Finite Group Databasebeta

← C61×#9512 #29512945

Subgroups — C61×#9512 #29512945

Order 15616.

558 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#2921C211yesmaximal, characteristic, complemented
2C61×#2482C211yesmaximal, characteristic
3C61×#1822C211yesmaximal, characteristic, complemented
4C61×#1462C212yesmaximal
5C61×#1306C212yesmaximal, complemented
6C2×#117×C61C2211yescharacteristic
7C22×C22⋊C4×C61C2211yescharacteristic
8C61×#433—24no—
9C61×#423—21no—
10C61×#407C2212yes—
11C61×#407C2212yes—
12C4×M16×C61—21no—
13C61×#399—21no—
14C61×#397—21no—
15C61×#388—21no—
16C61×#388—21no—
17C61×#385C411yescharacteristic
18C61×#385C411yescharacteristic
19C61×#381C2211yescharacteristic
20C61×#379C411yescharacteristic
21C61×#379C411yescharacteristic
22C61×#343—21no—
23C61×#343—21no—
24C61×#323—24no—
25C25×C61C2×C411yescharacteristic
26C23×C4×C61C2×C411yescharacteristic
27C23×C4×C61C2311yescharacteristic
28C2×M16×C61—22no—
29C2×M16×C61—22no—
30#117×C61—22no—
31#117×C61—22no—
32C2×C4⋊C4×C61—21no—
33C2×C4⋊C4×C61—21no—
34C2×C4⋊C4×C61D411yescharacteristic
35C2×C4⋊C4×C61D411yescharacteristic
36C2×C22⋊C4×C61—21no—
37C2×C22⋊C4×C61—21no—
38C2×C22⋊C4×C61—22no—
39C2×C22⋊C4×C61—21no—
40C2×C22⋊C4×C61—21no—
41C2×C22⋊C4×C61—22no—
42C2×C22⋊C4×C61—21no—
43C2×C22⋊C4×C61—21no—
44C2×C22⋊C4×C61C2×C411yescharacteristic
45C2×C22⋊C4×C61C2×C411yescharacteristic
46C2×C22⋊C4×C61C2×C411yescharacteristic
47C2×C22⋊C4×C61C2×C411yescharacteristic
48C2×C42×C61D411yescharacteristic
49C2×C42×C61D411yescharacteristic
50C4⋊C8×C61—24no—
51C22⋊C8×C61—22no—
52C22⋊C8×C61—22no—
53C22⋊C8×C61—22no—
54C22⋊C8×C61D414yes—
55#97×C61—22no—
56C4×C8×C61—22no—
57#95×C61—21no—
58#95×C61—21no—
59#95×C61—21no—
60#95×C61—21no—
61C24×C61—21no—
62C24×C61—22no—
63C24×C61—42no—
64C24×C61—41no—
65C24×C61—41no—
66C24×C61—81no—
67C24×C61C22×C411yescharacteristic
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—22no—
72C22×C4×C61—41no—
73C22×C4×C61—41no—
74C22×C4×C61—81no—
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22⋊C411yescharacteristic
77C22×C4×C61C22⋊C411yescharacteristic
78C22×C4×C61C22⋊C411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D412yes—
82C22×C4×C61#4112yes—
83M16×C61—42no—
84M16×C61—42no—
85M16×C61—42no—
86M16×C61—42no—
87C2×C8×C61—24no—
88C2×C8×C61—42no—
89C4⋊C4×C61—22no—
90C4⋊C4×C61—22no—
91C4⋊C4×C61—81no—
92C4⋊C4×C61—81no—
93C22⋊C4×C61—22no—
94C22⋊C4×C61—22no—
95C22⋊C4×C61—42no—
96C22⋊C4×C61—42no—
97C22⋊C4×C61—41no—
98C22⋊C4×C61—42no—
99C22⋊C4×C61—41no—
100C22⋊C4×C61—41no—
101C22⋊C4×C61—41no—
102C22⋊C4×C61—81no—
103C22⋊C4×C61—81no—
104C42×C61—21no—
105C42×C61—21no—
106C42×C61—21no—
107C42×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—22no—
111C23×C61—24no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—42no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—82no—
122C23×C61—82no—
123C23×C61—84no—
124C23×C61—84no—
125C23×C61C2×C22⋊C411yescharacteristic
126C23×C61C4×D412yes—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—42no—
136C2×C4×C61—42no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—82no—
151C2×C4×C61#12011yescharacteristic
152C2×C4×C61#12112yes—
153C2×C4×C61#12311yescharacteristic
154C8×C61—44no—
155C8×C61—82no—
156#9512C6111yesmaximal, characteristic, direct product factor, Sylow
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—22no—
160C22×C61—22no—
161C22×C61—22no—
162C22×C61—42no—
163C22×C61—42no—
164C22×C61—42no—
165C22×C61—42no—
166C22×C61—42no—
167C22×C61—81no—
168C22×C61—81no—
169C22×C61—84no—
170C22×C61—84no—
171C22×C61—81no—
172C22×C61—81no—
173C22×C61#38611yescharacteristic
174C22×C61#41011yescharacteristic
175C22×C61#41011yescharacteristic
176C4×C61—21no—
177C4×C61—22no—
178C4×C61—21no—
179C4×C61—41no—
180C4×C61—41no—
181C4×C61—41no—
182C4×C61—41no—
183C4×C61—81no—
184C4×C61—81no—
185C4×C61—81no—
186#2921C2×C6111yescharacteristic, complemented
187#2482C2×C6111yescharacteristic
