Finite Group Databasebeta

← #30597923

Subgroups — #30597923

Order 15616.

394 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 108 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#21461613C211yesmaximal, characteristic
2#21461320C211yesmaximal, characteristic
3#21461201C211yesmaximal, characteristic
4#21461033C211yesmaximal, characteristic
5#21460715C211yesmaximal, characteristic
6#21460709C211yesmaximal, characteristic
7#21454750C211yesmaximal, characteristic
8#16840780C2211yescharacteristic
9#16840780C2211yescharacteristic
10D61⋊(C4⋊C8)C2211yescharacteristic
11C2×#14519831—21no—
12C4×C4⋊#6923C2211yescharacteristic
13(C2×#6923)⋊C8—21no—
14#16840622C412yescomplemented
15#16840621C412yescomplemented
16#16840616C412yes—
17#16840615C412yes—
18#92420⋊C8—21no—
19#92420⋊C8—21no—
20#16840316C2211yescharacteristic
21#16839892C411yescharacteristic, complemented
22#16839890—21no—
23Q8×#92418C411yescharacteristic, complemented
24#16839886—21no—
25#16839886C411yescharacteristic, complemented
26#16839787—21no—
27#16839784C2211yescharacteristic
28#16839719—21no—
29C4×C8×D61C2211yescharacteristic
30C61×#446C411yescharacteristic, complemented
31C2×D61⋊C8—21no—
32C2×C4⋊#6923—21no—
33C2×C4×#6923—21no—
34#14519844—21no—
35#14519844C2×C412yes—
36#14519844C2×C412yes—
37C4⋊#92420—21no—
38#14519834—21no—
39#14519834C2×C412yes—
40#14519831—42no—
41C4×#92420—21no—
42C4×#92420—21no—
43(C2×#6923)⋊C4C2×C412yes—
44C2×#11758189—21no—
45C2×C8×D61D411yescharacteristic
46C2×C8×D61D411yescharacteristic
47#14519776C2×C411yescharacteristic
48#14519775C2×C411yescharacteristic
49#14519767—21no—
50#14519757C2×C411yescharacteristic
51#14519755—21no—
52#14519753C2×C411yescharacteristic
53C4×Dic122—21no—
54C4×Dic122C2×C411yescharacteristic
55#14519734—21no—
56C42×D61C2311yescharacteristic
57C4⋊#92418—21no—
58C4⋊#92418C2×C411yescharacteristic
59#14519706—21no—
60#14519706—21no—
61#14519706—21no—
62#14519687—21no—
63C4×#92418—21no—
64C4×#92418C2×C411yescharacteristic
65C8×Dic61—21no—
66C8×Dic61D411yescharacteristic
67C8×Dic61D411yescharacteristic
68C4×Q8×C61C2×C411yescharacteristic
69C4⋊C8×C61—21no—
70C4⋊C8×C61C2×C411yescharacteristic
71#97×C61—21no—
72C4×C8×C61C2×C411yescharacteristic
73C22×#6923—22no—
74C2×Q8×C61C4211yescharacteristic
75C2×C4×D61C22×C411yescharacteristic
76C2×C4×D61C2×D411yescharacteristic
77C2×C4×D61#4111yescharacteristic
78C2×Dic122—21no—
79C2×Dic122C4211yescharacteristic
80C2×#92420—22no—
81C2×#92420—22no—
82C2×#92420—22no—
83C4⋊#6923—42no—
84C4×#6923—41no—
85C4×#6923—41no—
86D61⋊C8—41no—
87D61⋊C8—41no—
88C2×C8×C61—21no—
89C2×C8×C61C22⋊C411yescharacteristic
90C2×C8×C61C22⋊C411yescharacteristic
91C4⋊C4×C61—21no—
92C4⋊C4×C61C4211yescharacteristic
93C42×C61—21no—
94C42×C61C22×C411yescharacteristic
95#11758198—21no—
96#11758198—21no—
97C4⋊Dic61—21no—
98C4⋊Dic61C4211yescharacteristic
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104C4×Dic61—21no—
105C4×Dic61C22×C411yescharacteristic
106C4×Dic61C2×D411yescharacteristic
107C4×Dic61#4111yescharacteristic
108C2×#92418—21no—
109C2×#92418C22⋊C411yescharacteristic
110C2×#92418C22⋊C411yescharacteristic
111#11758189—41no—
112#11758189—41no—
113C8×D61—21no—
114C8×D61—21no—
115C8×D61—21no—
116C8×D61—21no—
117C22×D61C4×D411yescharacteristic
118C2×#6923—42no—
119C2×#6923—42no—
120C2×#6923—42no—
121Q8×C61—41no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61C2×C4211yescharacteristic
125C2×C4×C61C2×C22⋊C411yescharacteristic
126C2×C4×C61#11711yescharacteristic
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61C4×D411yescharacteristic
130C2×Dic61C4×D411yescharacteristic
131C2×Dic61C4×D411yescharacteristic
132C4×D61—22no—
133C4×D61—41no—
134C4×D61AGL(1,ℤ/8)11yescharacteristic
135C4×D61#13711yescharacteristic
136C4×D61#13711yescharacteristic
137C4×D61#13711yescharacteristic
138Dic122—42no—
139Dic122—41no—
140#92420—42no—
141#92420—42no—
142#92420—42no—
143C8×C61—21no—
144C8×C61—21no—
145C8×C61—41no—
146#92418—21no—
147#92418—21no—
148#92418—41no—
149#8254—611nomaximal, Sylow
150C22×C61C4×C22⋊C411yescharacteristic
151C2×D61—21no—
152C2×D61—21no—
153C2×D61#44011yescharacteristic
154C2×D61#44111yescharacteristic
155#6923—82no—
