Finite Group Databasebeta

← #16822659

Subgroups — #16822659

Order 3712.

464 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745240C211yesmaximal, characteristic
2#14271069C211yesmaximal, characteristic, complemented
3#14271067C211yesmaximal, characteristic, complemented
4#14271060C211yesmaximal, characteristic, complemented
5#14271059C211yesmaximal, characteristic, complemented
6#14271057C211yesmaximal, characteristic
7#14271057C211yesmaximal, characteristic
8#14271056C211yesmaximal, characteristic
9#14271048C211yesmaximal, characteristic, complemented
10#14271047C211yesmaximal, characteristic, complemented
11#14271045C211yesmaximal, characteristic, complemented
12#14271044C211yesmaximal, characteristic, complemented
13#14271024C211yesmaximal, characteristic
14#14271021C211yesmaximal, characteristic
15C29×#388C211yesmaximal, characteristic
16C23×Dic29C2211yescharacteristic
17C22×Dic58C2211yescharacteristic
18C2×C4⋊C4×C29C2211yescharacteristic
19C2×C22⋊C4×C29C2211yescharacteristic
20C2×C22⋊C4×C29C2211yescharacteristic
21C2×C22⋊C4×C29C2211yescharacteristic
22C2×C42×C29C2211yescharacteristic
23C2×C22⋊Dic29C2211yescharacteristic
24C2×C22⋊Dic29C2211yescharacteristic
25C2×C22⋊Dic29C2211yescharacteristic
26C2×C4⋊Dic29C2211yescharacteristic
27C2×C4⋊Dic29C2211yescharacteristic
28C2×#90779C2211yescharacteristic
29C2×#90779C2211yescharacteristic
30C2×#90779C2211yescharacteristic
31C2×#90779C2211yescharacteristic
32C2×#90779C2211yescharacteristic
33C2×#90779C2211yescharacteristic
34C2×C4×Dic29C2211yescharacteristic
35C2×C4×Dic29C2211yescharacteristic
36C2×C4×Dic29C2211yescharacteristic
37#11745240C418yescomplemented
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
52C24×C29C2311yescharacteristic
53C22×C4×C29C2311yescharacteristic
54C22×C4×C29C2311yescharacteristic
55C22×C4×C29C2311yescharacteristic
56C22×C4×C29C2311yescharacteristic
57C22×C4×C29C2311yescharacteristic
58C22×C4×C29C2311yescharacteristic
59C22×Dic29—41no—
60C22×Dic29—41no—
61C22×Dic29C2×C414yes—
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—
74C22⋊C4×C29—41no—
75C22⋊C4×C29—41no—
76C22⋊C4×C29C2×C414yes—
77C42×C29—41no—
78C22⋊Dic29—41no—
79C22⋊Dic29—41no—
80C22⋊Dic29C2×C414yes—
81C4⋊Dic29—41no—
82C4⋊Dic29C2×C414yes—
83#90779—41no—
84#90779—41no—
85#90779—41no—
86#90779—41no—
87#90779C2×C414yes—
88#90779C2×C414yes—
89C4×Dic29—41no—
90C4×Dic29—41no—
91C4×Dic29—41no—
92C23×C29—21no—
93C23×C29—21no—
94C23×C29—21no—
95C23×C29—21no—
96C23×C29—21no—
97C23×C29—21no—
98C23×C29C22×C412yes—
99C23×C29C2411yescharacteristic
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×C29—21no—
111C2×C4×C29—21no—
112C2×C4×C29—21no—
113C2×C4×C29—21no—
114C2×C4×C29—21no—
115C2×C4×C29—21no—
116C2×C4×C29C22×C412yes—
117C2×C4×C29C22×C412yes—
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×Dic29—21no—
132C2×Dic29—21no—
133C2×Dic29—21no—
134C2×Dic29—21no—
135C2×Dic29—21no—
136C2×Dic29—21no—
137C2×Dic29—21no—
138C2×Dic29—44no—
139C2×Dic29C22×C412yes—
140C2×Dic29C22×C412yes—
141C2×Dic29C22×C412yes—
142C2×Dic29C22×C412yes—
143Dic58—44no—
144#2378—291nomaximal, Sylow
145C22×C29—22no—
146C22×C29—22no—
147C22×C29—22no—
148C22×C29—41no—
149C22×C29—41no—
150C22×C29—41no—
151C22×C29—41no—
152C22×C29C23×C411yescharacteristic
153C22×C29H(5,𝔽2)11yescharacteristic
154C22×C29H(5,𝔽2)11yescharacteristic
155C22×C29H(5,𝔽2)11yescharacteristic
156C22×C292−1+411yescharacteristic
157C22×C292−1+411yescharacteristic
158C22×C292−1+411yescharacteristic
159C4×C29—22no—
160C4×C29—22no—
161C4×C29—41no—
162C4×C29—41no—
163C4×C29—41no—
164C4×C29—41no—
165Dic29—22no—
166Dic29—22no—
167Dic29—22no—
168Dic29—22no—
169Dic29—41no—
170Dic29—41no—
171Dic29—41no—
172Dic29—41no—
173C2×C22⋊Q8—291no—
174#391—291no—
175#391—291no—
176#389—291no—
177#389—291no—
178#388—291no—
179#388—291no—
180#388—291no—
181#388D2911yescharacteristic
182#387—291no—
183#387—291no—
184#387—291no—
185#387—291no—
186#381—291no—
187#380—291no—
