Finite Group Databasebeta

← C2×C61×#3557 #29566171

Subgroups — C2×C61×#3557 #29566171

Order 15616.

6554 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3557C2132yesmaximal, direct product factor
2C2×C61×#563C214yesmaximal, complemented
3C2×C61×#559C212yesmaximal, complemented
4C2×C61×#557C212yesmaximal, complemented
5C2×C61×#556C212yesmaximal, complemented
6C2×C61×#554C212yesmaximal, complemented
7C2×C61×#552C214yesmaximal, complemented
8C2×C61×#542C212yesmaximal, complemented
9C2×C61×#542C214yesmaximal, complemented
10C2×C61×#541C211yesmaximal, characteristic, complemented
11C2×C61×#540C211yesmaximal, characteristic
12C2×C61×#539C214yesmaximal, complemented
13C2×C61×#533C211yesmaximal, characteristic, complemented
14C2×C61×#529C212yesmaximal, complemented
15C61×#563C22164yescomplemented
16C61×#559C22132yescomplemented
17C61×#557C22132yescomplemented
18C61×#556C22132yescomplemented
19C61×#554C22132yescomplemented
20C61×#552C22164yescomplemented
21C61×#542C22132yescomplemented
22C61×#542C22164yescomplemented
23C61×#541C22116yescomplemented
24C61×#540C22116yes—
25C61×#539C22164yescomplemented
26C61×#533C22116yescomplemented
27C2×C4⋊Q8×C61C2212yes—
28C2×C4⋊Q8×C61C2211yescharacteristic
29C2×C4⋊Q8×C61C2212yes—
30C2×C4⋊Q8×C61C2214yes—
31C2×#127×C61C2211yescharacteristic
32C61×#529C22132yescomplemented
33C2×#126×C61C2214yes—
34C2×#126×C61C2214yes—
35C2×#126×C61C2214yes—
36C2×#126×C61C2214yes—
37C2×#126×C61C2214yes—
38C2×#125×C61C2212yes—
39C2×#125×C61C2212yes—
40C2×#125×C61C2214yes—
41C2×#125×C61C2214yes—
42C2×#125×C61C2211yescharacteristic
43C2×#125×C61C2214yes—
44C2×#125×C61C2211yescharacteristic
45C2×#124×C61C2212yes—
46C2×#124×C61C2214yes—
47C2×#124×C61C2212yes—
48C2×#124×C61C2214yes—
49C2×#123×C61C2214yes—
50C2×#123×C61C2214yes—
51C2×#123×C61C2214yes—
52C2×#123×C61C2214yes—
53C2×#123×C61C2214yes—
54C2×C22⋊Q8×C61C2212yes—
55C2×C22⋊Q8×C61C2212yes—
56C2×C22⋊Q8×C61C2212yes—
57C2×C22⋊Q8×C61C2214yes—
58C2×C22⋊Q8×C61C2214yes—
59C2×C22⋊Q8×C61C2214yes—
60C2×C22⋊Q8×C61C2214yes—
61C2×C22⋊Q8×C61C2214yes—
62C2×#121×C61C2212yes—
63C2×#121×C61C2214yes—
64C2×C4×Q8×C61C2212yes—
65C2×C4×Q8×C61C2212yes—
66C2×C4×Q8×C61C2212yes—
67C2×C4×Q8×C61C2212yes—
68C2×C4×Q8×C61C2214yes—
69C2×C4×Q8×C61C2212yes—
70C2×C4×D4×C61C2214yes—
71C2×C4×D4×C61C2212yes—
72C2×C4×D4×C61C2214yes—
73C2×C4×D4×C61C2212yes—
74C2×C4×D4×C61C2212yes—
75C2×#117×C61C2214yes—
76C2×#117×C61C2211yescharacteristic
77C2×#117×C61C2211yescharacteristic
78C2×#117×C61C2214yes—
79C22×C4⋊C4×C61C2214yes—
80C22×C42×C61C2211yescharacteristic
81C22×Q8×C61C2312yes—
82C22×Q8×C61C2312yes—
