Finite Group Databasebeta

← #16832576

Subgroups — #16832576

Order 3712.

380 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271898C211yesmaximal, characteristic, complemented
2#14271553C211yesmaximal, characteristic, complemented
3#14271550C211yesmaximal, characteristic, complemented
4#14271545C211yesmaximal, characteristic, complemented
5#14271385C211yesmaximal, characteristic, complemented
6#14271382C211yesmaximal, characteristic, complemented
7#14271378C211yesmaximal, characteristic, complemented
8#14271375C211yesmaximal, characteristic, complemented
9#14271358C211yesmaximal, characteristic, complemented
10#14271355C211yesmaximal, characteristic, complemented
11#14271294C211yesmaximal, characteristic, complemented
12#14271263C211yesmaximal, characteristic, complemented
13#14271261C211yesmaximal, characteristic, complemented
14C4×#90782C211yesmaximal, characteristic, complemented
15C29×#559C211yesmaximal, characteristic, complemented
16C29×#127C2211yescharacteristic
17C29×#124—21no—
18C29×#124C2211yescharacteristic
19C29×#124C2211yescharacteristic
20C29×#123—21no—
21C29×#123—21no—
22C4×Q8×C29C2211yescharacteristic
23C4×Q8×C29C2211yescharacteristic
24C4×D4×C29—21no—
25C4×D4×C29C2211yescharacteristic
26C4×D4×C29C2211yescharacteristic
27#11745309—21no—
28C2×#90785C2211yescharacteristic
29C2×#90784C2211yescharacteristic
30C2×#90784C2211yescharacteristic
31C2×#90783C2211yescharacteristic
32C2×#90783C2211yescharacteristic
33C2×#90782C2211yescharacteristic
34C2×#90782C2211yescharacteristic
35C2×#90782C2211yescharacteristic
36C2×#90782C2211yescharacteristic
37#11745256—21no—
38#11745256—21no—
39#11745255—21no—
40#11745237C2211yescharacteristic
41#11745237C2211yescharacteristic
42#11745236C2211yescharacteristic
43C4×D116C2211yescharacteristic
44C4×D116C2211yescharacteristic
45C4×Dic58C2211yescharacteristic
46#11745183C2211yescharacteristic
47#11745180C2211yescharacteristic
48#11745180C2211yescharacteristic
49#11745158C2211yescharacteristic
50#11745157C2211yescharacteristic
51#11745157C2211yescharacteristic
52#11745155C2211yescharacteristic
53C4⋊#6597C2211yescharacteristic
54C4⋊#6597C2211yescharacteristic
55C4⋊#6597C2211yescharacteristic
56#11745151C2211yescharacteristic
57#11745151C2211yescharacteristic
58C4×#6597C2211yescharacteristic
59C2×Q8×C29D411yescharacteristic
60C2×Q8×C29C2311yescharacteristic
61C2×D4×C29—21no—
62C2×D4×C29—21no—
63C2×D4×C29C2311yescharacteristic
64C2×D4×C29C2311yescharacteristic
65C22×C4×C29—21no—
66C22×C4×C29—21no—
67C2×D116—21no—
68C2×D116—21no—
69C2×D116C2311yescharacteristic
70C2×D116C2311yescharacteristic
71C2×C4×D29—21no—
72C2×C4×D29—21no—
73C2×Dic58C2311yescharacteristic
74C4⋊C4×C29—21no—
75C4⋊C4×C29D411yescharacteristic
76C4⋊C4×C29D411yescharacteristic
77C4⋊C4×C29D411yescharacteristic
78C4⋊C4×C29C2311yescharacteristic
79C22⋊C4×C29—21no—
80C22⋊C4×C29—21no—
81C22⋊C4×C29—21no—
82C22⋊C4×C29—21no—
83C22⋊C4×C29—21no—
84C22⋊C4×C29—21no—
85C42×C29—21no—
86C42×C29C2311yescharacteristic
