Finite Group Databasebeta

← C61×#22062 #29525495

Subgroups — C61×#22062 #29525495

Order 15616.

900 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3002C211yesmaximal, characteristic
2C61×#2930C211yesmaximal, characteristic, complemented
3C61×#2879C211yesmaximal, characteristic, complemented
4C61×#1975C211yesmaximal, characteristic, complemented
5C61×#1974C211yesmaximal, characteristic, complemented
6C61×#1938C211yesmaximal, characteristic, complemented
7C61×#1937C211yesmaximal, characteristic, complemented
8C61×#1929C211yesmaximal, characteristic, complemented
9C61×#1929C211yesmaximal, characteristic, complemented
10C61×#1876C211yesmaximal, characteristic, complemented
11C61×#1876C211yesmaximal, characteristic, complemented
12C61×#1871C211yesmaximal, characteristic, complemented
13C61×#1855C211yesmaximal, characteristic, complemented
14C61×#1789C211yesmaximal, characteristic, complemented
15C61×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C2×#135×C61C2211yescharacteristic
18C2×#135×C61C2211yescharacteristic
19C2×#131×C61C2211yescharacteristic, complemented
20C22×M16×C61C2211yescharacteristic
21C22×M16×C61C2211yescharacteristic
22C61×#525C2211yescharacteristic
23C61×#452C411yescharacteristic, complemented
24C61×#452C411yescharacteristic, complemented
25C61×#451C411yescharacteristic, complemented
26C61×#450C411yescharacteristic, complemented
27C61×#449C411yescharacteristic, complemented
28C61×#449C411yescharacteristic, complemented
29C61×#448C411yescharacteristic, complemented
30C61×#447C411yescharacteristic, complemented
31C61×#436—21no—
32C61×#436—21no—
33C61×#435—21no—
34C61×#435—21no—
35C2×#108×C61C2211yescharacteristic, complemented
36C2×#108×C61C2211yescharacteristic, complemented
37C61×#424C2211yescharacteristic, complemented
38C2×#104×C61C2211yescharacteristic
39C2×#104×C61C2211yescharacteristic
40C2×#104×C61C2211yescharacteristic
41C2×#104×C61C2211yescharacteristic
42C2×#104×C61C2211yescharacteristic, complemented
43C2×#104×C61C2211yescharacteristic, complemented
44C61×#416C2211yescharacteristic
45C61×#416C2211yescharacteristic
46C61×#408—21no—
47C61×#408—21no—
48C61×#408C2211yescharacteristic
49C61×#408C2211yescharacteristic
50C61×#408C2211yescharacteristic
51C61×#408C2211yescharacteristic
52C61×#408C2211yescharacteristic, complemented
53C61×#407—21no—
54C61×#407—21no—
55C61×#407C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C61×#405C2211yescharacteristic, complemented
58C2×#97×C61C2211yescharacteristic, complemented
59C2×C4×C8×C61C2211yescharacteristic, complemented
60C4×C22⋊C4×C61C2211yescharacteristic
61C61×#341C2211yescharacteristic, complemented
62C61×#341C2211yescharacteristic, complemented
63C61×#339C2211yescharacteristic, complemented
64C61×#339C2211yescharacteristic, complemented
65C61×#336C2211yescharacteristic, complemented
66C61×#336C2211yescharacteristic, complemented
67C2×#41×C61—21no—
68C2×#41×C61—21no—
69C2×#41×C61—41no—
70C2×#41×C61—41no—
71C2×#41×C61—41no—
72C2×#41×C61—41no—
