Finite Group Databasebeta

← #16831401

Subgroups — #16831401

Order 3712.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271863C211yesmaximal, characteristic, complemented
2#14271821C211yesmaximal, characteristic, complemented
3#14271517C211yesmaximal, characteristic, complemented
4#14271503C211yesmaximal, characteristic, complemented
5#14271480C211yesmaximal, characteristic, complemented
6#14271471C211yesmaximal, characteristic, complemented
7#14271396C211yesmaximal, characteristic, complemented
8#14271389C211yesmaximal, characteristic, complemented
9#14271305C211yesmaximal, characteristic, complemented
10#14271300C211yesmaximal, characteristic, complemented
11C4×#90783C211yesmaximal, characteristic, complemented
12#14271228C211yesmaximal, characteristic, complemented
13#14271156C211yesmaximal, characteristic, complemented
14#103×D29C211yesmaximal, characteristic, complemented
15C29×#463C211yesmaximal, characteristic, complemented
16C2×Q8×D29C2211yescharacteristic
17C2×#90807C2211yescharacteristic
18C2×SD16×C29C2211yescharacteristic
19C2×D8×C29C2211yescharacteristic
20C29×#124C2211yescharacteristic
21C4×D4×C29C2211yescharacteristic
22#11745308C2211yescharacteristic
23#11745300C2211yescharacteristic
24#11745300C2211yescharacteristic
25#11745300C2211yescharacteristic
26C2×#90783C2211yescharacteristic
27#11745291—21no—
28C4×C22⋊D29—21no—
29C2×C8×D29C2211yescharacteristic
30C2×C8×D29C2211yescharacteristic
31#11745254C2211yescharacteristic
32C4⋊C4×D29C2211yescharacteristic
33#11745247—21no—
34#11745246—21no—
35#11745246—21no—
36#11745243—21no—
37#11745241—21no—
38#11745240—21no—
39C4×D116C2211yescharacteristic
40#11745232C2211yescharacteristic
41C4×Dic58C2211yescharacteristic
42C29×C4⋊C8C2211yescharacteristic
43C29×#103C2211yescharacteristic
44C29×#102C2211yescharacteristic
45#11745183C2211yescharacteristic
46#11745183C2211yescharacteristic
47#11745180C2211yescharacteristic
48#11745180C2211yescharacteristic
49#11745180C2211yescharacteristic
50#11745168C2211yescharacteristic
51#11745168C2211yescharacteristic
52#11745166C2211yescharacteristic
53#11745165C2211yescharacteristic
54#11745164C2211yescharacteristic
55#11745164C2211yescharacteristic
56#11745158C2211yescharacteristic
57#11745156C2211yescharacteristic
58C4×#6597C2211yescharacteristic
59C2×Q8×C29C2311yescharacteristic
60C2×D4×C29C2311yescharacteristic
61C2×D4×C29C2311yescharacteristic
62C22×C4×C29—21no—
63C2×C22⋊D29—21no—
64C2×C22⋊D29—21no—
65C2×C22⋊D29—21no—
66C2×C22⋊D29—21no—
67C22×Dic29—21no—
68Q8×D29—22no—
69Q8×D29—41no—
70#90807—22no—
71#90807—41no—
72C2×D116D411yescharacteristic
73C2×C4×D29—21no—
74C2×C4×D29—21no—
75C2×C4×D29C2311yescharacteristic
76C2×C4×D29C2311yescharacteristic
77C2×Dic58—21no—
78C2×Dic58C2311yescharacteristic
79SD16×C29—41no—
80D8×C29—41no—
81C2×C8×C29C2311yescharacteristic
82C2×C8×C29C2311yescharacteristic
83C4⋊C4×C29C2311yescharacteristic
84C22⋊C4×C29—21no—
85C22⋊C4×C29—21no—
86C22⋊C4×C29—21no—
87C42×C29C2311yescharacteristic
88C22⋊Dic29—21no—
