Finite Group Databasebeta

← #37575367

Subgroups — #37575367

Order 24448.

792 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20259280C211yesmaximal, characteristic, complemented
2C22×(C2×D191)⋊C4C211yesmaximal, characteristic
3C2×C22⋊C4×D191C211yesmaximal, characteristic
4#27132555C211yesmaximal, characteristic, complemented
5#27132555C211yesmaximal, characteristic, complemented
6#27132553C211yesmaximal, characteristic, complemented
7#27132553C211yesmaximal, characteristic, complemented
8#27132538C211yesmaximal, characteristic, complemented
9#27132525C211yesmaximal, characteristic, complemented
10#27132520C211yesmaximal, characteristic, complemented
11#27132518C211yesmaximal, characteristic
12C22⋊C4×Dic191C211yesmaximal, characteristic, complemented
13C4×C22⋊Dic191C211yesmaximal, characteristic, complemented
14#27132510C211yesmaximal, characteristic, complemented
15#385×C191C211yesmaximal, characteristic, complemented
16C24×D191C2211yescharacteristic
17C23×Dic191C2211yescharacteristic
18C22×C4×D191C2211yescharacteristic
19C22×C4×D191C2211yescharacteristic
20#20259280—24no—
21C2×C4⋊Dic191C2211yescharacteristic, complemented
22C2×C4⋊Dic191C2211yescharacteristic, complemented
23C2×C22⋊Dic191C2211yescharacteristic
24C2×C22⋊Dic191C2211yescharacteristic
25C2×(C2×D191)⋊C4—24no—
26C2×(C2×D191)⋊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×(C2×D191)⋊C4C2211yescharacteristic
34C2×(C2×D191)⋊C4C2211yescharacteristic
35C2×(C2×D191)⋊C4C2211yescharacteristic
36C22⋊C4×D191C418yescomplemented
37C2×C4×Dic191C2211yescharacteristic, complemented
38C2×C4×Dic191C2211yescharacteristic, complemented
39C2×C4×Dic191C2211yescharacteristic, complemented
40C2×C4×Dic191C2211yescharacteristic, complemented
41C191⋊#95C2211yescharacteristic, complemented
42C191⋊#95C2211yescharacteristic, complemented
43C191⋊#95C2211yescharacteristic, complemented
44C191⋊#95C2211yescharacteristic, complemented
45C191⋊#95C2211yescharacteristic, complemented
46C191⋊#95C2211yescharacteristic, complemented
47C23×C4×C191C2211yescharacteristic
48C2×C4⋊C4×C191C2211yescharacteristic, complemented
49C2×C4⋊C4×C191C2211yescharacteristic, complemented
50C2×C22⋊C4×C191C2211yescharacteristic
51C2×C22⋊C4×C191C2211yescharacteristic
52#95×C191C2211yescharacteristic, complemented
53#95×C191C2211yescharacteristic, complemented
54C23×D191—22no—
55C23×D191—22no—
56C23×D191—22no—
57C23×D191—22no—
58C23×D191—41no—
59C23×D191—41no—
60C23×D191C2×C414yes—
61C23×D191C2311yescharacteristic
62C23×D191C2311yescharacteristic
63C22×Dic191—22no—
64C22×Dic191—22no—
65C22×Dic191—41no—
66C22×Dic191C2311yescharacteristic
67C22×Dic191C2311yescharacteristic
68C22×Dic191C2311yescharacteristic
69C22×Dic191C2311yescharacteristic
70C22×Dic191C2311yescharacteristic
71C22×Dic191C2311yescharacteristic
72C2×C4×D191—22no—
73C2×C4×D191—22no—
74C2×C4×D191—41no—
75C2×C4×D191—41no—
76C2×C4×D191C2×C414yescomplemented
77C2×C4×D191C2×C414yescomplemented
78C4⋊Dic191—22no—
79C4⋊Dic191—41no—
80C22⋊Dic191—22no—
81C22⋊Dic191C2×C414yes—
82(C2×D191)⋊C4—22no—
83(C2×D191)⋊C4—22no—
84(C2×D191)⋊C4—22no—
