Finite Group Databasebeta

← #30604863

Subgroups — #30604863

Order 15616.

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

normal subgroups only

This group has 486 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#21461564C211yesmaximal, characteristic, complemented
2#21461060C211yesmaximal, characteristic, complemented
3#21460815C212yesmaximal, complemented
4#21460797C212yesmaximal, complemented
5#21451711C211yesmaximal, characteristic
6#16840778—21no—
7C2×#14519836—21no—
8C4×C22⋊#6923—21no—
9#16840640C2212yes—
10#16840606—21no—
11#16840606C2212yes—
12C2×#14519748C411yescharacteristic, complemented
13C2×#14519739C2211yescharacteristic
14#16839701C411yescharacteristic, complemented
15#16839699C2211yescharacteristic
16#16839678—21no—
17#16839671—21no—
18#16839670C2211yescharacteristic
19#16839655—21no—
20#16839638—21no—
21#16839624C411yescharacteristic, complemented
22C61×#394C411yescharacteristic, complemented
23C2×C22⋊#6923—22no—
24C2×C4×#6923—41no—
25C4⋊#92420—41no—
26#14519836—24no—
27C22⋊#92420—22no—
28C4×#92420—41no—
29(C2×#6923)⋊C4—41no—
30C22×D244D411yescharacteristic
31C22×C22⋊D61—21no—
32C22×C22⋊D61—21no—
33C22×C4×D61C2×C411yescharacteristic
34C22×C4×D61D411yescharacteristic
35#14519748—41no—
36#14519748—41no—
37#14519739—41no—
38#14519739—41no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198D411yescharacteristic
46C2×#11758198C2311yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684C2×C411yescharacteristic
52C22×D4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C22⋊C4×C61—21no—
55C2×C22⋊C4×C61—21no—
56#95×C61C2×C411yescharacteristic
57C24×C61—21no—
58C23×D61C22⋊C411yescharacteristic
59C23×D61C2×D411yescharacteristic
60C22×#6923—42no—
61C2×D4×C61—41no—
62C2×D4×C61—81no—
63C22×C4×C61—21no—
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22×C411yescharacteristic
67C2×C22⋊D61—42no—
68C2×C22⋊D61—42no—
69C2×C22⋊D61—81no—
70C2×C22⋊D61—81no—
71C2×C22⋊D61—81no—
72C2×C22⋊D61—81no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C2×D411yescharacteristic
77C2×D244—22no—
78C2×D244—22no—
79C2×D244—41no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—81no—
85C2×C4×D61—81no—
86C22⋊#6923—24no—
87C22⋊#6923—42no—
88C2×#92420—42no—
89C4×#6923—82no—
90C4⋊C4×C61—41no—
91C22⋊C4×C61—42no—
92C22⋊C4×C61—81no—
93C22⋊Dic61—41no—
94C22⋊Dic61—41no—
95C22⋊Dic61—81no—
96#11758198—41no—
97#11758198—41no—
98#11758198—81no—
99#11758198—81no—
100C4⋊Dic61—41no—
101C4⋊Dic61—81no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C23×C61—41no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61C2×C22⋊C411yescharacteristic
112C22×D61—21no—
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61#13512yes—
122C2×#6923—44no—
123C2×#6923—82no—
124C2×#6923—82no—
125D4×C61—82no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61#10412yes—
136C22⋊D61—84no—
137C22⋊D61—84no—
138C2×Dic61—21no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61#9911yescharacteristic
148C2×Dic61#9911yescharacteristic
149D244—44no—
150C4×D61—42no—
151C4×D61—81no—
152C4×D61—81no—
153C4×D61—81no—
154#92420—82no—
155#11729—611nomaximal, Sylow
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—81no—
159C22×C61—81no—
160C22×C61—81no—
161C22×C61—81no—
162C22×C61—81no—
163C22×C61—81no—
164C22×C61—81no—
165C22×C61C2×#9911yescharacteristic
166C22×C61#41611yescharacteristic
167C22×C61C2×#10411yescharacteristic
168C2×D61—22no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—42no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—81no—
176C2×D61—81no—
177C2×D61—81no—
178#6923—84no—
179C4×C61—22no—
180C4×C61—41no—
181C4×C61—41no—
182C4×C61—81no—
183Dic61—21no—
184Dic61—21no—
185Dic61—41no—
186Dic61—81no—
187Dic61—81no—
188#2635—611no—
189C4×#99—611no—
190#1460—611no—
191#1352—612no—
192#1343—612no—
193C2×C61—21no—
194C2×C61—21no—