73C2×#41×C61C2×C411yescharacteristic
74C2×#41×C61C2×C411yescharacteristic
75C2×#41×C61C2311yescharacteristic
76C2×#41×C61C2311yescharacteristic
77C2×#41×C61C2311yescharacteristic
78C22×Q8×C61C2×C411yescharacteristic
79C22×D4×C61—21no—
80C22×D4×C61C2×C411yescharacteristic
81C23×C4×C61—21no—
82C23×C4×C61C2311yescharacteristic
83#135×C61—41no—
84#135×C61—41no—
85#135×C61—41no—
86#135×C61—41no—
87C2×Q16×C61C2×C411yescharacteristic
88C2×Q16×C61C2×C411yescharacteristic
89C2×SD16×C61C2×C411yescharacteristic
90C2×SD16×C61C2×C411yescharacteristic
91C2×SD16×C61C2×C411yescharacteristic
92C2×SD16×C61C2×C411yescharacteristic
93C2×D8×C61C2×C411yescharacteristic
94C2×D8×C61C2×C411yescharacteristic
95#131×C61—41no—
96#131×C61—41no—
97C2×M16×C61—21no—
98C2×M16×C61—21no—
99C2×M16×C61—41no—
100C2×M16×C61—41no—
101C2×M16×C61—41no—
102C2×M16×C61—41no—
103C2×M16×C61D411yescharacteristic
104C2×M16×C61D411yescharacteristic
105C2×M16×C61D411yescharacteristic
106C2×M16×C61D411yescharacteristic
107C2×M16×C61C2311yescharacteristic
108C2×M16×C61C2311yescharacteristic
109C2×M16×C61C2311yescharacteristic
110C2×M16×C61C2311yescharacteristic
111C22×C8×C61—21no—
112C22×C8×C61—21no—
113C22×C8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C22×C8×C61C2311yescharacteristic
116C22×C8×C61C2311yescharacteristic
117#123×C61—21no—
118C22⋊Q8×C61C2×C411yescharacteristic
119C22⋊Q8×C61C2×C411yescharacteristic
120#121×C61C2×C411yescharacteristic
121#121×C61C2×C411yescharacteristic
122#120×C61—21no—
123C4×D4×C61—21no—
124C4×D4×C61—21no—
125#117×C61C2311yescharacteristic
126C2×C22⋊C4×C61—21no—
127C2×C42×C61C2311yescharacteristic
128C2×C42×C61C2311yescharacteristic
129#108×C61—41no—
130#108×C61—41no—
131C4⋊C8×C61—21no—
132C4⋊C8×C61—21no—
133#104×C61—41no—
134#104×C61—41no—
135#104×C61—41no—
136#104×C61—41no—
137#104×C61—41no—
138#104×C61—41no—
139#103×C61C2×C411yescharacteristic
140#103×C61C2×C411yescharacteristic
141#103×C61C2×C411yescharacteristic
142#103×C61C2×C411yescharacteristic
143#102×C61C2×C411yescharacteristic
144#102×C61C2×C411yescharacteristic
145#102×C61C2×C411yescharacteristic
146#102×C61C2×C411yescharacteristic
147C22⋊C8×C61—21no—
148C22⋊C8×C61—21no—
149C22⋊C8×C61—21no—
150C22⋊C8×C61—21no—
151C22⋊C8×C61—21no—
152C22⋊C8×C61—21no—
153C22⋊C8×C61—21no—
154C22⋊C8×C61—21no—
155C22⋊C8×C61—21no—
156C22⋊C8×C61—21no—
157C22⋊C8×C61—21no—
158C22⋊C8×C61—21no—
159C22⋊C8×C61C2×C411yescharacteristic
160C22⋊C8×C61C2×C411yescharacteristic
161C22⋊C8×C61C2×C411yescharacteristic
162C22⋊C8×C61C2×C411yescharacteristic
163#97×C61—21no—
164#97×C61—41no—
165C4×C8×C61—21no—
166C4×C8×C61—41no—
167#95×C61—21no—
168C24×C61—21no—
169C24×C61#4111yescharacteristic
170#41×C61—21no—
171#41×C61—21no—
172#41×C61—21no—
173#41×C61—21no—
174#41×C61—21no—
175#41×C61—21no—
176#41×C61—21no—
177#41×C61—21no—
178#41×C61—21no—
179#41×C61—21no—
180#41×C61—21no—
181#41×C61—21no—
182#41×C61—41no—
183#41×C61—41no—
184#41×C61—41no—
185#41×C61—41no—
186#41×C61—42no—
187#41×C61—42no—
188#41×C61—42no—
189#41×C61—42no—
