Finite Group Databasebeta

← #16822426

Subgroups — #16822426

Order 3712.

588 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745243C211yesmaximal, characteristic
2#14271054C211yesmaximal, characteristic, complemented
3#14271052C211yesmaximal, characteristic, complemented
4#14271047C211yesmaximal, characteristic, complemented
5#14271045C211yesmaximal, characteristic, complemented
6#14271042C211yesmaximal, characteristic
7#14271040C211yesmaximal, characteristic
8#14271030C211yesmaximal, characteristic, complemented
9#14271025C211yesmaximal, characteristic, complemented
10#14271021C211yesmaximal, characteristic, complemented
11C22⋊C4×Dic29C211yesmaximal, characteristic, complemented
12C4×#90781C211yesmaximal, characteristic, complemented
13#14271009C211yesmaximal, characteristic, complemented
14C2×#11745179C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C29C211yesmaximal, characteristic, complemented
16C23×C4×C29C2211yescharacteristic
17C22×C22⋊D29C2211yescharacteristic
18C23×Dic29C2211yescharacteristic
19C23×Dic29C2211yescharacteristic
20C22×C4×D29C2211yescharacteristic
21C2×C22⋊C4×C29C2211yescharacteristic
22C2×C22⋊C4×C29C2211yescharacteristic
23C2×C42×C29C2211yescharacteristic
24C2×C42×C29C2211yescharacteristic
25C2×C22⋊Dic29C2211yescharacteristic
26C2×#90781C2211yescharacteristic
27C2×#90781C2211yescharacteristic
28C2×#90781C2211yescharacteristic
29C2×#90781C2211yescharacteristic
30C2×#90781C2211yescharacteristic
31C2×#90779C2211yescharacteristic
32C2×#90779C2211yescharacteristic
33C2×#90779C2211yescharacteristic
34C2×C4×Dic29C2211yescharacteristic
35C2×C4×Dic29C2211yescharacteristic
36C2×C4×Dic29C2211yescharacteristic
37#11745243C418yescomplemented
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
53C23×D29C2311yescharacteristic
54C22×C4×C29—22no—
55C22×C4×C29—22no—
56C22×C4×C29—41no—
57C22×C4×C29C2311yescharacteristic
58C22×C4×C29C2311yescharacteristic
59C22×C4×C29C2311yescharacteristic
60C22×C4×C29C2311yescharacteristic
61C22×C4×C29C2311yescharacteristic
62C22×C4×C29C2311yescharacteristic
63C2×C22⋊D29—22no—
64C2×C22⋊D29—22no—
65C2×C22⋊D29C2×C414yes—
66C22×Dic29—22no—
67C22×Dic29—22no—
68C22×Dic29—41no—
69C22×Dic29—41no—
70C22×Dic29—41no—
71C22×Dic29C2×C414yes—
72C22×Dic29C2311yescharacteristic
73C22×Dic29C2311yescharacteristic
74C22×Dic29C2311yescharacteristic
75C22×Dic29C2311yescharacteristic
76C22×Dic29C2311yescharacteristic
77C22×Dic29C2311yescharacteristic
78C22×Dic29C2311yescharacteristic
79C2×C4×D29—41no—
80C2×C4×D29—41no—
81C2×C4×D29C2×C414yescomplemented
82C22⋊C4×C29—22no—
83C22⋊C4×C29C2×C414yes—
84C42×C29—22no—
85C42×C29—41no—
86C22⋊Dic29—22no—
87#90781—22no—
88#90781—22no—
89#90781—41no—
90#90781—41no—
91#90781C2×C414yescomplemented
92#90779—41no—
93#90779—41no—
94#90779C2×C414yescomplemented
95C4×Dic29—22no—
96C4×Dic29—41no—
97C4×Dic29C2×C414yescomplemented
98C23×C29—21no—
99C23×C29—21no—
100C23×C29—21no—
101C23×C29—21no—
102C23×C29C22×C412yes—
103C23×C29#4112yes—
104C23×C29#4112yes—
105C23×C29C2411yescharacteristic
106C22×D29—21no—
107C22×D29—21no—
108C22×D29—21no—
109C22×D29—21no—
110C22×D29—21no—
111C22×D29—21no—
112C22×D29C22×C412yes—
113C2×C4×C29—21no—
