Finite Group Databasebeta

← #30600380

Subgroups — #30600380

Order 15616.

588 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 122 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×#16840779C211yesmaximal, characteristic
2#21461675C211yesmaximal, characteristic
3C2×#16840621C212yesmaximal, complemented
4#21460697C212yesmaximal, complemented
5#21454169C211yesmaximal, characteristic
6#16840779—24no—
7C2×#14519844C2212yes—
8C2×#14519844C2212yes—
9C2×C22⋊#92420—21no—
10C2×C22⋊#92420—21no—
11C2×C4×#92420—21no—
12#16840628—21no—
13#16840621—24no—
14C2×#14519776C2211yescharacteristic
15C2×#14519754—21no—
16C22×C4×Dic61C2211yescharacteristic
17#16839666—21no—
18#16839661C411yescharacteristic
19#16839659—21no—
20#16839658C411yescharacteristic
21#16839631C2211yescharacteristic
22#16839622C411yescharacteristic
23#16839620—21no—
24C61×#380C411yescharacteristic
25C22×#92420—22no—
26C22×#92420—22no—
27#14519844—22no—
28#14519844—22no—
29#14519844—22no—
30#14519844D414yes—
31C22⋊#92420—24no—
32C22⋊#92420—42no—
33C4×#92420—24no—
34C22×Dic122—21no—
35C23×Dic61D411yescharacteristic
36C23×Dic61D411yescharacteristic
37#14519776—22no—
38#14519776—22no—
39#14519754—42no—
40#14519754—42no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×#11758196—21no—
45C2×#11758196—21no—
46C2×#11758196—21no—
47C2×#11758196—21no—
48C2×C22⋊Dic61—21no—
49C2×C4×Dic61—22no—
50C2×C4×Dic61—22no—
51C2×C4×Dic61C2×C411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54C2×C4×Dic61C2311yescharacteristic
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58C23×C4×C61C2×C411yescharacteristic
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C4⋊C4×C61C2×C411yescharacteristic
61C2×C22⋊C4×C61—21no—
62#95×C61—21no—
63C24×C61C22⋊C411yescharacteristic
64C22×C4×C61—22no—
65C22×C4×C61—22no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—41no—
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22×C411yescharacteristic
71C22×Dic61—22no—
72C22×Dic61—22no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—22no—
76C22×Dic61—22no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61D812yes—
82C22×Dic61SD1612yes—
83C22×Dic61C2×D411yescharacteristic
84C22×Dic61C2×D411yescharacteristic
85C2×Dic122—42no—
86C2×Dic122—41no—
87C2×Dic122—41no—
88C2×Dic122—42no—
89C2×#92420—24no—
90C2×#92420—42no—
91C2×#92420—42no—
92C2×#92420—42no—
93C2×#92420—42no—
94C2×#92420—42no—
95C4⋊C4×C61—22no—
96C4⋊C4×C61—41no—
97C22⋊C4×C61—42no—
98C22⋊Dic61—42no—
99C4⋊Dic61—22no—
100C4⋊Dic61—42no—
101C4⋊Dic61—41no—
102#11758196—42no—
103#11758196—41no—
104#11758196—41no—
105#11758196—41no—
106#11758196—41no—
107#11758196—42no—
108C4×Dic61—22no—
109C4×Dic61—21no—
110C4×Dic61—22no—
111C4×Dic61—21no—
112C4×Dic61C2×D412yes—
113C4×Dic61#4112yes—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61#10212yes—
121C23×C61C2×C22⋊C411yescharacteristic
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—44no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61#10112yes—
134C2×C4×C61C4×D412yes—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—24no—
138C2×Dic61—24no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—42no—
143C2×Dic61—42no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61#10212yes—
151C2×Dic61#12011yescharacteristic
152C2×Dic61#12112yes—
153C2×Dic61#12311yescharacteristic
154C2×Dic61C2×D811yescharacteristic
155C2×Dic61C2×SD1611yescharacteristic
156C2×Dic61#13512yes—
157C2×Dic61#13512yes—
158C2×Dic61#13712yes—
159Dic122—82no—
160Dic122—82no—
161#92420—44no—
162#92420—82no—
163#9130—611nomaximal, Sylow
164C22×C61—22no—
165C22×C61—22no—
166C22×C61—22no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61#38611yescharacteristic
172C22×C61C2×#10111yescharacteristic
173C22×C61#41311yescharacteristic
174C22×C61C2×#10211yescharacteristic
175C22×C61#41611yescharacteristic
176C22×C61#41611yescharacteristic
177C22×C61#41911yescharacteristic
178C4×C61—22no—
179C4×C61—22no—
180C4×C61—81no—
181C4×C61—81no—
182Dic61—22no—
183Dic61—41no—
184Dic61—81no—
185Dic61—81no—