190C2×Q8×C61—21no—
191C2×Q8×C61—41no—
192C2×Q8×C61—41no—
193C2×Q8×C61C22×C411yescharacteristic
194C2×Q8×C61C22×C411yescharacteristic
195C2×Q8×C61C22×C411yescharacteristic
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—21no—
204C2×D4×C61—41no—
205C2×D4×C61—41no—
206C2×D4×C61—42no—
207C2×D4×C61—42no—
208C2×D4×C61C22×C411yescharacteristic
209C2×D4×C61C22×C411yescharacteristic
210C2×D4×C61C22×C411yescharacteristic
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
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—42no—
224C22×C4×C61—42no—
225C22×C4×C61C22×C411yescharacteristic
226C22×C4×C61C22×C411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61#4111yescharacteristic
230C22×C4×C61C2411yescharacteristic
231Q16×C61—41no—
232Q16×C61—41no—
233SD16×C61—41no—
234SD16×C61—41no—
235SD16×C61—41no—
236SD16×C61—41no—
237D8×C61—41no—
238D8×C61—41no—
239M16×C61—21no—
240M16×C61—21no—
241M16×C61—21no—
242M16×C61—21no—
243M16×C61—21no—
244M16×C61—21no—
245M16×C61—21no—
246M16×C61—21no—
247M16×C61—41no—
248M16×C61—41no—
249M16×C61—41no—
250M16×C61—41no—
251M16×C61—42no—
252M16×C61—42no—
253C2×C8×C61—21no—
254C2×C8×C61—21no—
255C2×C8×C61—21no—
256C2×C8×C61—21no—
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—42no—
266C2×C8×C61—42no—
267C2×C8×C61C22×C411yescharacteristic
268C2×C8×C61C22×C411yescharacteristic
269C2×C8×C61C22×C411yescharacteristic
270C2×C8×C61C22×C411yescharacteristic
271C2×C8×C61C2×D411yescharacteristic
272C2×C8×C61C2×D411yescharacteristic
273C2×C8×C61C2×D411yescharacteristic
274C2×C8×C61C2×D411yescharacteristic
275C4⋊C4×C61—21no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61C22×C411yescharacteristic
278C4⋊C4×C61C22×C411yescharacteristic
279C22⋊C4×C61—21no—
280C22⋊C4×C61—21no—
281C22⋊C4×C61—21no—
282C22⋊C4×C61—21no—
283C22⋊C4×C61—21no—
284C22⋊C4×C61—42no—
285C42×C61—21no—
286C42×C61—21no—
287C42×C61—21no—
288C42×C61—21no—
289C42×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61—21no—
294C23×C61—21no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—42no—
298C23×C61—81no—
299C23×C61—81no—
300C23×C61C4×D411yescharacteristic
301C23×C61C4×D411yescharacteristic
302C23×C61C2×#4111yescharacteristic
303Q8×C61—21no—
304Q8×C61—21no—
305Q8×C61—21no—
306Q8×C61—21no—
307Q8×C61—21no—
308Q8×C61—21no—
309Q8×C61—42no—
310D4×C61—21no—
311D4×C61—21no—
312D4×C61—21no—
313D4×C61—21no—
314D4×C61—21no—
315D4×C61—21no—
316D4×C61—42no—
317D4×C61—42no—
318D4×C61—42no—
319D4×C61—41no—
320D4×C61—41no—
321D4×C61—41no—
322D4×C61—41no—
323D4×C61—41no—
324D4×C61—41no—
325D4×C61—81no—
326D4×C61—81no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—22no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—42no—
344C2×C4×C61—42no—
345C2×C4×C61—41no—
346C2×C4×C61—42no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61C4×D411yescharacteristic
358C2×C4×C61C4×D411yescharacteristic
359C2×C4×C61C23×C411yescharacteristic
360C2×C4×C61C22×D411yescharacteristic
361C2×C4×C61H(5,𝔽2)11yescharacteristic
362C2×C4×C61H(5,𝔽2)11yescharacteristic
