Finite Group Databasebeta

← #29600431

Subgroups — #29600431

Order 15616.

304 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 57 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#21456895C211yesmaximal, characteristic
2#21447512C211yesmaximal, characteristic
3#21447507C211yesmaximal, characteristic
4#21443991C211yesmaximal, characteristic, complemented
5#21443991C211yesmaximal, characteristic, complemented
6#21443988C211yesmaximal, characteristic, complemented
7C61×#1411C211yesmaximal, characteristic, complemented
8#16840373C411yescharacteristic
9#16840337C2211yescharacteristic
10#16840154C411yescharacteristic
11#16840130C2211yescharacteristic
12#16840117C411yescharacteristic
13#16839986—21no—
14#16839970—21no—
15#16839923—21no—
16#16839916—21no—
17#16839821C411yescharacteristic
18#16839745—21no—
19#101×D61—21no—
20#16839561C2211yescharacteristic
21#16839561C2211yescharacteristic
22#16839560—21no—
23#16839558—21no—
24C61×#494C2211yescharacteristic
25C61×#356C2211yescharacteristic
26C61×#356C2211yescharacteristic
27C2×#11758226D411yescharacteristic
28C2×Q8×D61D411yescharacteristic
29C2×#11758202—21no—
30C2×#11758201—21no—
31M16×D61—41no—
32M16×D61—41no—
33#14519775D411yescharacteristic
34#14519772—41no—
35#14519769C2×C411yescharacteristic
36#14519767—41no—
37#14519766D411yescharacteristic
38#14519765C2×C411yescharacteristic
39#14519762—41no—
40#14519755—41no—
41#14519753—21no—
42Q8×Dic61—21no—
43#14519734C2×C411yescharacteristic
44#14519706—21no—
45#14519702—21no—
46#14519701—21no—
47#14519701—21no—
48#14519699—21no—
49#14519696—21no—
50#14519696—21no—
51#14519695—41no—
52#14519693—41no—
53#14519689—21no—
54#14519688C2×C411yescharacteristic
55C2×Q16×C61—21no—
56C2×Q16×C61—21no—
57C4⋊Q8×C61C2×C411yescharacteristic
58C4⋊Q8×C61C2311yescharacteristic
59#101×C61—21no—
60#101×C61—21no—
61C4×C8×C61C2×C411yescharacteristic
62C2×Q8×C61—21no—
63C2×Q8×C61C2×D411yescharacteristic
64C2×Q8×C61C2×D411yescharacteristic
65#11758226—81no—
66Q8×D61—81no—
67C2×D244—21no—
68C2×D244C22⋊C411yescharacteristic
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61C22⋊C411yescharacteristic
72C2×Dic122—21no—
73C2×Dic122C22⋊C411yescharacteristic
74Q16×C61—81no—
75Q16×C61—81no—
76M16×C61—41no—
77M16×C61—41no—
78C2×C8×C61—21no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C42×C61C22×C411yescharacteristic
82#11758202—81no—
83#11758201—81no—
84#11758198—21no—
85#11758198—41no—
86#11758198—41no—
87#11758198—41no—
88C4⋊Dic61—21no—
89C4⋊Dic61—41no—
90#11758196—21no—
91#11758196—41no—
92#11758196—41no—
93#11758196—41no—
94C4×Dic61—41no—
95C4×Dic61C22⋊C411yescharacteristic
96#11758194—41no—
97#11758194—41no—
98C2×#92418—21no—
99#11758189—81no—
100#11758189—81no—
101C8×D61—81no—
102C8×D61—81no—
103C22×D61—21no—
104C22×D61#9911yescharacteristic
105Q8×C61—41no—
106Q8×C61—41no—
107Q8×C61—41no—
108Q8×C61—41no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—41no—
113C2×C4×C61C2×C22⋊C411yescharacteristic
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—41no—
117C2×Dic61#9911yescharacteristic
118D244—41no—
119D244—81no—
120C4×D61—41no—
121C4×D61—41no—
122C4×D61—41no—
123C4×D61—41no—
124C4×D61—41no—
125Dic122—41no—
126Dic122—81no—
127C8×C61—41no—
128C8×C61—81no—
129C8×C61—81no—
130#92418—41no—
131#92418—81no—
132#92418—81no—
133#13612—611nomaximal, Sylow
134C22×C61C2×#9911yescharacteristic
135C2×D61—21no—
136C2×D61—41no—
137C2×D61—41no—
138C2×D61—81no—
139C4×C61—21no—
140C4×C61—41no—
141C4×C61—41no—
