Finite Group Databasebeta

← #30605399

Subgroups — #30605399

Order 15616.

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

normal subgroups only

This group has 472 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#21461681C211yesmaximal, characteristic
2#21461057C211yesmaximal, characteristic
3#21460800C212yesmaximal, complemented
4#21460799C212yesmaximal, complemented
5#21450810C211yesmaximal, characteristic
6C2×#14519835—21no—
7C2×C22⋊#92420—21no—
8#16840704—21no—
9#16840640C2212yes—
10#16840608—21no—
11#16840606C2212yes—
12C2×#14519776C411yescharacteristic, complemented
13C2×#14519763—21no—
14C2×#14519737C2211yescharacteristic
15#16839689C2211yescharacteristic
16#16839688C2211yescharacteristic
17#16839687C411yescharacteristic, complemented
18#16839666—21no—
19#16839621—21no—
20#16839620—21no—
21#16839613C411yescharacteristic, complemented
22C61×#397C411yescharacteristic, complemented
23C22×#92420—41no—
24C2×C4⋊#6923—41no—
25C2×C22⋊#6923—22no—
26#14519835—42no—
27C22⋊#92420—22no—
28C22⋊#92420—41no—
29(C2×#6923)⋊C4—41no—
30C22×Dic122—21no—
31C22×C22⋊D61D411yescharacteristic
32C23×Dic61D411yescharacteristic
33C22×C4×D61D411yescharacteristic
34#14519776—41no—
35#14519776—41no—
36#14519763—42no—
37#14519763—42no—
38#14519737—41no—
39#14519737—41no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196D411yescharacteristic
44C2×C22⋊Dic61—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198C2311yescharacteristic
48C2×C4×Dic61—21no—
49C2×C4×Dic61C2×C411yescharacteristic
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684C2×C411yescharacteristic
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61C2×C411yescharacteristic
57#95×C61—21no—
58#95×C61C2×C411yescharacteristic
59C24×C61C22⋊C411yescharacteristic
60C23×D61C2×D411yescharacteristic
61C22×#6923—42no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22×C411yescharacteristic
66C2×C22⋊D61—41no—
67C2×C22⋊D61—41no—
68C2×C22⋊D61D812yes—
69C2×C22⋊D61SD1612yes—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—42no—
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C2×D411yescharacteristic
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—42no—
81C2×Dic122—42no—
82C2×Dic122—42no—
83C2×Dic122—42no—
84C22⋊#6923—42no—
85C22⋊#6923—42no—
86C2×#92420—42no—
87C2×#92420—82no—
88C4⋊#6923—82no—
89C4⋊C4×C61—41no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—42no—
92C22⋊Dic61—42no—
93#11758198—41no—
94#11758198—41no—
95#11758198—41no—
96#11758198—41no—
97#11758198—41no—
98C4⋊Dic61—41no—
99#11758196—41no—
100#11758196—42no—
101#11758196—41no—
102#11758196—41no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61—42no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61#10212yes—
111C23×C61C2×C22⋊C411yescharacteristic
112C22×D61—21no—
113C22×D61—21no—
114C22×D61—41no—
115C22×D61—41no—
116C22×D61C2×D811yescharacteristic
117C22×D61C2×SD1611yescharacteristic
118C2×#6923—82no—
119C2×#6923—82no—
120C2×#6923—82no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C22⋊D61—42no—
132C22⋊D61—42no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—22no—
136C2×Dic61—21no—
137C2×Dic61—42no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—81no—
146C2×Dic61#9911yescharacteristic
147C2×Dic61#9911yescharacteristic
148C2×Dic61#10212yes—
149C4×D61—42no—
150C4×D61—81no—
151Dic122—84no—
152#92420—82no—
153#11878—611nomaximal, Sylow
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—22no—
157C22×C61—42no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—81no—
161C22×C61C2×#9911yescharacteristic
162C22×C61C2×#10211yescharacteristic
163C22×C61#42111yescharacteristic
164C2×D61—21no—
165C2×D61—21no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—81no—
171#6923—162no—
172C4×C61—41no—
173C4×C61—41no—
174C4×C61—81no—
175C4×C61—81no—
176Dic61—21no—
177Dic61—22no—
178Dic61—41no—
179Dic61—81no—
180Dic61—81no—
