Finite Group Databasebeta

← C61×#26163 #29529596

Subgroups — C61×#26163 #29529596

Order 15616.

918 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#460C211yesmaximal, characteristic
2C2×C4×SD16×C61C211yesmaximal, characteristic, complemented
3C61×#2445C211yesmaximal, characteristic
4Q8×C4⋊C4×C61C211yesmaximal, characteristic, complemented
5C61×#2094C211yesmaximal, characteristic, complemented
6C61×#2088C211yesmaximal, characteristic, complemented
7C61×#2071C211yesmaximal, characteristic, complemented
8C61×#2041C211yesmaximal, characteristic
9C61×#1934C211yesmaximal, characteristic, complemented
10C61×#1916C211yesmaximal, characteristic, complemented
11C61×#1880C211yesmaximal, characteristic, complemented
12C61×#1880C211yesmaximal, characteristic, complemented
13C61×#1880C211yesmaximal, characteristic, complemented
14C61×#1865C211yesmaximal, characteristic, complemented
15C61×#1864C211yesmaximal, characteristic, complemented
16C22×SD16×C61C2211yescharacteristic
17C22×SD16×C61C2211yescharacteristic
18C2×#127×C61C2211yescharacteristic
19C2×#123×C61—21no—
20C2×C4×Q8×C61C2211yescharacteristic
21C2×C4×Q8×C61C2211yescharacteristic
22C2×C4×Q8×C61C2211yescharacteristic
23C2×C4×D4×C61C2211yescharacteristic
24C61×#460—24no—
25C4×SD16×C61—24no—
26C2×#106×C61C2211yescharacteristic
27C2×#106×C61C2211yescharacteristic
28C2×C4⋊C8×C61C2211yescharacteristic
29C2×#103×C61C2211yescharacteristic
30C2×#103×C61C2211yescharacteristic
31C2×#102×C61C2211yescharacteristic
32C2×#102×C61C2211yescharacteristic
33C2×#102×C61C2211yescharacteristic
34C2×#102×C61C2211yescharacteristic
35C2×#102×C61C2211yescharacteristic
36C2×#102×C61C2211yescharacteristic
37C2×C4×C8×C61C2211yescharacteristic
38C61×#394—21no—
39C61×#394—21no—
40C61×#390C2211yescharacteristic
41C61×#390C2211yescharacteristic
42C61×#390C2211yescharacteristic
43C61×#389—21no—
44C61×#389—21no—
45C61×#389C2211yescharacteristic
46C61×#389C2211yescharacteristic
47C61×#389C2211yescharacteristic
48C61×#386—21no—
49C61×#384—21no—
50C61×#384C2211yescharacteristic
51C4×C4⋊C4×C61—21no—
52C4×C4⋊C4×C61C2211yescharacteristic
53C61×#340C2211yescharacteristic
54C61×#340C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×Q8×C61C2311yescharacteristic
62C22×D4×C61—21no—
63C22×D4×C61—21no—
64C22×D4×C61C2311yescharacteristic
65C22×D4×C61C2311yescharacteristic
66C23×C4×C61—21no—
67C2×SD16×C61—22no—
68C2×SD16×C61—22no—
69C2×SD16×C61—22no—
70C2×SD16×C61—22no—
71C2×SD16×C61—22no—
72C2×SD16×C61D414yes—
73C22×C8×C61C2311yescharacteristic
74C22×C8×C61C2311yescharacteristic
75C22×C8×C61C2311yescharacteristic
76C22×C8×C61C2311yescharacteristic
77#127×C61—22no—
78#127×C61—41no—
79#123×C61—44no—
80C4×Q8×C61—22no—
81C4×Q8×C61—22no—
82C4×Q8×C61—22no—
83C4×Q8×C61—22no—
84C4×Q8×C61—41no—
85C4×Q8×C61—41no—
86C4×D4×C61—22no—
87C4×D4×C61—41no—
88C2×C4⋊C4×C61—21no—
89C2×C4⋊C4×C61—21no—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61D411yescharacteristic
97C2×C4⋊C4×C61D411yescharacteristic
