Finite Group Databasebeta

← #30599036

Subgroups — #30599036

Order 15616.

418 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 88 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#21461381C211yesmaximal, characteristic, complemented
2#21461379C211yesmaximal, characteristic, complemented
3#21461078C212yesmaximal
4#21460684C212yesmaximal, complemented
5C2×#16839837C211yesmaximal, characteristic
6#16840783C2212yes—
7#16840783C2212yes—
8#16840626—21no—
9#16840625—21no—
10#16840624—21no—
11#16840623—21no—
12#16840606—22no—
13#16840605—22no—
14C22×#11758194C411yescharacteristic
15C22×#11758189C411yescharacteristic
16C2×C4×C22⋊D61C2211yescharacteristic
17#16839837—21no—
18#16839837—21no—
19#16839837—21no—
20#16839837—21no—
21C2×#14519706C2211yescharacteristic
22C2×#14519689C411yescharacteristic
23C2×C8×Dic61C2211yescharacteristic
24C2×C22⋊C8×C61C411yescharacteristic
25C4⋊#92420—22no—
26C4⋊#92420—22no—
27C22⋊#92420—22no—
28C22⋊#92420—22no—
29#14519832—22no—
30#14519832—22no—
31C22×C22⋊D61Q811yescharacteristic
32C22×C4×D61C2×C411yescharacteristic
33C2×#11758194—21no—
34C2×#11758194—21no—
35C2×#11758194—42no—
36C2×#11758189—21no—
37C2×#11758189—21no—
38C2×#11758189—42no—
39C22×#92418C2×C411yescharacteristic
40C22×#92418C2×C411yescharacteristic
41C4×C22⋊D61—21no—
42C4×C22⋊D61—21no—
43C4×C22⋊D61—21no—
44C4×C22⋊D61—21no—
45C2×#11758196Q811yescharacteristic
46C2×C22⋊Dic61D411yescharacteristic
47C2×#11758198D411yescharacteristic
48C2×C4×Dic61C2311yescharacteristic
49#14519706—21no—
50#14519706—21no—
51#14519689—21no—
52#14519689—21no—
53C8×Dic61D411yescharacteristic
54C8×Dic61D411yescharacteristic
55C8×Dic61D411yescharacteristic
56C8×Dic61D411yescharacteristic
57C23×C4×C61C2×C411yescharacteristic
58C22×C8×C61C2×C411yescharacteristic
59C22×C8×C61C2×C411yescharacteristic
60C22⋊C8×C61—21no—
61C22⋊C8×C61—21no—
62C24×C61C4⋊C411yescharacteristic
63C23×D61C4⋊C411yescharacteristic
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—41no—
67C22×C4×C61—41no—
68C22×C4×C61C4⋊C411yescharacteristic
69C22×C4×C61C22×C411yescharacteristic
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61—42no—
73C22×Dic61C4⋊C411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C22×Dic61C2×Q811yescharacteristic
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—41no—
79C2×C4×D61—41no—
80C2×#92420—42no—
81C2×#92420—42no—
82C2×C8×C61—21no—
83C2×C8×C61—41no—
84C2×C8×C61—41no—
85C2×C8×C61C22⋊C411yescharacteristic
86C2×C8×C61C22⋊C411yescharacteristic
87C22⋊Dic61—21no—
88C22⋊Dic61—21no—
89#11758198—21no—
90#11758198—21no—
91#11758196—21no—
92#11758196—21no—
93C4×Dic61C2×D411yescharacteristic
94C4×Dic61C2×D411yescharacteristic
95C4×Dic61#4111yescharacteristic
96C4×Dic61#4111yescharacteristic
97#11758194—42no—
98#11758194—42no—
99C2×#92418—22no—
100C2×#92418—21no—
101C2×#92418—41no—
102C2×#92418C22⋊C411yescharacteristic
103C2×#92418C22⋊C411yescharacteristic
104#11758189—42no—
105#11758189—42no—
106C23×C61—21no—
107C23×C61—22no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61C2×C4⋊C411yescharacteristic
111C22×D61—21no—
112C22×D61—22no—
113C22×D61—41no—
114C22×D61—41no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—42no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61C2×C22⋊C411yescharacteristic
123C2×C4×C61#11711yescharacteristic
124C22⋊D61—42no—
125C22⋊D61—42no—
126C2×Dic61—22no—
127C2×Dic61—21no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61#12111yescharacteristic
131C2×Dic61#12111yescharacteristic
132C2×Dic61C22⋊Q811yescharacteristic
133C2×Dic61C22⋊Q811yescharacteristic
134C4×D61—42no—
135C4×D61—41no—
136C4×D61—41no—
137#92420—82no—
138#92420—82no—
139C8×C61—21no—
140C8×C61—21no—
141C8×C61—41no—
142#92418—21no—
143#92418—41no—
144#92418#10012yes—
145#8624—611nomaximal, Sylow
146C22×C61—21no—
147C22×C61—21no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—82no—
152C22×C61#38011yescharacteristic
153C22×C61#43012yes—
154C2×D61—41no—
