Finite Group Databasebeta

← #16831388

Subgroups — #16831388

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#14271822C211yesmaximal, characteristic, complemented
2#14271520C211yesmaximal, characteristic, complemented
3#14271504C211yesmaximal, characteristic, complemented
4#14271481C211yesmaximal, characteristic, complemented
5#14271467C211yesmaximal, characteristic, complemented
6#14271397C211yesmaximal, characteristic, complemented
7#14271390C211yesmaximal, characteristic, complemented
8#14271378C211yesmaximal, characteristic, complemented
9#14271306C211yesmaximal, characteristic, complemented
10#14271301C211yesmaximal, characteristic, complemented
11C4×#90783C211yesmaximal, characteristic, complemented
12D4×#6597C211yesmaximal, characteristic, complemented
13#14271157C211yesmaximal, characteristic, complemented
14C2×#11745158C211yesmaximal, characteristic, complemented
15C29×#553C211yesmaximal, characteristic, complemented
16C2×#90805C2211yescharacteristic
17C22×Dic58C2211yescharacteristic
18C29×#126—21no—
19C29×#125C2211yescharacteristic
20C29×#123—21no—
21C29×#121—21no—
22C29×#121C2211yescharacteristic
23C29×#121C2211yescharacteristic
24C4×D4×C29—21no—
25C4×D4×C29C2211yescharacteristic
26C4×D4×C29C2211yescharacteristic
27C29×#117C2211yescharacteristic
28C2×C4⋊C4×C29C2211yescharacteristic
29#11745301—21no—
30C2×#90783C2211yescharacteristic
31C2×#90783C2211yescharacteristic
32C2×#90782C2211yescharacteristic
33#11745292C2211yescharacteristic
34#11745286C2211yescharacteristic
35C22×#6597C2211yescharacteristic
36C22×#6597C2211yescharacteristic
37#11745258—21no—
38#11745247—21no—
39#11745243—21no—
40#11745237C2211yescharacteristic
41C4×Dic58C2211yescharacteristic
42#11745180C2211yescharacteristic
43C22⋊#6597C2211yescharacteristic
44C22⋊#6597C2211yescharacteristic
45#11745158C2211yescharacteristic
46#11745158C2211yescharacteristic
47#11745158C2211yescharacteristic
48#11745158C2211yescharacteristic
49#11745158C2211yescharacteristic
50#11745158C2211yescharacteristic
51#11745157C2211yescharacteristic
52#11745157C2211yescharacteristic
53#11745157C2211yescharacteristic
54#11745156C2211yescharacteristic
55#11745156C2211yescharacteristic
56#11745155C2211yescharacteristic
57C4⋊#6597C2211yescharacteristic
58C4×#6597C2211yescharacteristic
59C2×D4×C29—21no—
60C2×D4×C29—21no—
61C2×D4×C29D411yescharacteristic
62C2×D4×C29C2311yescharacteristic
63C22×C4×C29—21no—
64C22×C4×C29—21no—
65C22×C4×C29C2311yescharacteristic
66C22×C4×C29C2311yescharacteristic
67C2×C22⋊D29—21no—
68C2×C22⋊D29—21no—
69C22×Dic29—21no—
70#90805—22no—
71#90805—41no—
72C2×D116C2311yescharacteristic
73C2×C4×D29—21no—
74C2×Dic58—22no—
75C2×Dic58—21no—
76C2×Dic58—41no—
77C2×Dic58C2311yescharacteristic
78C2×Dic58C2311yescharacteristic
79C4⋊C4×C29—21no—
80C4⋊C4×C29—21no—
81C4⋊C4×C29—21no—
82C4⋊C4×C29D411yescharacteristic
83C4⋊C4×C29C2311yescharacteristic
84C4⋊C4×C29C2311yescharacteristic
85C4⋊C4×C29C2311yescharacteristic
86C22⋊C4×C29—21no—
87C22⋊C4×C29—21no—
88C22⋊C4×C29—21no—
