Finite Group Databasebeta

← #30607220

Subgroups — #30607220

Order 15616.

440 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462048C211yesmaximal, characteristic
2C2×#16840657C211yesmaximal, characteristic
3#21460874C212yesmaximal, complemented
4#21460873C212yesmaximal, complemented
5#405×D61C211yesmaximal, characteristic
6C2×#14519851C2212yes—
7C22×#11758187C2212yes—
8#16840657—21no—
9#16840657—21no—
10#16840657—21no—
11#16840657—21no—
12C2×M16×D61C411yescharacteristic
13C22×C8×D61C2211yescharacteristic
14#117×D61C411yescharacteristic
15#16839720C2211yescharacteristic
16#16839719—21no—
17#16839718C2211yescharacteristic
18#16839717C411yescharacteristic
19#16839716—21no—
20#97×D61—21no—
21C4×C8×D61—21no—
22C61×#405C411yescharacteristic
23#14519851—22no—
24#14519851—22no—
25C2×#11758187—22no—
26C2×#11758187—22no—
27C2×#11758187—22no—
28C2×#11758187—22no—
29C22×C4×D61C2×C411yescharacteristic
30C2×#11758194C2×C411yescharacteristic
31C2×#11758189—21no—
32M16×D61—22no—
33M16×D61—22no—
34C22×#92418C2311yescharacteristic
35C2×C8×D61—21no—
36C2×C8×D61—22no—
37C2×C8×D61—22no—
38C2×C8×D61D411yescharacteristic
39C2×C8×D61D411yescharacteristic
40C2×C8×D61D411yescharacteristic
41C2×C8×D61D411yescharacteristic
42#14519736C2×C411yescharacteristic
43#14519735C811yescharacteristic
44#14519735C811yescharacteristic
45#14519734—21no—
46#14519733—21no—
47C4⋊C4×D61C811yescharacteristic
48C4⋊C4×D61C811yescharacteristic
49C22⋊C4×D61—21no—
50C42×D61—21no—
51#14519688—21no—
52#14519687—21no—
53#14519687—21no—
54C4×#92418—21no—
55C8×Dic61—21no—
56C8×Dic61—21no—
57C2×M16×C61C2×C411yescharacteristic
58C22×C8×C61C2×C411yescharacteristic
59#117×C61C2×C411yescharacteristic
60#97×C61—21no—
61C4×C8×C61—21no—
62C23×D61M1611yescharacteristic
63C22×C4×C61C22×C411yescharacteristic
64C22×Dic61M1611yescharacteristic
65C2×C4×D61—21no—
66C2×C4×D61—21no—
67C2×C4×D61—21no—
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61C22⋊C411yescharacteristic
72C2×C4×D61C22⋊C411yescharacteristic
73C2×C4×D61C2×C811yescharacteristic
74C2×C4×D61C2×C811yescharacteristic
75M16×C61—21no—
76M16×C61M1612yes—
77C2×C8×C61—21no—
78C2×C8×C61—21no—
79C2×C8×C61—21no—
80C2×C8×C61C22⋊C411yescharacteristic
81C2×C8×C61C22⋊C411yescharacteristic
82C4⋊C4×C61C2×C811yescharacteristic
83C4⋊C4×C61C2×C811yescharacteristic
84C22⋊C4×C61—21no—
85C42×C61—21no—
86C22⋊Dic61—21no—
87#11758198—21no—
88#11758198—21no—
89C4⋊Dic61C2×C811yescharacteristic
90C4⋊Dic61C2×C811yescharacteristic
91#11758196—21no—
92#11758196—21no—
93C4×Dic61—21no—
94C4×Dic61—21no—
95C4×Dic61—21no—
96#11758194—21no—
97#11758194M1612yes—
98C2×#92418—21no—
99C2×#92418C2×D411yescharacteristic
100C2×#92418C2×D411yescharacteristic
101C2×#92418#4112yes—
102C2×#92418#4112yes—
103#11758189—24no—
104C8×D61—24no—
105C8×D61—22no—
106C8×D61—22no—
107C8×D61—22no—
108C8×D61—22no—
109#11758187—42no—
110#11758187—42no—
111C23×C61C2×M1611yescharacteristic
112C22×D61—21no—
113C22×D61—21no—
114C22×D61—22no—
115C22×D61—41no—
116C22×D61C22⋊C811yescharacteristic
117C22×D61C22⋊C811yescharacteristic
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61C2×C22⋊C411yescharacteristic
121C2×C4×C61#11711yescharacteristic
122C2×C4×C61#11711yescharacteristic
123C2×C4×C61C22×C811yescharacteristic
124C2×C4×C61C2×M1611yescharacteristic
125C2×C4×C61C2×M1611yescharacteristic
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61C22⋊C811yescharacteristic
131C2×Dic61C22⋊C811yescharacteristic
132C4×D61—21no—
133C4×D61—21no—
134C4×D61—21no—
135C4×D61—21no—
136C4×D61—21no—
137C4×D61—21no—
138C4×D61—21no—
139C4×D61—21no—
140C4×D61—42no—
141C4×D61—42no—
142C8×C61—21no—
143C8×C61—21no—
144C8×C61—22no—
145#92418—22no—
146#92418#12312yes—
147#92418#12312yes—
148#12848—611nomaximal, Sylow
149C22×C61—21no—
150C22×C61—21no—
151C22×C61C2×C22⋊C811yescharacteristic
152C22×C61#43211yescharacteristic
153C22×C61#43211yescharacteristic
154C2×D61—21no—
155C2×D61—21no—
156C2×D61—21no—
157C2×D61—21no—
158C2×D61—21no—
159C2×D61—42no—
160C2×D61—42no—
161C2×D61#35012yes—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61#38111yescharacteristic
