Finite Group Databasebeta

← #16828943

Subgroups — #16828943

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×#11745312C211yesmaximal, characteristic, complemented
2#14271709C211yesmaximal, characteristic, complemented
3#41×Dic29C211yesmaximal, characteristic, complemented
4#14271387C211yesmaximal, characteristic, complemented
5#14271383C211yesmaximal, characteristic, complemented
6#14271380C211yesmaximal, characteristic, complemented
7#14271376C211yesmaximal, characteristic, complemented
8#14271371C211yesmaximal, characteristic, complemented
9#14271366C211yesmaximal, characteristic, complemented
10#14271361C211yesmaximal, characteristic, complemented
11#14271356C211yesmaximal, characteristic, complemented
12C2×#11745162C211yesmaximal, characteristic, complemented
13#14271160C211yesmaximal, characteristic, complemented
14#14271159C211yesmaximal, characteristic, complemented
15C2×C29×#135C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C2×#41×C29C2211yescharacteristic
18C2×#90805C2211yescharacteristic
19C29×#135—24no—
20C2×Q16×C29C2211yescharacteristic
21C2×SD16×C29C2211yescharacteristic
22C2×SD16×C29C2211yescharacteristic
23C2×D8×C29C2211yescharacteristic
24C22×C8×C29C2211yescharacteristic
25#11745312—24no—
26#11745309C2211yescharacteristic
27Q8×Dic29C2211yescharacteristic
28Q8×Dic29C2211yescharacteristic
29#11745306C2211yescharacteristic
30C2×#90785C2211yescharacteristic
31C2×#90784C2211yescharacteristic
32#11745302C2211yescharacteristic
33#11745301—21no—
34#11745301—21no—
35#11745298C2211yescharacteristic
36D4×Dic29—21no—
37D4×Dic29—21no—
38D4×Dic29C2211yescharacteristic
39D4×Dic29C2211yescharacteristic
40C2×#90783C2211yescharacteristic
41C2×#90782C2211yescharacteristic
42C4×C22⋊D29—21no—
43C4×C22⋊D29—21no—
44#11745288—21no—
45#11745288C2211yescharacteristic
46C2×C4×Dic29—21no—
47C2×C4×Dic29C2211yescharacteristic
48C22×#6597C2211yescharacteristic
49#11745183C2211yescharacteristic
50#11745183C2211yescharacteristic
51#11745180C2211yescharacteristic
52#11745180C2211yescharacteristic
53#11745169C2211yescharacteristic
54#11745169C2211yescharacteristic
55#11745164C2211yescharacteristic
56#11745164C2211yescharacteristic
57#11745162C2211yescharacteristic
58#11745162C2211yescharacteristic
59#11745162C2211yescharacteristic
60#11745162C2211yescharacteristic
61#41×C29—22no—
62#41×C29—22no—
63#41×C29—22no—
64#41×C29D414yescomplemented
65C2×Q8×C29C2311yescharacteristic
66C2×Q8×C29C2311yescharacteristic
67C2×D4×C29—21no—
68C2×D4×C29—21no—
69C2×D4×C29C2311yescharacteristic
70C2×D4×C29C2311yescharacteristic
71C22×C4×C29—21no—
72C22×C4×C29—21no—
73C22×C4×C29C2311yescharacteristic
74C2×C22⋊D29—21no—
75C2×C22⋊D29—21no—
76C2×C22⋊D29—21no—
77C22×Dic29—21no—
78C22×Dic29—21no—
79C22×Dic29D411yescharacteristic
80C22×Dic29D411yescharacteristic
81#90805—22no—
82#90805—22no—
83C2×D116C2311yescharacteristic
84C2×C4×D29—21no—
85C2×Dic58C2311yescharacteristic
86Q16×C29—22no—
87SD16×C29—22no—
88SD16×C29—22no—
89D8×C29—22no—
90C2×C8×C29—22no—
91C2×C8×C29C2311yescharacteristic
92C2×C8×C29C2311yescharacteristic
93C22⋊Dic29—21no—
