Finite Group Databasebeta

← #37575920

Subgroups — #37575920

Order 24448.

610 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20259307C211yesmaximal, characteristic
2C2×#20259307C211yesmaximal, characteristic
3C2×#20259280C211yesmaximal, characteristic, complemented
4C2×C4⋊C4×D191C211yesmaximal, characteristic, complemented
5#27132596C211yesmaximal, characteristic, complemented
6#27132585C211yesmaximal, characteristic, complemented
7#27132585C211yesmaximal, characteristic, complemented
8#27132560C211yesmaximal, characteristic, complemented
9#27132559C211yesmaximal, characteristic, complemented
10#27132555C211yesmaximal, characteristic, complemented
11#27132552C211yesmaximal, characteristic, complemented
12#27132541C211yesmaximal, characteristic
13#27132537C211yesmaximal, characteristic, complemented
14#27132525C211yesmaximal, characteristic, complemented
15#398×C191C211yesmaximal, characteristic, complemented
16C22×D764C2211yescharacteristic
17C22×C4×D191C2211yescharacteristic
18C22×C4×D191C2211yescharacteristic
19C22×C4×D191C2211yescharacteristic
20#20259307—24no—
21#20259307—24no—
22#20259280—24no—
23C2×C4⋊Dic191C2211yescharacteristic
24C2×C4⋊Dic191C2211yescharacteristic
25C2×C4⋊Dic191C2211yescharacteristic
26C2×Dic191⋊C4C2211yescharacteristic
27C2×Dic191⋊C4C2211yescharacteristic
28C2×Dic191⋊C4C2211yescharacteristic
29C2×Dic191⋊C4C2211yescharacteristic
30C2×Dic191⋊C4C2211yescharacteristic
31C4⋊C4×D191—24no—
32C2×(C2×D191)⋊C4C2211yescharacteristic
33C2×(C2×D191)⋊C4C2211yescharacteristic
34C2×(C2×D191)⋊C4C2211yescharacteristic
35C2×(C2×D191)⋊C4C2211yescharacteristic
36C2×(C2×D191)⋊C4C2211yescharacteristic
37C2×(C2×D191)⋊C4C2211yescharacteristic
38C2×(C2×D191)⋊C4C2211yescharacteristic
39C2×(C2×D191)⋊C4C2211yescharacteristic
40C2×(C2×D191)⋊C4C2211yescharacteristic
41C2×C4×Dic191C2211yescharacteristic
42C2×C4×Dic191C2211yescharacteristic
43C191⋊#95C2211yescharacteristic
44C191⋊#95C2211yescharacteristic
45C191⋊#95C2211yescharacteristic
46C191⋊#95C2211yescharacteristic
47C191⋊#95C2211yescharacteristic
48C2×C4⋊C4×C191C2211yescharacteristic
49C2×C4⋊C4×C191C2211yescharacteristic
50C2×C4⋊C4×C191C2211yescharacteristic
51C2×C4⋊C4×C191C2211yescharacteristic
52#95×C191C2211yescharacteristic
53#95×C191C2211yescharacteristic
54#95×C191C2211yescharacteristic
55C23×D191C2311yescharacteristic
56C23×D191C2311yescharacteristic
57C2×D764—22no—
58C2×D764—22no—
59C2×D764—22no—
60C22×Dic191C2311yescharacteristic
61C22×Dic191C2311yescharacteristic
62C22×Dic191C2311yescharacteristic
63C22×Dic191C2311yescharacteristic
64C22×Dic191C2311yescharacteristic
65C22×Dic191C2311yescharacteristic
66C2×C4×D191—22no—
67C2×C4×D191—22no—
68C2×C4×D191—22no—
69C2×C4×D191—22no—
70C2×C4×D191—22no—
71C2×C4×D191—22no—
72C2×C4×D191—22no—
73C2×C4×D191—22no—
74C2×C4×D191D414yes—
75C4⋊Dic191—22no—
76C4⋊Dic191—22no—
77C4⋊Dic191—22no—
78Dic191⋊C4—22no—
79Dic191⋊C4—22no—
80Dic191⋊C4—22no—
81Dic191⋊C4—22no—
82Dic191⋊C4—22no—
83(C2×D191)⋊C4—22no—
84(C2×D191)⋊C4—22no—
85(C2×D191)⋊C4—22no—
86(C2×D191)⋊C4—22no—
87(C2×D191)⋊C4—22no—
88(C2×D191)⋊C4—22no—
89(C2×D191)⋊C4—22no—
90(C2×D191)⋊C4—22no—
91(C2×D191)⋊C4D414yes—
92C4×Dic191—22no—
93C4×Dic191—22no—
94C22×C4×C191C2311yescharacteristic
95C22×C4×C191C2311yescharacteristic
96C22×C4×C191C2311yescharacteristic
97C22×C4×C191C2311yescharacteristic
98C22×C4×C191C2311yescharacteristic
99C22×C4×C191C2311yescharacteristic
