Finite Group Databasebeta

← #37576107

Subgroups — #37576107

Order 24448.

832 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20259318C211yesmaximal, characteristic, complemented
2C2×#20259296C211yesmaximal, characteristic, complemented
3C2×#20259295C211yesmaximal, characteristic, complemented
4C2×#20259295C211yesmaximal, characteristic, complemented
5C2×#20259295C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊D191C211yesmaximal, characteristic, complemented
7#27132579C211yesmaximal, characteristic, complemented
8#27132578C211yesmaximal, characteristic, complemented
9#27132573C211yesmaximal, characteristic, complemented
10#27132571C211yesmaximal, characteristic, complemented
11#27132563C211yesmaximal, characteristic, complemented
12#27132560C211yesmaximal, characteristic, complemented
13#27132541C211yesmaximal, characteristic, complemented
14#27132510C211yesmaximal, characteristic, complemented
15#386×C191C211yesmaximal, characteristic, complemented
16C22×D764C2211yescharacteristic
17C22×D764C2211yescharacteristic
18C22×D764C2211yescharacteristic
19C22×C22⋊D191C2211yescharacteristic
20C22×C22⋊D191C2211yescharacteristic
21C22×C22⋊D191C2211yescharacteristic
22C22×C22⋊D191C2211yescharacteristic
23C22×C22⋊D191C2211yescharacteristic
24C22×C22⋊D191C2211yescharacteristic
25C22×C4×D191C2211yescharacteristic
26C22×C4×D191C2211yescharacteristic
27#20259318—24no—
28#20259296—24no—
29#20259295—24no—
30#20259295—24no—
31#20259295—24no—
32C4×C22⋊D191—24no—
33C2×C4⋊Dic191C2211yescharacteristic
34C2×Dic191⋊C4C2211yescharacteristic
35C2×Dic191⋊C4C2211yescharacteristic
36C2×Dic191⋊C4C2211yescharacteristic
37C2×C22⋊Dic191C2211yescharacteristic
38C2×C22⋊Dic191C2211yescharacteristic
39C2×(C2×D191)⋊C4C2211yescharacteristic
40C2×(C2×D191)⋊C4C2211yescharacteristic
41C2×(C2×D191)⋊C4C2211yescharacteristic
42C2×(C2×D191)⋊C4C2211yescharacteristic
43C2×(C2×D191)⋊C4C2211yescharacteristic
44C2×(C2×D191)⋊C4C2211yescharacteristic
45C2×(C2×D191)⋊C4C2211yescharacteristic
46C2×C4×Dic191C2211yescharacteristic
47C2×C4×Dic191C2211yescharacteristic
48C191⋊#95C2211yescharacteristic
49C191⋊#95C2211yescharacteristic
50C22×D4×C191C2211yescharacteristic
51C23×C4×C191C2211yescharacteristic
52C2×C22⋊C4×C191C2211yescharacteristic
53C2×C22⋊C4×C191C2211yescharacteristic
54C2×C22⋊C4×C191C2211yescharacteristic
55#95×C191C2211yescharacteristic
56#95×C191C2211yescharacteristic
57C23×D191C2311yescharacteristic
58C23×D191C2311yescharacteristic
59C23×D191C2311yescharacteristic
60C2×D764—22no—
61C2×D764—22no—
62C2×D764—22no—
63C2×D764—22no—
64C2×D764—22no—
65C2×D764—22no—
66C2×D764—41no—
67C2×D764—41no—
68C2×D764—41no—
69C2×C22⋊D191—22no—
70C2×C22⋊D191—22no—
71C2×C22⋊D191—22no—
72C2×C22⋊D191—22no—
73C2×C22⋊D191—22no—
74C2×C22⋊D191—22no—
75C2×C22⋊D191—22no—
76C2×C22⋊D191—22no—
77C2×C22⋊D191—22no—
78C2×C22⋊D191—22no—
79C2×C22⋊D191—22no—
80C2×C22⋊D191—22no—
81C2×C22⋊D191—22no—
82C2×C22⋊D191—41no—
83C2×C22⋊D191—41no—
84C2×C22⋊D191—41no—
85C2×C22⋊D191—41no—
86C2×C22⋊D191D414yescomplemented
87C22×Dic191C2311yescharacteristic
88C22×Dic191C2311yescharacteristic
89C22×Dic191C2311yescharacteristic
90C22×Dic191C2311yescharacteristic