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—82no—
158C4×C61—21no—
159C4×C61—41no—
160C4×C61C2×#10011yescharacteristic
161C4×C61#41311yescharacteristic
162Dic61—21no—
163Dic61—21no—
164Dic61—21no—
165Dic61—21no—
166Dic61—41no—
167C2×#436—611no—
168#1568—611no—
169#1568—611no—
170#1466—612no—
171#1290—612no—
172C2×C61—22no—
173C2×C61—81no—
174C2×C61#180011yescharacteristic
175C2×C61#181111yescharacteristic
176C2×C61#181211yescharacteristic
177D61—81no—
178C22×M16—611no—
179C22×M16—611no—
180C2×C4×D4—611no—
181#436—1221no—
182#436—1221no—
183#436—1221no—
184#436—1221no—
185#432—612no—
186#432—612no—
187C2×C4⋊C8—611no—
188C2×C22⋊C8—611no—
189C2×C22⋊C8#692311yescharacteristic
190C2×C4×C8—611no—
191#335—1221no—
192#335—1221no—
193#334—1221no—
194#334—1221no—
195#323—1222no—
196#323—1222no—
197C61#862411yescharacteristic, complemented, Sylow
198C22×D4—611no—
199C23×C4—611no—
200C23×C4C2×#692311yescharacteristic
201C2×M16—1221no—
202C2×M16—1221no—
203C2×M16—1221no—
204C2×M16—1221no—
205C2×M16—2442no—
206C2×M16—2442no—
207C22×C8—611no—
208C22×C8—611no—
209C22×C8C2×#692311yescharacteristic
210C22×C8C2×#692311yescharacteristic
211C4×D4—1221no—
212C4×D4—1221no—
213C4×D4—1221no—
214C4×D4—1221no—
215C2×C4⋊C4—611no—
216C2×C22⋊C4—611no—
217C2×C22⋊C4—611no—
218C2×C42—611no—
219C4⋊C8—1221no—
220C4⋊C8—1221no—
221C4⋊C8—1222no—
222C4⋊C8—1222no—
223C22⋊C8—21no—
224C22⋊C8—21no—
225C22⋊C8—1221no—
226C22⋊C8—1221no—
227C22⋊C8—1222no—
228C22⋊C8—1222no—
229#97—1222no—
230#97—1222no—
231C4×C8—611no—
232C4×C8—611no—
233C4×C8—611no—
234C4×C8—611no—
235C24—611no—
236C24C4⋊#692311yescharacteristic
237C2×D4—1221no—
238C2×D4—1221no—
239C2×D4—2442no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—1221no—
248C22×C4—1221no—
249C22×C4—2441no—
250C22×C4—2441no—
251C22×C4C4⋊#692311yescharacteristic
252C22×C4C22×#692311yescharacteristic
253M16—2442no—
254M16—2442no—
255M16—2442no—
256M16—2442no—
257C2×C8—21no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—611no—
261C2×C8—611no—
262C2×C8—1222no—
263C2×C8—1221no—
264C2×C8—2442no—
265C2×C8—2442no—
266C2×C8—2441no—
267C2×C8C22⋊#692311yescharacteristic
268C2×C8C22⋊#692311yescharacteristic
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C22⋊C4—1221no—
272C22⋊C4—1221no—
273C22⋊C4—1221no—
274C22⋊C4—1221no—
275C42—611no—
276C42—611no—
277C42—611no—
278C42—611no—
279C23—21no—
280C23—22no—
281C23—41no—
282C23—41no—
283C23—1222no—
284C23—1221no—
285C23—2441no—
286C23—2441no—
287C23C2×C4⋊#692311yescharacteristic
288D4—2442no—
289D4—2442no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—611no—
298C2×C4—611no—
299C2×C4—611no—
300C2×C4—611no—
301C2×C4—1222no—
302C2×C4—1221no—
303C2×C4—2442no—
304C2×C4—2441no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4C2×C22⋊#692311yescharacteristic
309C2×C4#1451985611yescharacteristic
310C8—21no—
311C8—21no—
312C8—41no—
313C8—612no—
314C8—1221no—
315C8—4882no—
316C8—4882no—
317C8—2441no—
318C22—21no—
319C22—21no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—82no—
324C22—4882no—
325C22—2441no—
326C22—2441no—
327C22—2441no—
328C22#1684070411yescharacteristic
329C22#1684077712yes—
330C4—21no—
331C4—41no—
332C4—1221no—
333C4—1221no—
334C4—1221no—
335C4—1221no—
336C4—2441no—
337C4D61⋊#10011yescharacteristic
338C4#1684074911yescharacteristic
339C2—22no—
340C2—81no—
341C2—4881no—
342C2#2146168411yescharacteristic
343C2#2146170011yescharacteristic
344C2#2146170111yescharacteristic
subgroupG/H
centerC22#16840704
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C22⋊C8×C61C4
socleC22×C61#380
prime radicalC22×C22⋊D61Q8
cosocleC2×C4×Dic61C23
hypercenterC2×C22⋊C8#6923
hypocenterC61#8624
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #21461381C2semidirect
2. #21461379C2semidirect
4. #21460684C2semidirect
197. C61#8624semidirect

Maximal subgroups

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

subgroupindex
#214613812
#214613792
#214610782
#214606842
C2×#168398372
#862461