Finite Group Databasebeta

← #37576110

Subgroups — #37576110

Order 24448.

832 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20259318C211yesmaximal, characteristic, complemented
2C2×#20259296C211yesmaximal, characteristic, complemented
3C2×#20259294C212yesmaximal, complemented
4C2×D4×Dic191C211yesmaximal, characteristic, complemented
5#27132578C212yesmaximal, complemented
6#27132571C212yesmaximal, complemented
7#27132564C211yesmaximal, characteristic, complemented
8#27132559C211yesmaximal, characteristic, complemented
9#27132540C212yesmaximal, complemented
10C4×C22⋊Dic191C211yesmaximal, characteristic, complemented
11C2×#121×C191C211yesmaximal, characteristic, complemented
12C22×D764C2211yescharacteristic
13C22×C22⋊D191C2212yes—
14C22×C22⋊D191C2212yes—
15C22×C22⋊D191C2212yes—
16C23×Dic191C2212yes—
17#20259318—24no—
18#20259296—24no—
19#20259294—28no—
20D4×Dic191—24no—
21C2×C4⋊Dic191C2211yescharacteristic
22C2×Dic191⋊C4C2212yes—
23C2×C22⋊Dic191C2211yescharacteristic
24C2×C22⋊Dic191C2212yes—
25C2×C22⋊Dic191C2211yescharacteristic
26C2×(C2×D191)⋊C4C2212yes—
27C2×(C2×D191)⋊C4C2212yes—
28C2×(C2×D191)⋊C4C2212yes—
29C2×C4×Dic191C2211yescharacteristic
30C2×C4×Dic191C2211yescharacteristic
31C191⋊#95C2211yescharacteristic
32C191⋊#95C2211yescharacteristic
33C191⋊#95C2212yes—
34C22×D4×C191C2212yes—
35C22×D4×C191C2211yescharacteristic
36C23×C4×C191C2211yescharacteristic
37#121×C191—24no—
38C2×C4⋊C4×C191C2211yescharacteristic
39C2×C22⋊C4×C191C2212yes—
40C23×D191C2312yes—
41C2×D764—22no—
42C2×D764—22no—
43C2×D764—22no—
44C2×C22⋊D191—24no—
45C2×C22⋊D191—24no—
46C2×C22⋊D191—24no—
47C2×C22⋊D191—24no—
48C2×C22⋊D191—24no—
49C2×C22⋊D191—24no—
50C2×C22⋊D191—42no—
51C2×C22⋊D191—42no—
52C2×C22⋊D191—42no—
53C22×Dic191—24no—
54C22×Dic191—24no—
55C22×Dic191—42no—
56C22×Dic191C2311yescharacteristic
57C22×Dic191C2311yescharacteristic
58C22×Dic191C2312yes—
59C22×Dic191C2311yescharacteristic
60C22×Dic191C2311yescharacteristic
61C4⋊Dic191D414yescomplemented
62Dic191⋊C4—24no—
63C22⋊Dic191—24no—
64C22⋊Dic191—22no—
65C22⋊Dic191D414yescomplemented
66(C2×D191)⋊C4—24no—
67(C2×D191)⋊C4—24no—
68(C2×D191)⋊C4—42no—
69C4×Dic191—22no—
70C4×Dic191—22no—
71C24×C191C2312yes—
72C24×C191C2311yescharacteristic
73C2×D4×C191—24no—
74C2×D4×C191—24no—
75C2×D4×C191—22no—
76C2×D4×C191—22no—
77C2×D4×C191—42no—
78C2×D4×C191D414yescomplemented
79C22×C4×C191—22no—
80C22×C4×C191—22no—
81C22×C4×C191—22no—
82C22×C4×C191C2311yescharacteristic
83C22×C4×C191C2312yes—
84C22×C4×C191C2311yescharacteristic
85C4⋊C4×C191—22no—
86C22⋊C4×C191—24no—
87C22×D191—22no—
88C22×D191—22no—
89C22×D191—22no—
90C22×D191—22no—
91C22×D191—22no—
92C22×D191—22no—
93C22×D191—22no—
94D764—44no—
95C22⋊D191—48no—
96C22⋊D191—48no—
97C22⋊D191—48no—
98C2×Dic191—21no—
99C2×Dic191—21no—
100C2×Dic191—21no—
101C2×Dic191—22no—
102C2×Dic191—21no—
103C2×Dic191—22no—
104C2×Dic191—21no—
105C2×Dic191—21no—
106C2×Dic191—21no—
107C2×Dic191—21no—
108C2×Dic191—21no—
109C2×Dic191—48no—
110C2×Dic191C2×D412yes—
111C2×Dic191C2×D414yes—
112C2×Dic191C2×D412yes—
113C2×Dic191#4112yes—
114C23×C191—21no—
