Finite Group Databasebeta

← C61×#9207 #29512640

Subgroups — C61×#9207 #29512640

Order 15616.

478 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3076C211yesmaximal, characteristic
2C8×#41×C61C211yesmaximal, characteristic
3C61×#1806C211yesmaximal, characteristic
4C61×#1503C211yesmaximal, characteristic, complemented
5C61×#1493C211yesmaximal, characteristic, complemented
6C61×#1301C211yesmaximal, characteristic, complemented
7C61×#1279C211yesmaximal, characteristic, complemented
8C61×#533C2211yescharacteristic
9C4×#41×C61C2211yescharacteristic
10C61×#479—21no—
11C61×#478—21no—
12C61×#477C411yescharacteristic, complemented
13C61×#476C411yescharacteristic, complemented
14C61×#475C411yescharacteristic, complemented
15C61×#474C411yescharacteristic, complemented
16C8×Q8×C61—21no—
17C8×D4×C61—21no—
18C8×D4×C61—22no—
19C61×#431—21no—
20C61×#431C2211yescharacteristic
21C61×#427—21no—
22C61×#423C2211yescharacteristic
23C2×C4⋊C8×C61C2211yescharacteristic
24C2×#104×C61—21no—
25C61×#416—21no—
26C2×C4×C8×C61—21no—
27C2×C4×C8×C61C2211yescharacteristic
28C4×C4⋊C4×C61C2211yescharacteristic
29C61×#339—21no—
30C61×#328—22no—
31C61×Q8⋊C8—21no—
32C61×Q8⋊C8—21no—
33C2×#41×C61D411yescharacteristic
34C2×M16×C61—21no—
35C22×C8×C61—22no—
36C22×C8×C61—21no—
37C22×C8×C61—21no—
38C4⋊Q8×C61C2×C411yescharacteristic
39C4⋊Q8×C61C2×C411yescharacteristic
40#125×C61—21no—
41C22⋊Q8×C61—21no—
42C22⋊Q8×C61—21no—
43C4×Q8×C61—21no—
44C4×Q8×C61—21no—
45C4×Q8×C61C2×C411yescharacteristic
46C4×Q8×C61D411yescharacteristic
47C4×D4×C61—21no—
48C4×D4×C61—21no—
49C4×D4×C61C2×C411yescharacteristic
50C4×D4×C61D411yescharacteristic
51#117×C61—21no—
52#117×C61—21no—
53#117×C61D411yescharacteristic
54C2×C4⋊C4×C61—21no—
55C2×C42×C61—21no—
56C2×C42×C61—21no—
57C2×C42×C61C2311yescharacteristic
58#107×C61—21no—
59#107×C61—21no—
60#106×C61—21no—
61#106×C61—21no—
62C4⋊C8×C61—22no—
63C4⋊C8×C61—21no—
64C4⋊C8×C61—21no—
65C4⋊C8×C61—21no—
66C4⋊C8×C61—21no—
67C4⋊C8×C61C2×C411yescharacteristic
68C4⋊C8×C61C2×C411yescharacteristic
69#104×C61—42no—
70#103×C61—21no—
71#103×C61—21no—
72#102×C61—21no—
73#102×C61—21no—
74C22⋊C8×C61—22no—
75C22⋊C8×C61D412yes—
76C4×C8×C61—22no—
77C4×C8×C61—21no—
78C4×C8×C61—21no—
79C4×C8×C61D411yescharacteristic
80C4×C8×C61D411yescharacteristic
81#95×C61—21no—
82#41×C61—21no—
83#41×C61—21no—
84#41×C61SD1612yes—
85#41×C61Q1612yes—
86C2×Q8×C61—21no—
87C2×Q8×C61—21no—
88C2×Q8×C61C22⋊C411yescharacteristic
89C2×D4×C61—21no—
90C2×D4×C61C22⋊C411yescharacteristic
91C22×C4×C61—21no—
92C22×C4×C61—21no—
93C22×C4×C61—21no—
94C22×C4×C61—41no—
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61#4111yescharacteristic
98M16×C61—41no—
99M16×C61—41no—
100C2×C8×C61—21no—
101C2×C8×C61—21no—
102C2×C8×C61—21no—
103C2×C8×C61—22no—
104C2×C8×C61—21no—
105C2×C8×C61—42no—
106C2×C8×C61—44no—
107C2×C8×C61—41no—
108C2×C8×C61—41no—
109C2×C8×C61—41no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61—22no—
113C4⋊C4×C61—21no—
114C4⋊C4×C61—21no—
115C4⋊C4×C61—21no—
116C4⋊C4×C61—21no—
117C4⋊C4×C61—41no—
118C4⋊C4×C61—41no—
119C4⋊C4×C61—41no—
120C4⋊C4×C61C22⋊C411yescharacteristic
121C4⋊C4×C61C22⋊C411yescharacteristic
122C22⋊C4×C61—21no—
123C22⋊C4×C61—21no—
124C22⋊C4×C61—21no—
125C22⋊C4×C61—41no—
126C42×C61—21no—
127C42×C61—21no—
128C42×C61—21no—
129C42×C61—41no—
130C42×C61—41no—
131C42×C61—41no—
132C42×C61C22×C411yescharacteristic
133C42×C61C2×D411yescharacteristic
134C42×C61C2×D411yescharacteristic