94C22⋊Dic29—21no—
95C22⋊Dic29—21no—
96C22⋊Dic29—21no—
97C22⋊Dic29—21no—
98#90785—22no—
99#90784—22no—
100#90783—22no—
101#90782—22no—
102#90781—21no—
103#90781—21no—
104C4⋊Dic29—21no—
105C4⋊Dic29—21no—
106C4⋊Dic29C2311yescharacteristic
107C4⋊Dic29C2311yescharacteristic
108#90779—21no—
109#90779—21no—
110C4×Dic29—21no—
111C4×Dic29—21no—
112C4×Dic29—21no—
113C4×Dic29D411yescharacteristic
114C4×Dic29D411yescharacteristic
115C4×Dic29C2311yescharacteristic
116C4×Dic29C2311yescharacteristic
117C2×#6597—22no—
118C2×#6597C2311yescharacteristic
119C2×#6597C2311yescharacteristic
120C23×C29—21no—
121C23×C29—21no—
122C23×C29C2×D411yescharacteristic
123C22×D29—21no—
124Q8×C29—21no—
125Q8×C29—21no—
126Q8×C29—21no—
127Q8×C29C2×D412yes—
128D4×C29—24no—
129D4×C29—21no—
130D4×C29—21no—
131D4×C29—21no—
132D4×C29—42no—
133D4×C29C2×D412yes—
134C2×C4×C29—21no—
135C2×C4×C29—24no—
136C2×C4×C29—21no—
137C2×C4×C29—42no—
138C2×C4×C29C2×D411yescharacteristic
139C2×C4×C29C2×D412yes—
140C2×C4×C29#4112yes—
141C2×C4×C29C2411yescharacteristic
142C22⋊D29—42no—
143C22⋊D29—42no—
144C22⋊D29—42no—
145C2×Dic29—22no—
146C2×Dic29—21no—
147C2×Dic29—21no—
148C2×Dic29—21no—
149C2×Dic29—41no—
150C2×Dic29—42no—
151C2×Dic29—42no—
152C2×Dic29C2×D411yescharacteristic
153C2×Dic29C2×D411yescharacteristic
154C2×Dic29C2×D411yescharacteristic
155C2×Dic29C2×D411yescharacteristic
156D116—21no—
157D116—21no—
158C4×D29—42no—
159Dic58—21no—
160Dic58—21no—
161C8×C29—21no—
162C8×C29—21no—
163#6597—21no—
164#6597—21no—
165#3035—291nomaximal, Sylow
166C22×C29—21no—
167C22×C29—21no—
168C22×C29—22no—
169C22×C29—41no—
170C22×C29—41no—
171C22×C29—41no—
172C22×C29—41no—
173C22×C29—41no—
174C22×C29#12112yes—
175C22×C29C22×D411yescharacteristic
176C2×D29—41no—
177C2×D29—41no—
178C2×D29—41no—
179C4×C29—22no—
180C4×C29—41no—
181C4×C29#12112yes—
182C4×C29C22×D411yescharacteristic
183C4×C29C2×#4111yescharacteristic
184Dic29—21no—
185Dic29—21no—
186Dic29—21no—
187Dic29—41no—
188Dic29—41no—
189Dic29—41no—
190Dic29#13512yescomplemented
191C2×#135—291no—
192C2×#135D2911yescharacteristic, complemented
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#416—291no—
206C2×C29—22no—
207C2×C29—42no—
208C2×C29—81no—
209C2×C29C2×#12111yescharacteristic
210C2×C29C2×#13511yescharacteristic
211C2×C29#57511yescharacteristic
212D29—81no—
213C2×#41—291no—
214C2×#41C2×D2911yescharacteristic
215C2×#41C2×D2911yescharacteristic
216#135—24no—
217#135—584no—
218C2×Q16—291no—
219C2×Q16C2×D2911yescharacteristic
220C2×SD16—291no—
221C2×SD16—291no—
222C2×SD16C2×D2911yescharacteristic
223C2×SD16C2×D2911yescharacteristic
224C2×D8—291no—
225C2×D8C2×D2911yescharacteristic
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—291no—
243#117—581no—
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#103—291no—
253#103—291no—
254#102—291no—
255#102—291no—
256#102—291no—
257#102—291no—
258C29#303511yescharacteristic, complemented, Sylow
259#41—22no—
260#41—22no—
261#41—22no—
262#41—582no—
263#41—582no—
264#41C22⋊D2914yescomplemented
265C2×Q8—291no—
266C2×Q8C22×D2911yescharacteristic
267C2×Q8C22×D2911yescharacteristic
