Finite Group Databasebeta

← #16822086

Subgroups — #16822086

Order 3712.

672 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×D29C211yesmaximal, characteristic
2#14271057C211yesmaximal, characteristic, complemented
3#14271056C211yesmaximal, characteristic, complemented
4#14271055C211yesmaximal, characteristic, complemented
5#14271054C211yesmaximal, characteristic, complemented
6#14271053C211yesmaximal, characteristic, complemented
7#14271052C211yesmaximal, characteristic, complemented
8#14271051C211yesmaximal, characteristic, complemented
9#14271022C211yesmaximal, characteristic, complemented
10#14271020C211yesmaximal, characteristic, complemented
11#14271018C211yesmaximal, characteristic
12#14271018C211yesmaximal, characteristic
13C4×#90781C211yesmaximal, characteristic, complemented
14#14271010C211yesmaximal, characteristic, complemented
15C29×#388C211yesmaximal, characteristic, complemented
16C24×D29C2211yescharacteristic
17C22×C4×D29C2211yescharacteristic
18C22×C4×D29C2211yescharacteristic
19C2×C4⋊C4×C29C2211yescharacteristic, complemented
20C2×C22⋊C4×C29C2211yescharacteristic
21C2×C22⋊C4×C29C2211yescharacteristic
22C2×C22⋊C4×C29C2211yescharacteristic
23C2×C42×C29C2211yescharacteristic, complemented
24C2×C22⋊Dic29C2211yescharacteristic
25C2×C22⋊Dic29C2211yescharacteristic
26C2×C22⋊Dic29C2211yescharacteristic
27C2×#90781C2211yescharacteristic
28C2×#90781C2211yescharacteristic
29C2×#90781C2211yescharacteristic
30C2×#90781C2211yescharacteristic
31C2×#90781C2211yescharacteristic
32C2×#90781C2211yescharacteristic
33C2×#90781C2211yescharacteristic
34C2×#90781C2211yescharacteristic
35C2×#90781C2211yescharacteristic
36C2×#90781C2211yescharacteristic
37C2×C4⋊Dic29C2211yescharacteristic, complemented
38C2×#90779C2211yescharacteristic, complemented
39C2×#90779C2211yescharacteristic, complemented
40C2×C4×Dic29C2211yescharacteristic, complemented
41C2×C4×Dic29C2211yescharacteristic, complemented
42C2×C4×Dic29C2211yescharacteristic, complemented
43C22⋊C4×D29C418yescomplemented
44C29×#95C2211yescharacteristic, complemented
45C29×#95C2211yescharacteristic, complemented
46#11745179C2211yescharacteristic, complemented
47#11745179C2211yescharacteristic, complemented
48#11745179C2211yescharacteristic, complemented
49#11745179C2211yescharacteristic, complemented
50#11745179C2211yescharacteristic, complemented
51#11745179C2211yescharacteristic, complemented
52C24×C29C2311yescharacteristic
53C23×D29—22no—
54C23×D29—22no—
55C23×D29—41no—
56C23×D29—41no—
57C23×D29—41no—
58C23×D29—41no—
59C23×D29C2×C414yes—
60C23×D29C2311yescharacteristic
61C23×D29C2311yescharacteristic
62C22×C4×C29C2311yescharacteristic
63C22×C4×C29C2311yescharacteristic
64C22×C4×C29C2311yescharacteristic
65C22×C4×C29C2311yescharacteristic
66C22×C4×C29C2311yescharacteristic
67C22×C4×C29C2311yescharacteristic
