Finite Group Databasebeta

← #37583931

Subgroups — #37583931

Order 24448.

358 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133268C211yesmaximal, characteristic, complemented
2#27132970C211yesmaximal, characteristic, complemented
3#27132963C211yesmaximal, characteristic, complemented
4#27132950C211yesmaximal, characteristic, complemented
5#27132940C211yesmaximal, characteristic, complemented
6#27132914C211yesmaximal, characteristic, complemented
7#27132911C211yesmaximal, characteristic, complemented
8#27132897C211yesmaximal, characteristic, complemented
9#27132894C211yesmaximal, characteristic, complemented
10#27132875C211yesmaximal, characteristic, complemented
11#27132875C211yesmaximal, characteristic, complemented
12#27132863C211yesmaximal, characteristic, complemented
13#27132858C211yesmaximal, characteristic, complemented
14#27132690C211yesmaximal, characteristic, complemented
15#542×C191C211yesmaximal, characteristic, complemented
16C2×#15690274C2211yescharacteristic
17C2×#15690274C2211yescharacteristic
18C2×#15690272C2211yescharacteristic
19C2×#15690272C2211yescharacteristic
20C2×#15690271C2211yescharacteristic
21C22×C191⋊C8C2211yescharacteristic
22#20259319C2211yescharacteristic
23#20259314C2211yescharacteristic
24#20259307—21no—
25#20259307—21no—
26#20259296C2211yescharacteristic
27#20259296C2211yescharacteristic
28#20259295—21no—
29#20259295—21no—
30C4×D764C2211yescharacteristic
31C4×D764C2211yescharacteristic
32#20259255C2211yescharacteristic
33#20259255C2211yescharacteristic
34#20259253C2211yescharacteristic
35#20259253C2211yescharacteristic
36C4⋊(C191⋊C8)C2211yescharacteristic
37C4⋊(C191⋊C8)C2211yescharacteristic
38C4⋊(C191⋊C8)C2211yescharacteristic
39C4⋊(C191⋊C8)C2211yescharacteristic
40#20259246C2211yescharacteristic
41#20259246C2211yescharacteristic
42#20259243C2211yescharacteristic
43#20259243C2211yescharacteristic
44#20259242C2211yescharacteristic
45#20259242C2211yescharacteristic
46#20259242C2211yescharacteristic
47#20259242C2211yescharacteristic
48C4⋊Q8×C191C2211yescharacteristic
49#126×C191—21no—
50#124×C191—21no—
51#124×C191C2211yescharacteristic
52#123×C191—21no—
53C22⋊Q8×C191—21no—
54C22⋊Q8×C191C2211yescharacteristic
55#121×C191C2211yescharacteristic
56C4×Q8×C191C2211yescharacteristic
57C4×D4×C191C2211yescharacteristic
58#117×C191C2211yescharacteristic
59C2×D764—21no—
60C2×D764—21no—
61C2×D764C2311yescharacteristic
62C2×D764C2311yescharacteristic
63C2×C22⋊D191—21no—
64C2×C22⋊D191—21no—
65C2×C4×D191—21no—
66C2×C4×D191—21no—
67#15690274—41no—
68#15690274—41no—
69#15690272—41no—
70#15690272—41no—
71#15690271—41no—
72C2×C191⋊C8—41no—
73C2×C191⋊C8C2311yescharacteristic
74C2×C191⋊C8C2311yescharacteristic
75C2×C191⋊C8C2311yescharacteristic
76C2×C191⋊C8C2311yescharacteristic
77C4⋊Dic191C2311yescharacteristic
78C4⋊Dic191C2311yescharacteristic
79Dic191⋊C4—21no—
80Dic191⋊C4—21no—
81(C2×D191)⋊C4—21no—
82(C2×D191)⋊C4—21no—
83(C2×D191)⋊C4—21no—
84(C2×D191)⋊C4—21no—
85C2×Q8×C191—21no—
86C2×Q8×C191C2311yescharacteristic
87C2×D4×C191—21no—
88C2×D4×C191C2311yescharacteristic
