Finite Group Databasebeta

← #29593194

Subgroups — #29593194

Order 15616.

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

normal subgroups only

This group has 372 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#21446980C211yesmaximal, characteristic, complemented
2#21444792C211yesmaximal, characteristic, complemented
3#21444758C211yesmaximal, characteristic
4#21443849C211yesmaximal, characteristic, complemented
5#21443822C211yesmaximal, characteristic
6#21443753C211yesmaximal, characteristic, complemented
7C61×#2832C211yesmaximal, characteristic
8#16840393C2211yescharacteristic
9#16839918—21no—
10#16839913—21no—
11#16839771—21no—
12#16839531C2211yescharacteristic
13#16839522—21no—
14#16839498—21no—
15#16839498—21no—
16#16839488C2211yescharacteristic
17#16839488C2211yescharacteristic
18C61×#400—21no—
19C61×#397—21no—
20C61×#395C2211yescharacteristic
21C61×#394—21no—
22C61×#394C2211yescharacteristic
23C61×#393—21no—
24C61×#393—21no—
25C61×#391C2211yescharacteristic
26C61×#388—21no—
27C2×#11758202—41no—
28C2×#11758200—41no—
29C2×#11758194—21no—
30#14519776—41no—
31#14519768—41no—
32#14519756—21no—
33#14519756—21no—
34#14519736—21no—
35#14519701—41no—
36#14519701—41no—
37#14519701—41no—
38#14519698—41no—
39C22⋊#92418—21no—
40C22⋊#92418—21no—
41C22×Q8×C61D411yescharacteristic
42C22×Q8×C61D411yescharacteristic
43C22×D4×C61D411yescharacteristic
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61C2311yescharacteristic
47C2×C22⋊C4×C61—21no—
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×C42×C61D411yescharacteristic
54#95×C61—21no—
55#95×C61—21no—
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—
63C2×Q8×C61—21no—
64C2×Q8×C61—21no—
65C2×Q8×C61—41no—
66C2×Q8×C61—41no—
67C2×Q8×C61—41no—
68C2×Q8×C61—81no—
69C2×D4×C61—41no—
70C2×D4×C61—81no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C2×Dic122—21no—
80C2×Dic122—21no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—81no—
83C4⋊C4×C61—81no—
84C22⋊C4×C61—41no—
85C22⋊C4×C61—41no—
86C22⋊C4×C61—81no—
87C22⋊C4×C61—81no—
88C22⋊C4×C61—81no—
89C22⋊C4×C61—81no—
90C22⋊C4×C61—81no—
91C42×C61—41no—
92C22⋊Dic61—41no—
93#11758202—82no—
94#11758200—82no—
95C4⋊Dic61—21no—
96C4⋊Dic61—21no—
97C4⋊Dic61—21no—
98C4⋊Dic61—21no—
99#11758196—41no—
100#11758196—41no—
101C4×Dic61—41no—
102#11758194—41no—
103#11758194—41no—
104C2×#92418—41no—
105C2×#92418—41no—
106C2×#92418—41no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61#12011yescharacteristic
115Q8×C61—42no—
116Q8×C61—42no—
117Q8×C61—81no—
118Q8×C61—81no—
119D4×C61—42no—
120D4×C61—81no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
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×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—41no—
142C2×C4×C61#13511yescharacteristic
143C2×C4×C61#13711yescharacteristic
144C2×Dic61—41no—
145C2×Dic61—41no—
146Dic122—81no—
147Dic122—81no—
148#92418—81no—
149#92418—81no—
150#92418—81no—
151#12275—611nomaximal, Sylow
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—81no—
155C22×C61—81no—
156C22×C61—81no—
157C22×C61—81no—
158C22×C61—81no—
159C22×C61—81no—
160C22×C61—81no—
161C22×C61#45211yescharacteristic
162C22×C61#45511yescharacteristic
163C22×C61B(4,𝔽2)11yescharacteristic
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61—81no—
169C4×C61—81no—
170C4×C61—81no—
171C4×C61—81no—
172C4×C61—81no—
173Dic61—81no—
174Dic61—81no—
175#2832D6111yescharacteristic
176#2028—611no—
177#1605—611no—
178#1599—611no—
179#1354—611no—
