Finite Group Databasebeta

← C61×#33955 #29537388

Subgroups — C61×#33955 #29537388

Order 15616.

458 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3383C211yesmaximal, characteristic, complemented
2C61×#3380C211yesmaximal, characteristic
3C61×#2255C211yesmaximal, characteristic, complemented
4C61×#2255C211yesmaximal, characteristic, complemented
5C61×#2253C211yesmaximal, characteristic, complemented
6C61×#2229C211yesmaximal, characteristic, complemented
7C61×#2229C211yesmaximal, characteristic, complemented
8C61×#2228C211yesmaximal, characteristic
9C61×#2228C211yesmaximal, characteristic
10C61×#2226C211yesmaximal, characteristic
11C61×#2225C211yesmaximal, characteristic, complemented
12C61×#2183C211yesmaximal, characteristic, complemented
13C61×#2175C211yesmaximal, characteristic
14C61×#2175C211yesmaximal, characteristic
15C4×SD32×C61C211yesmaximal, characteristic
16C61×#557—21no—
17C61×#554—21no—
18C2×SD32×C61C2211yescharacteristic
19C61×#500C2211yescharacteristic
20C61×#500C2211yescharacteristic
21C61×#499C2211yescharacteristic
22C61×#499C2211yescharacteristic
23C61×#499C2211yescharacteristic
24C61×#499C2211yescharacteristic
25C61×#479—21no—
26C61×#479—21no—
27C61×#478—21no—
28C61×#478—21no—
29C61×#476—21no—
30C61×#475—21no—
31C8×Q8×C61C2211yescharacteristic
32C4×Q16×C61C2211yescharacteristic
33C4×Q16×C61C2211yescharacteristic
34C4×Q16×C61C2211yescharacteristic
35C4×D8×C61C2211yescharacteristic
36C4×D8×C61C2211yescharacteristic
37C4×D8×C61C2211yescharacteristic
38C61×#367C2211yescharacteristic
39C61×#367C2211yescharacteristic
40C61×#367C2211yescharacteristic
41C61×#367C2211yescharacteristic
42C61×#367C2211yescharacteristic
43C61×#366C2211yescharacteristic
44C61×#366C2211yescharacteristic
45C61×#366C2211yescharacteristic
46C61×#366C2211yescharacteristic
47C61×C4⋊C16C2211yescharacteristic
48C61×C4⋊C16C2211yescharacteristic
49C61×C4⋊C16C2211yescharacteristic
50C61×#358C2211yescharacteristic
51C61×#358C2211yescharacteristic
52C61×#358C2211yescharacteristic
53C61×#357C2211yescharacteristic
54C61×#357C2211yescharacteristic
55C61×#357C2211yescharacteristic
56C61×#346C2211yescharacteristic
57C61×#346C2211yescharacteristic
58C4×C16×C61C2211yescharacteristic
59C2×Q16×C61C2311yescharacteristic
60C2×D8×C61C2311yescharacteristic
61C4⋊Q8×C61—21no—
62C4⋊Q8×C61—21no—
63C4⋊Q8×C61—41no—
64#125×C61—21no—
65#125×C61—21no—
66#125×C61—21no—
67#125×C61—21no—
68#125×C61—41no—
69#125×C61—41no—
70C22⋊Q8×C61—41no—
71C22⋊Q8×C61—41no—
72C22⋊Q8×C61—41no—
73C4×Q8×C61—21no—
74C4×Q8×C61—21no—
75C4×Q8×C61—21no—
76C4×Q8×C61—41no—
77C4×Q8×C61D411yescharacteristic
78C4×D4×C61—21no—
79C4×D4×C61—21no—
80C4×D4×C61—21no—
81C2×C4⋊C4×C61—41no—
82SD32×C61Q814yescomplemented
83C2×C16×C61C2311yescharacteristic
84C2×C16×C61C2311yescharacteristic
85C2×C16×C61C2311yescharacteristic
86C2×C16×C61C2311yescharacteristic
87#107×C61—21no—
88#107×C61—21no—
