Finite Group Databasebeta

← #29591069

Subgroups — #29591069

Order 15616.

408 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 79 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#21450803C211yesmaximal, characteristic
2#21445814C211yesmaximal, characteristic
3#21444141C211yesmaximal, characteristic
4#21443826C211yesmaximal, characteristic
5#21443825C211yesmaximal, characteristic
6#21443824C211yesmaximal, characteristic
7C61×#1346C211yesmaximal, characteristic
8C2×#14519776—21no—
9C2×#14519776C411yescharacteristic
10C2×#14519742C2211yescharacteristic
11#16839812—21no—
12#16839785—21no—
13C2×#14519695—21no—
14#16839694C411yescharacteristic
15#16839693C411yescharacteristic
16#16839692C2211yescharacteristic
17#16839666—21no—
18#16839659—21no—
19#16839657—21no—
20#16839613C411yescharacteristic
21#16839531C2211yescharacteristic
22#16839488C2211yescharacteristic
23#16839487—21no—
24C61×#398C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122—21no—
28C22×Dic122D411yescharacteristic
29C2×#11758194—21no—
30#14519776—41no—
31#14519776—41no—
32#14519776—42no—
33#14519776—42no—
34#14519742—41no—
35#14519742—41no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196C2×C411yescharacteristic
43C2×#11758196D411yescharacteristic
44C2×C4×Dic61—21no—
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48#14519706—41no—
49#14519706—41no—
50#14519706—41no—
51#14519695—42no—
52C22⋊#92418—21no—
53C8×Dic61—41no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684C2×C411yescharacteristic
58C2×M16×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61C2×C411yescharacteristic
61C2×C4⋊C4×C61C2311yescharacteristic
62C22⋊C8×C61—21no—
63#95×C61—21no—
64#95×C61C2×C411yescharacteristic
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—41no—
77C2×Dic122—41no—
78C2×Dic122—42no—
79C2×Dic122—42no—
80C2×Dic122—42no—
81C2×Dic122D812yes—
82C2×Dic122SD1612yes—
83M16×C61—41no—
84M16×C61—41no—
85C2×C8×C61—41no—
86C2×C8×C61—41no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—41no—
91C4⋊Dic61—42no—
92C4⋊Dic61—41no—
93#11758196—24no—
94#11758196—41no—
95#11758196—41no—
96#11758196—41no—
97#11758196—41no—
98#11758196—41no—
99#11758196—41no—
100#11758196—42no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61—42no—
108#11758194—41no—
109#11758194—41no—
110C2×#92418—41no—
111C2×#92418—41no—
112C23×C61C2×C22⋊C411yescharacteristic
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—22no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61C2×D811yescharacteristic
126C2×C4×C61C2×SD1611yescharacteristic
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—22no—
132C2×Dic61—22no—
133C2×Dic61—21no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61#9911yescharacteristic
141C2×Dic61#9911yescharacteristic
142C2×Dic61#10212yes—
143C2×Dic61#10212yes—
144Dic122—42no—
145Dic122—42no—
146Dic122—84no—
147C8×C61—81no—
148C8×C61—81no—
149#92418—81no—
150#92418—81no—
151#11883—611nomaximal, Sylow
152C22×C61—21no—
153C22×C61—21no—
154C22×C61C2×#9911yescharacteristic
155C22×C61C2×#10211yescharacteristic
156C22×C61#42111yescharacteristic
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—42no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—81no—
163Dic61—21no—
164Dic61—22no—
165Dic61—22no—
166Dic61—42no—
167Dic61—41no—
168Dic61—81no—
169Dic61#35612yes—
170#2546—611no—
171#1801—611no—
