Finite Group Databasebeta

← #37584080

Subgroups — #37584080

Order 24448.

478 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20259355C211yesmaximal, characteristic, complemented
2C2×#20259344C211yesmaximal, characteristic, complemented
3#27133322C211yesmaximal, characteristic, complemented
4#27133318C211yesmaximal, characteristic, complemented
5#27133057C211yesmaximal, characteristic, complemented
6#27132909C211yesmaximal, characteristic, complemented
7#27132904C211yesmaximal, characteristic, complemented
8#27132879C211yesmaximal, characteristic, complemented
9#27132874C211yesmaximal, characteristic, complemented
10#27132827C211yesmaximal, characteristic, complemented
11#27132827C211yesmaximal, characteristic, complemented
12#27132821C211yesmaximal, characteristic, complemented
13#27132810C211yesmaximal, characteristic, complemented
14#27132765C211yesmaximal, characteristic, complemented
15#435×C191C211yesmaximal, characteristic, complemented
16C2×#15690287C2211yescharacteristic
17C2×#15690287C2211yescharacteristic
18C2×#15690287C2211yescharacteristic
19C22×Dic382C2211yescharacteristic
20#20259355—24no—
21#20259344—24no—
22C2×Dic764C2211yescharacteristic
23C2×Dic764C2211yescharacteristic
24C2×Dic764C2211yescharacteristic
25C2×Dic764C2211yescharacteristic
26C2×#15690276C2211yescharacteristic
27C2×#15690276C2211yescharacteristic
28C2×#15690276C2211yescharacteristic
29C2×#15690276C2211yescharacteristic
30C2×D1528C2211yescharacteristic
31#20259322C2211yescharacteristic
32#20259310C2211yescharacteristic
33#20259308—21no—
34#20259304—21no—
35#20259304—21no—
36#20259301C2211yescharacteristic
37#20259301C2211yescharacteristic
38#20259301C2211yescharacteristic
39#20259300—21no—
40#20259296C2211yescharacteristic
41#20259294—21no—
42#20259293—21no—
43C4×Dic382C2211yescharacteristic
44C4×D764C2211yescharacteristic
45(C22⋊D191)⋊C4—21no—
46C4⋊C4×D191—21no—
47#20259256C2211yescharacteristic
48#20259247C2211yescharacteristic
49#20259247C2211yescharacteristic
50#20259247C2211yescharacteristic
51#20259247C2211yescharacteristic
52#20259244C2211yescharacteristic
53#20259244C2211yescharacteristic
54C2×M16×C191C2211yescharacteristic
55C22×C8×C191C2211yescharacteristic
56C4×D4×C191C2211yescharacteristic
57C4⋊C8×C191C2211yescharacteristic
58C22⋊C8×C191C2211yescharacteristic
59C22⋊C8×C191C2211yescharacteristic
60#97×C191C2211yescharacteristic
61#15690287—22no—
62#15690287—22no—
63#15690287—22no—
64#15690287—41no—
65#15690287—41no—
66#15690287—41no—
67C2×Dic382—22no—
68C2×Dic382—21no—
69C2×Dic382—41no—
70C2×Dic382C2311yescharacteristic
71C2×Dic382C2311yescharacteristic
72C2×Dic382C2311yescharacteristic
73C2×Dic382C2311yescharacteristic
74C2×D764C2311yescharacteristic
75C2×D764C2311yescharacteristic
76C2×C22⋊D191—21no—
77C2×C22⋊D191—21no—
78C2×C22⋊D191—21no—
79C2×C22⋊D191—21no—
80C22×Dic191—21no—
81C2×C4×D191—21no—
82C2×C4×D191—21no—
83C2×C4×D191—21no—
84C2×C4×D191—21no—
85Dic764—22no—
86Dic764—22no—
87Dic764—22no—
88Dic764—41no—
89#15690276—22no—
90#15690276—22no—
91#15690276—41no—
92#15690276D414yescomplemented
93D1528—22no—
94C4⋊Dic191—21no—
95C4⋊Dic191—21no—
96C4⋊Dic191C2311yescharacteristic
97C4⋊Dic191C2311yescharacteristic
98Dic191⋊C4—21no—
99Dic191⋊C4—21no—
100Dic191⋊C4—21no—
101Dic191⋊C4—21no—
102C22⋊Dic191—21no—
103C22⋊Dic191—21no—
104C22⋊Dic191—21no—
105(C2×D191)⋊C4—21no—
106(C2×D191)⋊C4—21no—
107(C2×D191)⋊C4—21no—
