Finite Group Databasebeta

← C61×#10179 #29513612

Subgroups — C61×#10179 #29513612

Order 15616.

560 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3208C211yesmaximal, characteristic
2C61×#3078C211yesmaximal, characteristic, complemented
3C2×C61×#460C211yesmaximal, characteristic
4C61×#1545C211yesmaximal, characteristic
5C61×#1481C211yesmaximal, characteristic, complemented
6C61×#1461C211yesmaximal, characteristic, complemented
7C61×#1301C211yesmaximal, characteristic, complemented
8C22×SD16×C61—21no—
9C61×#533C2211yescharacteristic
10C2×#127×C61C2211yescharacteristic
11C2×C4×Q8×C61C2211yescharacteristic
12C61×#492—21no—
13C61×#486—21no—
14C61×#479—22no—
15C61×#477—21no—
16C61×#475—21no—
17C61×#460—22no—
18C61×#460—22no—
19C61×#460—22no—
20C61×#450—22no—
21C61×#431C2211yescharacteristic
22C61×#431C2211yescharacteristic
23C61×#428—21no—
24C61×#423C2211yescharacteristic
25C2×C4⋊C8×C61C2211yescharacteristic
26C61×#419—21no—
27C2×#102×C61—21no—
28C61×#331—22no—
29C61×Q8⋊C8—22no—
30C61×#324—22no—
31C22×Q8×C61D411yescharacteristic
32C22×D4×C61—21no—
33C22×D4×C61—21no—
34C22×D4×C61—21no—
35C2×SD16×C61—24no—
36C2×SD16×C61—24no—
37C2×SD16×C61—42no—
38C2×SD16×C61—42no—
39C2×M16×C61—21no—
40C22×C8×C61—21no—
41C4⋊Q8×C61D411yescharacteristic
42C4⋊Q8×C61D411yescharacteristic
43#127×C61—21no—
44#127×C61—21no—
45#127×C61—21no—
46#127×C61D412yes—
47#125×C61—21no—
48C22⋊Q8×C61—21no—
49C22⋊Q8×C61—21no—
50C4×Q8×C61—21no—
51C4×Q8×C61—21no—
52C4×Q8×C61—21no—
53C4×Q8×C61—21no—
54C4×Q8×C61—21no—
55C4×Q8×C61—21no—
56#117×C61—21no—
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61D411yescharacteristic
59C2×C42×C61—21no—
60C2×C42×C61C2311yescharacteristic
61#107×C61—22no—
62#106×C61—22no—
63C4⋊C8×C61—21no—
64C4⋊C8×C61—21no—
65C4⋊C8×C61—21no—
66C4⋊C8×C61—21no—
67C4⋊C8×C61D412yes—
68C4⋊C8×C61D412yes—
69#103×C61—22no—
70#103×C61—22no—
71#102×C61—24no—
72#102×C61—24no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61D412yes—
75C4×C8×C61—21no—
76C4×C8×C61—21no—
77C24×C61—41no—
78C2×Q8×C61—21no—
79C2×Q8×C61—21no—
80C2×Q8×C61—21no—
81C2×Q8×C61—21no—
82C2×Q8×C61—21no—
83C2×Q8×C61—21no—
84C2×Q8×C61—21no—
85C2×Q8×C61SD1612yescomplemented
86C2×D4×C61—22no—
87C2×D4×C61—22no—
88C2×D4×C61—22no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—41no—
93C2×D4×C61—41no—
94C2×D4×C61—41no—
95C2×D4×C61—41no—
96C2×D4×C61—82no—
97C2×D4×C61—82no—
98C22×C4×C61—21no—
99C22×C4×C61—21no—
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61#4111yescharacteristic
103SD16×C61—48no—
104SD16×C61—84no—
105M16×C61—41no—
106M16×C61—41no—
107C2×C8×C61—22no—
108C2×C8×C61—22no—
109C2×C8×C61—22no—
110C2×C8×C61—41no—
111C2×C8×C61—41no—
112C2×C8×C61—41no—
113C4⋊C4×C61—21no—
114C4⋊C4×C61—21no—
115C4⋊C4×C61—21no—
116C4⋊C4×C61—21no—
117C4⋊C4×C61—21no—
118C4⋊C4×C61—21no—
119C4⋊C4×C61—41no—
120C4⋊C4×C61—41no—
121C4⋊C4×C61—41no—
122C4⋊C4×C61—41no—
123C22⋊C4×C61—41no—
124C42×C61—41no—
125C42×C61—41no—
126C42×C61—41no—
127C42×C61C2×D411yescharacteristic
128C42×C61C2×D411yescharacteristic
