Finite Group Databasebeta

← #37575962

Subgroups — #37575962

Order 24448.

788 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20259297C211yesmaximal, characteristic, complemented
2C2×#20259296C211yesmaximal, characteristic, complemented
3C2×#20259295C212yesmaximal, complemented
4C2×C4×C22⋊D191C211yesmaximal, characteristic, complemented
5C2×C4⋊C4×D191C211yesmaximal, characteristic, complemented
6#27132587C212yesmaximal, complemented
7#27132578C212yesmaximal, complemented
8#27132564C211yesmaximal, characteristic, complemented
9#27132559C211yesmaximal, characteristic, complemented
10#27132541C212yesmaximal, complemented
11#380×C191C211yesmaximal, characteristic, complemented
12C22×D764C2212yes—
13C22×D764C2211yescharacteristic
14C22×C22⋊D191C2212yes—
15C22×C22⋊D191C2211yescharacteristic
16C22×C4×D191C2212yes—
17C22×C4×D191C2211yescharacteristic
18#20259297—24no—
19#20259296—24no—
20#20259295—28no—
21C4×C22⋊D191—24no—
22C2×C4⋊Dic191C2211yescharacteristic
23C2×Dic191⋊C4C2212yes—
24C2×Dic191⋊C4C2212yes—
25C2×Dic191⋊C4C2211yescharacteristic
26C4⋊C4×D191—24no—
27C2×C22⋊Dic191C2211yescharacteristic
28C2×(C2×D191)⋊C4C2211yescharacteristic
29C2×(C2×D191)⋊C4C2212yes—
30C2×(C2×D191)⋊C4C2212yes—
31C2×(C2×D191)⋊C4C2212yes—
32C2×(C2×D191)⋊C4C2212yes—
33C2×C4×Dic191C2211yescharacteristic
34C191⋊#95C2212yes—
35C23×C4×C191C2211yescharacteristic
36C2×C4⋊C4×C191C2211yescharacteristic
37C2×C4⋊C4×C191C2211yescharacteristic
38C2×C22⋊C4×C191C2212yes—
39#95×C191C2212yes—
40C23×D191C2312yes—
41C23×D191C2311yescharacteristic
42C2×D764—24no—
43C2×D764—24no—
44C2×D764—24no—
45C2×D764—22no—
46C2×D764—22no—
47C2×D764—22no—
48C2×C22⋊D191—22no—
49C2×C22⋊D191—22no—
50C2×C22⋊D191—24no—
51C2×C22⋊D191—24no—
52C2×C22⋊D191—42no—
53C2×C22⋊D191D414yescomplemented
54C22×Dic191C2311yescharacteristic
55C22×Dic191C2312yes—
56C22×Dic191C2311yescharacteristic
57C22×Dic191C2311yescharacteristic
58C2×C4×D191—24no—
59C2×C4×D191—24no—
60C2×C4×D191—22no—
61C2×C4×D191—22no—
62C2×C4×D191—42no—
63C2×C4×D191D414yescomplemented
64C4⋊Dic191D414yescomplemented
65Dic191⋊C4—24no—
66Dic191⋊C4—22no—
67Dic191⋊C4—24no—
68C22⋊Dic191—22no—
69(C2×D191)⋊C4—22no—
70(C2×D191)⋊C4—24no—
71(C2×D191)⋊C4—24no—
72(C2×D191)⋊C4—24no—
73(C2×D191)⋊C4—42no—
74C4×Dic191—22no—
75C24×C191C2311yescharacteristic
76C22×C4×C191—22no—
77C22×C4×C191—22no—
78C22×C4×C191—22no—
79C22×C4×C191C2312yes—
80C22×C4×C191C2312yes—
81C22×C4×C191C2311yescharacteristic
82C22×C4×C191C2311yescharacteristic
83C4⋊C4×C191—22no—
84C4⋊C4×C191—22no—
85C22⋊C4×C191—24no—
86C22×D191—21no—
87C22×D191—21no—
88C22×D191—21no—
89C22×D191—21no—
90C22×D191—22no—
91C22×D191—22no—
92C22×D191—22no—
93C22×D191—22no—
94C22×D191—22no—
95C22×D191—22no—
96C22×D191—22no—
97C22×D191C2×D412yes—
98C22×D191C2×D412yes—
99C22×D191#4112yes—
100D764—48no—
101D764—44no—
102C22⋊D191—28no—
103C22⋊D191—48no—
104C2×Dic191—21no—
105C2×Dic191—21no—
106C2×Dic191—22no—
107C2×Dic191—21no—
108C2×Dic191—21no—
109C2×Dic191—22no—
110C2×Dic191—21no—
111C2×Dic191—21no—
112C2×Dic191—21no—
113C2×Dic191C2×D412yes—