180#1345—611no—
181#1319—611no—
182C2×C61—21no—
183C2×C61—21no—
184C2×C61—161no—
185C2×C61#160611yescharacteristic
186C2×C61#219911yescharacteristic
187C2×C61#220311yescharacteristic
188#544—611no—
189#451—1221no—
190#450—1221no—
191#419—1221no—
192#400—21no—
193#397—21no—
194#395C2×D6111yescharacteristic
195#394—21no—
196#394C2×D6111yescharacteristic
197#393—21no—
198#393—21no—
199#391C2×D6111yescharacteristic
200#388—21no—
201#343—611no—
202#339—1221no—
203#328—1221no—
204#328—1221no—
205#324—611no—
206#324—611no—
207C61#1227511yescharacteristic, complemented, Sylow
208C22×Q8C22⋊D6111yescharacteristic
209C22×Q8C22⋊D6111yescharacteristic
210C22×D4C22⋊D6111yescharacteristic
211C2×Q16—2441no—
212C2×SD16—2441no—
213C2×M16—1221no—
214C4⋊Q8—2441no—
215#125—2441no—
216C22⋊Q8—1221no—
217C22⋊Q8—1221no—
218#117—1221no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4C22×D6111yescharacteristic
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C42C22⋊D6111yescharacteristic
229#103—2441no—
230#103—2441no—
231#103—2441no—
232#102—2441no—
233C22⋊C8—1221no—
234C22⋊C8—1221no—
235#95—21no—
236#95—21no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95C22⋊D6111yescharacteristic
242#95C22⋊D6111yescharacteristic
243C24—21no—
244C2×Q8—21no—
245C2×Q8—21no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—81no—
250C2×Q8—1221no—
251C2×Q8—1221no—
252C2×D4—41no—
253C2×D4—81no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4C2×C22⋊D6111yescharacteristic
260C22×C4C2×C22⋊D6111yescharacteristic
261C22×C4C2×C22⋊D6111yescharacteristic
262Q16—4882no—
263SD16—4882no—
264M16—2441no—
265M16—2441no—
266C2×C8—2441no—
267C2×C8—2441no—
268C2×C8—2441no—
269C4⋊C4—41no—
270C4⋊C4—81no—
271C4⋊C4—81no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—2441no—
277C4⋊C4—2441no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—81no—
281C22⋊C4—81no—
282C22⋊C4—81no—
283C22⋊C4—81no—
284C22⋊C4—81no—
285C22⋊C4—2441no—
286C42—41no—
287C42—2441no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23#1451974611yescharacteristic
296Q8—42no—
297Q8—42no—
298Q8—81no—
299Q8—81no—
300Q8—4881no—
301Q8—4881no—
302D4—42no—
303D4—81no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
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—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4#1451979711yescharacteristic
328C2×C4#1451980711yescharacteristic
329C8—4881no—
330C8—4881no—
331C8—4881no—
332C22—21no—
333C22—21no—
334C22—81no—
335C22—81no—
336C22—81no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22#1683992411yescharacteristic
342C22#1683994011yescharacteristic
343C22#1683994911yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—81no—
349C4—81no—
350C4—81no—
351C4—81no—
352C4—81no—
353C4—4881no—
354C4—4881no—
355C2—21no—
356C2—21no—
357C2—161no—
358C2#2144479911yescharacteristic
359C2#2144782011yescharacteristic
360C2#2144784011yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2832C2
socleC22×C61B(4,𝔽2)
prime radicalC22×D4×C61D4
hypercenter#2832D61
hypocenterC61#12275
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2832

Complements

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

NH ≅ G/Ntype
1. #21446980C2semidirect
2. #21444792C2semidirect
4. #21443849C2semidirect
6. #21443753C2semidirect
207. C61#12275semidirect

Maximal subgroups

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

subgroupindex
#214469802
#214447922
#214447582
#214438492
#214438222
#214437532
C61×#28322
#1227561