Finite Group Databasebeta

← #28393896

Subgroups — #28393896

Order 14464.

1116 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D113C211yesmaximal, characteristic
2C2×#16813607C211yesmaximal, characteristic, complemented
3C2×#16813604C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D113C211yesmaximal, characteristic, complemented
5#20298514C211yesmaximal, characteristic, complemented
6#20298513C211yesmaximal, characteristic, complemented
7#20298512C211yesmaximal, characteristic, complemented
8#20298476C211yesmaximal, characteristic, complemented
9#20298474C211yesmaximal, characteristic, complemented
10#20298472C211yesmaximal, characteristic, complemented
11#20298469C211yesmaximal, characteristic, complemented
12#20298453C211yesmaximal, characteristic, complemented
13#20298453C211yesmaximal, characteristic, complemented
14#20298453C211yesmaximal, characteristic, complemented
15#394×C113C211yesmaximal, characteristic, complemented
16C24×D113C2211yescharacteristic
17C24×D113C2211yescharacteristic
18C22×D452C2211yescharacteristic
19C22×C22⋊D113C2211yescharacteristic
20C22×C22⋊D113C2211yescharacteristic
21C2×D4×D113—24no—
22C2×D4×D113—24no—
23C2×D4×D113—24no—
24C22×C4×D113C2211yescharacteristic
25C22×C4×D113C2211yescharacteristic, complemented
26C22×C4×D113C2211yescharacteristic, complemented
27#16813607—24no—
28#16813604—24no—
29C2×C4⋊Dic113C2211yescharacteristic, complemented
30C2×#14268626C2211yescharacteristic, complemented
31C2×#14268626C2211yescharacteristic, complemented
32C2×C22⋊Dic113C2211yescharacteristic, complemented
33C2×C22⋊Dic113C2211yescharacteristic, complemented
34C2×C22⋊Dic113C2211yescharacteristic, complemented
35C2×C22⋊Dic113C2211yescharacteristic, complemented
36C2×#14268624C2211yescharacteristic
37C2×#14268624C2211yescharacteristic
38C2×#14268624C2211yescharacteristic
39C2×#14268624C2211yescharacteristic
40C2×#14268624C2211yescharacteristic, complemented
41C2×#14268624C2211yescharacteristic, complemented
42C2×#14268624C2211yescharacteristic, complemented
43C2×#14268624C2211yescharacteristic, complemented
44C2×#14268624C2211yescharacteristic, complemented
45C2×#14268624C2211yescharacteristic, complemented
46C22⋊C4×D113—24no—
47#16813529C2211yescharacteristic, complemented
48#16813529C2211yescharacteristic, complemented
49#16813529C2211yescharacteristic, complemented
50C22×D4×C113C2211yescharacteristic
51C2×C4⋊C4×C113C2211yescharacteristic, complemented
52C2×C22⋊C4×C113C2211yescharacteristic, complemented
53C2×C22⋊C4×C113C2211yescharacteristic, complemented
54C2×C22⋊C4×C113C2211yescharacteristic, complemented
55C2×C22⋊C4×C113C2211yescharacteristic, complemented
56#95×C113C2211yescharacteristic, complemented
57C23×D113—22no—
58C23×D113—22no—
59C23×D113—22no—
60C23×D113—22no—
61C23×D113—22no—
62C23×D113—22no—
63C23×D113—22no—
64C23×D113—22no—
