Finite Group Databasebeta

← #29589934

Subgroups — #29589934

Order 15616.

364 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 93 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#21454526C211yesmaximal, characteristic
2#21447621C211yesmaximal, characteristic, complemented
3#21447616C211yesmaximal, characteristic, complemented
4#21443775C211yesmaximal, characteristic, complemented
5D4⋊#11758185C211yesmaximal, characteristic, complemented
6#21443773C211yesmaximal, characteristic, complemented
7C61×D4⋊C16C211yesmaximal, characteristic, complemented
8C2×#14519783—21no—
9#16840309C411yescharacteristic
10#16839840C411yescharacteristic
11#16839839C411yescharacteristic
12#16839837—21no—
13C8×D244C2211yescharacteristic
14C8×C22⋊D61—21no—
15#16839784C411yescharacteristic
16#16839727—21no—
17C4×C8×D61C2211yescharacteristic
18C4⋊#11758185C2211yescharacteristic
19#16839580—21no—
20#16839541—21no—
21#16839541—21no—
22#16839537—21no—
23C4×#11758185C2211yescharacteristic
24C8×D4×C61C2211yescharacteristic
25C61×C4⋊C16C2211yescharacteristic
26C4×C16×C61C2211yescharacteristic
27C2×#11758222—21no—
28#14519783—42no—
29#14519783—42no—
30C2×#11758194—21no—
31C2×#11758189—21no—
32C2×#11758189—21no—
33C2×C8×D61—21no—
34C2×C8×D61D411yescharacteristic
35C2×C8×D61D411yescharacteristic
36#14519776C811yescharacteristic
37#14519773C811yescharacteristic
38#14519763—21no—
39#14519752C811yescharacteristic
40#14519750—21no—
41#14519748C811yescharacteristic
42C4×D244C2×C411yescharacteristic
43C4×C22⋊D61—21no—
44C42×D61C2×C411yescharacteristic
45C2×#11758185—21no—
46C2×#11758185—21no—
47C4⋊#92418C2×C411yescharacteristic
48#14519706—21no—
49C22⋊#92418—21no—
50#14519689—21no—
51#14519689—21no—
52C4×#92418C2×C411yescharacteristic
53C8×Dic61D411yescharacteristic
54C8×Dic61D411yescharacteristic
55C22×C8×C61—21no—
56C4×D4×C61C2×C411yescharacteristic
57C2×C16×C61—21no—
58C2×C16×C61—21no—
59C4⋊C8×C61C2×C411yescharacteristic
60C22⋊C8×C61—21no—
61C4×C8×C61C2311yescharacteristic
62C2×D4×C61C2×C811yescharacteristic
63C22×C4×C61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67#11758222—42no—
68#11758222—42no—
69C2×D244—21no—
70C2×D244C2×C811yescharacteristic
71C2×C4×D61—21no—
72C2×C4×D61C22⋊C411yescharacteristic
73C2×C4×D61C2×C811yescharacteristic
74C2×C4×D61M1611yescharacteristic
75C2×Dic122—21no—
76C2×C8×C61—21no—
77C2×C8×C61—41no—
78C2×C8×C61—41no—
79C2×C8×C61C2×D411yescharacteristic
80C2×C8×C61C2×D411yescharacteristic
81C4⋊C4×C61C2×C811yescharacteristic
82C22⋊C4×C61—21no—
83C42×C61C22×C411yescharacteristic
84C22⋊Dic61—21no—
85#11758198—21no—
86#11758198—21no—
87C4⋊Dic61C2×C811yescharacteristic
88#11758196—21no—
89C4×Dic61C22⋊C411yescharacteristic
90C4×Dic61C2×C811yescharacteristic
91C4×Dic61M1611yescharacteristic
