Finite Group Databasebeta

← #29590226

Subgroups — #29590226

Order 15616.

452 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 83 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#21451587C211yesmaximal, characteristic
2#21445556C211yesmaximal, characteristic
3#21444132C211yesmaximal, characteristic
4#21443826C211yesmaximal, characteristic, complemented
5#21443825C211yesmaximal, characteristic, complemented
6#21443824C211yesmaximal, characteristic, complemented
7C61×#1346C211yesmaximal, characteristic, complemented
8C2×M16×D61—21no—
9C2×#14519776C411yescharacteristic
10C2×#14519755—21no—
11C2×#14519735C2211yescharacteristic
12#16839812—21no—
13#16839695—21no—
14#16839692C2211yescharacteristic
15#16839691—21no—
16#16839689C411yescharacteristic
17#16839688C411yescharacteristic
18#16839666—21no—
19#16839626C411yescharacteristic
20#16839531C2211yescharacteristic
21#16839530—21no—
22#16839488C2211yescharacteristic
23#16839485—21no—
24C61×#398C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122—21no—
28C22×C4×D61D411yescharacteristic
29C2×#11758194—21no—
30C2×#11758189—41no—
31M16×D61—24no—
32M16×D61—42no—
33C2×C8×D61—41no—
34#14519776—41no—
35#14519776—41no—
36#14519755—42no—
37#14519755—42no—
38#14519735—41no—
39#14519735—41no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×C4⋊Dic61D411yescharacteristic
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198C2×C411yescharacteristic
48C2×#11758198D411yescharacteristic
49C2×C4×Dic61C2×C411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51#14519706—41no—
52C22⋊#92418—21no—
53C8×Dic61—41no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58#14519684C2×C411yescharacteristic
59C2×M16×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61C2×C411yescharacteristic
62C2×C4⋊C4×C61C2311yescharacteristic
63C22⋊C8×C61—21no—
64#95×C61—21no—
65#95×C61C2×C411yescharacteristic
66C23×D61C22⋊C411yescharacteristic
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61C22×C411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C22⋊C411yescharacteristic
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—22no—
80C2×C4×D61D812yes—
81C2×C4×D61SD1612yes—
82C2×Dic122—41no—
83C2×Dic122—41no—
84C2×Dic122—42no—
85C2×Dic122—42no—
86M16×C61—22no—
87M16×C61—41no—
88C2×C8×C61—41no—
89C2×C8×C61—41no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94#11758198—41no—
95#11758198—41no—
96#11758198—42no—
97#11758198—42no—
98C4⋊Dic61—41no—
99C4⋊Dic61—41no—
100#11758196—42no—
101#11758196—41no—
102#11758196—41no—
103#11758196—42no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108#11758194—22no—
109#11758194—41no—
110C2×#92418—41no—
111C2×#92418—41no—
112#11758189—44no—
113C8×D61—44no—
114C23×C61C2×C22⋊C411yescharacteristic
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61#10212yes—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61C2×D811yescharacteristic
133C2×C4×C61C2×SD1611yescharacteristic
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61#9911yescharacteristic
145C2×Dic61#9911yescharacteristic
146C2×Dic61#10212yes—
147C2×Dic61#10412yes—
148C4×D61—22no—
149C4×D61—22no—
150C4×D61—22no—
151C4×D61—22no—
152Dic122—82no—
153Dic122—82no—
154C8×C61—42no—
155C8×C61—81no—
156#92418—42no—
157#92418—81no—
158#11700—611nomaximal, Sylow
159C22×C61—21no—
160C22×C61—21no—
161C22×C61C2×#9911yescharacteristic
162C22×C61C2×#10211yescharacteristic
163C22×C61C2×#10411yescharacteristic
164C2×D61—22no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—42no—
168C2×D61—81no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—41no—
172C4×C61—41no—
173C4×C61—81no—
174C4×C61—81no—
175Dic61—41no—
176Dic61—41no—
177Dic61—81no—
178Dic61—81no—
179Dic61#32712yes—
180Dic61#32712yes—
181#2621—611no—
182#1742—611no—