91C22×Dic191C2311yescharacteristic
92C2×C4×D191—22no—
93C2×C4×D191—22no—
94C2×C4×D191—22no—
95C2×C4×D191—22no—
96C2×C4×D191—22no—
97C2×C4×D191—41no—
98C4⋊Dic191—22no—
99Dic191⋊C4—22no—
100Dic191⋊C4—22no—
101Dic191⋊C4D414yescomplemented
102C22⋊Dic191—22no—
103C22⋊Dic191—41no—
104(C2×D191)⋊C4—22no—
105(C2×D191)⋊C4—22no—
106(C2×D191)⋊C4—22no—
107(C2×D191)⋊C4—22no—
108(C2×D191)⋊C4—22no—
109(C2×D191)⋊C4—41no—
110(C2×D191)⋊C4D414yescomplemented
111C4×Dic191—22no—
112C4×Dic191—22no—
113C24×C191C2311yescharacteristic
114C24×C191C2311yescharacteristic
115C2×D4×C191—22no—
116C2×D4×C191—22no—
117C2×D4×C191—41no—
118C22×C4×C191—22no—
119C22×C4×C191—22no—
120C22×C4×C191—41no—
121C22×C4×C191C2311yescharacteristic
122C22×C4×C191C2311yescharacteristic
123C22×C4×C191C2311yescharacteristic
124C22×C4×C191C2311yescharacteristic
125C22×C4×C191C2311yescharacteristic
126C22⋊C4×C191—22no—
127C22⋊C4×C191—22no—
128C22⋊C4×C191—22no—
129C22×D191—21no—
130C22×D191—21no—
131C22×D191—21no—
132C22×D191—21no—
133C22×D191—21no—
134C22×D191—21no—
135C22×D191—21no—
136C22×D191—21no—
137C22×D191—21no—
138C22×D191—21no—
139C22×D191—21no—
140C22×D191—21no—
141C22×D191—21no—
142C22×D191—21no—
143C22×D191—21no—
144C22×D191—21no—
145C22×D191—21no—
146C22×D191—21no—
147C22×D191—21no—
148C22×D191C2×D412yes—
149C22×D191C2×D412yes—
150D764—44no—
151D764—44no—
152D764—44no—
153C22⋊D191—28no—
154C22⋊D191—44no—
155C22⋊D191—44no—
156C22⋊D191—44no—
157C22⋊D191—44no—
158C22⋊D191—44no—
159C2×Dic191—21no—
160C2×Dic191—21no—
161C2×Dic191—21no—
162C2×Dic191—21no—
163C2×Dic191—21no—
164C2×Dic191—21no—
165C2×Dic191—21no—
166C2×Dic191—21no—
167C2×Dic191—21no—
168C2×Dic191—21no—
169C2×Dic191C2×D412yes—
170C2×Dic191C2×D412yes—
171C2×Dic191C2×D412yes—
172C2×Dic191C2×D412yes—
173C2×Dic191#4112yes—
174C4×D191—44no—
175C4×D191—44no—
176C23×C191—21no—
177C23×C191—21no—
178C23×C191—21no—
179C23×C191—21no—
180C23×C191—21no—
181C23×C191—21no—
182C23×C191—21no—
183C23×C191—21no—
184C23×C191—21no—
185C23×C191—21no—
186C23×C191—21no—
187C23×C191—21no—
188C23×C191—21no—
189C23×C191C2×D412yes—
190C23×C191C2411yescharacteristic
191D4×C191—44no—
192C2×C4×C191—21no—
193C2×C4×C191—21no—
194C2×C4×C191—21no—
195C2×C4×C191—21no—
196C2×C4×C191—21no—
197C2×C4×C191—21no—
198C2×C4×C191—21no—
199C2×C4×C191—21no—
200C2×C4×C191—21no—
201C2×C4×C191—21no—
202C2×C4×C191—21no—
203C2×C4×C191—21no—
204C2×C4×C191—44no—
205C2×C4×C191C2×D412yes—
206C2×C4×C191C2×D412yes—
207C2×C4×C191#4112yes—
208C22×C191—22no—
209C22×C191—22no—
210C22×C191—22no—
211C22×C191—41no—
212C22×C191—41no—
213C22×C191—41no—
214C22×C191—41no—
215C22×C191—41no—
216C22×C191—41no—
217C22×C191—41no—
218C22×C191—41no—
219C22×C191—41no—
220C22×C191—41no—
221C22×C191—41no—
222C22×C191C22×D411yescharacteristic
223C22×C191C22×D411yescharacteristic
224C22×C191C22×D411yescharacteristic
225C22×C191C2×#4111yescharacteristic
226C22×C191C2×#4111yescharacteristic
227C22×C191H(5,𝔽2)11yescharacteristic
228C22×C191H(5,𝔽2)11yescharacteristic
229C2×D191—22no—
230C2×D191—22no—
231C2×D191—22no—
232C2×D191—22no—
233C2×D191—22no—
234C2×D191—22no—
235C2×D191—41no—
236C2×D191—41no—
237C2×D191—41no—
238C2×D191—41no—
239C2×D191—41no—
240C2×D191—41no—