92#11758194—42no—
93C2×#92418—21no—
94C2×#92418C22⋊C411yescharacteristic
95C2×#92418C22⋊C411yescharacteristic
96#11758189—42no—
97#11758189—42no—
98C8×D61—21no—
99C8×D61—21no—
100C8×D61—41no—
101C8×D61—41no—
102C8×D61—41no—
103C16×C61—41no—
104C16×C61—41no—
105#11758185—41no—
106#11758185—41no—
107C23×C61—21no—
108C22×D61—21no—
109C22×D61C22⋊C811yescharacteristic
110D4×C61—21no—
111D4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61C2×C22⋊C411yescharacteristic
116C2×C4×C61C22×C811yescharacteristic
117C2×C4×C61C2×M1611yescharacteristic
118C22⋊D61—42no—
119C22⋊D61—42no—
120C22⋊D61—42no—
121C2×Dic61—21no—
122C2×Dic61C22⋊C811yescharacteristic
123C2×Dic61C22⋊C811yescharacteristic
124C2×Dic61C22⋊C811yescharacteristic
125D244—21no—
126D244—21no—
127D244—42no—
128C4×D61—21no—
129C4×D61—21no—
130C4×D61—21no—
131C4×D61—21no—
132C4×D61—41no—
133C4×D61—41no—
134C4×D61—41no—
135Dic122—42no—
136C8×C61—21no—
137C8×C61—41no—
138C8×C61AGL(1,ℤ/8)11yescharacteristic
139C8×C61AGL(1,ℤ/8)11yescharacteristic
140#92418—21no—
141#92418—21no—
142#92418—41no—
143#11632—611nomaximal, Sylow
144C22×C61—41no—
145C22×C61—41no—
146C22×C61—41no—
147C22×C61C2×C22⋊C811yescharacteristic
148C2×D61—21no—
149C2×D61—21no—
150C2×D61—21no—
151C2×D61—41no—
152C2×D61—41no—
153C2×D61—41no—
154C4×C61—21no—
155C4×C61—41no—
156C4×C61#41811yescharacteristic
157C4×C61#42111yescharacteristic
158C4×C61#50411yescharacteristic
159C4×C61#50411yescharacteristic
160Dic61—21no—
161Dic61—21no—
162Dic61—21no—
163Dic61—41no—
164#2931—611no—
165#2163—611no—
166#2162—611no—
167D4⋊C16—611no—
168D4⋊C16—611no—
169D4⋊C16—611no—
170D4⋊C16D6111yescharacteristic, complemented
171C2×C61—81no—
172C2×C61#147811yescharacteristic
173C2×C61#211311yescharacteristic
174C2×C61#211711yescharacteristic
175D61—41no—
176D61—81no—
177C2×#131—1221no—
178#532—611no—
179#436—611no—
180#436—611no—
181#436—1221no—
182C8×D4—611no—
183C8×D4—1221no—
184C8×D4C2×D6111yescharacteristic
185#423—611no—
186#408—1221no—
187C2×C4×C8—611no—
188C4⋊C16—611no—
189C4⋊C16—1221no—
190C4⋊C16C2×D6111yescharacteristic
191C22⋊C16—1221no—
192C22⋊C16—1221no—
193#346—1221no—
194C4×C16—611no—
195C4×C16C2×D6111yescharacteristic
196C61#1163211yescharacteristic, complemented, Sylow
197C2×#41—1221no—
198#131—2442no—
199#131—2442no—
200C2×M16—1221no—
201C2×M16—1221no—
202C2×M16—1221no—
203C22×C8—21no—
204C22×C8—611no—
205C22×C8—611no—
206C22×C8—1221no—
207C4⋊Q8—611no—
208#127—611no—
209#124—1221no—
210#121—611no—
211#121—611no—
212#121—1221no—
213C4×D4—611no—
214C4×D4—1221no—
215C4×D4C4×D6111yescharacteristic
216C2×C42—611no—
217C2×C16—21no—
218C2×C16—21no—
219C2×C16—1221no—
220C2×C16—1221no—
221C4⋊C8—611no—
222C4⋊C8—1221no—
223C4⋊C8C4×D6111yescharacteristic
224C22⋊C8—21no—
225C22⋊C8—1221no—
226C22⋊C8—1221no—