83C22×Q8×C61C2314yes—
84C22×Q8×C61C2312yes—
85C22×D4×C61C2312yes—
86C22×D4×C61C2314yes—
87C22×D4×C61C2314yes—
88C23×C4×C61C2311yescharacteristic
89C23×C4×C61C2312yes—
90C23×C4×C61C2314yes—
91C23×C4×C61C2314yes—
92C23×C4×C61C2314yes—
93C4⋊Q8×C61C23116yes—
94C4⋊Q8×C61C2318yes—
95C4⋊Q8×C61C23116yes—
96C4⋊Q8×C61C23132yes—
97#127×C61C2318yes—
98#126×C61C23132yes—
99#126×C61C23132yes—
100#126×C61C23132yes—
101#126×C61C23132yes—
102#126×C61C23132yes—
103#125×C61C23116yes—
104#125×C61C23132yes—
105#125×C61C23132yes—
106#125×C61C2318yes—
107#125×C61C23132yes—
108#125×C61C2318yes—
109#125×C61C23116yes—
110#124×C61C23132yes—
111#124×C61C23116yes—
112#124×C61C23132yes—
113#124×C61C23116yes—
114#123×C61C23132yes—
115#123×C61C23132yes—
116#123×C61C23132yes—
117#123×C61C23132yes—
118#123×C61C23132yes—
119C22⋊Q8×C61C23116yes—
120C22⋊Q8×C61C23116yes—
121C22⋊Q8×C61C23132yes—
122C22⋊Q8×C61C23132yes—
123C22⋊Q8×C61C23116yes—
124C22⋊Q8×C61C23132yes—
125C22⋊Q8×C61C23132yes—
126C22⋊Q8×C61C23132yes—
127#121×C61C23132yes—
128#121×C61C23116yes—
129C4×Q8×C61C23116yes—
130C4×Q8×C61C23116yes—
131C4×Q8×C61C23116yes—
132C4×Q8×C61C23132yes—
133C4×Q8×C61C23116yes—
134C4×Q8×C61C23116yes—
135C4×D4×C61C23132yes—
136C4×D4×C61C23132yes—
137C4×D4×C61C23116yes—
138C4×D4×C61C23116yes—
139C4×D4×C61C23116yes—
140#117×C61C2318yes—
141#117×C61C2318yes—
142#117×C61C23132yes—
143#117×C61C23132yes—
144C2×C4⋊C4×C61C2314yes—
145C2×C4⋊C4×C61C2312yes—
146C2×C4⋊C4×C61C2314yes—
147C2×C4⋊C4×C61C2312yes—
148C2×C4⋊C4×C61C2312yes—
149C2×C4⋊C4×C61C2312yes—
150C2×C4⋊C4×C61C2314yes—
151C2×C4⋊C4×C61C2314yes—
152C2×C4⋊C4×C61C2312yes—
153C2×C4⋊C4×C61C2312yes—
154C2×C4⋊C4×C61C2314yes—
155C2×C4⋊C4×C61C2314yes—
156C2×C4⋊C4×C61C23132yes—
157C2×C4⋊C4×C61C2312yes—
158C2×C4⋊C4×C61C2314yes—
159C2×C4⋊C4×C61C2314yes—
160C2×C4⋊C4×C61C2312yes—
161C2×C4⋊C4×C61C2314yes—
162C2×C4⋊C4×C61C2312yes—
163C2×C4⋊C4×C61C2312yes—
164C2×C4⋊C4×C61C2314yes—
165C2×C22⋊C4×C61C2314yes—
166C2×C22⋊C4×C61C2312yes—
167C2×C22⋊C4×C61C2314yes—
168C2×C22⋊C4×C61C2311yescharacteristic
169C2×C22⋊C4×C61C2311yescharacteristic
170C2×C22⋊C4×C61C2314yes—
171C2×C22⋊C4×C61C2314yes—
172C2×C22⋊C4×C61C2314yes—
173C2×C22⋊C4×C61C2314yes—
174C2×C22⋊C4×C61C2314yes—
175C2×C22⋊C4×C61C2314yes—
176C2×C22⋊C4×C61C2314yes—
177C2×C42×C61C2311yescharacteristic
178C2×C42×C61C2311yescharacteristic
179C2×C42×C61C2311yescharacteristic
180C2×C42×C61C2312yes—
181C2×C42×C61C2314yes—
182C2×C42×C61C2318yes—
183C2×C42×C61C2311yescharacteristic
184C2×C42×C61C2312yes—
185C2×C42×C61C2314yes—
186C2×C42×C61C2314yes—
187C24×C61C2411yescharacteristic
188C24×C61C2414yes—
