Finite Group Databasebeta

← #16822235

Subgroups — #16822235

Order 3712.

460 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745306C211yesmaximal, characteristic
2#14271070C211yesmaximal, characteristic
3#14271067C211yesmaximal, characteristic
4#14271067C211yesmaximal, characteristic
5#14271060C211yesmaximal, characteristic
6#14271058C211yesmaximal, characteristic
7#14271050C211yesmaximal, characteristic
8#14271047C211yesmaximal, characteristic
9#14271045C211yesmaximal, characteristic
10#14271044C211yesmaximal, characteristic
11#14271027C211yesmaximal, characteristic
12C4×#90779C211yesmaximal, characteristic
13#14271014C211yesmaximal, characteristic
14#14271008C211yesmaximal, characteristic
15C29×#391C211yesmaximal, characteristic
16C22×Q8×C29C2211yescharacteristic
17C22×Dic58C2211yescharacteristic
18C2×C4⋊C4×C29C2211yescharacteristic
19C2×C42×C29C2211yescharacteristic
20#11745306C418yescomplemented
21C2×C4⋊Dic29C2211yescharacteristic
22C2×#90779C2211yescharacteristic
23C2×#90779C2211yescharacteristic
24C2×#90779C2211yescharacteristic
25C2×#90779C2211yescharacteristic
26C2×#90779C2211yescharacteristic
27C2×#90779C2211yescharacteristic
28C2×#90779C2211yescharacteristic
29C2×#90779C2211yescharacteristic
30C2×C4×Dic29C2211yescharacteristic
31C2×C4×Dic29C2211yescharacteristic
32C2×C4×Dic29C2211yescharacteristic
33C2×C4×Dic29C2211yescharacteristic
34C2×C4×Dic29C2211yescharacteristic
35C2×C4×Dic29C2211yescharacteristic
36C29×#95C2211yescharacteristic
37C29×#95C2211yescharacteristic
38C29×#95C2211yescharacteristic
39C29×#95C2211yescharacteristic
40#11745179C2211yescharacteristic
41#11745179C2211yescharacteristic
42#11745179C2211yescharacteristic
43#11745179C2211yescharacteristic
44#11745179C2211yescharacteristic
45#11745179C2211yescharacteristic
46#11745179C2211yescharacteristic
47#11745179C2211yescharacteristic
48#11745179C2211yescharacteristic
49#11745179C2211yescharacteristic
50#11745179C2211yescharacteristic
51#11745179C2211yescharacteristic
52C2×Q8×C29—41no—
53C2×Q8×C29—41no—
54C2×Q8×C29C2×C414yes—
55C22×C4×C29C2311yescharacteristic
56C22×C4×C29C2311yescharacteristic
57C22×C4×C29C2311yescharacteristic
58C22×C4×C29C2311yescharacteristic
59C22×C4×C29C2311yescharacteristic
60C22×C4×C29C2311yescharacteristic
61C22×C4×C29C2311yescharacteristic
62C22×Dic29C2311yescharacteristic
63C22×Dic29C2311yescharacteristic
64C22×Dic29C2311yescharacteristic
65C22×Dic29C2311yescharacteristic
66C22×Dic29C2311yescharacteristic
67C22×Dic29C2311yescharacteristic
68C22×Dic29C2311yescharacteristic
69C22×Dic29C2311yescharacteristic
70C2×Dic58—41no—
71C2×Dic58—41no—
72C2×Dic58C2×C414yes—
73C4⋊C4×C29—41no—
74C42×C29—41no—
75C4⋊Dic29—41no—
76#90779—22no—
77#90779—22no—
78#90779—41no—
79#90779—41no—