100C22×C4×C191C2311yescharacteristic
101C4⋊C4×C191—22no—
102C4⋊C4×C191—22no—
103C4⋊C4×C191—22no—
104C4⋊C4×C191—22no—
105C22×D191—21no—
106C22×D191—21no—
107C22×D191—21no—
108C22×D191—21no—
109C22×D191—21no—
110C22×D191—21no—
111C22×D191—21no—
112C22×D191—21no—
113C22×D191—21no—
114C22×D191—21no—
115C22×D191—21no—
116C22×D191C2×D412yes—
117C22×D191C2×D412yes—
118C22×D191#4112yes—
119D764—44no—
120C2×Dic191—21no—
121C2×Dic191—21no—
122C2×Dic191—21no—
123C2×Dic191—21no—
124C2×Dic191—21no—
125C2×Dic191—21no—
126C2×Dic191—21no—
127C2×Dic191—21no—
128C2×Dic191—21no—
129C2×Dic191—21no—
130C2×Dic191—21no—
131C2×Dic191—21no—
132C2×Dic191—21no—
133C2×Dic191—21no—
134C2×Dic191—21no—
135C2×Dic191C2×D412yes—
136C2×Dic191C2×D412yes—
137C2×Dic191#4112yes—
138C4×D191—28no—
139C4×D191—28no—
140C4×D191—44no—
141C23×C191C2411yescharacteristic
142C2×C4×C191—21no—
143C2×C4×C191—21no—
144C2×C4×C191—21no—
145C2×C4×C191—21no—
146C2×C4×C191—21no—
147C2×C4×C191—21no—
148C2×C4×C191—21no—
149C2×C4×C191—21no—
150C2×C4×C191—21no—
151C2×C4×C191—21no—
152C2×C4×C191—21no—
153C2×C4×C191—21no—
154C2×C4×C191—21no—
155C2×C4×C191—21no—
156C2×C4×C191—21no—
157C2×C4×C191—21no—
158C2×C4×C191—21no—
159C2×C4×C191—21no—
160C2×C4×C191C2×D412yes—
161C2×C4×C191C2×D412yes—
162C2×C4×C191#4112yes—
163C22×C191C22×D411yescharacteristic
164C22×C191C22×D411yescharacteristic
165C22×C191C2×#4111yescharacteristic
166C22×C191C2×#4111yescharacteristic
167C22×C191C2×#4111yescharacteristic
168C22×C1912−1+411yescharacteristic
169C22×C1912−1+411yescharacteristic
170C2×D191—22no—
171C2×D191—22no—
172C2×D191—22no—
173C2×D191—22no—
174C2×D191—22no—
175C2×D191—22no—
176C2×D191—41no—
177C2×D191—41no—
178C2×D191—41no—
179C2×D191—41no—
180C2×D191—41no—
181C2×D191—41no—
182C2×D191—41no—
183C2×D191#12114yes—
184C4×C191—22no—
185C4×C191—22no—
186C4×C191—22no—
187C4×C191—41no—
188C4×C191—41no—
189C4×C191—41no—
190C4×C191—41no—
191Dic191—22no—
192Dic191—22no—
193Dic191—22no—
194Dic191—41no—
195Dic191—41no—
196Dic191—41no—
197C2×C191C2×#12111yescharacteristic
198C2×C191#52511yescharacteristic
199C2×C191#53611yescharacteristic
200C2×C191#54711yescharacteristic
201C2×C191#54711yescharacteristic
202C2×C191#55211yescharacteristic
203C2×C191#55211yescharacteristic
204D191—24no—
205D191—81no—
206C191#241311yescharacteristic, complemented, Sylow
207#2413—1911nomaximal, Sylow
208C2×#123—1911no—
209C2×#123—1911no—
210C2×#117—1911no—
211C22×C4⋊C4—1911no—
212#398—1911no—
213#398D19111yescharacteristic, complemented
214#396—1911no—
215#396—1911no—
216#389—1911no—
217#389—1911no—
218#388—1911no—
219#388—1911no—
220#386—1911no—
221#385—1911no—
222#381—1911no—
223C22×D4—1911no—
224C23×C4—1911no—
225C23×C4—1911no—
226C23×C4—1911no—
227#123—3824no—
228#123—3824no—
229#117—3824no—
230C2×C4⋊C4—3824no—
231C2×C4⋊C4—1911no—
232C2×C4⋊C4—1911no—
233C2×C4⋊C4—1911no—
234C2×C4⋊C4—1911no—
235C2×C4⋊C4—1911no—
236C2×C4⋊C4—1911no—
237C2×C4⋊C4—1911no—
238C2×C4⋊C4—1911no—
239C2×C4⋊C4C2×D19111yescharacteristic
240C2×C4⋊C4C2×D19111yescharacteristic
241C2×C4⋊C4C2×D19111yescharacteristic
242C2×C4⋊C4C2×D19111yescharacteristic
243C2×C22⋊C4—1911no—
244C2×C22⋊C4—1911no—
245C2×C22⋊C4—1911no—
246C2×C22⋊C4—1911no—
247C2×C22⋊C4—1911no—
248C2×C22⋊C4—1911no—
249C2×C22⋊C4—1911no—
250C2×C22⋊C4—1911no—
251C2×C22⋊C4—1911no—
252C2×C42—1911no—
253C2×C42—1911no—
254#95—1911no—
255#95—1911no—
256#95—1911no—
257#95—1911no—
258#95—1911no—
259#95C2×D19111yescharacteristic