114C2×Dic191C2×D412yes—
115C2×Dic191C2×D414yes—
116C4×D191—28no—
117C4×D191—48no—
118C23×C191—21no—
119C23×C191—21no—
120C23×C191—21no—
121C23×C191—21no—
122C23×C191—21no—
123C23×C191—21no—
124C23×C191C2×D412yes—
125C23×C191C2411yescharacteristic
126C2×C4×C191—22no—
127C2×C4×C191—22no—
128C2×C4×C191—22no—
129C2×C4×C191—22no—
130C2×C4×C191—21no—
131C2×C4×C191—21no—
132C2×C4×C191—21no—
133C2×C4×C191—22no—
134C2×C4×C191—22no—
135C2×C4×C191—44no—
136C2×C4×C191C2×D412yes—
137C2×C4×C191C2×D412yes—
138C2×C4×C191#4112yes—
139C22×C191—22no—
140C22×C191—22no—
141C22×C191—22no—
142C22×C191—41no—
143C22×C191—41no—
144C22×C191—41no—
145C22×C191—41no—
146C22×C191C22×D411yescharacteristic
147C22×C191C22×D411yescharacteristic
148C22×C191C22×D411yescharacteristic
149C22×C191C2×#4111yescharacteristic
150C22×C191C2×#4111yescharacteristic
151C22×C191H(5,𝔽2)11yescharacteristic
152C22×C1912−1+411yescharacteristic
153C2×D191—22no—
154C2×D191—22no—
155C2×D191—22no—
156C2×D191—22no—
157C2×D191—22no—
158C2×D191—22no—
159C2×D191—42no—
160C2×D191—42no—
161C2×D191—42no—
162C2×D191—42no—
163C2×D191—42no—
164C2×D191—42no—
165C2×D191—42no—
166C2×D191#12114yescomplemented
167C4×C191—41no—
168C4×C191—42no—
169C4×C191—42no—
170C4×C191#12114yescomplemented
171Dic191—22no—
172Dic191—22no—
173Dic191—24no—
174Dic191—41no—
175C2×C191—42no—
176C2×C191C2×#12111yescharacteristic
177C2×C191C2×#12111yescharacteristic
178C2×C191#53711yescharacteristic
179C2×C191D4211yescharacteristic
180C2×C191#54711yescharacteristic
181C2×C191#54811yescharacteristic
182C2×C191#55311yescharacteristic
183D191—24no—
184D191—82no—
185C191#241611yescharacteristic, complemented, Sylow
186#2416—1911nomaximal, Sylow
187C2×#121—1911no—
188C2×#121—1911no—
189C2×#121—1912no—
190C2×C4×D4—1911no—
191C22×C4⋊C4—1911no—
192#396—1912no—
193#394—1912no—
194#390—1911no—
195#389—1911no—
196#386—1912no—
197#380D19111yescharacteristic, complemented
198C22×D4—1911no—
199C22×D4—1912no—
200C22×D4—1912no—
201C22×D4—1911no—
202C23×C4—1911no—
203C23×C4—1912no—
204C23×C4C2×D19111yescharacteristic
205#121—3828no—
206#121—3824no—
207#121—3824no—
208C4×D4—3824no—
209C2×C4⋊C4—3824no—
210C2×C4⋊C4—1912no—
211C2×C4⋊C4—1911no—
212C2×C4⋊C4—1912no—
213C2×C4⋊C4—1911no—
214C2×C4⋊C4C2×D19111yescharacteristic
215C2×C4⋊C4C2×D19111yescharacteristic
216C2×C22⋊C4—1911no—
217C2×C22⋊C4—1911no—
218C2×C22⋊C4—1912no—
219C2×C22⋊C4—1912no—
220C2×C22⋊C4—1912no—
221C2×C22⋊C4—1912no—
222C2×C22⋊C4C2×D19112yes—
223C2×C42—1911no—
224#95—1912no—
225#95C2×D19112yes—
226C24—1912no—
227C24—1911no—
228C24C22×D19111yescharacteristic
229C2×D4—3824no—
230C2×D4—3824no—
231C2×D4—3824no—
232C2×D4—3822no—
233C2×D4—3822no—
234C2×D4—3824no—
235C2×D4—3824no—
236C2×D4—3822no—
237C2×D4—3822no—
238C2×D4—3822no—
239C2×D4—1914no—
240C2×D4—7642no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—3824no—
245C22×C4—3824no—
246C22×C4—3822no—
247C22×C4—3822no—
248C22×C4—1911no—
249C22×C4—1912no—
250C22×C4—1911no—
251C22×C4—1911no—
252C22×C4—1914no—
253C22×C4—7642no—
254C22×C4C22×D19112yes—