89C22⋊Dic29—21no—
90C22⋊Dic29—21no—
91#90783—22no—
92#90781—21no—
93#90781—21no—
94#90781D411yescharacteristic
95#90781D411yescharacteristic
96C4⋊Dic29D411yescharacteristic
97C4⋊Dic29C2311yescharacteristic
98C4⋊Dic29C2311yescharacteristic
99C4⋊Dic29C2311yescharacteristic
100#90779—21no—
101#90779—21no—
102#90779—21no—
103#90779—21no—
104#90779—21no—
105C4×Dic29—21no—
106C4×Dic29—21no—
107C2×#6597C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109C8×D29—41no—
110C8×D29—41no—
111C23×C29—21no—
112C23×C29—21no—
113C22×D29C2×D411yescharacteristic
114C22×D29C2×D411yescharacteristic
115Q8×C29—21no—
116Q8×C29—21no—
117D4×C29—21no—
118D4×C29—21no—
119D4×C29—21no—
120D4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—81no—
124C2×C4×C29C2×D411yescharacteristic
125C2×C4×C29C2×D411yescharacteristic
126C2×C4×C29C2411yescharacteristic
127C22⋊D29—42no—
128C22⋊D29—42no—
129C22⋊D29—42no—
130C22⋊D29—81no—
131C2×Dic29—21no—
132C2×Dic29—21no—
133C2×Dic29—21no—
134C2×Dic29—21no—
135C2×Dic29—42no—
136C2×Dic29C2×D411yescharacteristic
137C2×Dic29C2×D411yescharacteristic
138D116—22no—
139C4×D29—21no—
140C4×D29—21no—
141C4×D29—21no—
142C4×D29—21no—
143C4×D29—42no—
144C4×D29—81no—
145Dic58—21no—
146Dic58—42no—
147Dic58#4112yes—
148C8×C29—21no—
149C8×C29—21no—
150#6597—21no—
151#6597—21no—
152#3301—291nomaximal, Sylow
153C22×C29—41no—
154C22×C29—41no—
155C22×C29—41no—
156C22×C29—41no—
157C22×C29—41no—
158C22×C29—41no—
159C22×C29C22×D411yescharacteristic
160C2×D29—21no—
161C2×D29—21no—
162C2×D29—21no—
163C2×D29—21no—
164C2×D29—21no—
165C2×D29#13512yes—
166C4×C29—21no—
167C4×C29—21no—
168C4×C29—41no—
169C4×C29—41no—
170C4×C29C2×#4111yescharacteristic
171C4×C29H(5,𝔽2)11yescharacteristic
172Dic29—22no—
173Dic29—21no—
174Dic29—21no—
175Dic29—41no—
176Dic29—41no—
177Dic29—41no—
178#553—291no—
179#548—291no—
180#488—291no—
181#485—291no—
182#481—291no—
183#479—291no—
184#466—291no—
185#465—291no—
186#463D2911yescharacteristic, complemented
187#449—291no—
188#448—291no—
189C4×SD16—291no—
190C8×D4—291no—
191#416—291no—
192C2×#103—291no—
193C2×C29—81no—
194C2×C29—81no—
195C2×C29#54611yescharacteristic
196C2×C29C2×#13511yescharacteristic
197C2×C29#57711yescharacteristic
198D29—22no—
199D29—41no—
200C2×#41—291no—
201C22×Q8—291no—
202C2×SD16—291no—
203C2×SD16C2×D2911yescharacteristic
204C2×D8C2×D2911yescharacteristic
205C22×C8—291no—
206C22×C8—291no—
207#126—581no—
208#125—291no—
209#124—581no—
210#124C2×D2911yescharacteristic
211#123—581no—
212C22⋊Q8—291no—
213C22⋊Q8—581no—
214#121—291no—
215#121—291no—
216#121—291no—
217#121—581no—
218#121—581no—
219C4×Q8—291no—
220C4×D4—291no—
221C4×D4—581no—
222C4×D4—581no—
223C4×D4C2×D2911yescharacteristic
224#117—291no—
225C2×C4⋊C4—291no—
226#107—291no—
227#106—291no—
228#106—291no—
229C4⋊C8C2×D2911yescharacteristic
230#103—291no—
231#103—291no—
232#103—291no—
233#103—291no—
234#103—291no—
235#103C2×D2911yescharacteristic
236#102—291no—
237#102—291no—
238#102—291no—
239#102C2×D2911yescharacteristic
240C22⋊C8—291no—
241C22⋊C8—291no—
