Finite Group Databasebeta

← #30607243

Subgroups — #30607243

Order 15616.

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

normal subgroups only

This group has 628 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#21448406C211yesmaximal, characteristic
6C2×#14519838—21no—
7C2×#14519837C2212yes—
8C2×#14519835—21no—
9C2×#14519835C2212yes—
10#16840732—21no—
11#16840705—21no—
12C22×#11758224C2211yescharacteristic
13C2×#14519733C411yescharacteristic, complemented
14C22×#11758196C411yescharacteristic, complemented
15#16839666—21no—
16#16839662—21no—
17#16839642C411yescharacteristic, complemented
18#16839641C2211yescharacteristic
19#16839639C2211yescharacteristic
20#16839621—21no—
21#16839620—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×#11758196—21no—
44C2×#11758196—21no—
45C2×#11758196—42no—
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61C2×C411yescharacteristic
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×C4×Dic61—21no—
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—41no—
69C22×C4×C61—81no—
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—22no—
81C22×Dic61—22no—
82C22×Dic61—21no—
83C22×Dic61—21no—
84C22×Dic61—41no—
85C22×Dic61—41no—
86C22×Dic61—81no—
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—41no—
103C22⋊C4×C61—81no—
104C22⋊Dic61—41no—
105C22⋊Dic61—81no—
106#11758198—81no—
107#11758198—81no—
108#11758196—42no—
109#11758196—42no—
110#11758196—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—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—82no—
142C22⋊D61—44no—
143C22⋊D61—44no—
144C2×Dic61—28no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—44no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—82no—
159C2×Dic61#9912yes—
160C2×Dic61#9912yes—
161C2×Dic61#12312yes—
162C4×D61—44no—
163Dic122—44no—
164#92420—82no—
165#12855—611nomaximal, Sylow
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—22no—
169C22×C61—42no—
170C22×C61—42no—
171C22×C61—42no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—81no—
178C22×C61#38111yescharacteristic
179C22×C61C2×#9911yescharacteristic
180C22×C61C2×#9911yescharacteristic
181C2×D61—22no—
182C2×D61—41no—
183C2×D61—41no—
184C2×D61—42no—
185C2×D61—81no—
186#6923—162no—
187C4×C61—41no—
188C4×C61—81no—
189C4×C61—81no—
190Dic61—22no—
191Dic61—22no—
192Dic61—22no—
193Dic61—81no—
194Dic61—81no—
195#2311—611no—
196#1785—611no—
197#1782—611no—
198#1390—612no—
199#1390—612no—
200C2×C61—21no—
201C2×C61—21no—
202C2×C61—42no—
203C2×C61—81no—
204C2×C61#181911yescharacteristic
205C2×C61#212211yescharacteristic
206C2×C61#212311yescharacteristic
207D61—42no—
208C22×#41—611no—
209C2×#117—611no—
210C22×C4⋊C4—611no—
211C2×#101—1221no—
212C2×#100—612no—
213C2×#99—612no—
214C2×#99—1221no—
215#407—1221no—
216#391—1221no—
217#390—1221no—
218#386—611no—
219#386—611no—
220#386—611no—
221#386#692311yescharacteristic, complemented
222#381—1221no—
223#380—1221no—
224#380—1221no—
225C61#1285511yescharacteristic, complemented, Sylow
226C2×#41—1224no—
227C2×#41—2442no—
228C2×#41—2442no—
229C22×Q8—611no—
230C22×D4—611no—
231C22×D4—611no—
232C22×D4C2×#692311yescharacteristic
233C23×C4—611no—
234C23×C4—611no—
235C23×C4—611no—
236C23×C4—611no—
237C23×C4C2×#692311yescharacteristic
238C2×M16—1222no—
239#117—2442no—
240C2×C4⋊C4—1221no—
241C2×C4⋊C4—1221no—
242C2×C4⋊C4—1221no—
243C2×C4⋊C4—2442no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—611no—
246C2×C22⋊C4—1221no—
247C2×C22⋊C4—1221no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1222no—
250C2×C22⋊C4C2×#692311yescharacteristic
251C2×C42—1221no—
252#101—2442no—
253#100—1224no—
254#99—1224no—
255#99—2442no—
256C22⋊C8—2442no—
257#95—21no—
258#95—1221no—
259#95—1221no—
260#95—1221no—
261#95—2442no—
262C24—611no—
263C24C22⋊#692311yescharacteristic
264C24C22×#692311yescharacteristic
265#41—24416no—
266C2×Q8—1222no—
267C2×Q8—1222no—
268C2×Q8—2441no—
269C2×D4—22no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—614no—
273C2×D4—1222no—
274C2×D4—1222no—
275C2×D4—2441no—
276C2×D4—2441no—
277C2×D4—2441no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—41no—
281C22×C4—81no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—1222no—
286C22×C4—1222no—
287C22×C4—1222no—
288C22×C4—1222no—
289C22×C4—1222no—
290C22×C4—1222no—
291C22×C4—1222no—
292C22×C4—1221no—
293C22×C4—1221no—
294C22×C4—4881no—
295C22×C4—2441no—
296C22×C4—2441no—
297C22×C4—2442no—
298C22×C4—2441no—
299C22×C4C22⋊#692311yescharacteristic
300M16—2442no—
301M16—2442no—
302C2×C8—2442no—
303C4⋊C4—2442no—
304C4⋊C4—2442no—
305C4⋊C4—2442no—
306C22⋊C4—41no—
307C22⋊C4—81no—
308C22⋊C4—4881no—
309C22⋊C4—4881no—
310C22⋊C4—4881no—
311C22⋊C4—2442no—
312C22⋊C4—2442no—
313C22⋊C4—2441no—
314C42—2442no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—612no—
325C23—1221no—
326C23—1221no—
327C23—2441no—
328C23—2441no—
329C23C2×C22⋊#692311yescharacteristic
330C23#1451985612yes—
331Q8—2444no—
332D4—44no—
333D4—2444no—
334D4—2444no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—82no—
345C2×C4—612no—
346C2×C4—612no—
347C2×C4—612no—
348C2×C4—1228no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—4882no—
356C2×C4—4882no—
357C2×C4—4882no—
358C2×C4—4882no—
359C2×C4—2444no—
360C2×C4—2444no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C8—4882no—
368C22—21no—
369C22—21no—
370C22—22no—
371C22—42no—
372C22—42no—
373C22—42no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—81no—
380C22—1222no—
381C22—4881no—
382C22—2442no—
383C22—2441no—
384C22—2441no—
385C22#1684070511yescharacteristic
386C22D61⋊#9911yescharacteristic
387C22D61⋊#9911yescharacteristic
388C4—41no—
389C4—81no—
390C4—81no—
391C4—1222no—
392C4—1222no—
393C4—1222no—
394C4—9762no—
395C4—4881no—
396C4—4881no—
397C2—21no—
398C2—21no—
399C2—42no—
400C2—81no—
401C2—2442no—
402C2#2146171511yescharacteristic
403C2#2146207911yescharacteristic
404C2#2146208211yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC61×#386C4
socleC22×C61C2×#99
prime radicalC22×#11758224C22
cosocleC22×C22⋊D61C23
hypercenter#386#6923
hypocenterC61#12855
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×#11758196C4semidirect
17. #16839642C4semidirect
22. C61×#386C4semidirect
221. #386#6923semidirect
225. C61#12855semidirect

Maximal subgroups

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

subgroupindex
#214616562
#214616492
#214609042
#214609032
#214484062
#1285561