Finite Group Databasebeta

← #37582210

Subgroups — #37582210

Order 24448.

472 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20259354C211yesmaximal, characteristic, complemented
2C2×#20259328C211yesmaximal, characteristic, complemented
3#27133243C211yesmaximal, characteristic
4#27133236C211yesmaximal, characteristic, complemented
5#27132919C211yesmaximal, characteristic, complemented
6#27132918C211yesmaximal, characteristic, complemented
7#27132911C211yesmaximal, characteristic, complemented
8#27132910C211yesmaximal, characteristic, complemented
9#27132903C211yesmaximal, characteristic, complemented
10#27132895C211yesmaximal, characteristic, complemented
11#27132892C211yesmaximal, characteristic, complemented
12#27132704C211yesmaximal, characteristic, complemented
13#27132658C211yesmaximal, characteristic, complemented
14#103×D191C211yesmaximal, characteristic, complemented
15#467×C191C211yesmaximal, characteristic, complemented
16C2×#15690288C2211yescharacteristic
17C2×#15690287C2211yescharacteristic
18C2×Q8×D191C2211yescharacteristic
19#20259354—24no—
20C2×#15690277C2211yescharacteristic
21C2×#15690276C2211yescharacteristic
22C2×#15690274C2211yescharacteristic
23#20259328—24no—
24C2×#15690271C2211yescharacteristic
25C2×#15690270C2211yescharacteristic
26C2×#15690270C2211yescharacteristic
27C2×C8×D191C2211yescharacteristic
28C2×C8×D191C2211yescharacteristic
29#20259321—21no—
30#20259308—21no—
31#20259307—21no—
32#20259304—21no—
33#20259302C2211yescharacteristic
34#20259301C2211yescharacteristic
35#20259300—21no—
36#20259298C2211yescharacteristic
37#20259298C2211yescharacteristic
38#20259297—21no—
39#20259297C2211yescharacteristic
40#20259296C2211yescharacteristic
41#20259295—21no—
42#20259295—21no—
43#20259280C2211yescharacteristic
44C4⋊C4×D191C2211yescharacteristic
45#20259255C2211yescharacteristic
46#20259254C2211yescharacteristic
47#20259253C2211yescharacteristic
48#20259247C2211yescharacteristic
49#20259246C2211yescharacteristic
50#20259246C2211yescharacteristic
51#20259245C2211yescharacteristic
52#20259244C2211yescharacteristic
53#20259242C2211yescharacteristic
54C2×Q16×C191C2211yescharacteristic
55C22×C8×C191C2211yescharacteristic
56C22⋊Q8×C191C2211yescharacteristic
57C22⋊Q8×C191C2211yescharacteristic
58#107×C191C2211yescharacteristic
59#103×C191C2211yescharacteristic
60#103×C191C2211yescharacteristic
61#15690288—22no—
62#15690288—22no—
63#15690287—22no—
64#15690287—22no—
65C2×Dic382—21no—
66C2×Dic382D411yescharacteristic
67C2×Dic382C2311yescharacteristic
68Q8×D191—22no—
69Q8×D191—22no—
70C2×D764—21no—
71C2×D764—21no—
72C2×D764D411yescharacteristic
73C2×D764C2311yescharacteristic
74C2×C22⋊D191—21no—
75C2×C22⋊D191D411yescharacteristic
76C2×C22⋊D191D411yescharacteristic
77C2×C4×D191—21no—
78C2×C4×D191—21no—
79C2×C4×D191—21no—
80C2×C4×D191C2311yescharacteristic
81C2×C4×D191C2311yescharacteristic
82#15690277—22no—
83#15690276—22no—
84#15690274—22no—
85#15690271—22no—
86#15690270—22no—
87#15690270D414yescomplemented
88C2×C191⋊C8C2311yescharacteristic
89C2×C191⋊C8C2311yescharacteristic
90C8×D191—22no—
91C8×D191—22no—
92C4⋊Dic191—21no—
93C4⋊Dic191C2311yescharacteristic
94C4⋊Dic191C2311yescharacteristic
95Dic191⋊C4—21no—