68C22×Dic29C2311yescharacteristic
69C22×Dic29C2311yescharacteristic
70C22×Dic29C2311yescharacteristic
71C22×Dic29C2311yescharacteristic
72C22×Dic29C2311yescharacteristic
73C22×Dic29C2311yescharacteristic
74C2×C4×D29—41no—
75C2×C4×D29—41no—
76C2×C4×D29—41no—
77C2×C4×D29—41no—
78C2×C4×D29C2×C414yes—
79C2×C4×D29C2×C414yes—
80C4⋊C4×C29—41no—
81C22⋊C4×C29—41no—
82C22⋊C4×C29—41no—
83C22⋊C4×C29C2×C414yes—
84C42×C29—41no—
85C22⋊Dic29—41no—
86C22⋊Dic29—41no—
87C22⋊Dic29C2×C414yes—
88#90781—22no—
89#90781—22no—
90#90781—22no—
91#90781—22no—
92#90781—41no—
93#90781—41no—
94#90781—41no—
95#90781—41no—
96#90781C2×C414yes—
97#90781C2×C414yes—
98C4⋊Dic29—41no—
99#90779—41no—
100#90779—41no—
101C4×Dic29—41no—
102C4×Dic29—41no—
103C4×Dic29—41no—
104C23×C29—21no—
105C23×C29—21no—
106C23×C29—21no—
107C23×C29—21no—
108C23×C29—21no—
109C23×C29—21no—
110C23×C29C22×C412yes—
111C23×C29C2411yescharacteristic
112C22×D29—21no—
113C22×D29—21no—
114C22×D29—21no—
115C22×D29—21no—
116C22×D29—21no—
117C22×D29—21no—
118C22×D29—21no—
119C22×D29—21no—
120C22×D29—21no—
121C22×D29—21no—
122C22×D29—28no—
123C22×D29—44no—
124C22×D29—44no—
125C22×D29—44no—
126C22×D29—44no—
127C22×D29—44no—
128C22×D29—44no—
129C22×D29C22×C412yes—
130C22×D29C22×C412yes—
131C22×D29#4112yes—
132C22×D29#4112yes—
133C2×C4×C29—21no—
134C2×C4×C29—21no—
135C2×C4×C29—21no—
136C2×C4×C29—21no—
137C2×C4×C29—21no—
138C2×C4×C29—21no—
139C2×C4×C29—21no—
140C2×C4×C29—21no—
141C2×C4×C29—21no—
142C2×C4×C29—21no—
143C2×C4×C29—21no—
144C2×C4×C29—21no—
145C2×C4×C29—21no—
146C2×C4×C29—21no—
147C2×C4×C29—21no—
148C2×C4×C29—21no—
149C2×C4×C29C22×C412yes—
150C2×C4×C29C22×C412yes—
151C2×Dic29—21no—
152C2×Dic29—21no—
153C2×Dic29—21no—
154C2×Dic29—21no—
155C2×Dic29—21no—
156C2×Dic29—21no—
157C2×Dic29—21no—
158C2×Dic29—21no—
159C2×Dic29—21no—
160C2×Dic29—21no—
161C2×Dic29—21no—
162C2×Dic29—21no—
163C2×Dic29—21no—
164C2×Dic29—21no—
165C2×Dic29—21no—
166C2×Dic29—21no—
167C2×Dic29C22×C412yes—
168C2×Dic29C22×C412yes—
169C4×D29—44no—
170C4×D29—44no—
171#2312—291nomaximal, Sylow
172C22×C29—22no—
173C22×C29—22no—
174C22×C29—22no—
175C22×C29—41no—
176C22×C29—41no—
177C22×C29—41no—
178C22×C29—41no—
179C22×C29C23×C411yescharacteristic
180C22×C29C2×#4111yescharacteristic
181C22×C29C2×#4111yescharacteristic
182C22×C29H(5,𝔽2)11yescharacteristic
183C22×C29H(5,𝔽2)11yescharacteristic
184C22×C29H(5,𝔽2)11yescharacteristic
185C22×C29H(5,𝔽2)11yescharacteristic
186C2×D29—22no—
187C2×D29—22no—
188C2×D29—22no—
189C2×D29—22no—
190C2×D29—22no—
191C2×D29—22no—
192C2×D29—22no—
193C2×D29—22no—
194C2×D29—22no—
195C2×D29—416no—
196C2×D29—41no—
197C2×D29—41no—
198C2×D29—41no—
199C2×D29—41no—
200C2×D29#11714yes—
201C4×C29—22no—
202C4×C29—22no—
203C4×C29—41no—
204C4×C29—41no—
205C4×C29—41no—
206C4×C29—41no—
207Dic29—22no—
208Dic29—22no—
209Dic29—41no—
