Finite Group Databasebeta

← #30602136

Subgroups — #30602136

Order 15616.

512 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461605C211yesmaximal, characteristic
2C4×C4⋊#92420C211yesmaximal, characteristic
3#21460655C212yesmaximal
4#21460655C212yesmaximal
5#21448390C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×C4⋊#92420C2212yes—
8C2×#14519832—21no—
9C2×C4×#92420C2212yes—
10#16840628—21no—
11#16840628—21no—
12C2×#14519776C411yescharacteristic
13C2×#14519742—21no—
14#16839666—21no—
15#16839660C411yescharacteristic
16#16839657—21no—
17#16839631C411yescharacteristic
18C4⋊C4×Dic61C2211yescharacteristic
19C4⋊C4×Dic61C2211yescharacteristic
20#16839613—21no—
21C42×Dic61C2211yescharacteristic
22C61×#389C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—24no—
26C4⋊#92420—22no—
27C4⋊#92420Q814yescomplemented
28#14519832—42no—
29C4×#92420—24no—
30C22×Dic122—21no—
31#14519776—22no—
32#14519776—22no—
33#14519742—44no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61C2311yescharacteristic
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C42×C61C2×C411yescharacteristic
55#95×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22×C411yescharacteristic
61C22×Dic61—21no—
62C22×Dic61—21no—
63C22×Dic61C22⋊C411yescharacteristic
64C22×Dic61C22⋊C411yescharacteristic
65C22×Dic61C2×D411yescharacteristic
66C22×Dic61C2×D411yescharacteristic
67C2×Dic122—24no—
68C2×Dic122—42no—
69C2×Dic122—42no—
70C2×#92420—24no—
71C2×#92420—24no—
72C2×#92420—42no—
73C2×#92420—42no—
74C2×#92420—42no—
75C2×#92420—42no—
76C4⋊C4×C61—21no—
77C4⋊C4×C61—22no—
78C4⋊C4×C61—42no—
79C4⋊C4×C61M1612yes—
80C42×C61—22no—
81C4⋊Dic61—21no—
82C4⋊Dic61—22no—
83C4⋊Dic61M1612yes—
84#11758196—24no—
85#11758196—42no—
86#11758196—42no—
87#11758196—42no—
88C4×Dic61—21no—
89C4×Dic61—21no—
90C4×Dic61—22no—
91C4×Dic61—22no—
92C4×Dic61—41no—
93C4×Dic61—42no—
94C4×Dic61—42no—
95C4×Dic61SD1612yes—
96C4×Dic61Q1612yes—
97C4×Dic61C2×Q812yes—
98C4×Dic61#4112yes—
99C23×C61C2×C22⋊C411yescharacteristic
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—22no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61#10312yes—
112C2×C4×C61C4×Q812yes—
113C2×C4×C61C2×M1611yescharacteristic
114C2×C4×C61C2×M1611yescharacteristic
115C2×C4×C61#13112yes—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—22no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61#10312yes—
129C2×Dic61#10412yes—
130C2×Dic61C22⋊Q812yes—
131C2×Dic61#12411yescharacteristic
132C2×Dic61C4⋊Q811yescharacteristic
133C2×Dic61C2×SD1611yescharacteristic
134C2×Dic61C2×Q1611yescharacteristic
135C2×Dic61AGL(1,ℤ/8)12yes—
136Dic122—48no—
137#92420—44no—
138#92420—44no—
139#9868—611nomaximal, Sylow
140C22×C61#39111yescharacteristic
141C22×C61#40711yescharacteristic
142C22×C61#40811yescharacteristic
143C22×C61C2×#10311yescharacteristic
144C22×C61#41811yescharacteristic
145C22×C61C2×#10411yescharacteristic
146C22×C61#42111yescharacteristic
147C4×C61—22no—
148C4×C61—42no—
149C4×C61—41no—
150C4×C61—81no—
151C4×C61#44612yes—
152C4×C61#44612yes—
153Dic61—21no—
154Dic61—21no—
155Dic61—22no—
156Dic61—22no—
157Dic61—42no—
158Dic61—81no—
159Dic61#47612yes—
160Dic61#47712yes—
161C4×C4⋊Q8—611no—
162#1767—611no—
163C4×C4⋊C8—611no—
164#1279—612no—
165#1279—612no—
166C2×C61#148711yescharacteristic
167C2×C61#149011yescharacteristic
168C2×C61#149311yescharacteristic
169C2×C61#149611yescharacteristic
170C2×C61#198511yescharacteristic
