Finite Group Databasebeta

← #37575893

Subgroups — #37575893

Order 24448.

1246 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D191C211yesmaximal, characteristic, complemented
2C2×#20259296C211yesmaximal, characteristic, complemented
3C2×#20259294C211yesmaximal, characteristic, complemented
4C2×#20259292C211yesmaximal, characteristic, complemented
5C2×#20259292C211yesmaximal, characteristic, complemented
6C22×(C2×D191)⋊C4C211yesmaximal, characteristic, complemented
7#27132581C211yesmaximal, characteristic, complemented
8#27132579C211yesmaximal, characteristic, complemented
9#27132573C211yesmaximal, characteristic, complemented
10#27132572C211yesmaximal, characteristic, complemented
11#27132541C211yesmaximal, characteristic, complemented
12#27132540C211yesmaximal, characteristic, complemented
13#27132537C211yesmaximal, characteristic, complemented
14#27132518C211yesmaximal, characteristic, complemented
15#386×C191C211yesmaximal, characteristic, complemented
16C24×D191C2211yescharacteristic
17C24×D191C2211yescharacteristic
18C22×D764C2211yescharacteristic
19C22×D764C2211yescharacteristic
20C22×D764C2211yescharacteristic, complemented
21C22×D764C2211yescharacteristic, complemented
22C22×C22⋊D191C2211yescharacteristic
23C22×C22⋊D191C2211yescharacteristic
24C22×C22⋊D191C2211yescharacteristic, complemented
25C22×C22⋊D191C2211yescharacteristic, complemented
26C2×D4×D191—24no—
27C2×D4×D191—24no—
28C2×D4×D191—24no—
29C23×Dic191C2211yescharacteristic, complemented
30C22×C4×D191C2211yescharacteristic
31#20259296—24no—
32#20259294—24no—
33#20259292—24no—
34#20259292—24no—
35C2×C4⋊Dic191C2211yescharacteristic, complemented
36C2×Dic191⋊C4C2211yescharacteristic, complemented
37C2×C22⋊Dic191C2211yescharacteristic, complemented
38C2×(C2×D191)⋊C4—24no—
39C2×(C2×D191)⋊C4C2211yescharacteristic
40C2×(C2×D191)⋊C4C2211yescharacteristic
41C2×(C2×D191)⋊C4C2211yescharacteristic
42C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
45C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
46C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
47C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
48C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
49C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
50C191⋊#95C2211yescharacteristic, complemented
51C191⋊#95C2211yescharacteristic, complemented
52C22×D4×C191C2211yescharacteristic
53C23×C4×C191C2211yescharacteristic, complemented
54C2×C22⋊C4×C191C2211yescharacteristic, complemented
55C2×C22⋊C4×C191C2211yescharacteristic, complemented
56C2×C22⋊C4×C191C2211yescharacteristic, complemented
57#95×C191C2211yescharacteristic, complemented
58#95×C191C2211yescharacteristic, complemented
59C23×D191—22no—
60C23×D191—22no—
61C23×D191—22no—
62C23×D191—22no—
63C23×D191—22no—
64C23×D191—22no—
65C23×D191—22no—
66C23×D191—22no—
67C23×D191—22no—
68C23×D191—41no—
69C23×D191—41no—
70C23×D191—41no—
71C23×D191—41no—
72C23×D191D414yescomplemented
73C23×D191C2311yescharacteristic
74C23×D191C2311yescharacteristic
75C23×D191C2311yescharacteristic
76C23×D191C2311yescharacteristic
77C2×D764—22no—
78C2×D764—22no—
79C2×D764—22no—