65C23×D113—22no—
66C23×D113—41no—
67C23×D113—41no—
68C23×D113—41no—
69C23×D113—41no—
70C23×D113D414yes—
71C23×D113C2311yescharacteristic
72C23×D113C2311yescharacteristic
73C23×D113C2311yescharacteristic
74C2×D452—22no—
75C2×D452—22no—
76C2×D452D414yes—
77C2×C22⋊D113—22no—
78C2×C22⋊D113—22no—
79C2×C22⋊D113—22no—
80C2×C22⋊D113—22no—
81C2×C22⋊D113—22no—
82C2×C22⋊D113D414yes—
83D4×D113—232no—
84C22×Dic113C2311yescharacteristic
85C22×Dic113C2311yescharacteristic
86C22×Dic113C2311yescharacteristic
87C22×Dic113C2311yescharacteristic
88C22×Dic113C2311yescharacteristic
89C2×C4×D113—22no—
90C2×C4×D113—22no—
91C2×C4×D113—22no—
92C2×C4×D113—22no—
93C2×C4×D113—22no—
94C2×C4×D113—22no—
95C2×C4×D113—22no—
96C2×C4×D113—41no—
97C2×C4×D113—41no—
98C4⋊Dic113—22no—
99#14268626—22no—
100#14268626—22no—
101C22⋊Dic113—22no—
102C22⋊Dic113—22no—
103C22⋊Dic113—41no—
104C22⋊Dic113—41no—
105#14268624—22no—
106#14268624—22no—
107#14268624—22no—
108#14268624—22no—
109#14268624—22no—
110#14268624—22no—
111#14268624—22no—
112#14268624—22no—
113#14268624—41no—
114#14268624—41no—
115C24×C113C2311yescharacteristic
116C24×C113C2311yescharacteristic
117C2×D4×C113—22no—
118C2×D4×C113—22no—
119C2×D4×C113—22no—
120C22×C4×C113C2311yescharacteristic
121C22×C4×C113C2311yescharacteristic
122C22×C4×C113C2311yescharacteristic
123C22×C4×C113C2311yescharacteristic
124C22×C4×C113C2311yescharacteristic
125C4⋊C4×C113—22no—
126C22⋊C4×C113—22no—
127C22⋊C4×C113—22no—
128C22⋊C4×C113—41no—
129C22⋊C4×C113—41no—
130C23×C113—21no—
131C23×C113—21no—
132C23×C113—21no—
133C23×C113—21no—
134C23×C113—21no—
135C23×C113—21no—
136C23×C113—21no—
137C23×C113—21no—
138C23×C113—21no—
139C23×C113—21no—
140C23×C113—21no—
141C23×C113—21no—
142C23×C113C2×D412yes—
143C23×C113C2×D412yes—
144C23×C113C2411yescharacteristic
145C22×D113—21no—
146C22×D113—21no—
147C22×D113—21no—
148C22×D113—21no—
149C22×D113—21no—
150C22×D113—21no—
151C22×D113—21no—
152C22×D113—21no—
153C22×D113—28no—
154C22×D113—21no—
155C22×D113—21no—
156C22×D113—21no—
157C22×D113—21no—
158C22×D113—21no—
159C22×D113—21no—
160C22×D113—28no—
161C22×D113—28no—
162C22×D113—44no—
163C22×D113—44no—
164C22×D113—44no—
165C22×D113—44no—
166C22×D113—44no—
167C22×D113—44no—
168C22×D113—44no—
169C22×D113—44no—
170C22×D113—44no—
171C22×D113—44no—
172C22×D113—44no—
173C22×D113C2×D412yes—
174C22×D113C2×D412yes—
175C22×D113C2×D412yes—
176C22×D113C2×D412yes—
177C22×D113C2×D412yes—
178C22×D113#4112yes—
179C22×D113#4112yes—
180D4×C113—28no—
181C2×C4×C113—21no—
182C2×C4×C113—21no—
183C2×C4×C113—21no—
184C2×C4×C113—21no—
185C2×C4×C113—21no—
186C2×C4×C113—21no—
187C2×C4×C113—21no—
188C2×C4×C113—21no—
189C2×C4×C113—21no—
190C2×C4×C113—21no—
191C2×C4×C113—21no—
192C2×C4×C113—21no—
193C2×C4×C113—21no—
194C2×C4×C113—21no—
195C2×C4×C113C2×D412yes—
196C22⋊D113—28no—
197C22⋊D113—28no—
198C2×Dic113—21no—
199C2×Dic113—21no—