171C2×C61#198611yescharacteristic
172C2×C61#198711yescharacteristic
173C2×C4⋊Q8—611no—
174C2×C4×Q8—1221no—
175C2×C4⋊C8—612no—
176C2×C4⋊C8—1221no—
177C2×#97—1221no—
178C2×C4×C8—612no—
179#391—1221no—
180#389—611no—
181#389—1221no—
182#389#692311yescharacteristic
183#384—611no—
184C4×C4⋊C4—611no—
185C4×C4⋊C4—611no—
186C4×C4⋊C4—1221no—
187C43—611no—
188#336—1221no—
189#336—1221no—
190C61#986811yescharacteristic, complemented, Sylow
191C22×Q8—1221no—
192C22×C8—1222no—
193C22×C8—1222no—
194C4⋊Q8—1222no—
195C4⋊Q8—1222no—
196C4×Q8—2444no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—611no—
199C2×C4⋊C4—611no—
200C2×C4⋊C4—1221no—
201C2×C4⋊C4—1221no—
202C2×C4⋊C4—1221no—
203C2×C4⋊C4—1221no—
204C2×C4⋊C4C2×#692311yescharacteristic
205C2×C4⋊C4C2×#692311yescharacteristic
206C2×C42—611no—
207C2×C42—611no—
208C2×C42—611no—
209C2×C42—611no—
210C2×C42—611no—
211C2×C42—611no—
212C2×C42—1221no—
213C2×C42—1221no—
214C2×C42C2×#692311yescharacteristic
215C4⋊C8—614no—
216C4⋊C8—1222no—
217C4⋊C8—1224no—
218#97—2442no—
219C4×C8—1224no—
220#95—21no—
221#95—1221no—
222#95—1221no—
223#95—1221no—
224C2×Q8—1224no—
225C2×Q8—2442no—
226C2×Q8—2442no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—611no—
230C22×C4—611no—
231C22×C4—611no—
232C22×C4—611no—
233C22×C4—1221no—
234C22×C4—1221no—
235C22×C4C22⋊#692311yescharacteristic
236C22×C4C22⋊#692311yescharacteristic
237C22×C4C22×#692311yescharacteristic
238C2×C8—1224no—
239C2×C8—1224no—
240C2×C8—2442no—
241C2×C8—2442no—
242C2×C8—2442no—
243C2×C8—2442no—
244C4⋊C4—21no—
245C4⋊C4—22no—
246C4⋊C4—42no—
247C4⋊C4—612no—
248C4⋊C4—1224no—
249C4⋊C4—1221no—
250C4⋊C4—1222no—
251C4⋊C4—2442no—
252C4⋊C4—2442no—
253C4⋊C4—2442no—
254C4⋊C4#1175821312yes—
255C42—22no—
256C42—612no—
257C42—612no—
258C42—612no—
259C42—612no—
260C42—1222no—
261C42—1222no—
262C42—1221no—
263C42—1221no—
264C42—2441no—
265C42—2442no—
266C42—2442no—
267C23C2×C22⋊#692311yescharacteristic
268Q8—2448no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—612no—
281C2×C4—611no—
282C2×C4—611no—
283C2×C4—612no—
284C2×C4—611no—
285C2×C4—611no—
286C2×C4—612no—
287C2×C4—612no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—1222no—
295C2×C4—2441no—
296C2×C4—2441no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4#1451984012yes—
301C2×C4Q8×#692312yes—
302C2×C4D61⋊M1611yescharacteristic
303C2×C4C2×#1175821311yescharacteristic
304C2×C4#1451986412yes—
305C8—2444no—
306C8—2444no—
307C22(C2×#6923)⋊Q811yescharacteristic
308C22#1684073311yescharacteristic
309C22#1684073511yescharacteristic
310C22C2×#1451984011yescharacteristic
311C22#1684075411yescharacteristic
312C22D61⋊#10411yescharacteristic
313C22#1684075911yescharacteristic
314C4—22no—
315C4—42no—
316C4—41no—
317C4—81no—
318C4—612no—
319C4—612no—
320C4—1222no—
321C4—1222no—
322C4—1221no—
323C4—1221no—
324C4—4881no—
325C4—2442no—
326C4#1684081212yes—
327C4#1684081412yes—
328C2#2146114811yescharacteristic
329C2#2146115911yescharacteristic
330C2#2146116711yescharacteristic
331C2#2146117811yescharacteristic
332C2#2146199211yescharacteristic
333C2#2146199611yescharacteristic
334C2#2146199711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#9868
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
27. C4⋊#92420Q8semidirect
190. C61#9868semidirect

Maximal subgroups

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

subgroupindex
#214616052
C4×C4⋊#924202
#214606552
#214483902
#986861