Finite Group Databasebeta

← #37575982

Subgroups — #37575982

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×#20259291C211yesmaximal, characteristic
3C2×C4×C22⋊D191C211yesmaximal, characteristic, complemented
4#27132599C211yesmaximal, characteristic, complemented
5#27132591C211yesmaximal, characteristic, complemented
6#27132579C211yesmaximal, characteristic, complemented
7#27132578C211yesmaximal, characteristic, complemented
8#27132557C211yesmaximal, characteristic, complemented
9#27132556C211yesmaximal, characteristic, complemented
10#27132542C211yesmaximal, characteristic, complemented
11#27132539C211yesmaximal, characteristic, complemented
12#27132536C211yesmaximal, characteristic, complemented
13#27132523C211yesmaximal, characteristic, complemented
14#27132519C211yesmaximal, characteristic, complemented
15C22×C22⋊C4×C191C211yesmaximal, characteristic, complemented
16C22×C22⋊D191C2211yescharacteristic
17C22×C22⋊D191C2211yescharacteristic
18C22×C22⋊D191C2211yescharacteristic
19C22×C4×D191C2211yescharacteristic, complemented
20#20259304—24no—
21#20259291—24no—
22C4×C22⋊D191—24no—
23C2×C4⋊Dic191C2211yescharacteristic, complemented
24C2×C4⋊Dic191C2211yescharacteristic, complemented
25C2×Dic191⋊C4C2211yescharacteristic, complemented
26C2×Dic191⋊C4C2211yescharacteristic, complemented
27C2×Dic191⋊C4C2211yescharacteristic, complemented
28C2×C22⋊Dic191C2211yescharacteristic
29C2×C22⋊Dic191C2211yescharacteristic
30C2×C22⋊Dic191C2211yescharacteristic
31C2×C22⋊Dic191C2211yescharacteristic
32C2×C22⋊Dic191C2211yescharacteristic
33C2×C22⋊Dic191C2211yescharacteristic
34C2×C22⋊Dic191C2211yescharacteristic
35C2×C22⋊Dic191C2211yescharacteristic
36C2×C22⋊Dic191C2211yescharacteristic
37C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
38C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
39C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
40C2×C4×Dic191C2211yescharacteristic, complemented
41C191⋊#95C2211yescharacteristic, complemented
42C191⋊#95C2211yescharacteristic, complemented
43C191⋊#95C2211yescharacteristic, complemented
44C191⋊#95C2211yescharacteristic, complemented
45C191⋊#95C2211yescharacteristic, complemented
46C191⋊#95C2211yescharacteristic, complemented
47C25×C191C2211yescharacteristic
48C23×C4×C191C2211yescharacteristic
49C23×C4×C191C2211yescharacteristic
50C2×C22⋊C4×C191—24no—
51C2×C22⋊C4×C191C2211yescharacteristic
52C2×C22⋊C4×C191C2211yescharacteristic
53C2×C22⋊C4×C191C2211yescharacteristic
54C2×C22⋊C4×C191C2211yescharacteristic
55C23×D191C2311yescharacteristic
56C2×C22⋊D191—22no—
57C2×C22⋊D191—22no—
58C2×C22⋊D191—22no—
59C2×C22⋊D191—22no—
60C2×C22⋊D191—22no—
61C2×C22⋊D191—22no—
62C2×C22⋊D191—41no—
63C2×C22⋊D191—41no—
64C2×C22⋊D191D414yes—
65C22×Dic191C2311yescharacteristic
66C22×Dic191C2311yescharacteristic
67C22×Dic191C2311yescharacteristic
68C22×Dic191C2311yescharacteristic
69C22×Dic191C2311yescharacteristic
70C22×Dic191C2311yescharacteristic
71C22×Dic191C2311yescharacteristic
72C2×C4×D191—22no—
73C2×C4×D191—22no—
74C2×C4×D191—41no—
75C4⋊Dic191—22no—
76C4⋊Dic191—41no—
77Dic191⋊C4—22no—
78Dic191⋊C4—22no—
79Dic191⋊C4—41no—
80C22⋊Dic191—22no—
81C22⋊Dic191—22no—
82C22⋊Dic191—22no—
83C22⋊Dic191—22no—
84C22⋊Dic191—22no—
85C22⋊Dic191—22no—
86C22⋊Dic191—22no—
87C22⋊Dic191—41no—
88C22⋊Dic191—41no—
89(C2×D191)⋊C4—22no—
90(C2×D191)⋊C4—22no—
91(C2×D191)⋊C4—41no—
92C4×Dic191—22no—
93C24×C191—22no—
94C24×C191—22no—
95C24×C191—22no—
96C24×C191—22no—
97C24×C191—22no—
98C24×C191—41no—
99C24×C191—41no—
100C24×C191C2311yescharacteristic
101C24×C191C2311yescharacteristic
102C24×C191C2311yescharacteristic
103C22×C4×C191—22no—
104C22×C4×C191—22no—
105C22×C4×C191—22no—
106C22×C4×C191—22no—
107C22×C4×C191—41no—
108C22×C4×C191—41no—
109C22×C4×C191C2311yescharacteristic