188C2×C29—42no—
189C2×C29#51811yescharacteristic
190C2×C29#51911yescharacteristic
191C2×C29#52011yescharacteristic
192C2×C29#56211yescharacteristic
193C2×C29#56211yescharacteristic
194C2×C29#56311yescharacteristic
195C2×C29#56311yescharacteristic
196C22×Q8—291no—
197C23×C4—291no—
198C22⋊Q8—298no—
199C2×C4⋊C4—291no—
200C2×C4⋊C4—291no—
201C2×C4⋊C4—291no—
202C2×C4⋊C4—291no—
203C2×C4⋊C4—291no—
204C2×C4⋊C4—291no—
205C2×C4⋊C4—291no—
206C2×C4⋊C4—291no—
207C2×C4⋊C4C2×D2911yescharacteristic
208C2×C22⋊C4—291no—
209C2×C22⋊C4—291no—
210C2×C22⋊C4—291no—
211C2×C22⋊C4C2×D2911yescharacteristic
212C2×C22⋊C4C2×D2911yescharacteristic
213C2×C22⋊C4C2×D2911yescharacteristic
214C2×C42—291no—
215C2×C42—291no—
216C2×C42—291no—
217C2×C42C2×D2911yescharacteristic
218#95—291no—
219#95—291no—
220#95—291no—
221#95—291no—
222#95—291no—
223#95—291no—
224#95—291no—
225#95—291no—
226#95—291no—
227#95—291no—
228#95—291no—
229#95—291no—
230#95C2×D2911yescharacteristic
231#95C2×D2911yescharacteristic
232C29#237811yescharacteristic, complemented, Sylow
233C24C22×D2911yescharacteristic
234C2×Q8—294no—
235C2×Q8—1161no—
236C2×Q8—1161no—
237C22×C4—291no—
238C22×C4—291no—
239C22×C4—291no—
240C22×C4—291no—
241C22×C4—294no—
242C22×C4—291no—
243C22×C4—291no—
244C22×C4—291no—
245C22×C4—291no—
246C22×C4—1161no—
247C22×C4—1161no—
248C22×C4C22×D2911yescharacteristic
249C22×C4C22×D2911yescharacteristic
250C22×C4C22×D2911yescharacteristic
251C22×C4C22×D2911yescharacteristic
252C22×C4C22×D2911yescharacteristic
253C22×C4C22×D2911yescharacteristic
254C4⋊C4—41no—
255C4⋊C4—294no—
256C4⋊C4—294no—
257C4⋊C4—294no—
258C4⋊C4—1161no—
259C4⋊C4—1161no—
260C4⋊C4—1161no—
261C4⋊C4—1161no—
262C4⋊C4—1161no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—294no—
266C22⋊C4—1161no—
267C22⋊C4—1161no—
268C22⋊C4C4×D2914yes—
269C42—41no—
270C42—1161no—
271C42—1161no—
272C42—1161no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23C2×C4×D2912yes—
280C23C23×D2911yescharacteristic
281Q8—1164no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—292no—
299C2×C4—292no—
300C2×C4—292no—
301C2×C4—292no—
302C2×C4—581no—
303C2×C4—581no—
304C2×C4—581no—
305C2×C4—581no—
306C2×C4—581no—
307C2×C4—581no—
308C2×C4—581no—
309C2×C4—581no—
310C2×C4—581no—
311C2×C4—581no—
312C2×C4—581no—
313C2×C4—581no—
314C2×C4—581no—
315C2×C4—581no—
316C2×C4—581no—
317C2×C4—581no—
318C2×C4—581no—
319C2×C4—581no—
320C2×C4—581no—
321C2×C4—581no—
322C2×C4—1164no—
323C2×C4C2×C4×D2912yes—
324C2×C4C2×C4×D2912yes—
325C22—22no—
326C22—22no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22C22×C4×D2911yescharacteristic
333C22#1174535911yescharacteristic
334C22#1174535911yescharacteristic
335C22#1174536411yescharacteristic
336C22#1174536511yescharacteristic
337C22#1174536511yescharacteristic
338C22#1174536511yescharacteristic
339C4—22no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—582no—
346C4—582no—
347C4—582no—
348C4—582no—
349C4—1161no—
350C4—1161no—
351C4—1161no—
352C4—1161no—
353C2—42no—
354C2#1427163511yescharacteristic
355C2#1427164011yescharacteristic
356C2#1427164211yescharacteristic
357C2#1427190711yescharacteristic
358C2#1427190811yescharacteristic
359C2#1427191511yescharacteristic
360C2#1427191611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D29
commutatorC22×C29C23×C4
FittingC29×#388C2
socle, cosocleC23×C29C24
prime radicalC24×C29C23
hypercenter#388D29
hypocenterC29#2378
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #14271069C2semidirect
3. #14271067C2semidirect
4. #14271060C2semidirect
5. #14271059C2semidirect
9. #14271048C2semidirect
10. #14271047C2semidirect
11. #14271045C2semidirect
12. #14271044C2semidirect
37. #11745240C4semidirect
232. C29#2378semidirect

Maximal subgroups

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

subgroupindex
C2×#117452402
#142710692
#142710672
#142710602
#142710592
#142710572
#142710562
#142710482
#142710472
#142710452
#142710442
#142710242
#142710212
C29×#3882
#237829