Finite Group Databasebeta

← C61×#9346 #29512779

Subgroups — C61×#9346 #29512779

Order 15616.

444 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3095C211yesmaximal, characteristic
2C61×#2924C211yesmaximal, characteristic
3C61×#1825C211yesmaximal, characteristic
4C61×#1520C211yesmaximal, characteristic
5C61×#1472C211yesmaximal, characteristic
6C61×#1305C211yesmaximal, characteristic
7C61×#1298C211yesmaximal, characteristic
8C2×C22⋊Q8×C61C2211yescharacteristic
9C2×#117×C61C2211yescharacteristic
10C61×#485—21no—
11C61×#485—21no—
12C61×#484—21no—
13C61×#483—21no—
14C61×#433—22no—
15C61×#432—21no—
16C61×#431—21no—
17C61×#428C411yescharacteristic, complemented
18C61×#428C411yescharacteristic, complemented
19C61×#424—21no—
20C61×#419C411yescharacteristic, complemented
21C61×#419C411yescharacteristic, complemented
22C61×#407C2211yescharacteristic
23C61×#407C2211yescharacteristic
24C2×C22⋊C8×C61C2211yescharacteristic
25C2×C22⋊C8×C61C2211yescharacteristic
26C61×#405—21no—
27C61×#380C2211yescharacteristic
28C61×#340—21no—
29C61×#340—21no—
30C61×#328—21no—
31C61×#328—21no—
32C61×#324—22no—
33C22×Q8×C61C2×C411yescharacteristic
34C23×C4×C61C2311yescharacteristic
35C2×M16×C61—21no—
36C2×M16×C61C2×C411yescharacteristic
37C2×M16×C61C2×C411yescharacteristic
38C22×C8×C61—21no—
39C22×C8×C61—21no—
40C22⋊Q8×C61—21no—
41C22⋊Q8×C61—21no—
42C22⋊Q8×C61—21no—
43C22⋊Q8×C61—21no—
44#117×C61—21no—
45#117×C61—21no—
46#117×C61C2×C411yescharacteristic
47#117×C61C2×C411yescharacteristic
48#117×C61D411yescharacteristic
49#117×C61D411yescharacteristic
50C2×C4⋊C4×C61—21no—
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61D411yescharacteristic
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61—21no—
58C2×C42×C61—21no—
59#107×C61—21no—
60#107×C61—21no—
61#106×C61—21no—
62#106×C61—21no—
63C4⋊C8×C61—22no—
64C4⋊C8×C61—22no—
65#103×C61—21no—
66#103×C61—21no—
67#103×C61—21no—
68#103×C61—21no—
69C22⋊C8×C61—21no—
70C22⋊C8×C61—21no—
71C22⋊C8×C61—21no—
72C22⋊C8×C61—21no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61—21no—
75C22⋊C8×C61D412yes—
76C22⋊C8×C61D411yescharacteristic
77C22⋊C8×C61D411yescharacteristic
78#97×C61—22no—
79C4×C8×C61—22no—
80#95×C61—21no—
81C24×C61#4111yescharacteristic
82C2×Q8×C61—21no—
83C2×Q8×C61—21no—
84C2×Q8×C61—41no—
85C2×Q8×C61—41no—
86C22×C4×C61—21no—
87C22×C4×C61—21no—
88C22×C4×C61—21no—
89C22×C4×C61—21no—
90C22×C4×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61—41no—
93C22×C4×C61C22×C411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61#4111yescharacteristic
99M16×C61—41no—
100M16×C61—41no—
101M16×C61—41no—
102M16×C61—41no—
103C2×C8×C61—21no—
104C2×C8×C61—21no—
105C2×C8×C61—21no—
106C2×C8×C61—22no—
107C2×C8×C61—21no—
108C2×C8×C61—41no—
109C2×C8×C61—41no—
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—41no—
118C4⋊C4×C61—41no—
119C4⋊C4×C61—41no—
120C4⋊C4×C61—41no—
121C4⋊C4×C61C22⋊C411yescharacteristic
122C4⋊C4×C61C22⋊C411yescharacteristic
123C4⋊C4×C61C22⋊C411yescharacteristic
124C4⋊C4×C61C22⋊C411yescharacteristic
125C22⋊C4×C61—21no—
126C22⋊C4×C61—21no—
127C22⋊C4×C61—21no—
128C22⋊C4×C61—21no—
129C22⋊C4×C61—41no—
130C22⋊C4×C61—41no—
131C22⋊C4×C61—81no—
132C42×C61—21no—
133C42×C61—21no—
134C42×C61—21no—
135C42×C61—21no—
136C23×C61—21no—
137C23×C61—21no—
138C23×C61—41no—
139C23×C61—41no—
140C23×C61C4×D411yescharacteristic
141C23×C61#12111yescharacteristic
142C23×C61#12311yescharacteristic
143Q8×C61—41no—
144Q8×C61—41no—
145Q8×C61—81no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—42no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—81no—
165C2×C4×C61—81no—
166C2×C4×C61—81no—
167C2×C4×C61—81no—
168C2×C4×C61—81no—
169C2×C4×C61C2×C22⋊C411yescharacteristic
170C2×C4×C61C4×D411yescharacteristic
171C2×C4×C61#12011yescharacteristic
172C2×C4×C61#12111yescharacteristic
173C8×C61—41no—
174C8×C61—41no—
175C8×C61—42no—
176C8×C61—41no—
177C8×C61—41no—
178C8×C61—81no—
179#9346C6111yesmaximal, characteristic, direct product factor, Sylow
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—81no—
189C22×C61—81no—
190C22×C61#38611yescharacteristic
191C22×C61#47111yescharacteristic
192C22×C61#47311yescharacteristic
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—41no—
197C4×C61—41no—
198C4×C61—41no—
199C4×C61—41no—
200C4×C61—81no—
201C4×C61—81no—
202C4×C61—161no—
203C4×C61#41011yescharacteristic
204C4×C61#41011yescharacteristic
205#3095C2×C6111yescharacteristic
