Finite Group Databasebeta

← #37575338

Subgroups — #37575338

Order 24448.

1252 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D191C211yesmaximal, characteristic
2C2×C4×C22⋊D191C211yesmaximal, characteristic, complemented
3C2×(C22⋊D191)⋊C4C211yesmaximal, characteristic, complemented
4C22×(C2×D191)⋊C4C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D191C211yesmaximal, characteristic, complemented
6#27132563C211yesmaximal, characteristic, complemented
7#27132563C211yesmaximal, characteristic, complemented
8#27132543C211yesmaximal, characteristic, complemented
9#27132541C211yesmaximal, characteristic, complemented
10#27132541C211yesmaximal, characteristic, complemented
11#27132522C211yesmaximal, characteristic, complemented
12#27132518C211yesmaximal, characteristic, complemented
13#27132518C211yesmaximal, characteristic, complemented
14#27132510C211yesmaximal, characteristic, complemented
15#386×C191C211yesmaximal, characteristic, complemented
16C24×D191C2211yescharacteristic
17C24×D191C2211yescharacteristic
18C22×D764C2211yescharacteristic
19C22×C22⋊D191C2211yescharacteristic
20C22×C22⋊D191C2211yescharacteristic
21C2×D4×D191—24no—
22C2×D4×D191—24no—
23C2×D4×D191C418yescomplemented
24C23×Dic191C2211yescharacteristic, complemented
25C22×C4×D191C2211yescharacteristic
26C22×C4×D191C2211yescharacteristic, complemented
27C22×C4×D191C2211yescharacteristic, complemented
28C4×C22⋊D191—24no—
29(C22⋊D191)⋊C4—24no—
30C2×Dic191⋊C4C2211yescharacteristic, complemented
31C2×Dic191⋊C4C2211yescharacteristic, complemented
32C2×C22⋊Dic191C2211yescharacteristic, complemented
33C2×C22⋊Dic191C2211yescharacteristic, complemented
34C2×C22⋊Dic191C2211yescharacteristic, complemented
35C2×(C2×D191)⋊C4—24no—
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
43C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
45C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
46C22⋊C4×D191—24no—
47C2×C4×Dic191C2211yescharacteristic, complemented
48C2×C4×Dic191C2211yescharacteristic, complemented
49C191⋊#95C2211yescharacteristic, complemented
50C191⋊#95C2211yescharacteristic, complemented
51C22×D4×C191C2211yescharacteristic
52C23×C4×C191C2211yescharacteristic, complemented
53C2×C22⋊C4×C191C2211yescharacteristic, complemented
54C2×C22⋊C4×C191C2211yescharacteristic, complemented
55C2×C22⋊C4×C191C2211yescharacteristic, complemented
56#95×C191C2211yescharacteristic, complemented
57#95×C191C2211yescharacteristic, complemented
58C23×D191—22no—
59C23×D191—22no—
60C23×D191—22no—
61C23×D191—22no—
62C23×D191—22no—
63C23×D191—22no—
64C23×D191—22no—
65C23×D191—22no—
66C23×D191—41no—
67C23×D191—41no—
68C23×D191—41no—
69C23×D191—41no—
70C23×D191C2×C414yescomplemented
71C23×D191C2×C414yescomplemented
72C23×D191C2311yescharacteristic
73C23×D191C2311yescharacteristic
74C23×D191C2311yescharacteristic
75C2×D764—22no—
76C2×D764—22no—
77C2×D764C2×C414yescomplemented
78C2×C22⋊D191—22no—
79C2×C22⋊D191—22no—
80C2×C22⋊D191C2×C414yes—
81C2×C22⋊D191C2×C414yescomplemented
82C2×C22⋊D191D414yes—
