Finite Group Databasebeta

← C61×#22889 #29526322

Subgroups — C61×#22889 #29526322

Order 15616.

1020 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×#3002C211yesmaximal, characteristic
2C2×C61×#443C211yesmaximal, characteristic, complemented
3C61×#2933C211yesmaximal, characteristic, complemented
4C2×C61×#421C211yesmaximal, characteristic, complemented
5C61×#2880C211yesmaximal, characteristic, complemented
6C61×#1975C211yesmaximal, characteristic, complemented
7C61×#1937C211yesmaximal, characteristic, complemented
8C61×#1929C211yesmaximal, characteristic, complemented
9C61×#1897C211yesmaximal, characteristic, complemented
10C61×#1876C211yesmaximal, characteristic, complemented
11C61×#1876C211yesmaximal, characteristic, complemented
12C61×#1866C211yesmaximal, characteristic, complemented
13C61×#1855C211yesmaximal, characteristic, complemented
14C61×#1765C211yesmaximal, characteristic, complemented
15C61×#1750C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C2×#135×C61C2211yescharacteristic
18C2×#135×C61C2211yescharacteristic
19C2×#131×C61C2211yescharacteristic
20C2×#131×C61C2211yescharacteristic
21C2×#131×C61C2211yescharacteristic, complemented
22C22×M16×C61C2211yescharacteristic
23C61×#525C2211yescharacteristic
24C2×#117×C61C2211yescharacteristic
25C61×#452C411yescharacteristic, complemented
26C61×#452C411yescharacteristic, complemented
27C61×#451C411yescharacteristic, complemented
28C61×#450C411yescharacteristic, complemented
29C61×#449C411yescharacteristic, complemented
30C61×#449C411yescharacteristic, complemented
31C61×#448C411yescharacteristic, complemented
32C61×#447C411yescharacteristic, complemented
33C61×#443—24no—
34C61×#436—21no—
35C61×#435—21no—
36C61×#435—21no—
37C8×D4×C61—21no—
38C2×#108×C61C2211yescharacteristic, complemented
39C2×#108×C61C2211yescharacteristic, complemented
40C61×#424C2211yescharacteristic, complemented
41C61×#421—24no—
42C2×#104×C61C2211yescharacteristic
43C2×#104×C61C2211yescharacteristic
44C2×#104×C61C2211yescharacteristic
45C2×#104×C61C2211yescharacteristic
46C2×#104×C61C2211yescharacteristic, complemented
47C2×#104×C61C2211yescharacteristic, complemented
48C61×#416C2211yescharacteristic
49C61×#416C2211yescharacteristic
50C61×#408—21no—
51C61×#408—21no—
52C61×#408C2211yescharacteristic
53C61×#408C2211yescharacteristic
54C61×#408C2211yescharacteristic, complemented
55C61×#407—21no—
56C61×#407C2211yescharacteristic
57C2×C22⋊C8×C61—21no—
58C2×C22⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C61×#405C2211yescharacteristic, complemented
61C2×#97×C61C2211yescharacteristic, complemented
62C2×C4×C8×C61C2211yescharacteristic, complemented
63C61×#341C2211yescharacteristic, complemented
64C61×#341C2211yescharacteristic, complemented
65C61×#339C2211yescharacteristic, complemented
66C61×#339C2211yescharacteristic, complemented
67C61×#336C2211yescharacteristic, complemented
68C61×#336C2211yescharacteristic, complemented
69C2×#41×C61—21no—
70C2×#41×C61—21no—
71C2×#41×C61—22no—
72C2×#41×C61—22no—
73C2×#41×C61—41no—
74C2×#41×C61—41no—
75C2×#41×C61C2×C411yescharacteristic
