Finite Group Databasebeta

← C2×C61×#3349 #29564674

Subgroups — C2×C61×#3349 #29564674

Order 15616.

1834 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#556C211yesmaximal, characteristic
2C2×C61×#552C211yesmaximal, characteristic
3C61×#3349C2116yesmaximal, direct product factor
4C2×C61×#501C211yesmaximal, characteristic, complemented
5C2×C61×#484C211yesmaximal, characteristic, complemented
6C2×C61×#485C211yesmaximal, characteristic, complemented
7C2×C61×#485C211yesmaximal, characteristic, complemented
8C2×C61×#485C211yesmaximal, characteristic, complemented
9C2×C61×#479C211yesmaximal, characteristic, complemented
10C2×C61×#477C211yesmaximal, characteristic, complemented
11C2×C61×#470C211yesmaximal, characteristic, complemented
12C2×C61×#467C211yesmaximal, characteristic, complemented
13C2×C61×#441C211yesmaximal, characteristic, complemented
14C2×C61×#435C211yesmaximal, characteristic
15C2×C61×#428C211yesmaximal, characteristic, complemented
16C2×C61×#427C211yesmaximal, characteristic, complemented
17C22×Q16×C61C2211yescharacteristic
18C22×M16×C61C2211yescharacteristic
19C23×C8×C61C2211yescharacteristic
20C61×#556—24no—
21C61×#556C2218yes—
22C61×#552—24no—
23C61×#552C2218yes—
24C2×C4⋊Q8×C61C2211yescharacteristic
25C2×#126×C61—21no—
26C2×#126×C61—21no—
27C2×#126×C61—21no—
28C2×#125×C61—21no—
29C2×#125×C61C2211yescharacteristic
30C2×#124×C61—21no—
31C2×#123×C61—21no—
32C2×C22⋊Q8×C61C2211yescharacteristic
33C2×C22⋊Q8×C61C2211yescharacteristic
34C2×C22⋊Q8×C61C2211yescharacteristic
35C2×C22⋊Q8×C61C2211yescharacteristic
36C2×C4×Q8×C61—21no—
37C2×C4×Q8×C61C2211yescharacteristic
38C2×C4×Q8×C61C2211yescharacteristic
39C2×C4×D4×C61C2211yescharacteristic
40C2×#117×C61—21no—
41C2×#117×C61C2211yescharacteristic
42C2×#117×C61C2211yescharacteristic
43C2×#117×C61C2211yescharacteristic
44C22×C4⋊C4×C61C2211yescharacteristic
45C61×#501C2218yescomplemented
46C61×#485C2218yescomplemented
47C61×#485C2218yescomplemented
48C61×#485C2218yescomplemented
49C61×#484C2218yescomplemented
50C61×#479C2218yescomplemented
51C61×#477C2218yescomplemented
52C61×#470C2218yescomplemented
53C61×#467C2218yescomplemented
54C61×#441C2218yescomplemented
55C61×#435C2218yes—
56C61×#428C2218yescomplemented
57C61×#427C2218yescomplemented
58C2×#107×C61C2211yescharacteristic
59C2×#107×C61C2211yescharacteristic
60C2×#107×C61C2211yescharacteristic
61C2×#107×C61C2211yescharacteristic
62C2×#107×C61C2211yescharacteristic
63C2×#106×C61C2211yescharacteristic
64C2×#106×C61C2211yescharacteristic
65C2×#106×C61C2211yescharacteristic
66C2×#106×C61C2211yescharacteristic
67C2×C4⋊C8×C61C2211yescharacteristic
68C2×#103×C61C2211yescharacteristic
69C2×#103×C61C2211yescharacteristic
70C2×#103×C61C2211yescharacteristic
71C2×#103×C61C2211yescharacteristic
72C2×#103×C61C2211yescharacteristic
73C2×#103×C61C2211yescharacteristic
74C2×C22⋊C8×C61C2211yescharacteristic
75C2×C22⋊C8×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C22×Q8×C61—21no—
