Finite Group Databasebeta

← #29590663

Subgroups — #29590663

Order 15616.

394 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 73 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#21451023C211yesmaximal, characteristic
2#21445614C211yesmaximal, characteristic
3#21444161C211yesmaximal, characteristic
4#21443850C211yesmaximal, characteristic
5#21443849C211yesmaximal, characteristic
6#21443848C211yesmaximal, characteristic
7C61×#1354C211yesmaximal, characteristic
8C2×#14519775C411yescharacteristic
9C2×#14519742C2211yescharacteristic
10#16839816—21no—
11C2×#14519695—21no—
12M16×Dic61—21no—
13#16839683C411yescharacteristic
14#16839682C2211yescharacteristic
15#16839681C411yescharacteristic
16#16839666—21no—
17#16839659—21no—
18#16839657—21no—
19#16839631—21no—
20#16839613C411yescharacteristic
21#16839531C2211yescharacteristic
22#16839488C2211yescharacteristic
23#16839487—21no—
24C61×#395C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C22×Dic122D411yescharacteristic
29C2×#11758194—21no—
30#14519775—41no—
31#14519775—41no—
32#14519742—41no—
33#14519742—41no—
34C2×C4⋊Dic61—21no—
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196C2×C411yescharacteristic
41C2×#11758196D411yescharacteristic
42C2×C4×Dic61—21no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46#14519706—41no—
47#14519695—24no—
48C22⋊#92418—21no—
49#14519687—41no—
50#14519687—41no—
51C8×Dic61—41no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684C2×C411yescharacteristic
56C22×Q8×C61C2×C411yescharacteristic
57C2×M16×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61C2311yescharacteristic
60C22⋊C8×C61—21no—
61#95×C61—21no—
62#95×C61C2×C411yescharacteristic
63C2×Q8×C61—41no—
64C2×Q8×C61—81no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61C22×C411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C22⋊C411yescharacteristic
76C2×Dic122—21no—
77C2×Dic122—21no—
78C2×Dic122—22no—
79C2×Dic122—41no—
80C2×Dic122—41no—
81C2×Dic122—81no—
82M16×C61—22no—
83M16×C61—41no—
84C2×C8×C61—41no—
85C2×C8×C61—41no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—81no—
88C4⋊Dic61—81no—
89#11758196—24no—
90#11758196—41no—
91#11758196—41no—
92#11758196—42no—
93#11758196—41no—
94#11758196—41no—
95#11758196—81no—
96#11758196—81no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—42no—
104#11758194—22no—
105#11758194—41no—
106C2×#92418—41no—
107C2×#92418—41no—
108C23×C61C2×C22⋊C411yescharacteristic
109Q8×C61—82no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—22no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61#13711yescharacteristic
123C2×C4×C61#13711yescharacteristic
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—22no—
127C2×Dic61—22no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61#9911yescharacteristic
139C2×Dic61#9911yescharacteristic
140C2×Dic61#10412yes—
141Dic122—42no—
142Dic122—42no—
143Dic122—82no—
144C8×C61—42no—
145C8×C61—81no—
146#92418—42no—
147#92418—81no—
148#11795—611nomaximal, Sylow
149C22×C61—21no—
150C22×C61—21no—
151C22×C61C2×#9911yescharacteristic
152C22×C61#41911yescharacteristic
153C22×C61C2×#10411yescharacteristic
154C4×C61—21no—
155C4×C61—21no—
156C4×C61—42no—
157C4×C61—41no—
158C4×C61—41no—
159C4×C61—81no—
160Dic61—21no—
161Dic61—22no—
162Dic61—42no—
163Dic61—41no—
164Dic61—41no—