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—291no—
271C2×D4—581no—
272C2×D4—581no—
273C2×D4—581no—
274C2×D4C22×D2911yescharacteristic
275C2×D4C22×D2911yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—291no—
279C22×C4—291no—
280C22×C4—581no—
281C22×C4—581no—
282C22×C4—581no—
283C22×C4C22×D2911yescharacteristic
284Q16—22no—
285Q16—582no—
286SD16—22no—
287SD16—22no—
288SD16—582no—
289SD16—582no—
290D8—22no—
291D8—582no—
292C2×C8—22no—
293C2×C8—291no—
294C2×C8—291no—
295C2×C8—582no—
296C2×C8C22×D2911yescharacteristic
297C2×C8C22×D2911yescharacteristic
298C4⋊C4—291no—
299C4⋊C4—291no—
300C4⋊C4—581no—
301C4⋊C4—581no—
302C4⋊C4—581no—
303C4⋊C4—581no—
304C22⋊C4—581no—
305C22⋊C4—581no—
306C22⋊C4—581no—
307C22⋊C4—581no—
308C22⋊C4—581no—
309C22⋊C4—581no—
310C22⋊C4—581no—
311C42—291no—
312C42—291no—
313C42—291no—
314C42—291no—
315C42—581no—
316C42—581no—
317C42—581no—
318C23—21no—
319C23—21no—
320C23—581no—
321C23D4×D2911yescharacteristic
322Q8—21no—
323Q8—21no—
324Q8—21no—
325Q8—581no—
326Q8—581no—
327Q8C2×C22⋊D2912yes—
328D4—24no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—581no—
334D4—581no—
335D4—1162no—
336D4—1162no—
337D4—1162no—
338D4C2×C22⋊D2912yes—
339C2×C4—21no—
340C2×C4—24no—
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—581no—
350C2×C4—581no—
351C2×C4—1162no—
352C2×C4—1161no—
353C2×C4—1162no—
354C2×C4—1162no—
355C2×C4D4×D2911yescharacteristic
356C2×C4#9080712yes—
357C2×C4C2×C22⋊D2912yes—
358C2×C4C23×D2911yescharacteristic
359C8—21no—
360C8—21no—
361C8—581no—
362C8—581no—
363C22—21no—
364C22—21no—
365C22—22no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—1161no—
372C22—1161no—
373C22—1161no—
374C22#1174530112yes—
375C22C2×D4×D2911yescharacteristic
376C4—22no—
377C4—41no—
378C4—292no—
379C4—581no—
380C4—581no—
381C4—581no—
382C4—1161no—
383C4—1161no—
384C4—1161no—
385C4#1174530112yes—
386C4C2×#9080711yescharacteristic
387C4C22×C22⋊D2911yescharacteristic
388C2—22no—
389C2—42no—
390C2—81no—
391C2—2321no—
392C2C2×#1174530111yescharacteristic
393C2#135×D2911yescharacteristic
394C2#1427196011yescharacteristic
subgroupG/H
centerC2×C4D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC2×C29×#135C2
socleC22×C29C22×D4
hypercenterC2×#135D29
hypocenterC29#3035
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#11745312C2semidirect
2. #14271709C2semidirect
3. #41×Dic29C2semidirect
4. #14271387C2semidirect
5. #14271383C2semidirect
6. #14271380C2semidirect
7. #14271376C2semidirect
8. #14271371C2semidirect
9. #14271366C2semidirect
10. #14271361C2semidirect
11. #14271356C2semidirect
12. C2×#11745162C2semidirect
13. #14271160C2semidirect
14. #14271159C2semidirect
15. C2×C29×#135C2semidirect
64. #41×C29D4semidirect
190. Dic29#135semidirect
192. C2×#135D29semidirect
258. C29#3035semidirect
264. #41C22⋊D29semidirect

Maximal subgroups

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

subgroupindex
C2×#117453122
#142717092
#41×Dic292
#142713872
#142713832
#142713802
#142713762
#142713712
#142713662
#142713612
#142713562
C2×#117451622
#142711602
#142711592
C2×C29×#1352
#303529