Finite Group Databasebeta

← C2×C61×#3347 #29564672

Subgroups — C2×C61×#3347 #29564672

Order 15616.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#555C211yesmaximal, characteristic, complemented
2C2×C61×#553C211yesmaximal, characteristic, complemented
3C61×#3347C2116yesmaximal, direct product factor
4C2×C61×#501C211yesmaximal, characteristic, complemented
5C2×C61×#482C211yesmaximal, characteristic, complemented
6C2×C61×#482C211yesmaximal, characteristic, complemented
7C2×C61×#482C211yesmaximal, characteristic, complemented
8C2×C61×#480C211yesmaximal, characteristic, complemented
9C2×C61×#478C211yesmaximal, characteristic, complemented
10C2×C61×#474C211yesmaximal, characteristic, complemented
11C2×C61×#469C211yesmaximal, characteristic, complemented
12C2×C61×#466C211yesmaximal, characteristic, complemented
13C2×C61×#442C211yesmaximal, characteristic, complemented
14C2×C61×#435C211yesmaximal, characteristic, complemented
15C2×C61×#428C211yesmaximal, characteristic, complemented
16C2×C61×#427C211yesmaximal, characteristic, complemented
17C22×D8×C61C2211yescharacteristic
18C22×M16×C61C2211yescharacteristic
19C23×C8×C61C2211yescharacteristic
20C61×#555—24no—
21C61×#555C2218yescomplemented
22C61×#553—24no—
23C61×#553C2218yescomplemented
24C2×C4⋊Q8×C61C2211yescharacteristic
25C2×#126×C61—21no—
26C2×#125×C61C2211yescharacteristic
27C2×#124×C61—21no—
28C2×#124×C61—21no—
29C2×#123×C61—21no—
30C2×#121×C61—21no—
31C2×#121×C61—21no—
32C2×#121×C61C2211yescharacteristic
33C2×#121×C61C2211yescharacteristic
34C2×#121×C61C2211yescharacteristic
35C2×#121×C61C2211yescharacteristic
36C2×C4×D4×C61—21no—
37C2×C4×D4×C61C2211yescharacteristic
38C2×C4×D4×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×#482C2218yescomplemented
47C61×#482C2218yescomplemented
48C61×#482C2218yescomplemented
49C61×#480C2218yescomplemented
50C61×#478C2218yescomplemented
51C61×#474C2218yescomplemented
52C61×#469C2218yescomplemented
53C61×#466C2218yescomplemented
54C61×#442C2218yescomplemented
55C61×#435C2218yescomplemented
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×#102×C61C2211yescharacteristic
69C2×#102×C61C2211yescharacteristic
70C2×#102×C61C2211yescharacteristic
71C2×#102×C61C2211yescharacteristic
72C2×#102×C61C2211yescharacteristic
73C2×#102×C61C2211yescharacteristic
74C2×C22⋊C8×C61C2211yescharacteristic
75C2×C22⋊C8×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C22×Q8×C61—21no—
78C22×D4×C61—21no—
79C22×D4×C61—21no—
80C22×D4×C61—21no—
81C22×D4×C61—21no—
82C22×D4×C61D411yescharacteristic
83C22×D4×C61C2311yescharacteristic
84C22×D4×C61C2311yescharacteristic
85C23×C4×C61—21no—
86C23×C4×C61—21no—
87C23×C4×C61—21no—
88C23×C4×C61C2311yescharacteristic
89C23×C4×C61C2311yescharacteristic
90C2×D8×C61—24no—
91C2×D8×C61C2314yes—
92C2×M16×C61—24no—
93C2×M16×C61C2314yes—
94C22×C8×C61—24no—
95C22×C8×C61C2311yescharacteristic
96C22×C8×C61C2314yes—
97C22×C8×C61C2311yescharacteristic
