Finite Group Databasebeta

← #37575797

Subgroups — #37575797

Order 24448.

528 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×#20259287C211yesmaximal, characteristic, complemented
2C2×#20259280C211yesmaximal, characteristic
3#27132605C211yesmaximal, characteristic, complemented
4#27132598C211yesmaximal, characteristic
5#27132596C211yesmaximal, characteristic, complemented
6#27132585C211yesmaximal, characteristic
7#27132585C211yesmaximal, characteristic
8#27132584C211yesmaximal, characteristic, complemented
9#27132576C211yesmaximal, characteristic
10C4⋊C4×Dic191C211yesmaximal, characteristic, complemented
11C4⋊C4×Dic191C211yesmaximal, characteristic, complemented
12#27132514C211yesmaximal, characteristic, complemented
13#27132510C211yesmaximal, characteristic
14#27132510C211yesmaximal, characteristic
15#398×C191C211yesmaximal, characteristic, complemented
16C22×Dic382C2211yescharacteristic
17C22×C4×D191C2211yescharacteristic
18#20259287—24no—
19#20259280—24no—
20C2×C4⋊Dic191C2211yescharacteristic
21C2×C4⋊Dic191C2211yescharacteristic
22C2×C4⋊Dic191C2211yescharacteristic
23C2×Dic191⋊C4C2211yescharacteristic
24C2×Dic191⋊C4C2211yescharacteristic
25C2×Dic191⋊C4C2211yescharacteristic
26C2×Dic191⋊C4C2211yescharacteristic
27C2×(C2×D191)⋊C4C2211yescharacteristic
28C2×(C2×D191)⋊C4C2211yescharacteristic
29C2×(C2×D191)⋊C4C2211yescharacteristic
30C2×(C2×D191)⋊C4C2211yescharacteristic
31C2×(C2×D191)⋊C4C2211yescharacteristic
32C2×(C2×D191)⋊C4C2211yescharacteristic
33C2×C4×Dic191C2211yescharacteristic
34C2×C4×Dic191C2211yescharacteristic
35C2×C4×Dic191C2211yescharacteristic
36C2×C4×Dic191C2211yescharacteristic
37C2×C4×Dic191C2211yescharacteristic
38C2×C4×Dic191C2211yescharacteristic
39C191⋊#95C2211yescharacteristic
40C191⋊#95C2211yescharacteristic
41C191⋊#95C2211yescharacteristic
42C191⋊#95C2211yescharacteristic
43C191⋊#95C2211yescharacteristic
44C191⋊#95C2211yescharacteristic
45C191⋊#95C2211yescharacteristic
46C2×C4⋊C4×C191C2211yescharacteristic
47C2×C4⋊C4×C191C2211yescharacteristic
48C2×C4⋊C4×C191C2211yescharacteristic
49C2×C4⋊C4×C191C2211yescharacteristic
50#95×C191C2211yescharacteristic
51#95×C191C2211yescharacteristic
52#95×C191C2211yescharacteristic
53C23×D191C2311yescharacteristic
54C2×Dic382—22no—
55C2×Dic382—22no—
56C2×Dic382—22no—
57C22×Dic191C2311yescharacteristic
58C22×Dic191C2311yescharacteristic
59C22×Dic191C2311yescharacteristic
60C22×Dic191C2311yescharacteristic
61C22×Dic191C2311yescharacteristic
62C22×Dic191C2311yescharacteristic
63C22×Dic191C2311yescharacteristic
64C2×C4×D191—22no—
65C2×C4×D191—22no—
66C2×C4×D191Q814yescomplemented
67C4⋊Dic191—22no—
68C4⋊Dic191—22no—
69C4⋊Dic191—22no—
70Dic191⋊C4—22no—
71Dic191⋊C4—22no—
72Dic191⋊C4—22no—
73Dic191⋊C4—22no—
74(C2×D191)⋊C4—22no—
75(C2×D191)⋊C4—22no—
76(C2×D191)⋊C4—22no—
77(C2×D191)⋊C4—22no—
78(C2×D191)⋊C4—22no—
79(C2×D191)⋊C4—22no—
80C4×Dic191—22no—
81C4×Dic191—22no—
82C4×Dic191—22no—
83C4×Dic191—22no—
84C4×Dic191—22no—
85C4×Dic191D414yes—
86C22×C4×C191C2311yescharacteristic
87C22×C4×C191C2311yescharacteristic
88C22×C4×C191C2311yescharacteristic
89C22×C4×C191C2311yescharacteristic
90C22×C4×C191C2311yescharacteristic