186Dic61#45212yes—
187Dic61#46512yes—
188Dic61#46612yes—
189Dic61#48512yes—
190C2×#431—611no—
191#2857—611no—
192#1797—611no—
193C2×#332—612no—
194#1296—612no—
195C2×C61—42no—
196C2×C61#154011yescharacteristic
197C2×C61#154411yescharacteristic
198C2×C61#154611yescharacteristic
199C2×C61#155411yescharacteristic
200C2×C61#187311yescharacteristic
201C2×C61#189311yescharacteristic
202C2×C61#190111yescharacteristic
203C2×C4⋊Q8—611no—
204C2×C22⋊Q8—1221no—
205C22×C42—611no—
206#431—1224no—
207C2×C4⋊C8—612no—
208C2×C4⋊C8—612no—
209C2×C22⋊C8—1221no—
210C2×C22⋊C8—1221no—
211C2×C4×C8—1221no—
212#391—1221no—
213#389—611no—
214#389—611no—
215#389—1221no—
216#384—611no—
217#380—611no—
218#380—1221no—
219#380#692311yescharacteristic
220#336—1221no—
221#332—1224no—
222C61#913011yescharacteristic, complemented, Sylow
223C22×Q8—1221no—
224C23×C4—611no—
225C23×C4—611no—
226C23×C4C2×#692311yescharacteristic
227C22×C8—1222no—
228C22×C8—1222no—
229C4⋊Q8—1222no—
230C4⋊Q8—1222no—
231C22⋊Q8—2442no—
232C22⋊Q8—2442no—
233C2×C4⋊C4—611no—
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⋊C4C2×#692311yescharacteristic
241C2×C4⋊C4C2×#692311yescharacteristic
242C2×C22⋊C4—21no—
243C2×C22⋊C4—1221no—
244C2×C42—611no—
245C2×C42—611no—
246C2×C42—611no—
247C2×C42—611no—
248C2×C42—1222no—
249C2×C42—1222no—
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—1221no—
259#95—1221no—
260#95—1221no—
261C24C22⋊#692311yescharacteristic
262C2×Q8—2441no—
263C2×Q8—2441no—
264C2×Q8—2442no—
265C2×Q8—2442no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—41no—
271C22×C4—611no—
272C22×C4—611no—
273C22×C4—612no—
274C22×C4—612no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—1222no—
278C22×C4—1222no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1222no—
282C22×C4—1222no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4C22⋊#692311yescharacteristic
286C22×C4C22×#692311yescharacteristic
287C2×C8—1224no—
288C2×C8—2442no—
289C2×C8—2442no—
290C2×C8—2442no—
291C2×C8—2442no—
292C2×C8—2442no—
293C4⋊C4—22no—
294C4⋊C4—41no—
295C4⋊C4—1222no—
296C4⋊C4—2441no—
297C4⋊C4—2442no—
298C4⋊C4—2441no—
299C4⋊C4—2441no—
300C4⋊C4—2442no—
301C4⋊C4—2441no—
302C4⋊C4—2441no—
303C4⋊C4—2442no—
304C22⋊C4—42no—
305C22⋊C4—2442no—
306C42—612no—
307C42—612no—
308C42—1221no—
309C42—1222no—
310C42—1221no—
311C42—1222no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23#1451983912yes—
319C23C2×C22⋊#692311yescharacteristic
320Q8—4882no—
321Q8—4882no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—44no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—611no—
334C2×C4—612no—
335C2×C4—611no—
336C2×C4—611no—
337C2×C4—611no—
338C2×C4—612no—
339C2×C4—612no—
340C2×C4—612no—
341C2×C4—612no—
342C2×C4—1224no—
343C2×C4—1224no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
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#1451983812yes—
358C2×C4D4×#692312yes—
359C8—4882no—
360C8—2444no—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22#1684071011yescharacteristic
369C22C2×#1451983811yescharacteristic
370C22#1684074911yescharacteristic
371C22C2×#1451983911yescharacteristic
372C22#1684075211yescharacteristic
373C22#1684075211yescharacteristic
374C22#1684075511yescharacteristic
375C4—22no—
376C4—22no—
377C4—81no—
378C4—81no—
379C4—612no—
380C4—612no—
381C4—612no—
382C4—612no—
383C4—1222no—
384C4—4881no—
385C4—4881no—
386C4—2441no—
387C2—42no—
388C2#2146131711yescharacteristic
389C2#2146132411yescharacteristic
390C2#2146132811yescharacteristic
391C2#2146134511yescharacteristic
392C2#2146180511yescharacteristic
393C2#2146183311yescharacteristic
394C2#2146184611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#380C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#380#6923
hypocenterC61#9130
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. C2×#16840621C2semidirect
4. #21460697C2semidirect
222. C61#9130semidirect

Maximal subgroups

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

subgroupindex
C2×#168407792
#214616752
C2×#168406212
#214606972
#214541692
#913061