Finite Group Databasebeta

← C61×#13400 #29516833

Subgroups — C61×#13400 #29516833

Order 15616.

402 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3060C211yesmaximal, characteristic
2C2×C61×#365C211yesmaximal, characteristic, complemented
3C61×#2148C211yesmaximal, characteristic, complemented
4C61×#2145C211yesmaximal, characteristic, complemented
5C61×#2117C211yesmaximal, characteristic, complemented
6C61×#1814C211yesmaximal, characteristic, complemented
7C61×#1386C211yesmaximal, characteristic, complemented
8C2×#135×C61C2211yescharacteristic
9C2×#131×C61C2211yescharacteristic
10C61×#537—21no—
11C2×M32×C61C2211yescharacteristic
12C2×M32×C61C2211yescharacteristic
13C61×#470—21no—
14C61×#469—21no—
15C61×#465—22no—
16C2×#108×C61C2211yescharacteristic
17C61×#427C2211yescharacteristic
18C2×#106×C61C2211yescharacteristic
19C61×#421—21no—
20C61×#417—21no—
21C61×#365—22no—
22C61×#362—21no—
23C61×#361—21no—
24C61×#360—22no—
25C61×#350—22no—
26C61×#344—21no—
27C2×#41×C61—21no—
28C2×#41×C61D411yescharacteristic
29#135×C61—21no—
30#135×C61—21no—
31#135×C61—21no—
32#135×C61—21no—
33C2×Q16×C61D411yescharacteristic
34C2×SD16×C61—21no—
35C2×D8×C61D411yescharacteristic
36#131×C61—21no—
37#131×C61—21no—
38#131×C61—21no—
39#131×C61—21no—
40C2×M16×C61—21no—
41C2×M16×C61—21no—
42C2×M16×C61D411yescharacteristic
43C22×C8×C61—21no—
44C22×C8×C61C2311yescharacteristic
45C22⋊Q8×C61—22no—
46C22⋊Q8×C61—41no—
47#121×C61—22no—
48#121×C61—42no—
49#121×C61—41no—
50#117×C61—21no—
51C2×C4⋊C4×C61—21no—
52M32×C61—21no—
53M32×C61—21no—
54M32×C61—21no—
55M32×C61D412yescomplemented
56C2×C16×C61—21no—
57C2×C16×C61—21no—
58#108×C61—21no—
59#108×C61—21no—
60#107×C61—21no—
61#106×C61—21no—
62#106×C61—21no—
63#106×C61D412yes—
64#104×C61—42no—
65#103×C61—22no—
66#102×C61—22no—
67#41×C61—21no—
68#41×C61—21no—
69#41×C61—21no—
70#41×C61—21no—
71#41×C61—41no—
72#41×C61—41no—
73#41×C61—41no—
74#41×C61—41no—
75C2×Q8×C61—21no—
76C2×Q8×C61SD1611yescharacteristic
77C2×D4×C61—21no—
78C2×D4×C61—21no—
79C2×D4×C61—41no—
80C2×D4×C61—42no—
81C2×D4×C61SD1611yescharacteristic
82C22×C4×C61—21no—
83C22×C4×C61—41no—
84C22×C4×C61—41no—
85C22×C4×C61C2×D411yescharacteristic
86Q16×C61—21no—
87Q16×C61—21no—
88SD16×C61—41no—
89SD16×C61—41no—
90D8×C61—21no—
91D8×C61—21no—
92M16×C61—21no—
93M16×C61—21no—
94M16×C61—41no—
95M16×C61—41no—
96M16×C61—41no—
97M16×C61—41no—
98C2×C8×C61—21no—
99C2×C8×C61—41no—
100C2×C8×C61—41no—
101C2×C8×C61—41no—
102C2×C8×C61C2×D411yescharacteristic
103C2×C8×C61C2×D411yescharacteristic
104C2×C8×C61C2×D411yescharacteristic
105C2×C8×C61#4111yescharacteristic
106C2×C8×C61#4111yescharacteristic
107C2×C8×C61#4111yescharacteristic
108C4⋊C4×C61—22no—
109C4⋊C4×C61—42no—
110C4⋊C4×C61—41no—
111C4⋊C4×C61—41no—
112C22⋊C4×C61—42no—
113C22⋊C4×C61—42no—
114C22⋊C4×C61—41no—
115C42×C61—41no—
116C16×C61—22no—
117C16×C61—41no—
118C23×C61—21no—
119C23×C61—41no—
120C23×C61AGL(1,ℤ/8)11yescharacteristic