98C22×C8×C61C2311yescharacteristic
99C22×C8×C61C2311yescharacteristic
100C4⋊Q8×C61—22no—
101C4⋊Q8×C61C2314yes—
102#126×C61—28no—
103#125×C61—22no—
104#125×C61C2314yes—
105#124×C61—28no—
106#124×C61—28no—
107#123×C61—28no—
108#121×C61—28no—
109#121×C61—28no—
110#121×C61—22no—
111#121×C61—22no—
112#121×C61—22no—
113#121×C61—22no—
114#121×C61C2314yes—
115#121×C61C2314yes—
116#121×C61C2314yes—
117#121×C61C2314yes—
118C4×D4×C61—28no—
119C4×D4×C61—22no—
120C4×D4×C61—22no—
121C4×D4×C61D414yes—
122C4×D4×C61C2314yes—
123C4×D4×C61C2314yes—
124C4×D4×C61C2314yes—
125#117×C61—22no—
126#117×C61—22no—
127#117×C61—22no—
128#117×C61—28no—
129#117×C61C2314yes—
130#117×C61C2314yes—
131#117×C61C2314yes—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—22no—
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×C61—21no—
153C2×C22⋊C4×C61—21no—
154C2×C22⋊C4×C61D411yescharacteristic
155C2×C22⋊C4×C61D411yescharacteristic
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#102×C61C2314yes—
171#102×C61C2314yes—
172#102×C61C2314yes—
173#102×C61C2314yes—
174#102×C61C2314yes—
175#102×C61C2314yes—
176C22⋊C8×C61C2314yes—
177C22⋊C8×C61C2314yes—
178#97×C61C2314yes—
179C24×C61—21no—
180C24×C61—21no—
181C24×C61C2×D411yescharacteristic
182C24×C61C2×D411yescharacteristic
183C2×Q8×C61—24no—
184C2×Q8×C61—82no—
185C2×D4×C61—24no—
186C2×D4×C61—24no—
187C2×D4×C61—24no—
188C2×D4×C61—24no—
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61—22no—
192C2×D4×C61—22no—
193C2×D4×C61—22no—
194C2×D4×C61—22no—
195C2×D4×C61—42no—
196C2×D4×C61—44no—
197C2×D4×C61—82no—
198C2×D4×C61—82no—
199C2×D4×C61—82no—
200C2×D4×C61C2×D414yes—
201C2×D4×C61C2412yes—
202C2×D4×C61C2412yes—
203C22×C4×C61—22no—
204C22×C4×C61—22no—
205C22×C4×C61—22no—
206C22×C4×C61—22no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—24no—
214C22×C4×C61—24no—
215C22×C4×C61—24no—
216C22×C4×C61—44no—
217C22×C4×C61—82no—
218C22×C4×C61—82no—
219C22×C4×C61C2×D412yes—
220C22×C4×C61C2×D412yes—
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2412yes—
226C22×C4×C61C2412yes—
227C22×C4×C61C2411yescharacteristic
228D8×C61—28no—
229M16×C61—28no—
230C2×C8×C61—22no—
231C2×C8×C61—22no—
232C2×C8×C61—22no—
233C2×C8×C61—28no—
234C2×C8×C61#4114yes—
235C2×C8×C61C2412yes—
236C2×C8×C61C2412yes—
237C2×C8×C61C2412yes—
238C2×C8×C61C2412yes—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—24no—
242C4⋊C4×C61—24no—
243C4⋊C4×C61—24no—
244C4⋊C4×C61—24no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61C2×D414yes—
250C4⋊C4×C61C2412yes—
251C4⋊C4×C61C2412yes—
252C4⋊C4×C61C2412yes—
253C4⋊C4×C61C2412yes—
254C4⋊C4×C61C2412yes—
255C4⋊C4×C61C2412yes—
256C22⋊C4×C61—24no—
257C22⋊C4×C61—24no—
258C22⋊C4×C61—24no—
259C22⋊C4×C61—24no—
260C22⋊C4×C61—24no—
261C22⋊C4×C61—24no—
262C22⋊C4×C61—24no—
263C22⋊C4×C61—24no—
264C22⋊C4×C61—24no—
265C22⋊C4×C61C2×D414yes—
266C22⋊C4×C61C2×D414yes—
267C42×C61—24no—
268C42×C61—24no—
269C42×C61—24no—
270C42×C61C2×D412yes—