129C42×C61C2×D411yescharacteristic
130C42×C61C2×D411yescharacteristic
131C23×C61—42no—
132C23×C61—82no—
133C23×C61—82no—
134C23×C61—81no—
135C23×C61—81no—
136C23×C61#12111yescharacteristic
137Q8×C61—22no—
138Q8×C61—22no—
139Q8×C61—42no—
140Q8×C61—41no—
141Q8×C61—41no—
142Q8×C61—42no—
143D4×C61—44no—
144D4×C61—42no—
145D4×C61—42no—
146D4×C61—82no—
147D4×C61—82no—
148D4×C61—81no—
149D4×C61—81no—
150D4×C61—82no—
151C2×C4×C61—22no—
152C2×C4×C61—22no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—81no—
160C2×C4×C61#12011yescharacteristic
161C2×C4×C61#12011yescharacteristic
162C2×C4×C61#12011yescharacteristic
163C2×C4×C61#12111yescharacteristic
164C2×C4×C61#12111yescharacteristic
165C2×C4×C61#12711yescharacteristic
166C2×C4×C61C2×SD1611yescharacteristic
167C2×C4×C61#13511yescharacteristic
168C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C61#13711yescharacteristic
170C8×C61—42no—
171C8×C61—42no—
172C8×C61—42no—
173C8×C61—81no—
174#10179C6111yesmaximal, characteristic, direct product factor, Sylow
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—82no—
178C22×C61—82no—
179C22×C61—82no—
180C22×C61—162no—
181C22×C61—162no—
182C22×C61#39211yescharacteristic
183C22×C61#46511yescharacteristic
184C22×C61#46811yescharacteristic
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—21no—
188C4×C61—42no—
189C4×C61—81no—
190C4×C61—81no—
191C4×C61—81no—
192C4×C61#44811yescharacteristic
193C4×C61#44911yescharacteristic
194C4×C61#45011yescharacteristic
195C4×C61#45211yescharacteristic
196C4×C61#47112yes—
197#3208C2×C6111yescharacteristic
198#3078C2×C6111yescharacteristic, complemented
199C2×#460C2×C6111yescharacteristic
200#1545C2×C6111yescharacteristic
201#1481C2×C6111yescharacteristic, complemented
202#1461C2×C6111yescharacteristic, complemented
203#1301C2×C6111yescharacteristic, complemented
204C2×C61—21no—
205C2×C61—21no—
206C2×C61—162no—
207C2×C61#200011yescharacteristic
208C2×C61#200811yescharacteristic
209C2×C61#201911yescharacteristic
210C22×SD16—21no—
211#533C22×C6111yescharacteristic
212C2×#127C22×C6111yescharacteristic
213C2×C4×Q8C22×C6111yescharacteristic
214#492—21no—
215#486—21no—
216#479—22no—
217#477—21no—
218#475—21no—
219#460—22no—
220#460—22no—
221#460—22no—
222#450—22no—
223#431C22×C6111yescharacteristic
224#431C22×C6111yescharacteristic
225#428—21no—
226#423C22×C6111yescharacteristic
227C2×C4⋊C8C22×C6111yescharacteristic
228#419—21no—
229C2×#102—21no—
230#331—22no—
231Q8⋊C8—22no—
232#324—22no—
233C61#1017911yescharacteristic, direct product factor, Sylow
234C22×Q8D4×C6111yescharacteristic
235C22×D4—21no—
236C22×D4—21no—
237C22×D4—21no—
238C2×SD16—24no—
239C2×SD16—24no—
240C2×SD16—42no—
241C2×SD16—42no—
242C2×M16—21no—
243C22×C8—21no—
244C4⋊Q8D4×C6111yescharacteristic
245C4⋊Q8D4×C6111yescharacteristic
246#127—21no—
247#127—21no—
248#127—21no—
249#127D4×C6112yes—
250#125—21no—
251C22⋊Q8—21no—
252C22⋊Q8—21no—
253C4×Q8—21no—
254C4×Q8—21no—
255C4×Q8—21no—
256C4×Q8—21no—
257C4×Q8—21no—
258C4×Q8—21no—
