Finite Group Databasebeta

← C61×#9170 #29512603

Subgroups — C61×#9170 #29512603

Order 15616.

432 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3079C211yesmaximal, characteristic
2C61×#2925C211yesmaximal, characteristic
3C61×#1549C211yesmaximal, characteristic, complemented
4C2×C61×#333C211yesmaximal, characteristic, complemented
5C61×#1477C211yesmaximal, characteristic
6C61×#1301C211yesmaximal, characteristic, complemented
7C61×#1292C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C61C2211yescharacteristic
9C4×#41×C61C2211yescharacteristic
10C61×#477—21no—
11C61×#476—21no—
12C61×#475C412yes—
13C61×#474C412yes—
14C61×#433—22no—
15C61×#432—21no—
16C61×#431—21no—
17C61×#431C2211yescharacteristic
18C61×#428—21no—
19C61×#423C2211yescharacteristic
20C61×#423C2211yescharacteristic
21C2×C4⋊C8×C61C2211yescharacteristic
22C2×C4⋊C8×C61C2211yescharacteristic
23C61×#417—21no—
24C61×#408—21no—
25C61×#405—21no—
26C61×#333—21no—
27C61×#333—21no—
28C61×#332—22no—
29C61×Q8⋊C8—21no—
30C61×D4⋊C8—21no—
31C2×#41×C61D411yescharacteristic
32C22×Q8×C61—21no—
33C2×M16×C61—21no—
34C2×M16×C61—21no—
35C22×C8×C61—21no—
36C22×C8×C61—21no—
37C4⋊Q8×C61—21no—
38C4⋊Q8×C61—21no—
39C4⋊Q8×C61—21no—
40C4⋊Q8×C61C2×C412yes—
41C4×Q8×C61C2×C411yescharacteristic
42C4×Q8×C61D411yescharacteristic
43C4×D4×C61—21no—
44C4×D4×C61—21no—
45C4×D4×C61C2×C411yescharacteristic
46C4×D4×C61D411yescharacteristic
47#117×C61—21no—
48#117×C61D411yescharacteristic
49C2×C4⋊C4×C61—21no—
50C2×C4⋊C4×C61—21no—
51C2×C42×C61—21no—
52C2×C42×C61C2311yescharacteristic
53#107×C61—22no—
54#106×C61—22no—
55C4⋊C8×C61—21no—
56C4⋊C8×C61—21no—
57C4⋊C8×C61—21no—
58C4⋊C8×C61—21no—
59C4⋊C8×C61—21no—
60C4⋊C8×C61—21no—
61C4⋊C8×C61C2×C412yes—
62C4⋊C8×C61D412yes—
63C4⋊C8×C61D411yescharacteristic
64C4⋊C8×C61D411yescharacteristic
65#103×C61—22no—
66#102×C61—22no—
67C22⋊C8×C61—22no—
68C22⋊C8×C61—22no—
69C22⋊C8×C61—21no—
70#97×C61—22no—
71C4×C8×C61—22no—
72C4×C8×C61—21no—
73#41×C61—21no—
74#41×C61—21no—
75#41×C61—21no—
76#41×C61—21no—
77C2×Q8×C61—22no—
78C2×Q8×C61—41no—
79C2×Q8×C61—82no—
80C2×Q8×C61C22⋊C411yescharacteristic
81C2×D4×C61—21no—
82C2×D4×C61C22⋊C411yescharacteristic
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—21no—
86C22×C4×C61—41no—
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61#4111yescharacteristic
89C22×C4×C61#4111yescharacteristic
90M16×C61—41no—
91M16×C61—41no—
92M16×C61—41no—
93M16×C61—41no—
94C2×C8×C61—22no—
95C2×C8×C61—21no—
96C2×C8×C61—22no—
97C2×C8×C61—21no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C2×C8×C61—41no—
101C2×C8×C61—41no—
102C2×C8×C61—81no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—22no—
106C4⋊C4×C61—22no—
107C4⋊C4×C61—41no—
108C4⋊C4×C61—41no—
109C4⋊C4×C61C22⋊C411yescharacteristic
110C4⋊C4×C61C22⋊C411yescharacteristic
111C22⋊C4×C61—21no—
112C22⋊C4×C61—21no—
113C22⋊C4×C61—21no—
114C42×C61—21no—
115C42×C61—21no—
116C42×C61—21no—
