Finite Group Databasebeta

← #28393236

Subgroups — #28393236

Order 14464.

808 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813592C211yesmaximal, characteristic
2C2×C4×D452C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×D113C211yesmaximal, characteristic, complemented
4#20298499C211yesmaximal, characteristic, complemented
5#20298498C211yesmaximal, characteristic, complemented
6#20298491C211yesmaximal, characteristic, complemented
7#20298490C211yesmaximal, characteristic, complemented
8#20298489C211yesmaximal, characteristic, complemented
9#20298476C211yesmaximal, characteristic, complemented
10#20298476C211yesmaximal, characteristic, complemented
11#20298474C211yesmaximal, characteristic, complemented
12#20298469C211yesmaximal, characteristic, complemented
13#20298453C211yesmaximal, characteristic, complemented
14#20298445C211yesmaximal, characteristic, complemented
15#388×C113C211yesmaximal, characteristic, complemented
16C24×D113C2211yescharacteristic
17C22×D452C2211yescharacteristic
18C22×D452C2211yescharacteristic
19C22×C22⋊D113C2211yescharacteristic
20C22×C4×D113C2211yescharacteristic
21C22×C4×D113C2211yescharacteristic
22C22×C4×D113C2211yescharacteristic, complemented
23#16813592C418yescomplemented
24C4×D452—24no—
25C2×C4⋊Dic113C2211yescharacteristic, complemented
26C2×#14268626C2211yescharacteristic, complemented
27C2×C22⋊Dic113C2211yescharacteristic
28C2×C22⋊Dic113C2211yescharacteristic
29C2×#14268624C2211yescharacteristic
30C2×#14268624C2211yescharacteristic
31C2×#14268624C2211yescharacteristic
32C2×#14268624C2211yescharacteristic
33C2×#14268624C2211yescharacteristic
34C2×#14268624C2211yescharacteristic
35C2×#14268624C2211yescharacteristic
36C2×#14268624C2211yescharacteristic
37C2×#14268624C2211yescharacteristic, complemented
38C2×#14268624C2211yescharacteristic, complemented
39C2×#14268624C2211yescharacteristic, complemented
40C22⋊C4×D113—24no—
41C2×C4×Dic113C2211yescharacteristic, complemented
42C2×C4×Dic113C2211yescharacteristic, complemented
43#16813529C2211yescharacteristic, complemented
44#16813529C2211yescharacteristic, complemented
45#16813529C2211yescharacteristic, complemented
46#16813529C2211yescharacteristic, complemented
47C2×C4⋊C4×C113C2211yescharacteristic, complemented
48C2×C22⋊C4×C113C2211yescharacteristic
49C2×C22⋊C4×C113C2211yescharacteristic
50C2×C22⋊C4×C113C2211yescharacteristic
51C2×C42×C113C2211yescharacteristic, complemented
52#95×C113C2211yescharacteristic, complemented
53#95×C113C2211yescharacteristic, complemented
54C23×D113—22no—
55C23×D113—22no—
56C23×D113—41no—
57C23×D113—41no—
58C23×D113—41no—
59C23×D113—41no—
60C23×D113C2×C414yescomplemented
61C23×D113C2311yescharacteristic
62C23×D113C2311yescharacteristic
63C23×D113C2311yescharacteristic
64C2×D452—22no—
65C2×D452—22no—
66C2×D452—41no—
67C2×D452—41no—
68C2×D452C2×C414yes—
69C2×D452C2×C414yescomplemented
70C2×C22⋊D113—41no—
71C2×C22⋊D113—41no—
72C2×C22⋊D113C2×C414yescomplemented
73C22×Dic113C2311yescharacteristic
74C22×Dic113C2311yescharacteristic
75C22×Dic113C2311yescharacteristic
76C22×Dic113C2311yescharacteristic
77C22×Dic113C2311yescharacteristic
78C2×C4×D113—22no—
79C2×C4×D113—22no—
80C2×C4×D113—41no—
81C2×C4×D113—41no—
82C2×C4×D113—41no—
83C2×C4×D113—41no—
84C2×C4×D113—41no—
