Finite Group Databasebeta

← #30595883

Subgroups — #30595883

Order 15616.

464 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 98 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#21461675C211yesmaximal, characteristic
2#21461673C211yesmaximal, characteristic
3#21460639C212yesmaximal, complemented
4#21460638C212yesmaximal, complemented
5#21454153C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×C4⋊#92420—21no—
8C2×C22⋊#92420—21no—
9C2×C22⋊#92420—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C22×C4×Dic61C2211yescharacteristic
13#16839669C411yescharacteristic
14#16839669C2211yescharacteristic
15#16839658C411yescharacteristic
16#16839658C2211yescharacteristic
17#16839643—21no—
18#16839643—21no—
19#16839634—21no—
20#16839623—21no—
21#16839622C411yescharacteristic
22C2×C22⋊Q8×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519844—42no—
26C4⋊#92420—42no—
27C22⋊#92420—42no—
28C22⋊#92420—42no—
29C23×Dic61D411yescharacteristic
30C23×Dic61D411yescharacteristic
31C2×C4⋊Dic61C2×C411yescharacteristic
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×C22⋊Dic61—21no—
36C2×C4×Dic61—42no—
37C2×C4×Dic61C2×C411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61C2311yescharacteristic
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48C22×Q8×C61C2×C411yescharacteristic
49C23×C4×C61C2×C411yescharacteristic
50C22⋊Q8×C61—42no—
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C22⋊C4×C61—21no—
54C24×C61C22⋊C411yescharacteristic
55C2×Q8×C61—22no—
56C2×Q8×C61—41no—
57C2×Q8×C61—41no—
58C22×C4×C61—22no—
59C22×C4×C61—22no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—41no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22×C411yescharacteristic
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—41no—
70C22×Dic61—41no—
71C22×Dic61—41no—
72C22×Dic61—41no—
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61SD1612yes—
76C22×Dic61Q1612yes—
77C22×Dic61C2×D411yescharacteristic
78C22×Dic61C2×D411yescharacteristic
79C2×#92420—42no—
80C2×#92420—42no—
81C2×#92420—42no—
82C2×#92420—42no—
83C2×#92420—42no—
84C2×#92420—42no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—42no—
87C22⋊C4×C61—42no—
88C22⋊Dic61—42no—
89C4⋊Dic61—22no—
90C4⋊Dic61—41no—
91#11758196—42no—
92#11758196—41no—
93#11758196—41no—
94C4×Dic61—22no—
95C4×Dic61—22no—
96C4×Dic61—41no—
97C4×Dic61—41no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61#10312yes—
105C23×C61C2×C22⋊C411yescharacteristic
106Q8×C61—82no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—44no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61#9912yes—
119C2×C4×C61#13112yes—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—42no—
130C2×Dic61—42no—
131C2×Dic61—42no—
132C2×Dic61—42no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61#10312yes—
140C2×Dic61C2×SD1611yescharacteristic
141C2×Dic61C2×Q1611yescharacteristic
142C2×Dic61AGL(1,ℤ/8)11yescharacteristic
143C2×Dic61#13711yescharacteristic
144#92420—82no—
145#92420—82no—
146#7715—611nomaximal, Sylow
147C22×C61—22no—
148C22×C61—22no—
149C22×C61—22no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61#40811yescharacteristic
155C22×C61C2×#9911yescharacteristic
156C22×C61#41311yescharacteristic
157C22×C61C2×#10311yescharacteristic
158C22×C61#41711yescharacteristic
159C22×C61#42111yescharacteristic
160C22×C61#42111yescharacteristic
161C4×C61—22no—
162C4×C61—22no—
163C4×C61—81no—
164C4×C61—81no—
165Dic61—21no—
166Dic61—21no—
167Dic61—21no—
168Dic61—22no—
169Dic61—21no—
170Dic61—41no—
171Dic61—81no—
172Dic61—81no—
173#2855—611no—
174#1797—611no—
175#1797—611no—
