Finite Group Databasebeta

← #16828945

Subgroups — #16828945

Order 3712.

496 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745266C211yesmaximal, characteristic, complemented
2C2×#11745312C211yesmaximal, characteristic, complemented
3#14271709C211yesmaximal, characteristic, complemented
4#14271631C211yesmaximal, characteristic, complemented
5#14271388C211yesmaximal, characteristic, complemented
6#14271384C211yesmaximal, characteristic, complemented
7#14271381C211yesmaximal, characteristic, complemented
8#14271377C211yesmaximal, characteristic, complemented
9#14271372C211yesmaximal, characteristic, complemented
10#14271367C211yesmaximal, characteristic, complemented
11#14271362C211yesmaximal, characteristic, complemented
12#14271357C211yesmaximal, characteristic, complemented
13C2×#11745162C211yesmaximal, characteristic, complemented
14#14271157C211yesmaximal, characteristic, complemented
15C29×#416C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C2×#90805C2211yescharacteristic
18C2×#90805C2211yescharacteristic
19C22×C8×C29C2211yescharacteristic
20C29×#117C2211yescharacteristic
21#11745312—24no—
22#11745309C2211yescharacteristic
23#11745306C2211yescharacteristic
24C2×#90785C2211yescharacteristic
25C2×#90784C2211yescharacteristic
26#11745302C2211yescharacteristic
27#11745301—21no—
28#11745301—21no—
29#11745298C2211yescharacteristic
30C2×#90783C2211yescharacteristic
31C2×#90782C2211yescharacteristic
32C4×C22⋊D29—21no—
33C4×C22⋊D29—21no—
34C2×C4×Dic29C2211yescharacteristic
35C22×#6597C2211yescharacteristic
36C2×Dic116C2211yescharacteristic
37#11745266—24no—
38C2×D232C2211yescharacteristic
39C2×#90773C2211yescharacteristic
40C2×#90773C2211yescharacteristic
41#11745255C2211yescharacteristic
42#11745255C2211yescharacteristic
43#11745249C2211yescharacteristic
44#11745249C2211yescharacteristic
45#11745243—21no—
46#11745243—21no—
47#11745234—21no—
48C42×D29—21no—
49C29×#103C2211yescharacteristic
50C29×#103C2211yescharacteristic
51C29×#102C2211yescharacteristic
52C29×#102C2211yescharacteristic
53#11745162C2211yescharacteristic
54#11745162C2211yescharacteristic
55#11745162C2211yescharacteristic
56#11745162C2211yescharacteristic
57#11745158C2211yescharacteristic
58#11745158C2211yescharacteristic
59#11745157C2211yescharacteristic
60#11745157C2211yescharacteristic
61#41×C29—22no—
62#41×C29—22no—
63C2×Q8×C29C2311yescharacteristic
64C2×D4×C29—21no—
65C2×D4×C29C2311yescharacteristic
66C22×C4×C29—21no—
67C22×C4×C29C2311yescharacteristic
68C2×C22⋊D29—21no—
69C2×C22⋊D29—21no—
70C2×C22⋊D29—21no—
71C2×C22⋊D29—21no—
72C22×Dic29D411yescharacteristic
73C22×Dic29D411yescharacteristic
74#90805—22no—
75#90805—22no—
76#90805—22no—
77#90805D414yescomplemented
78C2×D116C2311yescharacteristic
79C2×D116C2311yescharacteristic
80C2×C4×D29—21no—
81C2×C4×D29—21no—
82C2×C4×D29—21no—
83C2×C4×D29—21no—
84C2×Dic58C2311yescharacteristic
85C2×Dic58C2311yescharacteristic
86C2×C8×C29—22no—
87C2×C8×C29C2311yescharacteristic
88C2×C8×C29C2311yescharacteristic
89C4⋊C4×C29C2311yescharacteristic
90C4⋊C4×C29C2311yescharacteristic
91C22⋊C4×C29—21no—
92C42×C29—21no—
93C22⋊Dic29—21no—
94C22⋊Dic29—21no—
95#90785—22no—
96#90784—22no—
97#90783—22no—
98#90782—22no—
99#90781—21no—
100#90781—21no—