91C22×C4×C191C2311yescharacteristic
92C22×C4×C191C2311yescharacteristic
93C4⋊C4×C191—22no—
94C4⋊C4×C191—22no—
95C4⋊C4×C191—22no—
96C4⋊C4×C191—22no—
97C22×D191—21no—
98C22×D191—21no—
99C22×D191—21no—
100C22×D191—21no—
101C22×D191—21no—
102C22×D191—21no—
103C22×D191C2×Q812yes—
104Dic382—28no—
105C2×Dic191—21no—
106C2×Dic191—21no—
107C2×Dic191—21no—
108C2×Dic191—21no—
109C2×Dic191—21no—
110C2×Dic191—21no—
111C2×Dic191—21no—
112C2×Dic191—21no—
113C2×Dic191—21no—
114C2×Dic191—21no—
115C2×Dic191—21no—
116C2×Dic191—21no—
117C2×Dic191—21no—
118C2×Dic191—21no—
119C2×Dic191—21no—
120C2×Dic191C2×D412yes—
121C2×Dic191C2×D412yes—
122C2×Dic191C2×Q812yes—
123C2×Dic191#4112yes—
124C2×Dic191#4112yes—
125C2×Dic191#4112yes—
126C4×D191—28no—
127C23×C191C2411yescharacteristic
128C2×C4×C191—21no—
129C2×C4×C191—21no—
130C2×C4×C191—21no—
131C2×C4×C191—21no—
132C2×C4×C191—21no—
133C2×C4×C191—21no—
134C2×C4×C191—21no—
135C2×C4×C191—21no—
136C2×C4×C191—21no—
137C2×C4×C191—21no—
138C2×C4×C191—21no—
139C2×C4×C191—21no—
140C2×C4×C191—21no—
141C2×C4×C191—21no—
142C2×C4×C191—21no—
143C2×C4×C191—21no—
144C2×C4×C191—21no—
145C2×C4×C191C2×D412yes—
146C2×C4×C191C2×Q812yes—
147C2×C4×C191#4112yes—
148C2×C4×C191#4112yes—
149C22×C191C22×D411yescharacteristic
150C22×C191C22×Q811yescharacteristic
151C22×C191C2×#4111yescharacteristic
152C22×C191C2×#4111yescharacteristic
153C22×C191C2×#4111yescharacteristic
154C22×C191C2×#4111yescharacteristic
155C22×C191C2×#4111yescharacteristic
156C2×D191—22no—
157C2×D191—22no—
158C2×D191—22no—
159C2×D191—41no—
160C2×D191—41no—
161C2×D191—41no—
162C2×D191—41no—
163C4×C191—22no—
164C4×C191—22no—
165C4×C191—22no—
166C4×C191—22no—
167C4×C191—41no—
168C4×C191—41no—
169C4×C191—41no—
170Dic191—22no—
171Dic191—22no—
172Dic191—22no—
173Dic191—41no—
174Dic191—41no—
175Dic191—41no—
176Dic191C22⋊Q814yes—
177C2×C191C2×C22⋊Q811yescharacteristic
178C2×C191#52511yescharacteristic
179C2×C191#52911yescharacteristic
180C2×C191#52911yescharacteristic
181C2×C191#53211yescharacteristic
182C2×C191#53311yescharacteristic
183C2×C191#53311yescharacteristic
184D191—42no—
185C191#239611yescharacteristic, complemented, Sylow
186#2396—1911nomaximal, Sylow
187C2×C4×Q8—1911no—
188C2×#117—1911no—
189#400—1911no—
190#399—1911no—
191#398—1911no—
192#398D19111yescharacteristic, complemented
193#396—1911no—
194#396—1911no—
195#395—1911no—
196#393—1911no—
197C4×C4⋊C4—1911no—
198C4×C4⋊C4—1911no—
199C4×C4⋊C4—1911no—
200C4×C22⋊C4—1911no—
201C4×C22⋊C4—1911no—
202C22×Q8—1911no—
203C23×C4—1911no—
204C4×Q8—3824no—
205#117—3824no—
206C2×C4⋊C4—1911no—
207C2×C4⋊C4—1911no—
208C2×C4⋊C4—1911no—
209C2×C4⋊C4—1911no—
210C2×C4⋊C4—1911no—
211C2×C4⋊C4—1911no—
212C2×C4⋊C4—1911no—
213C2×C4⋊C4C2×D19111yescharacteristic
214C2×C4⋊C4C2×D19111yescharacteristic
215C2×C4⋊C4C2×D19111yescharacteristic
216C2×C4⋊C4C2×D19111yescharacteristic
217C2×C22⋊C4—1911no—
218C2×C22⋊C4—1911no—
219C2×C22⋊C4—1911no—
220C2×C22⋊C4—1911no—
221C2×C22⋊C4—1911no—
222C2×C22⋊C4—1911no—
223C2×C42—1911no—
224C2×C42—1911no—
225C2×C42—1911no—
226C2×C42—1911no—
227C2×C42—1911no—
228C2×C42—1911no—
229#95—1911no—
230#95—1911no—
231#95—1911no—
232#95—1911no—
233#95—1911no—
234#95—1911no—
