Finite Group Databasebeta

← #37582177

Subgroups — #37582177

Order 24448.

484 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20259343C211yesmaximal, characteristic, complemented
2C2×#20259328C211yesmaximal, characteristic, complemented
3#27133243C211yesmaximal, characteristic, complemented
4#27133242C211yesmaximal, characteristic, complemented
5#27132920C211yesmaximal, characteristic, complemented
6#27132919C211yesmaximal, characteristic, complemented
7#27132915C211yesmaximal, characteristic, complemented
8#27132914C211yesmaximal, characteristic, complemented
9#27132893C211yesmaximal, characteristic, complemented
10#27132892C211yesmaximal, characteristic, complemented
11#27132889C211yesmaximal, characteristic, complemented
12#106×D191C211yesmaximal, characteristic, complemented
13#27132663C211yesmaximal, characteristic, complemented
14#27132661C211yesmaximal, characteristic, complemented
15#465×C191C211yesmaximal, characteristic, complemented
16C2×#15690288C2211yescharacteristic
17C2×#15690287C2211yescharacteristic
18C2×#15690286C2211yescharacteristic
19#20259343—24no—
20C2×#15690277C2211yescharacteristic
21C2×#15690276C2211yescharacteristic
22C2×#15690272C2211yescharacteristic
23#20259328—24no—
24C2×#15690271C2211yescharacteristic
25C2×#15690270C2211yescharacteristic
26C2×#15690270C2211yescharacteristic
27C2×C8×D191C2211yescharacteristic
28C2×C8×D191C2211yescharacteristic
29#20259302C2211yescharacteristic
30#20259301C2211yescharacteristic
31#20259300—21no—
32#20259299—21no—
33#20259298C2211yescharacteristic
34#20259297—21no—
35#20259297C2211yescharacteristic
36#20259296C2211yescharacteristic
37#20259295—21no—
38#20259295—21no—
39#20259295—21no—
40#20259294—21no—
41#20259293—21no—
42#20259293C2211yescharacteristic
43C4⋊C4×D191C2211yescharacteristic
44C4⋊C4×D191C2211yescharacteristic
45#20259254C2211yescharacteristic
46#20259253C2211yescharacteristic
47#20259253C2211yescharacteristic
48#20259247C2211yescharacteristic
49#20259246C2211yescharacteristic
50#20259245C2211yescharacteristic
51#20259244C2211yescharacteristic
52#20259243C2211yescharacteristic
53#20259242C2211yescharacteristic
54C2×SD16×C191C2211yescharacteristic
55C22×C8×C191C2211yescharacteristic
56C22⋊Q8×C191C2211yescharacteristic
57#121×C191C2211yescharacteristic
58#106×C191C2211yescharacteristic
59#103×C191C2211yescharacteristic
60#102×C191C2211yescharacteristic
61#15690288—22no—
62#15690288—22no—
63#15690287—22no—
64#15690287—22no—
65#15690286—22no—
66#15690286—22no—
67C2×Dic382D411yescharacteristic
68C2×Dic382C2311yescharacteristic
69C2×D764—21no—
70C2×D764—21no—
71C2×D764D411yescharacteristic
72C2×D764C2311yescharacteristic
73C2×C22⋊D191—21no—
74C2×C22⋊D191—21no—
75C2×C22⋊D191—21no—
76C2×C22⋊D191D411yescharacteristic
77C2×C22⋊D191D411yescharacteristic
78C22×Dic191—21no—
79C2×C4×D191—21no—
80C2×C4×D191—21no—
81C2×C4×D191—21no—
82C2×C4×D191C2311yescharacteristic
83C2×C4×D191C2311yescharacteristic
84#15690277—22no—
85#15690276—22no—
86#15690272—22no—
87#15690271—22no—
88#15690270—22no—
89#15690270—22no—
90C2×C191⋊C8C2311yescharacteristic
91C2×C191⋊C8C2311yescharacteristic
92C8×D191—22no—
93C8×D191D414yescomplemented
94C4⋊Dic191—21no—
95C4⋊Dic191C2311yescharacteristic
96C4⋊Dic191C2311yescharacteristic
97Dic191⋊C4—21no—
98Dic191⋊C4—21no—
99Dic191⋊C4—21no—
100Dic191⋊C4—21no—
