Finite Group Databasebeta

← #16822207

Subgroups — #16822207

Order 3712.

516 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745250C211yesmaximal, characteristic
2C2×C4×Dic58C211yesmaximal, characteristic
3C2×#11745249C211yesmaximal, characteristic
4#14271067C211yesmaximal, characteristic
5#14271067C211yesmaximal, characteristic
6#14271050C211yesmaximal, characteristic
7#14271049C211yesmaximal, characteristic
8#14271048C211yesmaximal, characteristic
9#14271047C211yesmaximal, characteristic
10#14271046C211yesmaximal, characteristic
11#14271045C211yesmaximal, characteristic
12#14271044C211yesmaximal, characteristic
13#14271027C211yesmaximal, characteristic
14#14271008C211yesmaximal, characteristic
15C29×#387C211yesmaximal, characteristic
16C22×Dic58C2211yescharacteristic
17C22×Dic58C2211yescharacteristic
18C2×C4⋊C4×C29C2211yescharacteristic
19C2×C4⋊C4×C29C2211yescharacteristic
20C2×C42×C29C2211yescharacteristic
21C2×C4⋊Dic29C2211yescharacteristic
22C2×C4⋊Dic29C2211yescharacteristic
23C2×#90779C2211yescharacteristic
24C2×#90779C2211yescharacteristic
25C2×#90779C2211yescharacteristic
26C2×#90779C2211yescharacteristic
27C2×#90779C2211yescharacteristic
28C2×#90779C2211yescharacteristic
29C2×C4×Dic29C2211yescharacteristic
30C2×C4×Dic29C2211yescharacteristic
31C2×C4×Dic29C2211yescharacteristic
32C2×C4×Dic29C2211yescharacteristic
33C2×C4×Dic29C2211yescharacteristic
34C2×C4×Dic29C2211yescharacteristic
35#11745250C418yescomplemented
36#11745249—24no—
37C4×Dic58—24no—
38C29×#95C2211yescharacteristic
39C29×#95C2211yescharacteristic
40C29×#95C2211yescharacteristic
41C29×#95C2211yescharacteristic
42#11745179C2211yescharacteristic
43#11745179C2211yescharacteristic
44#11745179C2211yescharacteristic
45#11745179C2211yescharacteristic
46#11745179C2211yescharacteristic
47#11745179C2211yescharacteristic
48#11745179C2211yescharacteristic
49#11745179C2211yescharacteristic
50#11745179C2211yescharacteristic
51#11745179C2211yescharacteristic
52#11745179C2211yescharacteristic
53#11745179C2211yescharacteristic
54C22×C4×C29C2311yescharacteristic
55C22×C4×C29C2311yescharacteristic
56C22×C4×C29C2311yescharacteristic
57C22×C4×C29C2311yescharacteristic
58C22×C4×C29C2311yescharacteristic
59C22×C4×C29C2311yescharacteristic
60C22×C4×C29C2311yescharacteristic
61C22×Dic29C2311yescharacteristic
62C22×Dic29C2311yescharacteristic
63C22×Dic29C2311yescharacteristic
64C22×Dic29C2311yescharacteristic
65C22×Dic29C2311yescharacteristic
66C22×Dic29C2311yescharacteristic
67C22×Dic29C2311yescharacteristic
68C22×Dic29C2311yescharacteristic
69C2×Dic58—22no—
70C2×Dic58—22no—
71C2×Dic58—22no—
72C2×Dic58—22no—
73C2×Dic58C2×C414yes—
74C2×Dic58C2×C414yes—
75C4⋊C4×C29—22no—
76C4⋊C4×C29C2×C414yes—
77C42×C29—22no—
78C4⋊Dic29—22no—
79C4⋊Dic29C2×C414yes—
80#90779—22no—
81#90779—22no—
82#90779—22no—
83#90779—22no—
84#90779C2×C414yes—
85#90779C2×C414yes—
86C4×Dic29—22no—
87C4×Dic29—22no—
88C4×Dic29—22no—
89C4×Dic29—22no—
90C4×Dic29C2×C414yes—
91C4×Dic29D414yes—
92C23×C29C2411yescharacteristic
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×C29—21no—
110C2×C4×C29C22×C412yes—
111C2×C4×C29C22×C412yes—
112C2×C4×C29C22×C412yes—
113C2×C4×C29C2×D412yes—
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×Dic29—21no—
131C2×Dic29C22×C412yes—
132C2×Dic29C22×C412yes—
133C2×Dic29C22×C412yes—
134C2×Dic29C22×C412yes—
135C2×Dic29C2×D412yes—
136C2×Dic29C2×D412yes—
137C2×Dic29#4112yes—
138Dic58—28no—
139Dic58—28no—
140#2327—291nomaximal, Sylow
141C22×C29C23×C411yescharacteristic
142C22×C29C22×D411yescharacteristic
143C22×C29C2×#4111yescharacteristic
144C22×C292−1+411yescharacteristic
145C22×C292−1+411yescharacteristic
146C22×C292−1+411yescharacteristic
147C22×C292−1+411yescharacteristic
148C4×C29—22no—
149C4×C29—22no—
150C4×C29—22no—
151C4×C29—22no—
152C4×C29—41no—
153C4×C29—41no—