117C42×C61C22×C411yescharacteristic
118C42×C61C2×D411yescharacteristic
119C42×C61C2×D411yescharacteristic
120C42×C61C2×D411yescharacteristic
121C23×C61—21no—
122C23×C61#12311yescharacteristic
123Q8×C61—21no—
124Q8×C61—21no—
125Q8×C61—82no—
126Q8×C61—82no—
127D4×C61—21no—
128D4×C61—21no—
129D4×C61—41no—
130D4×C61—41no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—42no—
142C2×C4×C61—81no—
143C2×C4×C61—82no—
144C2×C4×C61C2×C22⋊C411yescharacteristic
145C2×C4×C61C4×D411yescharacteristic
146C2×C4×C61C4×D411yescharacteristic
147C2×C4×C61#12011yescharacteristic
148C2×C4×C61#12111yescharacteristic
149C2×C4×C61#12111yescharacteristic
150C2×C4×C61#13511yescharacteristic
151C2×C4×C61#13511yescharacteristic
152C2×C4×C61#13711yescharacteristic
153C2×C4×C61#13711yescharacteristic
154C8×C61—42no—
155C8×C61—41no—
156C8×C61—41no—
157C8×C61—42no—
158C8×C61—81no—
159C8×C61—81no—
160#9170C6111yesmaximal, characteristic, direct product factor, Sylow
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61#38611yescharacteristic
167C22×C61#48511yescharacteristic
168C22×C61#48511yescharacteristic
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—41no—
173C4×C61—41no—
174C4×C61—41no—
175C4×C61—82no—
176C4×C61#41611yescharacteristic
177C4×C61#41911yescharacteristic
178C4×C61#45211yescharacteristic
179C4×C61#45211yescharacteristic
180C4×C61#47111yescharacteristic
181C4×C61#47311yescharacteristic
182#3079C2×C6111yescharacteristic
183#2925C2×C6111yescharacteristic
184#1549C2×C6111yescharacteristic, complemented
185C2×#333C2×C6111yescharacteristic, complemented
186#1477C2×C6111yescharacteristic
187#1301C2×C6111yescharacteristic, complemented
188#1292C2×C6111yescharacteristic, complemented
189C2×C61—21no—
190C2×C61—21no—
191C2×C61—81no—
192C2×C61#187311yescharacteristic
193C2×C61#190311yescharacteristic
194C2×C61#190811yescharacteristic
195C2×C4⋊Q8C22×C6111yescharacteristic
196C4×#41C22×C6111yescharacteristic
197#477—21no—
198#476—21no—
199#475C4×C6112yes—
200#474C4×C6112yes—
201#433—22no—
202#432—21no—
203#431—21no—
204#431C22×C6111yescharacteristic
205#428—21no—
206#423C22×C6111yescharacteristic
207#423C22×C6111yescharacteristic
208C2×C4⋊C8C22×C6111yescharacteristic
209C2×C4⋊C8C22×C6111yescharacteristic
210#417—21no—
211#408—21no—
212#405—21no—
213#333—21no—
214#333—21no—
215#332—22no—
216Q8⋊C8—21no—
217D4⋊C8—21no—
218C61#917011yescharacteristic, direct product factor, Sylow
219C2×#41D4×C6111yescharacteristic
220C22×Q8—21no—
221C2×M16—21no—
222C2×M16—21no—
223C22×C8—21no—
224C22×C8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8C2×C4×C6112yes—
229C4×Q8C2×C4×C6111yescharacteristic
230C4×Q8D4×C6111yescharacteristic
231C4×D4—21no—
232C4×D4—21no—
233C4×D4C2×C4×C6111yescharacteristic
234C4×D4D4×C6111yescharacteristic
235#117—21no—
236#117D4×C6111yescharacteristic
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C42—21no—
240C2×C42C23×C6111yescharacteristic