271C42×C61C2412yes—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61—22no—
277C23×C61—22no—
278C23×C61—22no—
279C23×C61—22no—
280C23×C61—42no—
281C23×C61—42no—
282C23×C61—42no—
283C23×C61—42no—
284C23×C61—42no—
285C23×C61—42no—
286C23×C61C22×D412yes—
287C23×C61C22×D412yes—
288C23×C61C22×D411yescharacteristic
289Q8×C61—84no—
290D4×C61—22no—
291D4×C61—22no—
292D4×C61—22no—
293D4×C61—22no—
294D4×C61—44no—
295D4×C61—48no—
296D4×C61—42no—
297D4×C61—42no—
298D4×C61—84no—
299D4×C61—84no—
300D4×C61—84no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—24no—
306C2×C4×C61—24no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—48no—
318C2×C4×C61—42no—
319C2×C4×C61—42no—
320C2×C4×C61—42no—
321C2×C4×C61—42no—
322C2×C4×C61—42no—
323C2×C4×C61—42no—
324C2×C4×C61—84no—
325C2×C4×C61—84no—
326C2×C4×C61C22×D412yes—
327C2×C4×C61C22×D412yes—
328C2×C4×C61C22×D412yes—
329C2×C4×C61C22×D412yes—
330C2×C4×C61C22×D411yescharacteristic
331C2×C4×C61C2×#4112yes—
332C2×C4×C612−1+412yes—
333C2×C4×C61C2511yescharacteristic
334C8×C61—22no—
335C8×C61—22no—
336C8×C61—22no—
337C8×C61C2×#4114yes—
338C2×#3347C6111yesmaximal, characteristic, direct product factor, Sylow
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—22no—
344C22×C61—22no—
345C22×C61—44no—
346C22×C61—44no—
347C22×C61—42no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—84no—
354C22×C61—84no—
355C22×C61#54712yes—
356C22×C61#57512yes—
357C22×C61#57612yes—
358C22×C61C23×D411yescharacteristic
359C4×C61—22no—
360C4×C61—22no—
361C4×C61—22no—
362C4×C61—22no—
363C4×C61—42no—
364C4×C61—42no—
365C4×C61—42no—
366C4×C61—42no—
367C4×C61—42no—
368C4×C61—42no—
369C4×C61#54712yes—
370C4×C61C22×#4111yescharacteristic
371C4×C61C2×2−1+411yescharacteristic
372C2×#555C2×C6111yescharacteristic, complemented
373C2×#553C2×C6111yescharacteristic, complemented
374#3347C2×C61116yesdirect product factor
375C2×#501C2×C6111yescharacteristic, complemented
376C2×#482C2×C6111yescharacteristic, complemented
377C2×#482C2×C6111yescharacteristic, complemented
378C2×#482C2×C6111yescharacteristic, complemented
379C2×#480C2×C6111yescharacteristic, complemented
380C2×#478C2×C6111yescharacteristic, complemented
381C2×#474C2×C6111yescharacteristic, complemented
382C2×#469C2×C6111yescharacteristic, complemented
383C2×#466C2×C6111yescharacteristic, complemented
384C2×#442C2×C6111yescharacteristic, complemented
385C2×#435C2×C6111yescharacteristic, complemented
386C2×#428C2×C6111yescharacteristic, complemented
387C2×#427C2×C6111yescharacteristic, complemented
388C2×C61—42no—
389C2×C61—42no—
390C2×C61—82no—
391C2×C61—82no—
392C2×C61#334714yesdirect product factor
393C2×C61C2×#54711yescharacteristic
394C2×C61C2×#57511yescharacteristic
395C2×C61C2×#57611yescharacteristic
396C22×D8C22×C6111yescharacteristic
397C22×M16C22×C6111yescharacteristic
398C23×C8C22×C6111yescharacteristic
399#555—24no—
400#555C22×C6118yescomplemented
401#553—24no—
402#553C22×C6118yescomplemented
