61×#542C22112yescomplemented
63C61×#538C22112yescomplemented
64C61×#538C22112yescomplemented
65C61×#538C22112yescomplemented
66C61×#538C22112yescomplemented
67C61×#538C22112yescomplemented
68C61×#538C22112yescomplemented
69C61×#538C22112yescomplemented
70C61×#536C2213yescomplemented
71C61×#536C22112yescomplemented
72C61×#535C2213yes—
73C61×#535C22112yescomplemented
74C61×#534C2216yescomplemented
75C61×#534C22112yescomplemented
76C61×#533C2213yescomplemented
77C61×#532C2216yescomplemented
78C61×#529C2216yescomplemented
79C61×#529C2216yescomplemented
80C61×#529C2216yescomplemented
81C61×#529C2216yescomplemented
82C61×#529C2216yescomplemented
83C2×#124×C61C2213yescomplemented
84C2×#124×C61C2216yescomplemented
85C2×#124×C61C2216yescomplemented
86C61×#525C22112yescomplemented
87C61×#525C22112yescomplemented
88C2×#120×C61C2216yescomplemented
89C2×#120×C61C2216yescomplemented
90C61×#519C2211yescharacteristic, complemented
91C61×#518C2213yescomplemented
92C61×#518C2216yescomplemented
93C4×#41×C61C2213yescomplemented
94C22×C22⋊C4×C61C2212yescomplemented
95C25×C61C2312yes—
96C2×#41×C61C2313yes—
97C2×#41×C61C2316yes—
98C2×#41×C61C23112yes—
99C2×#41×C61C2312yescomplemented
100C22×Q8×C61C2311yescharacteristic
101C22×Q8×C61C2312yes—
102C22×Q8×C61C2316yescomplemented
103C22×D4×C61C2313yes—
104C22×D4×C61C2316yes—
105C22×D4×C61C2316yes—
106C22×D4×C61C2316yes—
107C22×D4×C61C23112yescomplemented
108C23×C4×C61C2314yescomplemented
109C4⋊Q8×C61C2316yescomplemented
110C4⋊Q8×C61C2316yescomplemented
111C4⋊Q8×C61C23112yescomplemented
112C4⋊Q8×C61C2316yescomplemented
113#127×C61C2316yes—
114#127×C61C2316yes—
115#126×C61C23112yescomplemented
116#126×C61C23112yescomplemented
117#126×C61C23112yescomplemented
118#126×C61C23112yescomplemented
119#126×C61C23112yescomplemented
120#126×C61C23112yescomplemented
121#126×C61C23112yescomplemented
122#126×C61C23112yescomplemented
123#126×C61C23112yescomplemented
124#125×C61C2316yescomplemented
125#125×C61C2316yescomplemented
126#124×C61C2316yes—
127#124×C61C2316yes—
128#124×C61C23112yes—
129#124×C61C23112yes—
130#124×C61C2316yes—
131#124×C61C23112yes—
132#124×C61C23112yes—
133#124×C61C2316yes—
134#124×C61C2316yes—
135#124×C61C2313yes—
136#124×C61C2313yes—
137#124×C61C2313yes—
138#124×C61C2313yes—
139#124×C61C2316yes—
140#124×C61C2316yescomplemented
141#124×C61C23112yescomplemented
142#124×C61C23112yescomplemented
143#124×C61C2316yescomplemented
144#124×C61C2316yescomplemented
145#124×C61C23112yescomplemented
146#124×C61C23112yescomplemented
147#124×C61C23112yescomplemented
148#124×C61C23112yescomplemented
149#123×C61C23112yes—
150#123×C61C2316yes—
151#123×C61C23112yes—
152#123×C61C2316yes—
153#123×C61C23112yes—
154#123×C61C23112yes—
155#123×C61C23112yescomplemented
156#123×C61C23112yescomplemented
157#123×C61C23112yescomplemented
158#123×C61C23112yescomplemented
159#123×C61C23112yescomplemented
160#123×C61C23112yescomplemented
161#123×C61C23112yescomplemented
162#123×C61C23112yescomplemented
163#123×C61C23112yescomplemented
164C22⋊Q8×C61C23112yes—
165C22⋊Q8×C61C2316yes—
166C22⋊Q8×C61C2316yescomplemented
167C22⋊Q8×C61C23112yescomplemented
168C22⋊Q8×C61C23112yescomplemented
169C22⋊Q8×C61C23112yescomplemented
170C22⋊Q8×C61C2316yescomplemented
171C22⋊Q8×C61C23112yescomplemented
172C22⋊Q8×C61C23112yescomplemented
173C22⋊Q8×C61C23112yescomplemented
174C22⋊Q8×C61C23112yescomplemented
175C22⋊Q8×C61C23112yescomplemented
176C22⋊Q8×C61C2316yescomplemented
177C22⋊Q8×C61C2316yescomplemented
178C22⋊Q8×C61C23112yescomplemented
179#121×C61C2316yes—
180#121×C61C23112yes—
181#121×C61C23112yes—
182#121×C61C23112yes—
183#121×C61C2316yes—
184#121×C61C23112yes—
185#121×C61C23112yes—
186#121×C61C23112yes—
187#121×C61C2316yes—
188#121×C61C2316yes—
189#121×C61C2316yes—
190#121×C61C23112yes—