241#107—22no—
242#106—22no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8C2×C4×C6112yes—
250C4⋊C8D4×C6112yes—
251C4⋊C8D4×C6111yescharacteristic
252C4⋊C8D4×C6111yescharacteristic
253#103—22no—
254#102—22no—
255C22⋊C8—22no—
256C22⋊C8—22no—
257C22⋊C8—21no—
258#97—22no—
259C4×C8—22no—
260C4×C8—21no—
261#41—21no—
262#41—21no—
263#41—21no—
264#41—21no—
265C2×Q8—22no—
266C2×Q8—41no—
267C2×Q8—82no—
268C2×Q8C22⋊C4×C6111yescharacteristic
269C2×D4—21no—
270C2×D4C22⋊C4×C6111yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—41no—
275C22×C4C2×D4×C6111yescharacteristic
276C22×C4#41×C6111yescharacteristic
277C22×C4#41×C6111yescharacteristic
278M16—41no—
279M16—41no—
280M16—41no—
281M16—41no—
282C2×C8—22no—
283C2×C8—21no—
284C2×C8—22no—
285C2×C8—21no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—81no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4C22⋊C4×C6111yescharacteristic
298C4⋊C4C22⋊C4×C6111yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C42—21no—
303C42—21no—
304C42—21no—
305C42C22×C4×C6111yescharacteristic
306C42C2×D4×C6111yescharacteristic
307C42C2×D4×C6111yescharacteristic
308C42C2×D4×C6111yescharacteristic
309C23—21no—
310C23#123×C6111yescharacteristic
311Q8—21no—
312Q8—21no—
313Q8—82no—
314Q8—82no—
315D4—21no—
316D4—21no—
317D4—41no—
318D4—41no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—81no—
331C2×C4—82no—
332C2×C4C2×C22⋊C4×C6111yescharacteristic
333C2×C4C4×D4×C6111yescharacteristic
334C2×C4C4×D4×C6111yescharacteristic
335C2×C4#120×C6111yescharacteristic
336C2×C4#121×C6111yescharacteristic
337C2×C4#121×C6111yescharacteristic
338C2×C4#135×C6111yescharacteristic
339C2×C4#135×C6111yescharacteristic
340C2×C4#137×C6111yescharacteristic
341C2×C4#137×C6111yescharacteristic
342C8—42no—
343C8—41no—
344C8—41no—
345C8—42no—
346C8—81no—
347C8—81no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22C61×#38611yescharacteristic
354C22C61×#48511yescharacteristic
355C22C61×#48511yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—82no—
363C4C61×#41611yescharacteristic
364C4C61×#41911yescharacteristic
365C4C61×#45211yescharacteristic
366C4C61×#45211yescharacteristic
367C4C61×#47111yescharacteristic
368C4C61×#47311yescharacteristic
369C2—21no—
370C2—21no—
371C2—81no—
372C2C61×#187311yescharacteristic
373C2C61×#190311yescharacteristic
374C2C61×#190811yescharacteristic
subgroupG/H
center, socleC22×C61#386
commutatorC42C22×C4×C61
Frattini, cosocleC2×C42C23×C61
prime radicalC2×#41×C61D4
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
3. C61×#1549C2semidirect
4. C2×C61×#333C2semidirect
6. C61×#1301C2semidirect
7. C61×#1292C2semidirect
160. #9170C61direct (N × H)
184. #1549C2×C61semidirect
185. C2×#333C2×C61semidirect
187. #1301C2×C61semidirect
188. #1292C2×C61semidirect
218. C61#9170direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#30792
C61×#29252
C61×#15492
C2×C61×#3332
C61×#14772
C61×#13012
C61×#12922
#917061