Finite Group Databasebeta

← #37575987

Subgroups — #37575987

Order 24448.

800 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20259304C211yesmaximal, characteristic, complemented
2C2×#20259292C211yesmaximal, characteristic
3C2×C4×D764C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D191C211yesmaximal, characteristic, complemented
5#27132600C211yesmaximal, characteristic, complemented
6#27132588C211yesmaximal, characteristic, complemented
7#27132580C211yesmaximal, characteristic, complemented
8#27132579C211yesmaximal, characteristic, complemented
9#27132554C211yesmaximal, characteristic, complemented
10#27132541C211yesmaximal, characteristic, complemented
11#27132541C211yesmaximal, characteristic, complemented
12#27132537C211yesmaximal, characteristic, complemented
13#27132520C211yesmaximal, characteristic, complemented
14#27132518C211yesmaximal, characteristic, complemented
15#388×C191C211yesmaximal, characteristic, complemented
16C24×D191C2211yescharacteristic
17C22×D764C2211yescharacteristic
18C22×D764C2211yescharacteristic
19C22×C22⋊D191C2211yescharacteristic
20C22×C4×D191C2211yescharacteristic
21C22×C4×D191C2211yescharacteristic
22C22×C4×D191C2211yescharacteristic, complemented
23#20259304—24no—
24#20259292—24no—
25C4×D764—24no—
26C2×C4⋊Dic191C2211yescharacteristic, complemented
27C2×C4⋊Dic191C2211yescharacteristic, complemented
28C2×C4⋊Dic191C2211yescharacteristic, complemented
29C2×Dic191⋊C4C2211yescharacteristic, complemented
30C2×C22⋊Dic191C2211yescharacteristic
31C2×C22⋊Dic191C2211yescharacteristic
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×(C2×D191)⋊C4C2211yescharacteristic
39C2×(C2×D191)⋊C4C2211yescharacteristic
40C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
42C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
43C22⋊C4×D191—24no—
44C191⋊#95C2211yescharacteristic, complemented
45C191⋊#95C2211yescharacteristic, complemented
46C191⋊#95C2211yescharacteristic, complemented
47C191⋊#95C2211yescharacteristic, complemented
48C2×C4⋊C4×C191C2211yescharacteristic, complemented
49C2×C22⋊C4×C191C2211yescharacteristic
50C2×C22⋊C4×C191C2211yescharacteristic
51C2×C22⋊C4×C191C2211yescharacteristic
52C2×C42×C191C2211yescharacteristic, complemented
53#95×C191C2211yescharacteristic, complemented
54#95×C191C2211yescharacteristic, complemented
55C23×D191—22no—
56C23×D191—22no—
57C23×D191—22no—
58C23×D191—22no—
59C23×D191—22no—
60C23×D191—41no—
61C23×D191—41no—
62C23×D191C2311yescharacteristic
63C23×D191C2311yescharacteristic
64C23×D191C2311yescharacteristic
65C2×D764—22no—
66C2×D764—22no—
67C2×D764—22no—
68C2×D764—22no—
69C2×D764—41no—
70C2×D764D414yes—
71C2×C22⋊D191—22no—
72C2×C22⋊D191—22no—
73C2×C22⋊D191—41no—
74C22×Dic191C2311yescharacteristic
75C22×Dic191C2311yescharacteristic
76C22×Dic191C2311yescharacteristic
77C22×Dic191C2311yescharacteristic
78C22×Dic191C2311yescharacteristic
79C2×C4×D191—22no—
80C2×C4×D191—22no—
81C2×C4×D191—22no—
82C2×C4×D191—22no—
83C2×C4×D191—22no—
84C2×C4×D191—22no—
85C2×C4×D191—41no—
86C2×C4×D191—41no—
87C2×C4×D191—41no—
88C4⋊Dic191—22no—
89C4⋊Dic191—22no—
90C4⋊Dic191—41no—
91Dic191⋊C4—22no—
92C22⋊Dic191—22no—
93C22⋊Dic191—22no—