78C22×Q8×C61C2311yescharacteristic
79C22×Q8×C61C2311yescharacteristic
80C22×D4×C61D411yescharacteristic
81C23×C4×C61—21no—
82C23×C4×C61C2311yescharacteristic
83C23×C4×C61C2311yescharacteristic
84C2×Q16×C61—24no—
85C2×Q16×C61C2314yes—
86C2×M16×C61—24no—
87C2×M16×C61C2314yes—
88C22×C8×C61—24no—
89C22×C8×C61C2311yescharacteristic
90C22×C8×C61C2314yes—
91C22×C8×C61C2311yescharacteristic
92C22×C8×C61C2311yescharacteristic
93C22×C8×C61C2311yescharacteristic
94C4⋊Q8×C61—22no—
95C4⋊Q8×C61C2314yes—
96#126×C61—28no—
97#126×C61—28no—
98#126×C61—28no—
99#125×C61—28no—
100#125×C61—22no—
101#125×C61C2314yes—
102#124×C61—28no—
103#123×C61—28no—
104C22⋊Q8×C61—22no—
105C22⋊Q8×C61—22no—
106C22⋊Q8×C61—22no—
107C22⋊Q8×C61—22no—
108C22⋊Q8×C61C2314yes—
109C22⋊Q8×C61C2314yes—
110C22⋊Q8×C61C2314yes—
111C22⋊Q8×C61C2314yes—
112C4×Q8×C61—28no—
113C4×Q8×C61—22no—
114C4×Q8×C61—22no—
115C4×Q8×C61C2314yes—
116C4×Q8×C61C2314yes—
117C4×D4×C61D414yes—
118C4×D4×C61C2314yes—
119#117×C61—22no—
120#117×C61—22no—
121#117×C61—22no—
122#117×C61—28no—
123#117×C61C2314yes—
124#117×C61C2314yes—
125#117×C61C2314yes—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61—22no—
128C2×C4⋊C4×C61—21no—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61—21no—
136C2×C4⋊C4×C61—21no—
137C2×C4⋊C4×C61D411yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C4⋊C4×C61C2314yes—
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C22⋊C4×C61—21no—
146C2×C22⋊C4×C61—21no—
147C2×C22⋊C4×C61—21no—
148C2×C22⋊C4×C61—21no—
149C2×C22⋊C4×C61—21no—
150C2×C22⋊C4×C61—21no—
151C2×C22⋊C4×C61—21no—
152C2×C22⋊C4×C61D411yescharacteristic
153C2×C22⋊C4×C61D411yescharacteristic
154C2×C42×C61—21no—
155C2×C42×C61—21no—
156C2×C42×C61—21no—
157C2×C42×C61—21no—
158C2×C42×C61—21no—
159C2×C42×C61C2311yescharacteristic
160#107×C61C2314yes—
161#107×C61C2314yes—
162#107×C61C2314yes—
163#107×C61C2314yes—
164#107×C61C2314yes—
165#106×C61C2314yes—
166#106×C61C2314yes—
167#106×C61C2314yes—
168#106×C61C2314yes—
169C4⋊C8×C61C2314yes—
170#103×C61C2314yes—
171#103×C61C2314yes—
172#103×C61C2314yes—
173#103×C61C2314yes—
174#103×C61C2314yes—
175#103×C61C2314yes—
176C22⋊C8×C61C2314yes—
177C22⋊C8×C61C2314yes—
178#97×C61C2314yes—
179C24×C61C2×D411yescharacteristic
180C24×C61C2×D411yescharacteristic
181C2×Q8×C61—21no—
182C2×Q8×C61—21no—
183C2×Q8×C61—24no—
184C2×Q8×C61—22no—
185C2×Q8×C61—22no—
186C2×Q8×C61—22no—
187C2×Q8×C61—22no—
188C2×Q8×C61—44no—
189C2×Q8×C61C2412yes—
190C2×Q8×C61C2412yes—
191C2×D4×C61—42no—
192C2×D4×C61C2×D414yes—
193C22×C4×C61—22no—
194C22×C4×C61—22no—
195C22×C4×C61—22no—
196C22×C4×C61—22no—
197C22×C4×C61—24no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—44no—
207C22×C4×C61C2×D412yes—
208C22×C4×C61C2×D412yes—
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2412yes—
214C22×C4×C61C2412yes—
215C22×C4×C61C2411yescharacteristic
216Q16×C61—28no—
217M16×C61—28no—
218C2×C8×C61—22no—
