Finite Group Databasebeta

← #37573770

Subgroups — #37573770

Order 24448.

382 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 69 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#27133222C211yesmaximal, characteristic
2C2×#20259236C211yesmaximal, characteristic, complemented
3#27132543C211yesmaximal, characteristic, complemented
4#27132540C211yesmaximal, characteristic, complemented
5#27132538C211yesmaximal, characteristic, complemented
6#27132429C211yesmaximal, characteristic, complemented
7C2×#99×C191C211yesmaximal, characteristic, complemented
8C22×C22⋊D191C2211yescharacteristic
9C23×Dic191C2211yescharacteristic
10#20259305—21no—
11#20259303—21no—
12#20259294—21no—
13#20259294—21no—
14#20259291—21no—
15#20259290—21no—
16C2×C4⋊Dic191—21no—
17C2×C22⋊Dic191—21no—
18C2×C22⋊Dic191C2211yescharacteristic
19C2×C22⋊Dic191C2211yescharacteristic
20C2×(C2×D191)⋊C4—21no—
21#20259236—22no—
22C191⋊#95—21no—
23C191⋊#95—21no—
24C191⋊#95—21no—
25C22×D4×C191C2211yescharacteristic
26C2×C22⋊C4×C191C2211yescharacteristic
27C2×C22⋊C4×C191C2211yescharacteristic
28#99×C191—22no—
29C23×D191D411yescharacteristic
30C2×C22⋊D191—21no—
31C2×C22⋊D191—21no—
32C2×C22⋊D191—21no—
33C2×C22⋊D191—21no—
34C2×C22⋊D191—21no—
35C2×C22⋊D191—21no—
36C2×C22⋊D191—21no—
37C2×C22⋊D191—21no—
38C22×Dic191—21no—
39C22×Dic191—21no—
40C22×Dic191—21no—
41C22×Dic191—21no—
42C22×Dic191—42no—
43C22×Dic191D411yescharacteristic
44C22×Dic191D411yescharacteristic
45C22×Dic191D411yescharacteristic
46C4⋊Dic191—42no—
47Dic191⋊C4—21no—
48Dic191⋊C4—21no—
49C22⋊Dic191—21no—
50C22⋊Dic191—21no—
51C22⋊Dic191—21no—
52C22⋊Dic191—21no—
53C22⋊Dic191—21no—
54C22⋊Dic191—21no—
55C22⋊Dic191—42no—
56(C2×D191)⋊C4—21no—
57(C2×D191)⋊C4—21no—
58(C2×D191)⋊C4—42no—
59C24×C191D411yescharacteristic
60C24×C191C2311yescharacteristic
61C2×D4×C191—21no—
62C2×D4×C191—21no—
63C2×D4×C191—21no—
64C2×D4×C191—21no—
65C2×D4×C191—21no—
66C2×D4×C191—21no—
67C22×C4×C191—21no—
68C22×C4×C191—21no—
69C22×C4×C191D411yescharacteristic
70C22⋊C4×C191—21no—
71C22⋊C4×C191—21no—
72C22⋊C4×C191—21no—
73C22⋊C4×C191D412yescomplemented
74C22×D191—21no—
75C22×D191—21no—
76C22×D191—21no—
77C22×D191—41no—
78C22×D191—41no—
79C22⋊D191—41no—
80C22⋊D191—41no—
81C22⋊D191—41no—
82C22⋊D191—41no—
83C22⋊D191—81no—
84C22⋊D191—81no—
85C2×Dic191—22no—
86C2×Dic191—22no—
87C2×Dic191—22no—
88C2×Dic191—21no—
89C2×Dic191—21no—
90C2×Dic191—21no—
91C2×Dic191—21no—
92C2×Dic191—21no—
93C2×Dic191—41no—
94C2×Dic191—41no—
95C2×Dic191—41no—
96C2×Dic191—41no—
97C2×Dic191—41no—
98C2×Dic191—41no—
99C2×Dic191—41no—
100C2×Dic191—41no—
101C2×Dic191—41no—
102C23×C191—21no—
103C23×C191—21no—
104C23×C191—21no—
105C23×C191—41no—
106C23×C191—41no—