200C2×Dic113—21no—
201C2×Dic113—21no—
202C2×Dic113—21no—
203C2×Dic113—21no—
204C2×Dic113—21no—
205C2×Dic113—21no—
206C2×Dic113—21no—
207C2×Dic113—21no—
208C2×Dic113—21no—
209C2×Dic113—21no—
210C2×Dic113—21no—
211C2×Dic113—21no—
212C2×Dic113C2×D412yes—
213D452—28no—
214C4×D113—28no—
215C4×D113—44no—
216C4×D113—44no—
217C22×C113—22no—
218C22×C113—22no—
219C22×C113—22no—
220C22×C113—22no—
221C22×C113—22no—
222C22×C113—22no—
223C22×C113—41no—
224C22×C113—41no—
225C22×C113—41no—
226C22×C113—41no—
227C22×C113—41no—
228C22×C113—41no—
229C22×C113—41no—
230C22×C113—41no—
231C22×C113C22×D411yescharacteristic
232C22×C113C22×D411yescharacteristic
233C22×C113C22×D411yescharacteristic
234C22×C113C2×#4111yescharacteristic
235C22×C113C2×#4111yescharacteristic
236C22×C113H(5,𝔽2)11yescharacteristic
237C22×C113H(5,𝔽2)11yescharacteristic
238C2×D113—22no—
239C2×D113—22no—
240C2×D113—22no—
241C2×D113—22no—
242C2×D113—22no—
243C2×D113—22no—
244C2×D113—22no—
245C2×D113—22no—
246C2×D113—22no—
247C2×D113—22no—
248C2×D113—22no—
249C2×D113—22no—
250C2×D113—22no—
251C2×D113—22no—
252C2×D113—22no—
253C2×D113—416no—
254C2×D113—416no—
255C2×D113—41no—
256C2×D113—41no—
257C2×D113—41no—
258C2×D113—41no—
259C2×D113#12014yes—
260C2×D113#12314yescomplemented
261C4×C113—22no—
262C4×C113—41no—
263C4×C113—41no—
264C4×C113—41no—
265C4×C113—41no—
266Dic113—22no—
267Dic113—41no—
268Dic113—41no—
269Dic113—41no—
270Dic113—41no—
271C2×C113—42no—
272C2×C113—42no—
273C2×C113C2×#12011yescharacteristic
274C2×C113C2×#12311yescharacteristic
275C2×C113#53411yescharacteristic
276C2×C113#54611yescharacteristic
277C2×C113#54611yescharacteristic
278C2×C113#54611yescharacteristic
279C2×C113#54611yescharacteristic
280D113—24no—
281D113—24no—
282D113—42no—
283#2405—1131nomaximal, Sylow
284C113#240511yescharacteristic, complemented, Sylow
285C23×D4—1131no—
286C2×#123—1131no—
287C2×#123—1131no—
288C22×C22⋊C4—1131no—
289#394—1131no—
290#394—1131no—
291#394—1131no—
292#394D11311yescharacteristic, complemented
293#386—1131no—
294#386—1131no—
295#385—1131no—
296#385—1131no—
297#379—1131no—
298#379—1131no—
299#379—1131no—
300C25—1131no—
301C25—1131no—
302C22×D4—1131no—
303C22×D4—1131no—
304C22×D4—1131no—
305C22×D4—2264no—
306C22×D4—2264no—
307C22×D4—2264no—
308C22×D4C2×D11311yescharacteristic
309C23×C4—1131no—
310C23×C4—1131no—
311C23×C4—1131no—
312#123—2264no—
313#123—2264no—
314C2×C4⋊C4—1131no—
315C2×C4⋊C4—1131no—
316C2×C4⋊C4—1131no—
317C2×C4⋊C4C2×D11311yescharacteristic, complemented
318C2×C22⋊C4—1131no—
319C2×C22⋊C4—1131no—
320C2×C22⋊C4—1131no—
321C2×C22⋊C4—1131no—
322C2×C22⋊C4—1131no—
323C2×C22⋊C4—1131no—
324C2×C22⋊C4—1131no—
325C2×C22⋊C4—1131no—
326C2×C22⋊C4—1131no—
327C2×C22⋊C4—1131no—
328C2×C22⋊C4—1131no—
329C2×C22⋊C4—1131no—
330C2×C22⋊C4—1131no—
331C2×C22⋊C4—1131no—
332C2×C22⋊C4—2264no—
333C2×C22⋊C4C2×D11311yescharacteristic, complemented