85C2×C4×D113—41no—
86C2×C4×D113D414yescomplemented
87C4⋊Dic113—22no—
88#14268626—41no—
89C22⋊Dic113—22no—
90C22⋊Dic113—41no—
91#14268624—22no—
92#14268624—22no—
93#14268624—22no—
94#14268624—22no—
95#14268624—22no—
96#14268624—41no—
97#14268624—41no—
98#14268624—41no—
99#14268624—41no—
100#14268624C2×C414yescomplemented
101#14268624C2×C414yescomplemented
102C4×Dic113—41no—
103C4×Dic113—41no—
104C24×C113C2311yescharacteristic
105C22×C4×C113C2311yescharacteristic
106C22×C4×C113C2311yescharacteristic
107C22×C4×C113C2311yescharacteristic
108C22×C4×C113C2311yescharacteristic
109C22×C4×C113C2311yescharacteristic
110C22×C4×C113C2311yescharacteristic
111C4⋊C4×C113—41no—
112C22⋊C4×C113—22no—
113C22⋊C4×C113—41no—
114C22⋊C4×C113C2×C414yescomplemented
115C42×C113—22no—
116C23×C113—21no—
117C23×C113—21no—
118C23×C113—21no—
119C23×C113—21no—
120C23×C113—21no—
121C23×C113—21no—
122C23×C113C22×C412yes—
123C23×C113C2411yescharacteristic
124C22×D113—21no—
125C22×D113—21no—
126C22×D113—21no—
127C22×D113—21no—
128C22×D113—21no—
129C22×D113—21no—
130C22×D113—21no—
131C22×D113—21no—
132C22×D113—21no—
133C22×D113—21no—
134C22×D113—21no—
135C22×D113—21no—
136C22×D113—21no—
137C22×D113—21no—
138C22×D113—21no—
139C22×D113—21no—
140C22×D113—28no—
141C22×D113—44no—
142C22×D113—44no—
143C22×D113—44no—
144C22×D113—44no—
145C22×D113—44no—
146C22×D113—44no—
147C22×D113C22×C412yes—
148C22×D113C22×C412yes—
149C22×D113C22×C412yes—
150C22×D113C2×D412yes—
151C22×D113#4112yes—
152C2×C4×C113—21no—
153C2×C4×C113—21no—
154C2×C4×C113—21no—
155C2×C4×C113—21no—
156C2×C4×C113—21no—
157C2×C4×C113—21no—
158C2×C4×C113—21no—
159C2×C4×C113—21no—
160C2×C4×C113—21no—
161C2×C4×C113—21no—
162C2×C4×C113—21no—
163C2×C4×C113—21no—
164C2×C4×C113—21no—
165C2×C4×C113—21no—
166C2×C4×C113—21no—
167C2×C4×C113C22×C412yes—
168C2×C4×C113C22×C412yes—
169C2×C4×C113C2×D412yes—
170C22⋊D113—44no—
171C2×Dic113—21no—
172C2×Dic113—21no—
173C2×Dic113—21no—
174C2×Dic113—21no—
175C2×Dic113—21no—
176C2×Dic113—21no—
177C2×Dic113—21no—
178C2×Dic113—21no—
179C2×Dic113—21no—
180C2×Dic113—21no—
181C2×Dic113—21no—
182C2×Dic113—21no—
183C2×Dic113—21no—
184C2×Dic113C22×C412yes—
185C2×Dic113C2×D412yes—
186D452—28no—
187D452—44no—
188C4×D113—44no—
189C4×D113—44no—
190C4×D113—44no—
191C22×C113—22no—
192C22×C113—22no—
193C22×C113—22no—
194C22×C113—41no—
195C22×C113—41no—
196C22×C113—41no—
197C22×C113—41no—
198C22×C113C23×C411yescharacteristic
199C22×C113C22×D411yescharacteristic
200C22×C113C2×#4111yescharacteristic
201C22×C113H(5,𝔽2)11yescharacteristic
202C22×C113H(5,𝔽2)11yescharacteristic
203C22×C113H(5,𝔽2)11yescharacteristic
204C22×C113H(5,𝔽2)11yescharacteristic
205C2×D113—22no—
206C2×D113—22no—
207C2×D113—22no—
208C2×D113—22no—
209C2×D113—22no—
210C2×D113—22no—
211C2×D113—22no—
212C2×D113—22no—
213C2×D113—22no—
214C2×D113—22no—
215C2×D113—22no—
216C2×D113—22no—
217C2×D113—416no—
218C2×D113—41no—
219C2×D113—41no—
220C2×D113—41no—
221C2×D113—41no—
222C2×D113—41no—
223C2×D113—41no—
224C2×D113—41no—
225C2×D113—41no—
226C2×D113C4×D414yes—
227C4×C113—22no—
228C4×C113—22no—
229C4×C113—22no—
230C4×C113—41no—
231C4×C113—41no—
232C4×C113—41no—
233Dic113—22no—
234Dic113—22no—
235Dic113—41no—
236Dic113—41no—
237Dic113—41no—
238C2×C113—42no—
239C2×C113C2×C4×D411yescharacteristic
240C2×C113#51811yescharacteristic
