Finite Group Databasebeta

← #30603970

Subgroups — #30603970

Order 15616.

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

normal subgroups only

This group has 392 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#21462047C211yesmaximal, characteristic, complemented
2D61⋊(C22⋊C16)C211yesmaximal, characteristic, complemented
3#21460757C212yesmaximal, complemented
4#21460742C212yesmaximal, complemented
5#21454515C211yesmaximal, characteristic
6C2×#14519852—21no—
7C2×D61⋊C16—21no—
8#16840657—21no—
9#16840657—21no—
10C22⋊#11758187C2212yes—
11C22⋊#11758187C2212yes—
12C2×#14519783C411yescharacteristic
13C22×C8×D61C2211yescharacteristic
14#16840274C411yescharacteristic
15#16839835—21no—
16#16839835—21no—
17C8×D244—21no—
18C8×D244—21no—
19#16839789C2211yescharacteristic
20#16839730C2211yescharacteristic
21#16839725C411yescharacteristic
22C61×#405C411yescharacteristic
23#14519852—42no—
24D61⋊C16—42no—
25C2×#11758187—22no—
26C2×#11758187—22no—
27C2×#11758222C2×C411yescharacteristic
28C22×C4×D61C2×C411yescharacteristic
29#14519783—42no—
30C2×#11758194C2×C411yescharacteristic
31C2×#11758189—21no—
32C22×#92418C2311yescharacteristic
33C2×C8×D61—21no—
34C2×C8×D61—42no—
35C2×C8×D61D411yescharacteristic
36C2×C8×D61D411yescharacteristic
37C2×C8×D61D411yescharacteristic
38C2×C8×D61D411yescharacteristic
39#14519761—21no—
40#14519757C811yescharacteristic
41#14519757C811yescharacteristic
42#14519752C811yescharacteristic
43#14519752C811yescharacteristic
44#14519747—21no—
45C4×D244—21no—
46C4×D244—21no—
47C4⋊#92418—21no—
48C4⋊#92418—21no—
49#14519689—21no—
50#14519689—21no—
51#14519689—21no—
52#14519689—21no—
53C2×M16×C61C2×C411yescharacteristic
54C22×C8×C61C2×C411yescharacteristic
55#117×C61C2×C411yescharacteristic
56#97×C61—21no—
57C4×C8×C61—21no—
58C23×D61M1611yescharacteristic
59C22×C4×C61C22×C411yescharacteristic
60C2×C22⋊D61—21no—
61C22×Dic61M1611yescharacteristic
62#11758222—41no—
63#11758222—41no—
64C2×D244—21no—
65C2×D244—21no—
66C2×D244C2×C811yescharacteristic
67C2×C4×D61—21no—
68C2×C4×D61—41no—
69C2×C4×D61—41no—
70C2×C4×D61C22⋊C411yescharacteristic
71C2×C4×D61C22⋊C411yescharacteristic
72C2×C4×D61C2×C811yescharacteristic
73C2×C4×D61C2×C811yescharacteristic
74C2×Dic122C2×C811yescharacteristic
75M16×C61—41no—
76C2×C8×C61—22no—
77C2×C8×C61—21no—
78C2×C8×C61C22⋊C411yescharacteristic
79C2×C8×C61C22⋊C411yescharacteristic
80C4⋊C4×C61C2×C811yescharacteristic
81C4⋊C4×C61C2×C811yescharacteristic
82C22⋊C4×C61—21no—
83C42×C61—21no—
84#11758198—21no—
85#11758198—21no—
86#11758198—21no—
87#11758198—21no—
88C4⋊Dic61—21no—
89C4⋊Dic61—21no—
90#11758194—41no—
91C2×#92418—21no—
92C2×#92418—41no—
93C2×#92418C2×D411yescharacteristic
94C2×#92418C2×D411yescharacteristic
95#11758189—42no—
96C8×D61—22no—
97C8×D61—22no—
98C8×D61—41no—
99C8×D61—41no—
100C8×D61—42no—
101#11758187—42no—
102#11758187—42no—
103C23×C61C2×M1611yescharacteristic
104C22×D61—22no—
105C22×D61—21no—
106C22×D61—41no—
107C22×D61—41no—
108C22×D61C22⋊C811yescharacteristic
109C22×D61C22⋊C811yescharacteristic
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61C2×C22⋊C411yescharacteristic
115C2×C4×C61C22×C811yescharacteristic
116C22⋊D61—42no—
117C2×Dic61—21no—
118C2×Dic61—41no—
119C2×Dic61C22⋊C811yescharacteristic
120C2×Dic61C22⋊C811yescharacteristic
121D244—41no—
122D244—42no—
123D244—42no—
124C4×D61—21no—
125C4×D61—21no—
126C4×D61—21no—
127C4×D61—21no—
128C4×D61—41no—
129C4×D61—41no—
130C4×D61—41no—
131C4×D61—41no—
132Dic122—41no—
133C8×C61—21no—
134C8×C61—41no—
135C8×C61#9912yes—
136#92418—21no—
137#92418—21no—
138#92418—41no—
139#11470—611nomaximal, Sylow
140C22×C61—21no—
141C22×C61—21no—
142C22×C61—21no—
143C22×C61C2×C22⋊C811yescharacteristic
144C2×D61—21no—
145C2×D61—21no—
146C2×D61—21no—
147C2×D61—21no—
148C2×D61—21no—
149C2×D61—44no—
150C2×D61—41no—
151C2×D61—41no—
152C2×D61—41no—
153C2×D61#35012yes—
154C4×C61—21no—
155C4×C61—41no—
156C4×C61—41no—