83C2×C22⋊D191D414yes—
84D4×D191—232no—
85C22×Dic191—22no—
86C22×Dic191—22no—
87C22×Dic191—41no—
88C22×Dic191C2311yescharacteristic
89C22×Dic191C2311yescharacteristic
90C22×Dic191C2311yescharacteristic
91C22×Dic191C2311yescharacteristic
92C22×Dic191C2311yescharacteristic
93C2×C4×D191—22no—
94C2×C4×D191—22no—
95C2×C4×D191—22no—
96C2×C4×D191—22no—
97C2×C4×D191—22no—
98C2×C4×D191—22no—
99C2×C4×D191—41no—
100C2×C4×D191—41no—
101C2×C4×D191C2×C414yescomplemented
102Dic191⋊C4—22no—
103Dic191⋊C4—22no—
104C22⋊Dic191—22no—
105C22⋊Dic191—22no—
106C22⋊Dic191—41no—
107(C2×D191)⋊C4—22no—
108(C2×D191)⋊C4—22no—
109(C2×D191)⋊C4—22no—
110(C2×D191)⋊C4—22no—
111(C2×D191)⋊C4—22no—
112(C2×D191)⋊C4—22no—
113(C2×D191)⋊C4—22no—
114(C2×D191)⋊C4—41no—
115(C2×D191)⋊C4—41no—
116(C2×D191)⋊C4D414yescomplemented
117C4×Dic191—22no—
118C4×Dic191—22no—
119C24×C191C2311yescharacteristic
120C24×C191C2311yescharacteristic
121C2×D4×C191—22no—
122C2×D4×C191—22no—
123C2×D4×C191C2×C414yescomplemented
124C22×C4×C191—22no—
125C22×C4×C191—22no—
126C22×C4×C191—41no—
127C22×C4×C191C2311yescharacteristic
128C22×C4×C191C2311yescharacteristic
129C22×C4×C191C2311yescharacteristic
130C22×C4×C191C2311yescharacteristic
131C22×C4×C191C2311yescharacteristic
132C22⋊C4×C191—22no—
133C22⋊C4×C191—22no—
134C22⋊C4×C191—41no—
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—28no—
144C22×D191—21no—
145C22×D191—21no—
146C22×D191—21no—
147C22×D191—21no—
148C22×D191—21no—
149C22×D191—21no—
150C22×D191—28no—
151C22×D191—28no—
152C22×D191—28no—
153C22×D191—44no—
154C22×D191—44no—
155C22×D191—44no—
156C22×D191—44no—
157C22×D191—44no—
158C22×D191—44no—
159C22×D191—44no—
160C22×D191—44no—
161C22×D191—44no—
162C22×D191—44no—
163C22×D191C22×C412yes—
164C22×D191C22×C412yes—
165C22×D191C22×C412yes—
166C22×D191C2×D412yes—
167C22×D191C2×D412yes—
168C22×D191C2×D412yes—
169C22×D191#4112yes—
170D764—28no—
171C22⋊D191—28no—
172C22⋊D191C22⋊C4116yescomplemented
173C2×Dic191—21no—
174C2×Dic191—21no—
175C2×Dic191—21no—
176C2×Dic191—21no—
177C2×Dic191—21no—
178C2×Dic191—21no—
179C2×Dic191—21no—
180C2×Dic191—21no—
181C2×Dic191—21no—
182C2×Dic191—21no—
183C2×Dic191—21no—
184C2×Dic191—44no—
185C2×Dic191C22×C412yes—
186C2×Dic191C2×D412yes—
187C2×Dic191C2×D412yes—
188C2×Dic191C2×D412yescomplemented
189C4×D191—28no—
190C4×D191—44no—
191C4×D191—44no—
192C23×C191—21no—
193C23×C191—21no—
194C23×C191—21no—
195C23×C191—21no—
196C23×C191—21no—
197C23×C191—21no—
198C23×C191—21no—
199C23×C191—21no—
200C23×C191—21no—
201C23×C191—21no—
202C23×C191C22×C412yes—
203C23×C191C22×C412yes—
204C23×C191C2×D412yes—
205C23×C191C2×D412yes—
206C23×C191C2411yescharacteristic
207D4×C191—28no—
208C2×C4×C191—21no—
209C2×C4×C191—21no—
210C2×C4×C191—21no—
211C2×C4×C191—21no—
212C2×C4×C191—21no—
213C2×C4×C191—21no—
214C2×C4×C191—21no—
215C2×C4×C191—21no—
216C2×C4×C191—21no—
217C2×C4×C191—21no—
218C2×C4×C191—21no—
219C2×C4×C191—21no—
220C2×C4×C191—21no—
221C2×C4×C191—44no—
222C2×C4×C191C22×C412yes—
223C2×C4×C191C2×D412yescomplemented
224C22×C191—22no—