165C4×C61#40711yescharacteristic
166C4×C61#43111yescharacteristic
167C4×C61#43111yescharacteristic
168Dic61—21no—
169Dic61—21no—
170Dic61—41no—
171Dic61—41no—
172C2×#405—611no—
173#2112—611no—
174C2×C22⋊C16—611no—
175#1379—612no—
176#1379—612no—
177C2×C61—21no—
178C2×C61—21no—
179C2×C61#181711yescharacteristic
180C2×C61C2×#35011yescharacteristic
181C2×C61#211711yescharacteristic
182D61—22no—
183D61—41no—
184C22×M16—611no—
185C23×C8—611no—
186C2×#117—611no—
187C2×M32—612no—
188C22×C16—612no—
189#405—611no—
190#405—611no—
191#405—611no—
192#405—1221no—
193#405—1221no—
194#405#692311yescharacteristic
195C2×#97—1221no—
196C2×C4×C8—1221no—
197C22⋊C16—1221no—
198C22⋊C16—1221no—
199C22⋊C16—1221no—
200C22⋊C16—1221no—
201C61#1284811yescharacteristic, complemented, Sylow
202C23×C4—611no—
203C2×M16—611no—
204C2×M16—1221no—
205C2×M16—1222no—
206C2×M16—1222no—
207C2×M16C2×#692311yescharacteristic
208C22×C8—611no—
209C22×C8—611no—
210C22×C8—611no—
211C22×C8—611no—
212C22×C8—611no—
213C22×C8—1222no—
214C22×C8—1222no—
215C22×C8—1221no—
216C22×C8C2×#692311yescharacteristic
217#117—611no—
218#117—611no—
219#117—611no—
220#117—1221no—
221#117—1221no—
222#117C2×#692311yescharacteristic
223C2×C4⋊C4—611no—
224C2×C4⋊C4—611no—
225C2×C22⋊C4—1221no—
226C2×C42—1221no—
227M32—1222no—
228M32—1222no—
229C2×C16—1222no—
230C2×C16—1222no—
231C2×C16—1222no—
232C2×C16—1222no—
233#97—21no—
234#97—1221no—
235#97—1221no—
236#97—1221no—
237C4×C8—21no—
238C4×C8—1221no—
239C4×C8—1221no—
240C4×C8—1221no—
241C24—611no—
242C22×C4—611no—
243C22×C4—611no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—1221no—
248C22×C4—1221no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4C22×#692311yescharacteristic
254M16—21no—
255M16—612no—
256M16—1224no—
257M16—1221no—
258M16#1175821312yes—
259C2×C8—21no—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—611no—
263C2×C8—611no—
264C2×C8—612no—
265C2×C8—612no—
266C2×C8—1222no—
267C2×C8—1222no—
268C2×C8—1222no—
269C2×C8—1222no—
270C2×C8—1224no—
271C2×C8—1221no—
272C2×C8C22⋊#692311yescharacteristic
273C2×C8C22⋊#692311yescharacteristic
274C4⋊C4—611no—
275C4⋊C4—611no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4D61⋊C811yescharacteristic
279C4⋊C4D61⋊C811yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C42—21no—
285C42—1221no—
286C42—1221no—
287C42—1221no—
288C16—2442no—
289C16—2442no—
290C23—611no—
291C23—611no—
292C23—1222no—
293C23—1221no—
294C23—1221no—
295C23—2441no—
296C23D61⋊M1611yescharacteristic
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—611no—
300C2×C4—611no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—2442no—
314C2×C4—2442no—
315C2×C4C2×C22⋊#692311yescharacteristic
316C2×C4#1451985611yescharacteristic
317C2×C4#1451985611yescharacteristic
318C2×C4C2×D61⋊C811yescharacteristic
319C2×C4D61⋊M1611yescharacteristic
320C2×C4C2×#1175821311yescharacteristic
321C8—21no—
322C8—21no—
323C8—22no—
324C8—612no—
325C8—612no—
326C8—1222no—
327C22—21no—
328C22—21no—
329C22—612no—
330C22—1221no—
331C22—1221no—
332C22—1221no—
333C22—1221no—
334C22—1221no—
335C22—2442no—
336C22—2442no—
337C22D61⋊(C22⋊C8)11yescharacteristic
338C22#1684078411yescharacteristic
339C22#1684078511yescharacteristic
340C4—41no—
341C4—41no—
342C4—1221no—
343C4—1221no—
344C4—2441no—
345C4—2441no—
346C4#1684070511yescharacteristic
347C4#1684073311yescharacteristic
348C4#1684078011yescharacteristic
349C4#1684078111yescharacteristic
350C2—21no—
351C2—21no—
352C2—1222no—
353C2—2441no—
354C2#2146171111yescharacteristic
355C2D61⋊#35011yescharacteristic
356C2#2146206211yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#405C4
socleC22×C61C2×C22⋊C8
prime radicalC23×D61M16
cosocleC22×#92418C23
hypercenter#405#6923
hypocenterC61#12848
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #405

Complements

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

NH ≅ G/Ntype
3. #21460874C2semidirect
4. #21460873C2semidirect
201. C61#12848semidirect

Maximal subgroups

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

subgroupindex
#214620482
C2×#168406572
#214608742
#214608732
#405×D612
#1284861