363C2×C4×C61H(5,𝔽2)11yescharacteristic
364C2×C4×C61H(5,𝔽2)11yescharacteristic
365C8×C61—21no—
366C8×C61—21no—
367C8×C61—21no—
368C8×C61—21no—
369C8×C61—21no—
370C8×C61—21no—
371C8×C61—21no—
372C8×C61—21no—
373C8×C61—41no—
374C8×C61—41no—
375C8×C61—41no—
376C8×C61—41no—
377#22062C6111yesmaximal, characteristic, direct product factor, Sylow
378C22×C61—21no—
379C22×C61—21no—
380C22×C61—21no—
381C22×C61—21no—
382C22×C61—21no—
383C22×C61—21no—
384C22×C61—21no—
385C22×C61—21no—
386C22×C61—41no—
387C22×C61—41no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—81no—
396C22×C61—81no—
397C22×C61—84no—
398C22×C61C2×C4×D411yescharacteristic
399C22×C61#53811yescharacteristic
400C22×C61#53811yescharacteristic
401C4×C61—21no—
402C4×C61—21no—
403C4×C61—42no—
404C4×C61—41no—
405C4×C61—41no—
406C4×C61—41no—
407C4×C61—41no—
408C4×C61—41no—
409C4×C61—81no—
410C4×C61#51811yescharacteristic
411C4×C61#51811yescharacteristic
412C4×C61#53411yescharacteristic
413C4×C61#53511yescharacteristic
414#3002C2×C6111yescharacteristic
415#2930C2×C6111yescharacteristic, complemented
416#2879C2×C6111yescharacteristic, complemented
417#1975C2×C6111yescharacteristic, complemented
418#1974C2×C6111yescharacteristic, complemented
419#1938C2×C6111yescharacteristic, complemented
420#1937C2×C6111yescharacteristic, complemented
421#1929C2×C6111yescharacteristic, complemented
422#1929C2×C6111yescharacteristic, complemented
423#1876C2×C6111yescharacteristic, complemented
424#1876C2×C6111yescharacteristic, complemented
425#1871C2×C6111yescharacteristic, complemented
426#1855C2×C6111yescharacteristic, complemented
427#1789C2×C6111yescharacteristic, complemented
428#1753C2×C6111yescharacteristic, complemented
429C2×C61—21no—
430C2×C61—21no—
431C2×C61—41no—
432C2×C61—41no—
433C2×C61—81no—
434C2×C61—81no—
435C2×C61—81no—
436C2×C61#232111yescharacteristic
437C2×C61#295611yescharacteristic
438C2×C61#295711yescharacteristic
439C22×#41C22×C6111yescharacteristic
440C2×#135C22×C6111yescharacteristic
441C2×#135C22×C6111yescharacteristic
442C2×#131C22×C6111yescharacteristic, complemented
443C22×M16C22×C6111yescharacteristic
444C22×M16C22×C6111yescharacteristic
445#525C22×C6111yescharacteristic
446#452C4×C6111yescharacteristic, complemented
447#452C4×C6111yescharacteristic, complemented
448#451C4×C6111yescharacteristic, complemented
449#450C4×C6111yescharacteristic, complemented
450#449C4×C6111yescharacteristic, complemented
451#449C4×C6111yescharacteristic, complemented
452#448C4×C6111yescharacteristic, complemented
453#447C4×C6111yescharacteristic, complemented
454#436—21no—
455#436—21no—
456#435—21no—
457#435—21no—
458C2×#108C22×C6111yescharacteristic, complemented
459C2×#108C22×C6111yescharacteristic, complemented
460#424C22×C6111yescharacteristic, complemented
461C2×#104C22×C6111yescharacteristic
462C2×#104C22×C6111yescharacteristic
463C2×#104C22×C6111yescharacteristic
464C2×#104C22×C6111yescharacteristic
465C2×#104C22×C6111yescharacteristic, complemented