94(C2×D191)⋊C4—22no—
95(C2×D191)⋊C4—22no—
96(C2×D191)⋊C4—22no—
97(C2×D191)⋊C4—22no—
98(C2×D191)⋊C4—22no—
99(C2×D191)⋊C4—22no—
100(C2×D191)⋊C4—22no—
101(C2×D191)⋊C4—22no—
102(C2×D191)⋊C4—22no—
103(C2×D191)⋊C4—41no—
104(C2×D191)⋊C4—41no—
105C24×C191C2311yescharacteristic
106C22×C4×C191C2311yescharacteristic
107C22×C4×C191C2311yescharacteristic
108C22×C4×C191C2311yescharacteristic
109C22×C4×C191C2311yescharacteristic
110C22×C4×C191C2311yescharacteristic
111C22×C4×C191C2311yescharacteristic
112C4⋊C4×C191—41no—
113C22⋊C4×C191—22no—
114C22⋊C4×C191—41no—
115C22⋊C4×C191D414yescomplemented
116C42×C191—22no—
117C22×D191—21no—
118C22×D191—21no—
119C22×D191—21no—
120C22×D191—21no—
121C22×D191—28no—
122C22×D191—21no—
123C22×D191—21no—
124C22×D191—21no—
125C22×D191—21no—
126C22×D191—21no—
127C22×D191—21no—
128C22×D191—21no—
129C22×D191—21no—
130C22×D191—21no—
131C22×D191—21no—
132C22×D191—21no—
133C22×D191—21no—
134C22×D191—44no—
135C22×D191—44no—
136C22×D191—44no—
137C22×D191—44no—
138C22×D191—44no—
139C22×D191—44no—
140C22×D191C2×D412yes—
141C22×D191C2×D412yes—
142C22×D191#4112yes—
143C22×D191#4112yes—
144C22×D191#4112yes—
145D764—28no—
146D764—44no—
147C22⋊D191—44no—
148C2×Dic191—21no—
149C2×Dic191—21no—
150C2×Dic191—21no—
151C2×Dic191—21no—
152C2×Dic191—21no—
153C2×Dic191—21no—
154C2×Dic191—21no—
155C2×Dic191—21no—
156C2×Dic191—21no—
157C2×Dic191—21no—
158C2×Dic191—21no—
159C2×Dic191—21no—
160C2×Dic191—21no—
161C2×Dic191—21no—
162C2×Dic191—21no—
163C4×D191—44no—
164C4×D191—44no—
165C4×D191—44no—
166C23×C191—21no—
167C23×C191—21no—
168C23×C191—21no—
169C23×C191—21no—
170C23×C191—21no—
171C23×C191—21no—
172C23×C191C2×D412yes—
173C23×C191C2411yescharacteristic
174C2×C4×C191—21no—
175C2×C4×C191—21no—
176C2×C4×C191—21no—
177C2×C4×C191—21no—
178C2×C4×C191—21no—
179C2×C4×C191—21no—
180C2×C4×C191—21no—
181C2×C4×C191—21no—
182C2×C4×C191—21no—
183C2×C4×C191—21no—
184C2×C4×C191—21no—
185C2×C4×C191—21no—
186C2×C4×C191—21no—
187C2×C4×C191—21no—
188C2×C4×C191—21no—
189C2×C4×C191C2×D412yes—
190C2×C4×C191C2×D412yes—
191C2×C4×C191C2×D412yes—
192C22×C191—22no—
193C22×C191—22no—
194C22×C191—22no—
195C22×C191—41no—
196C22×C191—41no—
197C22×C191—41no—
198C22×C191—41no—
199C22×C191C22×D411yescharacteristic
200C22×C191C22×D411yescharacteristic
201C22×C191C2×#4111yescharacteristic
202C22×C191C2×#4111yescharacteristic
203C22×C191C2×#4111yescharacteristic
204C22×C191H(5,𝔽2)11yescharacteristic
205C22×C191H(5,𝔽2)11yescharacteristic
206C2×D191—22no—
207C2×D191—22no—
208C2×D191—22no—
209C2×D191—22no—
210C2×D191—22no—
211C2×D191—22no—
212C2×D191—22no—
213C2×D191—22no—
214C2×D191—22no—
215C2×D191—22no—
216C2×D191—22no—
217C2×D191—22no—
218C2×D191—416no—
219C2×D191—41no—
220C2×D191—41no—
221C2×D191—41no—
222C2×D191—41no—
223C2×D191—41no—
224C2×D191—41no—
225C2×D191—41no—
226C2×D191—41no—
227C2×D191#12314yescomplemented
228C4×C191—22no—
229C4×C191—22no—
230C4×C191—22no—
231C4×C191—41no—
232C4×C191—41no—
233C4×C191—41no—
234Dic191—41no—
235Dic191—41no—
236Dic191—41no—
237Dic191—41no—
238Dic191—41no—
239C2×C191—42no—
240C2×C191C2×#12311yescharacteristic
241C2×C191#52511yescharacteristic
242C2×C191#53811yescharacteristic