260#95C2×D19111yescharacteristic
261#95C2×D19111yescharacteristic
262C24—1911no—
263C24—1911no—
264C2×D4—3822no—
265C2×D4—3822no—
266C2×D4—3822no—
267C22×C4—3822no—
268C22×C4—3822no—
269C22×C4—3822no—
270C22×C4—3822no—
271C22×C4—3822no—
272C22×C4—3822no—
273C22×C4—3822no—
274C22×C4—3822no—
275C22×C4—1911no—
276C22×C4—1911no—
277C22×C4—1911no—
278C22×C4—1911no—
279C22×C4—1911no—
280C22×C4—1911no—
281C22×C4—1914no—
282C22×C4C22×D19111yescharacteristic
283C22×C4C22×D19111yescharacteristic
284C22×C4C22×D19111yescharacteristic
285C22×C4C22×D19111yescharacteristic
286C22×C4C22×D19111yescharacteristic
287C22×C4C22×D19111yescharacteristic
288C22×C4C22×D19111yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—3822no—
294C4⋊C4—3822no—
295C4⋊C4—3822no—
296C4⋊C4—3822no—
297C4⋊C4—3822no—
298C4⋊C4—3822no—
299C4⋊C4—3822no—
300C4⋊C4—3822no—
301C22⋊C4—3822no—
302C22⋊C4—3822no—
303C22⋊C4—3822no—
304C22⋊C4—3822no—
305C22⋊C4—3822no—
306C22⋊C4—3822no—
307C22⋊C4—3822no—
308C22⋊C4—3822no—
309C22⋊C4—1914no—
310C42—3822no—
311C42—3822no—
312C23—3821no—
313C23—3821no—
314C23—3821no—
315C23—3821no—
316C23—3821no—
317C23—3821no—
318C23—3821no—
319C23—3821no—
320C23—3821no—
321C23—3821no—
322C23—3821no—
323C23—1912no—
324C23—1912no—
325C23—1912no—
326C23C23×D19111yescharacteristic
327D4—7644no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—3828no—
347C2×C4—3828no—
348C2×C4—3821no—
349C2×C4—3821no—
350C2×C4—3821no—
351C2×C4—3821no—
352C2×C4—3821no—
353C2×C4—3821no—
354C2×C4—3821no—
355C2×C4—3821no—
356C2×C4—3821no—
357C2×C4—3821no—
358C2×C4—3821no—
359C2×C4—3821no—
360C2×C4—3821no—
361C2×C4—3821no—
362C2×C4—3821no—
363C2×C4—1912no—
364C2×C4—1912no—
365C2×C4—1912no—
366C2×C4—7644no—
367C2×C4D4×D19112yes—
368C2×C4D4×D19112yes—
369C2×C4#1569028812yes—
370C22—3822no—
371C22—3822no—
372C22—3822no—
373C22—3822no—
374C22—3822no—
375C22—3822no—
376C22—1914no—
377C22—7641no—
378C22—7641no—
379C22—7641no—
380C22—7641no—
381C22—7641no—
382C22—7641no—
383C22—7641no—
384C22C2×D4×D19111yescharacteristic
385C22C2×D4×D19111yescharacteristic
386C22#41×D19111yescharacteristic
387C22#41×D19111yescharacteristic
388C22C2×#1569028811yescharacteristic
389C22#2025936911yescharacteristic
390C22#2025937011yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—41no—
398C4—3822no—
399C4—3822no—
400C4—3822no—
401C4—7641no—
402C4—7641no—
403C4—7641no—
404C2—3824no—
405C2—15281no—
406C2#121×D19111yescharacteristic
407C2#2713317611yescharacteristic
408C2#2713323611yescharacteristic
409C2#2713331111yescharacteristic
410C2#2713331611yescharacteristic
411C2#2713334511yescharacteristic
412C2#2713335111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutator, socle, cosocleC23×C191C24
Fitting#398×C191C2
prime radicalC22×D764C22
hypercenter#398D191
hypocenterC191#2413
LCSG ▷ C23×C191 ▷ C191
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
3. C2×#20259280C2semidirect
4. C2×C4⋊C4×D191C2semidirect
5. #27132596C2semidirect
6. #27132585C2semidirect
7. #27132585C2semidirect
8. #27132560C2semidirect
9. #27132559C2semidirect
10. #27132555C2semidirect
11. #27132552C2semidirect
13. #27132537C2semidirect
14. #27132525C2semidirect
15. #398×C191C2semidirect
206. C191#2413semidirect
213. #398D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593072
C2×#202592802
C2×C4⋊C4×D1912
#271325962
#271325852
#271325602
#271325592
#271325552
#271325522
#271325412
#271325372
#271325252
#398×C1912
#2413191