80C2×D764—22no—
81C2×D764—22no—
82C2×D764—22no—
83C2×D764—22no—
84C2×D764—22no—
85C2×D764—22no—
86C2×D764—41no—
87C2×D764—41no—
88C2×D764—41no—
89C2×C22⋊D191—22no—
90C2×C22⋊D191—22no—
91C2×C22⋊D191—22no—
92C2×C22⋊D191—22no—
93C2×C22⋊D191—22no—
94C2×C22⋊D191—22no—
95C2×C22⋊D191—22no—
96C2×C22⋊D191—22no—
97C2×C22⋊D191—22no—
98C2×C22⋊D191—22no—
99C2×C22⋊D191—41no—
100C2×C22⋊D191D414yescomplemented
101D4×D191—232no—
102C22×Dic191—22no—
103C22×Dic191—22no—
104C22×Dic191—41no—
105C22×Dic191C2311yescharacteristic
106C22×Dic191C2311yescharacteristic
107C22×Dic191C2311yescharacteristic
108C22×Dic191C2311yescharacteristic
109C2×C4×D191—22no—
110C2×C4×D191—22no—
111C2×C4×D191—22no—
112C4⋊Dic191—22no—
113Dic191⋊C4—22no—
114C22⋊Dic191—22no—
115(C2×D191)⋊C4—22no—
116(C2×D191)⋊C4—22no—
117(C2×D191)⋊C4—22no—
118(C2×D191)⋊C4—22no—
119(C2×D191)⋊C4—22no—
120(C2×D191)⋊C4—22no—
121(C2×D191)⋊C4—22no—
122(C2×D191)⋊C4—22no—
123(C2×D191)⋊C4—22no—
124(C2×D191)⋊C4—41no—
125(C2×D191)⋊C4D414yescomplemented
126C24×C191C2311yescharacteristic
127C24×C191C2311yescharacteristic
128C2×D4×C191—22no—
129C2×D4×C191—22no—
130C2×D4×C191D414yescomplemented
131C22×C4×C191—22no—
132C22×C4×C191—22no—
133C22×C4×C191—41no—
134C22×C4×C191C2311yescharacteristic
135C22×C4×C191C2311yescharacteristic
136C22×C4×C191C2311yescharacteristic
137C22×C4×C191C2311yescharacteristic
138C22×C4×C191C2311yescharacteristic
139C22⋊C4×C191—22no—
140C22⋊C4×C191—22no—
141C22⋊C4×C191—41no—
142C22×D191—21no—
143C22×D191—21no—
144C22×D191—21no—
145C22×D191—21no—
146C22×D191—28no—
147C22×D191—28no—
148C22×D191—21no—
149C22×D191—21no—
150C22×D191—21no—
151C22×D191—21no—
152C22×D191—21no—
153C22×D191—21no—
154C22×D191—21no—
155C22×D191—21no—
156C22×D191—21no—
157C22×D191—21no—
158C22×D191—21no—
159C22×D191—21no—
160C22×D191—28no—
161C22×D191—21no—
162C22×D191—21no—
163C22×D191—21no—
164C22×D191—21no—
165C22×D191—21no—
166C22×D191—21no—
167C22×D191—21no—
168C22×D191—44no—
169C22×D191—44no—
170C22×D191—44no—
171C22×D191—44no—
172C22×D191—44no—
173C22×D191—44no—
174C22×D191—44no—
175C22×D191—44no—
176C22×D191—44no—
177C22×D191—44no—
178C22×D191—44no—
179C22×D191C2×D412yes—
180C22×D191C2×D412yes—
181C22×D191C2×D412yes—
182C22×D191C2×D412yes—
183C22×D191#4112yes—
184D764—28no—
185D764—44no—
186D764—44no—
187D764—44no—
188C22⋊D191—28no—
189C22⋊D191—28no—
190C22⋊D191—44no—
191C22⋊D191—44no—
192C2×Dic191—21no—
193C2×Dic191—21no—
194C2×Dic191—21no—
195C2×Dic191—21no—
196C2×Dic191—21no—
197C2×Dic191—21no—
198C2×Dic191—21no—
199C2×Dic191—21no—
200C2×Dic191—21no—
201C2×Dic191—21no—
202C2×Dic191—44no—
203C2×Dic191C2×D412yes—
204C2×Dic191C2×D412yescomplemented
205C4×D191—28no—
206C23×C191—21no—
207C23×C191—21no—
208C23×C191—21no—
209C23×C191—21no—
210C23×C191—21no—
211C23×C191—21no—
212C23×C191—21no—
213C23×C191—21no—
214C23×C191—21no—
215C23×C191—21no—
216C23×C191C2×D412yes—
217C23×C191C2×D412yes—
218C23×C191C2×D412yes—
219C23×C191C2×D412yes—
220C23×C191C2411yescharacteristic
221D4×C191—28no—
222C2×C4×C191—21no—
223C2×C4×C191—21no—
224C2×C4×C191—21no—
225C2×C4×C191—21no—
226C2×C4×C191—21no—
227C2×C4×C191—21no—