191#121×C61C23112yescomplemented
192#121×C61C23112yescomplemented
193#121×C61C23112yescomplemented
194#121×C61C23112yescomplemented
195#120×C61C2316yes—
196#120×C61C23112yes—
197#120×C61C2316yes—
198#120×C61C23112yes—
199#120×C61C23112yes—
200#120×C61C23112yes—
201#120×C61C23112yes—
202#120×C61C2316yes—
203#120×C61C2316yes—
204#120×C61C2316yes—
205#120×C61C2316yes—
206#120×C61C23112yescomplemented
207#120×C61C23112yescomplemented
208#120×C61C23112yescomplemented
209C4×Q8×C61C23112yescomplemented
210C4×Q8×C61C2312yescomplemented
211C4×Q8×C61C2316yescomplemented
212C4×Q8×C61C2316yescomplemented
213C4×Q8×C61C2316yescomplemented
214C4×Q8×C61C2316yescomplemented
215C4×Q8×C61C2312yescomplemented
216C4×D4×C61C2316yes—
217C4×D4×C61C2316yes—
218C4×D4×C61C2316yes—
219C4×D4×C61C23112yes—
220C4×D4×C61C23112yes—
221C4×D4×C61C23112yes—
222C4×D4×C61C2316yes—
223C4×D4×C61C2316yes—
224C4×D4×C61C2316yes—
225C4×D4×C61C23112yescomplemented
226C4×D4×C61C23112yescomplemented
227C4×D4×C61C2316yescomplemented
228C4×D4×C61C2316yescomplemented
229C4×D4×C61C23112yescomplemented
230C4×D4×C61C23112yescomplemented
231C4×D4×C61C23112yescomplemented
232C4×D4×C61C23112yescomplemented
233#117×C61C2313yes—
234#117×C61C2313yes—
235#117×C61C2313yes—
236#117×C61C23112yescomplemented
237#117×C61C23112yescomplemented
238#117×C61C2316yescomplemented
239#117×C61C23112yescomplemented
240#117×C61C23112yescomplemented
241#117×C61C23112yescomplemented
242C2×C22⋊C4×C61C2316yes—
243C2×C22⋊C4×C61C2316yes—
244C2×C22⋊C4×C61C2316yes—
245C2×C22⋊C4×C61C2316yes—
246C2×C22⋊C4×C61C23112yes—
247C2×C22⋊C4×C61C23112yescomplemented
248C2×C22⋊C4×C61C23112yescomplemented
249C2×C22⋊C4×C61C23112yescomplemented
250C2×C22⋊C4×C61C23112yescomplemented
251C2×C42×C61C2313yes—
252C2×C42×C61C2316yescomplemented
253C24×C61—44no—
254C24×C61—84no—
255C24×C61C2416yes—
256C24×C61C2416yes—
257C24×C61C2416yes—
258C24×C61C2412yes—
259#41×C61—46no—
260#41×C61—86no—
261#41×C61—812no—
262#41×C61—82no—
263C2×Q8×C61—42no—
264C2×Q8×C61—82no—
265C2×Q8×C61—86no—
266C2×Q8×C61C2411yescharacteristic
267C2×Q8×C61C2413yes—
268C2×Q8×C61C2413yes—
269C2×Q8×C61C2416yes—
270C2×Q8×C61C24112yes—
271C2×Q8×C61C2416yes—
272C2×Q8×C61C2412yes—
273C2×D4×C61—46no—
274C2×D4×C61—412no—
275C2×D4×C61—86no—
276C2×D4×C61—86no—
277C2×D4×C61—812no—
278C2×D4×C61C2416yes—
279C2×D4×C61C2413yes—
280C2×D4×C61C2416yes—
281C2×D4×C61C2413yes—
282C2×D4×C61C24112yes—
283C2×D4×C61C2416yes—
284C2×D4×C61C2416yes—
285C2×D4×C61C24112yes—
286C2×D4×C61C2413yes—
287C2×D4×C61C24112yes—
288C2×D4×C61C24112yes—
289C2×D4×C61C24112yes—
290C2×D4×C61C24112yes—
291C2×D4×C61C2416yes—
292C22×C4×C61—84no—
293C22×C4×C61C2413yes—
294C22×C4×C61C2416yes—
295C22×C4×C61C2416yes—
296C22×C4×C61C2416yes—
297C22×C4×C61C2416yes—
298C22×C4×C61C24112yes—
299C22×C4×C61C24112yes—
300C22×C4×C61C24112yes—
301C22×C4×C61C2416yes—
302C22×C4×C61C24112yes—
303C4⋊C4×C61C2416yes—
304C4⋊C4×C61C2416yes—
305C4⋊C4×C61C2416yes—
306C4⋊C4×C61C2416yes—
307C4⋊C4×C61C24112yes—
308C4⋊C4×C61C24112yes—
309C4⋊C4×C61C24112yes—
310C4⋊C4×C61C24112yes—
311C4⋊C4×C61C24112yes—
312C4⋊C4×C61C2416yes—
313C4⋊C4×C61C2416yes—
314C4⋊C4×C61C2416yes—
315C4⋊C4×C61C24112yes—
316C4⋊C4×C61C24112yes—
317C22⋊C4×C61C2411yescharacteristic
318C22⋊C4×C61C2416yes—
319C22⋊C4×C61C2413yes—
320C22⋊C4×C61C24112yes—
321C22⋊C4×C61C2416yes—
322C22⋊C4×C61C2416yes—
323C22⋊C4×C61C24112yes—
324C22⋊C4×C61C24112yes—
325C22⋊C4×C61C24112yes—
326C22⋊C4×C61C24112yes—
327C22⋊C4×C61C24112yes—
328C22⋊C4×C61C24112yes—
329C22⋊C4×C61C2416yes—
330C22⋊C4×C61C2416yes—
331C22⋊C4×C61C2416yes—
332C22⋊C4×C61C24112yes—
333C22⋊C4×C61C24112yes—
334C22⋊C4×C61C24112yes—
335C22⋊C4×C61C24112yes—
336C22⋊C4×C61C24112yes—
337C22⋊C4×C61C24112yes—
338C22⋊C4×C61C24112yes—
339C22⋊C4×C61C2416yes—
340C22⋊C4×C61C24112yes—
341C42×C61C2413yes—
342C42×C61C2413yes—