242C4×C8—291no—
243C29#330111yescharacteristic, complemented, Sylow
244#41—582no—
245#41—1161no—
246C2×Q8—291no—
247C2×Q8—581no—
248C2×Q8—582no—
249C2×Q8—1161no—
250C2×Q8C22×D2911yescharacteristic
251C2×D4—291no—
252C2×D4—581no—
253C2×D4—581no—
254C2×D4—581no—
255C2×D4—581no—
256C2×D4C22×D2911yescharacteristic
257C2×D4C22×D2911yescharacteristic
258C22×C4—21no—
259C22×C4—291no—
260C22×C4—291no—
261C22×C4—581no—
262C22×C4—581no—
263C22×C4—581no—
264SD16—41no—
265SD16—582no—
266D8—41no—
267C2×C8—291no—
268C2×C8—291no—
269C2×C8—1161no—
270C2×C8—1161no—
271C2×C8C22×D2911yescharacteristic
272C2×C8C22×D2911yescharacteristic
273C4⋊C4—291no—
274C4⋊C4—291no—
275C4⋊C4—291no—
276C4⋊C4—291no—
277C4⋊C4—581no—
278C4⋊C4—581no—
279C4⋊C4—581no—
280C4⋊C4—581no—
281C4⋊C4—581no—
282C4⋊C4C22×D2911yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—291no—
287C22⋊C4—291no—
288C22⋊C4—581no—
289C22⋊C4—581no—
290C22⋊C4—581no—
291C22⋊C4—581no—
292C22⋊C4—581no—
293C42—581no—
294C42—581no—
295C42C22×D2911yescharacteristic
296C23—21no—
297C23—21no—
298C23—291no—
299C23—291no—
300Q8—21no—
301Q8—21no—
302Q8—292no—
303Q8—581no—
304Q8—1162no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—582no—
310D4—1162no—
311D4—1162no—
312D4—1162no—
313D4—2321no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—81no—
317C2×C4—291no—
318C2×C4—291no—
319C2×C4—581no—
320C2×C4—581no—
321C2×C4—581no—
322C2×C4—581no—
323C2×C4—581no—
324C2×C4—581no—
325C2×C4—581no—
326C2×C4—581no—
327C2×C4—1162no—
328C2×C4—1162no—
329C2×C4—2321no—
330C2×C4D4×D2911yescharacteristic
331C2×C4D4×D2911yescharacteristic
332C2×C4C23×D2911yescharacteristic
333C8—21no—
334C8—21no—
335C8—581no—
336C8—581no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—292no—
344C22—581no—
345C22—581no—
346C22—581no—
347C22—581no—
348C22—581no—
349C22C2×D4×D2911yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—581no—
355C4—581no—
356C4—582no—
357C4—1161no—
358C4—1161no—
359C4—1161no—
360C4#1174535911yescharacteristic
361C4#41×D2911yescharacteristic
362C2—81no—
363C2—81no—
364C2—582no—
365C2—1161no—
366C2#1427181011yescharacteristic
367C2#135×D2911yescharacteristic
368C2#1427197311yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#463C2
socleC22×C29C22×D4
hypercenter#463D29
hypocenterC29#3301
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #14271863C2semidirect
2. #14271821C2semidirect
3. #14271517C2semidirect
4. #14271503C2semidirect
5. #14271480C2semidirect
6. #14271471C2semidirect
7. #14271396C2semidirect
8. #14271389C2semidirect
9. #14271305C2semidirect
10. #14271300C2semidirect
11. C4×#90783C2semidirect
12. #14271228C2semidirect
13. #14271156C2semidirect
14. #103×D29C2semidirect
15. C29×#463C2semidirect
186. #463D29semidirect
243. C29#3301semidirect

Maximal subgroups

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

subgroupindex
#142718632
#142718212
#142715172
#142715032
#142714802
#142714712
#142713962
#142713892
#142713052
#142713002
C4×#907832
#142712282
#142711562
#103×D292
C29×#4632
#330129