334C2×C22⋊C4C2×D11311yescharacteristic, complemented
335C2×C22⋊C4C2×D11311yescharacteristic, complemented
336C2×C22⋊C4C2×D11311yescharacteristic, complemented
337#95—1131no—
338#95—1131no—
339#95—1131no—
340#95C2×D11311yescharacteristic, complemented
341C24—1131no—
342C24—1131no—
343C24—1134no—
344C24—1131no—
345C24—4521no—
346C24—4521no—
347C24—4521no—
348C24—4521no—
349C24—2262no—
350C24—2262no—
351C24—2262no—
352C24—2262no—
353C24—2262no—
354C24—2262no—
355C24—2262no—
356C24—2262no—
357C24—2262no—
358C24C22×D11311yescharacteristic
359C24C22×D11311yescharacteristic
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—1134no—
364C2×D4—1134no—
365C2×D4—2262no—
366C2×D4—2262no—
367C2×D4—2262no—
368C2×D4—22632no—
369C2×D4—2262no—
370C2×D4—2262no—
371C2×D4—2262no—
372C2×D4—2262no—
373C22×C4—1131no—
374C22×C4—1131no—
375C22×C4—1131no—
376C22×C4—1131no—
377C22×C4—1131no—
378C22×C4—4521no—
379C22×C4—4521no—
380C22×C4—2262no—
381C22×C4—2262no—
382C22×C4—2262no—
383C22×C4—2262no—
384C22×C4—2262no—
385C22×C4—2262no—
386C22×C4—2262no—
387C22×C4C22×D11311yescharacteristic
388C22×C4C22×D11311yescharacteristic
389C22×C4C22×D11311yescharacteristic
390C22×C4C22×D11311yescharacteristic
391C22×C4C22×D11311yescharacteristic
392C4⋊C4—22no—
393C4⋊C4—2262no—
394C4⋊C4—2262no—
395C4⋊C4—2262no—
396C22⋊C4—22no—
397C22⋊C4—22no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—4521no—
401C22⋊C4—4521no—
402C22⋊C4—4521no—
403C22⋊C4—4521no—
404C22⋊C4—2262no—
405C22⋊C4—2262no—
406C22⋊C4—2262no—
407C22⋊C4—2262no—
408C22⋊C4—2262no—
409C22⋊C4—2262no—
410C22⋊C4—2262no—
411C22⋊C4—2262no—
412C22⋊C4—2262no—
413C22⋊C4—2262no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—1132no—
427C23—1132no—
428C23—1132no—
429C23—1132no—
430C23—1132no—
431C23—1132no—
432C23—1132no—
433C23—4524no—
434C23—4524no—
435C23—4524no—
436C23—4524no—
437C23—4524no—
438C23—4524no—
439C23—4524no—
440C23—4524no—
441C23—4524no—
442C23—4524no—
443C23—4524no—
444C23—2268no—
445C23—2268no—
446C23—2268no—
447C23—2261no—
448C23—2261no—
449C23—2261no—
450C23—2261no—
451C23—2261no—
452C23—2261no—
453C23—2261no—
454C23—2261no—
455C23—2261no—
456C23—2261no—
457C23—2261no—
458C23—2261no—
459C23—2261no—
460C23—2261no—
461C23D4×D11312yes—
462C23D4×D11312yes—
463C23C23×D11311yescharacteristic
464D4—28no—
465D4—2268no—
466D4—2268no—
467D4—2268no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—1132no—
483C2×C4—4524no—
484C2×C4—4524no—
485C2×C4—2268no—
486C2×C4—2261no—
487C2×C4—2261no—
488C2×C4—2261no—
489C2×C4—2261no—
490C2×C4—2261no—
491C2×C4—2261no—
492C2×C4—2261no—
493C2×C4—2261no—
494C2×C4—2261no—
495C2×C4—2261no—
496C2×C4—2261no—
497C2×C4—2261no—
498C2×C4—2261no—
499C2×C4—2261no—
500C2×C4D4×D11312yes—
501C22—22no—
502C22—22no—
503C22—22no—
504C22—22no—
505C22—22no—
506C22—22no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—41no—