76C2×#41×C61C2×C411yescharacteristic
77C2×#41×C61C2311yescharacteristic
78C2×#41×C61C2311yescharacteristic
79C2×#41×C61C2311yescharacteristic
80C22×Q8×C61C2×C411yescharacteristic
81C22×D4×C61—21no—
82C22×D4×C61C2×C411yescharacteristic
83C23×C4×C61—21no—
84C23×C4×C61C2311yescharacteristic
85#135×C61—22no—
86#135×C61—22no—
87#135×C61—41no—
88#135×C61—41no—
89C2×Q16×C61C2×C411yescharacteristic
90C2×Q16×C61C2×C411yescharacteristic
91C2×SD16×C61C2×C411yescharacteristic
92C2×SD16×C61C2×C411yescharacteristic
93C2×SD16×C61C2×C411yescharacteristic
94C2×SD16×C61C2×C411yescharacteristic
95C2×D8×C61C2×C411yescharacteristic
96C2×D8×C61C2×C411yescharacteristic
97#131×C61—22no—
98#131×C61—22no—
99#131×C61—22no—
100#131×C61—41no—
101#131×C61—41no—
102#131×C61—41no—
103C2×M16×C61—21no—
104C2×M16×C61—21no—
105C2×M16×C61—21no—
106C2×M16×C61—21no—
107C2×M16×C61—22no—
108C2×M16×C61—41no—
109C2×M16×C61C2311yescharacteristic
110C2×M16×C61C2311yescharacteristic
111C2×M16×C61C2311yescharacteristic
112C2×M16×C61C2311yescharacteristic
113C22×C8×C61—21no—
114C22×C8×C61—21no—
115C22×C8×C61—21no—
116C22×C8×C61—21no—
117C22×C8×C61C2311yescharacteristic
118C22×C8×C61C2311yescharacteristic
119C22×C8×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121#123×C61—21no—
122C22⋊Q8×C61C2×C411yescharacteristic
123C22⋊Q8×C61C2×C411yescharacteristic
124#121×C61C2×C411yescharacteristic
125#121×C61C2×C411yescharacteristic
126#120×C61—21no—
127C4×D4×C61—21no—
128C4×D4×C61—21no—
129#117×C61—22no—
130#117×C61—41no—
131#117×C61C2311yescharacteristic
132C2×C4⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C42×C61C2311yescharacteristic
135C2×C42×C61C2311yescharacteristic
136#108×C61—22no—
137#108×C61—41no—
138C4⋊C8×C61—21no—
139C4⋊C8×C61—21no—
140#104×C61—22no—
141#104×C61—22no—
142#104×C61—22no—
143#104×C61—22no—
144#104×C61—41no—
145#104×C61D414yescomplemented
146#103×C61C2×C411yescharacteristic
147#103×C61C2×C411yescharacteristic
148#103×C61C2×C411yescharacteristic
149#103×C61C2×C411yescharacteristic
150#102×C61C2×C411yescharacteristic
151#102×C61C2×C411yescharacteristic
152#102×C61C2×C411yescharacteristic
153#102×C61C2×C411yescharacteristic
154C22⋊C8×C61—21no—
155C22⋊C8×C61—21no—
156C22⋊C8×C61—21no—
157C22⋊C8×C61—21no—
158C22⋊C8×C61—21no—
159C22⋊C8×C61—21no—
160C22⋊C8×C61—21no—
161C22⋊C8×C61—21no—
162C22⋊C8×C61C2×C411yescharacteristic
163C22⋊C8×C61C2×C411yescharacteristic
164C22⋊C8×C61C2×C411yescharacteristic
165C22⋊C8×C61C2×C411yescharacteristic
166C22⋊C8×C61D411yescharacteristic
167C22⋊C8×C61D411yescharacteristic
168C22⋊C8×C61D411yescharacteristic
169C22⋊C8×C61D411yescharacteristic
170#97×C61—21no—
171#97×C61—41no—
172C4×C8×C61—21no—
173C4×C8×C61—22no—
174C24×C61—21no—
175C24×C61#4111yescharacteristic
176#41×C61—21no—
177#41×C61—21no—
178#41×C61—22no—
179#41×C61—22no—
180#41×C61—21no—
181#41×C61—21no—
182#41×C61—21no—
183#41×C61—21no—
184#41×C61—21no—
185#41×C61—21no—
186#41×C61—21no—
187#41×C61—21no—
188#41×C61—42no—
189#41×C61—42no—
190#41×C61—41no—
191#41×C61—41no—
192#41×C61—42no—
193#41×C61—42no—
194#41×C61C2×D412yes—
195#41×C61#4112yes—
196C2×Q8×C61—21no—
197C2×Q8×C61—22no—
