Finite Group Databasebeta

← #16829043

Subgroups — #16829043

Order 3712.

472 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745277C211yesmaximal, characteristic, complemented
2C2×#11745274C211yesmaximal, characteristic
3#14271733C211yesmaximal, characteristic, complemented
4#14271642C211yesmaximal, characteristic, complemented
5#14271384C211yesmaximal, characteristic, complemented
6#14271382C211yesmaximal, characteristic, complemented
7#14271376C211yesmaximal, characteristic, complemented
8#14271374C211yesmaximal, characteristic, complemented
9#14271372C211yesmaximal, characteristic, complemented
10#14271368C211yesmaximal, characteristic, complemented
11#14271366C211yesmaximal, characteristic, complemented
12#14271188C211yesmaximal, characteristic, complemented
13#14271161C211yesmaximal, characteristic, complemented
14#103×D29C211yesmaximal, characteristic, complemented
15C29×#463C211yesmaximal, characteristic, complemented
16C2×Q8×D29C2211yescharacteristic
17C2×#90807C2211yescharacteristic
18C2×#90807C2211yescharacteristic
19C2×SD16×C29C2211yescharacteristic
20C2×D8×C29C2211yescharacteristic
21C29×#124C2211yescharacteristic
22C4×D4×C29C2211yescharacteristic
23#11745306C2211yescharacteristic
24C2×#90785C2211yescharacteristic
25#11745298C2211yescharacteristic
26D4×Dic29C2211yescharacteristic
27C2×#90783C2211yescharacteristic
28C2×#90783C2211yescharacteristic
29C2×#90783C2211yescharacteristic
30C4×C22⋊D29—21no—
31C2×#90779—21no—
32#11745277—24no—
33#11745274—24no—
34C2×Dic116C2211yescharacteristic
35C2×Dic116C2211yescharacteristic
36C2×#90772C2211yescharacteristic
37C2×C8×D29C2211yescharacteristic
38C4⋊C4×D29C2211yescharacteristic
39#11745249C2211yescharacteristic
40#11745245—21no—
41#11745245—21no—
42#11745243—21no—
43#11745240—21no—
44#11745240—21no—
45#11745239—21no—
46#11745234C2211yescharacteristic
47#11745231C2211yescharacteristic
48C4×Dic58C2211yescharacteristic
49C29×C4⋊C8C2211yescharacteristic
50C29×#103C2211yescharacteristic
51C29×#102C2211yescharacteristic
52#11745183C2211yescharacteristic
53#11745180C2211yescharacteristic
54#11745164C2211yescharacteristic
55#11745164C2211yescharacteristic
56#11745162C2211yescharacteristic
57#11745162C2211yescharacteristic
58#11745158C2211yescharacteristic
59#11745158C2211yescharacteristic
60C4⋊#6597C2211yescharacteristic
61C2×Q8×C29C2311yescharacteristic
62C2×D4×C29C2311yescharacteristic
63C2×D4×C29C2311yescharacteristic
64C22×C4×C29—21no—
65C2×C22⋊D29—21no—
66C2×C22⋊D29—21no—
67C22×Dic29—21no—
68C22×Dic29—21no—
69C22×Dic29—21no—
70Q8×D29—22no—
71Q8×D29—22no—
72#90807—22no—
73#90807—22no—
74#90807—22no—
75#90807D414yes—
76C2×C4×D29—21no—
77C2×C4×D29—21no—
78C2×C4×D29C2311yescharacteristic
79C2×Dic58—21no—
80C2×Dic58C2311yescharacteristic
81C2×Dic58C2311yescharacteristic
82C2×Dic58C2311yescharacteristic
83SD16×C29—22no—
84D8×C29—22no—
85C2×C8×C29C2311yescharacteristic
86C2×C8×C29C2311yescharacteristic
87C4⋊C4×C29C2311yescharacteristic
88C22⋊C4×C29—21no—
89C22⋊C4×C29—21no—
90C22⋊C4×C29—21no—
91C42×C29C2311yescharacteristic
92C22⋊Dic29—21no—
93C22⋊Dic29—21no—
94C22⋊Dic29—21no—
95#90785—22no—