114C2×C4×C29—21no—
115C2×C4×C29—21no—
116C2×C4×C29—21no—
117C2×C4×C29—21no—
118C2×C4×C29—21no—
119C2×C4×C29—21no—
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—21no—
128C2×C4×C29—44no—
129C2×C4×C29C22×C412yes—
130C2×C4×C29C22×C412yes—
131C2×C4×C29#4112yes—
132C22⋊D29—28no—
133C2×Dic29—21no—
134C2×Dic29—21no—
135C2×Dic29—21no—
136C2×Dic29—21no—
137C2×Dic29—21no—
138C2×Dic29—21no—
139C2×Dic29—21no—
140C2×Dic29—21no—
141C2×Dic29—21no—
142C2×Dic29—21no—
143C2×Dic29—21no—
144C2×Dic29—21no—
145C2×Dic29—21no—
146C2×Dic29—21no—
147C2×Dic29—21no—
148C2×Dic29—21no—
149C2×Dic29—21no—
150C2×Dic29—44no—
151C2×Dic29—44no—
152C2×Dic29C22×C412yes—
153C2×Dic29C22×C412yes—
154C2×Dic29C22×C412yes—
155C2×Dic29#4112yes—
156C4×D29—44no—
157#2353—291nomaximal, Sylow
158C22×C29—22no—
159C22×C29—22no—
160C22×C29—22no—
161C22×C29—22no—
162C22×C29—22no—
163C22×C29—22no—
164C22×C29#11714yes—
165C22×C29C23×C411yescharacteristic
166C22×C29C2×#4111yescharacteristic
167C22×C29C2×#4111yescharacteristic
168C22×C29C2×#4111yescharacteristic
169C22×C29C2×#4111yescharacteristic
170C22×C29H(5,𝔽2)11yescharacteristic
171C22×C29H(5,𝔽2)11yescharacteristic
172C2×D29—22no—
173C2×D29—22no—
174C2×D29—22no—
175C2×D29—41no—
176C2×D29—41no—
177C2×D29—41no—
178C2×D29—41no—
179C4×C29—22no—
180C4×C29—22no—
181C4×C29—22no—
182C4×C29—41no—
183C4×C29—41no—
184C4×C29—41no—
185Dic29—22no—
186Dic29—22no—
187Dic29—22no—
188Dic29—22no—
189Dic29—41no—
190Dic29—41no—
191Dic29—41no—
192C2×C4×D4—291no—
193#388—291no—
194#388—291no—
195#387—291no—
196#387—291no—
197#386—291no—
198#386—291no—
199#383—291no—
200#381—291no—
201#380—291no—
202C4×C22⋊C4—291no—
203C4×C22⋊C4—291no—
204C4×C22⋊C4D2911yescharacteristic, complemented
205#376—291no—
206C2×#95—291no—
207C2×C29—24no—
208C2×C29C2×#11711yescharacteristic
209C2×C29C4×#4111yescharacteristic
210C2×C29#51811yescharacteristic
211C2×C29#55111yescharacteristic
212C2×C29#55111yescharacteristic
213C2×C29#55311yescharacteristic
214C2×C29#55311yescharacteristic
215D29—42no—
216C22×D4—291no—
217C23×C4—291no—
218C23×C4—291no—
219C23×C4—291no—
220C23×C4C2×D2911yescharacteristic
221C4×D4—298no—
222C2×C4⋊C4—291no—
223C2×C4⋊C4—291no—
224C2×C4⋊C4—291no—
225C2×C22⋊C4—291no—
226C2×C22⋊C4—291no—
227C2×C22⋊C4—291no—
228C2×C22⋊C4—291no—
229C2×C22⋊C4—291no—
230C2×C22⋊C4—291no—
231C2×C22⋊C4C2×D2911yescharacteristic
232C2×C22⋊C4C2×D2911yescharacteristic
233C2×C42—291no—
234C2×C42—291no—
235C2×C42—291no—
236C2×C42C2×D2911yescharacteristic
237C2×C42C2×D2911yescharacteristic
238#95—291no—
239#95—291no—
240#95—291no—
241#95—291no—
242#95—291no—
243#95—291no—
244#95—291no—
245#95—291no—
246#95—291no—
247#95—291no—
248#95—291no—
249#95—291no—
250#95C2×D2911yescharacteristic
251#95C2×D2911yescharacteristic
252C29#235311yescharacteristic, complemented, Sylow
253C24—291no—
254C24C22×D2911yescharacteristic
255C2×D4—294no—
256C2×D4—582no—
257C2×D4—582no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—41no—
261C22×C4—291no—
262C22×C4—291no—
263C22×C4—291no—
264C22×C4—291no—
265C22×C4—294no—
266C22×C4—294no—
267C22×C4—291no—
268C22×C4—291no—
269C22×C4—291no—
270C22×C4—582no—
271C22×C4—582no—
272C22×C4—1161no—
273C22×C4—1161no—
274C22×C4—1161no—
