Finite Group Databasebeta

← #37575553

Subgroups — #37575553

Order 24448.

688 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20259295C211yesmaximal, characteristic
2C2×(C22⋊D191)⋊C4C211yesmaximal, characteristic, complemented
3C2×#20259279C211yesmaximal, characteristic, complemented
4#27132564C211yesmaximal, characteristic, complemented
5#27132563C211yesmaximal, characteristic, complemented
6#27132563C211yesmaximal, characteristic, complemented
7#27132558C211yesmaximal, characteristic, complemented
8#27132552C211yesmaximal, characteristic, complemented
9#27132541C211yesmaximal, characteristic, complemented
10#27132540C211yesmaximal, characteristic, complemented
11#27132514C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic191C211yesmaximal, characteristic, complemented
13C4×(C2×D191)⋊C4C211yesmaximal, characteristic, complemented
14#27132510C211yesmaximal, characteristic, complemented
15#388×C191C211yesmaximal, characteristic, complemented
16C22×D764C2211yescharacteristic
17C22×C22⋊D191C2211yescharacteristic
18C22×C22⋊D191C2211yescharacteristic
19C23×Dic191C2211yescharacteristic
20C22×C4×D191C2211yescharacteristic
21C22×C4×D191C2211yescharacteristic
22#20259295C418yescomplemented
23(C22⋊D191)⋊C4—24no—
24#20259279—24no—
25C2×Dic191⋊C4C2211yescharacteristic
26C2×Dic191⋊C4C2211yescharacteristic
27C2×Dic191⋊C4C2211yescharacteristic
28C2×Dic191⋊C4C2211yescharacteristic
29C2×C22⋊Dic191C2211yescharacteristic
30C2×(C2×D191)⋊C4C2211yescharacteristic
31C2×(C2×D191)⋊C4C2211yescharacteristic
32C2×(C2×D191)⋊C4C2211yescharacteristic
33C2×(C2×D191)⋊C4C2211yescharacteristic
34C2×(C2×D191)⋊C4C2211yescharacteristic
35C2×(C2×D191)⋊C4C2211yescharacteristic
36C2×(C2×D191)⋊C4C2211yescharacteristic
37C2×(C2×D191)⋊C4C2211yescharacteristic
38C2×C4×Dic191C2211yescharacteristic
39C2×C4×Dic191C2211yescharacteristic
40C2×C4×Dic191C2211yescharacteristic
41C2×C4×Dic191C2211yescharacteristic
42C2×C4×Dic191C2211yescharacteristic
43C191⋊#95C2211yescharacteristic
44C191⋊#95C2211yescharacteristic
45C191⋊#95C2211yescharacteristic
46C191⋊#95C2211yescharacteristic
47C2×C4⋊C4×C191C2211yescharacteristic
48C2×C22⋊C4×C191C2211yescharacteristic
49C2×C22⋊C4×C191C2211yescharacteristic
50C2×C22⋊C4×C191C2211yescharacteristic
51C2×C42×C191C2211yescharacteristic
52#95×C191C2211yescharacteristic
53#95×C191C2211yescharacteristic
54C23×D191C2311yescharacteristic
55C23×D191C2311yescharacteristic
56C2×D764—41no—
57C2×D764—41no—
58C2×D764C2×C414yescomplemented
59C2×C22⋊D191—22no—
60C2×C22⋊D191—22no—
61C2×C22⋊D191—41no—
62C2×C22⋊D191—41no—
63C2×C22⋊D191C2×C414yes—
64C2×C22⋊D191C2×C414yescomplemented
65C22×Dic191—22no—
66C22×Dic191—22no—
67C22×Dic191—41no—
68C22×Dic191C2311yescharacteristic
69C22×Dic191C2311yescharacteristic
70C22×Dic191C2311yescharacteristic
71C22×Dic191C2311yescharacteristic