85(C2×D191)⋊C4—22no—
86(C2×D191)⋊C4—22no—
87(C2×D191)⋊C4—41no—
88(C2×D191)⋊C4—41no—
89(C2×D191)⋊C4C2×C414yescomplemented
90(C2×D191)⋊C4C2×C414yescomplemented
91(C2×D191)⋊C4D414yes—
92C4×Dic191—22no—
93C4×Dic191—22no—
94C4×Dic191—41no—
95C4×Dic191—41no—
96C24×C191C2311yescharacteristic
97C22×C4×C191—22no—
98C22×C4×C191—22no—
99C22×C4×C191—41no—
100C22×C4×C191C2311yescharacteristic
101C22×C4×C191C2311yescharacteristic
102C22×C4×C191C2311yescharacteristic
103C22×C4×C191C2311yescharacteristic
104C22×C4×C191C2311yescharacteristic
105C22×C4×C191C2311yescharacteristic
106C4⋊C4×C191—22no—
107C4⋊C4×C191—41no—
108C22⋊C4×C191—22no—
109C22⋊C4×C191C2×C414yes—
110C22×D191—21no—
111C22×D191—21no—
112C22×D191—21no—
113C22×D191—21no—
114C22×D191—28no—
115C22×D191—21no—
116C22×D191—21no—
117C22×D191—21no—
118C22×D191—21no—
119C22×D191—21no—
120C22×D191—21no—
121C22×D191—28no—
122C22×D191—44no—
123C22×D191—44no—
124C22×D191—44no—
125C22×D191—44no—
126C22×D191—44no—
127C22×D191C22×C412yes—
128C22×D191C22×C412yes—
129C22×D191C2×D412yes—
130C22×D191#4112yes—
131C2×Dic191—21no—
132C2×Dic191—21no—
133C2×Dic191—21no—
134C2×Dic191—21no—
135C2×Dic191—21no—
136C2×Dic191—21no—
137C2×Dic191—21no—
138C2×Dic191—21no—
139C2×Dic191—21no—
140C2×Dic191—21no—
141C2×Dic191—21no—
142C2×Dic191—21no—
143C2×Dic191—21no—
144C2×Dic191—21no—
145C2×Dic191—21no—
146C2×Dic191—44no—
147C2×Dic191C22×C412yes—
148C2×Dic191C22×C412yes—
149C2×Dic191C2×D412yes—
150C4×D191—28no—
151C4×D191—44no—
152C23×C191—21no—
153C23×C191—21no—
154C23×C191—21no—
155C23×C191—21no—
156C23×C191C22×C412yes—
157C23×C191#4112yes—
158C23×C191#4112yes—
159C23×C191C2411yescharacteristic
160C2×C4×C191—21no—
161C2×C4×C191—21no—
162C2×C4×C191—21no—
163C2×C4×C191—21no—
164C2×C4×C191—21no—
165C2×C4×C191—21no—
166C2×C4×C191—21no—
167C2×C4×C191—21no—
168C2×C4×C191—21no—
169C2×C4×C191—21no—
170C2×C4×C191—21no—
171C2×C4×C191—21no—
172C2×C4×C191—21no—
173C2×C4×C191—21no—
174C2×C4×C191—21no—
175C2×C4×C191—44no—
176C2×C4×C191C22×C412yes—
177C2×C4×C191C22×C412yes—
178C2×C4×C191C2×D412yes—
179C22×C191—22no—
180C22×C191—22no—
181C22×C191—22no—
182C22×C191—22no—
183C22×C191—22no—
184C22×C191—22no—
185C22×C191#11714yescomplemented
186C22×C191C23×C411yescharacteristic
187C22×C191C22×D411yescharacteristic
188C22×C191C2×#4111yescharacteristic
189C22×C191C2×#4111yescharacteristic
190C22×C191C2×#4111yescharacteristic
191C22×C191H(5,𝔽2)11yescharacteristic
192C22×C191H(5,𝔽2)11yescharacteristic
193C2×D191—22no—
194C2×D191—22no—
195C2×D191—22no—
196C2×D191—22no—
197C2×D191—22no—
198C2×D191—22no—
199C2×D191—22no—
200C2×D191—22no—
201C2×D191—22no—
202C2×D191—416no—
203C2×D191—41no—
204C2×D191—41no—
205C2×D191—41no—
206C2×D191—41no—
207C2×D191C4×D414yes—
208C4×C191—22no—
209C4×C191—22no—
210C4×C191—22no—
211C4×C191—41no—
212C4×C191—41no—
213C4×C191—41no—
214Dic191—22no—
215Dic191—22no—
216Dic191—22no—
217Dic191—41no—
218Dic191—41no—
219Dic191—41no—
220C2×C191—24no—
221C2×C191C2×#11711yescharacteristic
222C2×C191C2×C4×D411yescharacteristic
223C2×C191#51811yescharacteristic
224C2×C191#54611yescharacteristic