121Q8×C61—21no—
122Q8×C61—21no—
123Q8×C61—41no—
124Q8×C61—41no—
125D4×C61—21no—
126D4×C61—21no—
127D4×C61—41no—
128D4×C61—41no—
129D4×C61—41no—
130D4×C61—41no—
131D4×C61—81no—
132D4×C61—81no—
133D4×C61—162no—
134C2×C4×C61—21no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—42no—
138C2×C4×C61—41no—
139C2×C4×C61—81no—
140C2×C4×C61—81no—
141C2×C4×C61—81no—
142C2×C4×C61—161no—
143C2×C4×C61#12011yescharacteristic
144C2×C4×C61#12111yescharacteristic
145C2×C4×C61#12311yescharacteristic
146C2×C4×C61C2×SD1611yescharacteristic
147C2×C4×C61#13511yescharacteristic
148C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
149C8×C61—41no—
150C8×C61—81no—
151C8×C61#12111yescharacteristic
152C8×C61#12111yescharacteristic
153C8×C61#12311yescharacteristic
154C8×C61#12411yescharacteristic
155#13400C6111yesmaximal, characteristic, direct product factor, Sylow
156C22×C61—41no—
157C22×C61—42no—
158C22×C61—41no—
159C22×C61—81no—
160C22×C61—81no—
161C22×C61—81no—
162C22×C61#45011yescharacteristic
163C22×C61#46911yescharacteristic
164C22×C61#48211yescharacteristic
165C4×C61—41no—
166C4×C61—82no—
167C4×C61—81no—
168C4×C61—161no—
169C4×C61#39411yescharacteristic
170C4×C61#44911yescharacteristic
171C4×C61#46511yescharacteristic
172C4×C61#48111yescharacteristic
173#3060C2×C6111yescharacteristic
174C2×#365C2×C6111yescharacteristic, complemented
175#2148C2×C6111yescharacteristic, complemented
176#2145C2×C6111yescharacteristic, complemented
177#2117C2×C6111yescharacteristic, complemented
178#1814C2×C6111yescharacteristic, complemented
179#1386C2×C6111yescharacteristic, complemented
180C2×C61—21no—
181C2×C61—21no—
182C2×C61—21no—
183C2×C61—81no—
184C2×C61—161no—
185C2×C61#203411yescharacteristic
186C2×#135C22×C6111yescharacteristic
187C2×#131C22×C6111yescharacteristic
188#537—21no—
189C2×M32C22×C6111yescharacteristic
190C2×M32C22×C6111yescharacteristic
191#470—21no—
192#469—21no—
193#465—22no—
194C2×#108C22×C6111yescharacteristic
195#427C22×C6111yescharacteristic
196C2×#106C22×C6111yescharacteristic
197#421—21no—
198#417—21no—
199#365—22no—
200#362—21no—
201#361—21no—
202#360—22no—
203#350—22no—
204#344—21no—
205C61#1340011yescharacteristic, direct product factor, Sylow
206C2×#41—21no—
207C2×#41D4×C6111yescharacteristic
208#135—21no—
209#135—21no—
210#135—21no—
211#135—21no—
212C2×Q16D4×C6111yescharacteristic
213C2×SD16—21no—
214C2×D8D4×C6111yescharacteristic
215#131—21no—
216#131—21no—
217#131—21no—
218#131—21no—
219C2×M16—21no—
220C2×M16—21no—
221C2×M16D4×C6111yescharacteristic
222C22×C8—21no—
223C22×C8C23×C6111yescharacteristic
224C22⋊Q8—22no—
225C22⋊Q8—41no—
226#121—22no—
227#121—42no—
228#121—41no—
229#117—21no—
230C2×C4⋊C4—21no—
231M32—21no—
232M32—21no—
233M32—21no—
234M32D4×C6112yescomplemented
235C2×C16—21no—
236C2×C16—21no—
237#108—21no—
238#108—21no—
239#107—21no—
240#106—21no—
241#106—21no—
242#106D4×C6112yes—
243#104—42no—
244#103—22no—