87C42×C29C2311yescharacteristic
88C42×C29C2311yescharacteristic
89#90785—41no—
90#90784—22no—
91#90784—41no—
92#90783—22no—
93#90783—41no—
94#90782—22no—
95#90782—41no—
96#90782—41no—
97#90782—41no—
98#90781—21no—
99#90781—21no—
100#90781—21no—
101#90781—21no—
102#90781—21no—
103#90781—21no—
104C4⋊Dic29C2311yescharacteristic
105#90779—21no—
106C4×Dic29—21no—
107C2×#6597C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110C2×#6597C2311yescharacteristic
111C23×C29—21no—
112C23×C29—21no—
113C22×D29—21no—
114C22×D29—21no—
115Q8×C29—21no—
116Q8×C29—21no—
117Q8×C29—41no—
118D4×C29—21no—
119D4×C29—21no—
120D4×C29—21no—
121D4×C29—21no—
122D4×C29—42no—
123D4×C29—81no—
124C2×C4×C29—21no—
125C2×C4×C29—21no—
126C2×C4×C29—81no—
127C2×C4×C29—81no—
128C2×C4×C29C2×D411yescharacteristic
129C2×C4×C29C2×D411yescharacteristic
130C2×C4×C29C2×D411yescharacteristic
131C2×C4×C29C2×D411yescharacteristic
132C2×C4×C29C2×D411yescharacteristic
133C2×C4×C29C2×D411yescharacteristic
134C2×C4×C29C2411yescharacteristic
135C2×Dic29—21no—
136C2×Dic29—21no—
137D116—21no—
138D116—21no—
139D116—21no—
140D116—21no—
141D116—42no—
142D116—81no—
143C4×D29—81no—
144C4×D29—81no—
145Dic58—21no—
146Dic58—21no—
147#6597—21no—
148#6597—21no—
149#6597—21no—
150#6597#4112yes—
151#3403—291nomaximal, Sylow
152C22×C29—41no—
153C22×C29—41no—
154C22×C29—41no—
155C22×C29—41no—
156C22×C29—41no—
157C22×C29—41no—
158C22×C29C22×D411yescharacteristic
159C2×D29—41no—
160C2×D29—41no—
161C2×D29—41no—
162C2×D29—41no—
163C2×D29—41no—
164C2×D29—41no—
165C4×C29—21no—
166C4×C29—21no—
167C4×C29—21no—
168C4×C29—21no—
169C4×C29—21no—
170C4×C29—21no—
171C4×C29—41no—
172C4×C29—41no—
173C4×C29C2×#4111yescharacteristic
174C4×C29H(5,𝔽2)11yescharacteristic
175Dic29—41no—
176Dic29—41no—
177#559—291no—
178#559D2911yescharacteristic, complemented
179#496—291no—
180#496—291no—
181#495—291no—
182#464—291no—
183#464—291no—
184#463—291no—
185#463—291no—
186#459—291no—
187#459—291no—
188#446—291no—
189#440—291no—
190#440—291no—
191C4×D8—291no—
192C2×C29—81no—
193C2×C29—81no—
194C2×C29#55011yescharacteristic
195C2×C29#57511yescharacteristic
196C2×C29#57611yescharacteristic
197D29—81no—
198D29—81no—
199C2×Q16—291no—
200C2×SD16—291no—
201C2×SD16—291no—
202C2×SD16—291no—
203C2×SD16—291no—
204C2×D8—291no—
205C2×D8—291no—
206C2×D8—291no—
207C2×D8—291no—
208#127—291no—
209#127C2×D2911yescharacteristic
210#124—21no—
211#124—291no—
212#124—291no—
213#124—581no—
214#124C2×D2911yescharacteristic
215#124C2×D2911yescharacteristic
216#123—21no—
217#123—21no—
218#123—581no—
219#123—581no—
220C4×Q8—291no—
221C4×Q8C2×D2911yescharacteristic
222C4×Q8C2×D2911yescharacteristic
223C4×D4—21no—
224C4×D4—291no—
225C4×D4—291no—
226C4×D4—581no—
227C4×D4C2×D2911yescharacteristic
228C4×D4C2×D2911yescharacteristic
229#107—291no—
230C4⋊C8—291no—
231C4⋊C8—291no—
232C4⋊C8—291no—
233#103—291no—
234#103—291no—
235#102—291no—
236#102—291no—
237#102—291no—
238#102—291no—
239#97—291no—
240#97—291no—
241C4×C8—291no—