241C2×D191—41no—
242C2×D191—41no—
243C2×D191—41no—
244C2×D191—41no—
245C2×D191—41no—
246C2×D191—41no—
247C2×D191—41no—
248C2×D191—41no—
249C2×D191—41no—
250C4×C191—22no—
251C4×C191—22no—
252C4×C191—22no—
253C4×C191—41no—
254C4×C191—41no—
255Dic191—22no—
256Dic191—22no—
257Dic191—41no—
258Dic191—41no—
259Dic191#12114yescomplemented
260C2×C191—42no—
261C2×C191—81no—
262C2×C191C2×#12111yescharacteristic
263C2×C191#53211yescharacteristic
264C2×C191#54011yescharacteristic
265C2×C191D4211yescharacteristic
266C2×C191D4211yescharacteristic
267C2×C191#54611yescharacteristic
268C2×C191#55011yescharacteristic
269D191—42no—
270D191—42no—
271D191—81no—
272C191#242811yescharacteristic, complemented, Sylow
273#2428—1911nomaximal, Sylow
274C2×#127—1911no—
275C2×#121—1911no—
276C2×#121—1911no—
277C2×#121—1911no—
278C2×#121—1911no—
279C2×C4×D4—1911no—
280#394—1911no—
281#394—1911no—
282#392—1911no—
283#392—1911no—
284#390—1911no—
285#389—1911no—
286#386—1911no—
287#386D19111yescharacteristic, complemented
288C4×C22⋊C4—1911no—
289C22×D4—1911no—
290C22×D4—1911no—
291C22×D4—1911no—
292C22×D4—1911no—
293C22×D4—1911no—
294C22×D4—1911no—
295C22×D4—1911no—
296C22×D4—1911no—
297C22×D4—1911no—
298C22×D4C2×D19111yescharacteristic
299C23×C4—1911no—
300C23×C4—1911no—
301C23×C4C2×D19111yescharacteristic
302#127—3824no—
303#121—3824no—
304#121—3824no—
305#121—3824no—
306#121—3824no—
307C4×D4—3824no—
308C2×C4⋊C4—1911no—
309C2×C4⋊C4—1911no—
310C2×C4⋊C4—1911no—
311C2×C4⋊C4—1911no—
312C2×C22⋊C4—1911no—
313C2×C22⋊C4—1911no—
314C2×C22⋊C4—1911no—
315C2×C22⋊C4—1911no—
316C2×C22⋊C4—1911no—
317C2×C22⋊C4—1911no—
318C2×C22⋊C4—1911no—
319C2×C22⋊C4—1911no—
320C2×C22⋊C4—1911no—
321C2×C22⋊C4C2×D19111yescharacteristic
322C2×C22⋊C4C2×D19111yescharacteristic
323C2×C22⋊C4C2×D19111yescharacteristic
324C2×C42—1911no—
325C2×C42—1911no—
326#95—1911no—
327#95—1911no—
328#95C2×D19111yescharacteristic
329#95C2×D19111yescharacteristic
330C24—1911no—
331C24—1911no—
332C24—1911no—
333C24C22×D19111yescharacteristic
334C24C22×D19111yescharacteristic
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—41no—
338C2×D4—3822no—
339C2×D4—3822no—
340C2×D4—3822no—
341C2×D4—3822no—
342C2×D4—3822no—
343C2×D4—3822no—
344C2×D4—3822no—
345C2×D4—3822no—
346C2×D4—3822no—
347C2×D4—3822no—
348C2×D4—3822no—
349C2×D4—3822no—
350C2×D4—3822no—
351C2×D4—3822no—
352C2×D4—3822no—
353C2×D4—3822no—
354C2×D4—3822no—
355C2×D4—3822no—
356C2×D4—3822no—
357C2×D4—1914no—
358C2×D4—7641no—
359C2×D4—7641no—
360C2×D4—7641no—
361C2×D4—7641no—
362C2×D4—7641no—
363C2×D4—7641no—
364C2×D4—7641no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—41no—
368C22×C4—3822no—
369C22×C4—3822no—
370C22×C4—3822no—
371C22×C4—3822no—
372C22×C4—3822no—
373C22×C4—1911no—
374C22×C4—1911no—
375C22×C4—1911no—
376C22×C4—1911no—
377C22×C4—1911no—
378C22×C4—7641no—
379C22×C4C22×D19111yescharacteristic
380C22×C4C22×D19111yescharacteristic
381C22×C4C22×D19111yescharacteristic
382C22×C4C22×D19111yescharacteristic
383C22×C4C22×D19111yescharacteristic
384C4⋊C4—3822no—
385C4⋊C4—3822no—
386C4⋊C4—3822no—
387C4⋊C4—1914no—
388C22⋊C4—22no—
389C22⋊C4—22no—
390C22⋊C4—22no—
391C22⋊C4—3822no—
392C22⋊C4—3822no—
393C22⋊C4—3822no—