206#2924C2×C6111yescharacteristic
207#1825C2×C6111yescharacteristic
208#1520C2×C6111yescharacteristic
209#1472C2×C6111yescharacteristic
210#1305C2×C6111yescharacteristic
211#1298C2×C6111yescharacteristic
212C2×C61—21no—
213C2×C61—21no—
214C2×C61—41no—
215C2×C61—41no—
216C2×C61#188111yescharacteristic
217C2×C61#189911yescharacteristic
218C2×C61#190811yescharacteristic
219C2×C22⋊Q8C22×C6111yescharacteristic
220C2×#117C22×C6111yescharacteristic
221#485—21no—
222#485—21no—
223#484—21no—
224#483—21no—
225#433—22no—
226#432—21no—
227#431—21no—
228#428C4×C6111yescharacteristic, complemented
229#428C4×C6111yescharacteristic, complemented
230#424—21no—
231#419C4×C6111yescharacteristic, complemented
232#419C4×C6111yescharacteristic, complemented
233#407C22×C6111yescharacteristic
234#407C22×C6111yescharacteristic
235C2×C22⋊C8C22×C6111yescharacteristic
236C2×C22⋊C8C22×C6111yescharacteristic
237#405—21no—
238#380C22×C6111yescharacteristic
239#340—21no—
240#340—21no—
241#328—21no—
242#328—21no—
243#324—22no—
244C61#934611yescharacteristic, direct product factor, Sylow
245C22×Q8C2×C4×C6111yescharacteristic
246C23×C4C23×C6111yescharacteristic
247C2×M16—21no—
248C2×M16C2×C4×C6111yescharacteristic
249C2×M16C2×C4×C6111yescharacteristic
250C22×C8—21no—
251C22×C8—21no—
252C22⋊Q8—21no—
253C22⋊Q8—21no—
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256#117—21no—
257#117—21no—
258#117C2×C4×C6111yescharacteristic
259#117C2×C4×C6111yescharacteristic
260#117D4×C6111yescharacteristic
261#117D4×C6111yescharacteristic
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4C2×C4×C6111yescharacteristic
265C2×C4⋊C4D4×C6111yescharacteristic
266C2×C4⋊C4D4×C6111yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C42—21no—
271#107—21no—
272#107—21no—
273#106—21no—
274#106—21no—
275C4⋊C8—22no—
276C4⋊C8—22no—
277#103—21no—
278#103—21no—
279#103—21no—
280#103—21no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8—21no—
286C22⋊C8—21no—
287C22⋊C8D4×C6112yes—
288C22⋊C8D4×C6111yescharacteristic
289C22⋊C8D4×C6111yescharacteristic
290#97—22no—
291C4×C8—22no—
292#95—21no—
293C24#41×C6111yescharacteristic
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—41no—
297C2×Q8—41no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4C22×C4×C6111yescharacteristic
306C22×C4C2×D4×C6111yescharacteristic
307C22×C4C2×D4×C6111yescharacteristic
308C22×C4C2×D4×C6111yescharacteristic
309C22×C4C2×D4×C6111yescharacteristic
310C22×C4#41×C6111yescharacteristic
311M16—41no—
312M16—41no—
313M16—41no—
314M16—41no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—22no—
319C2×C8—21no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4C22⋊C4×C6111yescharacteristic
334C4⋊C4C22⋊C4×C6111yescharacteristic
335C4⋊C4C22⋊C4×C6111yescharacteristic
336C4⋊C4C22⋊C4×C6111yescharacteristic
337C22⋊C4—21no—
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—81no—
344C42—21no—
345C42—21no—
346C42—21no—
347C42—21no—
348C23—21no—
349C23—21no—
350C23—41no—
351C23—41no—
352C23C4×D4×C6111yescharacteristic
353C23#121×C6111yescharacteristic
354C23#123×C6111yescharacteristic
355Q8—41no—
356Q8—41no—
357Q8—81no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4C2×C22⋊C4×C6111yescharacteristic
382C2×C4C4×D4×C6111yescharacteristic
383C2×C4#120×C6111yescharacteristic
384C2×C4#121×C6111yescharacteristic
385C8—41no—
386C8—41no—
387C8—42no—
388C8—41no—
389C8—41no—
390C8—81no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—81no—
400C22—81no—
401C22C61×#38611yescharacteristic
402C22C61×#47111yescharacteristic
403C22C61×#47311yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—41no—
411C4—81no—
412C4—81no—
413C4—161no—
414C4C61×#41011yescharacteristic
415C4C61×#41011yescharacteristic
416C2—21no—
417C2—21no—
418C2—41no—
419C2—41no—
420C2C61×#188111yescharacteristic
421C2C61×#189911yescharacteristic
422C2C61×#190811yescharacteristic
subgroupG/H
center, socleC22×C61#386
commutatorC22×C4C22×C4×C61
Frattini, cosocleC23×C4C23×C61
prime radicalC24×C61#41
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
17. C61×#428C4semidirect
18. C61×#428C4semidirect
20. C61×#419C4semidirect
21. C61×#419C4semidirect
179. #9346C61direct (N × H)
228. #428C4×C61semidirect
229. #428C4×C61semidirect
231. #419C4×C61semidirect
232. #419C4×C61semidirect
244. C61#9346direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#30952
C61×#29242
C61×#18252
C61×#15202
C61×#14722
C61×#13052
C61×#12982
#934661