198C2×Q8×C61—41no—
199C2×Q8×C61C22×C411yescharacteristic
200C2×Q8×C61C22×C411yescharacteristic
201C2×Q8×C61C22×C411yescharacteristic
202C2×D4×C61—21no—
203C2×D4×C61—22no—
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61—21no—
208C2×D4×C61—21no—
209C2×D4×C61—21no—
210C2×D4×C61—21no—
211C2×D4×C61—41no—
212C2×D4×C61—42no—
213C2×D4×C61—42no—
214C2×D4×C61C22×C411yescharacteristic
215C2×D4×C61C22×C411yescharacteristic
216C2×D4×C61C22×C411yescharacteristic
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—42no—
230C22×C4×C61—42no—
231C22×C4×C61C22×C411yescharacteristic
232C22×C4×C61C22×C411yescharacteristic
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2×D411yescharacteristic
235C22×C4×C61#4111yescharacteristic
236C22×C4×C61C2411yescharacteristic
237Q16×C61—22no—
238Q16×C61—41no—
239SD16×C61—22no—
240SD16×C61—22no—
241SD16×C61—41no—
242SD16×C61—41no—
243D8×C61—22no—
244D8×C61—41no—
245M16×C61—21no—
246M16×C61—21no—
247M16×C61—21no—
248M16×C61—21no—
249M16×C61—21no—
250M16×C61—21no—
251M16×C61—21no—
252M16×C61—42no—
253M16×C61—42no—
254M16×C61—42no—
255M16×C61—42no—
256M16×C61C2×D412yes—
257C2×C8×C61—21no—
258C2×C8×C61—21no—
259C2×C8×C61—21no—
260C2×C8×C61—21no—
261C2×C8×C61—21no—
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C2×C8×C61—21no—
267C2×C8×C61—21no—
268C2×C8×C61—21no—
269C2×C8×C61—42no—
270C2×C8×C61—42no—
271C2×C8×C61—42no—
272C2×C8×C61—42no—
273C2×C8×C61C22×C411yescharacteristic
274C2×C8×C61C22×C411yescharacteristic
275C2×C8×C61C22×C411yescharacteristic
276C2×C8×C61C22×C411yescharacteristic
277C2×C8×C61C2×D411yescharacteristic
278C2×C8×C61C2×D411yescharacteristic
279C2×C8×C61C2×D411yescharacteristic
280C2×C8×C61C2×D411yescharacteristic
281C4⋊C4×C61—21no—
282C4⋊C4×C61—21no—
283C4⋊C4×C61—42no—
284C4⋊C4×C61C22×C411yescharacteristic
285C4⋊C4×C61C22×C411yescharacteristic
286C22⋊C4×C61—21no—
287C22⋊C4×C61—21no—
288C22⋊C4×C61—21no—
289C22⋊C4×C61—21no—
290C22⋊C4×C61—21no—
291C22⋊C4×C61—42no—
292C42×C61—21no—
293C42×C61—21no—
294C42×C61—21no—
295C42×C61—21no—
296C42×C61C2×D412yes—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—42no—
305C23×C61—42no—
306C23×C61—81no—
307C23×C61C4×D411yescharacteristic
308C23×C61C4×D411yescharacteristic
309C23×C61C2×#4111yescharacteristic
310Q8×C61—21no—
311Q8×C61—21no—
312Q8×C61—21no—
313Q8×C61—21no—
314Q8×C61—21no—
315Q8×C61—42no—
316Q8×C61C4×D412yes—
317D4×C61—22no—
318D4×C61—22no—
319D4×C61—21no—
320D4×C61—21no—
321D4×C61—21no—
322D4×C61—21no—
323D4×C61—21no—
324D4×C61—42no—
325D4×C61—42no—
326D4×C61—42no—
327D4×C61—42no—
328D4×C61—41no—
329D4×C61—41no—
330D4×C61—41no—
331D4×C61—41no—
332D4×C61—81no—
333D4×C61C4×D412yes—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—22no—
343C2×C4×C61—21no—
344C2×C4×C61—22no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—22no—
352C2×C4×C61—42no—
353C2×C4×C61—42no—
354C2×C4×C61—42no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61C4×D411yescharacteristic
365C2×C4×C61C4×D411yescharacteristic
366C2×C4×C61C23×C411yescharacteristic
367C2×C4×C61C22×D411yescharacteristic
368C2×C4×C61C22×D411yescharacteristic