219C2×C8×C61—22no—
220C2×C8×C61—22no—
221C2×C8×C61—28no—
222C2×C8×C61#4114yes—
223C2×C8×C61C2412yes—
224C2×C8×C61C2412yes—
225C2×C8×C61C2412yes—
226C2×C8×C61C2412yes—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—24no—
230C4⋊C4×C61—24no—
231C4⋊C4×C61—24no—
232C4⋊C4×C61—24no—
233C4⋊C4×C61—24no—
234C4⋊C4×C61—24no—
235C4⋊C4×C61—24no—
236C4⋊C4×C61—24no—
237C4⋊C4×C61—24no—
238C4⋊C4×C61—24no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61C2×D414yes—
244C4⋊C4×C61C2412yes—
245C4⋊C4×C61C2412yes—
246C4⋊C4×C61C2412yes—
247C4⋊C4×C61C2412yes—
248C4⋊C4×C61C2412yes—
249C4⋊C4×C61C2412yes—
250C22⋊C4×C61—24no—
251C22⋊C4×C61—24no—
252C22⋊C4×C61—24no—
253C22⋊C4×C61—24no—
254C22⋊C4×C61—24no—
255C22⋊C4×C61—24no—
256C22⋊C4×C61—24no—
257C22⋊C4×C61C2×D414yes—
258C22⋊C4×C61C2×D414yes—
259C42×C61—24no—
260C42×C61—24no—
261C42×C61—24no—
262C42×C61—24no—
263C42×C61—24no—
264C42×C61C2×D412yes—
265C42×C61C2412yes—
266C23×C61—22no—
267C23×C61—22no—
268C23×C61—22no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61C22×D412yes—
273C23×C61C22×D412yes—
274C23×C61C22×D411yescharacteristic
275Q8×C61—22no—
276Q8×C61—22no—
277Q8×C61—22no—
278Q8×C61—22no—
279Q8×C61—48no—
280Q8×C61—42no—
281Q8×C61—42no—
282D4×C61—44no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—24no—
288C2×C4×C61—24no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—48no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61—42no—
309C2×C4×C61—42no—
310C2×C4×C61C22×D412yes—
311C2×C4×C61C22×D412yes—
312C2×C4×C61C22×D412yes—
313C2×C4×C61C22×D412yes—
314C2×C4×C61C22×D411yescharacteristic
315C2×C4×C61C2×#4112yes—
316C2×C4×C612−1+412yes—
317C2×C4×C61C2511yescharacteristic
318C8×C61—22no—
319C8×C61—22no—
320C8×C61—22no—
321C8×C61C2×#4114yes—
322C2×#3349C6111yesmaximal, characteristic, direct product factor, Sylow
323C22×C61—22no—
324C22×C61—22no—
325C22×C61—22no—
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—22no—
329C22×C61—44no—
330C22×C61—44no—
331C22×C61#54712yes—
332C22×C61#57512yes—
333C22×C61#57812yes—
334C22×C61C23×D411yescharacteristic
335C4×C61—22no—
336C4×C61—22no—
337C4×C61—22no—
338C4×C61—22no—
339C4×C61—42no—
340C4×C61—42no—
341C4×C61—42no—
342C4×C61—42no—
343C4×C61—42no—
344C4×C61—42no—
345C4×C61—42no—
346C4×C61—42no—
347C4×C61#54712yes—
348C4×C61C22×#4111yescharacteristic
349C4×C61C2×2−1+411yescharacteristic
350C2×#556C2×C6111yescharacteristic
351C2×#552C2×C6111yescharacteristic
352#3349C2×C61116yesdirect product factor
353C2×#501C2×C6111yescharacteristic, complemented
354C2×#484C2×C6111yescharacteristic, complemented
355C2×#485C2×C6111yescharacteristic, complemented
356C2×#485C2×C6111yescharacteristic, complemented
357C2×#485C2×C6111yescharacteristic, complemented
358C2×#479C2×C6111yescharacteristic, complemented
359C2×#477C2×C6111yescharacteristic, complemented
360C2×#470C2×C6111yescharacteristic, complemented
361C2×#467C2×C6111yescharacteristic, complemented