243C2×C191D4211yescharacteristic
244C2×C191#54611yescharacteristic
245C2×C191#54611yescharacteristic
246C2×C191#55111yescharacteristic
247D191—24no—
248D191—42no—
249D191—42no—
250C191#241811yescharacteristic, complemented, Sylow
251#2418—1911nomaximal, Sylow
252C2×#123—1911no—
253C2×#120—1911no—
254C2×C4×D4—1911no—
255C22×C22⋊C4—1911no—
256#399—1911no—
257#397—1911no—
258#394—1911no—
259#394—1911no—
260#388—1911no—
261#388D19111yescharacteristic, complemented
262#386—1911no—
263#386—1911no—
264#385—1911no—
265#380—1911no—
266#379—1911no—
267C25—1911no—
268C22×D4—1911no—
269C22×D4—1911no—
270C22×D4—1911no—
271C23×C4—1911no—
272C23×C4—1911no—
273C23×C4—1911no—
274#123—3824no—
275#120—3824no—
276C4×D4—3824no—
277C2×C4⋊C4—1911no—
278C2×C4⋊C4—1911no—
279C2×C4⋊C4—1911no—
280C2×C4⋊C4—1911no—
281C2×C4⋊C4C2×D19111yescharacteristic, complemented
282C2×C22⋊C4—3824no—
283C2×C22⋊C4—1911no—
284C2×C22⋊C4—1911no—
285C2×C22⋊C4—1911no—
286C2×C22⋊C4—1911no—
287C2×C22⋊C4—1911no—
288C2×C22⋊C4—1911no—
289C2×C22⋊C4—1911no—
290C2×C22⋊C4—1911no—
291C2×C22⋊C4—1911no—
292C2×C22⋊C4—1911no—
293C2×C22⋊C4—1911no—
294C2×C22⋊C4—1911no—
295C2×C22⋊C4—1911no—
296C2×C22⋊C4C2×D19111yescharacteristic
297C2×C22⋊C4C2×D19111yescharacteristic
298C2×C22⋊C4C2×D19111yescharacteristic
299C2×C42C2×D19111yescharacteristic, complemented
300#95—1911no—
301#95—1911no—
302#95—1911no—
303#95—1911no—
304#95C2×D19111yescharacteristic, complemented
305#95C2×D19111yescharacteristic, complemented
306C24—3822no—
307C24—3822no—
308C24—3822no—
309C24—3822no—
310C24—3822no—
311C24—1911no—
312C24—1911no—
313C24—1911no—
314C24—7641no—
315C24—7641no—
316C24C22×D19111yescharacteristic
317C2×D4—3822no—
318C2×D4—3822no—
319C2×D4—3822no—
320C2×D4—3822no—
321C2×D4—3822no—
322C2×D4—3822no—
323C2×D4—1914no—
324C2×D4—7641no—
325C2×D4—7641no—
326C22×C4—3822no—
327C22×C4—3822no—
328C22×C4—3822no—
329C22×C4—3822no—
330C22×C4—3822no—
331C22×C4—3822no—
332C22×C4—1911no—
333C22×C4—1911no—
334C22×C4—1911no—
335C22×C4—1911no—
336C22×C4—1911no—
337C22×C4—7641no—
338C22×C4—7641no—
339C22×C4—7641no—
340C22×C4C22×D19111yescharacteristic
341C22×C4C22×D19111yescharacteristic
342C22×C4C22×D19111yescharacteristic
343C22×C4C22×D19111yescharacteristic
344C22×C4C22×D19111yescharacteristic
345C22×C4C22×D19111yescharacteristic
346C4⋊C4—41no—
347C4⋊C4—3822no—
348C4⋊C4—3822no—
349C4⋊C4—3822no—
350C4⋊C4—7641no—
351C22⋊C4—22no—
352C22⋊C4—41no—
353C22⋊C4—3822no—
354C22⋊C4—3822no—
355C22⋊C4—3822no—
356C22⋊C4—3822no—
357C22⋊C4—3822no—
358C22⋊C4—3822no—
359C22⋊C4—3822no—
360C22⋊C4—3822no—
361C22⋊C4—3822no—
362C22⋊C4—3822no—
363C22⋊C4—3822no—
364C22⋊C4—7641no—
365C22⋊C4—7641no—
366C22⋊C4D76414yescomplemented
367C42—22no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—3828no—
375C23—3821no—
376C23—3821no—
377C23—3821no—
378C23—3821no—
379C23—3821no—
380C23—3821no—
381C23—3821no—
382C23—3821no—
383C23—3821no—
384C23—3821no—
385C23—3821no—
386C23—3821no—
387C23—3821no—
388C23—3821no—
389C23—3821no—
390C23—3821no—
391C23—1912no—
392C23—1912no—
393C23—1912no—
394C23—1912no—
395C23—1912no—
396C23—7644no—
397C23—7644no—
398C23—7644no—
399C23—7644no—
400C23—7644no—
401C23—7644no—