142C4×C61—41no—
143C4×C61—81no—
144Dic61—21no—
145Dic61—41no—
146Dic61—41no—
147Dic61—81no—
148#3223—611no—
149#2135—611no—
150#2133—611no—
151#1413—611no—
152#1413—611no—
153#1411—611no—
154#1411D6111yescharacteristic, complemented
155C2×C61—21no—
156C2×C61#212711yescharacteristic
157D61—41no—
158D61—81no—
159#541—611no—
160#536—611no—
161#497—611no—
162#494C2×D6111yescharacteristic
163#491—611no—
164#488—611no—
165#464—1221no—
166#462—1221no—
167#452—1221no—
168#451—1221no—
169#433—611no—
170#413—1221no—
171C2×#101—1221no—
172#356—611no—
173#356—611no—
174#356—1221no—
175#356C2×D6111yescharacteristic
176#356C2×D6111yescharacteristic
177#355—1221no—
178C61#1361211yescharacteristic, complemented, Sylow
179C2×#41—611no—
180C22×Q8—611no—
181C2×Q16—21no—
182C2×Q16—21no—
183C2×Q16—1221no—
184C2×SD16—1221no—
185C2×M16—2441no—
186C2×M16—2441no—
187C4⋊Q8—611no—
188C4⋊Q8C4×D6111yescharacteristic
189C4⋊Q8C22×D6111yescharacteristic
190#126—2441no—
191#125—611no—
192#125—2441no—
193#124—611no—
194#124—611no—
195#123—2441no—
196C22⋊Q8—1221no—
197C22⋊Q8—2441no—
198C4×Q8—1221no—
199#117—611no—
200C4⋊C8—1221no—
201#103—1221no—
202#103—1221no—
203#103—1221no—
204#102—1221no—
205#101—21no—
206#101—21no—
207#101—1221no—
208#101—1221no—
209#101—2441no—
210#100—2441no—
211C22⋊C8—1221no—
212#97—611no—
213C4×C8C4×D6111yescharacteristic
214#41—4881no—
215C2×Q8—21no—
216C2×Q8—611no—
217C2×Q8—1221no—
218C2×Q8—4881no—
219C2×Q8D4×D6111yescharacteristic
220C2×Q8D4×D6111yescharacteristic
221C2×D4—611no—
222C2×D4—1221no—
223C22×C4—611no—
224C22×C4—1221no—
225C22×C4—1221no—
226Q16—81no—
227Q16—81no—
228Q16—4881no—
229SD16—4881no—
230M16—41no—
231M16—41no—
232M16—4881no—
233M16—4881no—
234M16—2441no—
235M16—2441no—
236C2×C8—21no—
237C2×C8—1221no—
238C2×C8—4881no—
239C2×C8—4881no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—1221no—
243C4⋊C4—1221no—
244C4⋊C4—2441no—
245C4⋊C4—2441no—
246C4⋊C4—2441no—
247C4⋊C4—2441no—
248C22⋊C4—1221no—
249C22⋊C4—2441no—
250C22⋊C4—2441no—
251C22⋊C4—2441no—
252C42—611no—
253C42—2441no—
254C42C2×C4×D6111yescharacteristic
255C23—611no—
256C23—1221no—
257Q8—41no—
258Q8—41no—
259Q8—41no—
260Q8—41no—
261Q8—4881no—
262Q8—2441no—
263D4—4881no—
264D4—2441no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—611no—
270C2×C4—1221no—
271C2×C4—1221no—
272C2×C4—2441no—
273C2×C4—2441no—
274C2×C4—2441no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4C22⋊C4×D6111yescharacteristic
279C8—41no—
280C8—81no—
281C8—81no—
282C8—4881no—
283C8—4881no—
284C8—2441no—
285C22—1221no—
286C22—4881no—
287C22—2441no—
288C22—2441no—
289C22#99×D6111yescharacteristic
290C4—21no—
291C4—41no—
292C4—41no—
293C4—41no—
294C4—81no—
295C4—1221no—
296C4—4881no—
297C4—2441no—
298C4—2441no—
299C2—21no—
300C2—4881no—
301C2—2441no—
302C2#2144748511yescharacteristic
subgroupG/H
centerC2#21447485
commutatorC42×C61C22×C4
FrattiniC4⋊Q8C22×D61
FittingC61×#1411C2
socleC2×C61#2127
prime radicalC2×#11758226D4
cosocleC4⋊Q8×C61C23
hypercenter#1411D61
hypocenterC61#13612
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #1411

Complements

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

NH ≅ G/Ntype
4. #21443991C2semidirect
5. #21443991C2semidirect
6. #21443988C2semidirect
7. C61×#1411C2semidirect
154. #1411D61semidirect
178. C61#13612semidirect

Maximal subgroups

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

subgroupindex
#214568952
#214475122
#214475072
#214439912
#214439882
C61×#14112
#1361261