101C22⋊Dic191—21no—
102C22⋊Dic191—21no—
103(C2×D191)⋊C4—21no—
104(C2×D191)⋊C4—21no—
105(C2×D191)⋊C4—21no—
106(C2×D191)⋊C4—21no—
107C2×Q8×C191C2311yescharacteristic
108C2×D4×C191—21no—
109C2×D4×C191C2311yescharacteristic
110C22×C4×C191C2311yescharacteristic
111SD16×C191—22no—
112C2×C8×C191—22no—
113C2×C8×C191C2311yescharacteristic
114C2×C8×C191C2311yescharacteristic
115C4⋊C4×C191—21no—
116C4⋊C4×C191C2311yescharacteristic
117C4⋊C4×C191C2311yescharacteristic
118C22⋊C4×C191—21no—
119C22⋊C4×C191—21no—
120C22×D191—21no—
121C22×D191C2×D411yescharacteristic
122C22×D191C2×D411yescharacteristic
123Dic382—22no—
124Dic382—21no—
125Dic382—21no—
126D764—22no—
127D764—21no—
128D764—21no—
129D764—42no—
130D764—81no—
131C22⋊D191—22no—
132C22⋊D191—22no—
133C22⋊D191—42no—
134C22⋊D191—81no—
135C22⋊D191—81no—
136C2×Dic191—21no—
137C2×Dic191—21no—
138C2×Dic191—21no—
139C2×Dic191—42no—
140C2×Dic191C2×D411yescharacteristic
141C2×Dic191C2×D411yescharacteristic
142C4×D191—21no—
143C4×D191—21no—
144C4×D191—42no—
145C4×D191—81no—
146C4×D191—81no—
147C4×D191C2×D412yes—
148C4×D191#4112yes—
149C191⋊C8—21no—
150C191⋊C8C2×D412yes—
151C23×C191—21no—
152C23×C191C2×D411yescharacteristic
153Q8×C191—21no—
154Q8×C191—21no—
155D4×C191—21no—
156D4×C191—21no—
157D4×C191—81no—
158C2×C4×C191—21no—
159C2×C4×C191—21no—
160C2×C4×C191—21no—
161C2×C4×C191—21no—
162C2×C4×C191—21no—
163C2×C4×C191C2×D411yescharacteristic
164C2×C4×C191C2411yescharacteristic
165C8×C191—21no—
166C8×C191C2×D412yes—
167C22×C191—21no—
168C22×C191—21no—
169C22×C191—21no—
170C22×C191—41no—
171C22×C191—41no—
172C22×C191—41no—
173C22×C191C22×D411yescharacteristic
174C2×D191—21no—
175C2×D191—21no—
176C2×D191—21no—
177C2×D191—21no—
178C2×D191—21no—
179C2×D191—41no—
180C2×D191—41no—
181C2×D191—41no—
182C2×D191#12112yes—
183C4×C191—21no—
184C4×C191—41no—
185C4×C191—41no—
186C4×C191—41no—
187C4×C191C22×D411yescharacteristic
188C4×C191C2×#4111yescharacteristic
189Dic191—21no—
190Dic191—41no—
191Dic191—41no—
192Dic191—41no—
193Dic191#12112yes—
194C2×C191—41no—
195C2×C191—81no—
196C2×C191C2×#12111yescharacteristic
197C2×C191#57711yescharacteristic
198C2×C191#57711yescharacteristic
199D191—22no—
200D191—41no—
201D191—81no—
202C191#306011yescharacteristic, complemented, Sylow
203#3060—1911nomaximal, Sylow
204C2×#135—1911no—
205C2×#131—1911no—
206#537—1911no—
207#537—1911no—
208#470—1911no—
209#470—1911no—
210#469—1911no—
211#469—1911no—
212#465—1911no—
213#465—1911no—
214#465—1911no—
215#465D19111yescharacteristic, complemented
216C2×#106—1911no—
217#417—1911no—
218#417—1911no—
219C2×#41—1911no—
220C2×#41—1911no—
221C2×#41—1911no—
222#135—3824no—
223C2×Q16—1911no—
224C2×SD16—1911no—
225C2×SD16C2×D19111yescharacteristic
226C2×D8—1911no—
227#131—3824no—
228C2×M16—1911no—
229C2×M16—1911no—
230C2×M16—1911no—
231C22×C8—1911no—
232C22×C8—1911no—
233C22×C8C2×D19111yescharacteristic
234C22⋊Q8—3821no—
235C22⋊Q8—3821no—
236C22⋊Q8—1911no—
237C22⋊Q8—1911no—
238C22⋊Q8—1911no—
239C22⋊Q8C2×D19111yescharacteristic
240#121—3821no—
241#121—3821no—
242#121—3821no—
243#121—3821no—
244#121—3821no—
245#121—3821no—
246#121—1911no—
247#121—1911no—
248#121—1911no—
249#121C2×D19111yescharacteristic
250C2×C4⋊C4—1911no—
251C2×C4⋊C4—1911no—
252#106—1911no—
253#106—1911no—
254#106—1911no—
255#106C2×D19111yescharacteristic
256#103—1911no—
257#103—1911no—
258#103—1911no—