115C23×C191—21no—
116C23×C191—22no—
117C23×C191—22no—
118C23×C191—21no—
119C23×C191—22no—
120C23×C191—21no—
121C23×C191—22no—
122C23×C191—21no—
123C23×C191—22no—
124C23×C191—22no—
125C23×C191—21no—
126C23×C191C2×D412yes—
127C23×C191C2×D414yes—
128C23×C191C2411yescharacteristic
129D4×C191—28no—
130D4×C191—48no—
131C2×C4×C191—21no—
132C2×C4×C191—22no—
133C2×C4×C191—21no—
134C2×C4×C191—22no—
135C2×C4×C191—21no—
136C2×C4×C191—22no—
137C2×C4×C191—44no—
138C2×C4×C191C2×D412yes—
139C2×C4×C191C2×D412yes—
140C2×C4×C191#4112yes—
141C22×C191—24no—
142C22×C191—22no—
143C22×C191—22no—
144C22×C191—24no—
145C22×C191—22no—
146C22×C191—24no—
147C22×C191—41no—
148C22×C191—42no—
149C22×C191—41no—
150C22×C191—42no—
151C22×C191—42no—
152C22×C191—41no—
153C22×C191—41no—
154C22×C191—42no—
155C22×C191C22×D411yescharacteristic
156C22×C191C22×D411yescharacteristic
157C22×C191C22×D411yescharacteristic
158C22×C191C2×#4111yescharacteristic
159C22×C191C2×#4111yescharacteristic
160C22×C191H(5,𝔽2)11yescharacteristic
161C22×C191H(5,𝔽2)11yescharacteristic
162C2×D191—42no—
163C2×D191—42no—
164C2×D191—42no—
165C2×D191—42no—
166C2×D191—42no—
167C2×D191—42no—
168C2×D191—42no—
169C4×C191—41no—
170C4×C191—42no—
171C4×C191#12114yescomplemented
172Dic191—22no—
173Dic191—24no—
174Dic191—22no—
175Dic191—22no—
176Dic191—41no—
177C2×C191—44no—
178C2×C191—42no—
179C2×C191C2×#12111yescharacteristic
180C2×C191#53211yescharacteristic
181C2×C191#54011yescharacteristic
182C2×C191D4211yescharacteristic
183C2×C191D4211yescharacteristic
184C2×C191#54611yescharacteristic
185C2×C191#55011yescharacteristic
186D191—82no—
187C191#242811yescharacteristic, complemented, Sylow
188#2428—1911nomaximal, Sylow
189C2×#127—1911no—
190C2×#121—1912no—
191C2×#121—1911no—
192C2×#121D19111yescharacteristic, complemented
193C2×C4×D4—1911no—
194#394—1912no—
195#392—1912no—
196#390—1911no—
197#389—1911no—
198#386—1912no—
199C4×C22⋊C4—1911no—
200C22×D4—1912no—
201C22×D4—1912no—
202C22×D4—1912no—
203C22×D4—1911no—
204C22×D4C2×D19112yes—
205C22×D4C2×D19111yescharacteristic
206C23×C4—1912no—
207C23×C4C2×D19111yescharacteristic
208#127—3824no—
209#121—24no—
210#121—3824no—
211#121—3828no—
212C4×D4—3824no—
213C2×C4⋊C4—1912no—
214C2×C4⋊C4—1911no—
215C2×C4⋊C4C2×D19111yescharacteristic
216C2×C22⋊C4—1912no—
217C2×C22⋊C4—1911no—
218C2×C22⋊C4—1912no—
219C2×C22⋊C4—1912no—
220C2×C22⋊C4—1911no—
221C2×C22⋊C4—1912no—
222C2×C22⋊C4C2×D19112yes—
223C2×C42—1911no—
224C2×C42—1911no—
225#95—1911no—
226#95—1911no—
227#95—1912no—
228C24—1912no—
229C24C22×D19111yescharacteristic
230C24C22×D19112yes—
231C2×D4—24no—
232C2×D4—24no—
233C2×D4—22no—
234C2×D4—22no—
235C2×D4—42no—
236C2×D4—3824no—
237C2×D4—3824no—
238C2×D4—3824no—
239C2×D4—3824no—
240C2×D4—3824no—
241C2×D4—3824no—
242C2×D4—3822no—
243C2×D4—3822no—
244C2×D4—3822no—
245C2×D4—7642no—
246C2×D4—7642no—
247C2×D4—7642no—
248C2×D4C22⋊D19114yescomplemented
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—3824no—
253C22×C4—3824no—
254C22×C4—1911no—
255C22×C4—1911no—
256C22×C4—1911no—
257C22×C4—1911no—
258C22×C4—1912no—
259C22×C4—7642no—
