Finite Group Databasebeta

← C61×#19736 #29523169

Subgroups — C61×#19736 #29523169

Order 15616.

636 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3231C211yesmaximal, characteristic
2C61×#3231C211yesmaximal, characteristic
3C61×#3231C211yesmaximal, characteristic
4C61×#3230C211yesmaximal, characteristic
5C61×#3229C211yesmaximal, characteristic
6C61×#3209C211yesmaximal, characteristic
7C61×#1723C211yesmaximal, characteristic, complemented
8C61×#1723C211yesmaximal, characteristic, complemented
9C61×#1718C211yesmaximal, characteristic, complemented
10C61×#1718C211yesmaximal, characteristic, complemented
11C61×#1718C211yesmaximal, characteristic, complemented
12C61×#1716C211yesmaximal, characteristic, complemented
13C61×#1710C211yesmaximal, characteristic, complemented
14C61×#1707C211yesmaximal, characteristic, complemented
15C61×#1454C211yesmaximal, characteristic
16C61×#533C2211yescharacteristic
17C61×#533C2211yescharacteristic
18C61×#533C2211yescharacteristic
19C2×C4⋊Q8×C61C2211yescharacteristic
20C61×#500C2211yescharacteristic
21C61×#500C2211yescharacteristic
22C61×#500C2211yescharacteristic
23C61×#500C2211yescharacteristic
24C61×#500C2211yescharacteristic
25C61×#498C2211yescharacteristic
26C61×#498C2211yescharacteristic
27C61×#498C2211yescharacteristic
28C61×#498C2211yescharacteristic
29C61×#498C2211yescharacteristic
30C61×#494C2211yescharacteristic
31C61×#494C2211yescharacteristic
32C61×#487C2211yescharacteristic
33C61×#487C2211yescharacteristic
34C61×#487C2211yescharacteristic
35C61×#487C2211yescharacteristic
36C61×#487C2211yescharacteristic
37C61×#487C2211yescharacteristic
38C61×#487C2211yescharacteristic
39C61×#487C2211yescharacteristic
40C61×#487C2211yescharacteristic
41C61×#487C2211yescharacteristic
42C61×#487C2211yescharacteristic
43C61×#487C2211yescharacteristic
44C61×#485—22no—
45C61×#485—22no—
46C61×#485—22no—
47C61×#484—22no—
48C61×#483—22no—
49C61×#479—22no—
50C61×#479—22no—
51C61×#479—22no—
52C61×#477—22no—
53C61×#475—22no—
54C61×#462—22no—
55C61×#451—22no—
56C61×#431C2211yescharacteristic
57C61×#431C2211yescharacteristic
58C61×#431C2211yescharacteristic
59C61×#322C2211yescharacteristic
60C61×#322C2211yescharacteristic
61C61×#322C2211yescharacteristic
62C82×C61C2211yescharacteristic
63C22×Q8×C61—21no—
64C2×Q16×C61—22no—
65C2×Q16×C61—22no—
66C4⋊Q8×C61—21no—
67C4⋊Q8×C61—21no—
68C4⋊Q8×C61—21no—
69C4⋊Q8×C61C2311yescharacteristic
70C4⋊Q8×C61C2311yescharacteristic
71C4⋊Q8×C61C2311yescharacteristic
72C4⋊Q8×C61C2311yescharacteristic
73C4⋊Q8×C61C2311yescharacteristic
74C4⋊Q8×C61C2311yescharacteristic
75C4⋊Q8×C61C2311yescharacteristic
76C4⋊Q8×C61C2311yescharacteristic
77#125×C61—21no—
78#125×C61—21no—
79#125×C61—21no—
80C22⋊Q8×C61—21no—
81C22⋊Q8×C61—21no—
82C22⋊Q8×C61—21no—
83C22⋊Q8×C61—21no—
84C22⋊Q8×C61—21no—
85C22⋊Q8×C61—21no—
86C4×Q8×C61—21no—
87C4×Q8×C61—21no—
88C4×Q8×C61—21no—
89C4×Q8×C61—21no—
90C4×Q8×C61—21no—
91C4×Q8×C61—21no—
92#117×C61—21no—
93#117×C61—21no—