228C2×C4×C191—21no—
229C2×C4×C191—21no—
230C2×C4×C191—21no—
231C2×C4×C191—21no—
232C2×C4×C191—21no—
233C2×C4×C191—21no—
234C2×C4×C191—21no—
235C2×C4×C191—44no—
236C2×C4×C191C2×D412yes—
237C2×C4×C191C2×D412yescomplemented
238C22×C191—22no—
239C22×C191—22no—
240C22×C191—22no—
241C22×C191—22no—
242C22×C191—22no—
243C22×C191—22no—
244C22×C191—22no—
245C22×C191—22no—
246C22×C191—22no—
247C22×C191—41no—
248C22×C191—41no—
249C22×C191—41no—
250C22×C191—41no—
251C22×C191#12014yescomplemented
252C22×C191C22×D411yescharacteristic
253C22×C191C22×D411yescharacteristic
254C22×C191C22×D411yescharacteristic
255C22×C191C22×D411yescharacteristic
256C22×C191C2×#4111yescharacteristic
257C22×C191H(5,𝔽2)11yescharacteristic
258C22×C191H(5,𝔽2)11yescharacteristic
259C2×D191—22no—
260C2×D191—22no—
261C2×D191—22no—
262C2×D191—22no—
263C2×D191—22no—
264C2×D191—22no—
265C2×D191—22no—
266C2×D191—22no—
267C2×D191—22no—
268C2×D191—22no—
269C2×D191—22no—
270C2×D191—22no—
271C2×D191—416no—
272C2×D191—416no—
273C2×D191—41no—
274C2×D191—41no—
275C2×D191—41no—
276C2×D191—41no—
277C2×D191—41no—
278C2×D191—41no—
279C2×D191—41no—
280C2×D191—41no—
281C2×D191—41no—
282C2×D191—41no—
283C2×D191—41no—
284C2×D191—41no—
285C2×D191—41no—
286C2×D191—41no—
287C2×D191—41no—
288C2×D191#12114yescomplemented
289C4×C191—22no—
290C4×C191—22no—
291C4×C191—41no—
292C4×C191—41no—
293C4×C191—41no—
294Dic191—22no—
295Dic191—22no—
296Dic191—41no—
297Dic191—41no—
298C2×C191—24no—
299C2×C191—42no—
300C2×C191C2×#12011yescharacteristic
301C2×C191C2×#12111yescharacteristic
302C2×C191#53411yescharacteristic
303C2×C191D4211yescharacteristic
304C2×C191D4211yescharacteristic
305C2×C191#54611yescharacteristic
306C2×C191#54611yescharacteristic
307D191—24no—
308D191—42no—
309D191—42no—
310D191—81no—
311C191#241011yescharacteristic, complemented, Sylow
312#2410—1911nomaximal, Sylow
313C23×D4—1911no—
314C2×#121—1911no—
315C2×#121—1911no—
316C2×#120—1911no—
317C2×#120—1911no—
318C22×C22⋊C4—1911no—
319#394—1911no—
320#394—1911no—
321#392—1911no—
322#392—1911no—
323#386—1911no—
324#386—1911no—
325#386D19111yescharacteristic, complemented
326#385—1911no—
327#379—1911no—
328C25—1911no—
329C25—1911no—
330C22×D4—3824no—
331C22×D4—3824no—
332C22×D4—3824no—
333C22×D4—1911no—
334C22×D4—1911no—
335C22×D4—1911no—
336C22×D4—1911no—
337C22×D4—1911no—
338C22×D4—1911no—
339C22×D4—1911no—
340C22×D4—1911no—
341C22×D4C2×D19111yescharacteristic
342C23×C4—1911no—
343C23×C4—1911no—
344C23×C4C2×D19111yescharacteristic, complemented
345#121—3824no—
346#121—3824no—
347#120—3824no—
348#120—3824no—
349C2×C4⋊C4—1911no—
350C2×C4⋊C4—1911no—
351C2×C22⋊C4—3824no—
352C2×C22⋊C4—1911no—
353C2×C22⋊C4—1911no—
354C2×C22⋊C4—1911no—
355C2×C22⋊C4—1911no—
356C2×C22⋊C4—1911no—
357C2×C22⋊C4—1911no—
358C2×C22⋊C4—1911no—
359C2×C22⋊C4—1911no—
360C2×C22⋊C4—1911no—
361C2×C22⋊C4—1911no—
362C2×C22⋊C4—1911no—
363C2×C22⋊C4—1911no—
364C2×C22⋊C4C2×D19111yescharacteristic, complemented
365C2×C22⋊C4C2×D19111yescharacteristic, complemented
366C2×C22⋊C4C2×D19111yescharacteristic, complemented
367#95—1911no—
368#95—1911no—
369#95C2×D19111yescharacteristic, complemented
