Finite Group Databasebeta

← #30607237

Subgroups — #30607237

Order 15616.

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

normal subgroups only

This group has 656 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#21461656C211yesmaximal, characteristic
2#21461649C211yesmaximal, characteristic
3#21460904C212yesmaximal, complemented
4#21460903C212yesmaximal, complemented
5#21448304C211yesmaximal, characteristic
6C2×#14519838—21no—
7C2×#14519837C2212yes—
8C2×#14519835—21no—
9C2×#14519835C2212yes—
10#16840732—21no—
11#16840705—21no—
12C22×#11758224C2211yescharacteristic
13C2×#14519733C411yescharacteristic, complemented
14C22×C4×Dic61C411yescharacteristic, complemented
15#16839666—21no—
16#16839662—21no—
17#16839642C411yescharacteristic, complemented
18#16839641C2211yescharacteristic
19#16839639C2211yescharacteristic
20C22⋊C4×Dic61—21no—
21#16839609—21no—
22C61×#386C411yescharacteristic, complemented
23C2×#11758217—22no—
24C2×C22⋊#6923—22no—
25#14519838—42no—
26#14519837—24no—
27#14519835—24no—
28#14519835—42no—
29C22⋊#92420—42no—
30(C2×#6923)⋊C4—42no—
31C2×#11758224—24no—
32C2×#11758224—42no—
33C2×#11758224—42no—
34C22×Dic122D411yescharacteristic
35C22×C22⋊D61D411yescharacteristic
36C22×C22⋊D61C2311yescharacteristic
37C23×Dic61C2×C411yescharacteristic
38C23×Dic61C2×C411yescharacteristic
39C23×Dic61D411yescharacteristic
40C22×C4×D61D411yescharacteristic
41#14519733—42no—
42C2×#11758196—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61C2×C411yescharacteristic
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×C4×Dic61—21no—
48C2×C4×Dic61—21no—
49C2×C4×Dic61—21no—
50C2×C4×Dic61—42no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54C22×D4×C61C2×C411yescharacteristic
55C23×C4×C61C2×C411yescharacteristic
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61C2×C411yescharacteristic
58#95×C61—21no—
59C24×C61C22⋊C411yescharacteristic
60C24×C61C22×C411yescharacteristic
61C23×D61C2×D411yescharacteristic
62C22×#6923—42no—
63C2×D4×C61—22no—
64C2×D4×C61—41no—
65C2×D4×C61—41no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—42no—
69C22×C4×C61—41no—
70C22×C4×C61C22⋊C411yescharacteristic
71C2×C22⋊D61—22no—
72C2×C22⋊D61—22no—
73C2×C22⋊D61—41no—
74C2×C22⋊D61—41no—
75C2×C22⋊D61—41no—
76C2×C22⋊D61#4114yes—
77C22×Dic61—22no—
78C22×Dic61—22no—
79C22×Dic61—22no—
80C22×Dic61—21no—
81C22×Dic61—22no—
82C22×Dic61—22no—
83C22×Dic61—21no—
84C22×Dic61—41no—
85C22×Dic61—42no—
86C22×Dic61—41no—
87C22×Dic61C22⋊C411yescharacteristic
88C22×Dic61C22⋊C411yescharacteristic
89C22×Dic61C2×D411yescharacteristic
90#11758224—416no—
91C2×C4×D61—22no—
92C2×C4×D61—22no—
93C2×C4×D61—41no—
94C2×Dic122—22no—
95C2×Dic122—22no—
96C2×Dic122—41no—
97C22⋊#6923—42no—
98C22⋊#6923—42no—
99#11758217—42no—
100#11758217—42no—
101C2×#92420—42no—
102C22⋊C4×C61—42no—
103C22⋊C4×C61—41no—
104C22⋊Dic61—42no—
105C22⋊Dic61—41no—
106#11758198—42no—
107#11758198—42no—
108#11758196—42no—
109C4×Dic61—42no—
110C4×Dic61—42no—
111C4×Dic61—42no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61C2×C22⋊C411yescharacteristic
122C23×C61#11712yes—
123C22×D61—21no—
124C22×D61—21no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61#12312yes—
128C2×#6923—82no—
129C2×#6923—82no—
130C2×#6923—82no—
131D4×C61—44no—
132C2×C4×C61—22no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—41no—
137C2×C4×C61—42no—
138C2×C4×C61—41no—
139C2×C4×C61—42no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C22⋊D61—44no—
144C22⋊D61—44no—
145C2×Dic61—28no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—22no—
153C2×Dic61—44no—
154C2×Dic61—41no—
155C2×Dic61—42no—
156C2×Dic61—41no—
157C2×Dic61—42no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61#9912yes—
162C2×Dic61#9912yes—
163C2×Dic61#12312yes—
164C4×D61—44no—
165Dic122—44no—
166#92420—82no—
167#12853—611nomaximal, Sylow
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—22no—
171C22×C61—42no—
172C22×C61—42no—
173C22×C61—42no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61—81no—
180C22×C61#38111yescharacteristic
181C22×C61C2×#9911yescharacteristic
182C22×C61C2×#9911yescharacteristic
183C2×D61—22no—
184C2×D61—41no—
185C2×D61—41no—
186C2×D61—42no—
187C2×D61—81no—
188#6923—162no—
189C4×C61—41no—
190C4×C61—42no—
191C4×C61—81no—
192Dic61—22no—
