Finite Group Databasebeta

← #30600375

Subgroups — #30600375

Order 15616.

588 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 120 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
1C2×#16840780C211yesmaximal, characteristic
2#21461676C211yesmaximal, characteristic
3C2×#16840622C212yesmaximal, complemented
4#21460697C212yesmaximal, complemented
5#21454168C211yesmaximal, characteristic
6#16840780—24no—
7C2×#14519844C2212yes—
8C2×#14519844C2212yes—
9C2×#14519834—21no—
10C2×#14519834—21no—
11C2×C4×#92420—21no—
12#16840628—21no—
13#16840622—24no—
14C2×#14519775C2211yescharacteristic
15C2×#14519757C411yescharacteristic
16C2×#14519753C411yescharacteristic
17C2×C42×D61C2211yescharacteristic
18#16839668C411yescharacteristic
19#16839659—21no—
20#16839659—21no—
21#16839631C2211yescharacteristic
22#16839621—21no—
23#16839621—21no—
24C61×#391C411yescharacteristic
25C22×#92420—22no—
26C22×#92420—22no—
27#14519844—22no—
28#14519844—22no—
29#14519844—22no—
30#14519844D414yes—
31#14519834—24no—
32#14519834—42no—
33C4×#92420—24no—
34C22×Dic122C2×C411yescharacteristic
35C22×C4×D61C2×C411yescharacteristic
36C22×C4×D61D411yescharacteristic
37C22×C4×D61D411yescharacteristic
38#14519775—22no—
39#14519775—22no—
40#14519757—42no—
41#14519753—42no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×#11758196—21no—
45C2×#11758196—21no—
46C2×#11758196—21no—
47C2×#11758196—21no—
48C2×#11758196—21no—
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61C2311yescharacteristic
54C42×D61—22no—
55C42×D61—22no—
56#14519684—21no—
57#14519684—21no—
58C22×Q8×C61C2×C411yescharacteristic
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C42×C61C2×C411yescharacteristic
61#95×C61—21no—
62#95×C61—21no—
63C23×D61C22⋊C411yescharacteristic
64C2×Q8×C61—22no—
65C2×Q8×C61—41no—
66C2×Q8×C61—41no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22×C411yescharacteristic
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C22×Dic61C2×D411yescharacteristic
77C2×C4×D61—22no—
78C2×C4×D61—22no—
79C2×C4×D61—22no—
80C2×C4×D61—22no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—22no—
84C2×C4×D61—22no—
85C2×C4×D61—41no—
86C2×C4×D61SD1612yes—
87C2×C4×D61Q1612yes—
88C2×Dic122—22no—
89C2×Dic122—41no—
90C2×Dic122—41no—
91C2×#92420—24no—
92C2×#92420—42no—
93C2×#92420—42no—
94C2×#92420—42no—
95C2×#92420—42no—
96C2×#92420—42no—
97C4⋊C4×C61—41no—
98C42×C61—22no—
99#11758198—42no—
100#11758198—42no—
101C4⋊Dic61—42no—
102C4⋊Dic61—41no—
103#11758196—42no—
104#11758196—41no—
105#11758196—42no—
106#11758196—41no—
107#11758196—42no—
108#11758196—42no—
109C4×Dic61—21no—
110C4×Dic61—22no—
111C4×Dic61—21no—
112C4×Dic61C2×D412yes—
113C4×Dic61#4112yes—
114C23×C61C2×C22⋊C411yescharacteristic
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61#10312yes—
122Q8×C61—82no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
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—41no—
136C2×C4×C61#10312yes—
137C2×C4×C61C4×D412yes—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61#10012yes—
147C2×Dic61#12011yescharacteristic
148C2×Dic61#12112yes—
149C2×Dic61#12311yescharacteristic
150C2×Dic61C2×SD1611yescharacteristic
151C2×Dic61C2×Q1611yescharacteristic
152C2×Dic61#13512yes—
153C2×Dic61#13512yes—
154C2×Dic61#13712yes—
155C4×D61—24no—
156C4×D61—24no—
157C4×D61—44no—
158C4×D61—42no—
159C4×D61—42no—
160Dic122—82no—
161#92420—44no—
162#92420—82no—
163#9128—611nomaximal, Sylow
164C22×C61#38611yescharacteristic
165C22×C61C2×#10011yescharacteristic
166C22×C61#41311yescharacteristic
167C22×C61C2×#10311yescharacteristic
168C22×C61#41611yescharacteristic
169C22×C61#41611yescharacteristic
170C22×C61#41911yescharacteristic
171C2×D61—22no—
172C2×D61—22no—
173C2×D61—22no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C4×C61—22no—
179C4×C61—22no—
180C4×C61—41no—
181C4×C61—81no—
182C4×C61—81no—
183Dic61—22no—
184Dic61—81no—
185Dic61—81no—
186Dic61#45212yes—
187Dic61#46512yes—
188Dic61#46712yes—
189Dic61#48512yes—
190C2×#431—611no—
191#2857—611no—
192#1797—611no—
193C2×#333—612no—