135C42×C61#4111yescharacteristic
136C23×C61—21no—
137C23×C61#12111yescharacteristic
138Q8×C61—21no—
139Q8×C61—41no—
140Q8×C61—41no—
141Q8×C61—81no—
142Q8×C61#10312yes—
143D4×C61—22no—
144D4×C61—22no—
145D4×C61—21no—
146D4×C61#10312yes—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—22no—
151C2×C4×C61—22no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—41no—
155C2×C4×C61—42no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—42no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—81no—
162C2×C4×C61—81no—
163C2×C4×C61C2×C22⋊C411yescharacteristic
164C2×C4×C61C4×D411yescharacteristic
165C2×C4×C61C4×D411yescharacteristic
166C2×C4×C61#12011yescharacteristic
167C2×C4×C61#12111yescharacteristic
168C2×C4×C61#12311yescharacteristic
169C2×C4×C61C2×SD1611yescharacteristic
170C2×C4×C61C2×Q1611yescharacteristic
171C2×C4×C61#13511yescharacteristic
172C2×C4×C61#13511yescharacteristic
173C8×C61—22no—
174C8×C61—42no—
175C8×C61—41no—
176C8×C61—41no—
177C8×C61—41no—
178C8×C61—81no—
179#9207C6111yesmaximal, characteristic, direct product factor, Sylow
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—22no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61#38611yescharacteristic
186C22×C61#46511yescharacteristic
187C22×C61#46711yescharacteristic
188C4×C61—21no—
189C4×C61—22no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—41no—
193C4×C61—41no—
194C4×C61—82no—
195C4×C61—81no—
196C4×C61—81no—
197C4×C61C2×#10311yescharacteristic
198C4×C61#41611yescharacteristic
199C4×C61#44311yescharacteristic
200C4×C61#44411yescharacteristic
201C4×C61#46511yescharacteristic
202C4×C61#46711yescharacteristic
203#3076C2×C6111yescharacteristic
204C8×#41C2×C6111yescharacteristic
205#1806C2×C6111yescharacteristic
206#1503C2×C6111yescharacteristic, complemented
207#1493C2×C6111yescharacteristic, complemented
208#1301C2×C6111yescharacteristic, complemented
209#1279C2×C6111yescharacteristic, complemented
210C2×C61—21no—
211C2×C61—21no—
212C2×C61—42no—
213C2×C61#187611yescharacteristic
214C2×C61#189211yescharacteristic
215C2×C61#190611yescharacteristic
216#533C22×C6111yescharacteristic
217C4×#41C22×C6111yescharacteristic
218#479—21no—
219#478—21no—
220#477C4×C6111yescharacteristic, complemented
221#476C4×C6111yescharacteristic, complemented
222#475C4×C6111yescharacteristic, complemented
223#474C4×C6111yescharacteristic, complemented
224C8×Q8—21no—
225C8×D4—21no—
226C8×D4—22no—
227#431—21no—
228#431C22×C6111yescharacteristic
229#427—21no—
230#423C22×C6111yescharacteristic
231C2×C4⋊C8C22×C6111yescharacteristic
232C2×#104—21no—
233#416—21no—
234C2×C4×C8—21no—
235C2×C4×C8C22×C6111yescharacteristic
236C4×C4⋊C4C22×C6111yescharacteristic
237#339—21no—
238#328—22no—
239Q8⋊C8—21no—
240Q8⋊C8—21no—
241C61#920711yescharacteristic, direct product factor, Sylow
242C2×#41D4×C6111yescharacteristic
243C2×M16—21no—
244C22×C8—22no—
245C22×C8—21no—
246C22×C8—21no—
247C4⋊Q8C2×C4×C6111yescharacteristic
248C4⋊Q8C2×C4×C6111yescharacteristic
249#125—21no—
250C22⋊Q8—21no—
251C22⋊Q8—21no—
252C4×Q8—21no—
253C4×Q8—21no—
254C4×Q8C2×C4×C6111yescharacteristic
255C4×Q8D4×C6111yescharacteristic
256C4×D4—21no—
257C4×D4—21no—
258C4×D4C2×C4×C6111yescharacteristic
259C4×D4D4×C6111yescharacteristic
260#117—21no—
261#117—21no—
262#117D4×C6111yescharacteristic
263C2×C4⋊C4—21no—
264C2×C42—21no—
265C2×C42—21no—
266C2×C42C23×C6111yescharacteristic
267#107—21no—
268#107—21no—