101#90781—21no—
102#90781—21no—
103#90779—21no—
104#90779—21no—
105#90779—21no—
106#90779—21no—
107C4×Dic29—21no—
108C4×Dic29—21no—
109C4×Dic29D411yescharacteristic
110C4×Dic29D411yescharacteristic
111C4×Dic29C2311yescharacteristic
112C4×Dic29C2311yescharacteristic
113C2×#6597—22no—
114C2×#6597C2311yescharacteristic
115C2×#6597C2311yescharacteristic
116Dic116—22no—
117D232—22no—
118#90773—22no—
119#90773—22no—
120C23×C29—21no—
121C23×C29C2×D411yescharacteristic
122C22×D29—21no—
123C22×D29—21no—
124Q8×C29—21no—
125Q8×C29—21no—
126D4×C29—21no—
127D4×C29—21no—
128D4×C29—42no—
129C2×C4×C29—21no—
130C2×C4×C29—21no—
131C2×C4×C29—21no—
132C2×C4×C29—42no—
133C2×C4×C29C2×D412yes—
134C2×C4×C29C2×D411yescharacteristic
135C2×C4×C29#4112yes—
136C2×C4×C29C2411yescharacteristic
137C22⋊D29—24no—
138C22⋊D29—42no—
139C22⋊D29—42no—
140C22⋊D29—42no—
141C2×Dic29—21no—
142C2×Dic29—22no—
143C2×Dic29—21no—
144C2×Dic29—41no—
145C2×Dic29C2×D411yescharacteristic
146C2×Dic29C2×D411yescharacteristic
147C2×Dic29C2×D411yescharacteristic
148C2×Dic29C2×D411yescharacteristic
149D116—21no—
150D116—21no—
151D116—21no—
152D116C2×D412yes—
153C4×D29—24no—
154C4×D29—42no—
155C4×D29—42no—
156C4×D29—42no—
157Dic58—21no—
158Dic58—21no—
159Dic58—21no—
160Dic58C2×D412yes—
161C8×C29—21no—
162C8×C29—21no—
163#6597—21no—
164#6597—21no—
165#3035—291nomaximal, Sylow
166C22×C29—21no—
167C22×C29—21no—
168C22×C29—41no—
169C22×C29—41no—
170C22×C29—41no—
171C22×C29#12112yes—
172C22×C29C22×D411yescharacteristic
173C2×D29—22no—
174C2×D29—41no—
175C2×D29—41no—
176C2×D29—41no—
177C2×D29—41no—
178C2×D29—41no—
179C4×C29—41no—
180C4×C29—41no—
181C4×C29—41no—
182C4×C29#12112yes—
183C4×C29C22×D411yescharacteristic
184C4×C29C2×#4111yescharacteristic
185Dic29—22no—
186Dic29—21no—
187Dic29—21no—
188Dic29—21no—
189Dic29—41no—
190Dic29#13512yescomplemented
191C2×#135—291no—
192C2×#135—291no—
193#532—291no—
194C4×#41—291no—
195#464—291no—
196#464—291no—
197#463—291no—
198#463—291no—
199#462—291no—
200#461—291no—
201#460—291no—
202#459—291no—
203C2×C4⋊C8—291no—
204#416—291no—
205#416D2911yescharacteristic, complemented
206C2×C29—22no—
207C2×C29—81no—
208C2×C29C2×#12111yescharacteristic
209C2×C29C2×#13511yescharacteristic
210C2×C29#57511yescharacteristic
211D29—42no—
212D29—81no—
213C2×#41—291no—
214C2×#41—291no—
215C2×#41C2×D2911yescharacteristic
216#135—584no—
217#135—584no—
218C2×Q16—291no—
219C2×Q16—291no—
220C2×SD16—291no—
221C2×SD16—291no—
222C2×SD16—291no—
223C2×SD16—291no—
224C2×D8—291no—
225C2×D8—291no—
226C22×C8—291no—
227C22×C8C2×D2911yescharacteristic
228C4⋊Q8—291no—
229#127—291no—
230#124—291no—
231#124—291no—
232#121—581no—
233#121—581no—
234C4×Q8—291no—
235C4×Q8—291no—
236C4×D4—291no—
237C4×D4—291no—
238C4×D4—581no—
239C4×D4—581no—
240C4×D4—581no—
241C4×D4—581no—
242#117—581no—
243#117C2×D2911yescharacteristic
244C2×C42—291no—
245C2×C42—581no—
246C4⋊C8—291no—
247C4⋊C8—291no—
248C4⋊C8—291no—
249C4⋊C8—291no—
250#103—291no—
251#103—291no—
252#103C2×D2911yescharacteristic
253#103C2×D2911yescharacteristic
254#102—291no—
255#102—291no—
256#102C2×D2911yescharacteristic
257#102C2×D2911yescharacteristic
258C29#303511yescharacteristic, complemented, Sylow
259#41—22no—
260#41—22no—
261#41—294no—
262#41—582no—
