Finite Group Databasebeta

← #37575989

Subgroups — #37575989

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×#20259307C211yesmaximal, characteristic, complemented
2C2×#20259292C211yesmaximal, characteristic
3C2×C4×D764C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D191C211yesmaximal, characteristic, complemented
5#27132599C211yesmaximal, characteristic, complemented
6#27132590C211yesmaximal, characteristic, complemented
7#27132581C211yesmaximal, characteristic, complemented
8#27132578C211yesmaximal, characteristic, complemented
9#27132554C211yesmaximal, characteristic, complemented
10#27132541C211yesmaximal, characteristic, complemented
11#27132539C211yesmaximal, characteristic, complemented
12#27132534C211yesmaximal, characteristic, complemented
13#27132522C211yesmaximal, 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#20259307—24no—
24#20259292—24no—
25C4×D764—24no—
26C2×C4⋊Dic191C2211yescharacteristic, complemented
27C2×Dic191⋊C4C2211yescharacteristic, complemented
28C2×Dic191⋊C4C2211yescharacteristic, 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—
89Dic191⋊C4—22no—
90Dic191⋊C4—41no—
91Dic191⋊C4—41no—
92C22⋊Dic191—22no—
93C22⋊Dic191—41no—
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—41no—
103(C2×D191)⋊C4—41no—
104(C2×D191)⋊C4D414yescomplemented
105C24×C191C2311yescharacteristic
106C22×C4×C191C2311yescharacteristic
107C22×C4×C191C2311yescharacteristic
108C22×C4×C191C2311yescharacteristic
109C22×C4×C191C2311yescharacteristic
110C22×C4×C191C2311yescharacteristic
111C22×C4×C191C2311yescharacteristic
112C4⋊C4×C191—22no—
113C22⋊C4×C191—22no—
114C22⋊C4×C191—22no—
115C22⋊C4×C191—22no—
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×D191C2×D412yes—
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×Dic191C2×D412yes—
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×C191#4112yes—
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×C191—21no—
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—41no—
231C4×C191—41no—
232C4×C191—41no—
233C4×C191—41no—
234Dic191—22no—
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—22no—
347C4⋊C4—3822no—
348C4⋊C4—3822no—
349C4⋊C4—7641no—
350C4⋊C4—7641no—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—22no—
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—1914no—
364C22⋊C4—7641no—
365C22⋊C4—7641no—
366C22⋊C4—7641no—
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—
402C23#1569028712yes—
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—21no—
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—1912no—
438C2×C4—7644no—
439C2×C4—7644no—
440C2×C4—7644no—
441C2×C4D4×D19112yes—
442C2×C4D4×D19112yes—
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
473C22C2×D4×D19111yescharacteristic
474C22#41×D19111yescharacteristic
475C22#41×D19111yescharacteristic
476C22C2×#1569028711yescharacteristic
477C22#2025936811yescharacteristic
478C22#2025936811yescharacteristic
479C4—22no—
480C4—22no—
481C4—41no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—3822no—
486C4—7641no—
487C4—7641no—
488C4—7641no—
489C4—7641no—
490C2—42no—
491C2—3824no—
492C2—7642no—
493C2—7642no—
494C2#123×D19111yescharacteristic
495C2#2713317211yescharacteristic
496C2#2713325211yescharacteristic
497C2#2713329711yescharacteristic
498C2#2713330611yescharacteristic
499C2#2713330911yescharacteristic
500C2#2713333711yescharacteristic
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×#20259307C2semidirect
3. C2×C4×D764C2semidirect
4. C2×C22⋊C4×D191C2semidirect
5. #27132599C2semidirect
6. #27132590C2semidirect
7. #27132581C2semidirect
8. #27132578C2semidirect
9. #27132554C2semidirect
10. #27132541C2semidirect
11. #27132539C2semidirect
12. #27132534C2semidirect
13. #27132522C2semidirect
14. #27132518C2semidirect
15. #388×C191C2semidirect
22. C22×C4×D191C22semidirect
26. C2×C4⋊Dic191C22semidirect
27. C2×Dic191⋊C4C22semidirect
28. C2×Dic191⋊C4C22semidirect
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
104. (C2×D191)⋊C4D4semidirect
227. C2×D191#123semidirect
250. C191#2418semidirect
261. #388D191semidirect
281. C2×C4⋊C4C2×D191semidirect
299. C2×C42C2×D191semidirect
304. #95C2×D191semidirect
305. #95C2×D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593072
C2×#202592922
C2×C4×D7642
C2×C22⋊C4×D1912
#271325992
#271325902
#271325812
#271325782
#271325542
#271325412
#271325392
#271325342
#271325222
#271325182
#388×C1912
#2418191