269#106—21no—
270#106—21no—
271C4⋊C8—22no—
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8C2×C4×C6111yescharacteristic
277C4⋊C8C2×C4×C6111yescharacteristic
278#104—42no—
279#103—21no—
280#103—21no—
281#102—21no—
282#102—21no—
283C22⋊C8—22no—
284C22⋊C8D4×C6112yes—
285C4×C8—22no—
286C4×C8—21no—
287C4×C8—21no—
288C4×C8D4×C6111yescharacteristic
289C4×C8D4×C6111yescharacteristic
290#95—21no—
291#41—21no—
292#41—21no—
293#41SD16×C6112yes—
294#41Q16×C6112yes—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8C22⋊C4×C6111yescharacteristic
298C2×D4—21no—
299C2×D4C22⋊C4×C6111yescharacteristic
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4C2×D4×C6111yescharacteristic
305C22×C4C2×D4×C6111yescharacteristic
306C22×C4#41×C6111yescharacteristic
307M16—41no—
308M16—41no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—22no—
313C2×C8—21no—
314C2×C8—42no—
315C2×C8—44no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—22no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4C22⋊C4×C6111yescharacteristic
330C4⋊C4C22⋊C4×C6111yescharacteristic
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—41no—
335C42—21no—
336C42—21no—
337C42—21no—
338C42—41no—
339C42—41no—
340C42—41no—
341C42C22×C4×C6111yescharacteristic
342C42C2×D4×C6111yescharacteristic
343C42C2×D4×C6111yescharacteristic
344C42#41×C6111yescharacteristic
345C23—21no—
346C23#121×C6111yescharacteristic
347Q8—21no—
348Q8—41no—
349Q8—41no—
350Q8—81no—
351Q8#103×C6112yes—
352D4—22no—
353D4—22no—
354D4—21no—
355D4#103×C6112yes—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4C2×C22⋊C4×C6111yescharacteristic
373C2×C4C4×D4×C6111yescharacteristic
374C2×C4C4×D4×C6111yescharacteristic
375C2×C4#120×C6111yescharacteristic
376C2×C4#121×C6111yescharacteristic
377C2×C4#123×C6111yescharacteristic
378C2×C4C2×SD16×C6111yescharacteristic
379C2×C4C2×Q16×C6111yescharacteristic
380C2×C4#135×C6111yescharacteristic
381C2×C4#135×C6111yescharacteristic
382C8—22no—
383C8—42no—
384C8—41no—
385C8—41no—
386C8—41no—
387C8—81no—
388C22—21no—
389C22—21no—
390C22—22no—
391C22—41no—
392C22—41no—
393C22C61×#38611yescharacteristic
394C22C61×#46511yescharacteristic
395C22C61×#46711yescharacteristic
396C4—21no—
397C4—22no—
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—82no—
403C4—81no—
404C4—81no—
405C4C2×#103×C6111yescharacteristic
406C4C61×#41611yescharacteristic
407C4C61×#44311yescharacteristic
408C4C61×#44411yescharacteristic
409C4C61×#46511yescharacteristic
410C4C61×#46711yescharacteristic
411C2—21no—
412C2—21no—
413C2—42no—
414C2C61×#187611yescharacteristic
415C2C61×#189211yescharacteristic
416C2C61×#190611yescharacteristic
subgroupG/H
centerC2×C4×C61#121
commutatorC42C22×C4×C61
Frattini, cosocleC2×C42C23×C61
socleC22×C61#386
prime radicalC2×#41×C61D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
4. C61×#1503C2semidirect
5. C61×#1493C2semidirect
6. C61×#1301C2semidirect
7. C61×#1279C2semidirect
12. C61×#477C4semidirect
13. C61×#476C4semidirect
14. C61×#475C4semidirect
15. C61×#474C4semidirect
179. #9207C61direct (N × H)
206. #1503C2×C61semidirect
207. #1493C2×C61semidirect
208. #1301C2×C61semidirect
209. #1279C2×C61semidirect
220. #477C4×C61semidirect
221. #476C4×C61semidirect
222. #475C4×C61semidirect
223. #474C4×C61semidirect
241. C61#9207direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#30762
C8×#41×C612
C61×#18062
C61×#15032
C61×#14932
C61×#13012
C61×#12792
#920761