Finite Group Databasebeta

← #29581329

Subgroups — #29581329

Order 15616.

484 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#16840130C211yesmaximal, characteristic
2#21453886C211yesmaximal, characteristic
3#21446793C211yesmaximal, characteristic
4C2×#16839504C211yesmaximal, characteristic
5C2×#16839503C211yesmaximal, characteristic
6#21443701C211yesmaximal, characteristic
7C2×C61×#501C211yesmaximal, characteristic
8C2×#14519769C2211yescharacteristic
9#16840130—22no—
10#16840130—22no—
11C2×#14519701—21no—
12C2×#14519701—21no—
13C2×#14519688C2211yescharacteristic
14C2×#14519688C2211yescharacteristic
15#16839701—21no—
16#16839700—21no—
17#16839695—22no—
18#16839693—21no—
19#16839692—21no—
20#16839628C2211yescharacteristic
21#16839524—22no—
22#16839504—22no—
23#16839503—22no—
24C2×C4⋊Q8×C61C2211yescharacteristic
25C2×#125×C61C2211yescharacteristic
26C61×#501—22no—
27C61×#501—22no—
28C2×#107×C61—21no—
29C2×#106×C61—21no—
30C2×#97×C61C2211yescharacteristic
31C22×#92418—21no—
32C22×#92418—21no—
33#14519769—21no—
34#14519769—21no—
35#14519769—21no—
36#14519769—21no—
37C2×C4⋊Dic61D411yescharacteristic
38C2×C4⋊Dic61D411yescharacteristic
39C2×C4⋊Dic61D412yes—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—22no—
43#14519701—24no—
44#14519701—24no—
45#14519688—21no—
46#14519688—21no—
47#14519688—21no—
48#14519688D412yes—
49#14519684—22no—
50#14519684—22no—
51#14519684—22no—
52#14519684—21no—
53#14519684—21no—
54C22×Q8×C61—21no—
55C22×C8×C61—21no—
56C4⋊Q8×C61—21no—
57C4⋊Q8×C61—21no—
58C4⋊Q8×C61—21no—
59C4⋊Q8×C61D412yes—
60#125×C61—21no—
61#125×C61—21no—
62#125×C61—21no—
63#125×C61—21no—
64C2×C4⋊C4×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61D411yescharacteristic
69C2×C4⋊C4×C61D411yescharacteristic
70C2×C42×C61C2311yescharacteristic
71#107×C61—24no—
72#106×C61—24no—
73#97×C61—21no—
74#97×C61D412yes—
75C2×Q8×C61—22no—
76C2×Q8×C61—44no—
77C2×Q8×C61—41no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—41no—
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×Dic61—22no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C2×C8×C61—24no—
88C2×C8×C61—22no—
89C4⋊C4×C61—21no—
90C4⋊C4×C61—22no—
91C4⋊C4×C61—21no—
92C4⋊C4×C61—22no—
93C4⋊C4×C61—21no—
94C4⋊C4×C61—21no—
95C4⋊C4×C61—41no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C42×C61C2×D411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C42×C61C2×D411yescharacteristic
104C42×C61#4111yescharacteristic
105C4⋊Dic61—21no—
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108C4⋊Dic61—21no—
109C4⋊Dic61—42no—
110#11758196—41no—
111#11758196—41no—
112#11758196—41no—
113#11758196—41no—
114#11758196—82no—
115C2×#92418—22no—
116C2×#92418—22no—
117C2×#92418—42no—
118C2×#92418—41no—
119C2×#92418—41no—
120C23×C61#12011yescharacteristic
121Q8×C61—44no—
122Q8×C61—82no—
123C2×C4×C61—22no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—22no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—42no—
130C2×C4×C61—42no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—82no—
134C2×C4×C61#12011yescharacteristic
135C2×C4×C61#12011yescharacteristic
136C2×C4×C61#12111yescharacteristic
137C2×C4×C61#12111yescharacteristic
138C2×C4×C61#12111yescharacteristic
139C2×C4×C61#12711yescharacteristic
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—42no—
143C2×Dic61—41no—
144C2×Dic61—42no—
145C2×Dic61—42no—
146C2×Dic61—42no—
147C2×Dic61—41no—
148C8×C61—24no—
149#92418—42no—
150#92418—42no—
151#10084—611nomaximal, Sylow
152C22×C61#39211yescharacteristic
153C22×C61#45412yes—
154C22×C61#45511yescharacteristic
155C22×C61#45611yescharacteristic
156C22×C61#45612yes—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—81no—
164C4×C61—82no—