362C2×#441C2×C6111yescharacteristic, complemented
363C2×#435C2×C6111yescharacteristic
364C2×#428C2×C6111yescharacteristic, complemented
365C2×#427C2×C6111yescharacteristic, complemented
366C2×C61—42no—
367C2×C61—42no—
368C2×C61#334914yesdirect product factor
369C2×C61C2×#54711yescharacteristic
370C2×C61C2×#57511yescharacteristic
371C2×C61C2×#57811yescharacteristic
372C22×Q16C22×C6111yescharacteristic
373C22×M16C22×C6111yescharacteristic
374C23×C8C22×C6111yescharacteristic
375#556—24no—
376#556C22×C6118yes—
377#552—24no—
378#552C22×C6118yes—
379C2×C4⋊Q8C22×C6111yescharacteristic
380C2×#126—21no—
381C2×#126—21no—
382C2×#126—21no—
383C2×#125—21no—
384C2×#125C22×C6111yescharacteristic
385C2×#124—21no—
386C2×#123—21no—
387C2×C22⋊Q8C22×C6111yescharacteristic
388C2×C22⋊Q8C22×C6111yescharacteristic
389C2×C22⋊Q8C22×C6111yescharacteristic
390C2×C22⋊Q8C22×C6111yescharacteristic
391C2×C4×Q8—21no—
392C2×C4×Q8C22×C6111yescharacteristic
393C2×C4×Q8C22×C6111yescharacteristic
394C2×C4×D4C22×C6111yescharacteristic
395C2×#117—21no—
396C2×#117C22×C6111yescharacteristic
397C2×#117C22×C6111yescharacteristic
398C2×#117C22×C6111yescharacteristic
399C22×C4⋊C4C22×C6111yescharacteristic
400#501C22×C6118yescomplemented
401#485C22×C6118yescomplemented
402#485C22×C6118yescomplemented
403#485C22×C6118yescomplemented
404#484C22×C6118yescomplemented
405#479C22×C6118yescomplemented
406#477C22×C6118yescomplemented
407#470C22×C6118yescomplemented
408#467C22×C6118yescomplemented
409#441C22×C6118yescomplemented
410#435C22×C6118yes—
411#428C22×C6118yescomplemented
412#427C22×C6118yescomplemented
413C2×#107C22×C6111yescharacteristic
414C2×#107C22×C6111yescharacteristic
415C2×#107C22×C6111yescharacteristic
416C2×#107C22×C6111yescharacteristic
417C2×#107C22×C6111yescharacteristic
418C2×#106C22×C6111yescharacteristic
419C2×#106C22×C6111yescharacteristic
420C2×#106C22×C6111yescharacteristic
421C2×#106C22×C6111yescharacteristic
422C2×C4⋊C8C22×C6111yescharacteristic
423C2×#103C22×C6111yescharacteristic
424C2×#103C22×C6111yescharacteristic
425C2×#103C22×C6111yescharacteristic
426C2×#103C22×C6111yescharacteristic
427C2×#103C22×C6111yescharacteristic
428C2×#103C22×C6111yescharacteristic
429C2×C22⋊C8C22×C6111yescharacteristic
430C2×C22⋊C8C22×C6111yescharacteristic
431C2×#97C22×C6111yescharacteristic
432C61C2×#334911yescharacteristic, direct product factor, Sylow
433C22×Q8—21no—
434C22×Q8C23×C6111yescharacteristic
435C22×Q8C23×C6111yescharacteristic
436C22×D4D4×C6111yescharacteristic
437C23×C4—21no—
438C23×C4C23×C6111yescharacteristic
439C23×C4C23×C6111yescharacteristic
440C2×Q16—24no—
441C2×Q16C23×C6114yes—
442C2×M16—24no—
443C2×M16C23×C6114yes—
444C22×C8—24no—
445C22×C8C23×C6111yescharacteristic
446C22×C8C23×C6114yes—
447C22×C8C23×C6111yescharacteristic
448C22×C8C23×C6111yescharacteristic
449C22×C8C23×C6111yescharacteristic
450C4⋊Q8—22no—
451C4⋊Q8C23×C6114yes—
452#126—28no—
453#126—28no—
454#126—28no—
