Finite Group Databasebeta

← #30605385

Subgroups — #30605385

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#21461682C211yesmaximal, characteristic
2#21461060C211yesmaximal, characteristic
3#21460800C212yesmaximal, complemented
4#21460799C212yesmaximal, complemented
5#21450122C211yesmaximal, characteristic
6#16840778—21no—
7C2×#14519836—21no—
8#16840704—21no—
9#16840640C2212yes—
10#16840606—21no—
11#16840606C2212yes—
12C2×#14519762—21no—
13C2×#14519739C2211yescharacteristic
14C2×C4⋊C4×D61C411yescharacteristic, complemented
15#16839692C411yescharacteristic, complemented
16#16839689C2211yescharacteristic
17#16839688C2211yescharacteristic
18#16839657—21no—
19#16839624—21no—
20#16839621—21no—
21#16839621C411yescharacteristic, complemented
22C61×#398C411yescharacteristic, complemented
23C2×C4⋊#6923—41no—
24C2×C22⋊#6923—22no—
25C4⋊#92420—41no—
26#14519836—42no—
27C22⋊#92420—22no—
28C4×#92420—41no—
29(C2×#6923)⋊C4—41no—
30C22×D244D411yescharacteristic
31C22×C4×D61—21no—
32C22×C4×D61C2×C411yescharacteristic
33C22×C4×D61D411yescharacteristic
34#14519762—42no—
35#14519762—42no—
36#14519739—41no—
37#14519739—41no—
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C4⋊C4×D61—41no—
43C4⋊C4×D61—41no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198D411yescharacteristic
48C2×#11758198C2311yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684C2×C411yescharacteristic
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C4⋊C4×C61C2×C411yescharacteristic
57#95×C61—21no—
58#95×C61C2×C411yescharacteristic
59C23×D61C22⋊C411yescharacteristic
60C23×D61C2×D411yescharacteristic
61C22×#6923—42no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22×C411yescharacteristic
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C2×D411yescharacteristic
71C2×D244—41no—
72C2×D244—41no—
73C2×D244D812yes—
74C2×D244SD1612yes—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—42no—
80C2×C4×D61—42no—
81C2×C4×D61—42no—
82C2×C4×D61—42no—
83C2×C4×D61—42no—
84C22⋊#6923—42no—
85C22⋊#6923—42no—
86C2×#92420—42no—
87C4⋊#6923—82no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—42no—
91#11758198—41no—
92#11758198—41no—
93#11758198—42no—
94#11758198—41no—
95#11758198—41no—
96#11758198—41no—
97#11758198—41no—
98C4⋊Dic61—41no—
99#11758196—42no—
100#11758196—42no—
101#11758196—41no—
102#11758196—41no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C23×C61C2×C22⋊C411yescharacteristic
106C22×D61—21no—
107C22×D61—21no—
108C22×D61—21no—
109C22×D61—21no—
110C22×D61—41no—
111C22×D61—41no—
112C22×D61—41no—
113C22×D61—41no—
114C22×D61#10212yes—
115C22×D61C2×D811yescharacteristic
116C22×D61C2×SD1611yescharacteristic
117C2×#6923—82no—
118C2×#6923—82no—
119C2×#6923—82no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
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—
131C2×C4×C61—41no—
132C2×C4×C61#10212yes—
133C2×Dic61—22no—
134C2×Dic61—21no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61#9911yescharacteristic
143C2×Dic61#9911yescharacteristic
144D244—42no—
145D244—42no—
146C4×D61—42no—
147C4×D61—42no—
148C4×D61—42no—
149C4×D61—81no—
150C4×D61—84no—
151#92420—82no—
152#11874—611nomaximal, Sylow
153C22×C61—21no—
154C22×C61—21no—
155C22×C61C2×#9911yescharacteristic
156C22×C61C2×#10211yescharacteristic
157C22×C61#42111yescharacteristic
158C2×D61—22no—
159C2×D61—21no—
160C2×D61—21no—
161C2×D61—42no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—42no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—81no—
170#6923—162no—
171C4×C61—22no—
172C4×C61—41no—
173C4×C61—41no—
174C4×C61—81no—
175C4×C61—81no—
176Dic61—21no—
177Dic61—41no—
178Dic61—81no—
179Dic61—81no—
180Dic61#35212yes—
181#2486—611no—
182#1799—611no—
183#1460—611no—
184#1344—612no—
185#1344—612no—
186C2×C61—21no—
187C2×C61—21no—