189C2×Q8×C61—28no—
190C2×Q8×C61—44no—
191C2×Q8×C61—48no—
192C2×Q8×C61—44no—
193C2×Q8×C61C2418yes—
194C2×Q8×C61C2418yes—
195C2×Q8×C61C24116yes—
196C2×Q8×C61C2418yes—
197C2×D4×C61—28no—
198C2×D4×C61—48no—
199C2×D4×C61—48no—
200C2×D4×C61C2418yes—
201C2×D4×C61C24116yes—
202C2×D4×C61C24116yes—
203C22×C4×C61—24no—
204C22×C4×C61—48no—
205C22×C4×C61—44no—
206C22×C4×C61—48no—
207C22×C4×C61—48no—
208C22×C4×C61C2414yes—
209C22×C4×C61C2412yes—
210C22×C4×C61C2414yes—
211C22×C4×C61C2412yes—
212C22×C4×C61C2412yes—
213C22×C4×C61C2411yescharacteristic
214C22×C4×C61C2412yes—
215C22×C4×C61C2414yes—
216C22×C4×C61C2412yes—
217C22×C4×C61C2412yes—
218C22×C4×C61C2414yes—
219C22×C4×C61C2418yes—
220C22×C4×C61C24116yes—
221C22×C4×C61C24116yes—
222C22×C4×C61C24116yes—
223C22×C4×C61C2411yescharacteristic
224C4⋊C4×C61C2418yes—
225C4⋊C4×C61C24116yes—
226C4⋊C4×C61C24116yes—
227C4⋊C4×C61C24116yes—
228C4⋊C4×C61C2418yes—
229C4⋊C4×C61C24116yes—
230C4⋊C4×C61C2418yes—
231C4⋊C4×C61C24116yes—
232C4⋊C4×C61C2418yes—
233C4⋊C4×C61C2418yes—
234C4⋊C4×C61C2418yes—
235C4⋊C4×C61C2418yes—
236C4⋊C4×C61C24116yes—
237C4⋊C4×C61C2418yes—
238C4⋊C4×C61C24116yes—
239C4⋊C4×C61C2418yes—
240C4⋊C4×C61C24116yes—
241C4⋊C4×C61C2418yes—
242C4⋊C4×C61C24116yes—
243C4⋊C4×C61C24116yes—
244C22⋊C4×C61C24116yes—
245C22⋊C4×C61C2418yes—
246C22⋊C4×C61C24116yes—
247C22⋊C4×C61C2414yes—
248C22⋊C4×C61C2414yes—
249C22⋊C4×C61C24116yes—
250C22⋊C4×C61C24116yes—
251C22⋊C4×C61C24116yes—
252C22⋊C4×C61C24116yes—
253C22⋊C4×C61C24116yes—
254C22⋊C4×C61C24116yes—
255C22⋊C4×C61C24116yes—
256C42×C61C2414yes—
257C42×C61C2418yes—
258C42×C61C2414yes—
259C42×C61C24116yes—
260C42×C61C2414yes—
261C42×C61C2418yes—
262C42×C61C2414yes—
263C42×C61C24116yes—
264C42×C61C24116yes—
265C23×C61—22no—
266C23×C61—28no—
267C23×C61—28no—
268C23×C61—24no—
269C23×C61—28no—
270C23×C61C2512yes—
271C23×C61C2518yes—
272C23×C61C2511yescharacteristic
273Q8×C61—216no—
274Q8×C61—48no—
275Q8×C61—416no—
276Q8×C61—48no—
277D4×C61—216no—
278D4×C61—416no—
279D4×C61—416no—
280C2×C4×C61—22no—
281C2×C4×C61—28no—
282C2×C4×C61—24no—
283C2×C4×C61—28no—
284C2×C4×C61—24no—
285C2×C4×C61—24no—
286C2×C4×C61—28no—
287C2×C4×C61—24no—
288C2×C4×C61—24no—
289C2×C4×C61—24no—
290C2×C4×C61—28no—
291C2×C4×C61—416no—
292C2×C4×C61—48no—
293C2×C4×C61—416no—
294C2×C4×C61—416no—
295C2×C4×C612−1+414yes—
296C2×C4×C61C2514yes—
297C2×C4×C61C2518yes—
298C2×C4×C61C2514yes—
299C2×C4×C61C2514yes—
300C2×C4×C61C2512yes—
301C2×C4×C61C2514yes—
302C2×C4×C61C2518yes—
303C2×C4×C61C2514yes—
304C2×C4×C61C2514yes—
305C2×C4×C61C2518yes—
306C2×C4×C61C2512yes—
307C2×#3557C6111yesmaximal, characteristic, direct product factor, Sylow