455#125—28no—
456#125—22no—
457#125C23×C6114yes—
458#124—28no—
459#123—28no—
460C22⋊Q8—22no—
461C22⋊Q8—22no—
462C22⋊Q8—22no—
463C22⋊Q8—22no—
464C22⋊Q8C23×C6114yes—
465C22⋊Q8C23×C6114yes—
466C22⋊Q8C23×C6114yes—
467C22⋊Q8C23×C6114yes—
468C4×Q8—28no—
469C4×Q8—22no—
470C4×Q8—22no—
471C4×Q8C23×C6114yes—
472C4×Q8C23×C6114yes—
473C4×D4D4×C6114yes—
474C4×D4C23×C6114yes—
475#117—22no—
476#117—22no—
477#117—22no—
478#117—28no—
479#117C23×C6114yes—
480#117C23×C6114yes—
481#117C23×C6114yes—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4D4×C6111yescharacteristic
494C2×C4⋊C4C23×C6111yescharacteristic
495C2×C4⋊C4C23×C6111yescharacteristic
496C2×C4⋊C4C23×C6114yes—
497C2×C4⋊C4C23×C6111yescharacteristic
498C2×C4⋊C4C23×C6111yescharacteristic
499C2×C4⋊C4C23×C6111yescharacteristic
500C2×C4⋊C4C23×C6111yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4D4×C6111yescharacteristic
509C2×C22⋊C4D4×C6111yescharacteristic
510C2×C42—21no—
511C2×C42—21no—
512C2×C42—21no—
513C2×C42—21no—
514C2×C42—21no—
515C2×C42C23×C6111yescharacteristic
516#107C23×C6114yes—
517#107C23×C6114yes—
518#107C23×C6114yes—
519#107C23×C6114yes—
520#107C23×C6114yes—
521#106C23×C6114yes—
522#106C23×C6114yes—
523#106C23×C6114yes—
524#106C23×C6114yes—
525C4⋊C8C23×C6114yes—
526#103C23×C6114yes—
527#103C23×C6114yes—
528#103C23×C6114yes—
529#103C23×C6114yes—
530#103C23×C6114yes—
531#103C23×C6114yes—
532C22⋊C8C23×C6114yes—
533C22⋊C8C23×C6114yes—
534#97C23×C6114yes—
535C24C2×D4×C6111yescharacteristic
536C24C2×D4×C6111yescharacteristic
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—24no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—44no—
545C2×Q8C24×C6112yes—
546C2×Q8C24×C6112yes—
547C2×D4—42no—
548C2×D4C2×D4×C6114yes—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—44no—
563C22×C4C2×D4×C6111yescharacteristic
564C22×C4C2×D4×C6111yescharacteristic
565C22×C4C2×D4×C6111yescharacteristic
566C22×C4C2×D4×C6111yescharacteristic
567C22×C4C2×D4×C6112yes—
568C22×C4C2×D4×C6112yes—
569C22×C4C24×C6112yes—
570C22×C4C24×C6112yes—
571C22×C4C24×C6111yescharacteristic
572Q16—28no—
573M16—28no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—28no—
578C2×C8#41×C6114yes—
579C2×C8C24×C6112yes—
580C2×C8C24×C6112yes—
581C2×C8C24×C6112yes—
582C2×C8C24×C6112yes—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4C2×D4×C6114yes—
600C4⋊C4C24×C6112yes—
601C4⋊C4C24×C6112yes—
602C4⋊C4C24×C6112yes—
603C4⋊C4C24×C6112yes—
604C4⋊C4C24×C6112yes—
605C4⋊C4C24×C6112yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—24no—
612C22⋊C4—24no—
613C22⋊C4C2×D4×C6114yes—
614C22⋊C4C2×D4×C6114yes—
615C42—24no—
616C42—24no—
617C42—24no—
618C42—24no—
619C42—24no—
620C42C2×D4×C6112yes—
621C42C24×C6112yes—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23C22×D4×C6112yes—
629C23C22×D4×C6112yes—
630C23C22×D4×C6111yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—22no—
634Q8—22no—
635Q8—48no—
636Q8—42no—
637Q8—42no—