235#95—1911no—
236#95C2×D19111yescharacteristic
237#95C2×D19111yescharacteristic
238#95C2×D19111yescharacteristic
239C24—1911no—
240C2×Q8—3822no—
241C2×Q8—3822no—
242C2×Q8—3822no—
243C22×C4—3822no—
244C22×C4—3822no—
245C22×C4—1911no—
246C22×C4—1911no—
247C22×C4—1911no—
248C22×C4—1911no—
249C22×C4—1911no—
250C22×C4—1911no—
251C22×C4—1914no—
252C22×C4—1911no—
253C22×C4C22×D19111yescharacteristic
254C22×C4C22×D19111yescharacteristic
255C22×C4C22×D19111yescharacteristic
256C22×C4C22×D19111yescharacteristic
257C22×C4C22×D19111yescharacteristic
258C22×C4C22×D19111yescharacteristic
259C22×C4C22×D19111yescharacteristic
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—3822no—
265C4⋊C4—3822no—
266C4⋊C4—3822no—
267C4⋊C4—3822no—
268C4⋊C4—3822no—
269C4⋊C4—3822no—
270C4⋊C4—3822no—
271C22⋊C4—3822no—
272C22⋊C4—3822no—
273C22⋊C4—3822no—
274C22⋊C4—3822no—
275C22⋊C4—3822no—
276C22⋊C4—3822no—
277C42—3822no—
278C42—3822no—
279C42—3822no—
280C42—3822no—
281C42—3822no—
282C42—1914no—
283C23—3821no—
284C23—3821no—
285C23—3821no—
286C23—3821no—
287C23—3821no—
288C23—3821no—
289C23—1912no—
290C23C23×D19111yescharacteristic
291Q8—3828no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—3828no—
310C2×C4—3821no—
311C2×C4—3821no—
312C2×C4—3821no—
313C2×C4—3821no—
314C2×C4—3821no—
315C2×C4—3821no—
316C2×C4—3821no—
317C2×C4—3821no—
318C2×C4—3821no—
319C2×C4—3821no—
320C2×C4—3821no—
321C2×C4—3821no—
322C2×C4—3821no—
323C2×C4—3821no—
324C2×C4—3821no—
325C2×C4—1912no—
326C2×C4—1912no—
327C2×C4—1912no—
328C2×C4—1912no—
329C2×C4—1912no—
330C2×C4—1912no—
331C2×C4D4×D19112yes—
332C2×C4Q8×D19112yes—
333C2×C4#1569028612yes—
334C2×C4#1569028812yes—
335C22—3822no—
336C22—3822no—
337C22—3822no—
338C22—7641no—
339C22—7641no—
340C22—7641no—
341C22—7641no—
342C22C2×D4×D19111yescharacteristic
343C22C2×Q8×D19111yescharacteristic
344C22#41×D19111yescharacteristic
345C22#41×D19111yescharacteristic
346C22#41×D19111yescharacteristic
347C22C2×#1569028611yescharacteristic
348C22C2×#1569028811yescharacteristic
349C4—22no—
350C4—22no—
351C4—22no—
352C4—22no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—3822no—
357C4—3822no—
358C4—3822no—
359C4—1914no—
360C4—7641no—
361C4—7641no—
362C4—7641no—
363C2—7642no—
364C2C22⋊Q8×D19111yescharacteristic
365C2#2713317611yescharacteristic
366C2#2713319011yescharacteristic
367C2#2713319811yescharacteristic
368C2#2713320811yescharacteristic
369C2#2713321811yescharacteristic
370C2#2713321911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutator, socle, cosocleC23×C191C24
Fitting#398×C191C2
prime radicalC23×D191C23
hypercenter#398D191
hypocenterC191#2396
LCSG ▷ C23×C191 ▷ C191
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#20259287C2semidirect
3. #27132605C2semidirect
5. #27132596C2semidirect
8. #27132584C2semidirect
10. C4⋊C4×Dic191C2semidirect
11. C4⋊C4×Dic191C2semidirect
12. #27132514C2semidirect
15. #398×C191C2semidirect
66. C2×C4×D191Q8semidirect
185. C191#2396semidirect
192. #398D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202592872
C2×#202592802
#271326052
#271325982
#271325962
#271325852
#271325842
#271325762
C4⋊C4×Dic1912
#271325142
#271325102
#398×C1912
#2396191