Finite Group Databasebeta

← #29592465

Subgroups — #29592465

Order 15616.

396 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 67 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#21447747C211yesmaximal, characteristic, complemented
2#21447730C211yesmaximal, characteristic
3#21447130C211yesmaximal, characteristic, complemented
4#21443831C211yesmaximal, characteristic, complemented
5#21443828C211yesmaximal, characteristic, complemented
6#21443759C211yesmaximal, characteristic, complemented
7C61×#3250C211yesmaximal, characteristic, complemented
8C22×D488C2211yescharacteristic
9C2×#14519720—21no—
10C2×#14519718—21no—
11C2×#14519699—21no—
12#16839664—21no—
13#16839562—21no—
14#16839562—21no—
15C22⋊#11758185C2211yescharacteristic
16C22⋊#11758185C2211yescharacteristic
17#16839525C2211yescharacteristic
18C61×#529—21no—
19C61×#479—21no—
20C61×#478—21no—
21C61×#467C2211yescharacteristic
22C61×#466C2211yescharacteristic
23C61×#465—21no—
24C61×#464—21no—
25C61×#463—21no—
26C2×C4⋊C8×C61C2211yescharacteristic
27C22×D244—21no—
28C2×D488—21no—
29C2×D488—21no—
30C2×D488—42no—
31C2×C4⋊Dic61—21no—
32C2×#11758198—41no—
33C2×#11758198—41no—
34#14519720—42no—
35#14519718—42no—
36C2×#11758185—21no—
37C2×#11758185—21no—
38#14519699—42no—
39C2×Q16×C61D411yescharacteristic
40C2×SD16×C61—21no—
41C2×D8×C61D411yescharacteristic
42C22×C8×C61D411yescharacteristic
43C22×C8×C61C2311yescharacteristic
44#126×C61—41no—
45#125×C61—21no—
46#124×C61—21no—
47#123×C61—41no—
48C22⋊Q8×C61—21no—
49#121×C61—21no—
50C4×Q8×C61—21no—
51C4×D4×C61—21no—
52C4×D4×C61—41no—
53#117×C61—41no—
54C2×C42×C61D411yescharacteristic
55#107×C61D411yescharacteristic
56#107×C61D411yescharacteristic
57#106×C61—21no—
58C4⋊C8×C61—21no—
59C4⋊C8×C61—21no—
60#103×C61—21no—
61#103×C61—21no—
62#102×C61—21no—
63#102×C61—21no—
64C23×D61—41no—
65C2×Q8×C61—21no—
66C2×D4×C61—21no—
67C2×D4×C61—41no—
68C22×C4×C61—41no—
69C22×C4×C61D811yescharacteristic
70C22×C4×C61D811yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×Dic61—41no—
73C2×D244—22no—
74C2×D244—41no—
75C2×D244—41no—
76C2×D244—41no—
77C2×D244—41no—
78C2×D244—41no—
79Q16×C61—41no—
80SD16×C61—81no—
81D8×C61—41no—
82C2×C8×C61—21no—
83C2×C8×C61—41no—
84C2×C8×C61—41no—
85C2×C8×C61C2×D411yescharacteristic
86C2×C8×C61C2×D411yescharacteristic
87C4⋊C4×C61—21no—
88C4⋊C4×C61—21no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—41no—
93C22⋊C4×C61—41no—
94C22⋊C4×C61—41no—
95C22⋊C4×C61—41no—
96C22⋊C4×C61—41no—
97C22⋊C4×C61—41no—
98C42×C61—21no—
99C42×C61—21no—
100C42×C61—41no—
101#11758198—82no—
102#11758198—82no—
103C4⋊Dic61—41no—
104C4⋊Dic61—41no—
105D488—22no—
106D488—22no—
107D488—41no—
108D488—41no—
109#11758185—41no—
110#11758185—41no—
111C23×C61—41no—
112C23×C61C2×D811yescharacteristic
113C22×D61—42no—
114C22×D61—81no—
115C22×D61—81no—
116C22×D61—81no—
117C22×D61—81no—
118C22×D61—81no—
119C22×D61—81no—
120Q8×C61—41no—
121Q8×C61—41no—
122D4×C61—41no—
123D4×C61—41no—
124D4×C61—81no—
125D4×C61—81no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—82no—
137C2×C4×C61#12011yescharacteristic
138C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
139C2×Dic61—81no—
140C2×Dic61—81no—
141C2×Dic61—81no—
142D244—42no—
143D244—42no—
144D244—81no—
145D244—81no—
146C8×C61—21no—
147C8×C61—21no—
148C8×C61—41no—
149#12160—611nomaximal, Sylow
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—81no—
153C22×C61—81no—
154C22×C61—81no—
155C22×C61#44711yescharacteristic
156C22×C61#50811yescharacteristic
157C22×C61#50911yescharacteristic
158C2×D61—82no—
159C2×D61—82no—
160C2×D61—82no—
161C2×D61—161no—
162C2×D61—161no—
163C2×D61—161no—
164C2×D61—161no—
165C4×C61—21no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61—81no—
169C4×C61—81no—
170C4×C61—81no—
171C4×C61#45411yescharacteristic
172C4×C61B(4,𝔽2)11yescharacteristic
173Dic61—161no—
174#3250D6111yescharacteristic, complemented
175#2187—611no—