370#95C2×D19111yescharacteristic, complemented
371C24—3822no—
372C24—3822no—
373C24—3822no—
374C24—3822no—
375C24—3822no—
376C24—3822no—
377C24—3822no—
378C24—3822no—
379C24—3822no—
380C24—1911no—
381C24—1911no—
382C24—1911no—
383C24—1911no—
384C24—1914no—
385C24—7641no—
386C24—7641no—
387C24—7641no—
388C24—7641no—
389C24C22×D19111yescharacteristic
390C24C22×D19111yescharacteristic
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—3822no—
394C2×D4—3822no—
395C2×D4—3822no—
396C2×D4—3822no—
397C2×D4—3822no—
398C2×D4—3822no—
399C2×D4—3822no—
400C2×D4—38232no—
401C2×D4—3822no—
402C2×D4—3822no—
403C2×D4—3822no—
404C2×D4—3822no—
405C2×D4—3822no—
406C2×D4—3822no—
407C2×D4—3822no—
408C2×D4—3822no—
409C2×D4—3822no—
410C2×D4—3822no—
411C2×D4—3822no—
412C2×D4—3822no—
413C2×D4—1914no—
414C2×D4—7641no—
415C2×D4—7641no—
416C2×D4—7641no—
417C2×D4—7641no—
418C2×D4D76414yescomplemented
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—41no—
422C22×C4—3822no—
423C22×C4—3822no—
424C22×C4—3822no—
425C22×C4—3822no—
426C22×C4—3822no—
427C22×C4—1911no—
428C22×C4—1911no—
429C22×C4—1911no—
430C22×C4—1911no—
431C22×C4—7641no—
432C22×C4C22×D19111yescharacteristic
433C22×C4C22×D19111yescharacteristic
434C22×C4C22×D19111yescharacteristic
435C22×C4C22×D19111yescharacteristic
436C22×C4C22×D19111yescharacteristic
437C4⋊C4—3822no—
438C4⋊C4—3822no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—41no—
442C22⋊C4—3822no—
443C22⋊C4—3822no—
444C22⋊C4—3822no—
445C22⋊C4—3822no—
446C22⋊C4—3822no—
447C22⋊C4—3822no—
448C22⋊C4—3822no—
449C22⋊C4—3822no—
450C22⋊C4—3822no—
451C22⋊C4—3822no—
452C22⋊C4—1914no—
453C22⋊C4—7641no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—3828no—
465C23—3828no—
466C23—3821no—
467C23—3821no—
468C23—3821no—
469C23—3821no—
470C23—3821no—
471C23—3821no—
472C23—3821no—
473C23—3821no—
474C23—3821no—
475C23—3821no—
476C23—3821no—
477C23—3821no—
478C23—3821no—
479C23—3821no—
480C23—3821no—
481C23—3821no—
482C23—3828no—
483C23—3821no—
484C23—3821no—
485C23—3821no—
486C23—3821no—
487C23—3821no—
488C23—3821no—
489C23—3821no—
490C23—1912no—
491C23—1912no—
492C23—1912no—
493C23—1912no—
494C23—1912no—
495C23—7644no—
496C23—7644no—
497C23—7644no—
498C23—7644no—
499C23—7644no—
500C23—7644no—
501C23—7644no—
502C23—7644no—
503C23—7644no—
504C23—7644no—
505C23—7644no—
506C23D4×D19112yes—
507C23D4×D19112yes—
508C23C2×D76412yes—
509C23C2×D76412yes—
510C23C23×D19111yescharacteristic
511D4—28no—
512D4—3828no—
513D4—3828no—
514D4—3828no—
515D4—7644no—
516D4—7644no—
517D4—7644no—
518D4—7644no—
519D4—7644no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—44no—
534C2×C4—3828no—
535C2×C4—3821no—
536C2×C4—3821no—
537C2×C4—3821no—
538C2×C4—3821no—
539C2×C4—3821no—
540C2×C4—3821no—
541C2×C4—3821no—
542C2×C4—3821no—
543C2×C4—3821no—
544C2×C4—3821no—
545C2×C4—1912no—
546C2×C4—1912no—
547C2×C4—7644no—
548C2×C4D4×D19112yescomplemented
549C2×C4C2×D76412yes—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—3822no—
564C22—3822no—
565C22—3822no—
566C22—3822no—
567C22—3822no—
568C22—3822no—
569C22—3822no—
570C22—3822no—
571C22—3822no—
572C22—3822no—
573C22—3822no—
