Finite Group Databasebeta

← #16831052

Subgroups — #16831052

Order 3712.

478 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745271C211yesmaximal, characteristic, complemented
2C2×#11745266C211yesmaximal, characteristic, complemented
3#14271822C211yesmaximal, characteristic, complemented
4#14271818C211yesmaximal, characteristic, complemented
5#14271557C211yesmaximal, characteristic, complemented
6#14271409C211yesmaximal, characteristic, complemented
7#14271404C211yesmaximal, characteristic, complemented
8#14271379C211yesmaximal, characteristic, complemented
9#14271374C211yesmaximal, characteristic, complemented
10#14271327C211yesmaximal, characteristic, complemented
11#14271327C211yesmaximal, characteristic, complemented
12#14271321C211yesmaximal, characteristic, complemented
13#14271310C211yesmaximal, characteristic, complemented
14#14271265C211yesmaximal, characteristic, complemented
15C29×#435C211yesmaximal, characteristic, complemented
16C2×#90805C2211yescharacteristic
17C2×#90805C2211yescharacteristic
18C2×#90805C2211yescharacteristic
19C22×Dic58C2211yescharacteristic
20C2×M16×C29C2211yescharacteristic
21C22×C8×C29C2211yescharacteristic
22C4×D4×C29C2211yescharacteristic
23#11745301—21no—
24#11745300—21no—
25#11745292C2211yescharacteristic
26#11745286C2211yescharacteristic
27#11745286C2211yescharacteristic
28#11745286C2211yescharacteristic
29#11745271—24no—
30C2×Dic116C2211yescharacteristic
31C2×Dic116C2211yescharacteristic
32C2×Dic116C2211yescharacteristic
33C2×Dic116C2211yescharacteristic
34#11745266—24no—
35C2×D232C2211yescharacteristic
36C2×#90773C2211yescharacteristic
37C2×#90773C2211yescharacteristic
38C2×#90773C2211yescharacteristic
39C2×#90773C2211yescharacteristic
40#11745258—21no—
41C4⋊C4×D29—21no—
42#11745247—21no—
43#11745245—21no—
44#11745245—21no—
45#11745243—21no—
46#11745237C2211yescharacteristic
47C4×D116C2211yescharacteristic
48#11745231C2211yescharacteristic
49C4×Dic58C2211yescharacteristic
50C29×C4⋊C8C2211yescharacteristic
51C29×C22⋊C8C2211yescharacteristic
52C29×C22⋊C8C2211yescharacteristic
53C29×#97C2211yescharacteristic
54#11745169C2211yescharacteristic
55#11745169C2211yescharacteristic
56#11745166C2211yescharacteristic
57#11745164C2211yescharacteristic
58#11745164C2211yescharacteristic
59#11745164C2211yescharacteristic
60#11745164C2211yescharacteristic
61C2×D4×C29D411yescharacteristic
62C22×C4×C29C2311yescharacteristic
63C22×C4×C29C2311yescharacteristic
64C2×C22⋊D29—21no—
65C2×C22⋊D29—21no—
66C2×C22⋊D29—21no—
67C2×C22⋊D29—21no—
68C22×Dic29—21no—
69#90805—22no—
70#90805—22no—
71#90805—22no—
72#90805—41no—
73#90805—41no—
74#90805—41no—
75C2×D116C2311yescharacteristic
76C2×D116C2311yescharacteristic
77C2×C4×D29—21no—
78C2×C4×D29—21no—
79C2×C4×D29—21no—
80C2×C4×D29—21no—
81C2×Dic58—22no—
82C2×Dic58—21no—
83C2×Dic58—41no—
84C2×Dic58C2311yescharacteristic
85C2×Dic58C2311yescharacteristic
86C2×Dic58C2311yescharacteristic
87C2×Dic58C2311yescharacteristic
88M16×C29—22no—
89C2×C8×C29—22no—
90C2×C8×C29C2311yescharacteristic
91C2×C8×C29C2311yescharacteristic
92C2×C8×C29C2311yescharacteristic
93C2×C8×C29C2311yescharacteristic
94C4⋊C4×C29D411yescharacteristic
95C22⋊C4×C29D411yescharacteristic
96C22⋊C4×C29D411yescharacteristic
97C42×C29C2311yescharacteristic
98C22⋊Dic29—21no—