80#90779C2×C414yes—
81#90779C2×C414yes—
82#90779C2×C414yes—
83#90779C2×C414yes—
84C4×Dic29—22no—
85C4×Dic29—41no—
86C4×Dic29—41no—
87C4×Dic29—41no—
88C4×Dic29C2×C414yes—
89C4×Dic29Q814yescomplemented
90C23×C29C2411yescharacteristic
91Q8×C29—44no—
92C2×C4×C29—21no—
93C2×C4×C29—21no—
94C2×C4×C29—21no—
95C2×C4×C29—21no—
96C2×C4×C29—21no—
97C2×C4×C29—21no—
98C2×C4×C29—21no—
99C2×C4×C29—21no—
100C2×C4×C29—21no—
101C2×C4×C29—21no—
102C2×C4×C29—21no—
103C2×C4×C29—21no—
104C2×C4×C29—21no—
105C2×C4×C29—21no—
106C2×C4×C29—21no—
107C2×C4×C29—21no—
108C2×C4×C29—21no—
109C2×C4×C29C22×C412yes—
110C2×C4×C29C22×C412yes—
111C2×C4×C29C22×C412yes—
112C2×C4×C29C2×Q812yes—
113C2×Dic29—21no—
114C2×Dic29—21no—
115C2×Dic29—21no—
116C2×Dic29—21no—
117C2×Dic29—21no—
118C2×Dic29—21no—
119C2×Dic29—21no—
120C2×Dic29—21no—
121C2×Dic29—21no—
122C2×Dic29—21no—
123C2×Dic29—21no—
124C2×Dic29—21no—
125C2×Dic29—21no—
126C2×Dic29—21no—
127C2×Dic29—21no—
128C2×Dic29—21no—
129C2×Dic29—21no—
130C2×Dic29C22×C412yes—
131C2×Dic29C22×C412yes—
132C2×Dic29C22×C412yes—
133C2×Dic29C22×C412yes—
134C2×Dic29C2×Q812yes—
135C2×Dic29C2×Q812yes—
136C2×Dic29#4112yes—
137Dic58—44no—
138#2331—291nomaximal, Sylow
139C22×C29C23×C411yescharacteristic
140C22×C29C22×Q811yescharacteristic
141C22×C29C2×#4111yescharacteristic
142C22×C29H(5,𝔽2)11yescharacteristic
143C22×C29H(5,𝔽2)11yescharacteristic
144C22×C292−1+411yescharacteristic
145C22×C292−1+411yescharacteristic
146C4×C29—22no—
147C4×C29—22no—
148C4×C29—22no—
149C4×C29—22no—
150C4×C29—41no—
151C4×C29—41no—
152C4×C29—41no—
153Dic29—22no—
154Dic29—22no—
155Dic29—22no—
156Dic29—22no—
157Dic29—41no—
158Dic29—41no—
159Dic29—41no—
160Dic29C4×Q814yes—
161C2×C4⋊Q8—291no—
162#391—291no—
163#391—291no—
164#391—291no—
165#391D2911yescharacteristic
166#389—291no—
167#389—291no—
168#387—291no—
169#387—291no—
170#387—291no—
171#387—291no—
172#382—291no—
173C4×C4⋊C4—291no—
174C4×C4⋊C4—291no—
175#376—291no—
176C2×C29C2×C4×Q811yescharacteristic
177C2×C29#51811yescharacteristic
178C2×C29#51911yescharacteristic
179C2×C29#54211yescharacteristic
180C2×C29#54211yescharacteristic
181C2×C29#54411yescharacteristic
182C2×C29#54411yescharacteristic
183C22×Q8—291no—
184C22×Q8C2×D2911yescharacteristic
185C4⋊Q8—298no—
186C2×C4⋊C4—291no—
187C2×C4⋊C4—291no—
188C2×C4⋊C4—291no—
189C2×C4⋊C4—291no—
190C2×C4⋊C4—291no—
191C2×C4⋊C4—291no—
192C2×C4⋊C4—291no—
193C2×C4⋊C4—291no—
194C2×C4⋊C4—291no—
195C2×C4⋊C4C2×D2911yescharacteristic
196C2×C42—291no—
197C2×C42—291no—
198C2×C42—291no—
199C2×C42—291no—
200C2×C42—291no—
201C2×C42—291no—
202C2×C42C2×D2911yescharacteristic
203#95—291no—
204#95—291no—
205#95—291no—
206#95—291no—
207#95—291no—
208#95—291no—
209#95—291no—
210#95—291no—
211#95—291no—
212#95—291no—
213#95—291no—
214#95—291no—