369C2×C4×C61C2×#4111yescharacteristic
370C2×C4×C61H(5,𝔽2)11yescharacteristic
371C2×C4×C61H(5,𝔽2)11yescharacteristic
372C8×C61—21no—
373C8×C61—21no—
374C8×C61—21no—
375C8×C61—21no—
376C8×C61—21no—
377C8×C61—21no—
378C8×C61—22no—
379C8×C61—21no—
380C8×C61—21no—
381C8×C61—41no—
382C8×C61—41no—
383C8×C61—41no—
384#22889C6111yesmaximal, characteristic, direct product factor, Sylow
385C22×C61—21no—
386C22×C61—21no—
387C22×C61—21no—
388C22×C61—21no—
389C22×C61—22no—
390C22×C61—21no—
391C22×C61—21no—
392C22×C61—21no—
393C22×C61—21no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—41no—
397C22×C61—41no—
398C22×C61—41no—
399C22×C61—41no—
400C22×C61—41no—
401C22×C61—41no—
402C22×C61—81no—
403C22×C61—81no—
404C22×C61—84no—
405C22×C61C2×C4×D411yescharacteristic
406C22×C61#54611yescharacteristic
407C22×C61#55111yescharacteristic
408C4×C61—21no—
409C4×C61—21no—
410C4×C61—22no—
411C4×C61—42no—
412C4×C61—41no—
413C4×C61—41no—
414C4×C61—41no—
415C4×C61—41no—
416C4×C61—81no—
417C4×C61C2×C4×D411yescharacteristic
418C4×C61#51811yescharacteristic
419C4×C61D4211yescharacteristic
420C4×C61#54611yescharacteristic
421#3002C2×C6111yescharacteristic
422C2×#443C2×C6111yescharacteristic, complemented
423#2933C2×C6111yescharacteristic, complemented
424C2×#421C2×C6111yescharacteristic, complemented
425#2880C2×C6111yescharacteristic, complemented
426#1975C2×C6111yescharacteristic, complemented
427#1937C2×C6111yescharacteristic, complemented
428#1929C2×C6111yescharacteristic, complemented
429#1897C2×C6111yescharacteristic, complemented
430#1876C2×C6111yescharacteristic, complemented
431#1876C2×C6111yescharacteristic, complemented
432#1866C2×C6111yescharacteristic, complemented
433#1855C2×C6111yescharacteristic, complemented
434#1765C2×C6111yescharacteristic, complemented
435#1750C2×C6111yescharacteristic, complemented
436C2×C61—21no—
437C2×C61—21no—
438C2×C61—41no—
439C2×C61—41no—
440C2×C61—42no—
441C2×C61—81no—
442C2×C61—81no—
443C2×C61#235811yescharacteristic
444C2×C61#295511yescharacteristic
445C2×C61#295711yescharacteristic
446C22×#41C22×C6111yescharacteristic
447C2×#135C22×C6111yescharacteristic
448C2×#135C22×C6111yescharacteristic
449C2×#131C22×C6111yescharacteristic
450C2×#131C22×C6111yescharacteristic
451C2×#131C22×C6111yescharacteristic, complemented
452C22×M16C22×C6111yescharacteristic
453#525C22×C6111yescharacteristic
454C2×#117C22×C6111yescharacteristic
455#452C4×C6111yescharacteristic, complemented
456#452C4×C6111yescharacteristic, complemented
457#451C4×C6111yescharacteristic, complemented
458#450C4×C6111yescharacteristic, complemented
459#449C4×C6111yescharacteristic, complemented
460#449C4×C6111yescharacteristic, complemented
461#448C4×C6111yescharacteristic, complemented
462#447C4×C6111yescharacteristic, complemented
463#443—24no—
464#436—21no—
465#435—21no—
466#435—21no—
467C8×D4—21no—
468C2×#108C22×C6111yescharacteristic, complemented
469C2×#108C22×C6111yescharacteristic, complemented
470#424C22×C6111yescharacteristic, complemented
471#421—24no—
472C2×#104C22×C6111yescharacteristic
473C2×#104C22×C6111yescharacteristic
474C2×#104C22×C6111yescharacteristic