89C22×C4×C191—21no—
90C22×C4×C191C2311yescharacteristic
91C4⋊C4×C191—21no—
92C4⋊C4×C191—21no—
93C4⋊C4×C191—21no—
94C4⋊C4×C191D411yescharacteristic
95C4⋊C4×C191D411yescharacteristic
96C4⋊C4×C191C2311yescharacteristic
97C4⋊C4×C191C2311yescharacteristic
98C22⋊C4×C191—21no—
99C22⋊C4×C191—21no—
100C22⋊C4×C191—21no—
101C22⋊C4×C191—21no—
102C22⋊C4×C191—21no—
103C22⋊C4×C191D411yescharacteristic
104C22⋊C4×C191D411yescharacteristic
105C42×C191—21no—
106C42×C191C2311yescharacteristic
107C42×C191C2311yescharacteristic
108C22×D191—21no—
109C22×D191—21no—
110D764—21no—
111D764—21no—
112D764—21no—
113D764—21no—
114D764—81no—
115D764—81no—
116C22⋊D191—81no—
117C22⋊D191—81no—
118C2×Dic191—21no—
119C2×Dic191—21no—
120C4×D191—81no—
121C4×D191—81no—
122C191⋊C8—21no—
123C191⋊C8—21no—
124C191⋊C8—21no—
125C191⋊C8—21no—
126C23×C191—21no—
127C23×C191C2×D411yescharacteristic
128Q8×C191—21no—
129Q8×C191—21no—
130Q8×C191—81no—
131D4×C191—21no—
132D4×C191—21no—
133D4×C191—81no—
134C2×C4×C191—21no—
135C2×C4×C191—21no—
136C2×C4×C191—21no—
137C2×C4×C191—21no—
138C2×C4×C191—21no—
139C2×C4×C191—81no—
140C2×C4×C191C2×D411yescharacteristic
141C2×C4×C191C2×D411yescharacteristic
142C2×C4×C191C2×D411yescharacteristic
143C2×C4×C191C2×D411yescharacteristic
144C2×C4×C191C2×D411yescharacteristic
145C2×C4×C191C2411yescharacteristic
146C22×C191—21no—
147C22×C191—21no—
148C22×C191—21no—
149C22×C191—41no—
150C22×C191—41no—
151C22×C191—41no—
152C22×C191C22×D411yescharacteristic
153C2×D191—41no—
154C2×D191—41no—
155C2×D191—41no—
156C2×D191—41no—
157C2×D191—41no—
158C2×D191—41no—
159C4×C191—21no—
160C4×C191—21no—
161C4×C191—21no—
162C4×C191—21no—
163C4×C191—21no—
164C4×C191—41no—
165C4×C191—41no—
166C4×C191—41no—
167C4×C191H(5,𝔽2)11yescharacteristic
168C4×C1912−1+411yescharacteristic
169Dic191—41no—
170Dic191—41no—
171C2×C191—41no—
172C2×C191—81no—
173C2×C191#53711yescharacteristic
174C2×C191#57611yescharacteristic
175C2×C191#57711yescharacteristic
176D191—81no—
177D191—81no—
178C191#325711yescharacteristic, complemented, Sylow
179#3257—1911nomaximal, Sylow
180#542D19111yescharacteristic, complemented
181#540—1911no—
182#479—1911no—
183#478—1911no—
184#476—1911no—
185#474—1911no—
186#469—1911no—
187#468—1911no—
188#466—1911no—
189#465—1911no—
190#463—1911no—
191#463—1911no—
192#460—1911no—
193#459—1911no—
194#424—1911no—
195C2×SD16—1911no—
196C2×SD16—1911no—
197C2×D8—1911no—
198C2×D8—1911no—
199C2×M16—1911no—
200C22×C8—1911no—
201C4⋊Q8C2×D19111yescharacteristic
202#127—1911no—
203#126—21no—
204#125—1911no—
205#124—21no—
206#124C2×D19111yescharacteristic
207#123—21no—
208#123—3821no—
209#123—3821no—
210C22⋊Q8—21no—
211C22⋊Q8C2×D19111yescharacteristic
212#121—3821no—
213#121—3821no—
214#121—1911no—
215#121—1911no—
216#121C2×D19111yescharacteristic
217C4×Q8C2×D19111yescharacteristic
218C4×D4—1911no—
219C4×D4—1911no—
220C4×D4C2×D19111yescharacteristic
221#117C2×D19111yescharacteristic
222#107—1911no—
223#107—1911no—
224#106—1911no—
225#106—1911no—
226C4⋊C8—1911no—
227C4⋊C8—1911no—
228C4⋊C8—1911no—
229C4⋊C8—1911no—
230#103—1911no—