89C22⋊C4×C29—21no—
90C22⋊C4×C29D411yescharacteristic
91C22⋊C4×C29D411yescharacteristic
92C42×C29—21no—
93C42×C29C2311yescharacteristic
94C22⋊Dic29—21no—
95#90783—22no—
96#90783—41no—
97#90782—41no—
98#90781—21no—
99#90781—21no—
100#90781—21no—
101C4⋊Dic29C2311yescharacteristic
102#90779—21no—
103#90779—21no—
104C4×Dic29—21no—
105C2×#6597—41no—
106C2×#6597—41no—
107C2×#6597C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110C2×#6597C2311yescharacteristic
111C23×C29—21no—
112C23×C29C2×D411yescharacteristic
113C23×C29C2×D411yescharacteristic
114C22×D29—21no—
115D4×C29—22no—
116D4×C29—21no—
117D4×C29—21no—
118D4×C29—42no—
119D4×C29—81no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29—21no—
125C2×C4×C29—21no—
126C2×C4×C29—21no—
127C2×C4×C29—81no—
128C2×C4×C29—81no—
129C2×C4×C29C2×D411yescharacteristic
130C2×C4×C29C2×D411yescharacteristic
131C2×C4×C29C2×D411yescharacteristic
132C2×C4×C29C2×D411yescharacteristic
133C2×C4×C29C2411yescharacteristic
134C22⋊D29—42no—
135C22⋊D29—42no—
136C2×Dic29—21no—
137C2×Dic29—21no—
138C2×Dic29—21no—
139C2×Dic29—42no—
140D116—21no—
141D116—21no—
142C4×D29—42no—
143Dic58—21no—
144Dic58—21no—
145Dic58—21no—
146Dic58—42no—
147Dic58#4112yes—
148#6597—21no—
149#6597—21no—
150#6597—21no—
151#6597—21no—
152#3301—291nomaximal, Sylow
153C22×C29—21no—
154C22×C29—21no—
155C22×C29—21no—
156C22×C29—21no—
157C22×C29—21no—
158C22×C29—41no—
159C22×C29—41no—
160C22×C29—41no—
161C22×C29#13512yes—
162C22×C29C22×D411yescharacteristic
163C2×D29—41no—
164C2×D29—41no—
165C2×D29—41no—
166C4×C29—21no—
167C4×C29—21no—
168C4×C29—21no—
169C4×C29—21no—
170C4×C29—41no—
171C4×C29—41no—
172C4×C29—41no—
173C4×C29C2×#4111yescharacteristic
174C4×C29H(5,𝔽2)11yescharacteristic
175Dic29—22no—
176Dic29—41no—
177Dic29—41no—
178#553D2911yescharacteristic, complemented
179#548—291no—
180#488—291no—
181#485—291no—
182#481—291no—
183#479—291no—
184#466—291no—
185#465—291no—
186#463—291no—
187#449—291no—
188#448—291no—
189C4×SD16—291no—
190C8×D4—291no—
191#416—291no—
192C2×#103—291no—
193C2×C29—22no—
194C2×C29—41no—
195C2×C29—81no—
196C2×C29#54611yescharacteristic
197C2×C29C2×#13511yescharacteristic
198C2×C29#57711yescharacteristic
199D29—81no—
200C2×#41—291no—
201C22×Q8—291no—
202C2×SD16—291no—
203C2×SD16—291no—
204C2×D8—291no—
205C22×C8—291no—
206C22×C8—291no—
207#126—21no—
208#125C2×D2911yescharacteristic
209#124—291no—
210#124—581no—
211#123—21no—
212C22⋊Q8—291no—
213C22⋊Q8—581no—
214#121—21no—
215#121—291no—
216#121—581no—
217#121C2×D2911yescharacteristic
218#121C2×D2911yescharacteristic
219C4×Q8—291no—
220C4×D4—21no—
221C4×D4—581no—
222C4×D4C2×D2911yescharacteristic
223C4×D4C2×D2911yescharacteristic
224#117C2×D2911yescharacteristic
225C2×C4⋊C4C2×D2911yescharacteristic
226#107—291no—
227#106—291no—
228#106—291no—
229C4⋊C8—291no—
230#103—291no—
231#103—291no—
232#103—291no—
233#103—291no—
234#103—291no—
235#103—291no—
236#102—291no—
237#102—291no—
238#102—291no—
239#102—291no—
240C22⋊C8—291no—
241C22⋊C8—291no—
242C4×C8—291no—