225C22×C191—22no—
226C22×C191—22no—
227C22×C191—22no—
228C22×C191—22no—
229C22×C191—22no—
230C22×C191—22no—
231C22×C191—22no—
232C22×C191—22no—
233C22×C191—41no—
234C22×C191—41no—
235C22×C191—41no—
236C22×C191—41no—
237C22×C191C2×C22⋊C414yescomplemented
238C22×C191C23×C411yescharacteristic
239C22×C191C22×D411yescharacteristic
240C22×C191C22×D411yescharacteristic
241C22×C191C22×D411yescharacteristic
242C22×C191C2×#4111yescharacteristic
243C22×C191H(5,𝔽2)11yescharacteristic
244C22×C191H(5,𝔽2)11yescharacteristic
245C2×D191—22no—
246C2×D191—22no—
247C2×D191—22no—
248C2×D191—22no—
249C2×D191—22no—
250C2×D191—22no—
251C2×D191—22no—
252C2×D191—22no—
253C2×D191—22no—
254C2×D191—22no—
255C2×D191—22no—
256C2×D191—22no—
257C2×D191—22no—
258C2×D191—22no—
259C2×D191—22no—
260C2×D191—416no—
261C2×D191—416no—
262C2×D191—41no—
263C2×D191—41no—
264C2×D191—41no—
265C2×D191—41no—
266C2×D191C2×C22⋊C414yescomplemented
267C2×D191C4×D414yescomplemented
268C4×C191—22no—
269C4×C191—22no—
270C4×C191—41no—
271C4×C191—41no—
272C4×C191—41no—
273Dic191—22no—
274Dic191—41no—
275Dic191—41no—
276Dic191—41no—
277Dic191C2×C22⋊C414yescomplemented
278C2×C191—24no—
279C2×C191—42no—
280C2×C191C22×C22⋊C411yescharacteristic
281C2×C191C2×C4×D411yescharacteristic
282C2×C191#51811yescharacteristic
283C2×C191D4211yescharacteristic
284C2×C191D4211yescharacteristic
285C2×C191#54611yescharacteristic
286C2×C191#54611yescharacteristic
287D191—24no—
288D191—24no—
289D191—42no—
290C191D4×C22⋊C411yescharacteristic, complemented, Sylow
291D4×C22⋊C4—1911nomaximal, Sylow
292C23×D4—1911no—
293C2×C4×D4—1911no—
294C2×C4×D4—1911no—
295C22×C22⋊C4—1911no—
296C22×C22⋊C4—1911no—
297#390—1911no—
298#390—1911no—
299#386—1911no—
300#386—1911no—
301#386—1911no—
302#386D19111yescharacteristic, complemented
303#380—1911no—
304#379—1911no—
305#379—1911no—
306C4×C22⋊C4—1911no—
307C25—1911no—
308C25—1911no—
309C22×D4—3824no—
310C22×D4—3824no—
311C22×D4—1911no—
312C22×D4—1918no—
313C22×D4—1911no—
314C22×D4—1911no—
315C22×D4C2×D19111yescharacteristic
316C23×C4—1911no—
317C23×C4—1911no—
318C23×C4—1911no—
319C23×C4—1911no—
320C23×C4C2×D19111yescharacteristic, complemented
321C4×D4—3824no—
322C4×D4—3824no—
323C2×C4⋊C4—1911no—
324C2×C4⋊C4—1911no—
325C2×C22⋊C4—3824no—
326C2×C22⋊C4—3824no—
327C2×C22⋊C4—1911no—
328C2×C22⋊C4—1911no—
329C2×C22⋊C4—1911no—
330C2×C22⋊C4—1911no—
331C2×C22⋊C4—1911no—
332C2×C22⋊C4—1911no—
333C2×C22⋊C4—1911no—
334C2×C22⋊C4—1911no—
335C2×C22⋊C4—1911no—
336C2×C22⋊C4—1911no—
337C2×C22⋊C4—1911no—
338C2×C22⋊C4—1911no—
339C2×C22⋊C4—1911no—
340C2×C22⋊C4C2×D19111yescharacteristic, complemented
341C2×C22⋊C4C2×D19111yescharacteristic, complemented
342C2×C22⋊C4C2×D19111yescharacteristic, complemented
343C2×C42—1911no—
344C2×C42—1911no—
345#95—1911no—
346#95—1911no—
347#95C2×D19111yescharacteristic, complemented
348#95C2×D19111yescharacteristic, complemented
349C24—3822no—
350C24—3822no—
351C24—3822no—
352C24—3822no—
353C24—3822no—
354C24—3822no—
355C24—3822no—
356C24—3822no—
357C24—1911no—
358C24—1911no—
359C24—1911no—
