Finite Group Databasebeta

← #29592902

Subgroups — #29592902

Order 15616.

412 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 59 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#21447172C211yesmaximal, characteristic, complemented
2#21444843C211yesmaximal, characteristic, complemented
3#21444741C211yesmaximal, characteristic
4#21443843C211yesmaximal, characteristic, complemented
5#21443816C211yesmaximal, characteristic
6#21443767C211yesmaximal, characteristic, complemented
7C61×#2826C211yesmaximal, characteristic
8#16840388C2211yescharacteristic
9#16840097—21no—
10#16839913—21no—
11#16839635—21no—
12#16839529C2211yescharacteristic
13#16839528—21no—
14#16839498—21no—
15#16839498—21no—
16#16839486C2211yescharacteristic
17#16839486C2211yescharacteristic
18C61×#400—21no—
19C61×#399C2211yescharacteristic
20C61×#397—21no—
21C61×#396—21no—
22C61×#394—21no—
23C61×#394—21no—
24C61×#392C2211yescharacteristic
25C61×#386—21no—
26C61×#385C2211yescharacteristic
27C2×#11758200—41no—
28#14519756—21no—
29#14519756—21no—
30#14519754—41no—
31#14519754—41no—
32C2×#11758196—41no—
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—21no—
35#14519710—41no—
36#14519700—41no—
37#14519698—41no—
38C22⋊#92418—21no—
39C22⋊#92418—21no—
40#14519684—41no—
41C22×D4×C61—21no—
42C22×D4×C61D411yescharacteristic
43C23×C4×C61D411yescharacteristic
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61D411yescharacteristic
48C2×C22⋊C4×C61—21no—
49C2×C22⋊C4×C61—21no—
50C2×C22⋊C4×C61—21no—
51C2×C22⋊C4×C61—21no—
52C2×C22⋊C4×C61—21no—
53C2×C22⋊C4×C61—21no—
54C2×C22⋊C4×C61D411yescharacteristic
55C2×C22⋊C4×C61C2311yescharacteristic
56#95×C61—21no—
57#95×C61—21no—
58#95×C61—21no—
59#95×C61—21no—
60#95×C61D411yescharacteristic
61#95×C61D411yescharacteristic
62C24×C61—21no—
63C24×C61C2×D411yescharacteristic
64C2×D4×C61—41no—
65C2×D4×C61—41no—
66C2×D4×C61—41no—
67C2×D4×C61—81no—
68C2×D4×C61—81no—
69C2×D4×C61—81no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61—41no—
76C22×C4×C61—81no—
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—41no—
82C2×Dic122—21no—
83C2×Dic122—21no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—81no—
86C4⋊C4×C61—81no—
87C4⋊C4×C61—81no—
88C22⋊C4×C61—21no—
89C22⋊C4×C61—21no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—81no—
92C22⋊C4×C61—81no—
93C22⋊C4×C61—81no—
94C22⋊C4×C61—81no—
95C22⋊C4×C61—81no—
96C22⋊C4×C61—81no—
97C22⋊Dic61—22no—
98C22⋊Dic61—41no—
99C22⋊Dic61—41no—
100C22⋊Dic61—41no—
101#11758200—82no—
102C4⋊Dic61—21no—
103C4⋊Dic61—21no—
104#11758196—41no—
105#11758196—41no—
106#11758196—82no—
107C2×#92418—41no—
108C2×#92418—41no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61#12011yescharacteristic
121C23×C61#13511yescharacteristic
122C23×C61#13711yescharacteristic
123D4×C61—42no—
124D4×C61—81no—
125D4×C61—82no—
126D4×C61—82no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
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—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—42no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—81no—
148C2×Dic61—42no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—81no—
152C2×Dic61—81no—
153C2×Dic61—81no—
154C2×Dic61—81no—
155Dic122—81no—
156Dic122—81no—
157#92418—81no—
158#92418—81no—
159#12231—611nomaximal, Sylow
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—81no—
169C22×C61—81no—
170C22×C61—81no—
171C22×C61—81no—
172C22×C61—81no—
173C22×C61—81no—
174C22×C61—81no—
175C22×C61—81no—
176C22×C61#45211yescharacteristic
177C22×C61#45611yescharacteristic
178C22×C61B(4,𝔽2)11yescharacteristic
179C4×C61—41no—
180C4×C61—41no—
181C4×C61—81no—
182C4×C61—81no—
183C4×C61—81no—
184C4×C61—81no—
185C4×C61—81no—
186Dic61—82no—
187Dic61—81no—
188Dic61—81no—
189#2826D6111yescharacteristic