195C2×C61—161no—
196C2×C61#150111yescharacteristic
197C2×C61#212111yescharacteristic
198C2×C61#212811yescharacteristic
199D61—42no—
200D61—81no—
201C2×#121—611no—
202C2×C4×D4—611no—
203#431—1221no—
204C2×#99—1221no—
205#400—611no—
206#399—611no—
207#394—1221no—
208#394#692311yescharacteristic, complemented
209#392—611no—
210#392—1221no—
211#388—1221no—
212#386—1221no—
213#381—611no—
214C4×C22⋊C4—1221no—
215#342—612no—
216#323—612no—
217#323—1221no—
218C61#1172911yescharacteristic, complemented, Sylow
219C22×D4—611no—
220C22×D4—1221no—
221C22×D4—1221no—
222C22×D4C2×#692311yescharacteristic
223C23×C4—611no—
224C23×C4—611no—
225#121—2441no—
226#121—2441no—
227C4×D4—2441no—
228C4×D4—2441no—
229C2×C4⋊C4—611no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4C2×#692311yescharacteristic
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—611no—
235C2×C22⋊C4—611no—
236C2×C22⋊C4—1222no—
237C2×C22⋊C4—1221no—
238C2×C22⋊C4—1221no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C42—611no—
242C2×C42—2441no—
243C4⋊C8—2441no—
244#99—1224no—
245C22⋊C8—1222no—
246C4×C8—2441no—
247#95—611no—
248#95—1221no—
249#95—1221no—
250#95—1221no—
251#95—2441no—
252#95C2×#692311yescharacteristic
253C24—21no—
254C24—611no—
255C24—611no—
256C2×D4—41no—
257C2×D4—81no—
258C2×D4—1222no—
259C2×D4—1222no—
260C2×D4—4881no—
261C2×D4—4881no—
262C2×D4—4881no—
263C2×D4—4881no—
264C2×D4—2441no—
265C2×D4—2442no—
266C2×D4—2442no—
267C22×C4—21no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—4881no—
277C22×C4—4881no—
278C22×C4—2442no—
279C22×C4C22⋊#692311yescharacteristic
280C22×C4C22⋊#692311yescharacteristic
281C22×C4C22×#692311yescharacteristic
282C2×C8—2442no—
283C4⋊C4—41no—
284C4⋊C4—4881no—
285C4⋊C4—2441no—
286C22⋊C4—42no—
287C22⋊C4—81no—
288C22⋊C4—1224no—
289C22⋊C4—4881no—
290C22⋊C4—4881no—
291C22⋊C4—4881no—
292C22⋊C4—2441no—
293C22⋊C4—2441no—
294C22⋊C4—2441no—
295C22⋊C4—2441no—
296C22⋊C4—2442no—
297C42—1221no—
298C42—1221no—
299C42—4882no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—612no—
308C23—1221no—
309C23—1221no—
310C23—1221no—
311C23—1221no—
312C23—1221no—
313C23—2441no—
314C23—2441no—
315C23—2441no—
316C23—2441no—
317C23C2×C22⋊#692311yescharacteristic
318D4—82no—
319D4—4884no—
320D4—4884no—
321D4—2444no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—611no—
332C2×C4—611no—
333C2×C4—1221no—
334C2×C4—4881no—
335C2×C4—4881no—
336C2×C4—4881no—
337C2×C4—4882no—
338C2×C4—4882no—
339C2×C4—2442no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2444no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4#1451984112yes—
350C8—4882no—
351C22—21no—
352C22—21no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—1222no—
361C22—4881no—
362C22—4881no—
363C22—4881no—
364C22—2442no—
365C22—2441no—
366C22—2441no—
367C22—2441no—
368C22—2441no—
369C22—2441no—
370C22D61⋊#9911yescharacteristic
371C22#1684075211yescharacteristic
372C22C2×#1451984111yescharacteristic
373C4—22no—
374C4—41no—
375C4—41no—
376C4—81no—
377C4—1221no—
378C4—1221no—
379C4—4881no—
380C4—4884no—
381C4—4881no—
382C4—2441no—
383C2—21no—
384C2—21no—
385C2—161no—
386C2—4881no—
387C2—2442no—
388C2#2146119511yescharacteristic
389C2#2146207511yescharacteristic
390C2#2146209911yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#394C4
socleC22×C61C2×#99
prime radical#21451711C2
cosocleC2×#11758198C23
hypercenter#394#6923
hypocenterC61#11729
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #21461564C2semidirect
2. #21461060C2semidirect
3. #21460815C2semidirect
4. #21460797C2semidirect
12. C2×#14519748C4semidirect
14. #16839701C4semidirect
21. #16839624C4semidirect
22. C61×#394C4semidirect
208. #394#6923semidirect
218. C61#11729semidirect

Maximal subgroups

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

subgroupindex
#214615642
#214610602
#214608152
#214607972
#214517112
#1172961