107C23×C191—41no—
108C23×C191—41no—
109C23×C191C2×D411yescharacteristic
110C23×C191C2×D411yescharacteristic
111C23×C191C2×D411yescharacteristic
112C23×C191C2×D411yescharacteristic
113C23×C191#4111yescharacteristic
114C23×C191#4111yescharacteristic
115C23×C191#4111yescharacteristic
116D4×C191—41no—
117D4×C191—41no—
118D4×C191—41no—
119D4×C191—41no—
120C2×C4×C191—21no—
121C2×C4×C191—22no—
122C2×C4×C191—21no—
123C2×C4×C191—21no—
124C2×C4×C191—41no—
125C2×C4×C191—41no—
126C2×C4×C191—41no—
127C2×C4×C191—41no—
128C2×C4×C191—41no—
129C22×C191—21no—
130C22×C191—21no—
131C22×C191—21no—
132C22×C191—21no—
133C22×C191—21no—
134C22×C191—21no—
135C22×C191—41no—
136C22×C191—41no—
137C22×C191—41no—
138C22×C191—41no—
139C22×C191—42no—
140C22×C191—41no—
141C22×C191—41no—
142C22×C191—41no—
143C22×C191—81no—
144C22×C191#12011yescharacteristic
145C22×C191#12111yescharacteristic
146C22×C191#12111yescharacteristic
147C22×C191#12111yescharacteristic
148C22×C191#12311yescharacteristic
149C22×C191#12311yescharacteristic
150C22×C191#12411yescharacteristic
151C2×D191—42no—
152C2×D191—41no—
153C2×D191—41no—
154C2×D191—41no—
155C2×D191—81no—
156C4×C191—42no—
157C4×C191—41no—
158C4×C191—81no—
159Dic191—41no—
160Dic191—42no—
161Dic191—41no—
162Dic191—41no—
163Dic191—81no—
164C2×C191—21no—
165C2×C191—21no—
166C2×C191—21no—
167C2×C191—21no—
168C2×C191—21no—
169C2×C191—21no—
170C2×C191—81no—
171C2×C191#39411yescharacteristic
172C2×C191B(4,𝔽2)11yescharacteristic
173C2×C191#45811yescharacteristic
174D191—81no—
175C191#204411yescharacteristic, complemented, Sylow
176#2044—1911nomaximal, Sylow
177#534—1911no—
178C2×#99—1911no—
179C2×#99D19111yescharacteristic, complemented
180#386—1911no—
181#386—1911no—
182#385—1911no—
183#342—1911no—
184C22×D4—1911no—
185C22×D4C2×D19111yescharacteristic
186C23×C4—1911no—
187#123—3821no—
188#123—3821no—
189#121—3821no—
190#121—3821no—
191#120—3821no—
192#120—3821no—
193C2×C4⋊C4—3821no—
194C2×C22⋊C4—3821no—
195C2×C22⋊C4—3821no—
196C2×C22⋊C4—1911no—
197C2×C22⋊C4—1911no—
198C2×C22⋊C4C2×D19111yescharacteristic
199C2×C22⋊C4C2×D19111yescharacteristic
200#99—22no—
201#99—3822no—
202#95—3821no—
203#95—3821no—
204#95—3821no—
205C24—1911no—
206C24D76411yescharacteristic
207C24C22×D19111yescharacteristic
208C2×D4—21no—
209C2×D4—21no—
210C2×D4—21no—
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—21no—
214C2×D4—3821no—
215C2×D4—3821no—
216C2×D4—3821no—
217C2×D4—3821no—
218C2×D4—3821no—
219C2×D4—3821no—
220C2×D4—3821no—
221C2×D4—3821no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—3821no—
225C22×C4—3821no—
226C22×C4—3821no—
227C22×C4—3821no—
228C22×C4—1911no—
229C22×C4—1911no—
230C22×C4—1911no—
231C22×C4—7642no—