260C22×C4C22×D19111yescharacteristic
261C22×C4C22×D19112yes—
262C22×C4C22×D19111yescharacteristic
263C4⋊C4—22no—
264C4⋊C4—3824no—
265C4⋊C4—1914no—
266C22⋊C4—24no—
267C22⋊C4—3824no—
268C22⋊C4—3824no—
269C22⋊C4—3822no—
270C22⋊C4—3824no—
271C22⋊C4—1914no—
272C22⋊C4—7642no—
273C42—3822no—
274C42—3822no—
275C23—22no—
276C23—21no—
277C23—22no—
278C23—21no—
279C23—21no—
280C23—22no—
281C23—21no—
282C23—22no—
283C23—21no—
284C23—22no—
285C23—22no—
286C23—21no—
287C23—3822no—
288C23—3822no—
289C23—3822no—
290C23—3822no—
291C23—3822no—
292C23—3822no—
293C23—3822no—
294C23D4×D19112yes—
295C23C2×C22⋊D19114yes—
296C23C23×D19111yescharacteristic
297D4—28no—
298D4—48no—
299D4—7648no—
300D4—7648no—
301D4—7648no—
302D4—7644no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—22no—
309C2×C4—44no—
310C2×C4—3821no—
311C2×C4—3822no—
312C2×C4—3821no—
313C2×C4—3821no—
314C2×C4—3821no—
315C2×C4—3821no—
316C2×C4—3822no—
317C2×C4—3821no—
318C2×C4—3821no—
319C2×C4—3821no—
320C2×C4—3821no—
321C2×C4—1912no—
322C2×C4—1914no—
323C2×C4—1912no—
324C2×C4—1912no—
325C2×C4—7648no—
326C2×C4D4×D19112yes—
327C2×C4C2×C22⋊D19112yes—
328C2×C4#1569028612yes—
329C22—22no—
330C22—22no—
331C22—24no—
332C22—22no—
333C22—24no—
334C22—24no—
335C22—42no—
336C22—41no—
337C22—42no—
338C22—42no—
339C22—41no—
340C22—42no—
341C22—41no—
342C22—41no—
343C22—7642no—
344C22—7642no—
345C22—7642no—
346C22—7642no—
347C22—7642no—
348C22—7642no—
349C22—7642no—
350C22C2×D4×D19111yescharacteristic
351C22C2×D4×D19111yescharacteristic
352C22C22×C22⋊D19111yescharacteristic
353C22#41×D19111yescharacteristic
354C22C2×#1569028611yescharacteristic
355C22#2025936711yescharacteristic
356C22#2025936811yescharacteristic
357C4—42no—
358C4—41no—
359C4—3822no—
360C4—3822no—
361C4—3824no—
362C4—3822no—
363C4—7641no—
364C4#2025929414yescomplemented
365C2—42no—
366C2—44no—
367C2—15282no—
368C2C2×#2025929411yescharacteristic
369C2#2713320811yescharacteristic
370C2#2713326611yescharacteristic
371C2D4×C22⋊D19111yescharacteristic
372C2#2713329711yescharacteristic
373C2#2713330111yescharacteristic
374C2#2713333111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutator, socle, cosocleC23×C191C24
FittingC2×#121×C191C2
hypercenterC2×#121D191
hypocenterC191#2428
LCSG ▷ C23×C191 ▷ C191
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#20259318C2semidirect
2. C2×#20259296C2semidirect
3. C2×#20259294C2semidirect
4. C2×D4×Dic191C2semidirect
5. #27132578C2semidirect
6. #27132571C2semidirect
7. #27132564C2semidirect
8. #27132559C2semidirect
9. #27132540C2semidirect
10. C4×C22⋊Dic191C2semidirect
11. C2×#121×C191C2semidirect
61. C4⋊Dic191D4semidirect
65. C22⋊Dic191D4semidirect
78. C2×D4×C191D4semidirect
171. C4×C191#121semidirect
187. C191#2428semidirect
192. C2×#121D191semidirect
248. C2×D4C22⋊D191semidirect
364. C4#20259294semidirect

Maximal subgroups

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

subgroupindex
C2×#202593182
C2×#202592962
C2×#202592942
C2×D4×Dic1912
#271325782
#271325712
#271325642
#271325592
#271325402
C4×C22⋊Dic1912
C2×#121×C1912
#2428191