Finite Group Databasebeta

← #29589654

Subgroups — #29589654

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#21450809C211yesmaximal, characteristic
2#21444161C211yesmaximal, characteristic
3#21444141C211yesmaximal, characteristic
4#21443753C211yesmaximal, characteristic
5#21443752C211yesmaximal, characteristic
6#21443752C211yesmaximal, characteristic
7C61×#1319C211yesmaximal, characteristic
8C2×#14519777C411yescharacteristic
9C2×#14519775C411yescharacteristic
10C2×#14519775C411yescharacteristic
11C2×#14519742C2211yescharacteristic
12#16839816—21no—
13#16839812—21no—
14#16839696—21no—
15#16839696—21no—
16#16839667C2211yescharacteristic
17#16839659—21no—
18#16839659—21no—
19C4×#11758196C411yescharacteristic
20#16839488C2211yescharacteristic
21#16839488C2211yescharacteristic
22#16839487—21no—
23#16839487—21no—
24C61×#391C2211yescharacteristic
25C61×#324C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C22×Dic122C2×C411yescharacteristic
29#14519777—42no—
30#14519775—41no—
31#14519775—41no—
32#14519775—42no—
33#14519742—41no—
34#14519742—41no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196D411yescharacteristic
43C2×#11758196D411yescharacteristic
44C2×C4×Dic61C2×C411yescharacteristic
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48#14519706—41no—
49#14519706—41no—
50C22⋊#92418—21no—
51C22⋊#92418—21no—
52#14519687—41no—
53C8×Dic61—41no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57C22×Q8×C61C2×C411yescharacteristic
58C2×C4⋊C4×C61C2311yescharacteristic
59C2×C42×C61C2×C411yescharacteristic
60C22⋊C8×C61—21no—
61C22⋊C8×C61—21no—
62#95×C61—21no—
63#95×C61—21no—
64C2×Q8×C61—21no—
65C2×Q8×C61—21no—
66C2×Q8×C61—41no—
67C2×Q8×C61—41no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79C2×Dic122—21no—
80C2×Dic122—21no—
81C2×Dic122—22no—
82C2×Dic122—21no—
83C2×Dic122—21no—
84C2×Dic122—41no—
85C2×Dic122—41no—
86C2×Dic122—41no—
87C2×C8×C61—41no—
88C2×C8×C61—41no—
89C4⋊C4×C61—41no—
90C42×C61—41no—
91C4⋊Dic61—42no—
92C4⋊Dic61—42no—
93#11758196—24no—
94#11758196—41no—
95#11758196—41no—
96#11758196—42no—
97#11758196—42no—
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—41no—
108C2×#92418—41no—
109C2×#92418—41no—
110C23×C61C2×C22⋊C411yescharacteristic
111Q8×C61—81no—
112Q8×C61—81no—
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×C61#13111yescharacteristic
126C2×C4×C61#13111yescharacteristic
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—22no—
130C2×Dic61—22no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61#9911yescharacteristic
142C2×Dic61#9911yescharacteristic
143C2×Dic61#10012yes—
144Dic122—42no—
145Dic122—42no—
146Dic122—81no—
147Dic122—81no—
148C8×C61—81no—
149C8×C61—81no—
150#92418—81no—
151#92418—81no—
152#11568—611nomaximal, Sylow
153C22×C61—21no—
154C22×C61—21no—
155C22×C61#40811yescharacteristic
156C22×C61C2×#9911yescharacteristic
157C22×C61C2×#10011yescharacteristic
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—42no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61—81no—
164Dic61—21no—
165Dic61—22no—
166Dic61—42no—
167Dic61—41no—
168Dic61—41no—
169Dic61—81no—
170Dic61#35612yes—
171#2546—611no—
172#1467—611no—
173#1461—611no—
174#1319—611no—
175#1319—611no—
176#1319—611no—