210Dic29—41no—
211Dic29—41no—
212Dic29—41no—
213C22×C22⋊C4—291no—
214#388—291no—
215#388—291no—
216#388—291no—
217#388—291no—
218#388—291no—
219#388—291no—
220#388—291no—
221#388D2911yescharacteristic, complemented
222#380—291no—
223#380—291no—
224#379—291no—
225#379—291no—
226C4×C22⋊C4—291no—
227C4×C22⋊C4—291no—
228C2×C29—42no—
229C2×C29C2×#11711yescharacteristic
230C2×C29#51811yescharacteristic
231C2×C29#51811yescharacteristic
232C2×C29#53811yescharacteristic
233C2×C29#53811yescharacteristic
234C2×C29#53811yescharacteristic
235C2×C29#53811yescharacteristic
236D29—24no—
237D29—42no—
238C25—291no—
239C23×C4—291no—
240C23×C4—291no—
241C2×C4⋊C4—291no—
242C2×C4⋊C4—291no—
243C2×C4⋊C4—291no—
244C2×C4⋊C4C2×D2911yescharacteristic, complemented
245C2×C22⋊C4—291no—
246C2×C22⋊C4—291no—
247C2×C22⋊C4—291no—
248C2×C22⋊C4—298no—
249C2×C22⋊C4—291no—
250C2×C22⋊C4—291no—
251C2×C22⋊C4—291no—
252C2×C22⋊C4—291no—
253C2×C22⋊C4—291no—
254C2×C22⋊C4—291no—
255C2×C22⋊C4—291no—
256C2×C22⋊C4—291no—
257C2×C22⋊C4—291no—
258C2×C22⋊C4—291no—
259C2×C22⋊C4C2×D2911yescharacteristic
260C2×C22⋊C4C2×D2911yescharacteristic
261C2×C22⋊C4C2×D2911yescharacteristic
262C2×C42—291no—
263C2×C42—291no—
264C2×C42—291no—
265C2×C42C2×D2911yescharacteristic, complemented
266#95—291no—
267#95—291no—
268#95—291no—
269#95—291no—
270#95—291no—
271#95—291no—
272#95C2×D2911yescharacteristic, complemented
273#95C2×D2911yescharacteristic, complemented
274C29#231211yescharacteristic, complemented, Sylow
275C24—291no—
276C24—291no—
277C24—294no—
278C24—582no—
279C24—582no—
280C24—1161no—
281C24—1161no—
282C24—1161no—
283C24—1161no—
284C24C22×D2911yescharacteristic
285C22×C4—291no—
286C22×C4—291no—
287C22×C4—294no—
288C22×C4—294no—
289C22×C4—291no—
290C22×C4—291no—
291C22×C4—291no—
292C22×C4—291no—
293C22×C4—1161no—
294C22×C4—1161no—
295C22×C4—1161no—
296C22×C4—1161no—
297C22×C4C22×D2911yescharacteristic
298C22×C4C22×D2911yescharacteristic
299C22×C4C22×D2911yescharacteristic
300C22×C4C22×D2911yescharacteristic
301C22×C4C22×D2911yescharacteristic
302C22×C4C22×D2911yescharacteristic
303C4⋊C4—41no—
304C4⋊C4—1161no—
305C4⋊C4—1161no—
306C4⋊C4—1161no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—294no—
310C22⋊C4—294no—
311C22⋊C4—294no—
312C22⋊C4—582no—
313C22⋊C4—582no—
314C22⋊C4—582no—
315C22⋊C4—582no—
316C22⋊C4—1161no—
317C22⋊C4—1161no—
318C22⋊C4—1161no—
319C22⋊C4—1161no—
320C22⋊C4—1161no—
321C22⋊C4—1161no—
322C22⋊C4C4×D2914yes—
323C42—41no—
324C42—1161no—
325C42—1161no—
326C42—1161no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—292no—
334C23—292no—
335C23—292no—
336C23—292no—
337C23—588no—
338C23—581no—
339C23—581no—
340C23—581no—
341C23—581no—
342C23—581no—
343C23—581no—
344C23—581no—
345C23—581no—
346C23—581no—
347C23—581no—
348C23—1164no—
349C23—1164no—
350C23—1164no—
351C23—1164no—
352C23—1164no—