638D4—44no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—48no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4C22×D4×C6112yes—
667C2×C4C22×D4×C6112yes—
668C2×C4C22×D4×C6112yes—
669C2×C4C22×D4×C6112yes—
670C2×C4C22×D4×C6111yescharacteristic
671C2×C4C2×#41×C6112yes—
672C2×C42−1+4×C6112yes—
673C2×C4C25×C6111yescharacteristic
674C8—22no—
675C8—22no—
676C8—22no—
677C8C2×#41×C6114yes—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—44no—
685C22—44no—
686C22C61×#54712yes—
687C22C61×#57512yes—
688C22C61×#57812yes—
689C22C23×D4×C6111yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—42no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—42no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4C61×#54712yes—
703C4C22×#41×C6111yescharacteristic
704C4C2×2−1+4×C6111yescharacteristic
705C2—42no—
706C2—42no—
707C2C61×#334914yesdirect product factor
708C2C2×C61×#54711yescharacteristic
709C2C2×C61×#57511yescharacteristic
710C2C2×C61×#57811yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC2×C4C25×C61
prime radicalC22×D4×C61D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C2×C4×D4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
3. C61×#3349C2direct (N × H)
4. C2×C61×#501C2semidirect
5. C2×C61×#484C2semidirect
6. C2×C61×#485C2semidirect
7. C2×C61×#485C2semidirect
8. C2×C61×#485C2semidirect
9. C2×C61×#479C2semidirect
10. C2×C61×#477C2semidirect
11. C2×C61×#470C2semidirect
12. C2×C61×#467C2semidirect
13. C2×C61×#441C2semidirect
15. C2×C61×#428C2semidirect
16. C2×C61×#427C2semidirect
45. C61×#501C22semidirect
46. C61×#485C22semidirect
47. C61×#485C22semidirect
48. C61×#485C22semidirect
49. C61×#484C22semidirect
50. C61×#479C22semidirect
51. C61×#477C22semidirect
52. C61×#470C22semidirect
53. C61×#467C22semidirect
54. C61×#441C22semidirect
56. C61×#428C22semidirect
57. C61×#427C22semidirect
322. C2×#3349C61direct (N × H)
352. #3349C2×C61direct (N × H)
353. C2×#501C2×C61semidirect
354. C2×#484C2×C61semidirect
355. C2×#485C2×C61semidirect
356. C2×#485C2×C61semidirect
357. C2×#485C2×C61semidirect
358. C2×#479C2×C61semidirect
359. C2×#477C2×C61semidirect
360. C2×#470C2×C61semidirect
361. C2×#467C2×C61semidirect
362. C2×#441C2×C61semidirect
364. C2×#428C2×C61semidirect
365. C2×#427C2×C61semidirect
368. C2×C61#3349direct (N × H)
400. #501C22×C61semidirect
401. #485C22×C61semidirect
402. #485C22×C61semidirect
403. #485C22×C61semidirect
404. #484C22×C61semidirect
405. #479C22×C61semidirect
406. #477C22×C61semidirect
407. #470C22×C61semidirect
408. #467C22×C61semidirect
409. #441C22×C61semidirect
411. #428C22×C61semidirect
412. #427C22×C61semidirect
432. C61C2×#3349direct (N × H)
707. C2C61×#3349direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#5562
C2×C61×#5522
C61×#33492
C2×C61×#5012
C2×C61×#4842
C2×C61×#4852
C2×C61×#4792
C2×C61×#4772
C2×C61×#4702
C2×C61×#4672
C2×C61×#4412
C2×C61×#4352
C2×C61×#4282
C2×C61×#4272
C2×#334961