154C4×C29—41no—
155Dic29—22no—
156Dic29—22no—
157Dic29—22no—
158Dic29—22no—
159Dic29—41no—
160Dic29—41no—
161Dic29—41no—
162Dic29C4×D414yes—
163C2×C4⋊Q8—291no—
164C2×C4×Q8—291no—
165C2×C4×Q8—291no—
166#391—291no—
167#391—291no—
168#387—291no—
169#387—291no—
170#387—291no—
171#387—291no—
172#387—291no—
173#387—291no—
174#387—291no—
175#387D2911yescharacteristic
176#382—291no—
177#376—291no—
178C2×C29C2×C4×D411yescharacteristic
179C2×C29#51911yescharacteristic
180C2×C29#51911yescharacteristic
181C2×C29#53611yescharacteristic
182C2×C29#53611yescharacteristic
183C2×C29#54111yescharacteristic
184C2×C29#54111yescharacteristic
185C22×Q8—291no—
186C22×Q8—291no—
187C4⋊Q8—298no—
188C4×Q8—584no—
189C4×Q8—584no—
190C2×C4⋊C4—291no—
191C2×C4⋊C4—291no—
192C2×C4⋊C4—291no—
193C2×C4⋊C4—291no—
194C2×C4⋊C4—291no—
195C2×C4⋊C4—291no—
196C2×C4⋊C4—291no—
197C2×C4⋊C4—291no—
198C2×C4⋊C4C2×D2911yescharacteristic
199C2×C4⋊C4C2×D2911yescharacteristic
200C2×C42—291no—
201C2×C42—291no—
202C2×C42—291no—
203C2×C42—291no—
204C2×C42—291no—
205C2×C42—291no—
206C2×C42C2×D2911yescharacteristic
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#95—291no—
216#95—291no—
217#95—291no—
218#95—291no—
219#95C2×D2911yescharacteristic
220#95C2×D2911yescharacteristic
221#95C2×D2911yescharacteristic
222#95C2×D2911yescharacteristic
223C29#232711yescharacteristic, complemented, Sylow
224C2×Q8—294no—
225C2×Q8—294no—
226C2×Q8—582no—
227C2×Q8—582no—
228C2×Q8—582no—
229C2×Q8—582no—
230C22×C4—291no—
231C22×C4—291no—
232C22×C4—291no—
233C22×C4—291no—
234C22×C4—291no—
235C22×C4—291no—
236C22×C4—291no—
237C22×C4—291no—
238C22×C4C22×D2911yescharacteristic
239C22×C4C22×D2911yescharacteristic
240C22×C4C22×D2911yescharacteristic
241C22×C4C22×D2911yescharacteristic
242C22×C4C22×D2911yescharacteristic
243C22×C4C22×D2911yescharacteristic
244C22×C4C22×D2911yescharacteristic
245C4⋊C4—22no—
246C4⋊C4—294no—
247C4⋊C4—294no—
248C4⋊C4—294no—
249C4⋊C4—582no—
250C4⋊C4—582no—
251C4⋊C4—582no—
252C4⋊C4—582no—
253C4⋊C4—582no—
254C4⋊C4C4×D2914yes—
255C42—22no—
256C42—294no—
257C42—294no—
258C42—582no—
259C42—582no—
260C42—582no—
261C42—582no—
262C23C23×D2911yescharacteristic
263Q8—588no—
264Q8—588no—
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—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—292no—
283C2×C4—292no—
284C2×C4—292no—
285C2×C4—292no—
286C2×C4—292no—
287C2×C4—292no—
288C2×C4—292no—
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×C4—581no—
303C2×C4—581no—
304C2×C4—581no—
305C2×C4—581no—
306C2×C4C2×C4×D2912yes—
307C2×C4C2×C4×D2912yes—
308C2×C4C2×C4×D2912yes—
309C2×C4D4×D2912yes—
310C22C22×C4×D2911yescharacteristic
311C22C2×D4×D2911yescharacteristic
312C22#1174536211yescharacteristic
313C22#41×D2911yescharacteristic
314C22#1174536511yescharacteristic
315C22#1174536511yescharacteristic
316C22#1174536511yescharacteristic
317C4—22no—
318C4—22no—
319C4—22no—
320C4—22no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—294no—
325C4—582no—
326C4—582no—
327C4—582no—
328C4—582no—
329C4—1161no—
330C4—1161no—
331C4—1161no—
332C2C4×D4×D2911yescharacteristic
333C2#1427163911yescharacteristic
334C2#1427164011yescharacteristic
335C2#1427173511yescharacteristic
336C2#1427173611yescharacteristic
337C2#1427177011yescharacteristic
338C2#1427177211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D29
commutatorC22×C29C23×C4
FittingC29×#387C2
socle, prime radical, cosocleC23×C29C24
hypercenter#387D29
hypocenterC29#2327
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
35. #11745250C4semidirect
223. C29#2327semidirect

Maximal subgroups

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

subgroupindex
C2×#117452502
C2×C4×Dic582
C2×#117452492
#142710672
#142710502
#142710492
#142710482
#142710472
#142710462
#142710452
#142710442
#142710272
#142710082
C29×#3872
#232729