72C22×Dic191C2311yescharacteristic
73C22×Dic191C2311yescharacteristic
74C2×C4×D191—22no—
75C2×C4×D191—22no—
76C2×C4×D191—22no—
77C2×C4×D191—22no—
78C2×C4×D191—41no—
79C2×C4×D191C2×C414yescomplemented
80Dic191⋊C4—22no—
81Dic191⋊C4—41no—
82Dic191⋊C4C2×C414yescomplemented
83Dic191⋊C4D414yescomplemented
84C22⋊Dic191—22no—
85(C2×D191)⋊C4—22no—
86(C2×D191)⋊C4—22no—
87(C2×D191)⋊C4—22no—
88(C2×D191)⋊C4—22no—
89(C2×D191)⋊C4—22no—
90(C2×D191)⋊C4—22no—
91(C2×D191)⋊C4—41no—
92(C2×D191)⋊C4C2×C414yescomplemented
93C4×Dic191—22no—
94C4×Dic191—22no—
95C4×Dic191—22no—
96C4×Dic191—41no—
97C4×Dic191—41no—
98C24×C191C2311yescharacteristic
99C22×C4×C191C2311yescharacteristic
100C22×C4×C191C2311yescharacteristic
101C22×C4×C191C2311yescharacteristic
102C22×C4×C191C2311yescharacteristic
103C22×C4×C191C2311yescharacteristic
104C22×C4×C191C2311yescharacteristic
105C4⋊C4×C191—41no—
106C22⋊C4×C191—22no—
107C22⋊C4×C191—41no—
108C22⋊C4×C191C2×C414yescomplemented
109C42×C191—22no—
110C22×D191—21no—
111C22×D191—21no—
112C22×D191—21no—
113C22×D191—21no—
114C22×D191—21no—
115C22×D191—21no—
116C22×D191—21no—
117C22×D191—21no—
118C22×D191—21no—
119C22×D191—21no—
120C22×D191—21no—
121C22×D191—21no—
122C22×D191C22×C412yes—
123C22×D191C22×C412yes—
124D764—44no—
125C22⋊D191—28no—
126C22⋊D191—44no—
127C2×Dic191—21no—
128C2×Dic191—21no—
129C2×Dic191—21no—
130C2×Dic191—21no—
131C2×Dic191—21no—
132C2×Dic191—21no—
133C2×Dic191—21no—
134C2×Dic191—21no—
135C2×Dic191—21no—
136C2×Dic191—21no—
137C2×Dic191—21no—
138C2×Dic191—44no—
139C2×Dic191C22×C412yes—
140C2×Dic191C22×C412yes—
141C2×Dic191C2×D412yes—
142C2×Dic191C2×D412yes—
143C2×Dic191#4112yes—
144C2×Dic191#4112yes—
145C2×Dic191#4112yes—
146C4×D191—28no—
147C4×D191—44no—
148C23×C191—21no—
149C23×C191—21no—
150C23×C191—21no—
151C23×C191—21no—
152C23×C191—21no—
153C23×C191—21no—
154C23×C191C22×C412yes—
155C23×C191C2411yescharacteristic
156C2×C4×C191—21no—
157C2×C4×C191—21no—
158C2×C4×C191—21no—
159C2×C4×C191—21no—
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×C191C22×C412yes—
172C2×C4×C191C22×C412yes—
173C2×C4×C191C2×D412yes—
174C22×C191—22no—
175C22×C191—22no—
176C22×C191—22no—
177C22×C191—41no—
178C22×C191—41no—
179C22×C191—41no—
180C22×C191—41no—
181C22×C191C23×C411yescharacteristic
182C22×C191C22×D411yescharacteristic
183C22×C191C2×#4111yescharacteristic
184C22×C191C2×#4111yescharacteristic
185C22×C191C2×#4111yescharacteristic
186C22×C191H(5,𝔽2)11yescharacteristic
187C22×C191H(5,𝔽2)11yescharacteristic
188C2×D191—22no—
189C2×D191—22no—
190C2×D191—22no—
191C2×D191—22no—
192C2×D191—22no—
193C2×D191—22no—
194C2×D191—41no—
195C2×D191—41no—
196C2×D191—41no—
197C2×D191—41no—
198C2×D191—41no—
199C2×D191—41no—
200C2×D191—41no—
201C2×D191—41no—
202C4×C191—22no—
203C4×C191—22no—
204C4×C191—22no—
205C4×C191—41no—
206C4×C191—41no—