360C24—1914no—
361C24—1914no—
362C24—7641no—
363C24—7641no—
364C24—7641no—
365C24—7641no—
366C24C22×D19111yescharacteristic
367C24C22×D19111yescharacteristic
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—3822no—
371C2×D4—3822no—
372C2×D4—38232no—
373C2×D4—3822no—
374C2×D4—3822no—
375C2×D4—1914no—
376C2×D4—1914no—
377C2×D4—1914no—
378C2×D4—1914no—
379C2×D4—1914no—
380C2×D4C4×D19114yescomplemented
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—41no—
384C22×C4—3822no—
385C22×C4—3822no—
386C22×C4—3822no—
387C22×C4—3822no—
388C22×C4—3822no—
389C22×C4—3822no—
390C22×C4—3822no—
391C22×C4—3822no—
392C22×C4—1911no—
393C22×C4—1911no—
394C22×C4—1911no—
395C22×C4—1911no—
396C22×C4—1914no—
397C22×C4—1911no—
398C22×C4—7641no—
399C22×C4—7641no—
400C22×C4—7641no—
401C22×C4C22×D19111yescharacteristic
402C22×C4C22×D19111yescharacteristic
403C22×C4C22×D19111yescharacteristic
404C22×C4C22×D19111yescharacteristic
405C22×C4C22×D19111yescharacteristic
406C4⋊C4—3822no—
407C4⋊C4—3822no—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—41no—
411C22⋊C4—3822no—
412C22⋊C4—3822no—
413C22⋊C4—3822no—
414C22⋊C4—3822no—
415C22⋊C4—3822no—
416C22⋊C4—3822no—
417C22⋊C4—3822no—
418C22⋊C4—3822no—
419C22⋊C4—3822no—
420C22⋊C4—1914no—
421C22⋊C4—7641no—
422C22⋊C4—7641no—
423C22⋊C4—7641no—
424C42—3822no—
425C42—3822no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—3828no—
437C23—3828no—
438C23—3828no—
439C23—3821no—
440C23—3821no—
441C23—3821no—
442C23—3821no—
443C23—3821no—
444C23—3821no—
445C23—3821no—
446C23—3821no—
447C23—3821no—
448C23—3821no—
449C23—3821no—
450C23—3821no—
451C23—3821no—
452C23—3821no—
453C23—3828no—
454C23—1912no—
455C23—1912no—
456C23—1912no—
457C23—1912no—
458C23—1912no—
459C23—1912no—
460C23—1912no—
461C23—7644no—
462C23—7644no—
463C23—7644no—
464C23—7644no—
465C23—7644no—
466C23—7644no—
467C23—7644no—
468C23—7644no—
469C23—7644no—
470C23—7644no—
471C23C2×C4×D19112yes—
472C23C2×C4×D19112yes—
473C23D4×D19112yes—
474C23D4×D19112yes—
475C23C23×D19111yescharacteristic
476D4—28no—
477D4—3828no—
478D4—3828no—
479D4—19116no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—44no—
494C2×C4—3828no—
495C2×C4—3821no—
496C2×C4—3821no—
497C2×C4—3821no—
498C2×C4—3821no—
499C2×C4—3821no—
500C2×C4—3821no—
501C2×C4—3821no—
502C2×C4—3821no—
503C2×C4—3821no—
504C2×C4—3821no—
505C2×C4—3821no—
506C2×C4—1912no—
507C2×C4—1912no—
508C2×C4—1912no—
509C2×C4—1912no—
510C2×C4—7644no—
511C2×C4—7644no—
512C2×C4—7644no—
513C2×C4C2×C4×D19112yes—
514C2×C4D4×D19112yescomplemented
515C22—22no—
516C22—22no—
517C22—22no—
518C22—22no—
519C22—22no—
520C22—22no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—3822no—
529C22—3822no—
530C22—3822no—
531C22—3822no—
532C22—3822no—
533C22—3822no—
534C22—3822no—
535C22—3822no—
536C22—3822no—
537C22—3822no—
538C22—3822no—
539C22—3822no—
540C22—3822no—
541C22—3822no—
542C22—3822no—
543C22—1914no—
544C22—1914no—
545C22—76416no—
546C22—76416no—
547C22—7641no—
548C22—7641no—
549C22—7641no—
550C22—7641no—
551C22C22⋊C4×D19114yescomplemented
