Finite Group Databasebeta

← #29592826

Subgroups — #29592826

Order 15616.

370 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 63 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#21446986C211yesmaximal, characteristic
2#21444843C211yesmaximal, characteristic
3#21444775C211yesmaximal, characteristic
4#21443843C211yesmaximal, characteristic
5#21443840C211yesmaximal, characteristic
6#21443749C211yesmaximal, characteristic
7C61×#2841C211yesmaximal, characteristic
8#16840388C2211yescharacteristic
9#16840097—21no—
10#16839918—21no—
11#16839625—21no—
12#16839529C2211yescharacteristic
13#16839528—21no—
14#16839498—21no—
15#16839498—21no—
16#16839486C2211yescharacteristic
17#16839486C2211yescharacteristic
18C61×#400—21no—
19C61×#399C2211yescharacteristic
20C61×#398—21no—
21C61×#398—21no—
22C61×#396—21no—
23C61×#395—21no—
24C61×#393C2211yescharacteristic
25C61×#381C2211yescharacteristic
26C61×#380—21no—
27C2×#11758202—41no—
28#14519756—21no—
29#14519756—21no—
30#14519754—41no—
31#14519754—41no—
32C2×C22⋊Dic61—21no—
33C2×C22⋊Dic61—21no—
34#14519710—41no—
35#14519701—41no—
36#14519700—41no—
37C22⋊#92418—21no—
38C22⋊#92418—21no—
39#14519684—41no—
40#14519684—41no—
41C22×Q8×C61D411yescharacteristic
42C23×C4×C61D411yescharacteristic
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61D411yescharacteristic
50C2×C22⋊C4×C61—21no—
51C2×C22⋊C4×C61—21no—
52C2×C22⋊C4×C61D411yescharacteristic
53C2×C22⋊C4×C61C2311yescharacteristic
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×C61C2×D411yescharacteristic
63C2×Q8×C61—41no—
64C2×Q8×C61—81no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—41no—
73C22×C4×C61—41no—
74C22×C4×C61Q1612yescomplemented
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—41no—
80C2×Dic122—21no—
81C2×Dic122—21no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—81no—
84C4⋊C4×C61—81no—
85C4⋊C4×C61—81no—
86C4⋊C4×C61—81no—
87C4⋊C4×C61—81no—
88C4⋊C4×C61—81no—
89C22⋊C4×C61—41no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—81no—
92C22⋊C4×C61—81no—
93C22⋊Dic61—41no—
94C22⋊Dic61—41no—
95C22⋊Dic61—41no—
96C22⋊Dic61—41no—
97#11758202—82no—
98C4⋊Dic61—21no—
99C4⋊Dic61—21no—
100#11758196—41no—
101#11758196—41no—
102C2×#92418—41no—
103C2×#92418—41no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61#12011yescharacteristic
109C23×C61C2×Q1611yescharacteristic
110C23×C61#13711yescharacteristic
111Q8×C61—42no—
112Q8×C61—81no—
113C2×C4×C61—22no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—42no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
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×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—81no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—81no—
140C2×Dic61—81no—
141C2×Dic61—81no—
142C2×Dic61—81no—
143C2×Dic61—81no—
144Dic122—81no—
145Dic122—81no—
146#92418—81no—
147#92418—81no—
148#12219—611nomaximal, Sylow
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—81no—
158C22×C61#45111yescharacteristic
159C22×C61#45511yescharacteristic
160C22×C61B(4,𝔽2)11yescharacteristic
161C4×C61—42no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61—81no—
165C4×C61—81no—
166C4×C61—81no—
167C4×C61—81no—
168C4×C61—81no—
169Dic61—81no—
170Dic61—81no—
171Dic61—161no—
172#2841D6111yescharacteristic
173#2030—611no—
174#1614—611no—
175#1602—611no—
176#1352—611no—
177#1351—611no—
178#1317—611no—
179C2×C61—21no—