98C2×C4⋊C4×C61C2311yescharacteristic
99C2×C4⋊C4×C61C2311yescharacteristic
100C2×C4⋊C4×C61C2311yescharacteristic
101C2×C4⋊C4×C61C2311yescharacteristic
102C2×C4⋊C4×C61C2311yescharacteristic
103C2×C22⋊C4×C61—21no—
104C2×C22⋊C4×C61—21no—
105C2×C22⋊C4×C61—21no—
106C2×C22⋊C4×C61—21no—
107C2×C22⋊C4×C61—21no—
108C2×C22⋊C4×C61—21no—
109C2×C22⋊C4×C61—21no—
110C2×C42×C61—21no—
111C2×C42×C61—21no—
112C2×C42×C61—21no—
113C2×C42×C61C2311yescharacteristic
114C2×C42×C61C2311yescharacteristic
115C2×C42×C61C2311yescharacteristic
116#106×C61—22no—
117#106×C61—41no—
118C4⋊C8×C61—22no—
119#103×C61—22no—
120#103×C61—22no—
121#102×C61—22no—
122#102×C61—22no—
123#102×C61—22no—
124#102×C61—22no—
125#102×C61—22no—
126#102×C61—41no—
127C4×C8×C61—22no—
128#95×C61—21no—
129#95×C61—21no—
130#95×C61—21no—
131#95×C61D411yescharacteristic
132#95×C61D411yescharacteristic
133C24×C61—21no—
134C24×C61—21no—
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×Q8×C61—21no—
138C2×Q8×C61C2×D412yes—
139C2×Q8×C61#4112yes—
140C2×Q8×C61#4112yes—
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—42no—
153C2×D4×C61—42no—
154C2×D4×C61—42no—
155C2×D4×C61—42no—
156C2×D4×C61—81no—
157C2×D4×C61—81no—
158C2×D4×C61C2×D412yes—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—42no—
166C22×C4×C61—42no—
167C22×C4×C61—81no—
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2411yescharacteristic
175SD16×C61—28no—
176SD16×C61—44no—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—21no—
184C2×C8×C61—21no—
185C2×C8×C61—21no—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61C2×D412yes—
189C4⋊C4×C61—24no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—41no—
200C4⋊C4×C61—42no—
201C4⋊C4×C61—42no—
202C4⋊C4×C61—42no—
203C4⋊C4×C61—42no—
204C4⋊C4×C61—81no—
205C4⋊C4×C61—81no—
206C4⋊C4×C61—81no—
207C4⋊C4×C61SD1614yescomplemented
208C4⋊C4×C61#4112yes—
209C22⋊C4×C61—42no—
210C22⋊C4×C61—42no—
211C22⋊C4×C61—42no—
212C22⋊C4×C61—42no—
213C22⋊C4×C61—81no—
214C22⋊C4×C61—81no—
215C22⋊C4×C61—81no—
216C42×C61—24no—
217C42×C61—21no—
218C42×C61—21no—
219C42×C61—21no—
220C42×C61—21no—
221C42×C61—21no—
222C42×C61—21no—
223C42×C61—42no—
224C42×C61—42no—
225C23×C61—22no—
226C23×C61—41no—
227C23×C61—41no—
228C23×C61—41no—
229C23×C61—41no—
230C23×C61—41no—
231C23×C61—41no—
232C23×C61—41no—
233C23×C61—41no—
234C23×C61—41no—
235C23×C61—41no—
236C23×C61—41no—
237C23×C61—41no—
238C23×C61—41no—
239C23×C61C22×D411yescharacteristic
240Q8×C61—22no—
241Q8×C61—22no—
242Q8×C61—22no—
243Q8×C61#12314yescomplemented
244D4×C61—22no—
245D4×C61—22no—
246D4×C61—41no—
247D4×C61—41no—
248D4×C61—41no—
249D4×C61—41no—
250D4×C61—41no—
251D4×C61—41no—
252D4×C61—84no—
253D4×C61—84no—
254C2×C4×C61—21no—
255C2×C4×C61—22no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—22no—
259C2×C4×C61—22no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—22no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—41no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—84no—