99C22⋊Dic29—21no—
100C22⋊Dic29—21no—
101#90781—21no—
102#90781—21no—
103#90781—21no—
104#90781—21no—
105C4⋊Dic29—21no—
106C4⋊Dic29—21no—
107C4⋊Dic29C2311yescharacteristic
108C4⋊Dic29C2311yescharacteristic
109#90779—21no—
110#90779—21no—
111#90779—21no—
112#90779—21no—
113C4×Dic29—21no—
114Dic116—22no—
115Dic116—22no—
116Dic116—22no—
117Dic116—41no—
118D232—22no—
119#90773—22no—
120#90773—22no—
121#90773—41no—
122#90773D414yescomplemented
123C23×C29C2×D411yescharacteristic
124C23×C29C2×D411yescharacteristic
125C22×D29—21no—
126C22×D29—21no—
127D4×C29—41no—
128C2×C4×C29—21no—
129C2×C4×C29—21no—
130C2×C4×C29—21no—
131C2×C4×C29—21no—
132C2×C4×C29C2×D411yescharacteristic
133C2×C4×C29C2×D411yescharacteristic
134C2×C4×C29C2×D411yescharacteristic
135C2×C4×C29C2×D411yescharacteristic
136C2×C4×C29C2411yescharacteristic
137C22⋊D29—42no—
138C22⋊D29—42no—
139C22⋊D29—42no—
140C22⋊D29—42no—
141C2×Dic29—21no—
142C2×Dic29—21no—
143C2×Dic29—21no—
144C2×Dic29—21no—
145C2×Dic29—21no—
146C2×Dic29—21no—
147C2×Dic29—42no—
148D116—21no—
149D116—21no—
150D116—21no—
151D116C2×D412yes—
152C4×D29—42no—
153C4×D29—42no—
154C4×D29—42no—
155C4×D29—42no—
156Dic58—21no—
157Dic58—21no—
158Dic58—21no—
159Dic58—21no—
160Dic58—21no—
161Dic58—21no—
162Dic58—21no—
163Dic58—42no—
164Dic58C2×D412yes—
165C8×C29—21no—
166C8×C29—21no—
167C8×C29—21no—
168C8×C29C2×D412yes—
169#3269—291nomaximal, Sylow
170C22×C29—21no—
171C22×C29—21no—
172C22×C29—21no—
173C22×C29—21no—
174C22×C29—21no—
175C22×C29—21no—
176C22×C29C22×D411yescharacteristic
177C2×D29—22no—
178C2×D29—41no—
179C2×D29—41no—
180C2×D29—41no—
181C2×D29—41no—
182C2×D29—41no—
183C4×C29—21no—
184C4×C29—21no—
185C4×C29—21no—
186C4×C29—21no—
187C4×C29C22×D411yescharacteristic
188C4×C29H(5,𝔽2)11yescharacteristic
189Dic29—22no—
190Dic29—41no—
191Dic29—41no—
192Dic29—41no—
193Dic29—41no—
194Dic29—41no—
195C2×#137—291no—
196C2×#135—291no—
197#548—291no—
198#547—291no—
199#497—291no—
200#468—291no—
201#467—291no—
202#463—291no—
203#462—291no—
204#452—291no—
205#452—291no—
206#451—291no—
207#449—291no—
208#440—291no—
209#435D2911yescharacteristic, complemented
210C2×C29—41no—
211C2×C29—41no—
212C2×C29D4211yescharacteristic
213C2×C29#57511yescharacteristic
214C2×C29#57811yescharacteristic
215D29—42no—
216D29—81no—
217C2×#41—291no—
218C2×#41—291no—
219C2×#41—291no—
220C22×Q8—291no—
221#137—584no—
222#135—584no—
223C2×Q16—291no—
224C2×Q16—291no—
225C2×Q16—291no—
226C2×Q16—291no—
227C2×SD16—291no—
228C2×SD16—291no—
229C2×SD16—291no—
230C2×SD16—291no—
231C2×D8—291no—
232C2×M16C2×D2911yescharacteristic
233C22×C8C2×D2911yescharacteristic
234C4⋊Q8—291no—
235#124—291no—
236#124—581no—
237#123—581no—
238#123—581no—
239C22⋊Q8—291no—
240C22⋊Q8—291no—
241C22⋊Q8—291no—
242C22⋊Q8—581no—
243#121—291no—
244#121—581no—
245#121—581no—
246C4×Q8—291no—
247C4×D4—291no—
248C4×D4—581no—
249C4×D4C2×D2911yescharacteristic
250C2×C4⋊C4—581no—
251#107—291no—
252C4⋊C8C2×D2911yescharacteristic
253#103—291no—
254#103—291no—
255#103—291no—
256#103—291no—
257#102—291no—
258#102—291no—
259C22⋊C8C2×D2911yescharacteristic
260C22⋊C8C2×D2911yescharacteristic
261#97C2×D2911yescharacteristic
262C29#326911yescharacteristic, complemented, Sylow
263#41—582no—
264#41—582no—
265#41—582no—
266#41—1161no—
267#41—1161no—
268#41—1161no—
269C2×Q8—291no—