475C2×#104C22×C6111yescharacteristic
476C2×#104C22×C6111yescharacteristic, complemented
477C2×#104C22×C6111yescharacteristic, complemented
478#416C22×C6111yescharacteristic
479#416C22×C6111yescharacteristic
480#408—21no—
481#408—21no—
482#408C22×C6111yescharacteristic
483#408C22×C6111yescharacteristic
484#408C22×C6111yescharacteristic, complemented
485#407—21no—
486#407C22×C6111yescharacteristic
487C2×C22⋊C8—21no—
488C2×C22⋊C8C22×C6111yescharacteristic
489C2×C22⋊C8C22×C6111yescharacteristic
490#405C22×C6111yescharacteristic, complemented
491C2×#97C22×C6111yescharacteristic, complemented
492C2×C4×C8C22×C6111yescharacteristic, complemented
493#341C22×C6111yescharacteristic, complemented
494#341C22×C6111yescharacteristic, complemented
495#339C22×C6111yescharacteristic, complemented
496#339C22×C6111yescharacteristic, complemented
497#336C22×C6111yescharacteristic, complemented
498#336C22×C6111yescharacteristic, complemented
499C61#2288911yescharacteristic, direct product factor, Sylow
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41C2×C4×C6111yescharacteristic
507C2×#41C2×C4×C6111yescharacteristic
508C2×#41C23×C6111yescharacteristic
509C2×#41C23×C6111yescharacteristic
510C2×#41C23×C6111yescharacteristic
511C22×Q8C2×C4×C6111yescharacteristic
512C22×D4—21no—
513C22×D4C2×C4×C6111yescharacteristic
514C23×C4—21no—
515C23×C4C23×C6111yescharacteristic
516#135—22no—
517#135—22no—
518#135—41no—
519#135—41no—
520C2×Q16C2×C4×C6111yescharacteristic
521C2×Q16C2×C4×C6111yescharacteristic
522C2×SD16C2×C4×C6111yescharacteristic
523C2×SD16C2×C4×C6111yescharacteristic
524C2×SD16C2×C4×C6111yescharacteristic
525C2×SD16C2×C4×C6111yescharacteristic
526C2×D8C2×C4×C6111yescharacteristic
527C2×D8C2×C4×C6111yescharacteristic
528#131—22no—
529#131—22no—
530#131—22no—
531#131—41no—
532#131—41no—
533#131—41no—
534C2×M16—21no—
535C2×M16—21no—
536C2×M16—21no—
537C2×M16—21no—
538C2×M16—22no—
539C2×M16—41no—
540C2×M16C23×C6111yescharacteristic
541C2×M16C23×C6111yescharacteristic
542C2×M16C23×C6111yescharacteristic
543C2×M16C23×C6111yescharacteristic
544C22×C8—21no—
545C22×C8—21no—
546C22×C8—21no—
547C22×C8—21no—
548C22×C8C23×C6111yescharacteristic
549C22×C8C23×C6111yescharacteristic
550C22×C8C23×C6111yescharacteristic
551C22×C8C23×C6111yescharacteristic
552#123—21no—
553C22⋊Q8C2×C4×C6111yescharacteristic
554C22⋊Q8C2×C4×C6111yescharacteristic
555#121C2×C4×C6111yescharacteristic
556#121C2×C4×C6111yescharacteristic
557#120—21no—
558C4×D4—21no—
559C4×D4—21no—
560#117—22no—
561#117—41no—
562#117C23×C6111yescharacteristic
563C2×C4⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C42C23×C6111yescharacteristic
566C2×C42C23×C6111yescharacteristic
567#108—22no—
568#108—41no—
569C4⋊C8—21no—
570C4⋊C8—21no—
571#104—22no—
572#104—22no—
573#104—22no—
574#104—22no—
575#104—41no—
576#104D4×C6114yescomplemented
577#103C2×C4×C6111yescharacteristic
578#103C2×C4×C6111yescharacteristic
579#103C2×C4×C6111yescharacteristic
580#103C2×C4×C6111yescharacteristic
581#102C2×C4×C6111yescharacteristic
582#102C2×C4×C6111yescharacteristic
583#102C2×C4×C6111yescharacteristic