96Dic191⋊C4—21no—
97Dic191⋊C4—21no—
98Dic191⋊C4—21no—
99C22⋊Dic191—21no—
100(C2×D191)⋊C4—21no—
101(C2×D191)⋊C4—21no—
102(C2×D191)⋊C4—21no—
103(C2×D191)⋊C4—21no—
104(C2×D191)⋊C4—21no—
105(C2×D191)⋊C4—21no—
106C4×Dic191—21no—
107C2×Q8×C191C2311yescharacteristic
108C2×Q8×C191C2311yescharacteristic
109C22×C4×C191C2311yescharacteristic
110Q16×C191—22no—
111C2×C8×C191—22no—
112C2×C8×C191C2311yescharacteristic
113C2×C8×C191C2311yescharacteristic
114C4⋊C4×C191—21no—
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—
126Dic382—42no—
127D764—22no—
128D764—21no—
129D764—21no—
130D764—42no—
131D764—81no—
132C22⋊D191—22no—
133C22⋊D191—22no—
134C22⋊D191—81no—
135C2×Dic191—21no—
136C2×Dic191—21no—
137C2×Dic191—21no—
138C2×Dic191C2×D411yescharacteristic
139C2×Dic191C2×D411yescharacteristic
140C4×D191—21no—
141C4×D191—21no—
142C4×D191—42no—
143C4×D191—42no—
144C4×D191—81no—
145C4×D191C2×D412yes—
146C4×D191#4112yes—
147C191⋊C8—21no—
148C191⋊C8C2×D412yes—
149C23×C191C2×D411yescharacteristic
150Q8×C191—21no—
151Q8×C191—21no—
152Q8×C191—21no—
153Q8×C191—21no—
154C2×C4×C191—21no—
155C2×C4×C191—21no—
156C2×C4×C191—21no—
157C2×C4×C191—21no—
158C2×C4×C191—21no—
159C2×C4×C191—21no—
160C2×C4×C191C2×D411yescharacteristic
161C2×C4×C191C2411yescharacteristic
162C8×C191—21no—
163C8×C191C2×D412yes—
164C22×C191—21no—
165C22×C191—21no—
166C22×C191—21no—
167C22×C191C22×D411yescharacteristic
168C2×D191—21no—
169C2×D191—21no—
170C2×D191—21no—
171C2×D191—21no—
172C2×D191—21no—
173C2×D191—41no—
174C2×D191—41no—
175C2×D191—41no—
176C2×D191#12112yes—
177C4×C191—21no—
178C4×C191—41no—
179C4×C191—41no—
180C4×C191—41no—
181C4×C191—41no—
182C4×C191C22×D411yescharacteristic
183C4×C191C2×#4111yescharacteristic
184Dic191—21no—
185Dic191—41no—
186Dic191—41no—
187Dic191—41no—
188Dic191#12112yes—
189C2×C191—41no—
190C2×C191C2×#12111yescharacteristic
191C2×C191#57711yescharacteristic
192C2×C191#57811yescharacteristic
193D191—22no—
194D191—41no—
195D191—81no—
196C191#306311yescharacteristic, complemented, Sylow
197#3063—1911nomaximal, Sylow
198C2×#137—1911no—
199C2×#131—1911no—
200#537—1911no—
201#536—1911no—
202#470—1911no—
203#470—1911no—
204#468—1911no—
205#468—1911no—
206#467—1911no—
207#467D19111yescharacteristic, complemented
208#465—1911no—
209#465—1911no—
210#428—1911no—
211#416—1911no—
212C2×#103—1911no—
213C2×#41—1911no—
214C2×#41—1911no—
215C22×Q8—1911no—
216#137—3824no—
217C2×Q16—1911no—
218C2×Q16C2×D19111yescharacteristic
219C2×SD16—1911no—
220C2×SD16—1911no—
221#131—3824no—
222C2×M16—1911no—
223C2×M16—1911no—
224C2×M16—1911no—
225C22×C8—1911no—
226C22×C8—1911no—
227C22×C8C2×D19111yescharacteristic
228C4⋊Q8—3821no—
229#124—3821no—
230#123—3821no—
231#123—3821no—
232C22⋊Q8—3821no—
233C22⋊Q8—1911no—
234C22⋊Q8—1911no—
235C22⋊Q8—1911no—
236C22⋊Q8—1911no—
237C22⋊Q8C2×D19111yescharacteristic
238C22⋊Q8C2×D19111yescharacteristic
239#121—3821no—
240#121—3821no—
241#121—3821no—
242#121—1911no—
243#121—1911no—
244#117—1911no—
245C2×C4⋊C4—1911no—
246#107—1911no—
247#107C2×D19111yescharacteristic
248#106—1911no—
249#106—1911no—
250#103—1911no—
251#103—1911no—
252#103—1911no—
253#103—1911no—
254#103C2×D19111yescharacteristic
255#103C2×D19111yescharacteristic
256#102—1911no—
257#102—1911no—