231#103—1911no—
232#102—1911no—
233#102—1911no—
234#102—1911no—
235#102—1911no—
236#102—1911no—
237#102—1911no—
238C2×Q8—21no—
239C2×Q8C22×D19111yescharacteristic
240C2×D4—21no—
241C2×D4—3821no—
242C2×D4—3821no—
243C2×D4—3821no—
244C2×D4—3821no—
245C2×D4—1911no—
246C2×D4—1911no—
247C2×D4C22×D19111yescharacteristic
248C22×C4—21no—
249C22×C4—3821no—
250C22×C4—3821no—
251C22×C4C22×D19111yescharacteristic
252SD16—7641no—
253SD16—7641no—
254D8—7641no—
255D8—7641no—
256M16—7641no—
257C2×C8—1911no—
258C2×C8—1911no—
259C2×C8—1911no—
260C2×C8—1911no—
261C2×C8—7641no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—3821no—
266C4⋊C4—3821no—
267C4⋊C4—1911no—
268C4⋊C4—1911no—
269C4⋊C4C22⋊D19111yescharacteristic
270C4⋊C4C22⋊D19111yescharacteristic
271C4⋊C4C22×D19111yescharacteristic
272C4⋊C4C22×D19111yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—3821no—
279C22⋊C4—3821no—
280C22⋊C4—3821no—
281C22⋊C4—3821no—
282C22⋊C4C22⋊D19111yescharacteristic
283C22⋊C4C22⋊D19111yescharacteristic
284C42—21no—
285C42C22×D19111yescharacteristic
286C42C22×D19111yescharacteristic
287C23—21no—
288C23—3821no—
289C23—3821no—
290C23C2×C22⋊D19111yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—81no—
294D4—21no—
295D4—21no—
296D4—81no—
297D4—3821no—
298D4—3821no—
299D4—3821no—
300D4—3821no—
301D4—15281no—
302D4—15281no—
303D4—15281no—
304D4—15281no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—3821no—
312C2×C4—3821no—
313C2×C4—15281no—
314C2×C4—15281no—
315C2×C4C2×C22⋊D19111yescharacteristic
316C2×C4C2×C22⋊D19111yescharacteristic
317C2×C4C2×C22⋊D19111yescharacteristic
318C2×C4C2×C22⋊D19111yescharacteristic
319C2×C4C2×C22⋊D19111yescharacteristic
320C2×C4C23×D19111yescharacteristic
321C8—3821no—
322C8—3821no—
323C8—3821no—
324C8—3821no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—7641no—
332C22—7641no—
333C22—7641no—
334C22—7641no—
335C22—7641no—
336C22—7641no—
337C22C22×C22⋊D19111yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—7641no—
347C4—7641no—
348C4#2025936811yescharacteristic
349C4#2025936911yescharacteristic
350C2—41no—
351C2—81no—
352C2—15281no—
353C2—15281no—
354C2#2713324111yescharacteristic
355C2#2713346611yescharacteristic
356C2#2713347111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#542×C191C2
socleC22×C191C22×D4
hypercenter#542D191
hypocenterC191#3257
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #27133268C2semidirect
2. #27132970C2semidirect
3. #27132963C2semidirect
4. #27132950C2semidirect
5. #27132940C2semidirect
6. #27132914C2semidirect
7. #27132911C2semidirect
8. #27132897C2semidirect
9. #27132894C2semidirect
10. #27132875C2semidirect
11. #27132875C2semidirect
12. #27132863C2semidirect
13. #27132858C2semidirect
14. #27132690C2semidirect
15. #542×C191C2semidirect
178. C191#3257semidirect
180. #542D191semidirect

Maximal subgroups

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

subgroupindex
#271332682
#271329702
#271329632
#271329502
#271329402
#271329142
#271329112
#271328972
#271328942
#271328752
#271328632
#271328582
#271326902
#542×C1912
#3257191