259#103C2×D19111yescharacteristic
260#102—1911no—
261#102—1911no—
262#102—1911no—
263#102C2×D19111yescharacteristic
264#41—3822no—
265#41—3822no—
266#41—3822no—
267#41—3822no—
268#41—3822no—
269#41—3822no—
270C2×Q8—1911no—
271C2×Q8—1911no—
272C2×Q8C22×D19111yescharacteristic
273C2×D4—21no—
274C2×D4—3821no—
275C2×D4—3821no—
276C2×D4—3821no—
277C2×D4—3821no—
278C2×D4—3821no—
279C2×D4—1911no—
280C2×D4—1911no—
281C2×D4—1911no—
282C2×D4—1911no—
283C2×D4C22×D19111yescharacteristic
284C22×C4—3821no—
285C22×C4—3821no—
286C22×C4—3821no—
287C22×C4—3821no—
288C22×C4—1911no—
289C22×C4—1911no—
290C22×C4C22×D19111yescharacteristic
291Q16—3822no—
292SD16—22no—
293SD16—3822no—
294D8—3822no—
295M16—3822no—
296M16—3822no—
297M16—3822no—
298C2×C8—22no—
299C2×C8—3822no—
300C2×C8—1911no—
301C2×C8—1911no—
302C2×C8—1914no—
303C2×C8C22×D19111yescharacteristic
304C2×C8C22×D19111yescharacteristic
305C4⋊C4—21no—
306C4⋊C4—3821no—
307C4⋊C4—3821no—
308C4⋊C4—3821no—
309C4⋊C4—3821no—
310C4⋊C4—3821no—
311C4⋊C4—1911no—
312C4⋊C4—1911no—
313C4⋊C4C22×D19111yescharacteristic
314C4⋊C4C22×D19111yescharacteristic
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—3821no—
318C22⋊C4—3821no—
319C22⋊C4—3821no—
320C22⋊C4—3821no—
321C22⋊C4—3821no—
322C22⋊C4—3821no—
323C23—21no—
324C23—3821no—
325C23—1911no—
326C23—1911no—
327C23D4×D19111yescharacteristic
328Q8—21no—
329Q8—21no—
330Q8—3822no—
331Q8—3821no—
332Q8—3821no—
333D4—21no—
334D4—21no—
335D4—81no—
336D4—3822no—
337D4—3822no—
338D4—3822no—
339D4—3821no—
340D4—3821no—
341D4—15281no—
342D4—15281no—
343D4—15281no—
344D4—7642no—
345D4—7642no—
346C2×C4—21no—
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—1911no—
357C2×C4—1911no—
358C2×C4—1912no—
359C2×C4—1912no—
360C2×C4—15281no—
361C2×C4—15281no—
362C2×C4—7642no—
363C2×C4—7642no—
364C2×C4D4×D19111yescharacteristic
365C2×C4C23×D19111yescharacteristic
366C8—21no—
367C8—3821no—
368C8—1912no—
369C8D4×D19112yes—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—3821no—
377C22—3821no—
378C22—3821no—
379C22—3821no—
380C22—3821no—
381C22—1912no—
382C22—7641no—
383C22—7641no—
384C22—7641no—
385C22C2×D4×D19111yescharacteristic
386C4—21no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—3821no—
391C4—1912no—
392C4—7641no—
393C4—7641no—
394C4—7641no—
395C4C2×D4×D19111yescharacteristic
396C4#41×D19111yescharacteristic
397C2—41no—
398C2—81no—
399C2—3822no—
400C2—15281no—
401C2—7641no—
402C2#121×D19111yescharacteristic
403C2#2713346911yescharacteristic
404C2#2713347011yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#465×C191C2
socleC22×C191C22×D4
hypercenter#465D191
hypocenterC191#3060
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#20259343C2semidirect
2. C2×#20259328C2semidirect
3. #27133243C2semidirect
4. #27133242C2semidirect
5. #27132920C2semidirect
6. #27132919C2semidirect
7. #27132915C2semidirect
8. #27132914C2semidirect
9. #27132893C2semidirect
10. #27132892C2semidirect
11. #27132889C2semidirect
12. #106×D191C2semidirect
13. #27132663C2semidirect
14. #27132661C2semidirect
15. #465×C191C2semidirect
93. C8×D191D4semidirect
202. C191#3060semidirect
215. #465D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593432
C2×#202593282
#271332432
#271332422
#271329202
#271329192
#271329152
#271329142
#271328932
#271328922
#271328892
#106×D1912
#271326632
#271326612
#465×C1912
#3060191