108(C2×D191)⋊C4—21no—
109C4×Dic191—21no—
110C2×D4×C191D411yescharacteristic
111C22×C4×C191C2311yescharacteristic
112C22×C4×C191C2311yescharacteristic
113M16×C191—22no—
114C2×C8×C191—22no—
115C2×C8×C191C2311yescharacteristic
116C2×C8×C191C2311yescharacteristic
117C2×C8×C191C2311yescharacteristic
118C2×C8×C191C2311yescharacteristic
119C4⋊C4×C191D411yescharacteristic
120C22⋊C4×C191D411yescharacteristic
121C22⋊C4×C191D411yescharacteristic
122C42×C191C2311yescharacteristic
123C22×D191—21no—
124C22×D191—21no—
125Dic382—21no—
126Dic382—21no—
127Dic382—21no—
128Dic382—21no—
129Dic382—21no—
130Dic382—21no—
131Dic382—21no—
132Dic382—42no—
133Dic382C2×D412yes—
134D764—21no—
135D764—21no—
136D764—21no—
137D764C2×D412yes—
138C22⋊D191—42no—
139C22⋊D191—42no—
140C22⋊D191—42no—
141C22⋊D191—42no—
142C2×Dic191—21no—
143C2×Dic191—21no—
144C2×Dic191—21no—
145C2×Dic191—21no—
146C2×Dic191—21no—
147C2×Dic191—21no—
148C2×Dic191—42no—
149C4×D191—42no—
150C4×D191—42no—
151C4×D191—42no—
152C4×D191—42no—
153C23×C191C2×D411yescharacteristic
154C23×C191C2×D411yescharacteristic
155D4×C191—41no—
156C2×C4×C191—21no—
157C2×C4×C191—21no—
158C2×C4×C191—21no—
159C2×C4×C191—21no—
160C2×C4×C191C2×D411yescharacteristic
161C2×C4×C191C2×D411yescharacteristic
162C2×C4×C191C2×D411yescharacteristic
163C2×C4×C191C2×D411yescharacteristic
164C2×C4×C191C2411yescharacteristic
165C8×C191—21no—
166C8×C191—21no—
167C8×C191—21no—
168C8×C191C2×D412yes—
169C22×C191—21no—
170C22×C191—21no—
171C22×C191—21no—
172C22×C191—21no—
173C22×C191—21no—
174C22×C191—21no—
175C22×C191C22×D411yescharacteristic
176C2×D191—22no—
177C2×D191—41no—
178C2×D191—41no—
179C2×D191—41no—
180C2×D191—41no—
181C2×D191—41no—
182C4×C191—21no—
183C4×C191—21no—
184C4×C191—21no—
185C4×C191—21no—
186C4×C191C22×D411yescharacteristic
187C4×C191H(5,𝔽2)11yescharacteristic
188Dic191—22no—
189Dic191—41no—
190Dic191—41no—
191Dic191—41no—
192Dic191—41no—
193Dic191—41no—
194C2×C191—41no—
195C2×C191—41no—
196C2×C191D4211yescharacteristic
197C2×C191#57511yescharacteristic
198C2×C191#57811yescharacteristic
199D191—42no—
200D191—81no—
201C191#326911yescharacteristic, complemented, Sylow
202#3269—1911nomaximal, Sylow
203C2×#137—1911no—
204C2×#135—1911no—
205#548—1911no—
206#547—1911no—
207#497—1911no—
208#468—1911no—
209#467—1911no—
210#463—1911no—
211#462—1911no—
212#452—1911no—
213#452—1911no—
214#451—1911no—
215#449—1911no—
216#440—1911no—
217#435D19111yescharacteristic, complemented
218C2×#41—1911no—
219C2×#41—1911no—
220C2×#41—1911no—
221C22×Q8—1911no—
222#137—3824no—
223#135—3824no—
224C2×Q16—1911no—
225C2×Q16—1911no—
226C2×Q16—1911no—
227C2×Q16—1911no—
228C2×SD16—1911no—
229C2×SD16—1911no—
230C2×SD16—1911no—
231C2×SD16—1911no—
232C2×D8—1911no—
233C2×M16C2×D19111yescharacteristic
234C22×C8C2×D19111yescharacteristic
235C4⋊Q8—1911no—
236#124—3821no—
237#124—1911no—
238#123—3821no—
239#123—3821no—
240C22⋊Q8—3821no—
241C22⋊Q8—1911no—
242C22⋊Q8—1911no—
243C22⋊Q8—1911no—
244#121—3821no—
245#121—3821no—
246#121—1911no—
247C4×Q8—1911no—
248C4×D4—3821no—
249C4×D4—1911no—
250C4×D4C2×D19111yescharacteristic
251C2×C4⋊C4—3821no—
252#107—1911no—
253C4⋊C8C2×D19111yescharacteristic
254#103—1911no—
255#103—1911no—
256#103—1911no—
257#103—1911no—
258#102—1911no—
259#102—1911no—
260C22⋊C8C2×D19111yescharacteristic
261C22⋊C8C2×D19111yescharacteristic
262#97C2×D19111yescharacteristic
263#41—3822no—
264#41—3822no—