466C2×#104C22×C6111yescharacteristic, complemented
467#416C22×C6111yescharacteristic
468#416C22×C6111yescharacteristic
469#408—21no—
470#408—21no—
471#408C22×C6111yescharacteristic
472#408C22×C6111yescharacteristic
473#408C22×C6111yescharacteristic
474#408C22×C6111yescharacteristic
475#408C22×C6111yescharacteristic, complemented
476#407—21no—
477#407—21no—
478#407C22×C6111yescharacteristic
479C2×C22⋊C8C22×C6111yescharacteristic
480#405C22×C6111yescharacteristic, complemented
481C2×#97C22×C6111yescharacteristic, complemented
482C2×C4×C8C22×C6111yescharacteristic, complemented
483C4×C22⋊C4C22×C6111yescharacteristic
484#341C22×C6111yescharacteristic, complemented
485#341C22×C6111yescharacteristic, complemented
486#339C22×C6111yescharacteristic, complemented
487#339C22×C6111yescharacteristic, complemented
488#336C22×C6111yescharacteristic, complemented
489#336C22×C6111yescharacteristic, complemented
490C61#2206211yescharacteristic, direct product factor, Sylow
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41C2×C4×C6111yescharacteristic
498C2×#41C2×C4×C6111yescharacteristic
499C2×#41C23×C6111yescharacteristic
500C2×#41C23×C6111yescharacteristic
501C2×#41C23×C6111yescharacteristic
502C22×Q8C2×C4×C6111yescharacteristic
503C22×D4—21no—
504C22×D4C2×C4×C6111yescharacteristic
505C23×C4—21no—
506C23×C4C23×C6111yescharacteristic
507#135—41no—
508#135—41no—
509#135—41no—
510#135—41no—
511C2×Q16C2×C4×C6111yescharacteristic
512C2×Q16C2×C4×C6111yescharacteristic
513C2×SD16C2×C4×C6111yescharacteristic
514C2×SD16C2×C4×C6111yescharacteristic
515C2×SD16C2×C4×C6111yescharacteristic
516C2×SD16C2×C4×C6111yescharacteristic
517C2×D8C2×C4×C6111yescharacteristic
518C2×D8C2×C4×C6111yescharacteristic
519#131—41no—
520#131—41no—
521C2×M16—21no—
522C2×M16—21no—
523C2×M16—41no—
524C2×M16—41no—
525C2×M16—41no—
526C2×M16—41no—
527C2×M16D4×C6111yescharacteristic
528C2×M16D4×C6111yescharacteristic
529C2×M16D4×C6111yescharacteristic
530C2×M16D4×C6111yescharacteristic
531C2×M16C23×C6111yescharacteristic
532C2×M16C23×C6111yescharacteristic
533C2×M16C23×C6111yescharacteristic
534C2×M16C23×C6111yescharacteristic
535C22×C8—21no—
536C22×C8—21no—
537C22×C8C23×C6111yescharacteristic
538C22×C8C23×C6111yescharacteristic
539C22×C8C23×C6111yescharacteristic
540C22×C8C23×C6111yescharacteristic
541#123—21no—
542C22⋊Q8C2×C4×C6111yescharacteristic
543C22⋊Q8C2×C4×C6111yescharacteristic
544#121C2×C4×C6111yescharacteristic
545#121C2×C4×C6111yescharacteristic
546#120—21no—
547C4×D4—21no—
548C4×D4—21no—
549#117C23×C6111yescharacteristic
550C2×C22⋊C4—21no—
551C2×C42C23×C6111yescharacteristic
552C2×C42C23×C6111yescharacteristic
553#108—41no—
554#108—41no—
555C4⋊C8—21no—
556C4⋊C8—21no—
557#104—41no—
558#104—41no—
559#104—41no—
560#104—41no—
561#104—41no—
562#104—41no—
563#103C2×C4×C6111yescharacteristic
564#103C2×C4×C6111yescharacteristic
565#103C2×C4×C6111yescharacteristic
566#103C2×C4×C6111yescharacteristic
567#102C2×C4×C6111yescharacteristic
568#102C2×C4×C6111yescharacteristic
569#102C2×C4×C6111yescharacteristic