94#117×C61—21no—
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61—21no—
97C2×C42×C61C2311yescharacteristic
98#107×C61—22no—
99#107×C61—22no—
100#107×C61—22no—
101#107×C61—22no—
102#107×C61—22no—
103#106×C61—22no—
104#106×C61—22no—
105#106×C61—22no—
106#106×C61—22no—
107#106×C61—22no—
108C4⋊C8×C61D412yes—
109C4⋊C8×C61D412yes—
110C4⋊C8×C61D412yes—
111#103×C61—22no—
112#103×C61—22no—
113#103×C61—22no—
114#103×C61—22no—
115#103×C61—22no—
116#103×C61—22no—
117#103×C61—22no—
118#103×C61—22no—
119#103×C61—22no—
120#103×C61—22no—
121#103×C61—22no—
122#103×C61—22no—
123C22⋊C8×C61D412yes—
124C22⋊C8×C61D412yes—
125C22⋊C8×C61D412yes—
126C4×C8×C61C2311yescharacteristic
127C4×C8×C61C2311yescharacteristic
128C4×C8×C61C2311yescharacteristic
129C4×C8×C61C2311yescharacteristic
130C4×C8×C61C2311yescharacteristic
131C4×C8×C61C2311yescharacteristic
132C2×Q8×C61—21no—
133C2×Q8×C61—21no—
134C2×Q8×C61—21no—
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×Q8×C61—21no—
138C2×Q8×C61—21no—
139C2×Q8×C61—21no—
140C2×Q8×C61—41no—
141C2×Q8×C61—82no—
142C22×C4×C61—41no—
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146Q16×C61—82no—
147Q16×C61—82no—
148C2×C8×C61C2×D412yes—
149C2×C8×C61C2×D412yes—
150C2×C8×C61C2×D412yes—
151C2×C8×C61C2×D412yes—
152C2×C8×C61C2×D412yes—
153C2×C8×C61C2×D412yes—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—21no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—41no—
171C4⋊C4×C61—41no—
172C4⋊C4×C61—41no—
173C4⋊C4×C61—41no—
174C4⋊C4×C61—41no—
175C4⋊C4×C61—41no—
176C4⋊C4×C61—41no—
177C4⋊C4×C61—41no—
178C22⋊C4×C61—41no—
179C22⋊C4×C61—41no—
180C22⋊C4×C61—41no—
181C42×C61—41no—
182C42×C61—41no—
183C42×C61—41no—
184C42×C61C2×D411yescharacteristic
185C42×C61C2×D411yescharacteristic
186C42×C61C2×D411yescharacteristic
187C42×C61C2411yescharacteristic
188C23×C61#12711yescharacteristic
189Q8×C61—42no—
190Q8×C61—42no—
191Q8×C61—42no—
192Q8×C61—42no—
193Q8×C61—42no—
194Q8×C61—42no—
195Q8×C61—42no—
196Q8×C61—42no—
197Q8×C61—82no—
198C2×C4×C61—22no—
199C2×C4×C61—22no—
200C2×C4×C61—22no—
201C2×C4×C61—41no—
202C2×C4×C61—41no—
203C2×C4×C61—41no—
204C2×C4×C61—41no—
205C2×C4×C61—41no—
206C2×C4×C61—41no—
207C2×C4×C61—41no—
208C2×C4×C61—41no—
209C2×C4×C61—82no—
210C2×C4×C61#12711yescharacteristic
211C2×C4×C61#12711yescharacteristic
212C2×C4×C61#12711yescharacteristic
213C2×C4×C61C22×D411yescharacteristic
214C2×C4×C61C22×D411yescharacteristic
215C2×C4×C61C22×D411yescharacteristic
216C8×C61—22no—
217C8×C61—22no—
218C8×C61—22no—
219C8×C61—22no—
220C8×C61—22no—
221C8×C61—22no—
222#19736C6111yesmaximal, characteristic, direct product factor, Sylow
223C22×C61—21no—
224C22×C61—21no—
225C22×C61—21no—
226C22×C61C2×#12711yescharacteristic
227C4×C61—21no—
228C4×C61—21no—
229C4×C61—21no—
230C4×C61—81no—
231C4×C61—81no—
232C4×C61—81no—
233C4×C61—81no—
234C4×C61—81no—
235C4×C61—81no—
236C4×C61—81no—
237C4×C61—81no—
238C4×C61#57712yes—
239C4×C61#57812yes—
240C4×C61#57812yes—