188#1822C2×C6111yescharacteristic, complemented
189#1462C2×C6112yes—
190#1306C2×C6112yescomplemented
191C2×C61—21no—
192C2×C61—21no—
193C2×C61—42no—
194C2×C61—82no—
195C2×C61#189111yescharacteristic
196C2×C61#189911yescharacteristic
197C2×C61#191411yescharacteristic
198C2×#117C22×C6111yescharacteristic
199C22×C22⋊C4C22×C6111yescharacteristic
200#433—24no—
201#423—21no—
202#407C22×C6112yes—
203#407C22×C6112yes—
204C4×M16—21no—
205#399—21no—
206#397—21no—
207#388—21no—
208#388—21no—
209#385C4×C6111yescharacteristic
210#385C4×C6111yescharacteristic
211#381C22×C6111yescharacteristic
212#379C4×C6111yescharacteristic
213#379C4×C6111yescharacteristic
214#343—21no—
215#343—21no—
216#323—24no—
217C61#951211yescharacteristic, direct product factor, Sylow
218C25C2×C4×C6111yescharacteristic
219C23×C4C2×C4×C6111yescharacteristic
220C23×C4C23×C6111yescharacteristic
221C2×M16—22no—
222C2×M16—22no—
223#117—22no—
224#117—22no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4D4×C6111yescharacteristic
228C2×C4⋊C4D4×C6111yescharacteristic
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—22no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—22no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4C2×C4×C6111yescharacteristic
238C2×C22⋊C4C2×C4×C6111yescharacteristic
239C2×C22⋊C4C2×C4×C6111yescharacteristic
240C2×C22⋊C4C2×C4×C6111yescharacteristic
241C2×C42D4×C6111yescharacteristic
242C2×C42D4×C6111yescharacteristic
243C4⋊C8—24no—
244C22⋊C8—22no—
245C22⋊C8—22no—
246C22⋊C8—22no—
247C22⋊C8D4×C6114yes—
248#97—22no—
249C4×C8—22no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254C24—21no—
255C24—22no—
256C24—42no—
257C24—41no—
258C24—41no—
259C24—81no—
260C24C22×C4×C6111yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—81no—
268C22×C4C22⋊C4×C6111yescharacteristic
269C22×C4C22⋊C4×C6111yescharacteristic
270C22×C4C22⋊C4×C6111yescharacteristic
271C22×C4C22⋊C4×C6111yescharacteristic
272C22×C4C2×D4×C6111yescharacteristic
273C22×C4C2×D4×C6111yescharacteristic
274C22×C4C2×D4×C6112yes—
275C22×C4#41×C6112yes—
276M16—42no—
277M16—42no—
278M16—42no—
279M16—42no—
280C2×C8—24no—
281C2×C8—42no—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—81no—
285C4⋊C4—81no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C22⋊C4—41no—
291C22⋊C4—42no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—81no—
296C22⋊C4—81no—
297C42—21no—
298C42—21no—
299C42—21no—
300C42—21no—
301C23—21no—
302C23—21no—
303C23—22no—
304C23—24no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—42no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—82no—
315C23—82no—
316C23—84no—
317C23—84no—
318C23C2×C22⋊C4×C6111yescharacteristic
319C23C4×D4×C6112yes—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—82no—
344C2×C4#120×C6111yescharacteristic
345C2×C4#121×C6112yes—
346C2×C4#123×C6111yescharacteristic
347C8—44no—
348C8—82no—
349C22—21no—
350C22—21no—
351C22—22no—
352C22—22no—
353C22—22no—
354C22—42no—
355C22—42no—
356C22—42no—
357C22—42no—
358C22—42no—
359C22—81no—
360C22—81no—
361C22—84no—
362C22—84no—
363C22—81no—
364C22—81no—
365C22C61×#38611yescharacteristic
366C22C61×#41011yescharacteristic
367C22C61×#41011yescharacteristic
368C4—21no—
369C4—22no—
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—81no—
376C4—81no—
377C4—81no—
378C2—21no—
379C2—21no—
380C2—42no—
381C2—82no—
382C2C61×#189111yescharacteristic
383C2C61×#189911yescharacteristic
384C2C61×#191411yescharacteristic
subgroupG/H
center, socleC22×C61#386
commutatorC24C22×C4×C61
Frattini, cosocleC23×C4C23×C61
prime radicalC25×C61C2×C4
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#2921C2semidirect
3. C61×#1822C2semidirect
5. C61×#1306C2semidirect
156. #9512C61direct (N × H)
186. #2921C2×C61semidirect
188. #1822C2×C61semidirect
190. #1306C2×C61semidirect
217. C61#9512direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#29212
C61×#24822
C61×#18222
C61×#14622
C61×#13062
#951261