394C22⋊C4—3822no—
395C22⋊C4—3822no—
396C22⋊C4—3822no—
397C22⋊C4—1914no—
398C22⋊C4—7641no—
399C22⋊C4—7641no—
400C42—3822no—
401C42—3822no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—3821no—
416C23—3821no—
417C23—3821no—
418C23—3821no—
419C23—3821no—
420C23—3821no—
421C23—3821no—
422C23—3821no—
423C23—3821no—
424C23—3821no—
425C23—3821no—
426C23—3821no—
427C23—3821no—
428C23—3821no—
429C23—3821no—
430C23—3821no—
431C23—3821no—
432C23—3821no—
433C23—3821no—
434C23—1912no—
435C23—1912no—
436C23D4×D19112yes—
437C23C23×D19111yescharacteristic
438D4—44no—
439D4—3828no—
440D4—7644no—
441D4—7644no—
442D4—7644no—
443D4—7644no—
444D4—7644no—
445D4—7644no—
446D4—7644no—
447D4—7644no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—44no—
461C2×C4—3821no—
462C2×C4—3821no—
463C2×C4—3821no—
464C2×C4—3821no—
465C2×C4—3821no—
466C2×C4—3821no—
467C2×C4—3821no—
468C2×C4—3821no—
469C2×C4—3821no—
470C2×C4—3821no—
471C2×C4—1912no—
472C2×C4—1912no—
473C2×C4—1912no—
474C2×C4—1912no—
475C2×C4—1912no—
476C2×C4—7644no—
477C2×C4—7644no—
478C2×C4D4×D19112yes—
479C2×C4D4×D19112yes—
480C2×C4#1569028712yes—
481C22—22no—
482C22—22no—
483C22—22no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—3822no—
496C22—3822no—
497C22—3822no—
498C22—3822no—
499C22—3822no—
500C22—3822no—
501C22—7641no—
502C22—7641no—
503C22—7641no—
504C22—7641no—
505C22—7641no—
506C22—7641no—
507C22—7641no—
508C22—7641no—
509C22—7641no—
510C22—7641no—
511C22—7641no—
512C22—7641no—
513C22—7641no—
514C22—7641no—
515C22—7641no—
516C22C2×D4×D19111yescharacteristic
517C22C2×D4×D19111yescharacteristic
518C22C2×D4×D19111yescharacteristic
519C22#41×D19111yescharacteristic
520C22C2×#1569028711yescharacteristic
521C22#2025936711yescharacteristic
522C22#2025936811yescharacteristic
523C4—22no—
524C4—22no—
525C4—22no—
526C4—41no—
527C4—41no—
528C4—3822no—
529C4—3822no—
530C4—1914no—
531C4—7641no—
532C4—7641no—
533C2—42no—
534C2—81no—
535C2—15281no—
536C2—7642no—
537C2—7642no—
538C2#121×D19111yescharacteristic
539C2#2713321011yescharacteristic
540C2#2713326511yescharacteristic
541C2#2713329511yescharacteristic
542C2#2713329711yescharacteristic
543C2#2713330311yescharacteristic
544C2#2713333411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutator, socle, cosocleC23×C191C24
Fitting#386×C191C2
hypercenter#386D191
hypocenterC191#2428
LCSG ▷ C23×C191 ▷ C191
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#20259318C2semidirect
2. C2×#20259296C2semidirect
3. C2×#20259295C2semidirect
4. C2×#20259295C2semidirect
5. C2×#20259295C2semidirect
6. C2×C4×C22⋊D191C2semidirect
7. #27132579C2semidirect
8. #27132578C2semidirect
9. #27132573C2semidirect
10. #27132571C2semidirect
11. #27132563C2semidirect
12. #27132560C2semidirect
13. #27132541C2semidirect
14. #27132510C2semidirect
15. #386×C191C2semidirect
86. C2×C22⋊D191D4semidirect
101. Dic191⋊C4D4semidirect
110. (C2×D191)⋊C4D4semidirect
259. Dic191#121semidirect
272. C191#2428semidirect
287. #386D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593182
C2×#202592962
C2×#202592952
C2×C4×C22⋊D1912
#271325792
#271325782
#271325732
#271325712
#271325632
#271325602
#271325412
#271325102
#386×C1912
#2428191