308C22×C61—22no—
309C22×C61—28no—
310C22×C61—28no—
311C22×C61—24no—
312C22×C61—28no—
313C22×C61—44no—
314C22×C61—416no—
315C22×C61C2×2−1+412yes—
316C22×C61#58514yes—
317C22×C61C2611yescharacteristic
318C4×C61—22no—
319C4×C61—28no—
320C4×C61—24no—
321C4×C61—28no—
322C4×C61—24no—
323C4×C61—24no—
324C4×C61—28no—
325C4×C61—24no—
326C4×C61—24no—
327C4×C61—24no—
328C4×C61C2×2−1+414yes—
329#3557C2×C61132yesdirect product factor
330C2×#563C2×C6114yescomplemented
331C2×#559C2×C6112yescomplemented
332C2×#557C2×C6112yescomplemented
333C2×#556C2×C6112yescomplemented
334C2×#554C2×C6112yescomplemented
335C2×#552C2×C6114yescomplemented
336C2×#542C2×C6112yescomplemented
337C2×#542C2×C6114yescomplemented
338C2×#541C2×C6111yescharacteristic, complemented
339C2×#540C2×C6111yescharacteristic
340C2×#539C2×C6114yescomplemented
341C2×#533C2×C6111yescharacteristic, complemented
342C2×#529C2×C6112yescomplemented
343C2×C61—42no—
344C2×C61—48no—
345C2×C61#355714yesdirect product factor
346C2×C61C22×2−1+411yescharacteristic
347C2×C61C2×#58512yes—
348#563C22×C61164yescomplemented
349#559C22×C61132yescomplemented
350#557C22×C61132yescomplemented
351#556C22×C61132yescomplemented
352#554C22×C61132yescomplemented
353#552C22×C61164yescomplemented
354#542C22×C61132yescomplemented
355#542C22×C61164yescomplemented
356#541C22×C61116yescomplemented
357#540C22×C61116yes—
358#539C22×C61164yescomplemented
359#533C22×C61116yescomplemented
360C2×C4⋊Q8C22×C6112yes—
361C2×C4⋊Q8C22×C6111yescharacteristic
362C2×C4⋊Q8C22×C6112yes—
363C2×C4⋊Q8C22×C6114yes—
364C2×#127C22×C6111yescharacteristic
365#529C22×C61132yescomplemented
366C2×#126C22×C6114yes—
367C2×#126C22×C6114yes—
368C2×#126C22×C6114yes—
369C2×#126C22×C6114yes—
370C2×#126C22×C6114yes—
371C2×#125C22×C6112yes—
372C2×#125C22×C6112yes—
373C2×#125C22×C6114yes—
374C2×#125C22×C6114yes—
375C2×#125C22×C6111yescharacteristic
376C2×#125C22×C6114yes—
377C2×#125C22×C6111yescharacteristic
378C2×#124C22×C6112yes—
379C2×#124C22×C6114yes—
380C2×#124C22×C6112yes—
381C2×#124C22×C6114yes—
382C2×#123C22×C6114yes—
383C2×#123C22×C6114yes—
384C2×#123C22×C6114yes—
385C2×#123C22×C6114yes—
386C2×#123C22×C6114yes—
387C2×C22⋊Q8C22×C6112yes—
388C2×C22⋊Q8C22×C6112yes—
389C2×C22⋊Q8C22×C6112yes—
390C2×C22⋊Q8C22×C6114yes—
391C2×C22⋊Q8C22×C6114yes—
392C2×C22⋊Q8C22×C6114yes—
393C2×C22⋊Q8C22×C6114yes—
394C2×C22⋊Q8C22×C6114yes—
395C2×#121C22×C6112yes—
396C2×#121C22×C6114yes—
397C2×C4×Q8C22×C6112yes—
398C2×C4×Q8C22×C6112yes—
399C2×C4×Q8C22×C6112yes—
400C2×C4×Q8C22×C6112yes—
401C2×C4×Q8C22×C6114yes—
402C2×C4×Q8C22×C6112yes—