343C42×C61C2416yes—
344C42×C61C2416yes—
345C42×C61C2416yes—
346C42×C61C2416yes—
347C42×C61C2416yes—
348C42×C61C2416yes—
349C42×C61C24112yes—
350C23×C61—212no—
351C23×C61—44no—
352C23×C61—42no—
353C23×C61—412no—
354C23×C61—412no—
355C23×C61—46no—
356C23×C61—46no—
357C23×C61—412no—
358C23×C61—816no—
359C23×C61C2516yes—
360C23×C61C2516yes—
361C23×C61C2516yes—
362C23×C61C2511yescharacteristic
363Q8×C61—41no—
364Q8×C61—43no—
365Q8×C61—46no—
366Q8×C61—46no—
367Q8×C61—412no—
368Q8×C61—42no—
369Q8×C61—43no—
370D4×C61—212no—
371D4×C61—43no—
372D4×C61—43no—
373D4×C61—46no—
374D4×C61—412no—
375D4×C61—412no—
376D4×C61—46no—
377D4×C61—412no—
378D4×C61—412no—
379D4×C61—412no—
380D4×C61—46no—
381D4×C61—46no—
382D4×C61—412no—
383D4×C61—43no—
384C2×C4×C61—26no—
385C2×C4×C61—412no—
386C2×C4×C61—412no—
387C2×C4×C61—46no—
388C2×C4×C61—46no—
389C2×C4×C61—46no—
390C2×C4×C61—412no—
391C2×C4×C61—412no—
392C2×C4×C61—46no—
393C2×C4×C61—46no—
394C2×C4×C61C2513yes—
395C2×C4×C61C2512yes—
396C2×C4×C61C2513yes—
397C2×C4×C61C2516yes—
398C2×C4×C61C2516yes—
399C2×C4×C61C2516yes—
400C2×C4×C61C2516yes—
401C2×C4×C61C25112yes—
402#63046C6111yesmaximal, characteristic, direct product factor, Sylow
403C22×C61—22no—
404C22×C61—26no—
405C22×C61—26no—
406C22×C61—26no—
407C22×C61—26no—
408C22×C61—212no—
409C22×C61—26no—
410C22×C61—212no—
411C22×C61—48no—
412C22×C61—812no—
413C22×C61—812no—
414C22×C61—166no—
415C22×C61#58512yes—
416C22×C61C2611yescharacteristic
417C4×C61—23no—
418C4×C61—23no—
419C4×C61—26no—
420C4×C61—22no—
421C4×C61—212no—
422C4×C61—26no—
423C4×C61—26no—
424C4×C61—26no—
425#3568C2×C6116yescomplemented
426#3561C2×C6116yescomplemented
427#3558C2×C6116yescomplemented
428#3545C2×C6113yescomplemented
429#3545C2×C6116yescomplemented
430#3540C2×C61112yescomplemented
431#3532C2×C6116yescomplemented
432#3529C2×C6112yescomplemented
433C2×H(3,𝔽4)C2×C6111yescharacteristic, complemented
434#3514C2×C6116yescomplemented
435#3510C2×C6113yescomplemented
436#3490C2×C6116yescomplemented
437C2×C61—22no—
438C2×C61—46no—
439C2×C61—46no—
440C2×C61—46no—
441C2×C61C2×#58511yescharacteristic
442C2×C61H(7,𝔽2)12yes—
443#563C22×C6116yescomplemented
444#563C22×C6116yescomplemented
445#563C22×C6113yescomplemented
446#562C22×C6116yescomplemented
447#562C22×C6116yescomplemented
448#562C22×C6116yescomplemented
449H(3,𝔽4)C22×C6111yescharacteristic, complemented
450H(3,𝔽4)C22×C6116yescomplemented
451H(3,𝔽4)C22×C6113yescomplemented
452H(3,𝔽4)C22×C6116yescomplemented
453H(3,𝔽4)C22×C6116yescomplemented
454H(3,𝔽4)C22×C6113yescomplemented
455#560C22×C61112yescomplemented
456#560C22×C6116yescomplemented
457#559C22×C61112yescomplemented
458#559C22×C6116yescomplemented
459#556C22×C61112yescomplemented
460#556C22×C6116yescomplemented
461#556C22×C61112yescomplemented
462#555C22×C61112yescomplemented
463#555C22×C6116yescomplemented
464#551C22×C61112yescomplemented
465#551C22×C61112yescomplemented
466#551C22×C61112yescomplemented
467#551C22×C61112yescomplemented
468#551C22×C61112yescomplemented
469#551C22×C6116yescomplemented
470#551C22×C61112yescomplemented
471#551C22×C6116yescomplemented
472D4×Q8C22×C6116yescomplemented
473#548C22×C6112yescomplemented
474#548C22×C6116yescomplemented
475#548C22×C61112yescomplemented
476#546C22×C6116yescomplemented
477#546C22×C61112yescomplemented
478#546C22×C61112yescomplemented
479#546C22×C61112yescomplemented
480#546C22×C61112yescomplemented
481#546C22×C61112yescomplemented
482#546C22×C6116yescomplemented
483D42C22×C6116yescomplemented
484D42C22×C6116yescomplemented
485#543C22×C6116yescomplemented
486#542C22×C6116yescomplemented
487#542C22×C6116yescomplemented
488#542C22×C61112yescomplemented
489#542C22×C61112yescomplemented
490#542C22×C61112yescomplemented
491#542C22×C61112yescomplemented
492#542C22×C61112yescomplemented
