Finite Group Databasebeta

← #29592447

Subgroups — #29592447

Order 15616.

372 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 57 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#21453885C211yesmaximal, characteristic, complemented
2#21447045C211yesmaximal, characteristic
3#21444822C211yesmaximal, characteristic
4#21443826C211yesmaximal, characteristic, complemented
5#21443825C211yesmaximal, characteristic, complemented
6#21443762C211yesmaximal, characteristic, complemented
7C61×#1610C211yesmaximal, characteristic
8C2×#14519767—21no—
9#16840073—21no—
10C2×#14519704—21no—
11#16839763—21no—
12#16839704—21no—
13#16839703—21no—
14#16839696—21no—
15#16839695—21no—
16#16839695—21no—
17#16839692C2211yescharacteristic
18#16839627C2211yescharacteristic
19#16839531C2211yescharacteristic
20#16839496—21no—
21#16839488C2211yescharacteristic
22C61×#537C2211yescharacteristic
23C61×#480—21no—
24C61×#398C2211yescharacteristic
25C61×#327—21no—
26C61×#324C2211yescharacteristic
27C2×#11758194—21no—
28#14519767—42no—
29#14519767—42no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61D411yescharacteristic
32C2×C4⋊Dic61D411yescharacteristic
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×C4×Dic61D411yescharacteristic
39#14519710—41no—
40#14519704—42no—
41#14519701—41no—
42#14519698—41no—
43#14519698—41no—
44C22⋊#92418—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684D411yescharacteristic
52C2×#41×C61—21no—
53C22⋊Q8×C61—41no—
54#121×C61—21no—
55#121×C61—21no—
56#121×C61—41no—
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61D411yescharacteristic
59C2×C4⋊C4×C61C2311yescharacteristic
60#107×C61—41no—
61#102×C61—41no—
62C22⋊C8×C61—21no—
63#95×C61—21no—
64#95×C61D411yescharacteristic
65#41×C61—41no—
66#41×C61—41no—
67#41×C61—41no—
68#41×C61—41no—
69C2×Q8×C61—21no—
70C2×D4×C61—21no—
71C2×D4×C61—21no—
72C2×D4×C61—21no—
73C2×D4×C61—41no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—41no—
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—21no—
84C2×C8×C61—41no—
85C4⋊C4×C61—21no—
86C4⋊C4×C61—21no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C22⋊C4×C61—41no—
93C4⋊Dic61—42no—
94C4⋊Dic61—41no—
95C4⋊Dic61—41no—
96#11758196—42no—
97#11758196—42no—
98#11758196—42no—
99#11758196—41no—
100#11758196—41no—
101#11758196—81no—
102C4×Dic61—21no—
103C4×Dic61D812yes—
104#11758194—41no—
105#11758194—41no—
106C2×#92418—41no—
107C2×#92418—41no—
108C23×C61—41no—
109C23×C61#12011yescharacteristic
110Q8×C61—41no—
111Q8×C61—41no—
112D4×C61—41no—
113D4×C61—41no—
114D4×C61—81no—
115D4×C61—81no—
116D4×C61—81no—
117D4×C61—81no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
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—81no—
132C2×C4×C61—81no—
133C2×C4×C61C2×D811yescharacteristic
134C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
135C2×Dic61—22no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—42no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C8×C61—81no—
147#92418—81no—
148#92418—81no—
149#12157—611nomaximal, Sylow
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—81no—
153C22×C61—81no—
154C22×C61—81no—
155C22×C61#44711yescharacteristic
156C22×C61#45411yescharacteristic
157C22×C61B(4,𝔽2)11yescharacteristic
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—81no—
163C4×C61—81no—
164C4×C61—81no—
165Dic61—42no—
166Dic61—81no—
167Dic61—81no—
168Dic61—81no—
169#2822—611no—
170#2040—611no—
171#1610—611no—
172#1610D6111yescharacteristic
173#1346—611no—
174#1346—611no—
175#1324—611no—
176C2×C61—21no—
177C2×C61—21no—
178C2×C61—161no—
179C2×C61#159811yescharacteristic
180C2×C61#220111yescharacteristic
181C2×C61#220311yescharacteristic
182#537C2×D6111yescharacteristic
183C2×#125—1221no—
184#480—21no—
185#480—1221no—
186C2×#104—1221no—
187#417—1221no—
188#400—1221no—
189#400—1221no—
190#398—611no—
191#398—1221no—
192#398—1221no—
193#398—1221no—
194#398C2×D6111yescharacteristic
195#382—611no—
196#343—611no—
197#327—21no—
198#327—1221no—
199#324—611no—
200#324C2×D6111yescharacteristic
201C61#1215711yescharacteristic, complemented, Sylow
202C2×#41—21no—
203C2×M16—1221no—
204#125—2442no—
205#125—2442no—
206C22⋊Q8—41no—
207#121—21no—
208#121—21no—
209#121—41no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4C22⋊D6111yescharacteristic
220C2×C4⋊C4C22×D6111yescharacteristic
221C2×C42—611no—
222#107—41no—
223#107—2441no—
224#104—2442no—
225#103—2441no—
226#102—41no—
227#102—2441no—
228#102—2441no—
229C22⋊C8—21no—
230C22⋊C8—1221no—
231#95—21no—
232#95—611no—
233#95—1221no—
234#95—1221no—
235#95—1221no—
236#95—1221no—
237#95—1221no—
238#95—1221no—
239#95C22⋊D6111yescharacteristic
240#41—41no—
241#41—41no—
242#41—41no—
243#41—41no—
244C2×Q8—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—41no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—41no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4D4×D6111yescharacteristic
257C22×C4D4×D6111yescharacteristic
258C22×C4C2×C22⋊D6111yescharacteristic
259M16—2441no—
260M16—2441no—
261C2×C8—41no—
262C2×C8—2441no—
263C2×C8—2441no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—4881no—
271C4⋊C4—2441no—
272C4⋊C4—2441no—
273C4⋊C4—2442no—
274C4⋊C4—2442no—
275C4⋊C4—2442no—
276C4⋊C4—2442no—
277C4⋊C4—2441no—
278C4⋊C4—2441no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C42—612no—
282C42—1221no—
283C23—41no—
284C23#1451974511yescharacteristic
285Q8—41no—
286Q8—41no—
287D4—41no—
288D4—41no—
289D4—81no—
290D4—81no—
291D4—81no—
292D4—81no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—1222no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2442no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4D8×D6111yescharacteristic
320C2×C4#1451980111yescharacteristic
321C8—81no—
322C8—4881no—
323C8—4881no—
324C22—21no—
325C22—21no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22#1683989411yescharacteristic
330C22#1683993311yescharacteristic
331C22#1683994811yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—81no—
337C4—81no—
338C4—81no—
339C4—4881no—
340C4—4881no—
341C4—4881no—
342C4—2442no—
343C2—21no—
344C2—21no—
345C2—161no—
346C2#2144475211yescharacteristic
347C2#2144783011yescharacteristic
348C2#2144783811yescharacteristic
subgroupG/H
centerC22#16839948
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1610C2
socleC22×C61B(4,𝔽2)
prime radicalC61×#537C22
hypercenter#1610D61
hypocenterC61#12157
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1610

Complements

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

NH ≅ G/Ntype
1. #21453885C2semidirect
4. #21443826C2semidirect
5. #21443825C2semidirect
6. #21443762C2semidirect
201. C61#12157semidirect

Maximal subgroups

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

subgroupindex
#214538852
#214470452
#214448222
#214438262
#214438252
#214437622
C61×#16102
#1215761