176#2184—611no—
177#2054—611no—
178#1348—611no—
179#1347—611no—
180#1322—611no—
181C2×C61—21no—
182C2×C61—21no—
183C2×C61—161no—
184C2×C61#159811yescharacteristic
185C2×C61#218611yescharacteristic
186C2×C61#219011yescharacteristic
187D61—162no—
188C22×D8—611no—
189#529—21no—
190C2×SD32—1221no—
191C2×D16—1221no—
192#479—21no—
193#478—21no—
194#467C2×D6111yescharacteristic
195#466C2×D6111yescharacteristic
196#465—21no—
197#464—21no—
198#463—21no—
199C2×C4⋊C8C2×D6111yescharacteristic
200C2×#102—1221no—
201#390—1221no—
202#357—1221no—
203#357—1221no—
204C22⋊C16—611no—
205C22⋊C16—611no—
206#340—611no—
207C61#1216011yescharacteristic, complemented, Sylow
208C22×D4—1221no—
209C2×Q16C22⋊D6111yescharacteristic
210C2×SD16—21no—
211C2×D8—1221no—
212C2×D8—1221no—
213C2×D8—2442no—
214C2×D8C22⋊D6111yescharacteristic
215C22×C8C22⋊D6111yescharacteristic
216C22×C8C22×D6111yescharacteristic
217#126—41no—
218#125—21no—
219#124—21no—
220#123—41no—
221C22⋊Q8—21no—
222#121—21no—
223C4×Q8—21no—
224C4×D4—21no—
225C4×D4—41no—
226#117—41no—
227C2×C4⋊C4—1221no—
228C2×C22⋊C4—2441no—
229C2×C22⋊C4—2441no—
230C2×C42C22⋊D6111yescharacteristic
231SD32—2442no—
232D16—2442no—
233C2×C16—1221no—
234C2×C16—1221no—
235#107C22⋊D6111yescharacteristic
236#107C22⋊D6111yescharacteristic
237#106—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240#103—21no—
241#103—21no—
242#102—21no—
243#102—21no—
244#102—2442no—
245C24—2441no—
246C2×Q8—21no—
247C2×D4—21no—
248C2×D4—41no—
249C2×D4—1222no—
250C2×D4—2441no—
251C2×D4—2441no—
252C2×D4—2441no—
253C2×D4—2441no—
254C2×D4—2441no—
255C22×C4—41no—
256C22×C4—2441no—
257C22×C4#1175819911yescharacteristic
258C22×C4#1175819911yescharacteristic
259C22×C4C2×C22⋊D6111yescharacteristic
260Q16—41no—
261SD16—81no—
262D8—41no—
263D8—1222no—
264D8—1222no—
265D8—2441no—
266D8—2441no—
267C2×C8—21no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8C2×C22⋊D6111yescharacteristic
271C2×C8C2×C22⋊D6111yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—4882no—
286C22⋊C4—4882no—
287C42—21no—
288C42—21no—
289C42—41no—
290C16—2441no—
291C16—2441no—
292C23—41no—
293C23—4881no—
294C23—4881no—
295C23—4881no—
296C23—4881no—
297C23—4881no—
298C23—4881no—
299C23—2442no—
300C23C2×#1175819911yescharacteristic
301Q8—41no—
302Q8—41no—
303D4—41no—
304D4—41no—
305D4—81no—
306D4—81no—
307D4—4881no—
308D4—4881no—
309D4—2442no—
310D4—2442no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—82no—
322C2×C4—4881no—
323C2×C4—4881no—
324C2×C4—4881no—
325C2×C4#1451974611yescharacteristic
326C2×C4#1451980311yescharacteristic
327C8—21no—
328C8—21no—
329C8—41no—
330C22—21no—
331C22—21no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22—9761no—
336C22—9761no—
337C22—9761no—
338C22—9761no—
339C22—4882no—
340C22—4882no—
341C22—4882no—
342C22#1683989611yescharacteristic
343C22#1684019211yescharacteristic
344C22#1684019711yescharacteristic
345C4—21no—
346C4—41no—
347C4—41no—
348C4—81no—
349C4—81no—
350C4—81no—
351C4—9761no—
352C4#1683993511yescharacteristic
353C4#1683994911yescharacteristic
354C2—21no—
355C2—21no—
356C2—161no—
357C2—9762no—
358C2#2144475411yescharacteristic
359C2#2144774211yescharacteristic
360C2#2144776511yescharacteristic
subgroupG/H
centerC22#16839896
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#3250C2
socleC22×C61#447
prime radical#21447730C2
hypercenter#3250D61
hypocenterC61#12160
LCSG ▷ C22×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #3250

Complements

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

NH ≅ G/Ntype
1. #21447747C2semidirect
3. #21447130C2semidirect
4. #21443831C2semidirect
5. #21443828C2semidirect
6. #21443759C2semidirect
7. C61×#3250C2semidirect
174. #3250D61semidirect
207. C61#12160semidirect

Maximal subgroups

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

subgroupindex
#214477472
#214477302
#214471302
#214438312
#214438282
#214437592
C61×#32502
#1216061