180C2×C61—21no—
181C2×C61—41no—
182C2×C61—41no—
183C2×C61#160211yescharacteristic
184C2×C61#220011yescharacteristic
185C2×C61#220111yescharacteristic
186#543—611no—
187#484—1221no—
188#451—1221no—
189#400—21no—
190#399C2×D6111yescharacteristic
191#398—21no—
192#398—21no—
193#396—21no—
194#395—21no—
195#393C2×D6111yescharacteristic
196#381—1221no—
197#381C2×D6111yescharacteristic
198#380—21no—
199#342—611no—
200#342—1221no—
201#328—1221no—
202#328—1221no—
203#323—611no—
204#323—611no—
205C61#1221911yescharacteristic, complemented, Sylow
206C22×Q8C22⋊D6111yescharacteristic
207C23×C4C22⋊D6111yescharacteristic
208C2×Q16—2441no—
209C22⋊Q8—1221no—
210C22⋊Q8—1221no—
211C22⋊Q8—2441no—
212C22⋊Q8—2441no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4C22⋊D6111yescharacteristic
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—1221no—
223C2×C22⋊C4—1221no—
224C2×C22⋊C4C22⋊D6111yescharacteristic
225C2×C22⋊C4C22×D6111yescharacteristic
226#107—2441no—
227#103—2441no—
228#103—2441no—
229C22⋊C8—1221no—
230C22⋊C8—1221no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237#95—2441no—
238#95—2441no—
239#95C22⋊D6111yescharacteristic
240#95C22⋊D6111yescharacteristic
241C24C2×C22⋊D6111yescharacteristic
242C2×Q8—41no—
243C2×Q8—81no—
244C2×Q8—1221no—
245C2×Q8—1221no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—2441no—
258C22×C4#1175820212yescomplemented
259C22×C4C2×C22⋊D6111yescharacteristic
260C22×C4C2×C22⋊D6111yescharacteristic
261Q16—4882no—
262C2×C8—2441no—
263C2×C8—2441no—
264C4⋊C4—41no—
265C4⋊C4—81no—
266C4⋊C4—81no—
267C4⋊C4—81no—
268C4⋊C4—81no—
269C4⋊C4—81no—
270C4⋊C4—81no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4—2441no—
274C4⋊C4—2441no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—81no—
278C22⋊C4—81no—
279C22⋊C4—2441no—
280C22⋊C4—2441no—
281C22⋊C4—2441no—
282C22⋊C4—2441no—
283C23—21no—
284C23—21no—
285C23—41no—
286C23—41no—
287C23#1451974611yescharacteristic
288C23C2×#1175820211yescharacteristic
289C23#1451980811yescharacteristic
290Q8—42no—
291Q8—81no—
292Q8—4881no—
293Q8—4881no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
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—81no—
318C2×C4—4881no—
319C2×C4—4881no—
320C2×C4—4881no—
321C2×C4—4881no—
322C2×C4—4881no—
323C2×C4—2441no—
324C2×C4—2441no—
325C8—4881no—
326C8—4881no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—81no—
336C22#1683991811yescharacteristic
337C22#1683994011yescharacteristic
338C22#1683994911yescharacteristic
339C4—41no—
340C4—41no—
341C4—42no—
342C4—81no—
343C4—81no—
344C4—81no—
345C4—81no—
346C4—81no—
347C4—9761no—
348C4—4881no—
349C4—4881no—
350C2—21no—
351C2—21no—
352C2—41no—
353C2—41no—
354C2#2144477611yescharacteristic
355C2#2144782611yescharacteristic
356C2#2144783211yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C22⋊C4×C61C23
FrattiniC2×C22⋊C4C22×D61
FittingC61×#2841C2
socleC22×C61B(4,𝔽2)
prime radicalC24×C61C2×D4
hypercenter#2841D61
hypocenterC61#12219
LCSG ▷ C2×C22⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2841

Complements

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

NH ≅ G/Ntype
74. C22×C4×C61Q16semidirect
205. C61#12219semidirect
258. C22×C4#11758202semidirect

Maximal subgroups

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

subgroupindex
#214469862
#214448432
#214447752
#214438432
#214438402
#214437492
C61×#28412
#1221961