96#90783—22no—
97#90783—22no—
98#90783—22no—
99#90781D411yescharacteristic
100#90781D411yescharacteristic
101C4⋊Dic29—21no—
102C4⋊Dic29—21no—
103C4⋊Dic29C2311yescharacteristic
104#90779—21no—
105#90779—21no—
106#90779—21no—
107#90779—21no—
108#90779—21no—
109#90779D411yescharacteristic
110#90779D411yescharacteristic
111C4×Dic29—21no—
112C4×Dic29—21no—
113C4×Dic29C2311yescharacteristic
114C2×#6597C2311yescharacteristic
115C2×#6597C2311yescharacteristic
116Dic116—22no—
117Dic116—22no—
118#90772—22no—
119C8×D29—22no—
120C23×C29—21no—
121C23×C29—21no—
122C22×D29C2×D411yescharacteristic
123Q8×C29—21no—
124Q8×C29—21no—
125D4×C29—21no—
126D4×C29—21no—
127D4×C29—21no—
128D4×C29C2×D412yes—
129C2×C4×C29—21no—
130C2×C4×C29—21no—
131C2×C4×C29—81no—
132C2×C4×C29C2×D411yescharacteristic
133C2×C4×C29C2×D411yescharacteristic
134C2×C4×C29C2411yescharacteristic
135C22⋊D29—24no—
136C22⋊D29—42no—
137C2×Dic29—21no—
138C2×Dic29—24no—
139C2×Dic29—21no—
140C2×Dic29—21no—
141C2×Dic29—21no—
142C2×Dic29—42no—
143C2×Dic29—81no—
144C2×Dic29C2×D411yescharacteristic
145C2×Dic29C2×D411yescharacteristic
146C2×Dic29C2×D411yescharacteristic
147C4×D29—42no—
148C4×D29—81no—
149C4×D29C2×D412yes—
150C4×D29#4112yes—
151Dic58—21no—
152Dic58—21no—
153Dic58—21no—
154Dic58—21no—
155Dic58—21no—
156Dic58—42no—
157Dic58C2×D412yes—
158C8×C29—21no—
159C8×C29—21no—
160#6597—21no—
161#6597—21no—
162#3046—291nomaximal, Sylow
163C22×C29—22no—
164C22×C29—41no—
165C22×C29—41no—
166C22×C29—41no—
167C22×C29—41no—
168C22×C29—41no—
169C22×C29C22×D411yescharacteristic
170C2×D29—21no—
171C2×D29—21no—
172C2×D29#12112yes—
173C4×C29—21no—
174C4×C29—21no—
175C4×C29—41no—
176C4×C29—41no—
177C4×C29C22×D411yescharacteristic
178C4×C29C2×#4111yescharacteristic
179Dic29—22no—
180Dic29—21no—
181Dic29—21no—
182Dic29—41no—
183Dic29—41no—
184Dic29—41no—
185Dic29#12112yes—
186C2×#137—291no—
187C2×#135—291no—
188#536—291no—
189#520—291no—
190#464—291no—
191#464—291no—
192#463—291no—
193#463D2911yescharacteristic, complemented
194#462—291no—
195#462—291no—
196#461—291no—
197#461—291no—
198#424—291no—
199#417—291no—
200C2×#103—291no—
201C2×C29—42no—
202C2×C29—81no—
203C2×C29C2×#12111yescharacteristic
204C2×C29#57711yescharacteristic
205C2×C29#57811yescharacteristic
206D29—22no—
207C2×#41—291no—
208C2×#41—291no—
209C22×Q8—291no—
210#137—584no—
211#135—584no—
212C2×Q16—291no—
213C2×Q16—291no—
214C2×Q16—291no—
215C2×SD16—291no—
216C2×SD16—291no—
217C2×SD16—291no—
218C2×SD16C2×D2911yescharacteristic
219C2×D8C2×D2911yescharacteristic
220C2×M16—291no—
221C22×C8—291no—
222C4⋊Q8—291no—
223C4⋊Q8—291no—
224#124—291no—
225#124C2×D2911yescharacteristic
226#123—581no—
227#123—581no—
228C22⋊Q8—581no—
229C22⋊Q8—581no—
230C4×Q8—291no—
231C4×Q8—291no—
232C4×D4—291no—
233C4×D4—581no—
234C4×D4—581no—
235C4×D4C2×D2911yescharacteristic
236#117—291no—
237#117—581no—
238C2×C4⋊C4—291no—
239C2×C4⋊C4—581no—
240C4⋊C8—291no—
241C4⋊C8—291no—
242C4⋊C8—291no—
243C4⋊C8C2×D2911yescharacteristic
244#103—291no—
245#103—291no—
246#103—291no—
247#103—291no—
248#103—291no—
249#103C2×D2911yescharacteristic
250#102—291no—
251#102C2×D2911yescharacteristic