403C2×C4⋊Q8C22×C6111yescharacteristic
404C2×#126—21no—
405C2×#125C22×C6111yescharacteristic
406C2×#124—21no—
407C2×#124—21no—
408C2×#123—21no—
409C2×#121—21no—
410C2×#121—21no—
411C2×#121C22×C6111yescharacteristic
412C2×#121C22×C6111yescharacteristic
413C2×#121C22×C6111yescharacteristic
414C2×#121C22×C6111yescharacteristic
415C2×C4×D4—21no—
416C2×C4×D4C22×C6111yescharacteristic
417C2×C4×D4C22×C6111yescharacteristic
418C2×C4×D4C22×C6111yescharacteristic
419C2×#117—21no—
420C2×#117C22×C6111yescharacteristic
421C2×#117C22×C6111yescharacteristic
422C2×#117C22×C6111yescharacteristic
423C22×C4⋊C4C22×C6111yescharacteristic
424#501C22×C6118yescomplemented
425#482C22×C6118yescomplemented
426#482C22×C6118yescomplemented
427#482C22×C6118yescomplemented
428#480C22×C6118yescomplemented
429#478C22×C6118yescomplemented
430#474C22×C6118yescomplemented
431#469C22×C6118yescomplemented
432#466C22×C6118yescomplemented
433#442C22×C6118yescomplemented
434#435C22×C6118yescomplemented
435#428C22×C6118yescomplemented
436#427C22×C6118yescomplemented
437C2×#107C22×C6111yescharacteristic
438C2×#107C22×C6111yescharacteristic
439C2×#107C22×C6111yescharacteristic
440C2×#107C22×C6111yescharacteristic
441C2×#107C22×C6111yescharacteristic
442C2×#106C22×C6111yescharacteristic
443C2×#106C22×C6111yescharacteristic
444C2×#106C22×C6111yescharacteristic
445C2×#106C22×C6111yescharacteristic
446C2×C4⋊C8C22×C6111yescharacteristic
447C2×#102C22×C6111yescharacteristic
448C2×#102C22×C6111yescharacteristic
449C2×#102C22×C6111yescharacteristic
450C2×#102C22×C6111yescharacteristic
451C2×#102C22×C6111yescharacteristic
452C2×#102C22×C6111yescharacteristic
453C2×C22⋊C8C22×C6111yescharacteristic
454C2×C22⋊C8C22×C6111yescharacteristic
455C2×#97C22×C6111yescharacteristic
456C61C2×#334711yescharacteristic, direct product factor, Sylow
457C22×Q8—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4D4×C6111yescharacteristic
463C22×D4C23×C6111yescharacteristic
464C22×D4C23×C6111yescharacteristic
465C23×C4—21no—
466C23×C4—21no—
467C23×C4—21no—
468C23×C4C23×C6111yescharacteristic
469C23×C4C23×C6111yescharacteristic
470C2×D8—24no—
471C2×D8C23×C6114yes—
472C2×M16—24no—
473C2×M16C23×C6114yes—
474C22×C8—24no—
475C22×C8C23×C6111yescharacteristic
476C22×C8C23×C6114yes—
477C22×C8C23×C6111yescharacteristic
478C22×C8C23×C6111yescharacteristic
479C22×C8C23×C6111yescharacteristic
480C4⋊Q8—22no—
481C4⋊Q8C23×C6114yes—
482#126—28no—
483#125—22no—
484#125C23×C6114yes—
485#124—28no—
486#124—28no—
487#123—28no—
488#121—28no—
489#121—28no—
490#121—22no—
491#121—22no—
492#121—22no—
493#121—22no—
494#121C23×C6114yes—
495#121C23×C6114yes—
496#121C23×C6114yes—
497#121C23×C6114yes—
498C4×D4—28no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4D4×C6114yes—
502C4×D4C23×C6114yes—
503C4×D4C23×C6114yes—
504C4×D4C23×C6114yes—
505#117—22no—
506#117—22no—
507#117—22no—
508#117—28no—
509#117C23×C6114yes—
510#117C23×C6114yes—
