Finite Group Databasebeta

← #30605485

Subgroups — #30605485

Order 15616.

568 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 76 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#21461684C211yesmaximal, characteristic
2#21461057C211yesmaximal, characteristic
3#21460820C212yesmaximal, complemented
4#21460819C212yesmaximal, complemented
5#21449177C211yesmaximal, characteristic
6#16840765—21no—
7C2×#14519837—21no—
8C2×C22⋊#92420—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840606—21no—
12C22×Q8×D61C411yescharacteristic
13C2×#14519754—21no—
14C2×#14519737C2211yescharacteristic
15#16839683C2211yescharacteristic
16#16839681C2211yescharacteristic
17#16839674C411yescharacteristic
18#16839666—21no—
19#16839638—21no—
20#16839636—21no—
21#16839621C411yescharacteristic
22C61×#393C411yescharacteristic
23C2×#11758217—22no—
24C22×#92420—41no—
25#14519844—41no—
26C4⋊#92420—41no—
27#14519837—42no—
28C22⋊#92420—22no—
29C22⋊#92420—41no—
30C22×Dic122—21no—
31C22×Dic122C2×C411yescharacteristic
32C2×Q8×D61—44no—
33C2×Q8×D61—41no—
34C2×Q8×D61—41no—
35C22×C22⋊D61D411yescharacteristic
36C23×Dic61D411yescharacteristic
37C22×C4×D61—21no—
38C22×C4×D61C2×C411yescharacteristic
39#14519754—44no—
40#14519737—41no—
41#14519737—41no—
42C2×C4⋊Dic61—21no—
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×#11758196C2311yescharacteristic
46C2×C22⋊Dic61—21no—
47C2×#11758198—21no—
48C2×#11758198D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684C2×C411yescharacteristic
54C22×Q8×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61C2×C411yescharacteristic
57#95×C61—21no—
58#95×C61C2×C411yescharacteristic
59C24×C61C22⋊C411yescharacteristic
60C23×D61C22⋊C411yescharacteristic
61C2×Q8×C61—42no—
62C2×Q8×C61—41no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22×C411yescharacteristic
67C2×C22⋊D61—41no—
68C2×C22⋊D61—41no—
69C2×C22⋊D61SD1612yes—
70C2×C22⋊D61Q1612yes—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—42no—
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C2×D411yescharacteristic
78C22×Dic61C2×D411yescharacteristic
79Q8×D61—44no—
80Q8×D61—44no—
81Q8×D61—44no—
82Q8×D61—44no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—42no—
86C2×C4×D61—42no—
87C2×C4×D61—42no—
88C2×C4×D61—42no—
89C2×Dic122—24no—
90C2×Dic122—42no—
91C2×Dic122—41no—
92C2×Dic122—41no—
93C2×Dic122—41no—
94C2×Dic122—42no—
95#11758217—42no—
96#11758217—42no—
97C2×#92420—42no—
98C2×#92420—42no—
99C2×#92420—82no—
100C22⋊C4×C61—41no—
101C22⋊C4×C61—42no—
102C22⋊Dic61—42no—
103#11758198—41no—
104#11758198—42no—
105C4⋊Dic61—42no—
106#11758196—41no—
107#11758196—42no—
108#11758196—42no—
109C4×Dic61—21no—
110C4×Dic61—21no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61#10312yes—
116C23×C61C2×C22⋊C411yescharacteristic
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61#10312yes—
122Q8×C61—42no—
123Q8×C61—42no—
124C2×C4×C61—22no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C22⋊D61—42no—
135C22⋊D61—42no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—22no—
139C2×Dic61—22no—
140C2×Dic61—21no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—42no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—81no—
149C2×Dic61#9911yescharacteristic
150C2×Dic61#9911yescharacteristic
151C2×Dic61C2×SD1611yescharacteristic
152C2×Dic61C2×Q1611yescharacteristic
153C4×D61—42no—
154C4×D61—48no—
155C4×D61—42no—
156Dic122—44no—
157Dic122—42no—
158Dic122—44no—
159Dic122—42no—
160#92420—82no—
161#92420—82no—
162#11904—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—22no—
166C22×C61—42no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—81no—
170C22×C61C2×#9911yescharacteristic
171C22×C61C2×#10311yescharacteristic
172C22×C61#42111yescharacteristic
173C2×D61—22no—
174C2×D61—42no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—42no—
178C4×C61—42no—
179C4×C61—41no—
180C4×C61—41no—
181C4×C61—81no—
182Dic61—21no—
183Dic61—21no—
184Dic61—21no—
185Dic61—41no—
186Dic61—42no—
