Finite Group Databasebeta

← C61×#19220 #29522653

Subgroups — C61×#19220 #29522653

Order 15616.

562 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3233C212yesmaximal
2C61×#3170C211yesmaximal, characteristic, complemented
3C61×#2966C211yesmaximal, characteristic
4C61×#1704C212yesmaximal, complemented
5C61×#1703C212yesmaximal, complemented
6C61×#1676C211yesmaximal, characteristic, complemented
7C61×#1675C211yesmaximal, characteristic, complemented
8C61×#1670C211yesmaximal, characteristic, complemented
9C61×#1669C211yesmaximal, characteristic, complemented
10C61×#1564C211yesmaximal, characteristic, complemented
11C61×#1554C212yesmaximal, complemented
12C61×#533C2212yes—
13C61×#529C2211yescharacteristic
14C61×#500C2211yescharacteristic
15C61×#499—22no—
16C61×#494C2211yescharacteristic
17C61×#488—22no—
18C61×#487C2212yes—
19C61×#485—22no—
20C61×#482—22no—
21C61×#477C2212yes—
22C61×#476C2212yes—
23C61×#475C2212yes—
24C61×#474C2212yes—
25C61×#467—21no—
26C61×#467—21no—
27C61×#446C2211yescharacteristic
28C8×Q8×C61C2211yescharacteristic
29C4×Q16×C61—21no—
30C4×Q16×C61—21no—
31C61×#436C2211yescharacteristic
32C61×#435—21no—
33C8×D4×C61—21no—
34C8×D4×C61C2211yescharacteristic
35C61×#433—21no—
36C61×#432C2211yescharacteristic
37C61×#431C2212yes—
38C61×#405—21no—
39C2×C4×C8×C61C2211yescharacteristic
40C61×#335C2211yescharacteristic
41C61×#335C2211yescharacteristic
42C61×#334C2212yes—
43C61×#333C2212yes—
44C61×#333C2212yes—
45C61×#332C2212yes—
46C61×#332C2212yes—
47C2×Q16×C61—21no—
48C2×Q16×C61—21no—
49C2×M16×C61—21no—
50C22×C8×C61—21no—
51C22×C8×C61D411yescharacteristic
52C22×C8×C61D411yescharacteristic
53C4⋊Q8×C61C2312yes—
54C4⋊Q8×C61C2312yes—
55#126×C61—21no—
56#125×C61—22no—
57#125×C61D411yescharacteristic
58#124×C61D411yescharacteristic
59#123×C61—21no—
60C22⋊Q8×C61—22no—
61C22⋊Q8×C61—22no—
62C22⋊Q8×C61D411yescharacteristic
63#121×C61D411yescharacteristic
64C4×Q8×C61—22no—
65C4×Q8×C61—22no—
66C4×Q8×C61C2311yescharacteristic
67C4×D4×C61—21no—
68C4×D4×C61C2311yescharacteristic
69#117×C61—21no—
70#117×C61—22no—
71C2×C42×C61C2311yescharacteristic
72#107×C61—21no—
73#107×C61—21no—
74#107×C61—22no—
75#107×C61—22no—
76#106×C61—22no—
77#106×C61—22no—
78C4⋊C8×C61—21no—
79C4⋊C8×C61—21no—
80C4⋊C8×C61C2311yescharacteristic
81C4⋊C8×C61C2311yescharacteristic
82C4⋊C8×C61C2312yes—
83C4⋊C8×C61C2312yes—
84#103×C61—22no—
85#103×C61—22no—
86#103×C61—22no—
87#103×C61—22no—
88#102×C61—22no—
89#102×C61—22no—
90C22⋊C8×C61—22no—
91C22⋊C8×C61—21no—
92C22⋊C8×C61—21no—
93C22⋊C8×C61—21no—
94#97×C61—21no—
95#97×C61—21no—
96C4×C8×C61—21no—
97C4×C8×C61—22no—
98C4×C8×C61D411yescharacteristic
99C4×C8×C61D411yescharacteristic
100C4×C8×C61C2311yescharacteristic
101C4×C8×C61C2311yescharacteristic
102C2×Q8×C61—22no—
103C2×Q8×C61—22no—
104C2×Q8×C61C2×D411yescharacteristic
105C2×D4×C61—21no—
106C2×D4×C61C2×D411yescharacteristic
107C22×C4×C61—21no—
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61#4111yescharacteristic
111Q16×C61—42no—
112Q16×C61—42no—
113M16×C61—42no—
114C2×C8×C61—22no—
115C2×C8×C61—21no—
116C2×C8×C61—22no—
117C2×C8×C61—22no—
118C2×C8×C61—21no—
119C2×C8×C61—41no—
120C2×C8×C61—42no—
121C2×C8×C61C2×D411yescharacteristic
122C2×C8×C61C2×D411yescharacteristic
123C2×C8×C61C2×D411yescharacteristic
124C2×C8×C61C2×D411yescharacteristic
125C4⋊C4×C61—21no—
126C4⋊C4×C61—21no—
127C4⋊C4×C61—21no—
128C4⋊C4×C61—21no—
129C4⋊C4×C61—22no—
130C4⋊C4×C61—22no—
131C4⋊C4×C61—22no—