215#95C2×D2911yescharacteristic
216#95C2×D2911yescharacteristic
217#95C2×D2911yescharacteristic
218#95C2×D2911yescharacteristic
219C29#233111yescharacteristic, complemented, Sylow
220C2×Q8—41no—
221C2×Q8—41no—
222C2×Q8—294no—
223C2×Q8—1161no—
224C2×Q8—1161no—
225C2×Q8C4×D2914yes—
226C22×C4—291no—
227C22×C4—291no—
228C22×C4—291no—
229C22×C4—291no—
230C22×C4—291no—
231C22×C4—291no—
232C22×C4—291no—
233C22×C4—291no—
234C22×C4C22×D2911yescharacteristic
235C22×C4C22×D2911yescharacteristic
236C22×C4C22×D2911yescharacteristic
237C22×C4C22×D2911yescharacteristic
238C22×C4C22×D2911yescharacteristic
239C22×C4C22×D2911yescharacteristic
240C22×C4C22×D2911yescharacteristic
241C4⋊C4—41no—
242C4⋊C4—294no—
243C4⋊C4—294no—
244C4⋊C4—294no—
245C4⋊C4—294no—
246C4⋊C4—582no—
247C4⋊C4—582no—
248C4⋊C4—1161no—
249C4⋊C4—1161no—
250C4⋊C4—1161no—
251C42—41no—
252C42—294no—
253C42—294no—
254C42—582no—
255C42—1161no—
256C42—1161no—
257C42—1161no—
258C23C23×D2911yescharacteristic
259Q8—44no—
260Q8—1164no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—292no—
279C2×C4—292no—
280C2×C4—292no—
281C2×C4—292no—
282C2×C4—292no—
283C2×C4—292no—
284C2×C4—292no—
285C2×C4—581no—
286C2×C4—581no—
287C2×C4—581no—
288C2×C4—581no—
289C2×C4—581no—
290C2×C4—581no—
291C2×C4—581no—
292C2×C4—581no—
293C2×C4—581no—
294C2×C4—581no—
295C2×C4—581no—
296C2×C4—581no—
297C2×C4—581no—
298C2×C4—581no—
299C2×C4—581no—
300C2×C4—581no—
301C2×C4—581no—
302C2×C4C2×C4×D2912yes—
303C2×C4C2×C4×D2912yes—
304C2×C4C2×C4×D2912yes—
305C2×C4Q8×D2912yes—
306C22C22×C4×D2911yescharacteristic
307C22#1174535911yescharacteristic
308C22#1174535911yescharacteristic
309C22C2×Q8×D2911yescharacteristic
310C22#1174536211yescharacteristic
311C22#41×D2911yescharacteristic
312C22#1174536511yescharacteristic
313C4—22no—
314C4—22no—
315C4—22no—
316C4—22no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—294no—
321C4—582no—
322C4—582no—
323C4—582no—
324C4—582no—
325C4—1161no—
326C4—1161no—
327C4—1161no—
328C2C4×Q8×D2911yescharacteristic
329C2#1427163611yescharacteristic
330C2#1427163911yescharacteristic
331C2#1427177711yescharacteristic
332C2#1427178311yescharacteristic
333C2#1427179011yescharacteristic
334C2#1427179211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D29
commutatorC22×C29C23×C4
FittingC29×#391C2
socle, prime radical, cosocleC23×C29C24
hypercenter#391D29
hypocenterC29#2331
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
20. #11745306C4semidirect
89. C4×Dic29Q8semidirect
219. C29#2331semidirect

Maximal subgroups

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

subgroupindex
C2×#117453062
#142710702
#142710672
#142710602
#142710582
#142710502
#142710472
#142710452
#142710442
#142710272
C4×#907792
#142710142
#142710082
C29×#3912
#233129