245#102—22no—
246#41—21no—
247#41—21no—
248#41—21no—
249#41—21no—
250#41—41no—
251#41—41no—
252#41—41no—
253#41—41no—
254C2×Q8—21no—
255C2×Q8SD16×C6111yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—41no—
259C2×D4—42no—
260C2×D4SD16×C6111yescharacteristic
261C22×C4—21no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4C2×D4×C6111yescharacteristic
265Q16—21no—
266Q16—21no—
267SD16—41no—
268SD16—41no—
269D8—21no—
270D8—21no—
271M16—21no—
272M16—21no—
273M16—41no—
274M16—41no—
275M16—41no—
276M16—41no—
277C2×C8—21no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8C2×D4×C6111yescharacteristic
282C2×C8C2×D4×C6111yescharacteristic
283C2×C8C2×D4×C6111yescharacteristic
284C2×C8#41×C6111yescharacteristic
285C2×C8#41×C6111yescharacteristic
286C2×C8#41×C6111yescharacteristic
287C4⋊C4—22no—
288C4⋊C4—42no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C22⋊C4—42no—
292C22⋊C4—42no—
293C22⋊C4—41no—
294C42—41no—
295C16—22no—
296C16—41no—
297C23—21no—
298C23—41no—
299C23AGL(1,ℤ/8)×C6111yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—41no—
303Q8—41no—
304D4—21no—
305D4—21no—
306D4—41no—
307D4—41no—
308D4—41no—
309D4—41no—
310D4—81no—
311D4—81no—
312D4—162no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—161no—
322C2×C4#120×C6111yescharacteristic
323C2×C4#121×C6111yescharacteristic
324C2×C4#123×C6111yescharacteristic
325C2×C4C2×SD16×C6111yescharacteristic
326C2×C4#135×C6111yescharacteristic
327C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
328C8—41no—
329C8—81no—
330C8#121×C6111yescharacteristic
331C8#121×C6111yescharacteristic
332C8#123×C6111yescharacteristic
333C8#124×C6111yescharacteristic
334C22—41no—
335C22—42no—
336C22—41no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22C61×#45011yescharacteristic
341C22C61×#46911yescharacteristic
342C22C61×#48211yescharacteristic
343C4—41no—
344C4—82no—
345C4—81no—
346C4—161no—
347C4C61×#39411yescharacteristic
348C4C61×#44911yescharacteristic
349C4C61×#46511yescharacteristic
350C4C61×#48111yescharacteristic
351C2—21no—
352C2—21no—
353C2—21no—
354C2—81no—
355C2—161no—
356C2C61×#203411yescharacteristic
subgroupG/H
center, socleC2×C61#2034
commutator, Frattini, cosocleC22×C8C23×C61
prime radicalC61×#3060C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C61 ◁ C22×C4×C61 ◁ C2×#131×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C61×#365C2semidirect
3. C61×#2148C2semidirect
4. C61×#2145C2semidirect
5. C61×#2117C2semidirect
6. C61×#1814C2semidirect
7. C61×#1386C2semidirect
55. M32×C61D4semidirect
155. #13400C61direct (N × H)
174. C2×#365C2×C61semidirect
175. #2148C2×C61semidirect
176. #2145C2×C61semidirect
177. #2117C2×C61semidirect
178. #1814C2×C61semidirect
179. #1386C2×C61semidirect
205. C61#13400direct (N × H)
234. M32D4×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#30602
C2×C61×#3652
C61×#21482
C61×#21452
C61×#21172
C61×#18142
C61×#13862
#1340061