241C2×C113#51811yescharacteristic
242C2×C113#53411yescharacteristic
243C2×C113#53511yescharacteristic
244C2×C113#53811yescharacteristic
245C2×C113#53811yescharacteristic
246D113—24no—
247D113—42no—
248D113—42no—
249#2321—1131nomaximal, Sylow
250C113#232111yescharacteristic, complemented, Sylow
251C2×#120—1131no—
252C2×C4×D4—1131no—
253C22×C22⋊C4—1131no—
254#390—1131no—
255#390—1131no—
256#388—1131no—
257#388—1131no—
258#388—1131no—
259#388D11311yescharacteristic, complemented
260#386—1131no—
261#386—1131no—
262#386—1131no—
263#385—1131no—
264#379—1131no—
265C4×C22⋊C4—1131no—
266C25—1131no—
267C22×D4—1131no—
268C22×D4—1131no—
269C22×D4—1131no—
270C23×C4—1131no—
271C23×C4—1131no—
272C23×C4—1131no—
273#120—1138no—
274C4×D4—2264no—
275C2×C4⋊C4—1131no—
276C2×C4⋊C4—1131no—
277C2×C4⋊C4C2×D11311yescharacteristic, complemented
278C2×C22⋊C4—1131no—
279C2×C22⋊C4—1131no—
280C2×C22⋊C4—1131no—
281C2×C22⋊C4—1131no—
282C2×C22⋊C4—1131no—
283C2×C22⋊C4—1131no—
284C2×C22⋊C4—1131no—
285C2×C22⋊C4—1131no—
286C2×C22⋊C4—1131no—
287C2×C22⋊C4—1131no—
288C2×C22⋊C4—1131no—
289C2×C22⋊C4—1131no—
290C2×C22⋊C4—1131no—
291C2×C22⋊C4—2264no—
292C2×C22⋊C4C2×D11311yescharacteristic
293C2×C22⋊C4C2×D11311yescharacteristic
294C2×C22⋊C4C2×D11311yescharacteristic
295C2×C42—1131no—
296C2×C42—1131no—
297C2×C42C2×D11311yescharacteristic, complemented
298#95—1131no—
299#95—1131no—
300#95—1131no—
301#95—1131no—
302#95C2×D11311yescharacteristic, complemented
303#95C2×D11311yescharacteristic, complemented
304C24—1131no—
305C24—1134no—
306C24—1131no—
307C24—1131no—
308C24—4521no—
309C24—4521no—
310C24—4521no—
311C24—4521no—
312C24—2262no—
313C24—2262no—
314C24C22×D11311yescharacteristic
315C2×D4—1134no—
316C2×D4—1134no—
317C2×D4—1134no—
318C2×D4—4521no—
319C2×D4—4521no—
320C2×D4—4521no—
321C2×D4—4521no—
322C2×D4—2262no—
323C2×D4—2262no—
324C22×C4—1131no—
325C22×C4—1131no—
326C22×C4—1134no—
327C22×C4—1131no—
328C22×C4—1131no—
329C22×C4—1131no—
330C22×C4—4521no—
331C22×C4—4521no—
332C22×C4—4521no—
333C22×C4—4521no—
334C22×C4—4521no—
335C22×C4—4521no—
336C22×C4—2262no—
337C22×C4—2262no—
338C22×C4C22×D11311yescharacteristic
339C22×C4C22×D11311yescharacteristic
340C22×C4C22×D11311yescharacteristic
341C22×C4C22×D11311yescharacteristic
342C22×C4C22×D11311yescharacteristic
343C22×C4C22×D11311yescharacteristic
344C4⋊C4—41no—
345C4⋊C4—4521no—
346C4⋊C4—2262no—
347C22⋊C4—22no—
348C22⋊C4—41no—
349C22⋊C4—1134no—
350C22⋊C4—1134no—
351C22⋊C4—4521no—
352C22⋊C4—4521no—
353C22⋊C4—4521no—
354C22⋊C4—4521no—
355C22⋊C4—4521no—
356C22⋊C4—2262no—
357C22⋊C4—2262no—
358C22⋊C4—2262no—
359C22⋊C4—2262no—
360C22⋊C4—2262no—
361C22⋊C4—2262no—
362C22⋊C4C4×D11314yescomplemented
363C42—22no—
364C42—4521no—
365C42—4521no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—1132no—
373C23—1132no—
374C23—1132no—
375C23—1132no—
376C23—1132no—
377C23—4524no—
378C23—4524no—
379C23—4524no—
380C23—4524no—
381C23—4524no—
382C23—4524no—
383C23—2268no—
384C23—2261no—
385C23—2261no—
386C23—2261no—
387C23—2261no—
388C23—2261no—
389C23—2261no—
390C23—2261no—
391C23—2261no—
392C23—2261no—
393C23—2261no—
394C23—2261no—
395C23—2261no—
396C23—2261no—
397C23—2261no—
398C23—2261no—
399C23—2261no—
400C23C2×C4×D11312yes—
401C23C23×D11311yescharacteristic
402D4—4524no—
403D4—4524no—
404D4—2268no—