225C2×C191#54611yescharacteristic
226C2×C191#55111yescharacteristic
227C2×C191#55111yescharacteristic
228D191—24no—
229D191—42no—
230C191#234211yescharacteristic, complemented, Sylow
231#2342—1911nomaximal, Sylow
232C2×#117—1911no—
233C22×C22⋊C4—1911no—
234C22×C22⋊C4—1911no—
235#388—1911no—
236#388—1911no—
237#388—1911no—
238#388—1911no—
239#385—1911no—
240#385D19111yescharacteristic, complemented
241#381—1911no—
242#380—1911no—
243#379—1911no—
244C4×C22⋊C4—1911no—
245C4×C22⋊C4—1911no—
246C4×C22⋊C4—1911no—
247C25—1911no—
248C23×C4—1911no—
249C23×C4—1911no—
250C23×C4—1911no—
251C23×C4C2×D19111yescharacteristic
252#117—3824no—
253C2×C4⋊C4—1911no—
254C2×C4⋊C4—1911no—
255C2×C4⋊C4C2×D19111yescharacteristic, complemented
256C2×C4⋊C4C2×D19111yescharacteristic, complemented
257C2×C22⋊C4—3824no—
258C2×C22⋊C4—1911no—
259C2×C22⋊C4—1911no—
260C2×C22⋊C4—1911no—
261C2×C22⋊C4—1911no—
262C2×C22⋊C4—1911no—
263C2×C22⋊C4—1911no—
264C2×C22⋊C4—1911no—
265C2×C22⋊C4—1911no—
266C2×C22⋊C4—1911no—
267C2×C22⋊C4—1911no—
268C2×C22⋊C4—1918no—
269C2×C22⋊C4—1911no—
270C2×C22⋊C4—1911no—
271C2×C22⋊C4C2×D19111yescharacteristic
272C2×C22⋊C4C2×D19111yescharacteristic
273C2×C42—1911no—
274C2×C42—1911no—
275C2×C42—1911no—
276C2×C42—1911no—
277#95—1911no—
278#95—1911no—
279#95—1911no—
280#95—1911no—
281#95—1911no—
282#95—1911no—
283#95C2×D19111yescharacteristic, complemented
284#95C2×D19111yescharacteristic, complemented
285C24—3822no—
286C24—3822no—
287C24—3822no—
288C24—3822no—
289C24—1911no—
290C24—1911no—
291C24—1914no—
292C24—7641no—
293C24—7641no—
294C24C22×D19111yescharacteristic
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—41no—
298C22×C4—3822no—
299C22×C4—3822no—
300C22×C4—3822no—
301C22×C4—3822no—
302C22×C4—1911no—
303C22×C4—1911no—
304C22×C4—1911no—
305C22×C4—1911no—
306C22×C4—1911no—
307C22×C4—1911no—
308C22×C4—1914no—
309C22×C4—1914no—
310C22×C4—7641no—
311C22×C4—7641no—
312C22×C4—7641no—
313C22×C4C22×D19111yescharacteristic
314C22×C4C22×D19111yescharacteristic
315C22×C4C22×D19111yescharacteristic
316C22×C4C22×D19111yescharacteristic
317C22×C4C22×D19111yescharacteristic
318C22×C4C22×D19111yescharacteristic
319C4⋊C4—22no—
320C4⋊C4—41no—
321C4⋊C4—3822no—
322C4⋊C4—7641no—
323C22⋊C4—22no—
324C22⋊C4—3822no—
325C22⋊C4—3822no—
326C22⋊C4—3822no—
327C22⋊C4—3822no—
328C22⋊C4—3822no—
329C22⋊C4—3822no—
330C22⋊C4—1914no—
331C22⋊C4—1914no—
332C22⋊C4—1914no—
333C22⋊C4—1914no—
334C22⋊C4—7641no—
335C22⋊C4—7641no—
336C22⋊C4C4×D19114yes—
337C42—3822no—
338C42—3822no—
339C42—7641no—
340C42—7641no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—3828no—
346C23—3821no—
347C23—3821no—
348C23—3821no—
349C23—3821no—
350C23—3821no—
351C23—3821no—
352C23—3821no—
353C23—3821no—
354C23—3821no—
355C23—3821no—
356C23—3828no—
357C23—1912no—
358C23—1912no—
359C23—1912no—
360C23—1912no—
361C23—7644no—
362C23—7644no—
363C23—7644no—
364C23—7644no—
365C23—7644no—
366C23C2×C4×D19112yes—
367C23#1569028612yes—
368C23#1569028812yes—
369C23C23×D19111yescharacteristic
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—44no—
386C2×C4—3828no—
387C2×C4—3821no—
