Finite Group Databasebeta

← C61×#10172 #29513605

Subgroups — C61×#10172 #29513605

Order 15616.

562 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3227C211yesmaximal, characteristic
2C2×C61×#498C211yesmaximal, characteristic, complemented
3C61×#3152C211yesmaximal, characteristic
4C61×#1997C211yesmaximal, characteristic, complemented
5C61×#1546C211yesmaximal, characteristic, complemented
6C61×#1492C211yesmaximal, characteristic
7C61×#1278C211yesmaximal, characteristic, complemented
8C2×#137×C61—22no—
9C61×#532C2211yescharacteristic
10C2×C4⋊Q8×C61C2211yescharacteristic
11C2×C4⋊Q8×C61C2211yescharacteristic
12C61×#498—22no—
13C61×#498—21no—
14C61×#498—22no—
15C61×#497—22no—
16C61×#494—21no—
17C61×#492—21no—
18C61×#486—21no—
19C61×#481—22no—
20C61×#476—22no—
21C61×#431C2211yescharacteristic
22C2×#106×C61—22no—
23C61×#423C2211yescharacteristic
24C4×M16×C61C2211yescharacteristic
25C2×C4×C8×C61C2211yescharacteristic
26C61×#343—22no—
27C61×#332—22no—
28C61×D4⋊C8—22no—
29C2×#41×C61—21no—
30C22×Q8×C61—21no—
31C22×Q8×C61—21no—
32#137×C61—44no—
33#137×C61—44no—
34C2×Q16×C61—24no—
35C2×SD16×C61—24no—
36C2×M16×C61—21no—
37C2×M16×C61D412yes—
38C22×C8×C61—21no—
39C4⋊Q8×C61—21no—
40C4⋊Q8×C61—21no—
41C4⋊Q8×C61—21no—
42C4⋊Q8×C61—21no—
43C4⋊Q8×C61—21no—
44C4⋊Q8×C61—21no—
45C4⋊Q8×C61—21no—
46C4⋊Q8×C61D412yes—
47C4⋊Q8×C61D411yescharacteristic
48#127×C61D411yescharacteristic
49#124×C61—21no—
50#121×C61—21no—
51#121×C61—21no—
52C4×D4×C61—21no—
53C4×D4×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61D412yes—
58C2×C42×C61C2311yescharacteristic
59#106×C61—28no—
60#106×C61—24no—
61C4⋊C8×C61—21no—
62C4⋊C8×C61—21no—
63C4⋊C8×C61D412yes—
64#102×C61—24no—
65C22⋊C8×C61—21no—
66#97×C61—21no—
67C4×C8×C61—21no—
68C4×C8×C61—21no—
69C4×C8×C61—21no—
70C4×C8×C61D412yes—
71#41×C61—42no—
72#41×C61—42no—
73C2×Q8×C61—21no—
74C2×Q8×C61—22no—
75C2×Q8×C61—41no—
76C2×Q8×C61—41no—
77C2×Q8×C61—41no—
78C2×Q8×C61—42no—
79C2×Q8×C61—42no—
80C2×Q8×C61—82no—
81C2×D4×C61—21no—
82C2×D4×C61—21no—
83C2×D4×C61—21no—
84C2×D4×C61—41no—
85C22×C4×C61—22no—
86C22×C4×C61—41no—
87C22×C4×C61—41no—
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61#4111yescharacteristic
91Q16×C61—48no—
92SD16×C61—48no—
93M16×C61—22no—
94M16×C61—42no—
95M16×C61SD1614yes—
96C2×C8×C61—24no—
97C2×C8×C61—22no—
98C2×C8×C61—22no—
99C2×C8×C61—22no—
100C2×C8×C61—41no—
101C4⋊C4×C61—22no—
102C4⋊C4×C61—22no—
103C4⋊C4×C61—22no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—22no—
106C4⋊C4×C61—21no—
107C4⋊C4×C61—41no—
108C4⋊C4×C61—41no—
109C4⋊C4×C61—41no—
110C4⋊C4×C61—41no—
111C22⋊C4×C61—41no—
112C22⋊C4×C61—41no—
113C42×C61C2×D411yescharacteristic
114C42×C61C2×D411yescharacteristic
115C42×C61C2×D411yescharacteristic
116C42×C61C2×D411yescharacteristic
117C23×C61—41no—
118C23×C61#12111yescharacteristic
119Q8×C61—44no—
120Q8×C61—42no—
121Q8×C61—82no—
122Q8×C61—82no—
123Q8×C61—81no—
124Q8×C61—81no—
125D4×C61—42no—
126D4×C61—42no—
127D4×C61—42no—
128D4×C61—82no—
129C2×C4×C61—22no—
130C2×C4×C61—22no—
131C2×C4×C61—41no—
132C2×C4×C61—42no—
133C2×C4×C61—42no—
134C2×C4×C61—82no—
135C2×C4×C61—81no—
136C2×C4×C61—81no—
137C2×C4×C61—82no—
138C2×C4×C61#12011yescharacteristic
139C2×C4×C61#12011yescharacteristic
140C2×C4×C61#12011yescharacteristic
141C2×C4×C61#12111yescharacteristic
142C2×C4×C61#12111yescharacteristic
143C2×C4×C61#12711yescharacteristic
144C2×C4×C61C2×SD1612yes—
145C2×C4×C61AGL(1,ℤ/8)12yes—
146C8×C61—24no—
147C8×C61—24no—
148C8×C61—42no—
149C8×C61—81no—
150#10172C6111yesmaximal, characteristic, direct product factor, Sylow
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—81no—
154C22×C61—81no—
155C22×C61—81no—
156C22×C61#39211yescharacteristic
157C22×C61#46012yes—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—81no—
161C4×C61—82no—
162C4×C61—82no—
163C4×C61#45012yes—
164C4×C61#45612yes—
165C4×C61#47112yes—
166C4×C61#49211yescharacteristic
167C4×C61#49611yescharacteristic
168#3227C2×C6111yescharacteristic