403C2×C4×D4C22×C6114yes—
404C2×C4×D4C22×C6112yes—
405C2×C4×D4C22×C6114yes—
406C2×C4×D4C22×C6112yes—
407C2×C4×D4C22×C6112yes—
408C2×#117C22×C6114yes—
409C2×#117C22×C6111yescharacteristic
410C2×#117C22×C6111yescharacteristic
411C2×#117C22×C6114yes—
412C22×C4⋊C4C22×C6114yes—
413C22×C42C22×C6111yescharacteristic
414C61C2×#355711yescharacteristic, direct product factor, Sylow
415C22×Q8C23×C6112yes—
416C22×Q8C23×C6112yes—
417C22×Q8C23×C6114yes—
418C22×Q8C23×C6112yes—
419C22×D4C23×C6112yes—
420C22×D4C23×C6114yes—
421C22×D4C23×C6114yes—
422C23×C4C23×C6111yescharacteristic
423C23×C4C23×C6114yes—
424C23×C4C23×C6114yes—
425C23×C4C23×C6114yes—
426C23×C4C23×C6112yes—
427C4⋊Q8C23×C61116yes—
428C4⋊Q8C23×C6118yes—
429C4⋊Q8C23×C61116yes—
430C4⋊Q8C23×C61132yes—
431#127C23×C6118yes—
432#126C23×C61132yes—
433#126C23×C61132yes—
434#126C23×C61132yes—
435#126C23×C61132yes—
436#126C23×C61132yes—
437#125C23×C61116yes—
438#125C23×C61116yes—
439#125C23×C61132yes—
440#125C23×C61132yes—
441#125C23×C6118yes—
442#125C23×C61132yes—
443#125C23×C6118yes—
444#124C23×C61116yes—
445#124C23×C61132yes—
446#124C23×C61116yes—
447#124C23×C61132yes—
448#123C23×C61132yes—
449#123C23×C61132yes—
450#123C23×C61132yes—
451#123C23×C61132yes—
452#123C23×C61132yes—
453C22⋊Q8C23×C61116yes—
454C22⋊Q8C23×C61116yes—
455C22⋊Q8C23×C61116yes—
456C22⋊Q8C23×C61132yes—
457C22⋊Q8C23×C61132yes—
458C22⋊Q8C23×C61132yes—
459C22⋊Q8C23×C61132yes—
460C22⋊Q8C23×C61132yes—
461#121C23×C61116yes—
462#121C23×C61132yes—
463C4×Q8C23×C61116yes—
464C4×Q8C23×C61116yes—
465C4×Q8C23×C61116yes—
466C4×Q8C23×C61116yes—
467C4×Q8C23×C61132yes—
468C4×Q8C23×C61116yes—
469C4×D4C23×C61132yes—
470C4×D4C23×C61116yes—
471C4×D4C23×C61132yes—
472C4×D4C23×C61116yes—
473C4×D4C23×C61116yes—
474#117C23×C61132yes—
475#117C23×C6118yes—
476#117C23×C6118yes—
477#117C23×C61132yes—
478C2×C4⋊C4C23×C6112yes—
479C2×C4⋊C4C23×C6114yes—
480C2×C4⋊C4C23×C6114yes—
481C2×C4⋊C4C23×C6114yes—
482C2×C4⋊C4C23×C61132yes—
483C2×C4⋊C4C23×C6112yes—
484C2×C4⋊C4C23×C6114yes—
485C2×C4⋊C4C23×C6112yes—
486C2×C4⋊C4C23×C6114yes—
487C2×C4⋊C4C23×C6112yes—
488C2×C4⋊C4C23×C6112yes—
489C2×C4⋊C4C23×C6112yes—
490C2×C4⋊C4C23×C6112yes—
491C2×C4⋊C4C23×C6114yes—
492C2×C4⋊C4C23×C6112yes—
493C2×C4⋊C4C23×C6114yes—
494C2×C4⋊C4C23×C6112yes—
495C2×C4⋊C4C23×C6114yes—
496C2×C4⋊C4C23×C6112yes—
497C2×C4⋊C4C23×C6114yes—
498C2×C4⋊C4C23×C6114yes—
499C2×C22⋊C4C23×C6114yes—
500C2×C22⋊C4C23×C6112yes—
501C2×C22⋊C4C23×C6114yes—
502C2×C22⋊C4C23×C6111yescharacteristic
503C2×C22⋊C4C23×C6111yescharacteristic
504C2×C22⋊C4C23×C6114yes—
505C2×C22⋊C4C23×C6114yes—
506C2×C22⋊C4C23×C6114yes—