353C23—1164no—
354C23C2×C4×D2912yes—
355C23C23×D2911yescharacteristic
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—292no—
373C2×C4—292no—
374C2×C4—581no—
375C2×C4—581no—
376C2×C4—581no—
377C2×C4—581no—
378C2×C4—581no—
379C2×C4—581no—
380C2×C4—581no—
381C2×C4—581no—
382C2×C4—581no—
383C2×C4—581no—
384C2×C4—581no—
385C2×C4—581no—
386C2×C4—581no—
387C2×C4—581no—
388C2×C4—581no—
389C2×C4—581no—
390C2×C4—1164no—
391C2×C4—1164no—
392C2×C4C2×C4×D2912yes—
393C2×C4C2×C4×D2912yes—
394C22—22no—
395C22—22no—
396C22—22no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—294no—
402C22—582no—
403C22—582no—
404C22—582no—
405C22—582no—
406C22—582no—
407C22—582no—
408C22—582no—
409C22—582no—
410C22—582no—
411C22—11616no—
412C22—1161no—
413C22—1161no—
414C22—1161no—
415C22—1161no—
416C22C22×C4×D2911yescharacteristic
417C22#1174535911yescharacteristic
418C22#1174535911yescharacteristic
419C22#41×D2911yescharacteristic
420C22#41×D2911yescharacteristic
421C22#1174536411yescharacteristic
422C22#1174536411yescharacteristic
423C4—22no—
424C4—22no—
425C4—41no—
426C4—41no—
427C4—41no—
428C4—41no—
429C4—582no—
430C4—582no—
431C4—1161no—
432C4—1161no—
433C4—1161no—
434C4—1161no—
435C2—42no—
436C2—584no—
437C2—1162no—
438C2#117×D2911yescharacteristic
439C2#1427163511yescharacteristic
440C2#1427163511yescharacteristic
441C2#1427174511yescharacteristic
442C2#1427174711yescharacteristic
443C2#1427174911yescharacteristic
444C2#1427175211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D29
commutatorC22×C29C23×C4
FittingC29×#388C2
socle, cosocleC23×C29C24
prime radicalC24×D29C22
hypercenter#388D29
hypocenterC29#2312
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #14271057C2semidirect
3. #14271056C2semidirect
4. #14271055C2semidirect
5. #14271054C2semidirect
6. #14271053C2semidirect
7. #14271052C2semidirect
8. #14271051C2semidirect
9. #14271022C2semidirect
10. #14271020C2semidirect
13. C4×#90781C2semidirect
14. #14271010C2semidirect
15. C29×#388C2semidirect
19. C2×C4⋊C4×C29C22semidirect
23. C2×C42×C29C22semidirect
37. C2×C4⋊Dic29C22semidirect
38. C2×#90779C22semidirect
39. C2×#90779C22semidirect
40. C2×C4×Dic29C22semidirect
41. C2×C4×Dic29C22semidirect
42. C2×C4×Dic29C22semidirect
43. C22⋊C4×D29C4semidirect
44. C29×#95C22semidirect
45. C29×#95C22semidirect
46. #11745179C22semidirect
47. #11745179C22semidirect
48. #11745179C22semidirect
49. #11745179C22semidirect
50. #11745179C22semidirect
51. #11745179C22semidirect
221. #388D29semidirect
244. C2×C4⋊C4C2×D29semidirect
265. C2×C42C2×D29semidirect
272. #95C2×D29semidirect
273. #95C2×D29semidirect
274. C29#2312semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×D292
#142710572
#142710562
#142710552
#142710542
#142710532
#142710522
#142710512
#142710222
#142710202
#142710182
C4×#907812
#142710102
C29×#3882
#231229