259#117—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4D4×C6111yescharacteristic
262C2×C42—21no—
263C2×C42C23×C6111yescharacteristic
264#107—22no—
265#106—22no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8D4×C6112yes—
271C4⋊C8D4×C6112yes—
272#103—22no—
273#103—22no—
274#102—24no—
275#102—24no—
276C22⋊C8—21no—
277C22⋊C8D4×C6112yes—
278C4×C8—21no—
279C4×C8—21no—
280C24—41no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8SD16×C6112yescomplemented
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—22no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—82no—
300C2×D4—82no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4C2×D4×C6111yescharacteristic
304C22×C4C2×D4×C6111yescharacteristic
305C22×C4#41×C6111yescharacteristic
306SD16—48no—
307SD16—84no—
308M16—41no—
309M16—41no—
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C22⋊C4—41no—
327C42—41no—
328C42—41no—
329C42—41no—
330C42C2×D4×C6111yescharacteristic
331C42C2×D4×C6111yescharacteristic
332C42C2×D4×C6111yescharacteristic
333C42C2×D4×C6111yescharacteristic
334C23—42no—
335C23—82no—
336C23—82no—
337C23—81no—
338C23—81no—
339C23#121×C6111yescharacteristic
340Q8—22no—
341Q8—22no—
342Q8—42no—
343Q8—41no—
344Q8—41no—
345Q8—42no—
346D4—44no—
347D4—42no—
348D4—42no—
349D4—82no—
350D4—82no—
351D4—81no—
352D4—81no—
353D4—82no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—81no—
363C2×C4#120×C6111yescharacteristic
364C2×C4#120×C6111yescharacteristic
365C2×C4#120×C6111yescharacteristic
366C2×C4#121×C6111yescharacteristic
367C2×C4#121×C6111yescharacteristic
368C2×C4#127×C6111yescharacteristic
369C2×C4C2×SD16×C6111yescharacteristic
370C2×C4#135×C6111yescharacteristic
371C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
372C2×C4#137×C6111yescharacteristic
373C8—42no—
374C8—42no—
375C8—42no—
376C8—81no—
377C22—21no—
378C22—21no—
379C22—82no—
380C22—82no—
381C22—82no—
382C22—162no—
383C22—162no—
384C22C61×#39211yescharacteristic
385C22C61×#46511yescharacteristic
386C22C61×#46811yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—42no—
391C4—81no—
392C4—81no—
393C4—81no—
394C4C61×#44811yescharacteristic
395C4C61×#44911yescharacteristic
396C4C61×#45011yescharacteristic
397C4C61×#45211yescharacteristic
398C4C61×#47112yes—
399C2—21no—
400C2—21no—
401C2—162no—
402C2C61×#200011yescharacteristic
403C2C61×#200811yescharacteristic
404C2C61×#201911yescharacteristic
subgroupG/H
center, socleC22×C61#392
commutator, Frattini, cosocleC2×C42C23×C61
prime radicalC2×#127×C61C22
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. C61×#3078C2semidirect
5. C61×#1481C2semidirect
6. C61×#1461C2semidirect
7. C61×#1301C2semidirect
85. C2×Q8×C61SD16semidirect
174. #10179C61direct (N × H)
198. #3078C2×C61semidirect
201. #1481C2×C61semidirect
202. #1461C2×C61semidirect
203. #1301C2×C61semidirect
233. C61#10179direct (N × H)
288. C2×Q8SD16×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#32082
C61×#30782
C2×C61×#4602
C61×#15452
C61×#14812
C61×#14612
C61×#13012
#1017961