507C2×C22⋊C4C23×C6114yes—
508C2×C22⋊C4C23×C6114yes—
509C2×C22⋊C4C23×C6114yes—
510C2×C22⋊C4C23×C6114yes—
511C2×C42C23×C6111yescharacteristic
512C2×C42C23×C6114yes—
513C2×C42C23×C6111yescharacteristic
514C2×C42C23×C6112yes—
515C2×C42C23×C6111yescharacteristic
516C2×C42C23×C6114yes—
517C2×C42C23×C6112yes—
518C2×C42C23×C6114yes—
519C2×C42C23×C6111yescharacteristic
520C2×C42C23×C6118yes—
521C24C24×C6111yescharacteristic
522C24C24×C6114yes—
523C2×Q8—28no—
524C2×Q8—44no—
525C2×Q8—48no—
526C2×Q8—44no—
527C2×Q8C24×C6118yes—
528C2×Q8C24×C6118yes—
529C2×Q8C24×C61116yes—
530C2×Q8C24×C6118yes—
531C2×D4—28no—
532C2×D4—48no—
533C2×D4—48no—
534C2×D4C24×C6118yes—
535C2×D4C24×C61116yes—
536C2×D4C24×C61116yes—
537C22×C4—24no—
538C22×C4—48no—
539C22×C4—44no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4C24×C6112yes—
543C22×C4C24×C6114yes—
544C22×C4C24×C6112yes—
545C22×C4C24×C6112yes—
546C22×C4C24×C6111yescharacteristic
547C22×C4C24×C6112yes—
548C22×C4C24×C6114yes—
549C22×C4C24×C6114yes—
550C22×C4C24×C6112yes—
551C22×C4C24×C6112yes—
552C22×C4C24×C6114yes—
553C22×C4C24×C6118yes—
554C22×C4C24×C61116yes—
555C22×C4C24×C61116yes—
556C22×C4C24×C61116yes—
557C22×C4C24×C6111yescharacteristic
558C4⋊C4C24×C6118yes—
559C4⋊C4C24×C61116yes—
560C4⋊C4C24×C61116yes—
561C4⋊C4C24×C61116yes—
562C4⋊C4C24×C6118yes—
563C4⋊C4C24×C61116yes—
564C4⋊C4C24×C6118yes—
565C4⋊C4C24×C61116yes—
566C4⋊C4C24×C6118yes—
567C4⋊C4C24×C6118yes—
568C4⋊C4C24×C6118yes—
569C4⋊C4C24×C6118yes—
570C4⋊C4C24×C61116yes—
571C4⋊C4C24×C6118yes—
572C4⋊C4C24×C61116yes—
573C4⋊C4C24×C6118yes—
574C4⋊C4C24×C61116yes—
575C4⋊C4C24×C6118yes—
576C4⋊C4C24×C61116yes—
577C4⋊C4C24×C61116yes—
578C22⋊C4C24×C61116yes—
579C22⋊C4C24×C6118yes—
580C22⋊C4C24×C61116yes—
581C22⋊C4C24×C6114yes—
582C22⋊C4C24×C6114yes—
583C22⋊C4C24×C61116yes—
584C22⋊C4C24×C61116yes—
585C22⋊C4C24×C61116yes—
586C22⋊C4C24×C61116yes—
587C22⋊C4C24×C61116yes—
588C22⋊C4C24×C61116yes—
589C22⋊C4C24×C61116yes—
590C42C24×C6114yes—
591C42C24×C6118yes—
592C42C24×C6114yes—
593C42C24×C61116yes—
594C42C24×C6114yes—
595C42C24×C6118yes—
596C42C24×C6114yes—
597C42C24×C61116yes—
598C42C24×C61116yes—
599C23—22no—
600C23—28no—
601C23—28no—
602C23—24no—
603C23—28no—
604C23C25×C6112yes—
605C23C25×C6118yes—
606C23C25×C6111yescharacteristic
607Q8—216no—
608Q8—48no—
609Q8—416no—
610Q8—48no—
611D4—216no—
612D4—416no—
613D4—416no—
614C2×C4—22no—
615C2×C4—28no—
616C2×C4—24no—
617C2×C4—28no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—28no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—28no—
625C2×C4—416no—
626C2×C4—48no—
627C2×C4—416no—
628C2×C4—416no—