176#1272—612no—
177#1271—612no—
178C2×C61—42no—
179C2×C61#146811yescharacteristic
180C2×C61#148111yescharacteristic
181C2×C61#149511yescharacteristic
182C2×C61#151311yescharacteristic
183C2×C61#152011yescharacteristic
184C2×C61#153511yescharacteristic
185C2×C61#155011yescharacteristic
186C2×C22⋊Q8#692311yescharacteristic
187C22×C42—611no—
188C2×C4⋊C8—1221no—
189C2×C4⋊C8—1221no—
190C2×C22⋊C8—1221no—
191C2×C22⋊C8—1221no—
192#391—611no—
193#391—611no—
194#389—611no—
195#389—611no—
196#387—1221no—
197#387—1221no—
198#385—1221no—
199#381—1221no—
200#380—611no—
201#336—612no—
202#336—612no—
203C61#771511yescharacteristic, complemented, Sylow
204C22×Q8C2×#692311yescharacteristic
205C23×C4—611no—
206C23×C4—611no—
207C23×C4C2×#692311yescharacteristic
208C22×C8—1222no—
209C22×C8—1222no—
210C22⋊Q8—42no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4C2×#692311yescharacteristic
217C2×C22⋊C4—21no—
218C2×C22⋊C4—1221no—
219C2×C42—611no—
220C2×C42—611no—
221C2×C42—611no—
222C2×C42—611no—
223C2×C42—2442no—
224C4⋊C8—2442no—
225C4⋊C8—2442no—
226C22⋊C8—2442no—
227C22⋊C8—2442no—
228#95—1221no—
229#95—1221no—
230#95—1221no—
231#95—1221no—
232#95—1221no—
233#95—1221no—
234#95—1221no—
235C24C22⋊#692311yescharacteristic
236C2×Q8—22no—
237C2×Q8—41no—
238C2×Q8—41no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—41no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—612no—
248C22×C4—612no—
249C22×C4—611no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—2441no—
255C22×C4—2441no—
256C22×C4—2441no—
257C22×C4—2441no—
258C22×C4C22⋊#692311yescharacteristic
259C22×C4C22×#692311yescharacteristic
260C2×C8—2442no—
261C2×C8—2442no—
262C2×C8—2442no—
263C2×C8—2442no—
264C2×C8—2442no—
265C2×C8—2442no—
266C4⋊C4—41no—
267C4⋊C4—42no—
268C4⋊C4—1222no—
269C4⋊C4—2441no—
270C4⋊C4—2441no—
271C4⋊C4—2441no—
272C4⋊C4—2442no—
273C22⋊C4—42no—
274C22⋊C4—2442no—
275C42—1222no—
276C42—1222no—
277C42—2441no—
278C42—2441no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23#1451984012yes—
286C23C2×C22⋊#692311yescharacteristic
287Q8—82no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—44no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—612no—
300C2×C4—611no—
301C2×C4—611no—
302C2×C4—611no—
303C2×C4—611no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—2442no—
314C2×C4—2442no—
315C2×C4—2442no—
316C2×C4—2442no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4#1451983512yes—
324C2×C4#1451986412yes—
325C8—4882no—
326C8—4882no—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22#1684073511yescharacteristic
335C22C2×#1451983511yescharacteristic
336C22#1684074911yescharacteristic
337C22C2×#1451984011yescharacteristic
338C22#1684075311yescharacteristic
339C22#1684075911yescharacteristic
340C22#1684076111yescharacteristic
341C4—22no—
342C4—22no—
343C4—81no—
344C4—81no—
345C4—1221no—
346C4—1222no—
347C4—1221no—
348C4—1221no—
349C4—1221no—
350C4—4881no—
351C4—4881no—
352C4—2441no—
353C2—42no—
354C2#2146108411yescharacteristic
355C2#2146112711yescharacteristic
356C2#2146117611yescharacteristic
357C2#2146123411yescharacteristic
358C2#2146125911yescharacteristic
359C2#2146130611yescharacteristic
360C2#2146133711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C22⋊Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×C22⋊Q8#6923
hypocenterC61#7715
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #21460639C2semidirect
4. #21460638C2semidirect
203. C61#7715semidirect

Maximal subgroups

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

subgroupindex
#214616752
#214616732
#214606392
#214606382
#214541532
#771561