511#117C23×C6114yes—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—22no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4D4×C6111yescharacteristic
518C2×C4⋊C4C23×C6111yescharacteristic
519C2×C4⋊C4C23×C6111yescharacteristic
520C2×C4⋊C4C23×C6114yes—
521C2×C4⋊C4C23×C6111yescharacteristic
522C2×C4⋊C4C23×C6111yescharacteristic
523C2×C4⋊C4C23×C6111yescharacteristic
524C2×C4⋊C4C23×C6111yescharacteristic
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4D4×C6111yescharacteristic
535C2×C22⋊C4D4×C6111yescharacteristic
536C2×C42—21no—
537C2×C42—21no—
538C2×C42—21no—
539C2×C42C23×C6111yescharacteristic
540#107C23×C6114yes—
541#107C23×C6114yes—
542#107C23×C6114yes—
543#107C23×C6114yes—
544#107C23×C6114yes—
545#106C23×C6114yes—
546#106C23×C6114yes—
547#106C23×C6114yes—
548#106C23×C6114yes—
549C4⋊C8C23×C6114yes—
550#102C23×C6114yes—
551#102C23×C6114yes—
552#102C23×C6114yes—
553#102C23×C6114yes—
554#102C23×C6114yes—
555#102C23×C6114yes—
556C22⋊C8C23×C6114yes—
557C22⋊C8C23×C6114yes—
558#97C23×C6114yes—
559C24—21no—
560C24—21no—
561C24C2×D4×C6111yescharacteristic
562C24C2×D4×C6111yescharacteristic
563C2×Q8—24no—
564C2×Q8—82no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—24no—
568C2×D4—24no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—42no—
576C2×D4—44no—
577C2×D4—82no—
578C2×D4—82no—
579C2×D4—82no—
580C2×D4C2×D4×C6114yes—
581C2×D4C24×C6112yes—
582C2×D4C24×C6112yes—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—44no—
597C22×C4—82no—
598C22×C4—82no—
599C22×C4C2×D4×C6111yescharacteristic
600C22×C4C2×D4×C6111yescharacteristic
601C22×C4C2×D4×C6111yescharacteristic
602C22×C4C2×D4×C6111yescharacteristic
603C22×C4C2×D4×C6112yes—
604C22×C4C2×D4×C6112yes—
605C22×C4C24×C6112yes—
606C22×C4C24×C6112yes—
607C22×C4C24×C6111yescharacteristic
608D8—28no—
609M16—28no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—28no—
614C2×C8#41×C6114yes—
615C2×C8C24×C6112yes—
616C2×C8C24×C6112yes—
617C2×C8C24×C6112yes—
618C2×C8C24×C6112yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4C2×D4×C6114yes—
630C4⋊C4C24×C6112yes—
631C4⋊C4C24×C6112yes—
632C4⋊C4C24×C6112yes—
633C4⋊C4C24×C6112yes—
634C4⋊C4C24×C6112yes—
635C4⋊C4C24×C6112yes—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4C2×D4×C6114yes—
646C22⋊C4C2×D4×C6114yes—
647C42—24no—
648C42—24no—
649C42—24no—
650C42C2×D4×C6112yes—
651C42C24×C6112yes—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23C22×D4×C6112yes—
667C23C22×D4×C6112yes—
668C23C22×D4×C6111yescharacteristic
669Q8—84no—
670D4—22no—
671D4—22no—
672D4—22no—
673D4—22no—
674D4—44no—
675D4—48no—
676D4—42no—
677D4—42no—
678D4—84no—
679D4—84no—
680D4—84no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—48no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—84no—
705C2×C4—84no—
706C2×C4C22×D4×C6112yes—
707C2×C4C22×D4×C6112yes—
708C2×C4C22×D4×C6112yes—
709C2×C4C22×D4×C6112yes—
710C2×C4C22×D4×C6111yescharacteristic
711C2×C4C2×#41×C6112yes—