165C4×C61—81no—
166Dic61—82no—
167Dic61—81no—
168Dic61—81no—
169C2×#501D6111yescharacteristic
170C2×#491—611no—
171#2822—611no—
172#1993—611no—
173C2×#330—611no—
174C2×#330—611no—
175#1295—611no—
176C2×C61#166312yes—
177C2×C61#166412yes—
178C2×C61#200311yescharacteristic
179C2×C61#200511yescharacteristic
180C2×C61#200711yescharacteristic
181C2×C4⋊Q8C2×D6111yescharacteristic
182C2×#125—611no—
183C2×#125C2×D6111yescharacteristic
184#501—22no—
185#501—22no—
186#491—1222no—
187#491—1222no—
188C2×#107—21no—
189C2×#106—21no—
190C2×#103—1221no—
191C2×#103—1221no—
192C2×#97—611no—
193C2×#97—611no—
194C2×#97C2×D6111yescharacteristic
195#400—1221no—
196#400—1221no—
197#398—1221no—
198#398—1222no—
199#398—1221no—
200#382—611no—
201#340—1222no—
202#330—1222no—
203#330—1222no—
204C61#1008411yescharacteristic, complemented, Sylow
205C22×Q8—21no—
206C22×C8—21no—
207C22×C8—1221no—
208C22×C8—1221no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8C22⋊D6112yes—
213#125—21no—
214#125—21no—
215#125—21no—
216#125—21no—
217#125—1221no—
218#125—1221no—
219#125—1221no—
220#125—1221no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4—612no—
228C2×C4⋊C4—1222no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4C22⋊D6111yescharacteristic
232C2×C4⋊C4C22⋊D6111yescharacteristic
233C2×C42C22×D6111yescharacteristic
234#107—24no—
235#106—24no—
236#103—1224no—
237#103—1224no—
238#97—21no—
239#97—612no—
240#97—1221no—
241#97—1221no—
242#97—1221no—
243#97C22⋊D6112yes—
244#95—1222no—
245#95—1222no—
246#95—1222no—
247#95—1221no—
248#95—1221no—
249C2×Q8—22no—
250C2×Q8—44no—
251C2×Q8—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—41no—
255C22×C4—1222no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4D4×D6111yescharacteristic
259C22×C4D4×D6111yescharacteristic
260C22×C4C2×C22⋊D6111yescharacteristic
261C2×C8—24no—
262C2×C8—22no—
263C2×C8—1222no—
264C2×C8—1222no—
265C2×C8—2441no—
266C2×C8—2442no—
267C2×C8—2441no—
268C4⋊C4—21no—
269C4⋊C4—22no—
270C4⋊C4—21no—
271C4⋊C4—22no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C4⋊C4—1221no—
283C4⋊C4—1221no—
284C4⋊C4—4882no—
285C4⋊C4—2442no—
286C4⋊C4—2441no—
287C4⋊C4—2441no—
288C4⋊C4—2441no—
289C4⋊C4—2441no—
290C42D4×D6111yescharacteristic
291C42#1175822411yescharacteristic
292C42C2×C22⋊D6111yescharacteristic
293C42C2×C22⋊D6111yescharacteristic
294C23#1451974511yescharacteristic
295Q8—44no—
296Q8—82no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—82no—
308C2×C4—2441no—
309C2×C4—2442no—
310C2×C4—2441no—
311C2×C4—2442no—
312C2×C4—2442no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2442no—
316C2×C4#1451974511yescharacteristic
317C2×C4#1451974611yescharacteristic
318C2×C4#1451974811yescharacteristic
319C2×C4#1451974911yescharacteristic
320C2×C4#1451974911yescharacteristic
321C2×C4#1451977311yescharacteristic
322C8—24no—
323C8—2442no—
324C8—2442no—
325C22#1683967011yescharacteristic
326C22#1683993312yes—
327C22#1683993811yescharacteristic
328C22#1683994311yescharacteristic
329C22#1683994412yes—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—81no—
337C4—82no—
338C4—81no—
339C4—4882no—
340C4—4881no—
341C4—4881no—
342C2#2144514612yes—
343C2#2144515112yes—
344C2#2144683811yescharacteristic
345C2#2144685511yescharacteristic
346C2#2144686411yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC2×C61×#501C2
socle, prime radicalC23×C61#120
hypercenterC2×#501D61
hypocenterC61#10084
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
204. C61#10084semidirect

Maximal subgroups

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

subgroupindex
C2×#168401302
#214538862
#214467932
C2×#168395042
C2×#168395032
#214437012
C2×C61×#5012
#1008461