177#1319D6111yescharacteristic
178C2×C61—21no—
179C2×C61—21no—
180C2×C61#147111yescharacteristic
181C2×C61#212911yescharacteristic
182C2×C61C2×#35611yescharacteristic
183C2×C4⋊Q8—611no—
184C2×C4⋊Q8—611no—
185C2×C4⋊Q8—611no—
186C2×C4×Q8—611no—
187#432—1221no—
188#431—1221no—
189#398—1221no—
190#398—1221no—
191#391—611no—
192#391C2×D6111yescharacteristic
193#389—1221no—
194#389—1221no—
195C4×C4⋊C4—611no—
196#324—611no—
197#324—611no—
198#324—1221no—
199#324—1221no—
200#324C2×D6111yescharacteristic
201#324C2×D6111yescharacteristic
202C61#1156811yescharacteristic, complemented, Sylow
203C22×Q8—611no—
204C22×Q8—611no—
205C22×Q8C4×D6111yescharacteristic
206C4⋊Q8—2442no—
207C4⋊Q8—2441no—
208C4⋊Q8—2441no—
209C4⋊Q8—2442no—
210C4×Q8—2441no—
211C4×Q8—2441no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4C22×D6111yescharacteristic
222C2×C42—611no—
223C2×C42—611no—
224C2×C42—611no—
225C2×C42—611no—
226C2×C42C4×D6111yescharacteristic
227C4⋊C8—2441no—
228C4⋊C8—2441no—
229C22⋊C8—21no—
230C22⋊C8—21no—
231C22⋊C8—1221no—
232C22⋊C8—1221no—
233#97—2441no—
234C4×C8—2441no—
235#95—21no—
236#95—21no—
237#95—1221no—
238#95—1221no—
239#95—1221no—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—1222no—
245C2×Q8—1221no—
246C2×Q8—1221no—
247C2×Q8—1221no—
248C2×Q8—1221no—
249C2×Q8—2441no—
250C2×Q8—2441no—
251C2×Q8—2441no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—611no—
255C22×C4—611no—
256C22×C4—611no—
257C22×C4—611no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4C2×C4×D6111yescharacteristic
261C22×C4D4×D6111yescharacteristic
262C22×C4D4×D6111yescharacteristic
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—2441no—
266C2×C8—2441no—
267C4⋊C4—41no—
268C4⋊C4—1224no—
269C4⋊C4—2441no—
270C4⋊C4—2441no—
271C4⋊C4—2441no—
272C4⋊C4—2441no—
273C4⋊C4—2442no—
274C4⋊C4—2442no—
275C4⋊C4—2442no—
276C4⋊C4—2442no—
277C4⋊C4—2442no—
278C42—41no—
279C42—1221no—
280C42—1221no—
281C42—1221no—
282C42—1221no—
283C42—1221no—
284C42—1221no—
285C42—2441no—
286C23C22⋊C4×D6111yescharacteristic
287Q8—81no—
288Q8—81no—
289Q8—4881no—
290Q8—4881no—
291Q8—2442no—
292Q8—2442no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—611no—
306C2×C4—611no—
307C2×C4—612no—
308C2×C4—1222no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1222no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4#1451978311yescharacteristic
323C2×C4#1451978511yescharacteristic
324C8—81no—
325C8—81no—
326C8—4881no—
327C8—4881no—
328C22—21no—
329C22—21no—
330C22#1683972711yescharacteristic
331C22#99×D6111yescharacteristic
332C22#100×D6111yescharacteristic
333C4—21no—
334C4—21no—
335C4—42no—
336C4—41no—
337C4—41no—
338C4—81no—
339C4—612no—
340C4—1221no—
341C4—1222no—
342C4—4881no—
343C4—2442no—
344C4—2441no—
345C4—2441no—
346C2—21no—
347C2—21no—
348C2#2144417711yescharacteristic
349C2#2144749211yescharacteristic
350C2#356×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1319C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1319D61
hypocenterC61#11568
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
202. C61#11568semidirect

Maximal subgroups

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

subgroupindex
#214508092
#214441612
#214441412
#214437532
#214437522
C61×#13192
#1156861