265#41—3822no—
266#41—7641no—
267#41—7641no—
268#41—7641no—
269C2×Q8—3822no—
270C2×Q8—3821no—
271C2×Q8—1911no—
272C2×Q8—1911no—
273C2×Q8—1911no—
274C2×Q8—1911no—
275C2×Q8—7641no—
276C2×D4—3821no—
277C2×D4—3821no—
278C2×D4—3821no—
279C2×D4—3821no—
280C2×D4—1911no—
281C2×D4—1911no—
282C2×D4D76411yescharacteristic
283C22×C4—3821no—
284C22×C4—3821no—
285C22×C4—3821no—
286C22×C4—3821no—
287C22×C4—3821no—
288C22×C4C22×D19111yescharacteristic
289C22×C4C22×D19111yescharacteristic
290Q16—3822no—
291Q16—3822no—
292Q16—3822no—
293Q16—7641no—
294SD16—3822no—
295SD16—3822no—
296SD16—1914no—
297SD16—7641no—
298D8—3822no—
299M16—22no—
300C2×C8—22no—
301C2×C8C22×D19111yescharacteristic
302C2×C8C22×D19111yescharacteristic
303C2×C8C22×D19111yescharacteristic
304C2×C8C22×D19111yescharacteristic
305C4⋊C4—3821no—
306C4⋊C4—3821no—
307C4⋊C4—3821no—
308C4⋊C4—3821no—
309C4⋊C4—3821no—
310C4⋊C4—3821no—
311C4⋊C4—1911no—
312C4⋊C4—1911no—
313C4⋊C4D76411yescharacteristic
314C22⋊C4—3821no—
315C22⋊C4—3821no—
316C22⋊C4—3821no—
317C22⋊C4—3821no—
318C22⋊C4—3821no—
319C22⋊C4—3821no—
320C22⋊C4—3821no—
321C22⋊C4D76411yescharacteristic
322C22⋊C4D76411yescharacteristic
323C42—3821no—
324C42C22×D19111yescharacteristic
325C23—3821no—
326C23—3821no—
327C23C2×D76411yescharacteristic
328C23C2×D76411yescharacteristic
329Q8—3821no—
330Q8—3821no—
331Q8—3821no—
332Q8—3821no—
333Q8—3821no—
334Q8—3821no—
335Q8—3821no—
336Q8—1912no—
337Q8—7642no—
338D4—41no—
339D4—3821no—
340D4—3821no—
341D4—3821no—
342D4—1912no—
343D4—7642no—
344D4—7642no—
345D4—7642no—
346D4—7642no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—3821no—
352C2×C4—3821no—
353C2×C4—3821no—
354C2×C4—3821no—
355C2×C4—3821no—
356C2×C4—3821no—
357C2×C4—7642no—
358C2×C4—7642no—
359C2×C4—7642no—
360C2×C4—7642no—
361C2×C4—7642no—
362C2×C4C2×D76411yescharacteristic
363C2×C4C2×D76411yescharacteristic
364C2×C4C2×D76411yescharacteristic
365C2×C4C2×D76411yescharacteristic
366C2×C4C23×D19111yescharacteristic
367C8—21no—
368C8—21no—
369C8—21no—
370C8D4×D19112yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—3822no—
378C22—7641no—
379C22—7641no—
380C22—7641no—
381C22—7641no—
382C22—7641no—
383C22C22×D76411yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—3822no—
389C4—7641no—
390C4—7641no—
391C4—7641no—
392C4—7641no—
393C4—7641no—
394C4C2×D4×D19111yescharacteristic
395C4#2025936811yescharacteristic
396C2—41no—
397C2—41no—
398C2—15281no—
399C2—7642no—
400C2D4×D76411yescharacteristic
401C2#2713346311yescharacteristic
402C2#2713348011yescharacteristic
subgroupG/H
centerC22C22×D764
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#435×C191C2
socleC22×C191C22×D4
hypercenter#435D191
hypocenterC191#3269
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#20259355C2semidirect
2. C2×#20259344C2semidirect
3. #27133322C2semidirect
4. #27133318C2semidirect
5. #27133057C2semidirect
6. #27132909C2semidirect
7. #27132904C2semidirect
8. #27132879C2semidirect
9. #27132874C2semidirect
10. #27132827C2semidirect
11. #27132827C2semidirect
12. #27132821C2semidirect
13. #27132810C2semidirect
14. #27132765C2semidirect
15. #435×C191C2semidirect
92. #15690276D4semidirect
201. C191#3269semidirect
217. #435D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593552
C2×#202593442
#271333222
#271333182
#271330572
#271329092
#271329042
#271328792
#271328742
#271328272
#271328212
#271328102
#271327652
#435×C1912
#3269191