270C2×Q8—291no—
271C2×Q8—291no—
272C2×Q8—291no—
273C2×Q8—582no—
274C2×Q8—581no—
275C2×Q8—1161no—
276C2×D4—291no—
277C2×D4—291no—
278C2×D4—581no—
279C2×D4—581no—
280C2×D4—581no—
281C2×D4—581no—
282C2×D4D11611yescharacteristic
283C22×C4—581no—
284C22×C4—581no—
285C22×C4—581no—
286C22×C4—581no—
287C22×C4—581no—
288C22×C4C22×D2911yescharacteristic
289C22×C4C22×D2911yescharacteristic
290Q16—582no—
291Q16—582no—
292Q16—582no—
293Q16—1161no—
294SD16—294no—
295SD16—582no—
296SD16—582no—
297SD16—1161no—
298D8—582no—
299M16—22no—
300C2×C8—22no—
301C2×C8C22×D2911yescharacteristic
302C2×C8C22×D2911yescharacteristic
303C2×C8C22×D2911yescharacteristic
304C2×C8C22×D2911yescharacteristic
305C4⋊C4—291no—
306C4⋊C4—291no—
307C4⋊C4—581no—
308C4⋊C4—581no—
309C4⋊C4—581no—
310C4⋊C4—581no—
311C4⋊C4—581no—
312C4⋊C4—581no—
313C4⋊C4D11611yescharacteristic
314C22⋊C4—581no—
315C22⋊C4—581no—
316C22⋊C4—581no—
317C22⋊C4—581no—
318C22⋊C4—581no—
319C22⋊C4—581no—
320C22⋊C4—581no—
321C22⋊C4D11611yescharacteristic
322C22⋊C4D11611yescharacteristic
323C42—581no—
324C42C22×D2911yescharacteristic
325C23—581no—
326C23—581no—
327C23C2×D11611yescharacteristic
328C23C2×D11611yescharacteristic
329Q8—292no—
330Q8—581no—
331Q8—581no—
332Q8—581no—
333Q8—581no—
334Q8—581no—
335Q8—581no—
336Q8—581no—
337Q8—1162no—
338D4—41no—
339D4—292no—
340D4—581no—
341D4—581no—
342D4—581no—
343D4—1162no—
344D4—1162no—
345D4—1162no—
346D4—1162no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—581no—
352C2×C4—581no—
353C2×C4—581no—
354C2×C4—581no—
355C2×C4—581no—
356C2×C4—581no—
357C2×C4—1162no—
358C2×C4—1162no—
359C2×C4—1162no—
360C2×C4—1162no—
361C2×C4—1162no—
362C2×C4C2×D11611yescharacteristic
363C2×C4C2×D11611yescharacteristic
364C2×C4C2×D11611yescharacteristic
365C2×C4C2×D11611yescharacteristic
366C2×C4C23×D2911yescharacteristic
367C8—21no—
368C8—21no—
369C8—21no—
370C8D4×D2912yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—582no—
378C22—1161no—
379C22—1161no—
380C22—1161no—
381C22—1161no—
382C22—1161no—
383C22C22×D11611yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—582no—
389C4—1161no—
390C4—1161no—
391C4—1161no—
392C4—1161no—
393C4—1161no—
394C4C2×D4×D2911yescharacteristic
395C4#1174536411yescharacteristic
396C2—41no—
397C2—41no—
398C2—1162no—
399C2—2321no—
400C2D4×D11611yescharacteristic
401C2#1427196311yescharacteristic
402C2#1427198011yescharacteristic
subgroupG/H
centerC22C22×D116
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#435C2
socleC22×C29C22×D4
hypercenter#435D29
hypocenterC29#3269
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#11745271C2semidirect
2. C2×#11745266C2semidirect
3. #14271822C2semidirect
4. #14271818C2semidirect
5. #14271557C2semidirect
6. #14271409C2semidirect
7. #14271404C2semidirect
8. #14271379C2semidirect
9. #14271374C2semidirect
10. #14271327C2semidirect
11. #14271327C2semidirect
12. #14271321C2semidirect
13. #14271310C2semidirect
14. #14271265C2semidirect
15. C29×#435C2semidirect
122. #90773D4semidirect
209. #435D29semidirect
262. C29#3269semidirect

Maximal subgroups

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

subgroupindex
C2×#117452712
C2×#117452662
#142718222
#142718182
#142715572
#142714092
#142714042
#142713792
#142713742
#142713272
#142713212
#142713102
#142712652
C29×#4352
#326929