132C4⋊C4×C61—22no—
133C4⋊C4×C61—42no—
134C4⋊C4×C61—42no—
135C4⋊C4×C61C2×D411yescharacteristic
136C4⋊C4×C61C2×D411yescharacteristic
137C22⋊C4×C61—21no—
138C22⋊C4×C61—21no—
139C22⋊C4×C61—21no—
140C22⋊C4×C61—21no—
141C22⋊C4×C61—21no—
142C22⋊C4×C61—42no—
143C42×C61—21no—
144C42×C61—42no—
145C42×C61C2×D411yescharacteristic
146C42×C61C2×D411yescharacteristic
147C42×C61#4111yescharacteristic
148C42×C61C2411yescharacteristic
149C23×C61—21no—
150C23×C61#12111yescharacteristic
151Q8×C61—21no—
152Q8×C61—21no—
153Q8×C61—42no—
154Q8×C61—42no—
155Q8×C61—82no—
156D4×C61—21no—
157D4×C61—21no—
158D4×C61—42no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—42no—
170C2×C4×C61—42no—
171C2×C4×C61#12111yescharacteristic
172C2×C4×C61#12111yescharacteristic
173C2×C4×C61#12111yescharacteristic
174C2×C4×C61C22×D411yescharacteristic
175C2×C4×C61C22×D411yescharacteristic
176C2×C4×C61C2×#4111yescharacteristic
177C8×C61—21no—
178C8×C61—21no—
179C8×C61—21no—
180C8×C61—41no—
181C8×C61—41no—
182C8×C61—42no—
183C8×C61—42no—
184C8×C61#13512yes—
185#19220C6111yesmaximal, characteristic, direct product factor, Sylow
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—41no—
190C22×C61—41no—
191C22×C61—41no—
192C22×C61C2×#12111yescharacteristic
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61—41no—
198C4×C61—41no—
199C4×C61—41no—
200C4×C61—82no—
201C4×C61—82no—
202C4×C61C2×#13511yescharacteristic
203C4×C61#57511yescharacteristic
204C4×C61#57811yescharacteristic
205C4×C61#57811yescharacteristic
206#3233C2×C6112yes—
207#3170C2×C6111yescharacteristic, complemented
208#2966C2×C6111yescharacteristic
209#1704C2×C6112yescomplemented
210#1703C2×C6112yescomplemented
211#1676C2×C6111yescharacteristic, complemented
212#1675C2×C6111yescharacteristic, complemented
213#1670C2×C6111yescharacteristic, complemented
214#1669C2×C6111yescharacteristic, complemented
215#1564C2×C6111yescharacteristic, complemented
216#1554C2×C6112yescomplemented
217C2×C61—41no—
218C2×C61—81no—
219C2×C61#303511yescharacteristic
220C2×C61#305911yescharacteristic
221C2×C61#306711yescharacteristic
222#533C22×C6112yes—
223#529C22×C6111yescharacteristic
224#500C22×C6111yescharacteristic
225#499—22no—
226#494C22×C6111yescharacteristic
227#488—22no—
228#487C22×C6112yes—
229#485—22no—
230#482—22no—
231#477C22×C6112yes—
232#476C22×C6112yes—
233#475C22×C6112yes—
234#474C22×C6112yes—
235#467—21no—
236#467—21no—
237#446C22×C6111yescharacteristic
238C8×Q8C22×C6111yescharacteristic
239C4×Q16—21no—
240C4×Q16—21no—
241#436C22×C6111yescharacteristic
242#435—21no—
243C8×D4—21no—
244C8×D4C22×C6111yescharacteristic
245#433—21no—
246#432C22×C6111yescharacteristic
247#431C22×C6112yes—
248#405—21no—
249C2×C4×C8C22×C6111yescharacteristic
250#335C22×C6111yescharacteristic
251#335C22×C6111yescharacteristic
252#334C22×C6112yes—
253#333C22×C6112yes—
254#333C22×C6112yes—
255#332C22×C6112yes—
256#332C22×C6112yes—
257C61#1922011yescharacteristic, direct product factor, Sylow
258C2×Q16—21no—
259C2×Q16—21no—
260C2×M16—21no—
261C22×C8—21no—
262C22×C8D4×C6111yescharacteristic
263C22×C8D4×C6111yescharacteristic
264C4⋊Q8C23×C6112yes—
265C4⋊Q8C23×C6112yes—
266#126—21no—
267#125—22no—
268#125D4×C6111yescharacteristic
269#124D4×C6111yescharacteristic
270#123—21no—
271C22⋊Q8—22no—
272C22⋊Q8—22no—
273C22⋊Q8D4×C6111yescharacteristic
274#121D4×C6111yescharacteristic
275C4×Q8—22no—
276C4×Q8—22no—
277C4×Q8C23×C6111yescharacteristic
278C4×D4—21no—