89#107×C61C2311yescharacteristic
90#107×C61C2311yescharacteristic
91#107×C61C2311yescharacteristic
92#107×C61C2311yescharacteristic
93#107×C61C2311yescharacteristic
94#107×C61C2311yescharacteristic
95#106×C61—21no—
96#106×C61—21no—
97#106×C61—21no—
98#106×C61—21no—
99C4⋊C8×C61D411yescharacteristic
100C4⋊C8×C61D411yescharacteristic
101C4⋊C8×C61D411yescharacteristic
102#103×C61—21no—
103#103×C61—21no—
104#103×C61—21no—
105#102×C61—21no—
106#102×C61—21no—
107#102×C61—21no—
108C4×C8×C61C2311yescharacteristic
109C4×C8×C61C2311yescharacteristic
110C4×C8×C61C2311yescharacteristic
111C2×Q8×C61—21no—
112C2×Q8×C61—41no—
113C2×Q8×C61—41no—
114C2×Q8×C61D811yescharacteristic
115C2×D4×C61—21no—
116C22×C4×C61—41no—
117C22×C4×C61—41no—
118C22×C4×C61—41no—
119Q16×C61—21no—
120Q16×C61C2×Q812yes—
121D8×C61—21no—
122D8×C61C2×Q812yes—
123C2×C8×C61C2×D411yescharacteristic
124C2×C8×C61C2×D411yescharacteristic
125C2×C8×C61C2×D411yescharacteristic
126C2×C8×C61C2411yescharacteristic
127C4⋊C4×C61—21no—
128C4⋊C4×C61—21no—
129C4⋊C4×C61—21no—
130C4⋊C4×C61—21no—
131C4⋊C4×C61—21no—
132C4⋊C4×C61—21no—
133C4⋊C4×C61—41no—
134C4⋊C4×C61—41no—
135C4⋊C4×C61—41no—
136C4⋊C4×C61—41no—
137C4⋊C4×C61—41no—
138C4⋊C4×C61—41no—
139C4⋊C4×C61—41no—
140C4⋊C4×C61—41no—
141C4⋊C4×C61—41no—
142C4⋊C4×C61—41no—
143C4⋊C4×C61—41no—
144C4⋊C4×C61—41no—
145C4⋊C4×C61—41no—
146C4⋊C4×C61D811yescharacteristic
147C4⋊C4×C61D811yescharacteristic
148C4⋊C4×C61D811yescharacteristic
149C22⋊C4×C61—41no—
150C22⋊C4×C61—41no—
151C22⋊C4×C61—41no—
152C42×C61—41no—
153C42×C61—41no—
154C42×C61—41no—
155C42×C61C2×D411yescharacteristic
156C42×C61C2×D411yescharacteristic
157C42×C61C2×D411yescharacteristic
158C16×C61—21no—
159C16×C61—21no—
160C16×C61—21no—
161C16×C61C2×Q812yes—
162C23×C61—41no—
163Q8×C61—22no—
164Q8×C61—41no—
165Q8×C61—41no—
166Q8×C61—82no—
167Q8×C61—161no—
168D4×C61—22no—
169D4×C61—41no—
170C2×C4×C61—41no—
171C2×C4×C61—41no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—82no—
178C2×C4×C61—161no—
179C2×C4×C61—161no—
180C2×C4×C61C2×D811yescharacteristic
181C2×C4×C61C2×D811yescharacteristic
182C2×C4×C61C2×D811yescharacteristic
183C2×C4×C61C2×D811yescharacteristic
184C2×C4×C61C2×D811yescharacteristic
185C2×C4×C61C2×D811yescharacteristic
186C2×C4×C61C22×D411yescharacteristic
187C8×C61—21no—
188C8×C61—21no—
189C8×C61—21no—
190C8×C61C22×Q811yescharacteristic
191C8×C612−1+411yescharacteristic
192#33955C6111yesmaximal, characteristic, direct product factor, Sylow
193C22×C61—42no—
194C22×C61—81no—
195C22×C61—81no—
196C22×C61C22×D811yescharacteristic
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—42no—
204C4×C61—81no—
205C4×C61—81no—
206C4×C61—81no—
207C4×C61—81no—
208C4×C61—81no—
209C4×C61—81no—
210C4×C61D4×Q811yescharacteristic
211C4×C61#57811yescharacteristic
212#3383C2×C6111yescharacteristic, complemented
213#3380C2×C6111yescharacteristic
214#2255C2×C6111yescharacteristic, complemented