194#1296—612no—
195C2×C61#154211yescharacteristic
196C2×C61#154311yescharacteristic
197C2×C61#154811yescharacteristic
198C2×C61#155411yescharacteristic
199C2×C61#187311yescharacteristic
200C2×C61#189211yescharacteristic
201C2×C61#190011yescharacteristic
202D61—42no—
203C2×C4⋊Q8—611no—
204C2×C22⋊Q8—611no—
205C2×C22⋊Q8—611no—
206C22×C42—611no—
207#431—1224no—
208C2×C4⋊C8—612no—
209C2×C4⋊C8—612no—
210C2×C22⋊C8—1221no—
211C2×C22⋊C8—1221no—
212C2×C4×C8—1221no—
213#391—611no—
214#391#692311yescharacteristic
215#389—1221no—
216#389—1221no—
217#384—611no—
218#380—1221no—
219#380—1221no—
220#336—1221no—
221#333—1224no—
222C61#912811yescharacteristic, complemented, Sylow
223C22×Q8—611no—
224C22×Q8C2×#692311yescharacteristic
225C23×C4—611no—
226C23×C4—611no—
227C23×C4—611no—
228C22×C8—1222no—
229C22×C8—1222no—
230C4⋊Q8—1222no—
231C4⋊Q8—1222no—
232C22⋊Q8—2442no—
233C22⋊Q8—2442no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—1221no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4—1221no—
241C2×C4⋊C4C2×#692311yescharacteristic
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C42—611no—
245C2×C42—611no—
246C2×C42—611no—
247C2×C42—1222no—
248C2×C42—1222no—
249C2×C42C2×#692311yescharacteristic
250C4⋊C8—614no—
251C4⋊C8—1222no—
252C4⋊C8—1222no—
253C4⋊C8—1222no—
254C22⋊C8—1224no—
255C22⋊C8—2442no—
256C4×C8—1224no—
257#95—21no—
258#95—21no—
259#95—1221no—
260#95—1221no—
261C24—611no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—1222no—
266C2×Q8—2441no—
267C2×Q8—2441no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—611no—
273C22×C4—612no—
274C22×C4—612no—
275C22×C4—1222no—
276C22×C4—1222no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1222no—
280C22×C4—1222no—
281C22×C4—1222no—
282C22×C4—1222no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—2441no—
286C22×C4C22⋊#692311yescharacteristic
287C22×C4C22⋊#692311yescharacteristic
288C22×C4C22×#692311yescharacteristic
289C2×C8—1224no—
290C2×C8—2442no—
291C2×C8—2442no—
292C2×C8—2442no—
293C2×C8—2442no—
294C2×C8—2442no—
295C4⋊C4—41no—
296C4⋊C4—2441no—
297C4⋊C4—2442no—
298C4⋊C4—2442no—
299C4⋊C4—2442no—
300C4⋊C4—2441no—
301C4⋊C4—2442no—
302C4⋊C4—2441no—
303C4⋊C4—2442no—
304C22⋊C4—2442no—
305C22⋊C4—2442no—
306C42—22no—
307C42—612no—
308C42—612no—
309C42—1221no—
310C42—1221no—
311C42—1222no—
312C23—612no—
313C23—1221no—
314C23—1221no—
315C23—1221no—
316C23—1221no—
317C23—1221no—
318C23—1221no—
319C23C2×C22⋊#692311yescharacteristic
320Q8—82no—
321Q8—4882no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—611no—
336C2×C4—612no—
337C2×C4—611no—
338C2×C4—611no—
339C2×C4—611no—
340C2×C4—612no—
341C2×C4—612no—
342C2×C4—612no—
343C2×C4—612no—
344C2×C4—1224no—
345C2×C4—1224no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—2444no—
349C2×C4—2442no—
350C2×C4—2442no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4#1451984012yes—
358C2×C4D4×#692312yes—
359C8—4882no—
360C8—2444no—
361C22—1222no—
362C22—1222no—
363C22—1222no—
364C22—2441no—
365C22—2441no—
366C22—2441no—
367C22—2441no—
368C22#1684071011yescharacteristic
369C22D61⋊#10011yescharacteristic
370C22#1684074811yescharacteristic
371C22C2×#1451984011yescharacteristic
372C22#1684075211yescharacteristic
373C22#1684075211yescharacteristic
374C22#1684075511yescharacteristic
375C4—22no—
376C4—22no—
377C4—41no—
378C4—81no—
379C4—81no—
380C4—612no—
381C4—612no—
382C4—612no—
383C4—612no—
384C4—1222no—
385C4—4881no—
386C4—4881no—
387C2—2442no—
388C2#2146132011yescharacteristic
389C2#2146132311yescharacteristic
390C2#2146133311yescharacteristic
391C2#2146134411yescharacteristic
392C2#2146180511yescharacteristic
393C2#2146183211yescharacteristic
394C2#2146184511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#391#6923
hypocenterC61#9128
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
3. C2×#16840622C2semidirect
4. #21460697C2semidirect
222. C61#9128semidirect

Maximal subgroups

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

subgroupindex
C2×#168407802
#214616762
C2×#168406222
#214606972
#214541682
#912861