493#538C22×C61112yescomplemented
494#538C22×C61112yescomplemented
495#538C22×C61112yescomplemented
496#538C22×C61112yescomplemented
497#538C22×C61112yescomplemented
498#538C22×C61112yescomplemented
499#538C22×C61112yescomplemented
500#536C22×C6113yescomplemented
501#536C22×C61112yescomplemented
502#535C22×C6113yes—
503#535C22×C61112yescomplemented
504#534C22×C6116yescomplemented
505#534C22×C61112yescomplemented
506#533C22×C6113yescomplemented
507#532C22×C6116yescomplemented
508#529C22×C6116yescomplemented
509#529C22×C6116yescomplemented
510#529C22×C6116yescomplemented
511#529C22×C6116yescomplemented
512#529C22×C6116yescomplemented
513C2×#124C22×C6113yescomplemented
514C2×#124C22×C6116yescomplemented
515C2×#124C22×C6116yescomplemented
516#525C22×C61112yescomplemented
517#525C22×C61112yescomplemented
518C2×#120C22×C6116yescomplemented
519C2×#120C22×C6116yescomplemented
520#519C22×C6111yescharacteristic, complemented
521#518C22×C6113yescomplemented
522#518C22×C6116yescomplemented
523C4×#41C22×C6113yescomplemented
524C22×C22⋊C4C22×C6112yescomplemented
525C61#6304611yescharacteristic, direct product factor, Sylow
526C25C23×C6112yes—
527C2×#41C23×C6113yes—
528C2×#41C23×C6116yes—
529C2×#41C23×C61112yes—
530C2×#41C23×C6112yescomplemented
531C22×Q8C23×C6111yescharacteristic
532C22×Q8C23×C6112yes—
533C22×Q8C23×C6116yescomplemented
534C22×D4C23×C6113yes—
535C22×D4C23×C6116yes—
536C22×D4C23×C6116yes—
537C22×D4C23×C6116yes—
538C22×D4C23×C61112yescomplemented
539C23×C4C23×C6114yescomplemented
540C4⋊Q8C23×C6116yescomplemented
541C4⋊Q8C23×C6116yescomplemented
542C4⋊Q8C23×C61112yescomplemented
543C4⋊Q8C23×C6116yescomplemented
544#127C23×C6116yes—
545#127C23×C6116yes—
546#126C23×C61112yescomplemented
547#126C23×C61112yescomplemented
548#126C23×C61112yescomplemented
549#126C23×C61112yescomplemented
550#126C23×C61112yescomplemented
551#126C23×C61112yescomplemented
552#126C23×C61112yescomplemented
553#126C23×C61112yescomplemented
554#126C23×C61112yescomplemented
555#125C23×C6116yescomplemented
556#125C23×C6116yescomplemented
557#124C23×C6116yes—
558#124C23×C6113yes—
559#124C23×C6113yes—
560#124C23×C6116yes—
561#124C23×C61112yes—
562#124C23×C6116yes—
563#124C23×C61112yes—
564#124C23×C61112yes—
565#124C23×C6116yes—
566#124C23×C6116yes—
567#124C23×C6113yes—
568#124C23×C6113yes—
569#124C23×C6116yes—
570#124C23×C61112yes—
571#124C23×C6116yescomplemented
572#124C23×C61112yescomplemented
573#124C23×C6116yescomplemented
574#124C23×C61112yescomplemented
575#124C23×C61112yescomplemented
576#124C23×C6116yescomplemented
577#124C23×C61112yescomplemented
578#124C23×C61112yescomplemented
579#124C23×C61112yescomplemented
580#123C23×C61112yes—
581#123C23×C61112yes—
582#123C23×C61112yes—
583#123C23×C6116yes—
584#123C23×C61112yes—
585#123C23×C6116yes—
586#123C23×C61112yescomplemented
587#123C23×C61112yescomplemented
588#123C23×C61112yescomplemented
589#123C23×C61112yescomplemented
590#123C23×C61112yescomplemented
591#123C23×C61112yescomplemented
592#123C23×C61112yescomplemented
593#123C23×C61112yescomplemented
594#123C23×C61112yescomplemented
595C22⋊Q8C23×C6116yes—
596C22⋊Q8C23×C61112yes—
597C22⋊Q8C23×C61112yescomplemented
598C22⋊Q8C23×C61112yescomplemented
599C22⋊Q8C23×C61112yescomplemented
600C22⋊Q8C23×C61112yescomplemented
601C22⋊Q8C23×C6116yescomplemented
602C22⋊Q8C23×C6116yescomplemented
603C22⋊Q8C23×C6116yescomplemented
604C22⋊Q8C23×C6116yescomplemented
605C22⋊Q8C23×C61112yescomplemented
606C22⋊Q8C23×C61112yescomplemented
607C22⋊Q8C23×C61112yescomplemented
608C22⋊Q8C23×C61112yescomplemented
609C22⋊Q8C23×C61112yescomplemented
610#121C23×C61112yes—
611#121C23×C61112yes—
612#121C23×C61112yes—
613#121C23×C61112yes—
614#121C23×C6116yes—
615#121C23×C6116yes—
616#121C23×C6116yes—
617#121C23×C6116yes—
618#121C23×C6116yes—
619#121C23×C61112yes—
