Finite Group Databasebeta

← #29590910

Subgroups — #29590910

Order 15616.

432 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 69 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#21451388C211yesmaximal, characteristic
2#21445901C211yesmaximal, characteristic, complemented
3#21444132C211yesmaximal, characteristic, complemented
4#21443846C211yesmaximal, characteristic, complemented
5#21443823C211yesmaximal, characteristic, complemented
6#21443821C211yesmaximal, characteristic, complemented
7C61×#1353C211yesmaximal, characteristic, complemented
8C2×#14519739C411yescharacteristic
9C2×#14519735C2211yescharacteristic
10#16839812—21no—
11#16839725—21no—
12#16839697C411yescharacteristic
13#16839679C2211yescharacteristic
14#16839672C411yescharacteristic
15#16839651—21no—
16#16839640—21no—
17#16839640—21no—
18#16839636—21no—
19#16839629C411yescharacteristic
20#16839531C2211yescharacteristic
21#16839530—21no—
22#16839488C2211yescharacteristic
23#16839485—21no—
24C61×#400C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×D244—21no—
28C22×D244C2×C411yescharacteristic
29C22×C4×D61—21no—
30C22×C4×D61D411yescharacteristic
31C2×#11758194—21no—
32#14519739—41no—
33#14519739—41no—
34#14519735—41no—
35#14519735—41no—
36C2×C4⋊Dic61D411yescharacteristic
37C2×#11758196—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198C2×C411yescharacteristic
44C2×#11758198D411yescharacteristic
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47#14519706—41no—
48C22⋊#92418—21no—
49#14519689—41no—
50#14519689—41no—
51C8×Dic61—41no—
52#14519684—21no—
53#14519684—21no—
54#14519684C2×C411yescharacteristic
55C2×M16×C61—21no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C4⋊C4×C61C2311yescharacteristic
58C22⋊C8×C61—21no—
59#95×C61—21no—
60#95×C61—21no—
61#95×C61C2×C411yescharacteristic
62C23×D61—21no—
63C23×D61C22⋊C411yescharacteristic
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C22×C411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×Dic61—21no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C2×D244—41no—
74C2×D244—42no—
75C2×D244—42no—
76C2×D244—42no—
77C2×D244—81no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—41no—
83C2×C4×D61—42no—
84C2×C4×D61—81no—
85C2×C4×D61—81no—
86M16×C61—41no—
87M16×C61—41no—
88C2×C8×C61—41no—
89C2×C8×C61—41no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—41no—
92#11758198—41no—
93#11758198—41no—
94#11758198—42no—
95#11758198—41no—
96#11758198—41no—
97#11758198—41no—
98#11758198—41no—
99#11758198—81no—
100#11758198—81no—
101C4⋊Dic61—41no—
102#11758196—81no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107#11758194—41no—
108#11758194—41no—
109C2×#92418—41no—
110C2×#92418—41no—
111C23×C61C2×C22⋊C411yescharacteristic
112C22×D61—22no—
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61#13511yescharacteristic
137C2×C4×C61#13511yescharacteristic
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61#9911yescharacteristic
148C2×Dic61#9911yescharacteristic
149D244—42no—
150D244—42no—
151D244—84no—
152C4×D61—41no—
153C4×D61—41no—
154C4×D61—41no—
155C4×D61—41no—
156C4×D61—84no—
157C8×C61—81no—
158C8×C61—81no—
159#92418—81no—
160#92418—81no—
161#11847—611nomaximal, Sylow
162C22×C61—21no—
163C22×C61—21no—
164C22×C61C2×#9911yescharacteristic
165C22×C61#41611yescharacteristic
166C22×C61#42111yescharacteristic
167C2×D61—42no—
168C2×D61—42no—
169C2×D61—42no—
170C2×D61—42no—
171C2×D61—41no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—81no—
175C2×D61—81no—
176C2×D61—81no—
177C2×D61—81no—
178C2×D61—81no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—41no—
182C4×C61—41no—
183C4×C61—81no—
184C4×C61—81no—
185Dic61—21no—
186Dic61—21no—
187Dic61—41no—
188Dic61—41no—
189Dic61—81no—
190#2598—611no—
191#1822—611no—
192#1458—611no—
193#1353—611no—
194#1353D6111yescharacteristic, complemented
195#1345—611no—