405C2×C4—21no—
406C2×C4—21no—
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—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—1132no—
421C2×C4—1132no—
422C2×C4—4524no—
423C2×C4—4524no—
424C2×C4—4524no—
425C2×C4—2261no—
426C2×C4—2261no—
427C2×C4—2261no—
428C2×C4—2261no—
429C2×C4—2261no—
430C2×C4—2261no—
431C2×C4—2261no—
432C2×C4—2261no—
433C2×C4—2261no—
434C2×C4—2261no—
435C2×C4—2261no—
436C2×C4—2261no—
437C2×C4—2261no—
438C2×C4C2×C4×D11312yes—
439C2×C4C2×C4×D11312yes—
440C2×C4D4×D11312yes—
441C22—22no—
442C22—22no—
443C22—22no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—1134no—
449C22—45216no—
450C22—4521no—
451C22—4521no—
452C22—4521no—
453C22—4521no—
454C22—4521no—
455C22—4521no—
456C22—4521no—
457C22—4521no—
458C22—2262no—
459C22—2262no—
460C22—2262no—
461C22—2262no—
462C22—2262no—
463C22—2262no—
464C22—2262no—
465C22—2262no—
466C22—2262no—
467C22—2262no—
468C22—2262no—
469C22—2262no—
470C22C22×C4×D11311yescharacteristic
471C22C2×D4×D11311yescharacteristic
472C22#41×D11311yescharacteristic
473C22#1681366711yescharacteristic
474C22#1681366811yescharacteristic
475C22#1681366811yescharacteristic
476C22#1681366811yescharacteristic
477C4—22no—
478C4—22no—
479C4—22no—
480C4—41no—
481C4—41no—
482C4—41no—
483C4—4521no—
484C4—4521no—
485C4—4521no—
486C4—2262no—
487C4—2262no—
488C2—42no—
489C2—4522no—
490C2—4522no—
491C2—2264no—
492C2C4×D4×D11311yescharacteristic
493C2#2029907011yescharacteristic
494C2#2029907211yescharacteristic
495C2#2029915911yescharacteristic
496C2#2029916411yescharacteristic
497C2#2029918211yescharacteristic
498C2#2029918711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
Fitting#388×C113C2
socle, cosocleC23×C113C24
prime radicalC2×#16813592C2
hypercenter#388D113
hypocenterC113#2321
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×C4×D452C2semidirect
3. C2×C22⋊C4×D113C2semidirect
4. #20298499C2semidirect
5. #20298498C2semidirect
6. #20298491C2semidirect
7. #20298490C2semidirect
8. #20298489C2semidirect
9. #20298476C2semidirect
10. #20298476C2semidirect
11. #20298474C2semidirect
12. #20298469C2semidirect
13. #20298453C2semidirect
14. #20298445C2semidirect
15. #388×C113C2semidirect
22. C22×C4×D113C22semidirect
23. #16813592C4semidirect
25. C2×C4⋊Dic113C22semidirect
26. C2×#14268626C22semidirect
37. C2×#14268624C22semidirect
38. C2×#14268624C22semidirect
39. C2×#14268624C22semidirect
41. C2×C4×Dic113C22semidirect
42. C2×C4×Dic113C22semidirect
43. #16813529C22semidirect
44. #16813529C22semidirect
45. #16813529C22semidirect
46. #16813529C22semidirect
47. C2×C4⋊C4×C113C22semidirect
51. C2×C42×C113C22semidirect
52. #95×C113C22semidirect
53. #95×C113C22semidirect
60. C23×D113C2×C4semidirect
69. C2×D452C2×C4semidirect
72. C2×C22⋊D113C2×C4semidirect
86. C2×C4×D113D4semidirect
100. #14268624C2×C4semidirect
101. #14268624C2×C4semidirect
114. C22⋊C4×C113C2×C4semidirect
250. C113#2321semidirect
259. #388D113semidirect
277. C2×C4⋊C4C2×D113semidirect
297. C2×C42C2×D113semidirect
302. #95C2×D113semidirect
303. #95C2×D113semidirect
362. C22⋊C4C4×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168135922
C2×C4×D4522
C2×C22⋊C4×D1132
#202984992
#202984982
#202984912
#202984902
#202984892
#202984762
#202984742
#202984692
#202984532
#202984452
#388×C1132
#2321113