183#1458—611no—
184#1346—611no—
185#1346—611no—
186#1346—611no—
187#1346D6111yescharacteristic, complemented
188C2×C61—21no—
189C2×C61—21no—
190C2×C61C2×#32711yescharacteristic
191C2×C61#212311yescharacteristic
192C2×C61#213511yescharacteristic
193D61—42no—
194C22×M16—1221no—
195C2×C4⋊Q8—611no—
196C2×C22⋊Q8—1221no—
197C2×#117—611no—
198#431—1221no—
199#398—611no—
200#398—1221no—
201#398C2×D6111yescharacteristic
202#397—611no—
203#397—611no—
204#397—1221no—
205#391—1221no—
206#382—611no—
207#343—611no—
208#343—1221no—
209#343C2×D6111yescharacteristic
210#324—611no—
211#324C2×D6111yescharacteristic
212#323—1221no—
213C61#1170011yescharacteristic, complemented, Sylow
214C22×Q8—1221no—
215C23×C4—611no—
216C2×M16—21no—
217C2×M16—1224no—
218C2×M16—1221no—
219C2×M16—2441no—
220C2×M16—2442no—
221C22×C8—2441no—
222C4⋊Q8—2441no—
223C4⋊Q8—2441no—
224C22⋊Q8—2442no—
225C22⋊Q8—2442no—
226#117—2441no—
227#117—2441no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—611no—
230C2×C4⋊C4—611no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4—1221no—
234C2×C4⋊C4C4×D6111yescharacteristic
235C2×C4⋊C4C22×D6111yescharacteristic
236C2×C22⋊C4—611no—
237C2×C22⋊C4—611no—
238C2×C22⋊C4—1221no—
239C2×C22⋊C4—1221no—
240C2×C42—611no—
241C2×C42—611no—
242C4⋊C8—2441no—
243C22⋊C8—21no—
244C22⋊C8—1221no—
245C4×C8—2441no—
246#95—21no—
247#95—611no—
248#95—1221no—
249#95—1221no—
250#95—1221no—
251#95—1221no—
252#95C4×D6111yescharacteristic
253C24—611no—
254C2×Q8—2442no—
255C2×Q8—2441no—
256C2×Q8—2441no—
257C2×Q8—2442no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—611no—
261C22×C4—612no—
262C22×C4—612no—
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1222no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4C2×C4×D6111yescharacteristic
271C22×C4D4×D6111yescharacteristic
272C22×C4D4×D6111yescharacteristic
273M16—22no—
274M16—41no—
275M16—1222no—
276M16—2444no—
277M16—2441no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—2444no—
281C2×C8—2441no—
282C2×C8—2441no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—2441no—
288C4⋊C4—2441no—
289C4⋊C4—2442no—
290C4⋊C4—2442no—
291C4⋊C4—2441no—
292C4⋊C4—2441no—
293C22⋊C4—2441no—
294C22⋊C4—2441no—
295C22⋊C4—2442no—
296C22⋊C4—2442no—
297C42—1221no—
298C42—1221no—
299C42—1221no—
300C42—1221no—
301C23—612no—
302C23—1221no—
303C23—1221no—
304C23—2441no—
305C23—2441no—
306C23C22⋊C4×D6111yescharacteristic
307Q8—4882no—
308Q8—4882no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—611no—
322C2×C4—611no—
323C2×C4—612no—
324C2×C4—612no—
325C2×C4—1222no—
326C2×C4—1222no—
327C2×C4—1222no—
328C2×C4—1222no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4D8×D6111yescharacteristic
340C2×C4SD16×D6111yescharacteristic
341C8—42no—
342C8—81no—
343C8—4881no—
344C8—2442no—
345C22—21no—
346C22—21no—
347C22—1222no—
348C22—4881no—
349C22—2442no—
350C22—2441no—
351C22—2441no—
352C22#99×D6111yescharacteristic
353C22#102×D6111yescharacteristic
354C22#104×D6111yescharacteristic
355C4—21no—
356C4—21no—
357C4—41no—
358C4—41no—
359C4—81no—
360C4—81no—
361C4—612no—
362C4—612no—
363C4—4881no—
364C4—4881no—
365C4—2441no—
366C4—2441no—
367C2—21no—
368C2—21no—
369C2—2442no—
370C2#327×D6111yescharacteristic
371C2#2144747111yescharacteristic
372C2#2144751211yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1346C2
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1346D61
hypocenterC61#11700
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
4. #21443826C2semidirect
5. #21443825C2semidirect
6. #21443824C2semidirect
7. C61×#1346C2semidirect
187. #1346D61semidirect
213. C61#11700semidirect

Maximal subgroups

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

subgroupindex
#214515872
#214455562
#214441322
#214438262
#214438252
#214438242
C61×#13462
#1170061