207C4×C191—41no—
208Dic191—22no—
209Dic191—22no—
210Dic191—22no—
211Dic191—22no—
212Dic191—41no—
213Dic191C4×D414yes—
214C2×C191—42no—
215C2×C191C2×C4×D411yescharacteristic
216C2×C191C4×#4111yescharacteristic
217C2×C191#51811yescharacteristic
218C2×C191#54611yescharacteristic
219C2×C191#55011yescharacteristic
220C2×C191#55311yescharacteristic
221C2×C191#55511yescharacteristic
222D191—42no—
223D191—42no—
224C191#236311yescharacteristic, complemented, Sylow
225#2363—1911nomaximal, Sylow
226C2×#121—1911no—
227C2×C4×D4—1911no—
228C2×#117—1911no—
229#390—1911no—
230#390—1911no—
231#390—1911no—
232#389—1911no—
233#388—1911no—
234#388D19111yescharacteristic, complemented
235#386—1911no—
236#386—1911no—
237C4×C4⋊C4—1911no—
238C4×C22⋊C4—1911no—
239C4×C22⋊C4—1911no—
240C4×C22⋊C4—1911no—
241C22×D4—1911no—
242C22×D4—1911no—
243C22×D4—1911no—
244C23×C4—1911no—
245C23×C4—1911no—
246C23×C4—1911no—
247#121—1918no—
248C4×D4—3824no—
249#117—3824no—
250C2×C4⋊C4—1911no—
251C2×C4⋊C4—1911no—
252C2×C4⋊C4—1911no—
253C2×C4⋊C4—1911no—
254C2×C4⋊C4C2×D19111yescharacteristic
255C2×C22⋊C4—1911no—
256C2×C22⋊C4—1911no—
257C2×C22⋊C4—1911no—
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⋊C4C2×D19111yescharacteristic
265C2×C22⋊C4C2×D19111yescharacteristic
266C2×C22⋊C4C2×D19111yescharacteristic
267C2×C42—1911no—
268C2×C42—1911no—
269C2×C42—1911no—
270C2×C42—1911no—
271C2×C42—1911no—
272C2×C42C2×D19111yescharacteristic
273#95—1911no—
274#95—1911no—
275#95—1911no—
276#95—1911no—
277#95C2×D19111yescharacteristic
278#95C2×D19111yescharacteristic
279C24—1911no—
280C24—1911no—
281C24C22×D19111yescharacteristic
282C2×D4—3822no—
283C2×D4—3822no—
284C2×D4—1914no—
285C2×D4—1914no—
286C2×D4—1914no—
287C2×D4—7641no—
288C2×D4—7641no—
289C2×D4—7641no—
290C2×D4—7641no—
291C22×C4—3822no—
292C22×C4—3822no—
293C22×C4—3822no—
294C22×C4—3822no—
295C22×C4—3822no—
296C22×C4—3822no—
297C22×C4—1911no—
298C22×C4—1911no—
299C22×C4—1911no—
300C22×C4—1911no—
301C22×C4—1911no—
302C22×C4—1914no—
303C22×C4—1911no—
304C22×C4—7641no—
305C22×C4—7641no—
306C22×C4C22×D19111yescharacteristic
307C22×C4C22×D19111yescharacteristic
308C22×C4C22×D19111yescharacteristic
309C22×C4C22×D19111yescharacteristic
310C22×C4C22×D19111yescharacteristic
311C22×C4C22×D19111yescharacteristic
312C4⋊C4—41no—
313C4⋊C4—3822no—
314C4⋊C4—1914no—
315C4⋊C4—1914no—
316C4⋊C4—7641no—
317C22⋊C4—22no—
318C22⋊C4—41no—
319C22⋊C4—3822no—
320C22⋊C4—3822no—
321C22⋊C4—3822no—
322C22⋊C4—3822no—
323C22⋊C4—3822no—
324C22⋊C4—3822no—
325C22⋊C4—3822no—
326C22⋊C4—1914no—
327C22⋊C4—7641no—
328C22⋊C4C4×D19114yescomplemented
329C42—22no—
330C42—3822no—
331C42—3822no—
332C42—3822no—
333C42—7641no—
334C42—7641no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—3821no—
342C23—3821no—
343C23—3821no—
344C23—3821no—
345C23—3821no—
346C23—3821no—
347C23—3821no—