169C2×#498C2×C6111yescharacteristic, complemented
170#3152C2×C6111yescharacteristic
171#1997C2×C6111yescharacteristic, complemented
172#1546C2×C6111yescharacteristic, complemented
173#1492C2×C6111yescharacteristic
174#1278C2×C6111yescharacteristic, complemented
175C2×C61—22no—
176C2×C61—161no—
177C2×C61#200511yescharacteristic
178C2×C61#201411yescharacteristic
179C2×C61#201911yescharacteristic
180C2×#137—22no—
181#532C22×C6111yescharacteristic
182C2×C4⋊Q8C22×C6111yescharacteristic
183C2×C4⋊Q8C22×C6111yescharacteristic
184#498—22no—
185#498—21no—
186#498—22no—
187#497—22no—
188#494—21no—
189#492—21no—
190#486—21no—
191#481—22no—
192#476—22no—
193#431C22×C6111yescharacteristic
194C2×#106—22no—
195#423C22×C6111yescharacteristic
196C4×M16C22×C6111yescharacteristic
197C2×C4×C8C22×C6111yescharacteristic
198#343—22no—
199#332—22no—
200D4⋊C8—22no—
201C61#1017211yescharacteristic, direct product factor, Sylow
202C2×#41—21no—
203C22×Q8—21no—
204C22×Q8—21no—
205#137—44no—
206#137—44no—
207C2×Q16—24no—
208C2×SD16—24no—
209C2×M16—21no—
210C2×M16D4×C6112yes—
211C22×C8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8D4×C6112yes—
220C4⋊Q8D4×C6111yescharacteristic
221#127D4×C6111yescharacteristic
222#124—21no—
223#121—21no—
224#121—21no—
225C4×D4—21no—
226C4×D4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4D4×C6112yes—
231C2×C42C23×C6111yescharacteristic
232#106—28no—
233#106—24no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8D4×C6112yes—
237#102—24no—
238C22⋊C8—21no—
239#97—21no—
240C4×C8—21no—
241C4×C8—21no—
242C4×C8—21no—
243C4×C8D4×C6112yes—
244#41—42no—
245#41—42no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—42no—
252C2×Q8—42no—
253C2×Q8—82no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C22×C4—22no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4C2×D4×C6111yescharacteristic
262C22×C4C2×D4×C6111yescharacteristic
263C22×C4#41×C6111yescharacteristic
264Q16—48no—
265SD16—48no—
266M16—22no—
267M16—42no—
268M16SD16×C6114yes—
269C2×C8—24no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—41no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—21no—
278C4⋊C4—22no—
279C4⋊C4—21no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C42C2×D4×C6111yescharacteristic
287C42C2×D4×C6111yescharacteristic
288C42C2×D4×C6111yescharacteristic
289C42C2×D4×C6111yescharacteristic
290C23—41no—
291C23#121×C6111yescharacteristic
292Q8—44no—
293Q8—42no—
294Q8—82no—
295Q8—82no—
296Q8—81no—
297Q8—81no—
298D4—42no—
299D4—42no—
300D4—42no—
301D4—82no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—82no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—82no—
311C2×C4#120×C6111yescharacteristic
312C2×C4#120×C6111yescharacteristic
313C2×C4#120×C6111yescharacteristic
314C2×C4#121×C6111yescharacteristic
315C2×C4#121×C6111yescharacteristic
316C2×C4#127×C6111yescharacteristic
317C2×C4C2×SD16×C6112yes—
318C2×C4AGL(1,ℤ/8)×C6112yes—
319C8—24no—
320C8—24no—
321C8—42no—
322C8—81no—
323C22—21no—
324C22—21no—
325C22—81no—
326C22—81no—
327C22—81no—
328C22C61×#39211yescharacteristic
329C22C61×#46012yes—
330C4—21no—
331C4—21no—
332C4—81no—
333C4—82no—
334C4—82no—
335C4C61×#45012yes—
336C4C61×#45612yes—
337C4C61×#47112yes—
338C4C61×#49211yescharacteristic
339C4C61×#49611yescharacteristic
340C2—22no—
341C2—161no—
342C2C61×#200511yescharacteristic
343C2C61×#201411yescharacteristic
344C2C61×#201911yescharacteristic
subgroupG/H
center, socleC22×C61#392
commutator, Frattini, cosocleC2×C42C23×C61
prime radicalC61×#532C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C61×#498C2semidirect
4. C61×#1997C2semidirect
5. C61×#1546C2semidirect
7. C61×#1278C2semidirect
150. #10172C61direct (N × H)
169. C2×#498C2×C61semidirect
171. #1997C2×C61semidirect
172. #1546C2×C61semidirect
174. #1278C2×C61semidirect
201. C61#10172direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#32272
C2×C61×#4982
C61×#31522
C61×#19972
C61×#15462
C61×#14922
C61×#12782
#1017261