181Dic61#35412yes—
182#2547—611no—
183#1799—611no—
184#1459—611no—
185#1344—612no—
186#1344—612no—
187C2×C61—21no—
188C2×C61—21no—
189C2×C61—42no—
190C2×C61#151911yescharacteristic
191C2×C61#212311yescharacteristic
192C2×C61C2×#35411yescharacteristic
193D61—41no—
194D61—41no—
195C2×C4⋊Q8—611no—
196C2×#124—1221no—
197C2×C4×D4—611no—
198C2×#99—1221no—
199C2×C22⋊C8—1221no—
200#397—611no—
201#397—611no—
202#397—611no—
203#397#692311yescharacteristic, complemented
204#391—1221no—
205#380—1221no—
206#380—1221no—
207#380—1221no—
208C4×C4⋊C4—611no—
209#342—612no—
210#324—1221no—
211#323—612no—
212C61#1187811yescharacteristic, complemented, Sylow
213C22×Q8—1221no—
214C22×D4—611no—
215C23×C4—611no—
216C23×C4—611no—
217C22×C8—2441no—
218C4⋊Q8—2441no—
219C4⋊Q8—2441no—
220#124—2442no—
221#124—2442no—
222C4×D4—2441no—
223C4×D4—2441no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—2441no—
229C2×C4⋊C4C2×#692311yescharacteristic
230C2×C22⋊C4—21no—
231C2×C22⋊C4—611no—
232C2×C22⋊C4—1221no—
233C2×C22⋊C4—1221no—
234C2×C22⋊C4—1221no—
235C2×C22⋊C4—1222no—
236C2×C22⋊C4C2×#692311yescharacteristic
237C2×C42—611no—
238C2×C42—1221no—
239#99—2442no—
240C22⋊C8—1222no—
241C22⋊C8—2441no—
242#95—21no—
243#95—611no—
244#95—1221no—
245#95—1221no—
246#95—1221no—
247#95—2441no—
248#95C2×#692311yescharacteristic
249C24—611no—
250C24C22⋊#692311yescharacteristic
251C2×Q8—2442no—
252C2×Q8—2442no—
253C2×Q8—2442no—
254C2×D4—612no—
255C2×D4—612no—
256C2×D4—2441no—
257C2×D4—2441no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4—2442no—
270C22×C4—2442no—
271C22×C4—2442no—
272C22×C4C22⋊#692311yescharacteristic
273C22×C4C22×#692311yescharacteristic
274C2×C8—4882no—
275C2×C8—2442no—
276C4⋊C4—41no—
277C4⋊C4—4882no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C4⋊C4—2442no—
283C22⋊C4—41no—
284C22⋊C4—42no—
285C22⋊C4—2441no—
286C22⋊C4—2441no—
287C22⋊C4—2441no—
288C22⋊C4—2441no—
289C22⋊C4—2441no—
290C22⋊C4—2442no—
291C22⋊C4—2442no—
292C22⋊C4—2442no—
293C42—1221no—
294C42—1221no—
295C42—2442no—
296C23—21no—
297C23—21no—
298C23—41no—
299C23—41no—
300C23—611no—
301C23—611no—
302C23—1221no—
303C23—1221no—
304C23—2441no—
305C23—2441no—
306C23#1451983912yes—
307C23C2×C22⋊#692311yescharacteristic
308Q8—4884no—
309D4—2442no—
310D4—2442no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—611no—
322C2×C4—611no—
323C2×C4—612no—
324C2×C4—1222no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—4881no—
329C2×C4—4881no—
330C2×C4—4882no—
331C2×C4—4882no—
332C2×C4—4882no—
333C2×C4—2442no—
334C2×C4—2442no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C8—4882no—
343C22—21no—
344C22—21no—
345C22—22no—
346C22—42no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22—1221no—
351C22—1221no—
352C22—4881no—
353C22—2441no—
354C22—2441no—
355C22—2441no—
356C22—2441no—
357C22D61⋊#9911yescharacteristic
358C22C2×#1451983911yescharacteristic
359C22#1684075911yescharacteristic
360C4—41no—
361C4—41no—
362C4—81no—
363C4—81no—
364C4—612no—
365C4—1222no—
366C4—1221no—
367C4—9762no—
368C4—4881no—
369C4—4881no—
370C4—2441no—
371C2—21no—
372C2—21no—
373C2—42no—
374C2—2441no—
375C2—2441no—
376C2#2146125411yescharacteristic
377C2#2146208211yescharacteristic
378C2D61⋊#35411yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#397C4
socleC22×C61C2×#99
prime radicalC22×C22⋊D61D4
cosocleC2×#11758198C23
hypercenter#397#6923
hypocenterC61#11878
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #397

Complements

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

NH ≅ G/Ntype
3. #21460800C2semidirect
4. #21460799C2semidirect
12. C2×#14519776C4semidirect
17. #16839687C4semidirect
21. #16839613C4semidirect
22. C61×#397C4semidirect
203. #397#6923semidirect
212. C61#11878semidirect

Maximal subgroups

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

subgroupindex
#214616812
#214610572
#214608002
#214607992
#214508102
#1187861