252C29#304611yescharacteristic, complemented, Sylow
253#41—294no—
254#41—582no—
255#41—582no—
256#41—582no—
257C2×Q8—291no—
258C2×Q8—291no—
259C2×Q8—291no—
260C2×Q8—581no—
261C2×Q8—582no—
262C2×Q8—582no—
263C2×Q8C22×D2911yescharacteristic
264C2×D4—581no—
265C2×D4—581no—
266C2×D4C22×D2911yescharacteristic
267C2×D4C22×D2911yescharacteristic
268C22×C4—21no—
269C22×C4—291no—
270C22×C4—581no—
271C22×C4—581no—
272C22×C4—581no—
273C22×C4—581no—
274C22×C4—581no—
275Q16—582no—
276Q16—582no—
277Q16—582no—
278SD16—22no—
279SD16—582no—
280SD16—582no—
281SD16—582no—
282D8—22no—
283M16—582no—
284C2×C8—291no—
285C2×C8—291no—
286C2×C8—582no—
287C2×C8C22×D2911yescharacteristic
288C2×C8C22×D2911yescharacteristic
289C4⋊C4—291no—
290C4⋊C4—291no—
291C4⋊C4—291no—
292C4⋊C4—581no—
293C4⋊C4—581no—
294C4⋊C4—581no—
295C4⋊C4—581no—
296C4⋊C4—581no—
297C4⋊C4—581no—
298C4⋊C4—581no—
299C4⋊C4C22×D2911yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—291no—
304C22⋊C4—291no—
305C22⋊C4—581no—
306C22⋊C4—581no—
307C22⋊C4—581no—
308C42—291no—
309C42—581no—
310C42—581no—
311C42C22×D2911yescharacteristic
312C23—21no—
313C23—21no—
314C23—291no—
315Q8—21no—
316Q8—21no—
317Q8—292no—
318Q8—581no—
319Q8—581no—
320Q8—581no—
321Q8—581no—
322Q8—581no—
323Q8—1162no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—584no—
328D4—1162no—
329D4D4×D2912yes—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—81no—
333C2×C4—291no—
334C2×C4—292no—
335C2×C4—292no—
336C2×C4—291no—
337C2×C4—291no—
338C2×C4—584no—
339C2×C4—581no—
340C2×C4—581no—
341C2×C4—581no—
342C2×C4—581no—
343C2×C4—1162no—
344C2×C4—1162no—
345C2×C4—2321no—
346C2×C4—2321no—
347C2×C4D4×D2911yescharacteristic
348C2×C4D4×D2911yescharacteristic
349C2×C4C23×D2911yescharacteristic
350C8—21no—
351C8—21no—
352C8—581no—
353C8—581no—
354C22—22no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—292no—
361C22—581no—
362C22—581no—
363C22C2×D4×D2911yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—292no—
369C4—582no—
370C4—581no—
371C4—581no—
372C4—1161no—
373C4—1161no—
374C4—1161no—
375C4C2×D4×D2911yescharacteristic
376C4#41×D2911yescharacteristic
377C2—42no—
378C2—81no—
379C2—582no—
380C2#121×D2911yescharacteristic
381C2#1427197311yescharacteristic
382C2#1427197711yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#463C2
socleC22×C29C22×D4
prime radicalC2×#11745274C2
hypercenter#463D29
hypocenterC29#3046
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#11745277C2semidirect
3. #14271733C2semidirect
4. #14271642C2semidirect
5. #14271384C2semidirect
6. #14271382C2semidirect
7. #14271376C2semidirect
8. #14271374C2semidirect
9. #14271372C2semidirect
10. #14271368C2semidirect
11. #14271366C2semidirect
12. #14271188C2semidirect
13. #14271161C2semidirect
14. #103×D29C2semidirect
15. C29×#463C2semidirect
193. #463D29semidirect
252. C29#3046semidirect

Maximal subgroups

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

subgroupindex
C2×#117452772
C2×#117452742
#142717332
#142716422
#142713842
#142713822
#142713762
#142713742
#142713722
#142713682
#142713662
#142711882
#142711612
#103×D292
C29×#4632
#304629