584#102C2×C4×C6111yescharacteristic
585C22⋊C8—21no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—21no—
592C22⋊C8—21no—
593C22⋊C8C2×C4×C6111yescharacteristic
594C22⋊C8C2×C4×C6111yescharacteristic
595C22⋊C8C2×C4×C6111yescharacteristic
596C22⋊C8C2×C4×C6111yescharacteristic
597C22⋊C8D4×C6111yescharacteristic
598C22⋊C8D4×C6111yescharacteristic
599C22⋊C8D4×C6111yescharacteristic
600C22⋊C8D4×C6111yescharacteristic
601#97—21no—
602#97—41no—
603C4×C8—21no—
604C4×C8—22no—
605C24—21no—
606C24#41×C6111yescharacteristic
607#41—21no—
608#41—21no—
609#41—22no—
610#41—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—42no—
620#41—42no—
621#41—41no—
622#41—41no—
623#41—42no—
624#41—42no—
625#41C2×D4×C6112yes—
626#41#41×C6112yes—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—41no—
630C2×Q8C22×C4×C6111yescharacteristic
631C2×Q8C22×C4×C6111yescharacteristic
632C2×Q8C22×C4×C6111yescharacteristic
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4C22×C4×C6111yescharacteristic
646C2×D4C22×C4×C6111yescharacteristic
647C2×D4C22×C4×C6111yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4C22×C4×C6111yescharacteristic
663C22×C4C22×C4×C6111yescharacteristic
664C22×C4C2×D4×C6111yescharacteristic
665C22×C4C2×D4×C6111yescharacteristic
666C22×C4#41×C6111yescharacteristic
667C22×C4C24×C6111yescharacteristic
668Q16—22no—
669Q16—41no—
670SD16—22no—
671SD16—22no—
672SD16—41no—
673SD16—41no—
674D8—22no—
675D8—41no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—42no—
684M16—42no—
685M16—42no—
686M16—42no—
687M16C2×D4×C6112yes—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8—42no—
703C2×C8—42no—
704C2×C8C22×C4×C6111yescharacteristic
705C2×C8C22×C4×C6111yescharacteristic
706C2×C8C22×C4×C6111yescharacteristic
707C2×C8C22×C4×C6111yescharacteristic
708C2×C8C2×D4×C6111yescharacteristic
709C2×C8C2×D4×C6111yescharacteristic
710C2×C8C2×D4×C6111yescharacteristic
711C2×C8C2×D4×C6111yescharacteristic
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—42no—
715C4⋊C4C22×C4×C6111yescharacteristic
716C4⋊C4C22×C4×C6111yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—42no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42C2×D4×C6112yes—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—81no—
738C23C4×D4×C6111yescharacteristic
739C23C4×D4×C6111yescharacteristic
740C23C2×#41×C6111yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—21no—
745Q8—21no—
746Q8—42no—
747Q8C4×D4×C6112yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—81no—
764D4C4×D4×C6112yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4C4×D4×C6111yescharacteristic
796C2×C4C4×D4×C6111yescharacteristic
797C2×C4C23×C4×C6111yescharacteristic
798C2×C4C22×D4×C6111yescharacteristic
799C2×C4C22×D4×C6111yescharacteristic
800C2×C4C2×#41×C6111yescharacteristic
801C2×C4H(5,𝔽2)×C6111yescharacteristic
802C2×C4H(5,𝔽2)×C6111yescharacteristic
803C8—21no—
804C8—21no—
805C8—22no—
806C8—21no—
807C8—21no—
808C8—21no—
809C8—21no—
810C8—21no—
811C8—21no—
812C8—41no—
813C8—41no—
814C8—41no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—81no—
833C22—81no—
834C22—84no—