348C23—3821no—
349C23—3821no—
350C23—3821no—
351C23—3821no—
352C23—3821no—
353C23—1912no—
354C23—1912no—
355C23C2×C4×D19112yes—
356C23C23×D19111yescharacteristic
357D4—3828no—
358D4—7644no—
359D4—7644no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—3828no—
376C2×C4—3821no—
377C2×C4—3821no—
378C2×C4—3821no—
379C2×C4—3821no—
380C2×C4—3821no—
381C2×C4—3821no—
382C2×C4—3821no—
383C2×C4—3821no—
384C2×C4—3821no—
385C2×C4—3821no—
386C2×C4—3821no—
387C2×C4—1912no—
388C2×C4—1912no—
389C2×C4—1912no—
390C2×C4—1912no—
391C2×C4—1912no—
392C2×C4—1912no—
393C2×C4—1912no—
394C2×C4—7644no—
395C2×C4—7644no—
396C2×C4C2×C4×D19112yes—
397C2×C4C2×C4×D19112yes—
398C2×C4D4×D19112yes—
399C22—22no—
400C22—22no—
401C22—22no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—3822no—
407C22—3822no—
408C22—3822no—
409C22—3822no—
410C22—3822no—
411C22—3822no—
412C22—7641no—
413C22—7641no—
414C22—7641no—
415C22—7641no—
416C22—7641no—
417C22—7641no—
418C22—7641no—
419C22—7641no—
420C22C22×C4×D19111yescharacteristic
421C22C2×D4×D19111yescharacteristic
422C22#41×D19111yescharacteristic
423C22#41×D19111yescharacteristic
424C22#41×D19111yescharacteristic
425C22#2025936711yescharacteristic
426C22#2025936811yescharacteristic
427C4—22no—
428C4—22no—
429C4—22no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—3822no—
434C4—3822no—
435C4—3822no—
436C4—3822no—
437C4—1914no—
438C4—7641no—
439C2—42no—
440C2—7642no—
441C2—7642no—
442C2C4×D4×D19111yescharacteristic
443C2#2713313111yescharacteristic
444C2#2713313511yescharacteristic
445C2#2713330511yescharacteristic
446C2#2713333111yescharacteristic
447C2#2713336411yescharacteristic
448C2#2713337511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutatorC22×C191C23×C4
Fitting#388×C191C2
socle, cosocleC23×C191C24
prime radicalC2×#20259295C2
hypercenter#388D191
hypocenterC191#2363
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×(C22⋊D191)⋊C4C2semidirect
3. C2×#20259279C2semidirect
4. #27132564C2semidirect
5. #27132563C2semidirect
6. #27132563C2semidirect
7. #27132558C2semidirect
8. #27132552C2semidirect
9. #27132541C2semidirect
10. #27132540C2semidirect
11. #27132514C2semidirect
12. C22⋊C4×Dic191C2semidirect
13. C4×(C2×D191)⋊C4C2semidirect
14. #27132510C2semidirect
15. #388×C191C2semidirect
22. #20259295C4semidirect
58. C2×D764C2×C4semidirect
64. C2×C22⋊D191C2×C4semidirect
79. C2×C4×D191C2×C4semidirect
82. Dic191⋊C4C2×C4semidirect
83. Dic191⋊C4D4semidirect
92. (C2×D191)⋊C4C2×C4semidirect
108. C22⋊C4×C191C2×C4semidirect
224. C191#2363semidirect
234. #388D191semidirect
328. C22⋊C4C4×D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202592952
C2×(C22⋊D191)⋊C42
C2×#202592792
#271325642
#271325632
#271325582
#271325522
#271325412
#271325402
#271325142
C22⋊C4×Dic1912
C4×(C2×D191)⋊C42
#271325102
#388×C1912
#2363191