Finite Group Databasebeta

← #30605168

Subgroups — #30605168

Order 15616.

586 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 68 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#21461719C211yesmaximal, characteristic
2#21461068C211yesmaximal, characteristic
3#21460820C212yesmaximal, complemented
4#21460819C212yesmaximal, complemented
5#395×D61C211yesmaximal, characteristic
6#16840734—21no—
7#16840733—21no—
8#16840642—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840607—21no—
12C22×Q8×D61C411yescharacteristic
13C2×C4⋊C4×D61—21no—
14C2×C4⋊C4×D61C2211yescharacteristic
15#16839683—21no—
16#16839683C2211yescharacteristic
17#16839682—21no—
18#16839682C411yescharacteristic
19#16839681C2211yescharacteristic
20#95×D61—21no—
21#95×D61C411yescharacteristic
22C61×#395C411yescharacteristic
23C2×#11758213—41no—
24C2×#11758217—22no—
25#14519834—41no—
26#14519834—41no—
27#14519834—41no—
28C22⋊#92420—22no—
29C22×Dic122—21no—
30C22×Dic122C2×C411yescharacteristic
31C2×Q8×D61—44no—
32C2×Q8×D61—41no—
33C2×Q8×D61—41no—
34C22×C4×D61—21no—
35C22×C4×D61—21no—
36C22×C4×D61C2×C411yescharacteristic
37C22×C4×D61D411yescharacteristic
38C22×C4×D61D411yescharacteristic
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61D411yescharacteristic
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196D411yescharacteristic
44C2×#11758196C2311yescharacteristic
45C4⋊C4×D61—41no—
46C4⋊C4×D61—41no—
47C4⋊C4×D61—44no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684C2×C411yescharacteristic
53C22×Q8×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61C2×C411yescharacteristic
56#95×C61—21no—
57#95×C61C2×C411yescharacteristic
58C23×D61C22⋊C411yescharacteristic
59C2×Q8×C61—42no—
60C2×Q8×C61—41no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22×C411yescharacteristic
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61C22⋊C411yescharacteristic
69C22×Dic61C2×D411yescharacteristic
70C22×Dic61C2×D411yescharacteristic
71Q8×D61—44no—
72Q8×D61—44no—
73Q8×D61—44no—
74Q8×D61—44no—
75C2×C4×D61—24no—
76C2×C4×D61—24no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—22no—
83C2×C4×D61—21no—
84C2×C4×D61—41no—
85C2×C4×D61—42no—
86C2×C4×D61—42no—
87C2×C4×D61—42no—
88C2×C4×D61—41no—
89C2×C4×D61—41no—
90C2×C4×D61—42no—
91C2×C4×D61—42no—
92C2×Dic122—42no—
93C2×Dic122—42no—
94C2×Dic122—42no—
95C2×Dic122—41no—
96C2×Dic122—42no—
97#11758217—42no—
98#11758217—42no—
99C2×#92420—42no—
100C2×#92420—42no—
101#11758213—82no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—42no—
104C4⋊Dic61—41no—
105C4⋊Dic61—42no—
106#11758196—41no—
107#11758196—41no—
108#11758196—42no—
109#11758196—42no—
110C23×C61C2×C22⋊C411yescharacteristic
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—22no—
114C22×D61—22no—
115C22×D61#9911yescharacteristic
116C22×D61#9911yescharacteristic
117Q8×C61—42no—
118Q8×C61—42no—
119C2×C4×C61—22no—
120C2×C4×C61—22no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—22no—
135C2×Dic61—22no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61#13712yes—
145C4×D61—42no—
146C4×D61—42no—
147C4×D61—48no—
148C4×D61—42no—
149C4×D61—44no—
150C4×D61—42no—
151C4×D61—44no—
152C4×D61—42no—
153C4×D61—81no—
154Dic122—48no—
155Dic122—42no—
156Dic122—42no—
157#92420—82no—
158#92420—82no—
159#11815—611nomaximal, Sylow
160C22×C61—21no—
161C22×C61—21no—
162C22×C61C2×#9911yescharacteristic
163C22×C61#41911yescharacteristic
164C22×C61#42111yescharacteristic
165C2×D61—24no—
166C2×D61—24no—
167C2×D61—21no—
168C2×D61—21no—
169C2×D61—21no—
170C2×D61—21no—
171C2×D61AΣL(1,𝔽16)12yes—
172C2×D61#35612yes—
173C4×C61—42no—
174C4×C61—42no—
175C4×C61—41no—
176C4×C61—41no—
177C4×C61—41no—
178Dic61—22no—
179Dic61—42no—
180Dic61—41no—
181Dic61—41no—
182Dic61—42no—
183C2×#395—611no—
184#1821—611no—
185#1463—611no—
186#1354—612no—