279C4×D4C23×C6111yescharacteristic
280#117—21no—
281#117—22no—
282C2×C42C23×C6111yescharacteristic
283#107—21no—
284#107—21no—
285#107—22no—
286#107—22no—
287#106—22no—
288#106—22no—
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8C23×C6111yescharacteristic
292C4⋊C8C23×C6111yescharacteristic
293C4⋊C8C23×C6112yes—
294C4⋊C8C23×C6112yes—
295#103—22no—
296#103—22no—
297#103—22no—
298#103—22no—
299#102—22no—
300#102—22no—
301C22⋊C8—22no—
302C22⋊C8—21no—
303C22⋊C8—21no—
304C22⋊C8—21no—
305#97—21no—
306#97—21no—
307C4×C8—21no—
308C4×C8—22no—
309C4×C8D4×C6111yescharacteristic
310C4×C8D4×C6111yescharacteristic
311C4×C8C23×C6111yescharacteristic
312C4×C8C23×C6111yescharacteristic
313C2×Q8—22no—
314C2×Q8—22no—
315C2×Q8C2×D4×C6111yescharacteristic
316C2×D4—21no—
317C2×D4C2×D4×C6111yescharacteristic
318C22×C4—21no—
319C22×C4C2×D4×C6111yescharacteristic
320C22×C4C2×D4×C6111yescharacteristic
321C22×C4#41×C6111yescharacteristic
322Q16—42no—
323Q16—42no—
324M16—42no—
325C2×C8—22no—
326C2×C8—21no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—21no—
330C2×C8—41no—
331C2×C8—42no—
332C2×C8C2×D4×C6111yescharacteristic
333C2×C8C2×D4×C6111yescharacteristic
334C2×C8C2×D4×C6111yescharacteristic
335C2×C8C2×D4×C6111yescharacteristic
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—42no—
345C4⋊C4—42no—
346C4⋊C4C2×D4×C6111yescharacteristic
347C4⋊C4C2×D4×C6111yescharacteristic
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—21no—
351C22⋊C4—21no—
352C22⋊C4—21no—
353C22⋊C4—42no—
354C42—21no—
355C42—42no—
356C42C2×D4×C6111yescharacteristic
357C42C2×D4×C6111yescharacteristic
358C42#41×C6111yescharacteristic
359C42C24×C6111yescharacteristic
360C23—21no—
361C23#121×C6111yescharacteristic
362Q8—21no—
363Q8—21no—
364Q8—42no—
365Q8—42no—
366Q8—82no—
367D4—21no—
368D4—21no—
369D4—42no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4#121×C6111yescharacteristic
383C2×C4#121×C6111yescharacteristic
384C2×C4#121×C6111yescharacteristic
385C2×C4C22×D4×C6111yescharacteristic
386C2×C4C22×D4×C6111yescharacteristic
387C2×C4C2×#41×C6111yescharacteristic
388C8—21no—
389C8—21no—
390C8—21no—
391C8—41no—
392C8—41no—
393C8—42no—
394C8—42no—
395C8#135×C6112yes—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22C2×#121×C6111yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—82no—
411C4—82no—
412C4C2×#135×C6111yescharacteristic
413C4C61×#57511yescharacteristic
414C4C61×#57811yescharacteristic
415C4C61×#57811yescharacteristic
416C2—41no—
417C2—81no—
418C2C61×#303511yescharacteristic
419C2C61×#305911yescharacteristic
420C2C61×#306711yescharacteristic
subgroupG/H
center, socleC22×C61C2×#121
commutator, Frattini, cosocleC42C24×C61
prime radical#121×C61D4
LCSG ▷ 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×#3170C2semidirect
4. C61×#1704C2semidirect
5. C61×#1703C2semidirect
6. C61×#1676C2semidirect
7. C61×#1675C2semidirect
8. C61×#1670C2semidirect
9. C61×#1669C2semidirect
10. C61×#1564C2semidirect
11. C61×#1554C2semidirect
185. #19220C61direct (N × H)
207. #3170C2×C61semidirect
209. #1704C2×C61semidirect
210. #1703C2×C61semidirect
211. #1676C2×C61semidirect
212. #1675C2×C61semidirect
213. #1670C2×C61semidirect
214. #1669C2×C61semidirect
215. #1564C2×C61semidirect
216. #1554C2×C61semidirect
257. C61#19220direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#32332
C61×#31702
C61×#29662
C61×#17042
C61×#17032
C61×#16762
C61×#16752
C61×#16702
C61×#16692
C61×#15642
C61×#15542
#1922061