241#3231C2×C6111yescharacteristic
242#3231C2×C6111yescharacteristic
243#3231C2×C6111yescharacteristic
244#3230C2×C6111yescharacteristic
245#3229C2×C6111yescharacteristic
246#3209C2×C6111yescharacteristic
247#1723C2×C6111yescharacteristic, complemented
248#1723C2×C6111yescharacteristic, complemented
249#1718C2×C6111yescharacteristic, complemented
250#1718C2×C6111yescharacteristic, complemented
251#1718C2×C6111yescharacteristic, complemented
252#1716C2×C6111yescharacteristic, complemented
253#1710C2×C6111yescharacteristic, complemented
254#1707C2×C6111yescharacteristic, complemented
255#1454C2×C6111yescharacteristic
256C2×C61—41no—
257C2×C61#315411yescharacteristic
258C2×C61#315611yescharacteristic
259C2×C61#315611yescharacteristic
260#533C22×C6111yescharacteristic
261#533C22×C6111yescharacteristic
262#533C22×C6111yescharacteristic
263C2×C4⋊Q8C22×C6111yescharacteristic
264#500C22×C6111yescharacteristic
265#500C22×C6111yescharacteristic
266#500C22×C6111yescharacteristic
267#500C22×C6111yescharacteristic
268#500C22×C6111yescharacteristic
269#498C22×C6111yescharacteristic
270#498C22×C6111yescharacteristic
271#498C22×C6111yescharacteristic
272#498C22×C6111yescharacteristic
273#498C22×C6111yescharacteristic
274#494C22×C6111yescharacteristic
275#494C22×C6111yescharacteristic
276#487C22×C6111yescharacteristic
277#487C22×C6111yescharacteristic
278#487C22×C6111yescharacteristic
279#487C22×C6111yescharacteristic
280#487C22×C6111yescharacteristic
281#487C22×C6111yescharacteristic
282#487C22×C6111yescharacteristic
283#487C22×C6111yescharacteristic
284#487C22×C6111yescharacteristic
285#487C22×C6111yescharacteristic
286#487C22×C6111yescharacteristic
287#487C22×C6111yescharacteristic
288#485—22no—
289#485—22no—
290#485—22no—
291#484—22no—
292#483—22no—
293#479—22no—
294#479—22no—
295#479—22no—
296#477—22no—
297#475—22no—
298#462—22no—
299#451—22no—
300#431C22×C6111yescharacteristic
301#431C22×C6111yescharacteristic
302#431C22×C6111yescharacteristic
303#322C22×C6111yescharacteristic
304#322C22×C6111yescharacteristic
305#322C22×C6111yescharacteristic
306C82C22×C6111yescharacteristic
307C61#1973611yescharacteristic, direct product factor, Sylow
308C22×Q8—21no—
309C2×Q16—22no—
310C2×Q16—22no—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8C23×C6111yescharacteristic
315C4⋊Q8C23×C6111yescharacteristic
316C4⋊Q8C23×C6111yescharacteristic
317C4⋊Q8C23×C6111yescharacteristic
318C4⋊Q8C23×C6111yescharacteristic
319C4⋊Q8C23×C6111yescharacteristic
320C4⋊Q8C23×C6111yescharacteristic
321C4⋊Q8C23×C6111yescharacteristic
322#125—21no—
323#125—21no—
324#125—21no—
325C22⋊Q8—21no—
326C22⋊Q8—21no—
327C22⋊Q8—21no—
328C22⋊Q8—21no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331C4×Q8—21no—
332C4×Q8—21no—
333C4×Q8—21no—
334C4×Q8—21no—
335C4×Q8—21no—
336C4×Q8—21no—
337#117—21no—
338#117—21no—
339#117—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C42C23×C6111yescharacteristic
343#107—22no—
344#107—22no—
345#107—22no—