110C22×C4×C191C2311yescharacteristic
111C22×C4×C191C2311yescharacteristic
112C22×C4×C191C2311yescharacteristic
113C22⋊C4×C191—22no—
114C22⋊C4×C191—22no—
115C22⋊C4×C191—22no—
116C22⋊C4×C191D414yescomplemented
117C22×D191—21no—
118C22×D191—21no—
119C22×D191—21no—
120C22×D191—21no—
121C22×D191—21no—
122C22×D191—21no—
123C22×D191C2×D412yes—
124C22⋊D191—28no—
125C22⋊D191—44no—
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—21no—
139C2×Dic191—21no—
140C2×Dic191—21no—
141C2×Dic191—21no—
142C2×Dic191—21no—
143C2×Dic191—21no—
144C2×Dic191—21no—
145C2×Dic191—21no—
146C2×Dic191—21no—
147C2×Dic191C2×D412yes—
148C4×D191—44no—
149C23×C191—21no—
150C23×C191—21no—
151C23×C191—21no—
152C23×C191—21no—
153C23×C191—28no—
154C23×C191—21no—
155C23×C191—21no—
156C23×C191—21no—
157C23×C191—21no—
158C23×C191—21no—
159C23×C191—21no—
160C23×C191—21no—
161C23×C191—21no—
162C23×C191—21no—
163C23×C191—21no—
164C23×C191—21no—
165C23×C191—21no—
166C23×C191—44no—
167C23×C191—44no—
168C23×C191—44no—
169C23×C191—44no—
170C23×C191—44no—
171C23×C191—44no—
172C23×C191C2×D412yes—
173C23×C191C2×D412yes—
174C23×C191#4112yes—
175C23×C191#4112yes—
176C23×C191#4112yes—
177C23×C191C2411yescharacteristic
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—44no—
189C2×C4×C191—44no—
190C2×C4×C191C2×D412yes—
191C2×C4×C191C2×D412yes—
192C22×C191—22no—
193C22×C191—22no—
194C22×C191—22no—
195C22×C191—22no—
196C22×C191—22no—
197C22×C191—22no—
198C22×C191—22no—
199C22×C191—22no—
200C22×C191—22no—
201C22×C191—22no—
202C22×C191—22no—
203C22×C191—22no—
204C22×C191—416no—
205C22×C191—41no—
206C22×C191—41no—
207C22×C191—41no—
208C22×C191—41no—
209C22×C191—41no—
210C22×C191—41no—
211C22×C191—41no—
212C22×C191—41no—
213C22×C191#12314yescomplemented
214C22×C191C22×D411yescharacteristic
215C22×C191C22×D411yescharacteristic
216C22×C191C2×#4111yescharacteristic
217C22×C191C2×#4111yescharacteristic
218C22×C191C2×#4111yescharacteristic
219C22×C191H(5,𝔽2)11yescharacteristic
220C22×C191H(5,𝔽2)11yescharacteristic
221C2×D191—22no—
222C2×D191—22no—
223C2×D191—22no—
224C2×D191—41no—
225C2×D191—41no—
226C2×D191—41no—
227C2×D191—41no—
228C4×C191—22no—
229C4×C191—22no—
230C4×C191—41no—
231C4×C191—41no—
232Dic191—22no—
233Dic191—41no—
234Dic191—41no—
235Dic191—41no—
236Dic191—41no—
237Dic191—41no—
238Dic191—41no—
239C2×C191—24no—
240C2×C191—42no—
241C2×C191—42no—
242C2×C191C2×#12311yescharacteristic
243C2×C191#52511yescharacteristic
244C2×C191#53811yescharacteristic
245C2×C191D4211yescharacteristic
246C2×C191#54611yescharacteristic
247C2×C191#54611yescharacteristic
248C2×C191#55111yescharacteristic
249D191—42no—
250C191#241811yescharacteristic, complemented, Sylow
251#2418—1911nomaximal, Sylow
252C2×#123—1911no—
253C2×#120—1911no—
254C2×C4×D4—1911no—
255C22×C22⋊C4D19111yescharacteristic, complemented
256#399—1911no—
257#397—1911no—
258#394—1911no—
259#394—1911no—
260#388—1911no—
261#388—1911no—
262#386—1911no—
263#386—1911no—
264#385—1911no—
265#380—1911no—
266#379—1911no—
267C25C2×D19111yescharacteristic
268C22×D4—1911no—
269C22×D4—1911no—
270C22×D4—1911no—
271C23×C4—1911no—
272C23×C4C2×D19111yescharacteristic
273C23×C4C2×D19111yescharacteristic
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⋊C4—1911no—
282C2×C22⋊C4—24no—
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⋊C4C2×D19111yescharacteristic
296C2×C22⋊C4C2×D19111yescharacteristic
297C2×C22⋊C4C2×D19111yescharacteristic
298C2×C22⋊C4C2×D19111yescharacteristic
299C2×C42—1911no—
300#95—1911no—
301#95—1911no—
302#95—1911no—
303#95—1911no—
304#95—1911no—
305#95—1911no—
306C24—22no—
307C24—22no—
308C24—22no—
309C24—22no—
310C24—22no—
311C24—41no—
312C24—41no—
313C24—1911no—
314C24C22×D19111yescharacteristic
315C24C22×D19111yescharacteristic