570#102C2×C4×C6111yescharacteristic
571C22⋊C8—21no—
572C22⋊C8—21no—
573C22⋊C8—21no—
574C22⋊C8—21no—
575C22⋊C8—21no—
576C22⋊C8—21no—
577C22⋊C8—21no—
578C22⋊C8—21no—
579C22⋊C8—21no—
580C22⋊C8—21no—
581C22⋊C8—21no—
582C22⋊C8—21no—
583C22⋊C8C2×C4×C6111yescharacteristic
584C22⋊C8C2×C4×C6111yescharacteristic
585C22⋊C8C2×C4×C6111yescharacteristic
586C22⋊C8C2×C4×C6111yescharacteristic
587#97—21no—
588#97—41no—
589C4×C8—21no—
590C4×C8—41no—
591#95—21no—
592C24—21no—
593C24#41×C6111yescharacteristic
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—21no—
604#41—21no—
605#41—21no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610#41—42no—
611#41—42no—
612#41—42no—
613#41—42no—
614C2×Q8—21no—
615C2×Q8—41no—
616C2×Q8—41no—
617C2×Q8C22×C4×C6111yescharacteristic
618C2×Q8C22×C4×C6111yescharacteristic
619C2×Q8C22×C4×C6111yescharacteristic
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4C22×C4×C6111yescharacteristic
633C2×D4C22×C4×C6111yescharacteristic
634C2×D4C22×C4×C6111yescharacteristic
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4C22×C4×C6111yescharacteristic
650C22×C4C22×C4×C6111yescharacteristic
651C22×C4C2×D4×C6111yescharacteristic
652C22×C4C2×D4×C6111yescharacteristic
653C22×C4#41×C6111yescharacteristic
654C22×C4C24×C6111yescharacteristic
655Q16—41no—
656Q16—41no—
657SD16—41no—
658SD16—41no—
659SD16—41no—
660SD16—41no—
661D8—41no—
662D8—41no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—21no—
669M16—21no—
670M16—21no—
671M16—41no—
672M16—41no—
673M16—41no—
674M16—41no—
675M16—42no—
676M16—42no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—42no—
690C2×C8—42no—
691C2×C8C22×C4×C6111yescharacteristic
692C2×C8C22×C4×C6111yescharacteristic
693C2×C8C22×C4×C6111yescharacteristic
694C2×C8C22×C4×C6111yescharacteristic
695C2×C8C2×D4×C6111yescharacteristic
696C2×C8C2×D4×C6111yescharacteristic
697C2×C8C2×D4×C6111yescharacteristic
698C2×C8C2×D4×C6111yescharacteristic
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4C22×C4×C6111yescharacteristic
702C4⋊C4C22×C4×C6111yescharacteristic
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—42no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—41no—
720C23—41no—
721C23—42no—
722C23—81no—
723C23—81no—
724C23C4×D4×C6111yescharacteristic
725C23C4×D4×C6111yescharacteristic
726C23C2×#41×C6111yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—21no—
732Q8—21no—
733Q8—42no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—42no—
741D4—42no—
742D4—42no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—81no—
750D4—81no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4C4×D4×C6111yescharacteristic
782C2×C4C4×D4×C6111yescharacteristic
783C2×C4C23×C4×C6111yescharacteristic
784C2×C4C22×D4×C6111yescharacteristic
785C2×C4H(5,𝔽2)×C6111yescharacteristic
786C2×C4H(5,𝔽2)×C6111yescharacteristic
787C2×C4H(5,𝔽2)×C6111yescharacteristic
788C2×C4H(5,𝔽2)×C6111yescharacteristic
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—21no—
794C8—21no—
795C8—21no—