188C2×C61#151911yescharacteristic
189C2×C61C2×#35211yescharacteristic
190C2×C61#212911yescharacteristic
191D61—41no—
192D61—42no—
193D61—41no—
194C2×#123—1221no—
195C2×C4×D4—611no—
196C22×C4⋊C4—611no—
197#431—1221no—
198C2×#99—1221no—
199#398—611no—
200#398#692311yescharacteristic, complemented
201#397—611no—
202#397—611no—
203#389—1221no—
204#381—1221no—
205#380—611no—
206#380—1221no—
207#380—1221no—
208#342—612no—
209#323—612no—
210#323—1221no—
211C61#1187411yescharacteristic, complemented, Sylow
212C22×D4—611no—
213C23×C4—611no—
214C23×C4—611no—
215C23×C4—1221no—
216#123—2442no—
217#123—2442no—
218C4×D4—2441no—
219C4×D4—2441no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4—2441no—
226C2×C4⋊C4—2441no—
227C2×C4⋊C4—2441no—
228C2×C4⋊C4C2×#692311yescharacteristic
229C2×C4⋊C4C2×#692311yescharacteristic
230C2×C22⋊C4—611no—
231C2×C22⋊C4—611no—
232C2×C22⋊C4—1221no—
233C2×C22⋊C4—1221no—
234C2×C22⋊C4—1221no—
235C2×C22⋊C4—1222no—
236C2×C42—611no—
237C4⋊C8—2441no—
238#99—2442no—
239C22⋊C8—1222no—
240C4×C8—2441no—
241#95—21no—
242#95—611no—
243#95—1221no—
244#95—1221no—
245#95—1221no—
246#95—2441no—
247#95C2×#692311yescharacteristic
248C24—611no—
249C24—611no—
250C2×D4—612no—
251C2×D4—612no—
252C2×D4—2441no—
253C2×D4—2441no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—611no—
257C22×C4—611no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—2442no—
265C22×C4—2442no—
266C22×C4—2442no—
267C22×C4—2442no—
268C22×C4—2442no—
269C22×C4—2442no—
270C22×C4C22⋊#692311yescharacteristic
271C22×C4C22⋊#692311yescharacteristic
272C22×C4C22×#692311yescharacteristic
273C2×C8—2442no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—42no—
277C4⋊C4—4882no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C4⋊C4—2442no—
282C4⋊C4—2442no—
283C22⋊C4—2441no—
284C22⋊C4—2441no—
285C22⋊C4—2442no—
286C22⋊C4—2441no—
287C22⋊C4—2441no—
288C22⋊C4—2441no—
289C22⋊C4—2441no—
290C22⋊C4—2442no—
291C22⋊C4—2442no—
292C42—1221no—
293C42—1221no—
294C23—612no—
295C23—611no—
296C23—611no—
297C23—1221no—
298C23—1221no—
299C23—1221no—
300C23—1221no—
301C23—2441no—
302C23—2441no—
303C23—2441no—
304C23—2441no—
305C23C2×C22⋊#692311yescharacteristic
306D4—2442no—
307D4—2442no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—611no—
321C2×C4—611no—
322C2×C4—1222no—
323C2×C4—1221no—
324C2×C4—4881no—
325C2×C4—4884no—
326C2×C4—4882no—
327C2×C4—4882no—
328C2×C4—4882no—
329C2×C4—2442no—
330C2×C4—2442no—
331C2×C4—2442no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4#1451983912yes—
340C8—4882no—
341C22—21no—
342C22—21no—
343C22—1221no—
344C22—1222no—
345C22—1221no—
346C22—4881no—
347C22—2441no—
348C22—2441no—
349C22—2442no—
350C22—2442no—
351C22—2441no—
352C22—2441no—
353C22—2441no—
354C22—2441no—
355C22D61⋊#9911yescharacteristic
356C22C2×#1451983911yescharacteristic
357C22#1684075911yescharacteristic
358C4—22no—
359C4—41no—
360C4—41no—
361C4—81no—
362C4—81no—
363C4—612no—
364C4—1221no—
365C4—9762no—
366C4—4881no—
367C4—4881no—
368C4—2441no—
369C2—21no—
370C2—21no—
371C2—2441no—
372C2—2441no—
373C2—2442no—
374C2#2146125411yescharacteristic
375C2D61⋊#35211yescharacteristic
376C2#2146210211yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#398C4
socleC22×C61C2×#99
prime radicalC22×D244D4
cosocleC2×#11758198C23
hypercenter#398#6923
hypocenterC61#11874
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #398

Complements

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

NH ≅ G/Ntype
3. #21460800C2semidirect
4. #21460799C2semidirect
14. C2×C4⋊C4×D61C4semidirect
15. #16839692C4semidirect
21. #16839621C4semidirect
22. C61×#398C4semidirect
200. #398#6923semidirect
211. C61#11874semidirect

Maximal subgroups

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

subgroupindex
#214616822
#214610602
#214608002
#214607992
#214501222
#1187461