620#121C23×C61112yes—
621#121C23×C61112yes—
622#121C23×C61112yescomplemented
623#121C23×C61112yescomplemented
624#121C23×C61112yescomplemented
625#121C23×C61112yescomplemented
626#120C23×C6116yes—
627#120C23×C6116yes—
628#120C23×C61112yes—
629#120C23×C61112yes—
630#120C23×C61112yes—
631#120C23×C61112yes—
632#120C23×C6116yes—
633#120C23×C6116yes—
634#120C23×C6116yes—
635#120C23×C61112yes—
636#120C23×C6116yes—
637#120C23×C61112yescomplemented
638#120C23×C61112yescomplemented
639#120C23×C61112yescomplemented
640C4×Q8C23×C6116yescomplemented
641C4×Q8C23×C6112yescomplemented
642C4×Q8C23×C6116yescomplemented
643C4×Q8C23×C6112yescomplemented
644C4×Q8C23×C6116yescomplemented
645C4×Q8C23×C6116yescomplemented
646C4×Q8C23×C61112yescomplemented
647C4×D4C23×C6116yes—
648C4×D4C23×C6116yes—
649C4×D4C23×C6116yes—
650C4×D4C23×C61112yes—
651C4×D4C23×C61112yes—
652C4×D4C23×C6116yes—
653C4×D4C23×C6116yes—
654C4×D4C23×C61112yes—
655C4×D4C23×C6116yes—
656C4×D4C23×C6116yescomplemented
657C4×D4C23×C61112yescomplemented
658C4×D4C23×C61112yescomplemented
659C4×D4C23×C61112yescomplemented
660C4×D4C23×C61112yescomplemented
661C4×D4C23×C6116yescomplemented
662C4×D4C23×C61112yescomplemented
663C4×D4C23×C61112yescomplemented
664#117C23×C6113yes—
665#117C23×C6113yes—
666#117C23×C6113yes—
667#117C23×C6116yescomplemented
668#117C23×C61112yescomplemented
669#117C23×C61112yescomplemented
670#117C23×C61112yescomplemented
671#117C23×C61112yescomplemented
672#117C23×C61112yescomplemented
673C2×C22⋊C4C23×C6116yes—
674C2×C22⋊C4C23×C6116yes—
675C2×C22⋊C4C23×C6116yes—
676C2×C22⋊C4C23×C6116yes—
677C2×C22⋊C4C23×C61112yes—
678C2×C22⋊C4C23×C61112yescomplemented
679C2×C22⋊C4C23×C61112yescomplemented
680C2×C22⋊C4C23×C61112yescomplemented
681C2×C22⋊C4C23×C61112yescomplemented
682C2×C42C23×C6113yes—
683C2×C42C23×C6116yescomplemented
684C24—44no—
685C24—84no—
686C24C24×C6116yes—
687C24C24×C6116yes—
688C24C24×C6116yes—
689C24C24×C6112yes—
690#41—46no—
691#41—86no—
692#41—812no—
693#41—82no—
694C2×Q8—42no—
695C2×Q8—82no—
696C2×Q8—86no—
697C2×Q8C24×C6111yescharacteristic
698C2×Q8C24×C6113yes—
699C2×Q8C24×C6113yes—
700C2×Q8C24×C6116yes—
701C2×Q8C24×C61112yes—
702C2×Q8C24×C6116yes—
703C2×Q8C24×C6112yes—
704C2×D4—46no—
705C2×D4—412no—
706C2×D4—86no—
707C2×D4—86no—
708C2×D4—812no—
709C2×D4C24×C6116yes—
710C2×D4C24×C6113yes—
711C2×D4C24×C6116yes—
712C2×D4C24×C6113yes—
713C2×D4C24×C61112yes—
714C2×D4C24×C6116yes—
715C2×D4C24×C6116yes—
716C2×D4C24×C61112yes—
717C2×D4C24×C6113yes—
718C2×D4C24×C61112yes—
719C2×D4C24×C61112yes—
720C2×D4C24×C61112yes—
721C2×D4C24×C61112yes—
722C2×D4C24×C6116yes—
723C22×C4—84no—
724C22×C4C24×C6113yes—
725C22×C4C24×C6116yes—
726C22×C4C24×C6116yes—
727C22×C4C24×C6116yes—
728C22×C4C24×C6116yes—
729C22×C4C24×C61112yes—
730C22×C4C24×C61112yes—
731C22×C4C24×C61112yes—
732C22×C4C24×C6116yes—
733C22×C4C24×C61112yes—
734C4⋊C4C24×C6116yes—
735C4⋊C4C24×C6116yes—
736C4⋊C4C24×C6116yes—
737C4⋊C4C24×C6116yes—
738C4⋊C4C24×C61112yes—
739C4⋊C4C24×C61112yes—
740C4⋊C4C24×C61112yes—
741C4⋊C4C24×C61112yes—
742C4⋊C4C24×C61112yes—
743C4⋊C4C24×C6116yes—
744C4⋊C4C24×C6116yes—
745C4⋊C4C24×C6116yes—
746C4⋊C4C24×C61112yes—
747C4⋊C4C24×C61112yes—
748C22⋊C4C24×C6111yescharacteristic
749C22⋊C4C24×C6116yes—
750C22⋊C4C24×C6113yes—
751C22⋊C4C24×C61112yes—
752C22⋊C4C24×C6116yes—
753C22⋊C4C24×C6116yes—
754C22⋊C4C24×C61112yes—
755C22⋊C4C24×C61112yes—
756C22⋊C4C24×C61112yes—
757C22⋊C4C24×C61112yes—
758C22⋊C4C24×C61112yes—
759C22⋊C4C24×C61112yes—
760C22⋊C4C24×C6116yes—
761C22⋊C4C24×C6116yes—
762C22⋊C4C24×C6116yes—
763C22⋊C4C24×C61112yes—
764C22⋊C4C24×C61112yes—
765C22⋊C4C24×C61112yes—
766C22⋊C4C24×C61112yes—
767C22⋊C4C24×C61112yes—
768C22⋊C4C24×C61112yes—
769C22⋊C4C24×C61112yes—
770C22⋊C4C24×C6116yes—
771C22⋊C4C24×C61112yes—
772C42C24×C6113yes—
773C42C24×C6113yes—