157C4×C61C2×#9911yescharacteristic
158C4×C61#41311yescharacteristic
159Dic61—21no—
160Dic61—21no—
161Dic61—41no—
162#2929—611no—
163#2112—611no—
164C2×C22⋊C16—611no—
165#1323—612no—
166#1315—612no—
167C2×C61—41no—
168C2×C61#145911yescharacteristic
169C2×C61C2×#35011yescharacteristic
170C2×C61#211711yescharacteristic
171D61—22no—
172D61—41no—
173D61—81no—
174C2×#131—611no—
175C23×C8—611no—
176#525—611no—
177C2×M32—1221no—
178C22×C16—1221no—
179#435—1221no—
180#435—1221no—
181C8×D4—1221no—
182C8×D4—1221no—
183#424—611no—
184#408—611no—
185#407—611no—
186#405#692311yescharacteristic
187C22⋊C16—612no—
188C22⋊C16—612no—
189C22⋊C16—1221no—
190C22⋊C16—1221no—
191C61#1147011yescharacteristic, complemented, Sylow
192C2×#41—611no—
193C23×C4—611no—
194#131—2442no—
195C2×M16—611no—
196C2×M16—1221no—
197C2×M16C2×#692311yescharacteristic
198C22×C8—611no—
199C22×C8—611no—
200C22×C8—611no—
201C22×C8—611no—
202C22×C8—611no—
203C22×C8—1221no—
204C22×C8—2442no—
205C22×C8C2×#692311yescharacteristic
206#123—1221no—
207C22⋊Q8—611no—
208C22⋊Q8—611no—
209#121—611no—
210#121—611no—
211#120—1221no—
212C4×D4—1221no—
213C4×D4—1221no—
214#117C2×#692311yescharacteristic
215M32—2442no—
216C2×C16—1222no—
217C2×C16—1222no—
218C2×C16—2442no—
219C4⋊C8—1221no—
220C4⋊C8—1221no—
221C22⋊C8—1221no—
222C22⋊C8—1221no—
223C22⋊C8—1221no—
224C22⋊C8—1221no—
225#97—21no—
226C4×C8—21no—
227C24—611no—
228#41—2441no—
229#41—2441no—
230C2×Q8—611no—
231C2×D4—611no—
232C2×D4—1221no—
233C2×D4—1221no—
234C2×D4—1221no—
235C22×C4—611no—
236C22×C4—611no—
237C22×C4—611no—
238C22×C4—611no—
239C22×C4—611no—
240C22×C4—1221no—
241C22×C4—2441no—
242C22×C4—2441no—
243C22×C4C22×#692311yescharacteristic
244M16—41no—
245M16—2442no—
246M16—2441no—
247C2×C8—22no—
248C2×C8—21no—
249C2×C8—611no—
250C2×C8—611no—
251C2×C8—1222no—
252C2×C8—1222no—
253C2×C8—1221no—
254C2×C8—2441no—
255C2×C8—2441no—
256C2×C8—2442no—
257C2×C8—2441no—
258C2×C8C22⋊#692311yescharacteristic
259C2×C8C22⋊#692311yescharacteristic
260C4⋊C4—1221no—
261C4⋊C4—1221no—
262C4⋊C4D61⋊C811yescharacteristic
263C4⋊C4D61⋊C811yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—1221no—
266C22⋊C4—1221no—
267C22⋊C4—1221no—
268C22⋊C4—1221no—
269C42—21no—
270C16—2442no—
271C16—2442no—
272C23—611no—
273C23—611no—
274C23—1222no—
275C23—1221no—
276C23—2441no—
277C23—2441no—
278C23D61⋊M1611yescharacteristic
279Q8—2441no—
280D4—2441no—
281D4—2442no—
282D4—2442no—
283D4—2442no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—611no—
289C2×C4—611no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—2441no—
296C2×C4—2441no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4C2×C22⋊#692311yescharacteristic
301C2×C4C2×D61⋊C811yescharacteristic
302C8—21no—
303C8—41no—
304C8—1221no—
305C8—1221no—
306C8—2441no—
307C8#1451983612yes—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—612no—
312C22—1221no—
313C22—1221no—
314C22—1221no—
315C22—1221no—
316C22—1221no—
317C22—2444no—
318C22—2441no—
319C22—2441no—
320C22—2441no—
321C22D61⋊(C22⋊C8)11yescharacteristic
322C4—21no—
323C4—41no—
324C4—41no—
325C4—1221no—
326C4—1221no—
327C4—2441no—
328C4C2×#1451983611yescharacteristic
329C4#1684074811yescharacteristic
330C2—41no—
331C2—1222no—
332C2—4881no—
333C2—2441no—
334C2#2146105611yescharacteristic
335C2D61⋊#35011yescharacteristic
336C2#2146206211yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#405C4
socleC22×C61C2×C22⋊C8
prime radical#16840274C4
cosocleC22×#92418C23
hypercenter#405#6923
hypocenterC61#11470
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #405

Complements

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

NH ≅ G/Ntype
1. #21462047C2semidirect
2. D61⋊(C22⋊C16)C2semidirect
3. #21460757C2semidirect
4. #21460742C2semidirect
191. C61#11470semidirect

Maximal subgroups

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

subgroupindex
#214620472
D61⋊(C22⋊C16)2
#214607572
#214607422
#214545152
#1147061