258#41—3822no—
259#41—3822no—
260#41—3822no—
261#41—3822no—
262C2×Q8—3821no—
263C2×Q8—3822no—
264C2×Q8—3822no—
265C2×Q8—1911no—
266C2×Q8—1911no—
267C2×Q8C22×D19111yescharacteristic
268C2×Q8C22×D19111yescharacteristic
269C2×D4—3821no—
270C2×D4—3821no—
271C2×D4—3821no—
272C2×D4—1911no—
273C2×D4—1911no—
274C2×D4—1911no—
275C2×D4—1911no—
276C22×C4—3821no—
277C22×C4—3821no—
278C22×C4—3821no—
279C22×C4—1911no—
280C22×C4—1911no—
281C22×C4C22×D19111yescharacteristic
282Q16—22no—
283Q16—3822no—
284SD16—3822no—
285SD16—3822no—
286M16—3822no—
287M16—3822no—
288M16—1914no—
289C2×C8—22no—
290C2×C8—3822no—
291C2×C8—3822no—
292C2×C8—1911no—
293C2×C8—1911no—
294C2×C8C22×D19111yescharacteristic
295C2×C8C22×D19111yescharacteristic
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—3821no—
299C4⋊C4—3821no—
300C4⋊C4—3821no—
301C4⋊C4—3821no—
302C4⋊C4—3821no—
303C4⋊C4—1911no—
304C4⋊C4—1911no—
305C4⋊C4C22×D19111yescharacteristic
306C4⋊C4C22×D19111yescharacteristic
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—3821no—
310C22⋊C4—3821no—
311C22⋊C4—3821no—
312C22⋊C4—3821no—
313C22⋊C4—3821no—
314C22⋊C4—3821no—
315C22⋊C4—3821no—
316C42—3821no—
317C23—3821no—
318C23—1911no—
319C23—1911no—
320C23D4×D19111yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—21no—
325Q8—3822no—
326Q8—3821no—
327Q8—3821no—
328Q8—7642no—
329D4—3822no—
330D4—3822no—
331D4—3822no—
332D4—3821no—
333D4—3821no—
334D4—15281no—
335D4—15281no—
336D4—7642no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—3821no—
344C2×C4—3821no—
345C2×C4—3821no—
346C2×C4—3821no—
347C2×C4—3821no—
348C2×C4—1911no—
349C2×C4—1911no—
350C2×C4—1912no—
351C2×C4—1912no—
352C2×C4—15281no—
353C2×C4—7642no—
354C2×C4—7642no—
355C2×C4D4×D19111yescharacteristic
356C2×C4C23×D19111yescharacteristic
357C8—21no—
358C8—3821no—
359C8—1912no—
360C8D4×D19112yes—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—3821no—
365C22—3821no—
366C22—3821no—
367C22—3821no—
368C22—3821no—
369C22—1912no—
370C22—7641no—
371C22—7641no—
372C22—7641no—
373C22C2×D4×D19111yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—3821no—
380C4—1912no—
381C4—7641no—
382C4—7641no—
383C4—7641no—
384C4C2×D4×D19111yescharacteristic
385C4#41×D19111yescharacteristic
386C2—41no—
387C2—3822no—
388C2—15281no—
389C2—7641no—
390C2#121×D19111yescharacteristic
391C2#2713347011yescharacteristic
392C2#2713347611yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#467×C191C2
socleC22×C191C22×D4
prime radical#27133243C2
hypercenter#467D191
hypocenterC191#3063
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. C2×#20259354C2semidirect
2. C2×#20259328C2semidirect
4. #27133236C2semidirect
5. #27132919C2semidirect
6. #27132918C2semidirect
7. #27132911C2semidirect
8. #27132910C2semidirect
9. #27132903C2semidirect
10. #27132895C2semidirect
11. #27132892C2semidirect
12. #27132704C2semidirect
13. #27132658C2semidirect
14. #103×D191C2semidirect
15. #467×C191C2semidirect
87. #15690270D4semidirect
196. C191#3063semidirect
207. #467D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593542
C2×#202593282
#271332432
#271332362
#271329192
#271329182
#271329112
#271329102
#271329032
#271328952
#271328922
#271327042
#271326582
#103×D1912
#467×C1912
#3063191