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—41no—
159C4×C61—41no—
160C4×C61#41711yescharacteristic
161C4×C61#41911yescharacteristic
162Dic61—21no—
163Dic61—41no—
164Dic61—41no—
165Dic61#44011yescharacteristic
166Dic61#44111yescharacteristic
167Dic61#44412yes—
168#2960—611no—
169#1770—611no—
170#1542—611no—
171#1503—611no—
172#1452—611no—
173#1303—611no—
174#1301—611no—
175C2×C61#175711yescharacteristic
176C2×C61#176311yescharacteristic
177C2×C61#176511yescharacteristic
178D61—21no—
179D61—21no—
180#533—611no—
181#446—611no—
182#446—1221no—
183#446#692311yescharacteristic, complemented
184C8×Q8—611no—
185C8×Q8—611no—
186C8×Q8—1221no—
187#431—611no—
188#431—611no—
189#424—1221no—
190#423—611no—
191C2×C4⋊C8—611no—
192#405—1221no—
193C2×#97—1221no—
194C2×C4×C8—611no—
195C4×C4⋊C4—611no—
196#336—1221no—
197#333—612no—
198#332—612no—
199#328—612no—
200#328—612no—
201#322—1221no—
202#322—1221no—
203C61#825411yescharacteristic, complemented, Sylow
204C2×M16—1221no—
205C22×C8—611no—
206C22×C8—611no—
207C22×C8—1221no—
208C4⋊Q8—611no—
209C4⋊Q8—611no—
210#125—1221no—
211C22⋊Q8—611no—
212C22⋊Q8—611no—
213C22⋊Q8—1221no—
214C4×Q8—611no—
215C4×Q8—1221no—
216C4×Q8C2×#692311yescharacteristic
217#117—1221no—
218C2×C4⋊C4—1221no—
219C2×C42—611no—
220C2×C42—1221no—
221C4⋊C8—21no—
222C4⋊C8—612no—
223C4⋊C8—612no—
224C4⋊C8—611no—
225C4⋊C8—1221no—
226C4⋊C8—1221no—
227C4⋊C8—1221no—
228C4⋊C8—1221no—
229C4⋊C8—1221no—
230C4⋊C8—1221no—
231C4⋊C8C2×#692311yescharacteristic
232C22⋊C8—612no—
233C22⋊C8—1221no—
234#97—21no—
235#97—1221no—
236#97—2442no—
237C4×C8—611no—
238C4×C8—611no—
239C4×C8—611no—
240C4×C8—1221no—
241C4×C8—1221no—
242C4×C8—1221no—
243C4×C8—1221no—
244C4×C8C2×#692311yescharacteristic
245#95—612no—
246C2×Q8—611no—
247C2×Q8—1221no—
248C2×Q8C4×#692311yescharacteristic
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—1222no—
253M16—2441no—
254M16—2441no—
255C2×C8—21no—
256C2×C8—611no—
257C2×C8—611no—
258C2×C8—1221no—
259C2×C8—1221no—
260C2×C8—1221no—
261C2×C8—1221no—
262C2×C8—1222no—
263C2×C8—1222no—
264C2×C8—1222no—
265C2×C8—1221no—
266C2×C8—2441no—
267C2×C8—2441no—
268C2×C8C22⋊#692311yescharacteristic
269C2×C8C22⋊#692311yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—611no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4—2442no—
279C4⋊C4C4×#692311yescharacteristic
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C42—21no—
283C42—611no—
284C42—611no—
285C42—611no—
286C42—1221no—
287C42—2441no—
288C42—2441no—
289C42C22×#692311yescharacteristic
290C23—611no—
291Q8—41no—
292Q8—2441no—
293Q8—2442no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—611no—
297C2×C4—611no—
298C2×C4—611no—
299C2×C4—611no—
300C2×C4—611no—
301C2×C4—611no—
302C2×C4—611no—
303C2×C4—1222no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—2441no—
307C2×C4—2442no—
308C2×C4—2442no—
309C2×C4—2442no—
310C2×C4C2×C4×#692311yescharacteristic
311C2×C4C2×C22⋊#692311yescharacteristic
312C2×C4#1451985611yescharacteristic
313C8—21no—
314C8—21no—
315C8—41no—
316C8—1221no—
317C8—1221no—
318C8—2442no—
319C8—2442no—
320C8—2442no—
321C8—2441no—
322C22—611no—
323C22—611no—
324C22—1221no—
325C22—1221no—
326C22C4×C22⋊#692311yescharacteristic
327C4—21no—
328C4—21no—
329C4—41no—
330C4—41no—
331C4—611no—
332C4—611no—
333C4—612no—
334C4—1221no—
335C4—4882no—
336C4—2441no—
337C4—2441no—
338C4#1684075311yescharacteristic
339C4#1684075511yescharacteristic
340C2—1221no—
341C2—1221no—
342C2#2146157511yescharacteristic
343C2#2146159111yescharacteristic
344C2#2146159711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC42C22×#6923
FittingC61×#446C4
socleC22×C61C4×C22⋊C4
prime radicalC22×D61C4×D4
cosocleC42×D61C23
hypercenter#446#6923
hypocenterC61#8254
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #446

Complements

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

NH ≅ G/Ntype
14. #16840622C4semidirect
15. #16840621C4semidirect
21. #16839892C4semidirect
23. Q8×#92418C4semidirect
25. #16839886C4semidirect
30. C61×#446C4semidirect
183. #446#6923semidirect
203. C61#8254semidirect

Maximal subgroups

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

subgroupindex
#214616132
#214613202
#214612012
#214610332
#214607152
#214607092
#214547502
#825461