215#2255C2×C6111yescharacteristic, complemented
216#2253C2×C6111yescharacteristic, complemented
217#2229C2×C6111yescharacteristic, complemented
218#2229C2×C6111yescharacteristic, complemented
219#2228C2×C6111yescharacteristic
220#2228C2×C6111yescharacteristic
221#2226C2×C6111yescharacteristic
222#2225C2×C6111yescharacteristic, complemented
223#2183C2×C6111yescharacteristic, complemented
224#2175C2×C6111yescharacteristic
225#2175C2×C6111yescharacteristic
226C4×SD32C2×C6111yescharacteristic
227C2×C61—82no—
228C2×C61Q8×D811yescharacteristic
229C2×C61#341411yescharacteristic
230C2×C61#341611yescharacteristic
231#557—21no—
232#554—21no—
233C2×SD32C22×C6111yescharacteristic
234#500C22×C6111yescharacteristic
235#500C22×C6111yescharacteristic
236#499C22×C6111yescharacteristic
237#499C22×C6111yescharacteristic
238#499C22×C6111yescharacteristic
239#499C22×C6111yescharacteristic
240#479—21no—
241#479—21no—
242#478—21no—
243#478—21no—
244#476—21no—
245#475—21no—
246C8×Q8C22×C6111yescharacteristic
247C4×Q16C22×C6111yescharacteristic
248C4×Q16C22×C6111yescharacteristic
249C4×Q16C22×C6111yescharacteristic
250C4×D8C22×C6111yescharacteristic
251C4×D8C22×C6111yescharacteristic
252C4×D8C22×C6111yescharacteristic
253#367C22×C6111yescharacteristic
254#367C22×C6111yescharacteristic
255#367C22×C6111yescharacteristic
256#367C22×C6111yescharacteristic
257#367C22×C6111yescharacteristic
258#366C22×C6111yescharacteristic
259#366C22×C6111yescharacteristic
260#366C22×C6111yescharacteristic
261#366C22×C6111yescharacteristic
262C4⋊C16C22×C6111yescharacteristic
263C4⋊C16C22×C6111yescharacteristic
264C4⋊C16C22×C6111yescharacteristic
265#358C22×C6111yescharacteristic
266#358C22×C6111yescharacteristic
267#358C22×C6111yescharacteristic
268#357C22×C6111yescharacteristic
269#357C22×C6111yescharacteristic
270#357C22×C6111yescharacteristic
271#346C22×C6111yescharacteristic
272#346C22×C6111yescharacteristic
273C4×C16C22×C6111yescharacteristic
274C61#3395511yescharacteristic, direct product factor, Sylow
275C2×Q16C23×C6111yescharacteristic
276C2×D8C23×C6111yescharacteristic
277C4⋊Q8—21no—
278C4⋊Q8—21no—
279C4⋊Q8—41no—
280#125—21no—
281#125—21no—
282#125—21no—
283#125—21no—
284#125—41no—
285#125—41no—
286C22⋊Q8—41no—
287C22⋊Q8—41no—
288C22⋊Q8—41no—
289C4×Q8—21no—
290C4×Q8—21no—
291C4×Q8—21no—
292C4×Q8—41no—
293C4×Q8D4×C6111yescharacteristic
294C4×D4—21no—
295C4×D4—21no—
296C4×D4—21no—
297C2×C4⋊C4—41no—
298SD32Q8×C6114yescomplemented
299C2×C16C23×C6111yescharacteristic
300C2×C16C23×C6111yescharacteristic
301C2×C16C23×C6111yescharacteristic
302C2×C16C23×C6111yescharacteristic
303#107—21no—
304#107—21no—
305#107C23×C6111yescharacteristic
306#107C23×C6111yescharacteristic
307#107C23×C6111yescharacteristic
308#107C23×C6111yescharacteristic
309#107C23×C6111yescharacteristic
310#107C23×C6111yescharacteristic
311#106—21no—
312#106—21no—
313#106—21no—
314#106—21no—
315C4⋊C8D4×C6111yescharacteristic