288C2×C4×C61C2×SD1612yes—
289C2×C4×C61C2×SD1612yes—
290C2×C4×C61C2×SD1612yes—
291C2×C4×C61C22×D411yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×C4×C61C2×#4111yescharacteristic
294C2×C4×C61C2×#4111yescharacteristic
295C2×C4×C61H(5,𝔽2)11yescharacteristic
296C2×C4×C612−1+411yescharacteristic
297C8×C61—22no—
298C8×C61—41no—
299C8×C61—41no—
300C8×C61—41no—
301#26163C6111yesmaximal, characteristic, direct product factor, Sylow
302C22×C61—42no—
303C22×C61—42no—
304C22×C61—42no—
305C22×C61—81no—
306C22×C61—81no—
307C22×C61—81no—
308C22×C61—81no—
309C22×C61—81no—
310C22×C61—81no—
311C22×C61—81no—
312C22×C61—81no—
313C22×C61—81no—
314C22×C61—81no—
315C22×C61—81no—
316C22×C61#52511yescharacteristic
317C22×C61D4211yescharacteristic
318C22×C61#54811yescharacteristic
319C22×C61C22×SD1611yescharacteristic
320C22×C61#57511yescharacteristic
321C22×C61#57611yescharacteristic
322C22×C61#57711yescharacteristic
323C4×C61—22no—
324C4×C61—24no—
325C4×C61—22no—
326C4×C61—22no—
327C4×C61—41no—
328C4×C61—42no—
329C4×C61—41no—
330C4×C61—41no—
331C4×C61—81no—
332C4×C61—81no—
333C4×C61—81no—
334C4×C61—81no—
335C4×C61C2×#12311yescharacteristic
336C4×C61#53911yescharacteristic
337C4×C61#54711yescharacteristic
338C4×C61#55311yescharacteristic
339C2×#460C2×C6111yescharacteristic
340C2×C4×SD16C2×C6111yescharacteristic, complemented
341#2445C2×C6111yescharacteristic
342Q8×C4⋊C4C2×C6111yescharacteristic, complemented
343#2094C2×C6111yescharacteristic, complemented
344#2088C2×C6111yescharacteristic, complemented
345#2071C2×C6111yescharacteristic, complemented
346#2041C2×C6111yescharacteristic
347#1934C2×C6111yescharacteristic, complemented
348#1916C2×C6111yescharacteristic, complemented
349#1880C2×C6111yescharacteristic, complemented
350#1880C2×C6111yescharacteristic, complemented
351#1880C2×C6111yescharacteristic, complemented
352#1865C2×C6111yescharacteristic, complemented
353#1864C2×C6111yescharacteristic, complemented
354C2×C61—82no—
355C2×C61—161no—
356C2×C61#244311yescharacteristic
357C2×C61#310311yescharacteristic
358C2×C61#311911yescharacteristic
359C2×C61#326811yescharacteristic
360C2×C61D4×SD1611yescharacteristic
361C2×C61#336211yescharacteristic
362C2×C61#337111yescharacteristic
363C22×SD16C22×C6111yescharacteristic
364C22×SD16C22×C6111yescharacteristic
365C2×#127C22×C6111yescharacteristic
366C2×#123—21no—
367C2×C4×Q8C22×C6111yescharacteristic
368C2×C4×Q8C22×C6111yescharacteristic
369C2×C4×Q8C22×C6111yescharacteristic
370C2×C4×D4C22×C6111yescharacteristic
371#460—24no—
372C4×SD16—24no—
373C2×#106C22×C6111yescharacteristic
374C2×#106C22×C6111yescharacteristic
375C2×C4⋊C8C22×C6111yescharacteristic
376C2×#103C22×C6111yescharacteristic
377C2×#103C22×C6111yescharacteristic
378C2×#102C22×C6111yescharacteristic
379C2×#102C22×C6111yescharacteristic
380C2×#102C22×C6111yescharacteristic
381C2×#102C22×C6111yescharacteristic
382C2×#102C22×C6111yescharacteristic
383C2×#102C22×C6111yescharacteristic