629C2×C42−1+4×C6114yes—
630C2×C4C25×C6114yes—
631C2×C4C25×C6118yes—
632C2×C4C25×C6114yes—
633C2×C4C25×C6114yes—
634C2×C4C25×C6112yes—
635C2×C4C25×C6114yes—
636C2×C4C25×C6118yes—
637C2×C4C25×C6114yes—
638C2×C4C25×C6114yes—
639C2×C4C25×C6118yes—
640C2×C4C25×C6112yes—
641C22—22no—
642C22—28no—
643C22—28no—
644C22—24no—
645C22—28no—
646C22—44no—
647C22—416no—
648C22C2×2−1+4×C6112yes—
649C22C61×#58514yes—
650C22C26×C6111yescharacteristic
651C4—22no—
652C4—28no—
653C4—24no—
654C4—28no—
655C4—24no—
656C4—24no—
657C4—28no—
658C4—24no—
659C4—24no—
660C4—24no—
661C4C2×2−1+4×C6114yes—
662C2—42no—
663C2—48no—
664C2C61×#355714yesdirect product factor
665C2C22×2−1+4×C6111yescharacteristic
666C2C2×C61×#58512yes—
subgroupG/H
center, socleC23×C61C25
commutator, Frattini, cosocleC22C26×C61
prime radicalC2×C61×#540C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3557C2direct (N × H)
2. C2×C61×#563C2semidirect
3. C2×C61×#559C2semidirect
4. C2×C61×#557C2semidirect
5. C2×C61×#556C2semidirect
6. C2×C61×#554C2semidirect
7. C2×C61×#552C2semidirect
8. C2×C61×#542C2semidirect
9. C2×C61×#542C2semidirect
10. C2×C61×#541C2semidirect
12. C2×C61×#539C2semidirect
13. C2×C61×#533C2semidirect
14. C2×C61×#529C2semidirect
15. C61×#563C22semidirect
16. C61×#559C22semidirect
17. C61×#557C22semidirect
18. C61×#556C22semidirect
19. C61×#554C22semidirect
20. C61×#552C22semidirect
21. C61×#542C22semidirect
22. C61×#542C22semidirect
23. C61×#541C22semidirect
25. C61×#539C22semidirect
26. C61×#533C22semidirect
32. C61×#529C22semidirect
307. C2×#3557C61direct (N × H)
329. #3557C2×C61direct (N × H)
330. C2×#563C2×C61semidirect
331. C2×#559C2×C61semidirect
332. C2×#557C2×C61semidirect
333. C2×#556C2×C61semidirect
334. C2×#554C2×C61semidirect
335. C2×#552C2×C61semidirect
336. C2×#542C2×C61semidirect
337. C2×#542C2×C61semidirect
338. C2×#541C2×C61semidirect
340. C2×#539C2×C61semidirect
341. C2×#533C2×C61semidirect
342. C2×#529C2×C61semidirect
345. C2×C61#3557direct (N × H)
348. #563C22×C61semidirect
349. #559C22×C61semidirect
350. #557C22×C61semidirect
351. #556C22×C61semidirect
352. #554C22×C61semidirect
353. #552C22×C61semidirect
354. #542C22×C61semidirect
355. #542C22×C61semidirect
356. #541C22×C61semidirect
358. #539C22×C61semidirect
359. #533C22×C61semidirect
365. #529C22×C61semidirect
414. C61C2×#3557direct (N × H)
664. C2C61×#3557direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35572
C2×C61×#5632
C2×C61×#5592
C2×C61×#5572
C2×C61×#5562
C2×C61×#5542
C2×C61×#5522
C2×C61×#5422
C2×C61×#5412
C2×C61×#5402
C2×C61×#5392
C2×C61×#5332
C2×C61×#5292
C2×#355761