187#1354—612no—
188C2×C61—21no—
189C2×C61—21no—
190C2×C61#151111yescharacteristic
191C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
192C2×C61C2×#35611yescharacteristic
193D61—22no—
194D61—22no—
195C23×Q8—611no—
196C22×C4⋊C4—611no—
197C22×C4⋊C4—1221no—
198#407—1221no—
199#407—1221no—
200#395—611no—
201#395—611no—
202#395—611no—
203#395—1221no—
204#395—1221no—
205#395#692311yescharacteristic
206C2×#95—611no—
207C2×#95—1221no—
208#343—612no—
209#343—1221no—
210#324—612no—
211#324—1221no—
212C61#1181511yescharacteristic, complemented, Sylow
213C22×Q8—611no—
214C22×Q8—1221no—
215C22×Q8—2444no—
216C22×Q8—2441no—
217C22×Q8—2441no—
218C22×Q8C2×#692311yescharacteristic
219C23×C4—611no—
220C23×C4—611no—
221C23×C4—611no—
222C23×C4—1221no—
223C23×C4—1221no—
224C2×M16—1222no—
225C2×M16—2441no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—611no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4—2441no—
234C2×C4⋊C4—2441no—
235C2×C4⋊C4—2444no—
236C2×C4⋊C4C2×#692311yescharacteristic
237C22⋊C8—1222no—
238C22⋊C8—2441no—
239C22⋊C8—2441no—
240C22⋊C8—2441no—
241#95—21no—
242#95—611no—
243#95—1221no—
244#95—1221no—
245#95—1221no—
246#95—1221no—
247#95C2×#692311yescharacteristic
248C24—611no—
249C2×Q8—42no—
250C2×Q8—41no—
251C2×Q8—2442no—
252C2×Q8—2441no—
253C2×Q8—2442no—
254C2×Q8—2442no—
255C2×Q8—2442no—
256C2×Q8—2444no—
257C2×Q8—2444no—
258C2×Q8—2444no—
259C2×Q8—2444no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—611no—
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—1222no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—1224no—
273C22×C4—1224no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—2441no—
277C22×C4—2442no—
278C22×C4—2441no—
279C22×C4—2441no—
280C22×C4—2442no—
281C22×C4—2442no—
282C22×C4—2442no—
283C22×C4—2442no—
284C22×C4C22⋊#692311yescharacteristic
285C22×C4C22⋊#692311yescharacteristic
286C22×C4C22×#692311yescharacteristic
287M16—4882no—
288M16—2442no—
289M16—2442no—
290C2×C8—2442no—
291C2×C8—2442no—
292C4⋊C4—41no—
293C4⋊C4—42no—
294C4⋊C4—2441no—
295C4⋊C4—2441no—
296C4⋊C4—2441no—
297C4⋊C4—2442no—
298C4⋊C4—2442no—
299C4⋊C4—2442no—
300C23—611no—
301C23—611no—
302C23—1222no—
303C23—1222no—
304C23—1221no—
305C23—1221no—
306C23C2×C22⋊#692311yescharacteristic
307Q8—42no—
308Q8—42no—
309Q8—2442no—
310Q8—2448no—
311Q8—2442no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—612no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1222no—
329C2×C4—1222no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—4881no—
333C2×C4—2442no—
334C2×C4—2442no—
335C2×C4—2442no—
336C2×C4—2444no—
337C2×C4—2442no—
338C2×C4—2448no—
339C2×C4—2444no—
340C2×C4—2442no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C8—4882no—
348C8—4882no—
349C22—21no—
350C22—21no—
351C22—612no—
352C22—612no—
353C22—1224no—
354C22—1224no—
355C22—1221no—
356C22—1221no—
357C22—1221no—
358C22—1221no—
359C22D61⋊#9911yescharacteristic
360C22#1684075511yescharacteristic
361C22#1684075911yescharacteristic
362C4—42no—
363C4—42no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—1222no—
368C4—2442no—
369C4—2441no—
370C4—2442no—
371C4—2441no—
372C2—21no—
373C2—21no—
374C2—1222no—
375C2—1222no—
376C2#2146122811yescharacteristic
377C2D61⋊AΣL(1,𝔽16)11yescharacteristic
378C2D61⋊#35611yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#395C4
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×#11758196C23
hypercenter#395#6923
hypocenterC61#11815
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #395

Complements

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

NH ≅ G/Ntype
3. #21460820C2semidirect
4. #21460819C2semidirect
212. C61#11815semidirect

Maximal subgroups

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

subgroupindex
#214617192
#214610682
#214608202
#214608192
#395×D612
#1181561