384C2×C4×C8C22×C6111yescharacteristic
385#394—21no—
386#394—21no—
387#390C22×C6111yescharacteristic
388#390C22×C6111yescharacteristic
389#390C22×C6111yescharacteristic
390#389—21no—
391#389—21no—
392#389C22×C6111yescharacteristic
393#389C22×C6111yescharacteristic
394#389C22×C6111yescharacteristic
395#386—21no—
396#384—21no—
397#384C22×C6111yescharacteristic
398C4×C4⋊C4—21no—
399C4×C4⋊C4C22×C6111yescharacteristic
400#340C22×C6111yescharacteristic
401#340C22×C6111yescharacteristic
402#340C22×C6111yescharacteristic
403#340C22×C6111yescharacteristic
404#336C22×C6111yescharacteristic
405#336C22×C6111yescharacteristic
406#336C22×C6111yescharacteristic
407#336C22×C6111yescharacteristic
408C61#2616311yescharacteristic, direct product factor, Sylow
409C22×Q8C23×C6111yescharacteristic
410C22×D4—21no—
411C22×D4—21no—
412C22×D4C23×C6111yescharacteristic
413C22×D4C23×C6111yescharacteristic
414C23×C4—21no—
415C2×SD16—22no—
416C2×SD16—22no—
417C2×SD16—22no—
418C2×SD16—22no—
419C2×SD16—22no—
420C2×SD16D4×C6114yes—
421C22×C8C23×C6111yescharacteristic
422C22×C8C23×C6111yescharacteristic
423C22×C8C23×C6111yescharacteristic
424C22×C8C23×C6111yescharacteristic
425#127—22no—
426#127—41no—
427#123—44no—
428C4×Q8—22no—
429C4×Q8—22no—
430C4×Q8—22no—
431C4×Q8—22no—
432C4×Q8—41no—
433C4×Q8—41no—
434C4×D4—22no—
435C4×D4—41no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4D4×C6111yescharacteristic
445C2×C4⋊C4D4×C6111yescharacteristic
446C2×C4⋊C4C23×C6111yescharacteristic
447C2×C4⋊C4C23×C6111yescharacteristic
448C2×C4⋊C4C23×C6111yescharacteristic
449C2×C4⋊C4C23×C6111yescharacteristic
450C2×C4⋊C4C23×C6111yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C42—21no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42C23×C6111yescharacteristic
462C2×C42C23×C6111yescharacteristic
463C2×C42C23×C6111yescharacteristic
464#106—22no—
465#106—41no—
466C4⋊C8—22no—
467#103—22no—
468#103—22no—
469#102—22no—
470#102—22no—
471#102—22no—
472#102—22no—
473#102—22no—
474#102—41no—
475C4×C8—22no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95D4×C6111yescharacteristic
480#95D4×C6111yescharacteristic
481C24—21no—
482C24—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8C2×D4×C6112yes—
487C2×Q8#41×C6112yes—
488C2×Q8#41×C6112yes—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—81no—
505C2×D4—81no—
506C2×D4C2×D4×C6112yes—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—81no—
516C22×C4C2×D4×C6111yescharacteristic
517C22×C4C2×D4×C6111yescharacteristic
518C22×C4C2×D4×C6111yescharacteristic
519C22×C4C2×D4×C6111yescharacteristic
520C22×C4C2×D4×C6111yescharacteristic
521C22×C4C2×D4×C6111yescharacteristic
522C22×C4C24×C6111yescharacteristic
523SD16—28no—
524SD16—44no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8C2×D4×C6112yes—
537C4⋊C4—24no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—41no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—81no—
553C4⋊C4—81no—
554C4⋊C4—81no—
555C4⋊C4SD16×C6114yescomplemented
