Finite Group Databasebeta

← #30601133

Subgroups — #30601133

Order 15616.

518 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 82 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
1#21462670C211yesmaximal, characteristic
2#21461352C212yesmaximal, complemented
3#21461079C211yesmaximal, characteristic
4#21460670C212yesmaximal, complemented
5#21450812C211yesmaximal, characteristic
6#16840793—24no—
7#16840782C2212yes—
8#16840782C2212yes—
9#16840732—21no—
10C2×C22⋊#92420—21no—
11#16840622—24no—
12#16840605—21no—
13#16840605—21no—
14C2×#14519775C2211yescharacteristic
15C2×#14519764C411yescharacteristic
16C2×D4×Dic61C2211yescharacteristic
17#16839690—21no—
18#16839690—21no—
19#16839669C411yescharacteristic
20#16839668C411yescharacteristic
21#16839620—21no—
22#16839620—21no—
23C4×#11758196C2211yescharacteristic
24C2×#124×C61C411yescharacteristic
25C2×#11758217—22no—
26C22×#92420—22no—
27#14519844—22no—
28#14519844D414yes—
29C22⋊#92420—22no—
30C22⋊#92420—22no—
31C22⋊#92420—22no—
32C22⋊#92420—22no—
33#14519832—22no—
34#14519832—22no—
35C22×Dic122C2×C411yescharacteristic
36C23×Dic61D411yescharacteristic
37C23×Dic61D411yescharacteristic
38#14519775—22no—
39#14519775—22no—
40#14519764—42no—
41D4×Dic61—22no—
42D4×Dic61—22no—
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×#11758196—21no—
45C2×#11758196—21no—
46C2×#11758196—21no—
47C2×C22⋊Dic61—21no—
48C2×C22⋊Dic61—21no—
49C2×C22⋊Dic61D411yescharacteristic
50C2×C22⋊Dic61D411yescharacteristic
51C2×C4×Dic61C2×C411yescharacteristic
52C2×C4×Dic61C2311yescharacteristic
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58C22×Q8×C61C2×C411yescharacteristic
59C22×D4×C61C2×C411yescharacteristic
60#124×C61—42no—
61C2×C22⋊C4×C61—21no—
62C2×C22⋊C4×C61—21no—
63C2×C42×C61C2×C411yescharacteristic
64C24×C61C22⋊C411yescharacteristic
65C24×C61C22⋊C411yescharacteristic
66C2×Q8×C61—22no—
67C2×Q8×C61—41no—
68C2×Q8×C61—41no—
69C2×D4×C61—22no—
70C2×D4×C61—22no—
71C2×D4×C61—41no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61C22×C411yescharacteristic
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—42no—
82C22×Dic61—42no—
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C2×D411yescharacteristic
86C22×Dic61C2×D411yescharacteristic
87C2×Dic122—22no—
88C2×Dic122—41no—
89C2×Dic122—41no—
90#11758217—82no—
91C2×#92420—24no—
92C2×#92420—42no—
93C2×#92420—82no—
94C22⋊C4×C61—42no—
95C22⋊C4×C61—42no—
96C42×C61—41no—
97C22⋊Dic61—22no—
98C22⋊Dic61—22no—
99C22⋊Dic61—42no—
100C22⋊Dic61—42no—
101C4⋊Dic61—22no—
102#11758196—42no—
103#11758196—41no—
104#11758196—42no—
105#11758196—41no—
106C4×Dic61—41no—
107C4×Dic61C2×D412yes—
108C4×Dic61#4112yes—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61#10012yes—
119C23×C61C2×C22⋊C411yescharacteristic
120Q8×C61—82no—
121D4×C61—44no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61C4×D412yes—
131C2×Dic61—22no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—41no—
135C2×Dic61—42no—
136C2×Dic61—42no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—81no—
146C2×Dic61—81no—
147C2×Dic61#12011yescharacteristic
148C2×Dic61#12112yes—
149C2×Dic61#12311yescharacteristic
150Dic122—82no—
151#92420—44no—
152#92420—82no—
153#9451—611nomaximal, Sylow
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—22no—
157C22×C61—42no—
158C22×C61—42no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—81no—
165C22×C61—81no—
166C22×C61#38611yescharacteristic
167C22×C61C2×#10011yescharacteristic
168C22×C61#41311yescharacteristic
169C4×C61—22no—
170C4×C61—81no—
171C4×C61—81no—
172Dic61—21no—
173Dic61—22no—