796C8—21no—
797C8—41no—
798C8—41no—
799C8—41no—
800C8—41no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—81no—
819C22—81no—
820C22—84no—
821C22C2×C4×D4×C6111yescharacteristic
822C22C61×#53811yescharacteristic
823C22C61×#53811yescharacteristic
824C4—21no—
825C4—21no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—81no—
833C4C61×#51811yescharacteristic
834C4C61×#51811yescharacteristic
835C4C61×#53411yescharacteristic
836C4C61×#53511yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2—81no—
843C2—81no—
844C2C61×#232111yescharacteristic
845C2C61×#295611yescharacteristic
846C2C61×#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 ◁ C22×M16×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#2930C2semidirect
3. C61×#2879C2semidirect
4. C61×#1975C2semidirect
5. C61×#1974C2semidirect
6. C61×#1938C2semidirect
7. C61×#1937C2semidirect
8. C61×#1929C2semidirect
9. C61×#1929C2semidirect
10. C61×#1876C2semidirect
11. C61×#1876C2semidirect
12. C61×#1871C2semidirect
13. C61×#1855C2semidirect
14. C61×#1789C2semidirect
15. C61×#1753C2semidirect
19. C2×#131×C61C22semidirect
23. C61×#452C4semidirect
24. C61×#452C4semidirect
25. C61×#451C4semidirect
26. C61×#450C4semidirect
27. C61×#449C4semidirect
28. C61×#449C4semidirect
29. C61×#448C4semidirect
30. C61×#447C4semidirect
35. C2×#108×C61C22semidirect
36. C2×#108×C61C22semidirect
37. C61×#424C22semidirect
42. C2×#104×C61C22semidirect
43. C2×#104×C61C22semidirect
52. C61×#408C22semidirect
57. C61×#405C22semidirect
58. C2×#97×C61C22semidirect
59. C2×C4×C8×C61C22semidirect
61. C61×#341C22semidirect
62. C61×#341C22semidirect
63. C61×#339C22semidirect
64. C61×#339C22semidirect
65. C61×#336C22semidirect
66. C61×#336C22semidirect
377. #22062C61direct (N × H)
415. #2930C2×C61semidirect
416. #2879C2×C61semidirect
417. #1975C2×C61semidirect
418. #1974C2×C61semidirect
419. #1938C2×C61semidirect
420. #1937C2×C61semidirect
421. #1929C2×C61semidirect
422. #1929C2×C61semidirect
423. #1876C2×C61semidirect
424. #1876C2×C61semidirect
425. #1871C2×C61semidirect
426. #1855C2×C61semidirect
427. #1789C2×C61semidirect
428. #1753C2×C61semidirect
442. C2×#131C22×C61semidirect
446. #452C4×C61semidirect
447. #452C4×C61semidirect
448. #451C4×C61semidirect
449. #450C4×C61semidirect
450. #449C4×C61semidirect
451. #449C4×C61semidirect
452. #448C4×C61semidirect
453. #447C4×C61semidirect
458. C2×#108C22×C61semidirect
459. C2×#108C22×C61semidirect
460. #424C22×C61semidirect
465. C2×#104C22×C61semidirect
466. C2×#104C22×C61semidirect
475. #408C22×C61semidirect
480. #405C22×C61semidirect
481. C2×#97C22×C61semidirect
482. C2×C4×C8C22×C61semidirect
484. #341C22×C61semidirect
485. #341C22×C61semidirect
486. #339C22×C61semidirect
487. #339C22×C61semidirect
488. #336C22×C61semidirect
489. #336C22×C61semidirect
490. C61#22062direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#30022
C61×#29302
C61×#28792
C61×#19752
C61×#19742
C61×#19382
C61×#19372
C61×#19292
C61×#18762
C61×#18712
C61×#18552
C61×#17892
C61×#17532
#2206261