255C22×C4C22×D19111yescharacteristic
256C22×C4C22×D19112yes—
257C22×C4C22×D19111yescharacteristic
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—3824no—
261C4⋊C4—3822no—
262C4⋊C4—3824no—
263C4⋊C4—1914no—
264C22⋊C4—24no—
265C22⋊C4—3822no—
266C22⋊C4—3824no—
267C22⋊C4—3824no—
268C22⋊C4—3824no—
269C22⋊C4—3822no—
270C22⋊C4—7642no—
271C42—3822no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—3821no—
279C23—3821no—
280C23—3821no—
281C23—3821no—
282C23—3822no—
283C23—3822no—
284C23—3822no—
285C23—3822no—
286C23—3822no—
287C23—3822no—
288C23—3822no—
289C23—1912no—
290C23—1912no—
291C23—1912no—
292C23D4×D19112yes—
293C23C23×D19111yescharacteristic
294D4—3828no—
295D4—7648no—
296D4—7648no—
297D4—7644no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—22no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—44no—
308C2×C4—3821no—
309C2×C4—3821no—
310C2×C4—3822no—
311C2×C4—3821no—
312C2×C4—3821no—
313C2×C4—3822no—
314C2×C4—3828no—
315C2×C4—3821no—
316C2×C4—3821no—
317C2×C4—3821no—
318C2×C4—1912no—
319C2×C4—1912no—
320C2×C4—1914no—
321C2×C4—7648no—
322C2×C4D4×D19112yes—
323C2×C4D4×D19112yes—
324C2×C4#1569028712yes—
325C22—22no—
326C22—22no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—3822no—
333C22—3822no—
334C22—3822no—
335C22—3822no—
336C22—3822no—
337C22—3822no—
338C22—1914no—
339C22—7642no—
340C22—7642no—
341C22—7642no—
342C22—7642no—
343C22—7642no—
344C22—7642no—
345C22—7642no—
346C22C2×D4×D19111yescharacteristic
347C22C2×D4×D19111yescharacteristic
348C22C2×D4×D19111yescharacteristic
349C22#41×D19111yescharacteristic
350C22C2×#1569028711yescharacteristic
351C22#2025936811yescharacteristic
352C22#2025937011yescharacteristic
353C4—42no—
354C4—42no—
355C4—41no—
356C4—3824no—
357C4—3822no—
358C4—3822no—
359C4—7641no—
360C4#2025929514yescomplemented
361C2—42no—
362C2—3824no—
363C2—15282no—
364C2#121×D19111yescharacteristic
365C2C2×#2025929511yescharacteristic
366C2#2713324311yescharacteristic
367C2#2713329711yescharacteristic
368C2#2713331411yescharacteristic
369C2#2713332311yescharacteristic
370C2#2713335711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutator, socle, cosocleC23×C191C24
Fitting#380×C191C2
hypercenter#380D191
hypocenterC191#2416
LCSG ▷ C23×C191 ▷ C191
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C2×#20259297C2semidirect
2. C2×#20259296C2semidirect
3. C2×#20259295C2semidirect
4. C2×C4×C22⋊D191C2semidirect
5. C2×C4⋊C4×D191C2semidirect
6. #27132587C2semidirect
7. #27132578C2semidirect
8. #27132564C2semidirect
9. #27132559C2semidirect
10. #27132541C2semidirect
11. #380×C191C2semidirect
53. C2×C22⋊D191D4semidirect
63. C2×C4×D191D4semidirect
64. C4⋊Dic191D4semidirect
166. C2×D191#121semidirect
170. C4×C191#121semidirect
185. C191#2416semidirect
197. #380D191semidirect
360. C4#20259295semidirect

Maximal subgroups

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

subgroupindex
C2×#202592972
C2×#202592962
C2×#202592952
C2×C4×C22⋊D1912
C2×C4⋊C4×D1912
#271325872
#271325782
#271325642
#271325592
#271325412
#380×C1912
#2416191