774C42C24×C6116yes—
775C42C24×C6116yes—
776C42C24×C6116yes—
777C42C24×C6116yes—
778C42C24×C6116yes—
779C42C24×C6116yes—
780C42C24×C61112yes—
781C23—212no—
782C23—44no—
783C23—42no—
784C23—412no—
785C23—412no—
786C23—46no—
787C23—46no—
788C23—412no—
789C23—816no—
790C23C25×C6116yes—
791C23C25×C6116yes—
792C23C25×C6116yes—
793C23C25×C6111yescharacteristic
794Q8—41no—
795Q8—43no—
796Q8—46no—
797Q8—46no—
798Q8—412no—
799Q8—42no—
800Q8—43no—
801D4—212no—
802D4—43no—
803D4—43no—
804D4—46no—
805D4—412no—
806D4—412no—
807D4—46no—
808D4—412no—
809D4—412no—
810D4—412no—
811D4—46no—
812D4—46no—
813D4—412no—
814D4—43no—
815C2×C4—26no—
816C2×C4—412no—
817C2×C4—412no—
818C2×C4—46no—
819C2×C4—46no—
820C2×C4—46no—
821C2×C4—412no—
822C2×C4—412no—
823C2×C4—46no—
824C2×C4—46no—
825C2×C4C25×C6113yes—
826C2×C4C25×C6112yes—
827C2×C4C25×C6113yes—
828C2×C4C25×C6116yes—
829C2×C4C25×C6116yes—
830C2×C4C25×C6116yes—
831C2×C4C25×C6116yes—
832C2×C4C25×C61112yes—
833C22—22no—
834C22—26no—
835C22—26no—
836C22—26no—
837C22—26no—
838C22—212no—
839C22—26no—
840C22—212no—
841C22—48no—
842C22—812no—
843C22—812no—
844C22—166no—
845C22C61×#58512yes—
846C22C26×C6111yescharacteristic
847C4—23no—
848C4—23no—
849C4—26no—
850C4—22no—
851C4—212no—
852C4—26no—
853C4—26no—
854C4—26no—
855C2—22no—
856C2—46no—
857C2—46no—
858C2—46no—
859C2C2×C61×#58511yescharacteristic
860C2C61×H(7,𝔽2)12yes—
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×#3568C2semidirect
2. C61×#3561C2semidirect
3. C61×#3558C2semidirect
4. C61×#3545C2semidirect
5. C61×#3545C2semidirect
6. C61×#3540C2semidirect
7. C61×#3532C2semidirect
8. C61×#3529C2semidirect
9. C2×C61×H(3,𝔽4)C2semidirect
10. C61×#3514C2semidirect
11. C61×#3510C2semidirect
12. C61×#3490C2semidirect
13. C61×#563C22semidirect
14. C61×#563C22semidirect
15. C61×#563C22semidirect
16. C61×#562C22semidirect
17. C61×#562C22semidirect
18. C61×#562C22semidirect
19. C61×H(3,𝔽4)C22semidirect
20. C61×H(3,𝔽4)C22semidirect
21. C61×H(3,𝔽4)C22semidirect
22. C61×H(3,𝔽4)C22semidirect
23. C61×H(3,𝔽4)C22semidirect
24. C61×H(3,𝔽4)C22semidirect
25. C61×#560C22semidirect
26. C61×#560C22semidirect
27. C61×#559C22semidirect
28. C61×#559C22semidirect
29. C61×#556C22semidirect
30. C61×#556C22semidirect
31. C61×#556C22semidirect
32. C61×#555C22semidirect
33. C61×#555C22semidirect
34. C61×#551C22semidirect
35. C61×#551C22semidirect
36. C61×#551C22semidirect
37. C61×#551C22semidirect
38. C61×#551C22semidirect
39. C61×#551C22semidirect
40. C61×#551C22semidirect
41. C61×#551C22semidirect
42. D4×Q8×C61C22semidirect
43. C61×#548C22semidirect
44. C61×#548C22semidirect
45. C61×#548C22semidirect
46. C61×#546C22semidirect
47. C61×#546C22semidirect
48. C61×#546C22semidirect
49. C61×#546C22semidirect
50. C61×#546C22semidirect
51. C61×#546C22semidirect
52. C61×#546C22semidirect
53. D42×C61C22semidirect
54. D42×C61C22semidirect
55. C61×#543C22semidirect
56. C61×#542C22semidirect
57. C61×#542C22semidirect
58. C61×#542C22semidirect
59. C61×#542C22semidirect
60. C61×#542C22semidirect
61. C61×#542C22semidirect
62. C61×#542C22semidirect
63. C61×#538C22semidirect
64. C61×#538C22semidirect
65. C61×#538C22semidirect
66. C61×#538C22semidirect
67. C61×#538C22semidirect
68. C61×#538C22semidirect
69. C61×#538C22semidirect
70. C61×#536C22semidirect
71. C61×#536C22semidirect
73. C61×#535C22semidirect
74. C61×#534C22semidirect
75. C61×#534C22semidirect
76. C61×#533C22semidirect
77. C61×#532C22semidirect
78. C61×#529C22semidirect
79. C61×#529C22semidirect
80. C61×#529C22semidirect
81. C61×#529C22semidirect
82. C61×#529C22semidirect
83. C2×#124×C61C22semidirect
84. C2×#124×C61C22semidirect
85. C2×#124×C61C22semidirect
86. C61×#525C22semidirect
87. C61×#525C22semidirect
88. C2×#120×C61C22semidirect
89. C2×#120×C61C22semidirect
90. C61×#519C22semidirect