227C22⋊C8—1221no—
228C4×C8—611no—
229C4×C8—611no—
230C4×C8—611no—
231C4×C8C22×D6111yescharacteristic
232#41—2442no—
233#41—2442no—
234C2×Q8—1221no—
235C2×D4—611no—
236C2×D4—1221no—
237C2×D4—1221no—
238C2×D4—1221no—
239C2×D4—1221no—
240C2×D4C8×D6111yescharacteristic
241C22×C4—21no—
242C22×C4—611no—
243C22×C4—611no—
244C22×C4—611no—
245C22×C4—1221no—
246M16—2442no—
247M16—2442no—
248M16—2442no—
249C2×C8—21no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—611no—
253C2×C8—611no—
254C2×C8—1221no—
255C2×C8—1221no—
256C2×C8—1221no—
257C2×C8—2441no—
258C2×C8—2441no—
259C2×C8—2441no—
260C2×C8D4×D6111yescharacteristic
261C2×C8D4×D6111yescharacteristic
262C4⋊C4—611no—
263C4⋊C4—1221no—
264C4⋊C4C8×D6111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—1221no—
267C22⋊C4—1221no—
268C22⋊C4—1221no—
269C42—611no—
270C42—611no—
271C42—611no—
272C42C2×C4×D6111yescharacteristic
273C16—41no—
274C16—41no—
275C16—2441no—
276C16—2441no—
277C23—21no—
278C23—611no—
279C23—1221no—
280Q8—2442no—
281D4—21no—
282D4—21no—
283D4—1221no—
284D4—1221no—
285D4—2442no—
286D4—2442no—
287D4—2442no—
288D4—2442no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—611no—
293C2×C4—611no—
294C2×C4—611no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4C22⋊C4×D6111yescharacteristic
304C2×C4C2×C8×D6111yescharacteristic
305C2×C4M16×D6111yescharacteristic
306C8—21no—
307C8—41no—
308C8—1221no—
309C8—1221no—
310C8—2441no—
311C8#1451980111yescharacteristic
312C8#1451980411yescharacteristic
313C22—41no—
314C22—41no—
315C22—41no—
316C22—1221no—
317C22—1221no—
318C22—1221no—
319C22—2441no—
320C22—2441no—
321C22—2441no—
322C22C22⋊C8×D6111yescharacteristic
323C4—21no—
324C4—41no—
325C4—1221no—
326C4—1221no—
327C4—1221no—
328C4—2441no—
329C4#1683976511yescharacteristic
330C4#1683977711yescharacteristic
331C4#1684017811yescharacteristic
332C4#1684018011yescharacteristic
333C2—81no—
334C2—4881no—
335C2—2441no—
336C2#2144420811yescharacteristic
337C2#2144743111yescharacteristic
338C2#2144744511yescharacteristic
subgroupG/H
centerC2×C8D4×D61
commutatorC2×C4×C61C22×C8
FrattiniC4×C8C22×D61
FittingC61×D4⋊C16C2
socleC22×C61C2×C22⋊C8
prime radical#16840309C4
cosocleC4×C8×C61C23
hypercenterD4⋊C16D61
hypocenterC61#11632
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ D4⋊C16

Complements

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

NH ≅ G/Ntype
2. #21447621C2semidirect
3. #21447616C2semidirect
4. #21443775C2semidirect
5. D4⋊#11758185C2semidirect
6. #21443773C2semidirect
7. C61×D4⋊C16C2semidirect
170. D4⋊C16D61semidirect
196. C61#11632semidirect

Maximal subgroups

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

subgroupindex
#214545262
#214476212
#214476162
#214437752
D4⋊#117581852
#214437732
C61×D4⋊C162
#1163261