174Dic61—41no—
175Dic61—41no—
176Dic61—81no—
177Dic61—81no—
178Dic61#45512yes—
179#2973—611no—
180#2547—611no—
181#1558—612no—
182#1466—611no—
183#1285—612no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61—42no—
187C2×C61—81no—
188C2×C61#188511yescharacteristic
189C2×C61#190011yescharacteristic
190C2×C61#190911yescharacteristic
191C2×C4⋊Q8—611no—
192C2×#124—611no—
193C2×#124#692311yescharacteristic
194C2×C4×D4—611no—
195#435—1224no—
196#432—612no—
197#432—612no—
198#407—1221no—
199C2×C22⋊C8—1221no—
200#397—1221no—
201#397—1221no—
202#391—611no—
203#391—611no—
204#380—1221no—
205#380—1221no—
206C4×C4⋊C4—611no—
207#333—1224no—
208#323—1221no—
209#323—1221no—
210C61#945111yescharacteristic, complemented, Sylow
211C22×Q8—611no—
212C22×Q8C2×#692311yescharacteristic
213C22×D4C2×#692311yescharacteristic
214C23×C4—611no—
215C23×C4—611no—
216C2×M16—1222no—
217C22×C8—1222no—
218C4⋊Q8—1222no—
219C4⋊Q8—1222no—
220#124—42no—
221#124—2442no—
222C4×D4—1222no—
223C4×D4—1222no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4—1221no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—611no—
231C2×C22⋊C4—611no—
232C2×C22⋊C4—1221no—
233C2×C22⋊C4—1221no—
234C2×C42—611no—
235C2×C42—611no—
236C2×C42C2×#692311yescharacteristic
237C4⋊C8—614no—
238C4⋊C8—1222no—
239C22⋊C8—1222no—
240C22⋊C8—1222no—
241C22⋊C8—1222no—
242C22⋊C8—1222no—
243#97—1222no—
244#97—1222no—
245#95—1221no—
246#95—1221no—
247#95—1221no—
248#95—1221no—
249#95—1221no—
250C24C22⋊#692311yescharacteristic
251C24C22⋊#692311yescharacteristic
252C2×Q8—22no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×Q8—1222no—
256C2×Q8—2441no—
257C2×Q8—2441no—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—41no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—2442no—
274C22×C4—2442no—
275C22×C4C22×#692311yescharacteristic
276M16—4882no—
277C2×C8—1224no—
278C2×C8—4882no—
279C2×C8—2442no—
280C4⋊C4—1222no—
281C4⋊C4—2441no—
282C4⋊C4—2442no—
283C4⋊C4—2441no—
284C4⋊C4—2442no—
285C22⋊C4—42no—
286C22⋊C4—42no—
287C22⋊C4—1222no—
288C22⋊C4—1222no—
289C22⋊C4—2442no—
290C22⋊C4—2442no—
291C42—41no—
292C42—612no—
293C42—612no—
294C42—2441no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23#1451983712yes—
305C23C2×C22⋊#692311yescharacteristic
306Q8—82no—
307Q8—4882no—
308D4—44no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—611no—
318C2×C4—612no—
319C2×C4—611no—
320C2×C4—1222no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—4881no—
324C2×C4—4881no—
325C2×C4—2442no—
326C2×C4—2442no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4D4×#692312yes—
337C8—4882no—
338C8—2444no—
339C22—21no—
340C22—21no—
341C22—22no—
342C22—42no—
343C22—42no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22—81no—
351C22#1684071011yescharacteristic
352C22C2×#1451983711yescharacteristic
353C22#1684074911yescharacteristic
354C4—22no—
355C4—81no—
356C4—81no—
357C4—612no—
358C4—1221no—
359C4—1222no—
360C4—4881no—
361C4—4881no—
362C4—2441no—
363C4—2441no—
364C2—21no—
365C2—21no—
366C2—42no—
367C2—81no—
368C2#2146182411yescharacteristic
369C2#2146184411yescharacteristic
370C2#2146186011yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#124×C61C4
socleC22×C61#386
prime radicalC22×D4×C61C2×C4
cosocleC2×C4×Dic61C23
hypercenterC2×#124#6923
hypocenterC61#9451
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. #21461352C2semidirect
4. #21460670C2semidirect
210. C61#9451semidirect

Maximal subgroups

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

subgroupindex
#214626702
#214613522
#214610792
#214606702
#214508122
#945161