172#1461—611no—
173#1346—611no—
174#1346—611no—
175#1346—611no—
176#1346D6111yescharacteristic
177C2×C61—21no—
178C2×C61—21no—
179C2×C61#151911yescharacteristic
180C2×C61#212311yescharacteristic
181C2×C61C2×#35611yescharacteristic
182C2×C4⋊Q8—611no—
183C2×C4⋊Q8—1221no—
184C2×C4×Q8—611no—
185#431—1221no—
186#423—1221no—
187C2×#101—1221no—
188#398—611no—
189#398—611no—
190#398—611no—
191#398C2×D6111yescharacteristic
192#391—1221no—
193#389—1221no—
194#389—1221no—
195C4×C4⋊C4—611no—
196#343—611no—
197#343C2×D6111yescharacteristic
198#324—611no—
199#324—1221no—
200#324C2×D6111yescharacteristic
201C61#1188311yescharacteristic, complemented, Sylow
202C22×Q8—611no—
203C22×Q8—1221no—
204C2×M16—21no—
205C2×M16—1221no—
206C4⋊Q8—2441no—
207C4⋊Q8—2441no—
208C4⋊Q8—2442no—
209C4⋊Q8—2442no—
210C4×Q8—2441no—
211C4×Q8—2441no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—611no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4C4×D6111yescharacteristic
222C2×C4⋊C4C22×D6111yescharacteristic
223C2×C42—611no—
224C2×C42—611no—
225C2×C42—611no—
226C2×C42—1221no—
227C4⋊C8—2441no—
228C4⋊C8—2441no—
229C4⋊C8—2441no—
230#101—2442no—
231C22⋊C8—21no—
232C22⋊C8—1221no—
233C4×C8—2441no—
234#95—21no—
235#95—611no—
236#95—1221no—
237#95—1221no—
238#95—1221no—
239#95C4×D6111yescharacteristic
240C2×Q8—612no—
241C2×Q8—612no—
242C2×Q8—2441no—
243C2×Q8—2441no—
244C2×Q8—2442no—
245C2×Q8—2442no—
246C2×Q8—2442no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4C2×C4×D6111yescharacteristic
256C22×C4D4×D6111yescharacteristic
257C22×C4D4×D6111yescharacteristic
258M16—41no—
259M16—41no—
260M16—2441no—
261M16—2441no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—2441no—
265C2×C8—2441no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—1224no—
271C4⋊C4—2441no—
272C4⋊C4—2441no—
273C4⋊C4—2441no—
274C4⋊C4—2441no—
275C4⋊C4—2441no—
276C4⋊C4—2442no—
277C4⋊C4—2442no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C42—1221no—
281C42—1221no—
282C42—1221no—
283C42—1221no—
284C42—1221no—
285C42—1221no—
286C42—2442no—
287C23C22⋊C4×D6111yescharacteristic
288Q8—4884no—
289Q8—2442no—
290Q8—2442no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—611no—
304C2×C4—611no—
305C2×C4—612no—
306C2×C4—612no—
307C2×C4—1222no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1222no—
313C2×C4—1221no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4D8×D6111yescharacteristic
321C2×C4SD16×D6111yescharacteristic
322C8—81no—
323C8—81no—
324C8—4881no—
325C8—4881no—
326C22—21no—
327C22—21no—
328C22#99×D6111yescharacteristic
329C22#102×D6111yescharacteristic
330C22#1683977711yescharacteristic
331C4—21no—
332C4—21no—
333C4—42no—
334C4—41no—
335C4—41no—
336C4—81no—
337C4—612no—
338C4—1222no—
339C4—1222no—
340C4—1221no—
341C4—4881no—
342C4—2442no—
343C4—2441no—
344C2—21no—
345C2—21no—
346C2#2144438511yescharacteristic
347C2#2144747111yescharacteristic
348C2#356×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1346C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1346D61
hypocenterC61#11883
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

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

NH ≅ G/Ntype
201. C61#11883semidirect

Maximal subgroups

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

subgroupindex
#214508032
#214458142
#214441412
#214438262
#214438252
#214438242
C61×#13462
#1188361