91. C61×#518C22semidirect
92. C61×#518C22semidirect
93. C4×#41×C61C22semidirect
94. C22×C22⋊C4×C61C22semidirect
99. C2×#41×C61C23semidirect
102. C22×Q8×C61C23semidirect
107. C22×D4×C61C23semidirect
108. C23×C4×C61C23semidirect
109. C4⋊Q8×C61C23semidirect
110. C4⋊Q8×C61C23semidirect
111. C4⋊Q8×C61C23semidirect
112. C4⋊Q8×C61C23semidirect
115. #126×C61C23semidirect
116. #126×C61C23semidirect
117. #126×C61C23semidirect
118. #126×C61C23semidirect
119. #126×C61C23semidirect
120. #126×C61C23semidirect
121. #126×C61C23semidirect
122. #126×C61C23semidirect
123. #126×C61C23semidirect
124. #125×C61C23semidirect
125. #125×C61C23semidirect
140. #124×C61C23semidirect
141. #124×C61C23semidirect
142. #124×C61C23semidirect
143. #124×C61C23semidirect
144. #124×C61C23semidirect
145. #124×C61C23semidirect
146. #124×C61C23semidirect
147. #124×C61C23semidirect
148. #124×C61C23semidirect
155. #123×C61C23semidirect
156. #123×C61C23semidirect
157. #123×C61C23semidirect
158. #123×C61C23semidirect
159. #123×C61C23semidirect
160. #123×C61C23semidirect
161. #123×C61C23semidirect
162. #123×C61C23semidirect
163. #123×C61C23semidirect
166. C22⋊Q8×C61C23semidirect
167. C22⋊Q8×C61C23semidirect
168. C22⋊Q8×C61C23semidirect
169. C22⋊Q8×C61C23semidirect
170. C22⋊Q8×C61C23semidirect
171. C22⋊Q8×C61C23semidirect
172. C22⋊Q8×C61C23semidirect
173. C22⋊Q8×C61C23semidirect
174. C22⋊Q8×C61C23semidirect
175. C22⋊Q8×C61C23semidirect
176. C22⋊Q8×C61C23semidirect
177. C22⋊Q8×C61C23semidirect
178. C22⋊Q8×C61C23semidirect
191. #121×C61C23semidirect
192. #121×C61C23semidirect
193. #121×C61C23semidirect
194. #121×C61C23semidirect
206. #120×C61C23semidirect
207. #120×C61C23semidirect
208. #120×C61C23semidirect
209. C4×Q8×C61C23semidirect
210. C4×Q8×C61C23semidirect
211. C4×Q8×C61C23semidirect
212. C4×Q8×C61C23semidirect
213. C4×Q8×C61C23semidirect
214. C4×Q8×C61C23semidirect
215. C4×Q8×C61C23semidirect
225. C4×D4×C61C23semidirect
226. C4×D4×C61C23semidirect
227. C4×D4×C61C23semidirect
228. C4×D4×C61C23semidirect
229. C4×D4×C61C23semidirect
230. C4×D4×C61C23semidirect
231. C4×D4×C61C23semidirect
232. C4×D4×C61C23semidirect
236. #117×C61C23semidirect
237. #117×C61C23semidirect
238. #117×C61C23semidirect
239. #117×C61C23semidirect
240. #117×C61C23semidirect
241. #117×C61C23semidirect
247. C2×C22⋊C4×C61C23semidirect
248. C2×C22⋊C4×C61C23semidirect
249. C2×C22⋊C4×C61C23semidirect
250. C2×C22⋊C4×C61C23semidirect
252. C2×C42×C61C23semidirect
402. #63046C61direct (N × H)
425. #3568C2×C61semidirect
426. #3561C2×C61semidirect
427. #3558C2×C61semidirect
428. #3545C2×C61semidirect
429. #3545C2×C61semidirect
430. #3540C2×C61semidirect
431. #3532C2×C61semidirect
432. #3529C2×C61semidirect
433. C2×H(3,𝔽4)C2×C61semidirect
434. #3514C2×C61semidirect
435. #3510C2×C61semidirect
436. #3490C2×C61semidirect
443. #563C22×C61semidirect
444. #563C22×C61semidirect
445. #563C22×C61semidirect
446. #562C22×C61semidirect
447. #562C22×C61semidirect
448. #562C22×C61semidirect
449. H(3,𝔽4)C22×C61semidirect
450. H(3,𝔽4)C22×C61semidirect
451. H(3,𝔽4)C22×C61semidirect
452. H(3,𝔽4)C22×C61semidirect
453. H(3,𝔽4)C22×C61semidirect
454. H(3,𝔽4)C22×C61semidirect
455. #560C22×C61semidirect
456. #560C22×C61semidirect
457. #559C22×C61semidirect
458. #559C22×C61semidirect
459. #556C22×C61semidirect
460. #556C22×C61semidirect
461. #556C22×C61semidirect
462. #555C22×C61semidirect
463. #555C22×C61semidirect
464. #551C22×C61semidirect
465. #551C22×C61semidirect
466. #551C22×C61semidirect
467. #551C22×C61semidirect
468. #551C22×C61semidirect
469. #551C22×C61semidirect
470. #551C22×C61semidirect
471. #551C22×C61semidirect
472. D4×Q8C22×C61semidirect
473. #548C22×C61semidirect
474. #548C22×C61semidirect
475. #548C22×C61semidirect
476. #546C22×C61semidirect
477. #546C22×C61semidirect
478. #546C22×C61semidirect