574C22—3822no—
575C22—1914no—
576C22—76416no—
577C22—76416no—
578C22—7641no—
579C22—7641no—
580C22—7641no—
581C22—7641no—
582C22—7641no—
583C22—7641no—
584C22—7641no—
585C22—7641no—
586C22—7641no—
587C22—7641no—
588C22—7641no—
589C22—7641no—
590C22—7641no—
591C22—7641no—
592C22—7641no—
593C22#2025929214yescomplemented
594C22C2×D4×D19111yescharacteristic
595C22C2×D4×D19111yescharacteristic
596C22C2×D4×D19111yescharacteristic
597C22C22×D76411yescharacteristic
598C22#41×D19111yescharacteristic
599C22#2025936711yescharacteristic
600C22#2025936811yescharacteristic
601C4—22no—
602C4—22no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—3822no—
607C4—3822no—
608C4—7641no—
609C4—7641no—
610C2—24no—
611C2—42no—
612C2—3824no—
613C2—15281no—
614C2—7642no—
615C2—7642no—
616C2C2×#2025929211yescharacteristic
617C2#121×D19111yescharacteristic
618C2#2713322111yescharacteristic
619C2#2713329511yescharacteristic
620C2D4×D76411yescharacteristic
621C2#2713330511yescharacteristic
622C2#2713330811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutator, socle, cosocleC23×C191C24
Fitting#386×C191C2
hypercenter#386D191
hypocenterC191#2410
LCSG ▷ C23×C191 ▷ C191
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C22×D4×D191C2semidirect
2. C2×#20259296C2semidirect
3. C2×#20259294C2semidirect
4. C2×#20259292C2semidirect
5. C2×#20259292C2semidirect
6. C22×(C2×D191)⋊C4C2semidirect
7. #27132581C2semidirect
8. #27132579C2semidirect
9. #27132573C2semidirect
10. #27132572C2semidirect
11. #27132541C2semidirect
12. #27132540C2semidirect
13. #27132537C2semidirect
14. #27132518C2semidirect
15. #386×C191C2semidirect
20. C22×D764C22semidirect
21. C22×D764C22semidirect
24. C22×C22⋊D191C22semidirect
25. C22×C22⋊D191C22semidirect
29. C23×Dic191C22semidirect
35. C2×C4⋊Dic191C22semidirect
36. C2×Dic191⋊C4C22semidirect
37. C2×C22⋊Dic191C22semidirect
42. C2×(C2×D191)⋊C4C22semidirect
43. C2×(C2×D191)⋊C4C22semidirect
44. C2×(C2×D191)⋊C4C22semidirect
45. C2×(C2×D191)⋊C4C22semidirect
46. C2×(C2×D191)⋊C4C22semidirect
47. C2×(C2×D191)⋊C4C22semidirect
48. C2×(C2×D191)⋊C4C22semidirect
49. C2×(C2×D191)⋊C4C22semidirect
50. C191⋊#95C22semidirect
51. C191⋊#95C22semidirect
53. C23×C4×C191C22semidirect
54. C2×C22⋊C4×C191C22semidirect
55. C2×C22⋊C4×C191C22semidirect
56. C2×C22⋊C4×C191C22semidirect
57. #95×C191C22semidirect
58. #95×C191C22semidirect
72. C23×D191D4semidirect
100. C2×C22⋊D191D4semidirect
125. (C2×D191)⋊C4D4semidirect
130. C2×D4×C191D4semidirect
204. C2×Dic191C2×D4semidirect
237. C2×C4×C191C2×D4semidirect
251. C22×C191#120semidirect
288. C2×D191#121semidirect
311. C191#2410semidirect
325. #386D191semidirect
344. C23×C4C2×D191semidirect
364. C2×C22⋊C4C2×D191semidirect
365. C2×C22⋊C4C2×D191semidirect
366. C2×C22⋊C4C2×D191semidirect
369. #95C2×D191semidirect
370. #95C2×D191semidirect
418. C2×D4D764semidirect
548. C2×C4D4×D191semidirect
593. C22#20259292semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D1912
C2×#202592962
C2×#202592942
C2×#202592922
C22×(C2×D191)⋊C42
#271325812
#271325792
#271325732
#271325722
#271325412
#271325402
#271325372
#271325182
#386×C1912
#2410191