835C22C2×C4×D4×C6111yescharacteristic
836C22C61×#54611yescharacteristic
837C22C61×#55111yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—42no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—81no—
847C4C2×C4×D4×C6111yescharacteristic
848C4C61×#51811yescharacteristic
849C4D42×C6111yescharacteristic
850C4C61×#54611yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—81no—
858C2C61×#235811yescharacteristic
859C2C61×#295511yescharacteristic
860C2C61×#295711yescharacteristic
subgroupG/H
centerC2×C4×C61C22×D4
commutatorC2×C4C23×C4×C61
Frattini, cosocleC22×C4C24×C61
socleC22×C61C2×C4×D4
prime radicalC61×#3002C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C61 ◁ C2×C22⋊C8×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C61×#443C2semidirect
3. C61×#2933C2semidirect
4. C2×C61×#421C2semidirect
5. C61×#2880C2semidirect
6. C61×#1975C2semidirect
7. C61×#1937C2semidirect
8. C61×#1929C2semidirect
9. C61×#1897C2semidirect
10. C61×#1876C2semidirect
11. C61×#1876C2semidirect
12. C61×#1866C2semidirect
13. C61×#1855C2semidirect
14. C61×#1765C2semidirect
15. C61×#1750C2semidirect
21. C2×#131×C61C22semidirect
25. C61×#452C4semidirect
26. C61×#452C4semidirect
27. C61×#451C4semidirect
28. C61×#450C4semidirect
29. C61×#449C4semidirect
30. C61×#449C4semidirect
31. C61×#448C4semidirect
32. C61×#447C4semidirect
38. C2×#108×C61C22semidirect
39. C2×#108×C61C22semidirect
40. C61×#424C22semidirect
46. C2×#104×C61C22semidirect
47. C2×#104×C61C22semidirect
54. C61×#408C22semidirect
60. C61×#405C22semidirect
61. C2×#97×C61C22semidirect
62. C2×C4×C8×C61C22semidirect
63. C61×#341C22semidirect
64. C61×#341C22semidirect
65. C61×#339C22semidirect
66. C61×#339C22semidirect
67. C61×#336C22semidirect
68. C61×#336C22semidirect
145. #104×C61D4semidirect
384. #22889C61direct (N × H)
422. C2×#443C2×C61semidirect
423. #2933C2×C61semidirect
424. C2×#421C2×C61semidirect
425. #2880C2×C61semidirect
426. #1975C2×C61semidirect
427. #1937C2×C61semidirect
428. #1929C2×C61semidirect
429. #1897C2×C61semidirect
430. #1876C2×C61semidirect
431. #1876C2×C61semidirect
432. #1866C2×C61semidirect
433. #1855C2×C61semidirect
434. #1765C2×C61semidirect
435. #1750C2×C61semidirect
451. C2×#131C22×C61semidirect
455. #452C4×C61semidirect
456. #452C4×C61semidirect
457. #451C4×C61semidirect
458. #450C4×C61semidirect
459. #449C4×C61semidirect
460. #449C4×C61semidirect
461. #448C4×C61semidirect
462. #447C4×C61semidirect
468. C2×#108C22×C61semidirect
469. C2×#108C22×C61semidirect
470. #424C22×C61semidirect
476. C2×#104C22×C61semidirect
477. C2×#104C22×C61semidirect
484. #408C22×C61semidirect
490. #405C22×C61semidirect
491. C2×#97C22×C61semidirect
492. C2×C4×C8C22×C61semidirect
493. #341C22×C61semidirect
494. #341C22×C61semidirect
495. #339C22×C61semidirect
496. #339C22×C61semidirect
497. #336C22×C61semidirect
498. #336C22×C61semidirect
499. C61#22889direct (N × H)
576. #104D4×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#30022
C2×C61×#4432
C61×#29332
C2×C61×#4212
C61×#28802
C61×#19752
C61×#19372
C61×#19292
C61×#18972
C61×#18762
C61×#18662
C61×#18552
C61×#17652
C61×#17502
#2288961