242C29#340311yescharacteristic, complemented, Sylow
243C2×Q8—291no—
244C2×Q8C22⋊D2911yescharacteristic
245C2×Q8C22×D2911yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—291no—
249C2×D4—291no—
250C2×D4—581no—
251C2×D4—581no—
252C2×D4C22×D2911yescharacteristic
253C2×D4C22×D2911yescharacteristic
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—581no—
257C22×C4—581no—
258Q16—1161no—
259SD16—582no—
260SD16—582no—
261SD16—1161no—
262SD16—1161no—
263D8—582no—
264D8—1161no—
265D8—1161no—
266D8—1161no—
267C2×C8—291no—
268C2×C8—291no—
269C2×C8—291no—
270C2×C8—291no—
271C4⋊C4—21no—
272C4⋊C4—291no—
273C4⋊C4—581no—
274C4⋊C4C22⋊D2911yescharacteristic
275C4⋊C4C22⋊D2911yescharacteristic
276C4⋊C4C22⋊D2911yescharacteristic
277C4⋊C4C22×D2911yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—581no—
285C22⋊C4—581no—
286C22⋊C4—581no—
287C22⋊C4—581no—
288C22⋊C4—581no—
289C22⋊C4—581no—
290C42—21no—
291C42—581no—
292C42C22×D2911yescharacteristic
293C42C22×D2911yescharacteristic
294C42C22×D2911yescharacteristic
295C23—21no—
296C23—21no—
297C23—581no—
298C23—581no—
299Q8—21no—
300Q8—21no—
301Q8—41no—
302Q8—581no—
303Q8—581no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—581no—
311D4—581no—
312D4—581no—
313D4—581no—
314D4—1162no—
315D4—2321no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—581no—
321C2×C4—581no—
322C2×C4—2321no—
323C2×C4—2321no—
324C2×C4C2×C22⋊D2911yescharacteristic
325C2×C4C2×C22⋊D2911yescharacteristic
326C2×C4C2×C22⋊D2911yescharacteristic
327C2×C4C2×C22⋊D2911yescharacteristic
328C2×C4C2×C22⋊D2911yescharacteristic
329C2×C4C2×C22⋊D2911yescharacteristic
330C2×C4C23×D2911yescharacteristic
331C8—292no—
332C8—581no—
333C8—581no—
334C8—581no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—1161no—
342C22—1161no—
343C22—1161no—
344C22—1161no—
345C22—1161no—
346C22—1161no—
347C22C22×C22⋊D2911yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—1161no—
357C4—1161no—
358C4#41×D2911yescharacteristic
359C4#1174536411yescharacteristic
360C2—81no—
361C2—81no—
362C2—2321no—
363C2—2321no—
364C2#1427183211yescharacteristic
365C2#1427196111yescharacteristic
366C2#1427196611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#559C2
socleC22×C29C22×D4
hypercenter#559D29
hypocenterC29#3403
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #14271898C2semidirect
2. #14271553C2semidirect
3. #14271550C2semidirect
4. #14271545C2semidirect
5. #14271385C2semidirect
6. #14271382C2semidirect
7. #14271378C2semidirect
8. #14271375C2semidirect
9. #14271358C2semidirect
10. #14271355C2semidirect
11. #14271294C2semidirect
12. #14271263C2semidirect
13. #14271261C2semidirect
14. C4×#90782C2semidirect
15. C29×#559C2semidirect
178. #559D29semidirect
242. C29#3403semidirect

Maximal subgroups

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

subgroupindex
#142718982
#142715532
#142715502
#142715452
#142713852
#142713822
#142713782
#142713752
#142713582
#142713552
#142712942
#142712632
#142712612
C4×#907822
C29×#5592
#340329