243C29#330111yescharacteristic, complemented, Sylow
244#41—582no—
245#41—1161no—
246C2×Q8—291no—
247C2×Q8—291no—
248C2×Q8—582no—
249C2×Q8—581no—
250C2×Q8—1161no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—291no—
254C2×D4—581no—
255C2×D4—581no—
256C2×D4C22⋊D2911yescharacteristic
257C2×D4C22×D2911yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—581no—
261C22×C4—581no—
262C22×C4C22×D2911yescharacteristic
263C22×C4C22×D2911yescharacteristic
264SD16—582no—
265SD16—1161no—
266D8—1161no—
267C2×C8—291no—
268C2×C8—291no—
269C2×C8—291no—
270C2×C8—291no—
271C2×C8—1161no—
272C2×C8—1161no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—291no—
277C4⋊C4—581no—
278C4⋊C4—581no—
279C4⋊C4C22⋊D2911yescharacteristic
280C4⋊C4C22×D2911yescharacteristic
281C4⋊C4C22×D2911yescharacteristic
282C4⋊C4C22×D2911yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—581no—
288C22⋊C4—581no—
289C22⋊C4—581no—
290C22⋊C4—581no—
291C22⋊C4C22⋊D2911yescharacteristic
292C22⋊C4C22⋊D2911yescharacteristic
293C42—21no—
294C42—581no—
295C42C22×D2911yescharacteristic
296C23—21no—
297C23—581no—
298C23C2×C22⋊D2911yescharacteristic
299C23C2×C22⋊D2911yescharacteristic
300Q8—292no—
301Q8—581no—
302Q8—581no—
303Q8—581no—
304Q8—1162no—
305D4—22no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—581no—
311D4—581no—
312D4—1162no—
313D4—1162no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—581no—
324C2×C4—581no—
325C2×C4—581no—
326C2×C4—1162no—
327C2×C4—1162no—
328C2×C4C2×C22⋊D2911yescharacteristic
329C2×C4C2×C22⋊D2911yescharacteristic
330C2×C4C2×C22⋊D2911yescharacteristic
331C2×C4C2×C22⋊D2911yescharacteristic
332C2×C4C23×D2911yescharacteristic
333C8—581no—
334C8—581no—
335C8—581no—
336C8—581no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—1161no—
346C22—1161no—
347C22—1161no—
348C22#1174531212yes—
349C22C22×C22⋊D2911yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—582no—
358C4—1161no—
359C4—1161no—
360C4#41×D2911yescharacteristic
361C4#1174536411yescharacteristic
362C2—22no—
363C2—41no—
364C2—81no—
365C2—2321no—
366C2#1427180111yescharacteristic
367C2C2×#1174531211yescharacteristic
368C2#1427197411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#553C2
socleC22×C29C22×D4
hypercenter#553D29
hypocenterC29#3301
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #14271822C2semidirect
2. #14271520C2semidirect
3. #14271504C2semidirect
4. #14271481C2semidirect
5. #14271467C2semidirect
6. #14271397C2semidirect
7. #14271390C2semidirect
8. #14271378C2semidirect
9. #14271306C2semidirect
10. #14271301C2semidirect
11. C4×#90783C2semidirect
12. D4×#6597C2semidirect
13. #14271157C2semidirect
14. C2×#11745158C2semidirect
15. C29×#553C2semidirect
178. #553D29semidirect
243. C29#3301semidirect

Maximal subgroups

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

subgroupindex
#142718222
#142715202
#142715042
#142714812
#142714672
#142713972
#142713902
#142713782
#142713062
#142713012
C4×#907832
D4×#65972
#142711572
C2×#117451582
C29×#5532
#330129