346#107—22no—
347#107—22no—
348#106—22no—
349#106—22no—
350#106—22no—
351#106—22no—
352#106—22no—
353C4⋊C8D4×C6112yes—
354C4⋊C8D4×C6112yes—
355C4⋊C8D4×C6112yes—
356#103—22no—
357#103—22no—
358#103—22no—
359#103—22no—
360#103—22no—
361#103—22no—
362#103—22no—
363#103—22no—
364#103—22no—
365#103—22no—
366#103—22no—
367#103—22no—
368C22⋊C8D4×C6112yes—
369C22⋊C8D4×C6112yes—
370C22⋊C8D4×C6112yes—
371C4×C8C23×C6111yescharacteristic
372C4×C8C23×C6111yescharacteristic
373C4×C8C23×C6111yescharacteristic
374C4×C8C23×C6111yescharacteristic
375C4×C8C23×C6111yescharacteristic
376C4×C8C23×C6111yescharacteristic
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—41no—
386C2×Q8—82no—
387C22×C4—41no—
388C22×C4C2×D4×C6111yescharacteristic
389C22×C4C2×D4×C6111yescharacteristic
390C22×C4C2×D4×C6111yescharacteristic
391Q16—82no—
392Q16—82no—
393C2×C8C2×D4×C6112yes—
394C2×C8C2×D4×C6112yes—
395C2×C8C2×D4×C6112yes—
396C2×C8C2×D4×C6112yes—
397C2×C8C2×D4×C6112yes—
398C2×C8C2×D4×C6112yes—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C22⋊C4—41no—
424C22⋊C4—41no—
425C22⋊C4—41no—
426C42—41no—
427C42—41no—
428C42—41no—
429C42C2×D4×C6111yescharacteristic
430C42C2×D4×C6111yescharacteristic
431C42C2×D4×C6111yescharacteristic
432C42C24×C6111yescharacteristic
433C23#127×C6111yescharacteristic
434Q8—42no—
435Q8—42no—
436Q8—42no—
437Q8—42no—
438Q8—42no—
439Q8—42no—
440Q8—42no—
441Q8—42no—
442Q8—82no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—82no—
455C2×C4#127×C6111yescharacteristic
456C2×C4#127×C6111yescharacteristic
457C2×C4#127×C6111yescharacteristic
458C2×C4C22×D4×C6111yescharacteristic
459C2×C4C22×D4×C6111yescharacteristic
460C2×C4C22×D4×C6111yescharacteristic
461C8—22no—
462C8—22no—
463C8—22no—
464C8—22no—
465C8—22no—
466C8—22no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22C2×#127×C6111yescharacteristic
471C4—21no—
472C4—21no—
473C4—21no—
474C4—81no—
475C4—81no—
476C4—81no—
477C4—81no—
478C4—81no—
479C4—81no—
480C4—81no—
481C4—81no—
482C4C61×#57712yes—
483C4C61×#57812yes—
484C4C61×#57812yes—
485C2—41no—
486C2C61×#315411yescharacteristic
487C2C61×#315611yescharacteristic
488C2C61×#315611yescharacteristic
subgroupG/H
center, socleC22×C61C2×#127
commutator, Frattini, cosocleC42C24×C61
prime radicalC23×C61#127
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
7. C61×#1723C2semidirect
8. C61×#1723C2semidirect
9. C61×#1718C2semidirect
10. C61×#1718C2semidirect
11. C61×#1718C2semidirect
12. C61×#1716C2semidirect
13. C61×#1710C2semidirect
14. C61×#1707C2semidirect
222. #19736C61direct (N × H)
247. #1723C2×C61semidirect
248. #1723C2×C61semidirect
249. #1718C2×C61semidirect
250. #1718C2×C61semidirect
251. #1718C2×C61semidirect
252. #1716C2×C61semidirect
253. #1710C2×C61semidirect
254. #1707C2×C61semidirect
307. C61#19736direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#32312
C61×#32302
C61×#32292
C61×#32092
C61×#17232
C61×#17182
C61×#17162
C61×#17102
C61×#17072
C61×#14542
#1973661