388C2×C4—3821no—
389C2×C4—3821no—
390C2×C4—3821no—
391C2×C4—3821no—
392C2×C4—3821no—
393C2×C4—3821no—
394C2×C4—3821no—
395C2×C4—3821no—
396C2×C4—3821no—
397C2×C4—3821no—
398C2×C4—3821no—
399C2×C4—3821no—
400C2×C4—3821no—
401C2×C4—3821no—
402C2×C4—1912no—
403C2×C4—1912no—
404C2×C4—1912no—
405C2×C4—7644no—
406C2×C4—7644no—
407C2×C4C2×C4×D19112yes—
408C2×C4C2×C4×D19112yes—
409C2×C4D4×D19112yes—
410C22—22no—
411C22—22no—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—22no—
416C22—3822no—
417C22—3822no—
418C22—3822no—
419C22—3822no—
420C22—3822no—
421C22—3822no—
422C22—3822no—
423C22—3822no—
424C22—3822no—
425C22—1914no—
426C22—76416no—
427C22—7641no—
428C22—7641no—
429C22—7641no—
430C22—7641no—
431C22#2025928014yescomplemented
432C22C22×C4×D19111yescharacteristic
433C22C2×D4×D19111yescharacteristic
434C22#41×D19111yescharacteristic
435C22C2×#1569028611yescharacteristic
436C22C2×#1569028811yescharacteristic
437C22#2025936711yescharacteristic
438C22#2025936811yescharacteristic
439C4—22no—
440C4—22no—
441C4—22no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—3822no—
446C4—3822no—
447C4—3822no—
448C4—7641no—
449C4—7641no—
450C4—7641no—
451C2—24no—
452C2—3824no—
453C2—7642no—
454C2C2×#2025928011yescharacteristic
455C2C4×D4×D19111yescharacteristic
456C2#2713313511yescharacteristic
457C2#2713330011yescharacteristic
458C2#2713330411yescharacteristic
459C2#2713333611yescharacteristic
460C2#2713334011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutatorC22×C191C23×C4
Fitting#385×C191C2
socle, cosocleC23×C191C24
prime radicalC24×D191C22
hypercenter#385D191
hypocenterC191#2342
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#20259280C2semidirect
4. #27132555C2semidirect
5. #27132555C2semidirect
6. #27132553C2semidirect
7. #27132553C2semidirect
8. #27132538C2semidirect
9. #27132525C2semidirect
10. #27132520C2semidirect
12. C22⋊C4×Dic191C2semidirect
13. C4×C22⋊Dic191C2semidirect
14. #27132510C2semidirect
15. #385×C191C2semidirect
21. C2×C4⋊Dic191C22semidirect
22. C2×C4⋊Dic191C22semidirect
36. C22⋊C4×D191C4semidirect
37. C2×C4×Dic191C22semidirect
38. C2×C4×Dic191C22semidirect
39. C2×C4×Dic191C22semidirect
40. C2×C4×Dic191C22semidirect
41. C191⋊#95C22semidirect
42. C191⋊#95C22semidirect
43. C191⋊#95C22semidirect
44. C191⋊#95C22semidirect
45. C191⋊#95C22semidirect
46. C191⋊#95C22semidirect
48. C2×C4⋊C4×C191C22semidirect
49. C2×C4⋊C4×C191C22semidirect
52. #95×C191C22semidirect
53. #95×C191C22semidirect
76. C2×C4×D191C2×C4semidirect
77. C2×C4×D191C2×C4semidirect
89. (C2×D191)⋊C4C2×C4semidirect
90. (C2×D191)⋊C4C2×C4semidirect
185. C22×C191#117semidirect
230. C191#2342semidirect
240. #385D191semidirect
255. C2×C4⋊C4C2×D191semidirect
256. C2×C4⋊C4C2×D191semidirect
283. #95C2×D191semidirect
284. #95C2×D191semidirect
431. C22#20259280semidirect

Maximal subgroups

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

subgroupindex
C2×#202592802
C22×(C2×D191)⋊C42
C2×C22⋊C4×D1912
#271325552
#271325532
#271325382
#271325252
#271325202
#271325182
C22⋊C4×Dic1912
C4×C22⋊Dic1912
#271325102
#385×C1912
#2342191