Finite Group Databasebeta

← #30605267

Subgroups — #30605267

Order 15616.

506 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 70 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#21461714C211yesmaximal, characteristic
2C2×#16840606C211yesmaximal, characteristic
3#21460816C212yesmaximal, complemented
4#21460799C212yesmaximal, complemented
5#21450089C211yesmaximal, characteristic
6C2×C22⋊#92420—21no—
7#16840703—21no—
8#16840640—21no—
9#16840640C2212yes—
10#16840606—21no—
11#16840606C2212yes—
12C22×#11758198C2211yescharacteristic
13#16839697C411yescharacteristic, complemented
14#16839697C2211yescharacteristic
15#16839688C411yescharacteristic, complemented
16#16839688C2211yescharacteristic
17#16839653—21no—
18#16839653—21no—
19#16839634—21no—
20#16839625C411yescharacteristic, complemented
21#16839617—21no—
22C2×#117×C61C411yescharacteristic, complemented
23C22×#92420—41no—
24C2×C22⋊#6923—22no—
25C2×C22⋊#6923—41no—
26C2×C22⋊#6923—41no—
27C22⋊#92420—22no—
28C22⋊#92420—41no—
29C24×D61D411yescharacteristic
30C23×Dic61D411yescharacteristic
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×C22⋊Dic61—21no—
34C2×#11758198—21no—
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×#11758198—41no—
39C2×#11758198—41no—
40C2×#11758198C2×C411yescharacteristic
41C2×#11758198D411yescharacteristic
42C2×#11758198D411yescharacteristic
43C2×#11758198C2311yescharacteristic
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684C2×C411yescharacteristic
48#14519684C2×C411yescharacteristic
49C23×C4×C61C2×C411yescharacteristic
50#117×C61—41no—
51#117×C61—41no—
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C22⋊C4×C61—21no—
55C2×C42×C61—21no—
56C24×C61C22⋊C411yescharacteristic
57C23×D61—21no—
58C23×D61—21no—
59C23×D61—22no—
60C23×D61—41no—
61C23×D61—42no—
62C23×D61—81no—
63C23×D61C22⋊C411yescharacteristic
64C23×D61C2×D411yescharacteristic
65C22×#6923—42no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—42no—
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22×C411yescharacteristic
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—81no—
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C2×D411yescharacteristic
80C22⋊#6923—42no—
81C22⋊#6923—42no—
82C22⋊#6923—82no—
83C22⋊#6923—82no—
84C2×#92420—42no—
85C2×#92420—82no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C22⋊C4×C61—41no—
89C22⋊C4×C61—41no—
90C42×C61—42no—
91C22⋊Dic61—42no—
92#11758198—41no—
93#11758198—41no—
94#11758198—41no—
95#11758198—41no—
96#11758198—42no—
97#11758198—42no—
98#11758198—81no—
99#11758198—81no—
100#11758196—81no—
101#11758196—81no—
102C23×C61—22no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—41no—
106C23×C61#9911yescharacteristic
107C23×C61#9911yescharacteristic
108C23×C61C2×C22⋊C411yescharacteristic
109C22×D61—21no—
110C22×D61—21no—
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—21no—
114C22×D61—42no—
115C22×D61—42no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—42no—
121C22×D61—42no—
122C22×D61—81no—
123C22×D61—81no—
124C22×D61—84no—
125C22×D61—84no—
126C22×D61#13512yes—
127C2×#6923—82no—
128C2×#6923—82no—
129C2×#6923—82no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—42no—
133C2×C4×C61—42no—
134C2×C4×C61—41no—
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—41no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—42no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—81no—
154#92420—82no—
155#11841—611nomaximal, Sylow
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—42no—
164C22×C61—42no—
165C22×C61#35212yes—
166C22×C61C2×#9911yescharacteristic
167C22×C61#41611yescharacteristic
168C22×C61#42111yescharacteristic
169C2×D61—22no—
170C2×D61—41no—
171C2×D61—41no—
172C2×D61—42no—
173C2×D61—42no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—81no—
178C2×D61—84no—
179C2×D61—84no—
180C2×D61—81no—
181#6923—162no—
182C4×C61—41no—
183C4×C61—41no—
184C4×C61—81no—
185C4×C61—81no—
186Dic61—41no—
187Dic61—41no—
188Dic61—81no—
189Dic61—81no—
