Finite Group Databasebeta

← C61×#10190 #29513623

Subgroups — C61×#10190 #29513623

Order 15616.

496 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3230C211yesmaximal, characteristic, complemented
2C61×#3077C211yesmaximal, characteristic
3C2×C61×#474C211yesmaximal, characteristic
4C61×#1548C211yesmaximal, characteristic, complemented
5C61×#1481C211yesmaximal, characteristic, complemented
6C61×#1460C211yesmaximal, characteristic
7C61×#1301C211yesmaximal, characteristic, complemented
8C61×#533C2211yescharacteristic
9C2×C4⋊Q8×C61C2211yescharacteristic
10C2×C4×D4×C61C2211yescharacteristic
11C61×#500—21no—
12C61×#487—21no—
13C61×#484—22no—
14C61×#478—22no—
15C61×#477—22no—
16C61×#476—21no—
17C61×#474—22no—
18C61×#474—21no—
19C61×#474—22no—
20C61×#431C2211yescharacteristic
21C61×#431C2211yescharacteristic
22C61×#428—21no—
23C2×#107×C61—21no—
24C61×#423C2211yescharacteristic
25C2×C4⋊C8×C61C2211yescharacteristic
26C61×#418—21no—
27C2×#102×C61—21no—
28C61×#333—22no—
29C61×Q8⋊C8—22no—
30C61×#323—22no—
31C22×Q8×C61—21no—
32C22×D4×C61D411yescharacteristic
33C23×C4×C61—21no—
34C2×M16×C61—21no—
35C22×C8×C61—21no—
36C4⋊Q8×C61—21no—
37C4⋊Q8×C61—21no—
38C4⋊Q8×C61—21no—
39C4⋊Q8×C61D412yes—
40C4⋊Q8×C61D411yescharacteristic
41C4⋊Q8×C61D411yescharacteristic
42#125×C61—21no—
43C22⋊Q8×C61—21no—
44C22⋊Q8×C61—21no—
45C4×Q8×C61—21no—
46C4×Q8×C61—21no—
47C4×D4×C61—21no—
48C4×D4×C61—21no—
49C4×D4×C61—21no—
50C4×D4×C61—21no—
51#117×C61—21no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C22⋊C4×C61—21no—
56C2×C42×C61C2311yescharacteristic
57#107×C61—24no—
58#107×C61—22no—
59#107×C61—24no—
60#106×C61—22no—
61C4⋊C8×C61—21no—
62C4⋊C8×C61—21no—
63C4⋊C8×C61—21no—
64C4⋊C8×C61—21no—
65C4⋊C8×C61D412yes—
66C4⋊C8×C61D412yes—
67#103×C61—24no—
68#102×C61—24no—
69#102×C61—22no—
70#102×C61—22no—
71C22⋊C8×C61—21no—
72C22⋊C8×C61D412yes—
73C4×C8×C61—21no—
74C4×C8×C61—21no—
75C24×C61—21no—
76C2×Q8×C61—21no—
77C2×Q8×C61—21no—
78C2×Q8×C61—22no—
79C2×Q8×C61—41no—
80C2×Q8×C61—82no—
81C2×D4×C61—21no—
82C2×D4×C61—21no—
83C2×D4×C61—21no—
84C2×D4×C61—21no—
85C2×D4×C61—21no—
86C2×D4×C61Q1612yes—
87C22×C4×C61—21no—
88C22×C4×C61—41no—
89C22×C4×C61—41no—
90C22×C4×C61—41no—
91C22×C4×C61—82no—
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61#4111yescharacteristic
95M16×C61—41no—
96M16×C61—41no—
97C2×C8×C61—22no—
98C2×C8×C61—22no—
99C2×C8×C61—22no—
100C2×C8×C61—41no—
101C2×C8×C61—41no—
102C2×C8×C61—41no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—22no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—22no—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—21no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61—41no—
112C4⋊C4×C61—41no—
113C4⋊C4×C61—41no—
114C4⋊C4×C61—41no—
115C22⋊C4×C61—41no—
116C22⋊C4×C61—41no—
117C22⋊C4×C61—41no—
118C42×C61—41no—
119C42×C61C2×D411yescharacteristic
120C42×C61C2×D411yescharacteristic
121C42×C61C2×D411yescharacteristic
122C42×C61C2×D411yescharacteristic
123C23×C61—22no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—81no—
127C23×C61—81no—
128C23×C61#12111yescharacteristic
129Q8×C61—42no—
130Q8×C61—42no—
131Q8×C61—82no—
132Q8×C61—82no—
133D4×C61—22no—
134D4×C61—22no—
135D4×C61—41no—
136D4×C61—41no—
137C2×C4×C61—22no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—42no—
143C2×C4×C61—82no—
144C2×C4×C61—82no—
145C2×C4×C61—82no—
146C2×C4×C61—81no—
147C2×C4×C61#12011yescharacteristic
148C2×C4×C61#12011yescharacteristic
149C2×C4×C61#12011yescharacteristic
150C2×C4×C61#12111yescharacteristic
151C2×C4×C61#12111yescharacteristic
152C2×C4×C61#12711yescharacteristic
153C2×C4×C61C2×Q1611yescharacteristic
154C2×C4×C61#13511yescharacteristic
155C2×C4×C61#13711yescharacteristic
156C2×C4×C61#13711yescharacteristic
157C8×C61—42no—
158C8×C61—42no—
159C8×C61—42no—
160C8×C61—81no—
161#10190C6111yesmaximal, characteristic, direct product factor, Sylow
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—42no—
165C22×C61—82no—
166C22×C61—82no—
167C22×C61—81no—
168C22×C61—81no—
169C22×C61#39211yescharacteristic
170C22×C61#46711yescharacteristic
171C22×C61#47011yescharacteristic
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—81no—
176C4×C61—81no—
177C4×C61—82no—
178C4×C61—81no—
179C4×C61#45111yescharacteristic
180C4×C61#45111yescharacteristic