316C4⋊C8D4×C6111yescharacteristic
317C4⋊C8D4×C6111yescharacteristic
318#103—21no—
319#103—21no—
320#103—21no—
321#102—21no—
322#102—21no—
323#102—21no—
324C4×C8C23×C6111yescharacteristic
325C4×C8C23×C6111yescharacteristic
326C4×C8C23×C6111yescharacteristic
327C2×Q8—21no—
328C2×Q8—41no—
329C2×Q8—41no—
330C2×Q8D8×C6111yescharacteristic
331C2×D4—21no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335Q16—21no—
336Q16C2×Q8×C6112yes—
337D8—21no—
338D8C2×Q8×C6112yes—
339C2×C8C2×D4×C6111yescharacteristic
340C2×C8C2×D4×C6111yescharacteristic
341C2×C8C2×D4×C6111yescharacteristic
342C2×C8C24×C6111yescharacteristic
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C4⋊C4D8×C6111yescharacteristic
363C4⋊C4D8×C6111yescharacteristic
364C4⋊C4D8×C6111yescharacteristic
365C22⋊C4—41no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C42—41no—
369C42—41no—
370C42—41no—
371C42C2×D4×C6111yescharacteristic
372C42C2×D4×C6111yescharacteristic
373C42C2×D4×C6111yescharacteristic
374C16—21no—
375C16—21no—
376C16—21no—
377C16C2×Q8×C6112yes—
378C23—41no—
379Q8—22no—
380Q8—41no—
381Q8—41no—
382Q8—82no—
383Q8—161no—
384D4—22no—
385D4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—82no—
394C2×C4—161no—
395C2×C4—161no—
396C2×C4C2×D8×C6111yescharacteristic
397C2×C4C2×D8×C6111yescharacteristic
398C2×C4C2×D8×C6111yescharacteristic
399C2×C4C2×D8×C6111yescharacteristic
400C2×C4C2×D8×C6111yescharacteristic
401C2×C4C2×D8×C6111yescharacteristic
402C2×C4C22×D4×C6111yescharacteristic
403C8—21no—
404C8—21no—
405C8—21no—
406C8C22×Q8×C6111yescharacteristic
407C82−1+4×C6111yescharacteristic
408C22—42no—
409C22—81no—
410C22—81no—
411C22C22×D8×C6111yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—42no—
419C4—81no—
420C4—81no—
421C4—81no—
422C4—81no—
423C4—81no—
424C4—81no—
425C4D4×Q8×C6111yescharacteristic
426C4C61×#57811yescharacteristic
427C2—82no—
428C2Q8×D8×C6111yescharacteristic
429C2C61×#341411yescharacteristic
430C2C61×#341611yescharacteristic
subgroupG/H
center, socleC22×C61C22×D8
commutator, Frattini, cosocleC2×C8C24×C61
prime radicalC2×D8×C61C23
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C4×Q8×C61 ◁ C8×Q8×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3383C2semidirect
3. C61×#2255C2semidirect
4. C61×#2255C2semidirect
5. C61×#2253C2semidirect
6. C61×#2229C2semidirect
7. C61×#2229C2semidirect
11. C61×#2225C2semidirect
12. C61×#2183C2semidirect
82. SD32×C61Q8semidirect
192. #33955C61direct (N × H)
212. #3383C2×C61semidirect
214. #2255C2×C61semidirect
215. #2255C2×C61semidirect
216. #2253C2×C61semidirect
217. #2229C2×C61semidirect
218. #2229C2×C61semidirect
222. #2225C2×C61semidirect
223. #2183C2×C61semidirect
274. C61#33955direct (N × H)
298. SD32Q8×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#33832
C61×#33802
C61×#22552
C61×#22532
C61×#22292
C61×#22282
C61×#22262
C61×#22252
C61×#21832
C61×#21752
C4×SD32×C612
#3395561