193Dic61—22no—
194Dic61—22no—
195Dic61—42no—
196Dic61—81no—
197#2297—611no—
198#1785—611no—
199#1782—611no—
200#1390—612no—
201#1390—612no—
202C2×C61—21no—
203C2×C61—21no—
204C2×C61—42no—
205C2×C61—81no—
206C2×C61#181911yescharacteristic
207C2×C61#212011yescharacteristic
208C2×C61#212011yescharacteristic
209D61—42no—
210C22×#41—611no—
211C2×#117—611no—
212C22×C42—611no—
213C2×#101—1221no—
214C2×#100—612no—
215C2×#99—612no—
216C2×#99—1221no—
217#407—1221no—
218#391—1221no—
219#390—1221no—
220#386—611no—
221#386—611no—
222#386—611no—
223#386#692311yescharacteristic, complemented
224#381—1221no—
225C4×C22⋊C4—1221no—
226C4×C22⋊C4—1221no—
227C61#1285311yescharacteristic, complemented, Sylow
228C2×#41—1224no—
229C2×#41—2442no—
230C2×#41—2442no—
231C22×Q8—611no—
232C22×D4—611no—
233C22×D4—611no—
234C22×D4C2×#692311yescharacteristic
235C23×C4—611no—
236C23×C4—611no—
237C23×C4—611no—
238C23×C4—611no—
239C23×C4C2×#692311yescharacteristic
240C2×M16—1222no—
241#117—2442no—
242C2×C4⋊C4—1221no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—611no—
245C2×C22⋊C4—1221no—
246C2×C22⋊C4—1221no—
247C2×C22⋊C4—1221no—
248C2×C22⋊C4—1222no—
249C2×C22⋊C4C2×#692311yescharacteristic
250C2×C42—1221no—
251C2×C42—1221no—
252C2×C42—1221no—
253C2×C42—2442no—
254#101—2442no—
255#100—1224no—
256#99—1224no—
257#99—2442no—
258C22⋊C8—2442no—
259#95—21no—
260#95—1221no—
261#95—1221no—
262#95—1221no—
263#95—2442no—
264C24—611no—
265C24C22⋊#692311yescharacteristic
266C24C22×#692311yescharacteristic
267#41—24416no—
268C2×Q8—1222no—
269C2×Q8—1222no—
270C2×Q8—2441no—
271C2×D4—22no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—614no—
275C2×D4—1222no—
276C2×D4—1222no—
277C2×D4—2441no—
278C2×D4—2441no—
279C2×D4—2441no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—42no—
283C22×C4—41no—
284C22×C4—611no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—1222no—
288C22×C4—1222no—
289C22×C4—1222no—
290C22×C4—1222no—
291C22×C4—1222no—
292C22×C4—1222no—
293C22×C4—1222no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—2441no—
297C22×C4—2441no—
298C22×C4—2442no—
299C22×C4—2442no—
300C22×C4—2441no—
301C22×C4C22⋊#692311yescharacteristic
302M16—2442no—
303M16—2442no—
304C2×C8—2442no—
305C4⋊C4—2442no—
306C22⋊C4—42no—
307C22⋊C4—41no—
308C22⋊C4—2442no—
309C22⋊C4—2442no—
310C22⋊C4—2442no—
311C22⋊C4—2442no—
312C22⋊C4—2442no—
313C22⋊C4—2441no—
314C42—2442no—
315C42—2442no—
316C42—2442no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—612no—
327C23—1221no—
328C23—1221no—
329C23—2441no—
330C23—2441no—
331C23C2×C22⋊#692311yescharacteristic
332C23#1451985612yes—
333Q8—2444no—
334D4—44no—
335D4—2444no—
336D4—2444no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—612no—
349C2×C4—612no—
350C2×C4—612no—
351C2×C4—1228no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—1222no—
359C2×C4—4882no—
360C2×C4—4882no—
361C2×C4—4882no—
362C2×C4—2444no—
363C2×C4—2444no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2442no—
369C2×C4—2441no—
370C2×C4—2442no—
371C8—4882no—
372C22—21no—
373C22—21no—
374C22—22no—
375C22—42no—
376C22—42no—
377C22—42no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—81no—
384C22—1222no—
385C22—4881no—
386C22—2442no—
387C22—2441no—
388C22—2441no—
389C22#1684070511yescharacteristic
390C22D61⋊#9911yescharacteristic
391C22D61⋊#9911yescharacteristic
392C4—42no—
393C4—41no—
394C4—81no—
395C4—1222no—
396C4—1222no—
397C4—1222no—
398C4—9762no—
399C4—4881no—
400C4—2442no—
401C2—21no—
402C2—21no—
403C2—42no—
404C2—81no—
405C2—2442no—
406C2#2146171511yescharacteristic
407C2#2146207111yescharacteristic
408C2#2146207311yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC61×#386C4
socleC22×C61C2×#99
prime radicalC22×#11758224C22
cosocleC22×C22⋊D61C23
hypercenter#386#6923
hypocenterC61#12853
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #386

Complements

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

NH ≅ G/Ntype
3. #21460904C2semidirect
4. #21460903C2semidirect
13. C2×#14519733C4semidirect
14. C22×C4×Dic61C4semidirect
17. #16839642C4semidirect
22. C61×#386C4semidirect
223. #386#6923semidirect
227. C61#12853semidirect

Maximal subgroups

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

subgroupindex
#214616562
#214616492
#214609042
#214609032
#214483042
#1285361