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—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—3822no—
333C22×C4—3822no—
334C22×C4—1911no—
335C22×C4—1911no—
336C22×C4—1911no—
337C22×C4—1911no—
338C22×C4—1911no—
339C22×C4—1911no—
340C22×C4—1911no—
341C22×C4—7641no—
342C22×C4C22×D19111yescharacteristic
343C22×C4C22×D19111yescharacteristic
344C22×C4C22×D19111yescharacteristic
345C22×C4C22×D19111yescharacteristic
346C4⋊C4—3822no—
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—7641no—
364C22⋊C4—7641no—
365C22⋊C4—7641no—
366C22⋊C4C22⋊D19114yescomplemented
367C42—3822no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—28no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—44no—
386C23—44no—
387C23—44no—
388C23—44no—
389C23—44no—
390C23—44no—
391C23—3821no—
392C23—3821no—
393C23—3821no—
394C23—3821no—
395C23—3821no—
396C23—3821no—
397C23—1912no—
398C23D4×D19112yes—
399C23C2×C22⋊D19112yes—
400C23#1569028612yes—
401C23#1569028712yes—
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—44no—
418C2×C4—44no—
419C2×C4—3821no—
420C2×C4—3821no—
421C2×C4—3821no—
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—3821no—
438C2×C4—3821no—
439C2×C4—1912no—
440C2×C4—7644no—
441C2×C4C2×C22⋊D19112yes—
442C2×C4C2×C22⋊D19112yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—416no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—3822no—
465C22—3822no—
466C22—3822no—
467C22—7641no—
468C22—7641no—
469C22—7641no—
470C22—7641no—
471C22#2025930414yescomplemented
472C22C2×D4×D19111yescharacteristic
473C22C22×C22⋊D19111yescharacteristic
474C22C2×#1569028611yescharacteristic
475C22C2×#1569028711yescharacteristic
476C22C2×#1569028711yescharacteristic
477C22#2025936711yescharacteristic
478C22#2025936711yescharacteristic
479C4—22no—
480C4—22no—
481C4—41no—
482C4—41no—
483C4—3822no—
484C4—7641no—
485C4—7641no—
486C4—7641no—
487C4—7641no—
488C4—7641no—
489C4—7641no—
490C2—24no—
491C2—42no—
492C2—42no—
493C2—7642no—
494C2C2×#2025930411yescharacteristic
495C2#2713317411yescharacteristic
496C2#2713325111yescharacteristic
497C2D4×C22⋊D19111yescharacteristic
498C2#2713330311yescharacteristic
499C2#2713330711yescharacteristic
500C2#2713333911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutator, socle, cosocleC23×C191C24
FittingC22×C22⋊C4×C191C2
prime radicalC2×#20259291C2
hypercenterC22×C22⋊C4D191
hypocenterC191#2418
LCSG ▷ C23×C191 ▷ C191
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#20259304C2semidirect
3. C2×C4×C22⋊D191C2semidirect
4. #27132599C2semidirect
5. #27132591C2semidirect
6. #27132579C2semidirect
7. #27132578C2semidirect
8. #27132557C2semidirect
9. #27132556C2semidirect
10. #27132542C2semidirect
11. #27132539C2semidirect
12. #27132536C2semidirect
13. #27132523C2semidirect
14. #27132519C2semidirect
15. C22×C22⋊C4×C191C2semidirect
19. C22×C4×D191C22semidirect
23. C2×C4⋊Dic191C22semidirect
24. C2×C4⋊Dic191C22semidirect
25. C2×Dic191⋊C4C22semidirect
26. C2×Dic191⋊C4C22semidirect
27. C2×Dic191⋊C4C22semidirect
37. C2×(C2×D191)⋊C4C22semidirect
38. C2×(C2×D191)⋊C4C22semidirect
39. C2×(C2×D191)⋊C4C22semidirect
40. C2×C4×Dic191C22semidirect
41. C191⋊#95C22semidirect
42. C191⋊#95C22semidirect
43. C191⋊#95C22semidirect
44. C191⋊#95C22semidirect
45. C191⋊#95C22semidirect
46. C191⋊#95C22semidirect
116. C22⋊C4×C191D4semidirect
213. C22×C191#123semidirect
250. C191#2418semidirect
255. C22×C22⋊C4D191semidirect
366. C22⋊C4C22⋊D191semidirect
471. C22#20259304semidirect

Maximal subgroups

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

subgroupindex
C2×#202593042
C2×#202592912
C2×C4×C22⋊D1912
#271325992
#271325912
#271325792
#271325782
#271325572
#271325562
#271325422
#271325392
#271325362
#271325232
#271325192
C22×C22⋊C4×C1912
#2418191