479. #546C22×C61semidirect
480. #546C22×C61semidirect
481. #546C22×C61semidirect
482. #546C22×C61semidirect
483. D42C22×C61semidirect
484. D42C22×C61semidirect
485. #543C22×C61semidirect
486. #542C22×C61semidirect
487. #542C22×C61semidirect
488. #542C22×C61semidirect
489. #542C22×C61semidirect
490. #542C22×C61semidirect
491. #542C22×C61semidirect
492. #542C22×C61semidirect
493. #538C22×C61semidirect
494. #538C22×C61semidirect
495. #538C22×C61semidirect
496. #538C22×C61semidirect
497. #538C22×C61semidirect
498. #538C22×C61semidirect
499. #538C22×C61semidirect
500. #536C22×C61semidirect
501. #536C22×C61semidirect
503. #535C22×C61semidirect
504. #534C22×C61semidirect
505. #534C22×C61semidirect
506. #533C22×C61semidirect
507. #532C22×C61semidirect
508. #529C22×C61semidirect
509. #529C22×C61semidirect
510. #529C22×C61semidirect
511. #529C22×C61semidirect
512. #529C22×C61semidirect
513. C2×#124C22×C61semidirect
514. C2×#124C22×C61semidirect
515. C2×#124C22×C61semidirect
516. #525C22×C61semidirect
517. #525C22×C61semidirect
518. C2×#120C22×C61semidirect
519. C2×#120C22×C61semidirect
520. #519C22×C61semidirect
521. #518C22×C61semidirect
522. #518C22×C61semidirect
523. C4×#41C22×C61semidirect
524. C22×C22⋊C4C22×C61semidirect
525. C61#63046direct (N × H)
530. C2×#41C23×C61semidirect
533. C22×Q8C23×C61semidirect
538. C22×D4C23×C61semidirect
539. C23×C4C23×C61semidirect
540. C4⋊Q8C23×C61semidirect
541. C4⋊Q8C23×C61semidirect
542. C4⋊Q8C23×C61semidirect
543. C4⋊Q8C23×C61semidirect
546. #126C23×C61semidirect
547. #126C23×C61semidirect
548. #126C23×C61semidirect
549. #126C23×C61semidirect
550. #126C23×C61semidirect
551. #126C23×C61semidirect
552. #126C23×C61semidirect
553. #126C23×C61semidirect
554. #126C23×C61semidirect
555. #125C23×C61semidirect
556. #125C23×C61semidirect
571. #124C23×C61semidirect
572. #124C23×C61semidirect
573. #124C23×C61semidirect
574. #124C23×C61semidirect
575. #124C23×C61semidirect
576. #124C23×C61semidirect
577. #124C23×C61semidirect
578. #124C23×C61semidirect
579. #124C23×C61semidirect
586. #123C23×C61semidirect
587. #123C23×C61semidirect
588. #123C23×C61semidirect
589. #123C23×C61semidirect
590. #123C23×C61semidirect
591. #123C23×C61semidirect
592. #123C23×C61semidirect
593. #123C23×C61semidirect
594. #123C23×C61semidirect
597. C22⋊Q8C23×C61semidirect
598. C22⋊Q8C23×C61semidirect
599. C22⋊Q8C23×C61semidirect
600. C22⋊Q8C23×C61semidirect
601. C22⋊Q8C23×C61semidirect
602. C22⋊Q8C23×C61semidirect
603. C22⋊Q8C23×C61semidirect
604. C22⋊Q8C23×C61semidirect
605. C22⋊Q8C23×C61semidirect
606. C22⋊Q8C23×C61semidirect
607. C22⋊Q8C23×C61semidirect
608. C22⋊Q8C23×C61semidirect
609. C22⋊Q8C23×C61semidirect
622. #121C23×C61semidirect
623. #121C23×C61semidirect
624. #121C23×C61semidirect
625. #121C23×C61semidirect
637. #120C23×C61semidirect
638. #120C23×C61semidirect
639. #120C23×C61semidirect
640. C4×Q8C23×C61semidirect
641. C4×Q8C23×C61semidirect
642. C4×Q8C23×C61semidirect
643. C4×Q8C23×C61semidirect
644. C4×Q8C23×C61semidirect
645. C4×Q8C23×C61semidirect
646. C4×Q8C23×C61semidirect
656. C4×D4C23×C61semidirect
657. C4×D4C23×C61semidirect
658. C4×D4C23×C61semidirect
659. C4×D4C23×C61semidirect
660. C4×D4C23×C61semidirect
661. C4×D4C23×C61semidirect
662. C4×D4C23×C61semidirect
663. C4×D4C23×C61semidirect
667. #117C23×C61semidirect
668. #117C23×C61semidirect
669. #117C23×C61semidirect
670. #117C23×C61semidirect
671. #117C23×C61semidirect
672. #117C23×C61semidirect
678. C2×C22⋊C4C23×C61semidirect
679. C2×C22⋊C4C23×C61semidirect
680. C2×C22⋊C4C23×C61semidirect
681. C2×C22⋊C4C23×C61semidirect
683. C2×C42C23×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#35682
C61×#35612
C61×#35582
C61×#35452
C61×#35402
C61×#35322
C61×#35292
C2×C61×H(3,𝔽4)2
C61×#35142
C61×#35102
C61×#34902
#6304661