190#2062—611no—
191#1614—611no—
192#1596—611no—
193#1352—611no—
194#1343—611no—
195#1326—611no—
196C2×C61—21no—
197C2×C61—21no—
198C2×C61—41no—
199C2×C61—41no—
200C2×C61—161no—
201C2×C61#160311yescharacteristic
202C2×C61#220011yescharacteristic
203C2×C61#220011yescharacteristic
204#543—611no—
205#484—1221no—
206#450—1221no—
207#400—21no—
208#399C2×D6111yescharacteristic
209#397—21no—
210#396—21no—
211#394—21no—
212#394—21no—
213#392C2×D6111yescharacteristic
214#386—21no—
215#385—1221no—
216#385C2×D6111yescharacteristic
217#342—611no—
218#342—1221no—
219#328—1221no—
220#328—1221no—
221#323—611no—
222#323—611no—
223C61#1223111yescharacteristic, complemented, Sylow
224C22×D4—21no—
225C22×D4C22⋊D6111yescharacteristic
226C23×C4C22⋊D6111yescharacteristic
227C2×SD16—2441no—
228C22⋊Q8—1221no—
229C22⋊Q8—1221no—
230C22⋊Q8—2441no—
231C22⋊Q8—2441no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—2441no—
236C2×C4⋊C4C22⋊D6111yescharacteristic
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4—1221no—
245C2×C22⋊C4C22⋊D6111yescharacteristic
246C2×C22⋊C4C22×D6111yescharacteristic
247#107—2441no—
248#103—2441no—
249#102—2441no—
250C22⋊C8—1221no—
251C22⋊C8—1221no—
252#95—21no—
253#95—21no—
254#95—21no—
255#95—21no—
256#95—2441no—
257#95C22⋊D6111yescharacteristic
258#95C22⋊D6111yescharacteristic
259C24—21no—
260C24C2×C22⋊D6111yescharacteristic
261C2×Q8—1221no—
262C2×Q8—1221no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—81no—
267C2×D4—81no—
268C2×D4—81no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—41no—
275C22×C4—81no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—2441no—
279C22×C4C2×C22⋊D6111yescharacteristic
280C22×C4C2×C22⋊D6111yescharacteristic
281SD16—4882no—
282C2×C8—2441no—
283C2×C8—2441no—
284C4⋊C4—41no—
285C4⋊C4—81no—
286C4⋊C4—81no—
287C4⋊C4—81no—
288C4⋊C4—1221no—
289C4⋊C4—1221no—
290C4⋊C4—4882no—
291C4⋊C4—2441no—
292C4⋊C4—2441no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—41no—
296C22⋊C4—81no—
297C22⋊C4—81no—
298C22⋊C4—81no—
299C22⋊C4—81no—
300C22⋊C4—81no—
301C22⋊C4—81no—
302C22⋊C4—1222no—
303C22⋊C4—2441no—
304C22⋊C4—2441no—
305C22⋊C4—2441no—
306C23—21no—
307C23—21no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23#1451974611yescharacteristic
318C23#1451979711yescharacteristic
319C23#1451980711yescharacteristic
320Q8—4881no—
321Q8—4881no—
322D4—42no—
323D4—81no—
324D4—82no—
325D4—82no—
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—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—81no—
347C2×C4—4881no—
348C2×C4—4881no—
349C2×C4—4881no—
350C2×C4—4881no—
351C2×C4—2442no—
352C2×C4—2441no—
353C2×C4—2441no—
354C8—4881no—
355C8—4881no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22#1683992411yescharacteristic
373C22#1683994511yescharacteristic
374C22#1683994911yescharacteristic
375C4—41no—
376C4—41no—
377C4—81no—
378C4—81no—
379C4—81no—
380C4—81no—
381C4—81no—
382C4—4882no—
383C4—4881no—
384C4—4881no—
385C2—21no—
386C2—21no—
387C2—41no—
388C2—41no—
389C2—161no—
390C2#2144478211yescharacteristic
391C2#2144782611yescharacteristic
392C2#2144782611yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C22⋊C4×C61C23
FrattiniC2×C22⋊C4C22×D61
FittingC61×#2826C2
socleC22×C61B(4,𝔽2)
prime radicalC61×#392C22
hypercenter#2826D61
hypocenterC61#12231
LCSG ▷ C2×C22⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2826

Complements

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

NH ≅ G/Ntype
1. #21447172C2semidirect
2. #21444843C2semidirect
4. #21443843C2semidirect
6. #21443767C2semidirect
223. C61#12231semidirect

Maximal subgroups

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

subgroupindex
#214471722
#214448432
#214447412
#214438432
#214438162
#214437672
C61×#28262
#1223161