263#41—582no—
264#41—582no—
265C2×Q8—291no—
266C2×Q8—291no—
267C2×Q8C22×D2911yescharacteristic
268C2×D4—21no—
269C2×D4—291no—
270C2×D4—291no—
271C2×D4—581no—
272C2×D4—581no—
273C2×D4—581no—
274C2×D4—581no—
275C2×D4C22×D2911yescharacteristic
276C22×C4—21no—
277C22×C4—291no—
278C22×C4—291no—
279C22×C4—581no—
280C22×C4—581no—
281C22×C4—581no—
282C22×C4—581no—
283C22×C4C22×D2911yescharacteristic
284Q16—582no—
285Q16—582no—
286SD16—582no—
287SD16—582no—
288SD16—582no—
289SD16—582no—
290D8—582no—
291D8—582no—
292C2×C8—22no—
293C2×C8—291no—
294C2×C8—291no—
295C2×C8—582no—
296C2×C8C22×D2911yescharacteristic
297C2×C8C22×D2911yescharacteristic
298C4⋊C4—581no—
299C4⋊C4—581no—
300C4⋊C4—581no—
301C4⋊C4—581no—
302C4⋊C4C22×D2911yescharacteristic
303C4⋊C4C22×D2911yescharacteristic
304C22⋊C4—21no—
305C22⋊C4—581no—
306C22⋊C4—581no—
307C22⋊C4—581no—
308C22⋊C4—581no—
309C22⋊C4—581no—
310C22⋊C4—581no—
311C42—21no—
312C42—291no—
313C42—291no—
314C42—291no—
315C42—291no—
316C42—581no—
317C42—581no—
318C23—21no—
319C23—581no—
320C23—581no—
321C23D4×D2911yescharacteristic
322Q8—21no—
323Q8—21no—
324Q8—292no—
325Q8—581no—
326Q8—581no—
327Q8—581no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—292no—
332D4—584no—
333D4—581no—
334D4—581no—
335D4—581no—
336D4—1162no—
337D4—1162no—
338D4—1162no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—291no—
344C2×C4—291no—
345C2×C4—291no—
346C2×C4—291no—
347C2×C4—582no—
348C2×C4—581no—
349C2×C4—584no—
350C2×C4—581no—
351C2×C4—1162no—
352C2×C4—1162no—
353C2×C4—1161no—
354C2×C4—1162no—
355C2×C4#9080512yes—
356C2×C4D4×D2912yes—
357C2×C4D4×D2911yescharacteristic
358C2×C4C23×D2911yescharacteristic
359C8—21no—
360C8—21no—
361C8—581no—
362C8—581no—
363C22—21no—
364C22—21no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—582no—
369C22—1161no—
370C22—1161no—
371C22—1161no—
372C22—1161no—
373C22—1161no—
374C22#1174524612yes—
375C22C2×D4×D2911yescharacteristic
376C4—41no—
377C4—41no—
378C4—41no—
379C4—292no—
380C4—582no—
381C4—581no—
382C4—581no—
383C4—581no—
384C4—1161no—
385C4#1174524612yes—
386C4C2×#9080511yescharacteristic
387C4C2×D4×D2911yescharacteristic
388C2—22no—
389C2—81no—
390C2—1162no—
391C2—2321no—
392C2C2×#1174524611yescharacteristic
393C2#135×D2911yescharacteristic
394C2#1427196011yescharacteristic
subgroupG/H
centerC2×C4D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#416C2
socleC22×C29C22×D4
hypercenter#416D29
hypocenterC29#3035
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C2×#11745266C2semidirect
2. C2×#11745312C2semidirect
3. #14271709C2semidirect
4. #14271631C2semidirect
5. #14271388C2semidirect
6. #14271384C2semidirect
7. #14271381C2semidirect
8. #14271377C2semidirect
9. #14271372C2semidirect
10. #14271367C2semidirect
11. #14271362C2semidirect
12. #14271357C2semidirect
13. C2×#11745162C2semidirect
14. #14271157C2semidirect
15. C29×#416C2semidirect
77. #90805D4semidirect
190. Dic29#135semidirect
205. #416D29semidirect
258. C29#3035semidirect

Maximal subgroups

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

subgroupindex
C2×#117452662
C2×#117453122
#142717092
#142716312
#142713882
#142713842
#142713812
#142713772
#142713722
#142713672
#142713622
#142713572
C2×#117451622
#142711572
C29×#4162
#303529