165Dic61—81no—
166Dic61#35612yes—
167#2567—611no—
168C4×#101—611no—
169#1467—611no—
170#1354—611no—
171#1354—611no—
172#1354—611no—
173#1354D6111yescharacteristic
174C2×C61—21no—
175C2×C61—21no—
176C2×C61#150811yescharacteristic
177C2×C61#212211yescharacteristic
178C2×C61C2×#35611yescharacteristic
179C2×C4⋊Q8—611no—
180C2×C4×Q8—611no—
181#432—1221no—
182C2×#101—1221no—
183C4×M16—1221no—
184#395—611no—
185#395—611no—
186#395—611no—
187#395C2×D6111yescharacteristic
188#391—1221no—
189#389—1221no—
190#389—1221no—
191#384—1221no—
192C4×C4⋊C4—611no—
193#343—611no—
194#343C2×D6111yescharacteristic
195#324—611no—
196#324—1221no—
197#324C2×D6111yescharacteristic
198C61#1179511yescharacteristic, complemented, Sylow
199C22×Q8—611no—
200C22×Q8—611no—
201C22×Q8C4×D6111yescharacteristic
202C2×M16—21no—
203C2×M16—1221no—
204C4⋊Q8—2441no—
205C4⋊Q8—2441no—
206C4×Q8—2441no—
207C4×Q8—2441no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—611no—
210C2×C4⋊C4—611no—
211C2×C4⋊C4—1221no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4C22×D6111yescharacteristic
218C2×C42—611no—
219C2×C42—611no—
220C2×C42—611no—
221C2×C42—1221no—
222C4⋊C8—2441no—
223#101—1224no—
224C22⋊C8—21no—
225C22⋊C8—1221no—
226#97—2441no—
227#97—2441no—
228C4×C8—2441no—
229#95—21no—
230#95—611no—
231#95—1221no—
232#95—1221no—
233#95—1221no—
234#95C4×D6111yescharacteristic
235C2×Q8—41no—
236C2×Q8—81no—
237C2×Q8—1222no—
238C2×Q8—1221no—
239C2×Q8—1221no—
240C2×Q8—4881no—
241C2×Q8—2441no—
242C2×Q8—2441no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4C2×C4×D6111yescharacteristic
252C22×C4D4×D6111yescharacteristic
253C22×C4D4×D6111yescharacteristic
254M16—22no—
255M16—41no—
256M16—1222no—
257M16—2441no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—2441no—
261C2×C8—2441no—
262C4⋊C4—41no—
263C4⋊C4—81no—
264C4⋊C4—1224no—
265C4⋊C4—4881no—
266C4⋊C4—4881no—
267C4⋊C4—4881no—
268C4⋊C4—2441no—
269C4⋊C4—2441no—
270C4⋊C4—2441no—
271C4⋊C4—2441no—
272C4⋊C4—2442no—
273C42—1221no—
274C42—1221no—
275C42—1221no—
276C42—1221no—
277C42—1221no—
278C42—1221no—
279C42—2442no—
280C23C22⋊C4×D6111yescharacteristic
281Q8—82no—
282Q8—4882no—
283Q8—2442no—
284Q8—2442no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—611no—
298C2×C4—611no—
299C2×C4—612no—
300C2×C4—1222no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1222no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4#1451980611yescharacteristic
315C2×C4#1451980911yescharacteristic
316C8—42no—
317C8—81no—
318C8—4881no—
319C8—2442no—
320C22—21no—
321C22—21no—
322C22#99×D6111yescharacteristic
323C22#1683976911yescharacteristic
324C22#104×D6111yescharacteristic
325C4—21no—
326C4—21no—
327C4—42no—
328C4—41no—
329C4—41no—
330C4—81no—
331C4—612no—
332C4—1221no—
333C4—1222no—
334C4—4881no—
335C4—2442no—
336C4—2441no—
337C4—2441no—
338C2—21no—
339C2—21no—
340C2#2144433711yescharacteristic
341C2#2144746711yescharacteristic
342C2#356×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1354C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1354D61
hypocenterC61#11795
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
198. C61#11795semidirect

Maximal subgroups

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

subgroupindex
#214510232
#214456142
#214441612
#214438502
#214438492
#214438482
C61×#13542
#1179561