275C22×C4—1161no—
276C22×C4—1161no—
277C22×C4C22×D2911yescharacteristic
278C22×C4C22×D2911yescharacteristic
279C22×C4C22×D2911yescharacteristic
280C22×C4C22×D2911yescharacteristic
281C22×C4C22×D2911yescharacteristic
282C22×C4C22×D2911yescharacteristic
283C4⋊C4—294no—
284C4⋊C4—1161no—
285C4⋊C4—1161no—
286C22⋊C4—22no—
287C22⋊C4—294no—
288C22⋊C4—582no—
289C22⋊C4—582no—
290C22⋊C4—582no—
291C22⋊C4—1161no—
292C22⋊C4—1161no—
293C22⋊C4C4×D2914yes—
294C42—22no—
295C42—41no—
296C42—294no—
297C42—582no—
298C42—1161no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—292no—
304C23—581no—
305C23—581no—
306C23—581no—
307C23—581no—
308C23—581no—
309C23—581no—
310C23C2×C4×D2912yes—
311C23#9080512yes—
312C23#9080512yes—
313C23C23×D2911yescharacteristic
314D4—588no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—44no—
331C2×C4—292no—
332C2×C4—292no—
333C2×C4—292no—
334C2×C4—292no—
335C2×C4—581no—
336C2×C4—581no—
337C2×C4—581no—
338C2×C4—581no—
339C2×C4—581no—
340C2×C4—581no—
341C2×C4—581no—
342C2×C4—581no—
343C2×C4—581no—
344C2×C4—581no—
345C2×C4—581no—
346C2×C4—581no—
347C2×C4—581no—
348C2×C4—581no—
349C2×C4—581no—
350C2×C4—581no—
351C2×C4—581no—
352C2×C4—1164no—
353C2×C4—1164no—
354C2×C4—1164no—
355C2×C4C2×C4×D2912yes—
356C2×C4C2×C4×D2912yes—
357C2×C4#9080712yes—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—582no—
365C22—582no—
366C22—582no—
367C22—1161no—
368C22—1161no—
369C22—1161no—
370C22—1161no—
371C22#1174523414yes—
372C22C22×C4×D2911yescharacteristic
373C22C2×#9080511yescharacteristic
374C22C2×#9080511yescharacteristic
375C22C2×#9080711yescharacteristic
376C22#1174535911yescharacteristic
377C22#41×D2911yescharacteristic
378C22#1174536411yescharacteristic
379C4—22no—
380C4—22no—
381C4—22no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—582no—
386C4—582no—
387C4—582no—
388C4—582no—
389C4—1161no—
390C4—1161no—
391C4—1161no—
392C2—24no—
393C2—1162no—
394C2C2×#1174523411yescharacteristic
395C2C4×#9080711yescharacteristic
396C2#1427163511yescharacteristic
397C2#1427183711yescharacteristic
398C2#1427183911yescharacteristic
399C2#1427185911yescharacteristic
400C2#1427186211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D29
commutatorC22×C29C23×C4
FittingC4×C22⋊C4×C29C2
socle, cosocleC23×C29C24
prime radicalC22×C22⋊D29C22
hypercenterC4×C22⋊C4D29
hypocenterC29#2353
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #14271054C2semidirect
3. #14271052C2semidirect
4. #14271047C2semidirect
5. #14271045C2semidirect
8. #14271030C2semidirect
9. #14271025C2semidirect
10. #14271021C2semidirect
11. C22⋊C4×Dic29C2semidirect
12. C4×#90781C2semidirect
13. #14271009C2semidirect
14. C2×#11745179C2semidirect
15. C4×C22⋊C4×C29C2semidirect
37. #11745243C4semidirect
81. C2×C4×D29C2×C4semidirect
91. #90781C2×C4semidirect
94. #90779C2×C4semidirect
97. C4×Dic29C2×C4semidirect
204. C4×C22⋊C4D29semidirect
252. C29#2353semidirect

Maximal subgroups

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

subgroupindex
C2×#117452432
#142710542
#142710522
#142710472
#142710452
#142710422
#142710402
#142710302
#142710252
#142710212
C22⋊C4×Dic292
C4×#907812
#142710092
C2×#117451792
C4×C22⋊C4×C292
#235329