552C22C22×C4×D19111yescharacteristic
553C22C2×D4×D19111yescharacteristic
554C22C2×D4×D19111yescharacteristic
555C22C2×D4×D19111yescharacteristic
556C22#41×D19111yescharacteristic
557C22#2025936711yescharacteristic
558C22#2025936811yescharacteristic
559C4—22no—
560C4—22no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—3822no—
565C4—1914no—
566C4—7641no—
567C4—7641no—
568C4—7641no—
569C2—24no—
570C2—42no—
571C2—3824no—
572C2—3824no—
573C2—7642no—
574C2C2×C22⋊C4×D19111yescharacteristic
575C2C4×D4×D19111yescharacteristic
576C2#2713313511yescharacteristic
577C2#2713329511yescharacteristic
578C2#2713329711yescharacteristic
579C2#2713330211yescharacteristic
580C2#2713330511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutatorC22×C191C23×C4
Fitting#386×C191C2
socle, cosocleC23×C191C24
prime radicalC22×D4×D191C2
hypercenter#386D191
hypocenterC191D4×C22⋊C4
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D191C2semidirect
3. C2×(C22⋊D191)⋊C4C2semidirect
4. C22×(C2×D191)⋊C4C2semidirect
5. C2×C22⋊C4×D191C2semidirect
6. #27132563C2semidirect
7. #27132563C2semidirect
8. #27132543C2semidirect
9. #27132541C2semidirect
10. #27132541C2semidirect
11. #27132522C2semidirect
12. #27132518C2semidirect
13. #27132518C2semidirect
14. #27132510C2semidirect
15. #386×C191C2semidirect
23. C2×D4×D191C4semidirect
24. C23×Dic191C22semidirect
26. C22×C4×D191C22semidirect
27. C22×C4×D191C22semidirect
30. C2×Dic191⋊C4C22semidirect
31. C2×Dic191⋊C4C22semidirect
32. C2×C22⋊Dic191C22semidirect
33. C2×C22⋊Dic191C22semidirect
34. C2×C22⋊Dic191C22semidirect
40. C2×(C2×D191)⋊C4C22semidirect
41. C2×(C2×D191)⋊C4C22semidirect
42. C2×(C2×D191)⋊C4C22semidirect
43. C2×(C2×D191)⋊C4C22semidirect
44. C2×(C2×D191)⋊C4C22semidirect
45. C2×(C2×D191)⋊C4C22semidirect
47. C2×C4×Dic191C22semidirect
48. C2×C4×Dic191C22semidirect
49. C191⋊#95C22semidirect
50. C191⋊#95C22semidirect
52. C23×C4×C191C22semidirect
53. C2×C22⋊C4×C191C22semidirect
54. C2×C22⋊C4×C191C22semidirect
55. C2×C22⋊C4×C191C22semidirect
56. #95×C191C22semidirect
57. #95×C191C22semidirect
70. C23×D191C2×C4semidirect
71. C23×D191C2×C4semidirect
77. C2×D764C2×C4semidirect
81. C2×C22⋊D191C2×C4semidirect
101. C2×C4×D191C2×C4semidirect
116. (C2×D191)⋊C4D4semidirect
123. C2×D4×C191C2×C4semidirect
172. C22⋊D191C22⋊C4semidirect
188. C2×Dic191C2×D4semidirect
223. C2×C4×C191C2×D4semidirect
237. C22×C191C2×C22⋊C4semidirect
266. C2×D191C2×C22⋊C4semidirect
267. C2×D191C4×D4semidirect
277. Dic191C2×C22⋊C4semidirect
290. C191D4×C22⋊C4semidirect
302. #386D191semidirect
320. C23×C4C2×D191semidirect
340. C2×C22⋊C4C2×D191semidirect
341. C2×C22⋊C4C2×D191semidirect
342. C2×C22⋊C4C2×D191semidirect
347. #95C2×D191semidirect
348. #95C2×D191semidirect
380. C2×D4C4×D191semidirect
514. C2×C4D4×D191semidirect
551. C22C22⋊C4×D191semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D1912
C2×C4×C22⋊D1912
C2×(C22⋊D191)⋊C42
C22×(C2×D191)⋊C42
C2×C22⋊C4×D1912
#271325632
#271325432
#271325412
#271325222
#271325182
#271325102
#386×C1912
D4×C22⋊C4191