556C4⋊C4#41×C6112yes—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—81no—
562C22⋊C4—81no—
563C22⋊C4—81no—
564C42—24no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—42no—
572C42—42no—
573C23—22no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23C22×D4×C6111yescharacteristic
588Q8—22no—
589Q8—22no—
590Q8—22no—
591Q8#123×C6114yescomplemented
592D4—22no—
593D4—22no—
594D4—41no—
595D4—41no—
596D4—41no—
597D4—41no—
598D4—41no—
599D4—41no—
600D4—84no—
601D4—84no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—84no—
636C2×C4C2×SD16×C6112yes—
637C2×C4C2×SD16×C6112yes—
638C2×C4C2×SD16×C6112yes—
639C2×C4C22×D4×C6111yescharacteristic
640C2×C4C2×#41×C6111yescharacteristic
641C2×C4C2×#41×C6111yescharacteristic
642C2×C4C2×#41×C6111yescharacteristic
643C2×C4H(5,𝔽2)×C6111yescharacteristic
644C2×C42−1+4×C6111yescharacteristic
645C8—22no—
646C8—41no—
647C8—41no—
648C8—41no—
649C22—42no—
650C22—42no—
651C22—42no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22—81no—
663C22C61×#52511yescharacteristic
664C22D42×C6111yescharacteristic
665C22C61×#54811yescharacteristic
666C22C22×SD16×C6111yescharacteristic
667C22C61×#57511yescharacteristic
668C22C61×#57611yescharacteristic
669C22C61×#57711yescharacteristic
670C4—22no—
671C4—24no—
672C4—22no—
673C4—22no—
674C4—41no—
675C4—42no—
676C4—41no—
677C4—41no—
678C4—81no—
679C4—81no—
680C4—81no—
681C4—81no—
682C4C2×#123×C6111yescharacteristic
683C4C61×#53911yescharacteristic
684C4C61×#54711yescharacteristic
685C4C61×#55311yescharacteristic
686C2—82no—
687C2—161no—
688C2C61×#244311yescharacteristic
689C2C61×#310311yescharacteristic
690C2C61×#311911yescharacteristic
691C2C61×#326811yescharacteristic
692C2D4×SD16×C6111yescharacteristic
693C2C61×#336211yescharacteristic
694C2C61×#337111yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×#127×C61C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C4×C4⋊C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×SD16×C61C2semidirect
4. Q8×C4⋊C4×C61C2semidirect
5. C61×#2094C2semidirect
6. C61×#2088C2semidirect
7. C61×#2071C2semidirect
9. C61×#1934C2semidirect
10. C61×#1916C2semidirect
11. C61×#1880C2semidirect
12. C61×#1880C2semidirect
13. C61×#1880C2semidirect
14. C61×#1865C2semidirect
15. C61×#1864C2semidirect
207. C4⋊C4×C61SD16semidirect
243. Q8×C61#123semidirect
301. #26163C61direct (N × H)
340. C2×C4×SD16C2×C61semidirect
342. Q8×C4⋊C4C2×C61semidirect
343. #2094C2×C61semidirect
344. #2088C2×C61semidirect
345. #2071C2×C61semidirect
347. #1934C2×C61semidirect
348. #1916C2×C61semidirect
349. #1880C2×C61semidirect
350. #1880C2×C61semidirect
351. #1880C2×C61semidirect
352. #1865C2×C61semidirect
353. #1864C2×C61semidirect
408. C61#26163direct (N × H)
555. C4⋊C4SD16×C61semidirect
591. Q8#123×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4602
C2×C4×SD16×C612
C61×#24452
Q8×C4⋊C4×C612
C61×#20942
C61×#20882
C61×#20712
C61×#20412
C61×#19342
C61×#19162
C61×#18802
C61×#18652
C61×#18642
#2616361