190#2482—611no—
191#1819—611no—
192C2×#323—611no—
193#1352—612no—
194#1344—612no—
195C2×C61—21no—
196C2×C61—21no—
197C2×C61—22no—
198C2×C61—41no—
199C2×C61#151611yescharacteristic
200C2×C61C2×#35211yescharacteristic
201C2×C61#212711yescharacteristic
202D61—42no—
203D61—81no—
204C2×#117#692311yescharacteristic, complemented
205C22×C22⋊C4—611no—
206C2×C22⋊C8—1221no—
207#399—611no—
208#399—611no—
209#397—611no—
210#397—611no—
211#388—1221no—
212#388—1221no—
213#385—1221no—
214#381—611no—
215#379—1221no—
216#379—1221no—
217#342—612no—
218#342—1221no—
219#323—612no—
220#323—1221no—
221C61#1184111yescharacteristic, complemented, Sylow
222C25—611no—
223C23×C4—611no—
224C23×C4C2×#692311yescharacteristic
225C22×C8—2441no—
226#117—41no—
227#117—41no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4C2×#692311yescharacteristic
231C2×C4⋊C4C2×#692311yescharacteristic
232C2×C22⋊C4—21no—
233C2×C22⋊C4—611no—
234C2×C22⋊C4—611no—
235C2×C22⋊C4—611no—
236C2×C22⋊C4—611no—
237C2×C22⋊C4—1221no—
238C2×C22⋊C4—1221no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C22⋊C4—1222no—
243C2×C22⋊C4—2441no—
244C2×C22⋊C4—2441no—
245C2×C22⋊C4—2441no—
246C2×C22⋊C4—2441no—
247C2×C42—21no—
248C22⋊C8—1222no—
249C22⋊C8—2441no—
250#95—611no—
251#95—611no—
252#95—1221no—
253#95—1221no—
254#95—1221no—
255C24—611no—
256C24—611no—
257C24—1222no—
258C24—1221no—
259C24—1221no—
260C24—4881no—
261C24—2441no—
262C24—2442no—
263C24C22⋊#692311yescharacteristic
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—42no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—4881no—
276C22×C4—2442no—
277C22×C4C22⋊#692311yescharacteristic
278C22×C4C22×#692311yescharacteristic
279C2×C8—4882no—
280C2×C8—2442no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—4881no—
284C4⋊C4—4881no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—4881no—
288C22⋊C4—4881no—
289C22⋊C4—4882no—
290C22⋊C4—4882no—
291C22⋊C4—2441no—
292C22⋊C4—2441no—
293C22⋊C4—2441no—
294C22⋊C4—2441no—
295C22⋊C4—2442no—
296C22⋊C4—2442no—
297C22⋊C4—2442no—
298C22⋊C4—2442no—
299C22⋊C4—2442no—
300C42—42no—
301C23—21no—
302C23—21no—
303C23—22no—
304C23—41no—
305C23—612no—
306C23—1221no—
307C23—1221no—
308C23—1221no—
309C23—1221no—
310C23—1221no—
311C23—4881no—
312C23—4881no—
313C23—4884no—
314C23—4884no—
315C23—2442no—
316C23—2442no—
317C23—2442no—
318C23—2441no—
319C23—2441no—
320C23—2441no—
321C23—2441no—
322C23—2442no—
323C23#1451983511yescharacteristic
324C23#1451983511yescharacteristic
325C23C2×C22⋊#692311yescharacteristic
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—4882no—
341C2×C4—4882no—
342C2×C4—4882no—
343C2×C4—4881no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2442no—
351C2×C4—2441no—
352C2×C4—2441no—
353C8—4882no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—42no—
362C22—42no—
363C22—1222no—
364C22—4881no—
365C22—4884no—
366C22—4881no—
367C22—4884no—
368C22—2442no—
369C22—2442no—
370C22—2441no—
371C22—2441no—
372C22—2441no—
373C22—2441no—
374C22—2441no—
375C22#1684066412yes—
376C22C2×#1451983511yescharacteristic
377C22#1684075211yescharacteristic
378C22#1684075911yescharacteristic
379C4—41no—
380C4—41no—
381C4—81no—
382C4—81no—
383C4—9762no—
384C4—4881no—
385C4—4881no—
386C4—2441no—
387C4—2441no—
388C2—21no—
389C2—21no—
390C2—22no—
391C2—41no—
392C2—4881no—
393C2—2442no—
394C2#2146124511yescharacteristic
395C2C2×#1684066411yescharacteristic
396C2#2146209411yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#117×C61C4
socleC22×C61C2×#99
prime radicalC24×D61D4
cosocleC2×#11758198C23
hypercenterC2×#117#6923
hypocenterC61#11841
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. #21460816C2semidirect
4. #21460799C2semidirect
13. #16839697C4semidirect
15. #16839688C4semidirect
20. #16839625C4semidirect
22. C2×#117×C61C4semidirect
204. C2×#117#6923semidirect
221. C61#11841semidirect

Maximal subgroups

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

subgroupindex
#214617142
C2×#168406062
#214608162
#214607992
#214500892
#1184161