187Dic61—81no—
188Dic61AΣL(1,𝔽16)12yes—
189#2409—611no—
190#1800—611no—
191#1459—611no—
192#1354—612no—
193#1354—612no—
194C2×C61—21no—
195C2×C61—21no—
196C2×C61—42no—
197C2×C61#152011yescharacteristic
198C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
199C2×C61#213511yescharacteristic
200D61—42no—
201C23×Q8—611no—
202C2×C22⋊Q8—1221no—
203C2×C4×D4—611no—
204#423—1221no—
205C2×#100—1221no—
206C2×C22⋊C8—1221no—
207#395—611no—
208#395—611no—
209#393—611no—
210#393#692311yescharacteristic
211#391—1221no—
212#386—1221no—
213#385—1221no—
214#380—611no—
215#343—612no—
216#324—612no—
217#323—1221no—
218C61#1190411yescharacteristic, complemented, Sylow
219C22×Q8—611no—
220C22×Q8—1221no—
221C22×Q8—2441no—
222C22×Q8—2441no—
223C22×Q8—2444no—
224C22×Q8C2×#692311yescharacteristic
225C22×D4—611no—
226C23×C4—611no—
227C23×C4—611no—
228C23×C4—1221no—
229C2×M16—1222no—
230C22×C8—2441no—
231C22⋊Q8—2444no—
232C4×D4—2441no—
233C4×D4—2441no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—1221no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—611no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C22⋊C4C2×#692311yescharacteristic
243C2×C42—611no—
244C4⋊C8—2441no—
245C4⋊C8—2441no—
246#100—2442no—
247C22⋊C8—1222no—
248C22⋊C8—2441no—
249#95—21no—
250#95—611no—
251#95—1221no—
252#95—1221no—
253#95—1221no—
254#95C2×#692311yescharacteristic
255C24—611no—
256C24C22⋊#692311yescharacteristic
257C2×Q8—42no—
258C2×Q8—41no—
259C2×Q8—1224no—
260C2×Q8—2441no—
261C2×Q8—2441no—
262C2×Q8—2441no—
263C2×Q8—2442no—
264C2×Q8—2442no—
265C2×Q8—2444no—
266C2×Q8—2444no—
267C2×Q8—2444no—
268C2×Q8—2444no—
269C2×D4—612no—
270C2×D4—612no—
271C2×D4—2441no—
272C2×D4—2441no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—2442no—
285C22×C4—2442no—
286C22×C4—2442no—
287C22×C4—2442no—
288C22×C4—2442no—
289C22×C4C22⋊#692311yescharacteristic
290C22×C4C22×#692311yescharacteristic
291M16—2442no—
292M16—2442no—
293C2×C8—4882no—
294C2×C8—2442no—
295C2×C8—2442no—
296C4⋊C4—2441no—
297C4⋊C4—2442no—
298C4⋊C4—2442no—
299C4⋊C4—2442no—
300C22⋊C4—41no—
301C22⋊C4—42no—
302C22⋊C4—2441no—
303C22⋊C4—2442no—
304C22⋊C4—2442no—
305C42—1221no—
306C42—1221no—
307C23—21no—
308C23—21no—
309C23—41no—
310C23—41no—
311C23—612no—
312C23—1221no—
313C23—1221no—
314C23—2441no—
315C23—2441no—
316C23#1451984012yes—
317C23C2×C22⋊#692311yescharacteristic
318Q8—42no—
319Q8—42no—
320Q8—2444no—
321Q8—2444no—
322Q8—2442no—
323Q8—2442no—
324D4—2442no—
325D4—2442no—
326C2×C4—22no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—611no—
337C2×C4—611no—
338C2×C4—611no—
339C2×C4—611no—
340C2×C4—1222no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1222no—
344C2×C4—1221no—
345C2×C4—4881no—
346C2×C4—2442no—
347C2×C4—2442no—
348C2×C4—2448no—
349C2×C4—2442no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C8—4882no—
357C8—4882no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—42no—
362C22—41no—
363C22—41no—
364C22—81no—
365C22—1222no—
366C22—2442no—
367C22—2442no—
368C22—2441no—
369C22—2441no—
370C22D61⋊#9911yescharacteristic
371C22C2×#1451984011yescharacteristic
372C22#1684075911yescharacteristic
373C4—42no—
374C4—41no—
375C4—41no—
376C4—81no—
377C4—612no—
378C4—1221no—
379C4—1221no—
380C4—1221no—
381C4—4881no—
382C4—2441no—
383C4—2442no—
384C2—21no—
385C2—21no—
386C2—42no—
387C2—2442no—
388C2#2146125711yescharacteristic
389C2D61⋊AΣL(1,𝔽16)11yescharacteristic
390C2#2146212211yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#393C4
socleC22×C61C2×#99
prime radicalC22×C22⋊D61D4
cosocleC2×#11758196C23
hypercenter#393#6923
hypocenterC61#11904
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #393

Complements

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

NH ≅ G/Ntype
3. #21460820C2semidirect
4. #21460819C2semidirect
218. C61#11904semidirect

Maximal subgroups

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

subgroupindex
#214616842
#214610572
#214608202
#214608192
#214491772
#1190461