402C23C2×D76412yes—
403C23C23×D19111yescharacteristic
404D4—3828no—
405D4—7644no—
406D4—7644no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—3821no—
423C2×C4—3821no—
424C2×C4—3821no—
425C2×C4—3821no—
426C2×C4—3821no—
427C2×C4—3821no—
428C2×C4—3821no—
429C2×C4—3821no—
430C2×C4—3821no—
431C2×C4—3821no—
432C2×C4—3821no—
433C2×C4—3821no—
434C2×C4—3821no—
435C2×C4—3821no—
436C2×C4—3821no—
437C2×C4—7644no—
438C2×C4—7644no—
439C2×C4—7644no—
440C2×C4D4×D19112yes—
441C2×C4C2×D76412yes—
442C2×C4C2×D76412yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—3822no—
451C22—3822no—
452C22—3822no—
453C22—3822no—
454C22—3822no—
455C22—3822no—
456C22—3822no—
457C22—3822no—
458C22—3822no—
459C22—3822no—
460C22—3822no—
461C22—3822no—
462C22—1914no—
463C22—76416no—
464C22—7641no—
465C22—7641no—
466C22—7641no—
467C22—7641no—
468C22—7641no—
469C22—7641no—
470C22—7641no—
471C22—7641no—
472C22C2×D4×D19111yescharacteristic
473C22C22×D76411yescharacteristic
474C22#41×D19111yescharacteristic
475C22#41×D19111yescharacteristic
476C22#41×D19111yescharacteristic
477C22#2025936711yescharacteristic
478C22#2025936811yescharacteristic
479C4—22no—
480C4—22no—
481C4—22no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—7641no—
486C4—7641no—
487C4—7641no—
488C4—7641no—
489C4—7641no—
490C2—42no—
491C2—3824no—
492C2—7642no—
493C2—7642no—
494C2#123×D19111yescharacteristic
495C2#2713317511yescharacteristic
496C2#2713324711yescharacteristic
497C2D4×D76411yescharacteristic
498C2#2713330811yescharacteristic
499C2#2713331011yescharacteristic
500C2#2713333811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutator, socle, cosocleC23×C191C24
Fitting#388×C191C2
prime radicalC2×#20259292C2
hypercenter#388D191
hypocenterC191#2418
LCSG ▷ C23×C191 ▷ C191
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#20259304C2semidirect
3. C2×C4×D764C2semidirect
4. C2×C22⋊C4×D191C2semidirect
5. #27132600C2semidirect
6. #27132588C2semidirect
7. #27132580C2semidirect
8. #27132579C2semidirect
9. #27132554C2semidirect
10. #27132541C2semidirect
11. #27132541C2semidirect
12. #27132537C2semidirect
13. #27132520C2semidirect
14. #27132518C2semidirect
15. #388×C191C2semidirect
22. C22×C4×D191C22semidirect
26. C2×C4⋊Dic191C22semidirect
27. C2×C4⋊Dic191C22semidirect
28. C2×C4⋊Dic191C22semidirect
29. C2×Dic191⋊C4C22semidirect
40. C2×(C2×D191)⋊C4C22semidirect
41. C2×(C2×D191)⋊C4C22semidirect
42. C2×(C2×D191)⋊C4C22semidirect
44. C191⋊#95C22semidirect
45. C191⋊#95C22semidirect
46. C191⋊#95C22semidirect
47. C191⋊#95C22semidirect
48. C2×C4⋊C4×C191C22semidirect
52. C2×C42×C191C22semidirect
53. #95×C191C22semidirect
54. #95×C191C22semidirect
115. C22⋊C4×C191D4semidirect
227. C2×D191#123semidirect
250. C191#2418semidirect
261. #388D191semidirect
281. C2×C4⋊C4C2×D191semidirect
299. C2×C42C2×D191semidirect
304. #95C2×D191semidirect
305. #95C2×D191semidirect
366. C22⋊C4D764semidirect

Maximal subgroups

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

subgroupindex
C2×#202593042
C2×#202592922
C2×C4×D7642
C2×C22⋊C4×D1912
#271326002
#271325882
#271325802
#271325792
#271325542
#271325412
#271325372
#271325202
#271325182
#388×C1912
#2418191