181C4×C61#45211yescharacteristic
182C4×C61#45211yescharacteristic
183C4×C61#47212yes—
184#3230C2×C6111yescharacteristic, complemented
185#3077C2×C6111yescharacteristic
186C2×#474C2×C6111yescharacteristic
187#1548C2×C6111yescharacteristic, complemented
188#1481C2×C6111yescharacteristic, complemented
189#1460C2×C6111yescharacteristic
190#1301C2×C6111yescharacteristic, complemented
191C2×C61—21no—
192C2×C61—21no—
193C2×C61—82no—
194C2×C61#200111yescharacteristic
195C2×C61#200911yescharacteristic
196C2×C61#201811yescharacteristic
197#533C22×C6111yescharacteristic
198C2×C4⋊Q8C22×C6111yescharacteristic
199C2×C4×D4C22×C6111yescharacteristic
200#500—21no—
201#487—21no—
202#484—22no—
203#478—22no—
204#477—22no—
205#476—21no—
206#474—21no—
207#474—22no—
208#474—22no—
209#431C22×C6111yescharacteristic
210#431C22×C6111yescharacteristic
211#428—21no—
212C2×#107—21no—
213#423C22×C6111yescharacteristic
214C2×C4⋊C8C22×C6111yescharacteristic
215#418—21no—
216C2×#102—21no—
217#333—22no—
218Q8⋊C8—22no—
219#323—22no—
220C61#1019011yescharacteristic, direct product factor, Sylow
221C22×Q8—21no—
222C22×D4D4×C6111yescharacteristic
223C23×C4—21no—
224C2×M16—21no—
225C22×C8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8D4×C6112yes—
230C4⋊Q8D4×C6111yescharacteristic
231C4⋊Q8D4×C6111yescharacteristic
232#125—21no—
233C22⋊Q8—21no—
234C22⋊Q8—21no—
235C4×Q8—21no—
236C4×Q8—21no—
237C4×D4—21no—
238C4×D4—21no—
239C4×D4—21no—
240C4×D4—21no—
241#117—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4D4×C6111yescharacteristic
245C2×C22⋊C4—21no—
246C2×C42C23×C6111yescharacteristic
247#107—24no—
248#107—22no—
249#107—24no—
250#106—22no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8D4×C6112yes—
256C4⋊C8D4×C6112yes—
257#103—24no—
258#102—24no—
259#102—22no—
260#102—22no—
261C22⋊C8—21no—
262C22⋊C8D4×C6112yes—
263C4×C8—21no—
264C4×C8—21no—
265C24—21no—
266C2×Q8—21no—
267C2×Q8—21no—
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—82no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4Q16×C6112yes—
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—82no—
282C22×C4C2×D4×C6111yescharacteristic
283C22×C4C2×D4×C6111yescharacteristic
284C22×C4#41×C6111yescharacteristic
285M16—41no—
286M16—41no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C4⋊C4—21no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C42—41no—
309C42C2×D4×C6111yescharacteristic
310C42C2×D4×C6111yescharacteristic
311C42C2×D4×C6111yescharacteristic
312C42C2×D4×C6111yescharacteristic
313C23—22no—
314C23—41no—
315C23—41no—
316C23—81no—
317C23—81no—
318C23#121×C6111yescharacteristic
319Q8—42no—
320Q8—42no—
321Q8—82no—
322Q8—82no—
323D4—22no—
324D4—22no—
325D4—41no—
326D4—41no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—81no—
337C2×C4#120×C6111yescharacteristic
338C2×C4#120×C6111yescharacteristic
339C2×C4#120×C6111yescharacteristic
340C2×C4#121×C6111yescharacteristic
341C2×C4#121×C6111yescharacteristic
342C2×C4#127×C6111yescharacteristic
343C2×C4C2×Q16×C6111yescharacteristic
344C2×C4#135×C6111yescharacteristic
345C2×C4#137×C6111yescharacteristic
346C2×C4#137×C6111yescharacteristic
347C8—42no—
348C8—42no—
349C8—42no—
350C8—81no—
351C22—21no—
352C22—21no—
353C22—42no—
354C22—82no—
355C22—82no—
356C22—81no—
357C22—81no—
358C22C61×#39211yescharacteristic
359C22C61×#46711yescharacteristic
360C22C61×#47011yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—81no—
365C4—81no—
366C4—82no—
367C4—81no—
368C4C61×#45111yescharacteristic
369C4C61×#45111yescharacteristic
370C4C61×#45211yescharacteristic
371C4C61×#45211yescharacteristic
372C4C61×#47212yes—
373C2—21no—
374C2—21no—
375C2—82no—
376C2C61×#200111yescharacteristic
377C2C61×#200911yescharacteristic
378C2C61×#201811yescharacteristic
subgroupG/H
center, socleC22×C61#392
commutator, Frattini, cosocleC2×C42C23×C61
prime radicalC22×D4×C61D4
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
1. C61×#3230C2semidirect
4. C61×#1548C2semidirect
5. C61×#1481C2semidirect
7. C61×#1301C2semidirect
161. #10190C61direct (N × H)
184. #3230C2×C61semidirect
187. #1548C2×C61semidirect
188. #1481C2×C61semidirect
190. #1301C2×C61semidirect
220. C61#10190direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#32302
C61×#30772
C2×C61×#4742
C61×#15482
C61×#14812
C61×#14602
C61×#13012
#1019061