232C22×C4D76411yescharacteristic
233C4⋊C4—3821no—
234C4⋊C4—3821no—
235C4⋊C4—7642no—
236C22⋊C4—21no—
237C22⋊C4—21no—
238C22⋊C4—21no—
239C22⋊C4—3821no—
240C22⋊C4—3821no—
241C22⋊C4—3821no—
242C22⋊C4—3821no—
243C22⋊C4—3821no—
244C22⋊C4—3821no—
245C22⋊C4—3821no—
246C22⋊C4—3821no—
247C22⋊C4—7642no—
248C22⋊C4—7642no—
249C22⋊C4C22⋊D19112yescomplemented
250C23—21no—
251C23—21no—
252C23—21no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23—41no—
257C23—3821no—
258C23—3821no—
259C23—3821no—
260C23—7641no—
261C23—7641no—
262C23D4×D19111yescharacteristic
263C23D4×D19111yescharacteristic
264C23C2×C22⋊D19111yescharacteristic
265C23C2×D76411yescharacteristic
266C23#1569028611yescharacteristic
267C23#1569028611yescharacteristic
268C23#1569028711yescharacteristic
269D4—41no—
270D4—41no—
271D4—41no—
272D4—41no—
273D4—15281no—
274D4—15281no—
275D4—7641no—
276D4—7641no—
277D4—7641no—
278D4—7641no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—3822no—
289C2×C4—3822no—
290C2×C4—3822no—
291C2×C4—3821no—
292C2×C4—3821no—
293C2×C4—3821no—
294C2×C4—3821no—
295C2×C4—3821no—
296C2×C4—7641no—
297C2×C4—7641no—
298C2×C4—7641no—
299C2×C4—7641no—
300C2×C4—7641no—
301C2×C4—7641no—
302C2×C4—7641no—
303C2×C4—7641no—
304C2×C4—7641no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—42no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—81no—
320C22—15281no—
321C22—7642no—
322C22—7641no—
323C22—7641no—
324C22—7641no—
325C22#2025929211yescharacteristic
326C22#2025929311yescharacteristic
327C22#2025929411yescharacteristic
328C22#2025929611yescharacteristic
329C22#2025930411yescharacteristic
330C22#2025930611yescharacteristic
331C22#2025930811yescharacteristic
332C4—42no—
333C4—41no—
334C4—81no—
335C4—15281no—
336C4—7641no—
337C4—7642no—
338C4—7641no—
339C4—7641no—
340C2—21no—
341C2—21no—
342C2—21no—
343C2—21no—
344C2—21no—
345C2—21no—
346C2—81no—
347C2—15281no—
348C2#2713257911yescharacteristic
349C2#2713285111yescharacteristic
350C2#2713285411yescharacteristic
subgroupG/H
centerC22#20259292
commutator, cosocleC24×C191C23
FrattiniC24C22×D191
FittingC2×#99×C191C2
socleC22×C191#120
prime radical#27133222C2
hypercenterC2×#99D191
hypocenterC191#2044
LCSG ▷ C24×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#20259236C2semidirect
3. #27132543C2semidirect
4. #27132540C2semidirect
5. #27132538C2semidirect
6. #27132429C2semidirect
7. C2×#99×C191C2semidirect
73. C22⋊C4×C191D4semidirect
175. C191#2044semidirect
179. C2×#99D191semidirect
249. C22⋊C4C22⋊D191semidirect

Maximal subgroups

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

subgroupindex
#271332222
C2×#202592362
#271325432
#271325402
#271325382
#271324292
C2×#99×C1912
#2044191