513C22—41no—
514C22—41no—
515C22—1134no—
516C22—1134no—
517C22—45216no—
518C22—45216no—
519C22—4521no—
520C22—4521no—
521C22—4521no—
522C22—4521no—
523C22—2262no—
524C22—2262no—
525C22—2262no—
526C22—2262no—
527C22—2262no—
528C22—2262no—
529C22—2262no—
530C22—2262no—
531C22—2262no—
532C22—2262no—
533C22—2262no—
534C22—2262no—
535C22—2262no—
536C22—2262no—
537C22—2262no—
538C22C2×D4×D11311yescharacteristic
539C22C2×D4×D11311yescharacteristic
540C22C2×D4×D11311yescharacteristic
541C22#41×D11311yescharacteristic
542C22#41×D11311yescharacteristic
543C22#1681366711yescharacteristic
544C22#1681366811yescharacteristic
545C4—22no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—4521no—
551C4—4521no—
552C4—4521no—
553C4—4521no—
554C4—2262no—
555C2—42no—
556C2—42no—
557C2—4522no—
558C2—2264no—
559C2—2264no—
560C2#120×D11311yescharacteristic
561C2#123×D11311yescharacteristic
562C2#2029915611yescharacteristic
563C2#2029923711yescharacteristic
564C2#2029924011yescharacteristic
565C2#2029924111yescharacteristic
566C2#2029924511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutator, socle, cosocleC23×C113C24
Fitting#394×C113C2
prime radicalC22×D4×D113C2
hypercenter#394D113
hypocenterC113#2405
LCSG ▷ C23×C113 ▷ C113
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#16813607C2semidirect
3. C2×#16813604C2semidirect
4. C2×C22⋊C4×D113C2semidirect
5. #20298514C2semidirect
6. #20298513C2semidirect
7. #20298512C2semidirect
8. #20298476C2semidirect
9. #20298474C2semidirect
10. #20298472C2semidirect
11. #20298469C2semidirect
12. #20298453C2semidirect
13. #20298453C2semidirect
14. #20298453C2semidirect
15. #394×C113C2semidirect
25. C22×C4×D113C22semidirect
26. C22×C4×D113C22semidirect
29. C2×C4⋊Dic113C22semidirect
30. C2×#14268626C22semidirect
31. C2×#14268626C22semidirect
32. C2×C22⋊Dic113C22semidirect
33. C2×C22⋊Dic113C22semidirect
34. C2×C22⋊Dic113C22semidirect
35. C2×C22⋊Dic113C22semidirect
40. C2×#14268624C22semidirect
41. C2×#14268624C22semidirect
42. C2×#14268624C22semidirect
43. C2×#14268624C22semidirect
44. C2×#14268624C22semidirect
45. C2×#14268624C22semidirect
47. #16813529C22semidirect
48. #16813529C22semidirect
49. #16813529C22semidirect
51. C2×C4⋊C4×C113C22semidirect
52. C2×C22⋊C4×C113C22semidirect
53. C2×C22⋊C4×C113C22semidirect
54. C2×C22⋊C4×C113C22semidirect
55. C2×C22⋊C4×C113C22semidirect
56. #95×C113C22semidirect
260. C2×D113#123semidirect
284. C113#2405semidirect
292. #394D113semidirect
317. C2×C4⋊C4C2×D113semidirect
333. C2×C22⋊C4C2×D113semidirect
334. C2×C22⋊C4C2×D113semidirect
335. C2×C22⋊C4C2×D113semidirect
336. C2×C22⋊C4C2×D113semidirect
340. #95C2×D113semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D1132
C2×#168136072
C2×#168136042
C2×C22⋊C4×D1132
#202985142
#202985132
#202985122
#202984762
#202984742
#202984722
#202984692
#202984532
#394×C1132
#2405113