196#1345—611no—
197C2×C61—21no—
198C2×C61—21no—
199C2×C61#151611yescharacteristic
200C2×C61#212011yescharacteristic
201C2×C61#213411yescharacteristic
202D61—81no—
203D61—82no—
204C2×C4×D4—611no—
205C2×#117—611no—
206#431—1221no—
207#407—1221no—
208#400C2×D6111yescharacteristic
209#399—611no—
210#394—611no—
211#392—611no—
212#388—1221no—
213#386—1221no—
214#386—1221no—
215#385—1221no—
216#383—611no—
217#343—611no—
218#343—1221no—
219#343C2×D6111yescharacteristic
220#324—611no—
221#324C2×D6111yescharacteristic
222#323—1221no—
223C61#1184711yescharacteristic, complemented, Sylow
224C22×D4—611no—
225C22×D4—1221no—
226C23×C4—611no—
227C23×C4—1221no—
228C2×M16—21no—
229C2×M16—1221no—
230C4×D4—2441no—
231C4×D4—2441no—
232#117—2441no—
233#117—2441no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4C4×D6111yescharacteristic
237C2×C4⋊C4C22×D6111yescharacteristic
238C2×C22⋊C4—611no—
239C2×C22⋊C4—611no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4—1221no—
245C2×C42—611no—
246C2×C42—611no—
247C4⋊C8—2441no—
248C22⋊C8—21no—
249C22⋊C8—1221no—
250C22⋊C8—2441no—
251C22⋊C8—2441no—
252C4×C8—2441no—
253#95—21no—
254#95—21no—
255#95—611no—
256#95—1221no—
257#95—1221no—
258#95C4×D6111yescharacteristic
259C24—611no—
260C24—1221no—
261C2×D4—4881no—
262C2×D4—2441no—
263C2×D4—2442no—
264C2×D4—2442no—
265C2×D4—2442no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—4881no—
277C22×C4—4881no—
278C22×C4—2441no—
279C22×C4—2442no—
280C22×C4C2×C4×D6111yescharacteristic
281C22×C4D4×D6111yescharacteristic
282C22×C4D4×D6111yescharacteristic
283M16—41no—
284M16—41no—
285M16—2441no—
286M16—2441no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—2441no—
290C2×C8—2441no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—4881no—
294C4⋊C4—2441no—
295C22⋊C4—4881no—
296C22⋊C4—4881no—
297C22⋊C4—2441no—
298C22⋊C4—2441no—
299C22⋊C4—2441no—
300C22⋊C4—2441no—
301C22⋊C4—2442no—
302C22⋊C4—2441no—
303C22⋊C4—2441no—
304C42—1221no—
305C42—1221no—
306C42—1221no—
307C42—1221no—
308C23—1222no—
309C23—1221no—
310C23—1221no—
311C23—1221no—
312C23—2441no—
313C23—2441no—
314C23—2441no—
315C23—2441no—
316C23—2441no—
317C23—2441no—
318C23—2441no—
319C23—2441no—
320C23C22⋊C4×D6111yescharacteristic
321D4—4884no—
322D4—2442no—
323D4—2442no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—611no—
337C2×C4—611no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—4884no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4#1451979811yescharacteristic
353C2×C4#1451980011yescharacteristic
354C8—81no—
355C8—81no—
356C8—4881no—
357C8—4881no—
358C22—21no—
359C22—21no—
360C22—4881no—
361C22—4881no—
362C22—4881no—
363C22—4881no—
364C22—4881no—
365C22—2442no—
366C22—2442no—
367C22—2442no—
368C22—2441no—
369C22—2442no—
370C22—2441no—
371C22—2441no—
372C22#99×D6111yescharacteristic
373C22#1683975711yescharacteristic
374C22#1683977711yescharacteristic
375C4—21no—
376C4—21no—
377C4—41no—
378C4—41no—
379C4—81no—
380C4—81no—
381C4—1221no—
382C4—1221no—
383C4—4881no—
384C4—2441no—
385C4—2441no—
386C2—21no—
387C2—21no—
388C2—4882no—
389C2—4881no—
390C2#2144437411yescharacteristic
391C2#2144745911yescharacteristic
392C2#2144750911yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1353C2
socleC22×C61C2×#99
prime radical#16839672C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1353D61
hypocenterC61#11847
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1353

Complements

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

NH ≅ G/Ntype
2. #21445901C2semidirect
3. #21444132C2semidirect
4. #21443846C2semidirect
5. #21443823C2semidirect
6. #21443821C2semidirect
7. C61×#1353C2semidirect
194. #1353D61semidirect
223. C61#11847semidirect

Maximal subgroups

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

subgroupindex
#214513882
#214459012
#214441322
#214438462
#214438232
#214438212
C61×#13532
#1184761