712C2×C42−1+4×C6112yes—
713C2×C4C25×C6111yescharacteristic
714C8—22no—
715C8—22no—
716C8—22no—
717C8C2×#41×C6114yes—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—44no—
725C22—44no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—84no—
733C22—84no—
734C22C61×#54712yes—
735C22C61×#57512yes—
736C22C61×#57612yes—
737C22C23×D4×C6111yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—42no—
743C4—42no—
744C4—42no—
745C4—42no—
746C4—42no—
747C4—42no—
748C4C61×#54712yes—
749C4C22×#41×C6111yescharacteristic
750C4C2×2−1+4×C6111yescharacteristic
751C2—42no—
752C2—42no—
753C2—82no—
754C2—82no—
755C2C61×#334714yesdirect product factor
756C2C2×C61×#54711yescharacteristic
757C2C2×C61×#57511yescharacteristic
758C2C2×C61×#57611yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC2×C4C25×C61
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
1. C2×C61×#555C2semidirect
2. C2×C61×#553C2semidirect
3. C61×#3347C2direct (N × H)
4. C2×C61×#501C2semidirect
5. C2×C61×#482C2semidirect
6. C2×C61×#482C2semidirect
7. C2×C61×#482C2semidirect
8. C2×C61×#480C2semidirect
9. C2×C61×#478C2semidirect
10. C2×C61×#474C2semidirect
11. C2×C61×#469C2semidirect
12. C2×C61×#466C2semidirect
13. C2×C61×#442C2semidirect
14. C2×C61×#435C2semidirect
15. C2×C61×#428C2semidirect
16. C2×C61×#427C2semidirect
21. C61×#555C22semidirect
23. C61×#553C22semidirect
45. C61×#501C22semidirect
46. C61×#482C22semidirect
47. C61×#482C22semidirect
48. C61×#482C22semidirect
49. C61×#480C22semidirect
50. C61×#478C22semidirect
51. C61×#474C22semidirect
52. C61×#469C22semidirect
53. C61×#466C22semidirect
54. C61×#442C22semidirect
55. C61×#435C22semidirect
56. C61×#428C22semidirect
57. C61×#427C22semidirect
338. C2×#3347C61direct (N × H)
372. C2×#555C2×C61semidirect
373. C2×#553C2×C61semidirect
374. #3347C2×C61direct (N × H)
375. C2×#501C2×C61semidirect
376. C2×#482C2×C61semidirect
377. C2×#482C2×C61semidirect
378. C2×#482C2×C61semidirect
379. C2×#480C2×C61semidirect
380. C2×#478C2×C61semidirect
381. C2×#474C2×C61semidirect
382. C2×#469C2×C61semidirect
383. C2×#466C2×C61semidirect
384. C2×#442C2×C61semidirect
385. C2×#435C2×C61semidirect
386. C2×#428C2×C61semidirect
387. C2×#427C2×C61semidirect
392. C2×C61#3347direct (N × H)
400. #555C22×C61semidirect
402. #553C22×C61semidirect
424. #501C22×C61semidirect
425. #482C22×C61semidirect
426. #482C22×C61semidirect
427. #482C22×C61semidirect
428. #480C22×C61semidirect
429. #478C22×C61semidirect
430. #474C22×C61semidirect
431. #469C22×C61semidirect
432. #466C22×C61semidirect
433. #442C22×C61semidirect
434. #435C22×C61semidirect
435. #428C22×C61semidirect
436. #427C22×C61semidirect
456. C61C2×#3347direct (N × H)
755. C2C61×#3347direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#5552
C2×C61×#5532
C61×#33472
C2×C61×#5012
C2×C61×#4822
C2×C61×#4802
C2×C61×#4782
C2×C61×#4742
C2×C61×#4692
C2×C61×#4662
C2×C61×#4422
C2×C61×#4352
C2×C61×#4282
C2×C61×#4272
C2×#334761