Finite Group Databasebeta

← #16829685

Subgroups — #16829685

Order 3712.

396 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
1#14271643C211yesmaximal, characteristic, complemented
2#14271479C211yesmaximal, characteristic, complemented
3#14271474C211yesmaximal, characteristic, complemented
4#14271467C211yesmaximal, characteristic, complemented
5#14271460C211yesmaximal, characteristic, complemented
6#14271360C211yesmaximal, characteristic, complemented
7#14271355C211yesmaximal, characteristic, complemented
8#14271306C211yesmaximal, characteristic, complemented
9#14271306C211yesmaximal, characteristic, complemented
10#14271273C211yesmaximal, characteristic, complemented
11#14271263C211yesmaximal, characteristic, complemented
12C4×#90783C211yesmaximal, characteristic, complemented
13C4×#90782C211yesmaximal, characteristic, complemented
14#14271224C211yesmaximal, characteristic, complemented
15C29×#540C211yesmaximal, characteristic, complemented
16C2×#90805C2211yescharacteristic
17C29×#127C2211yescharacteristic
18C29×#125C2211yescharacteristic
19C29×#123—21no—
20C29×#123—21no—
21C29×#121—21no—
22C29×#121—21no—
23C29×#121C2211yescharacteristic
24C29×#121C2211yescharacteristic
25C4×D4×C29C2211yescharacteristic
26C4×D4×C29C2211yescharacteristic
27C29×#117C2211yescharacteristic
28C2×#90783C2211yescharacteristic
29C2×#90783C2211yescharacteristic
30C2×#90782C2211yescharacteristic
31C2×#90782C2211yescharacteristic
32C2×C4⋊Dic29C2211yescharacteristic
33#11745254—21no—
34C4⋊C4×D29—21no—
35#11745243—21no—
36#11745243—21no—
37C4×D116C2211yescharacteristic
38C4×D116C2211yescharacteristic
39C4×Dic58C2211yescharacteristic
40C4×Dic58C2211yescharacteristic
41#11745180C2211yescharacteristic
42#11745180C2211yescharacteristic
43#11745180C2211yescharacteristic
44#11745180C2211yescharacteristic
45C22⋊#6597C2211yescharacteristic
46C22⋊#6597C2211yescharacteristic
47#11745158C2211yescharacteristic
48#11745158C2211yescharacteristic
49#11745157C2211yescharacteristic
50#11745157C2211yescharacteristic
51#11745156C2211yescharacteristic
52#11745156C2211yescharacteristic
53#11745155C2211yescharacteristic
54#11745155C2211yescharacteristic
55C4⋊#6597C2211yescharacteristic
56C4⋊#6597C2211yescharacteristic
57#11745151C2211yescharacteristic
58C4×#6597C2211yescharacteristic
59C2×D4×C29—21no—
60C2×D4×C29—21no—
61C2×D4×C29—21no—
62C2×D4×C29—21no—
63C2×D4×C29C2311yescharacteristic
64C2×D4×C29C2311yescharacteristic
65C22×C4×C29—21no—
66C22×C4×C29—21no—
67C22×C4×C29C2311yescharacteristic
68C2×C22⋊D29—21no—
69C22×Dic29—21no—
70#90805—22no—
71#90805—22no—
72C2×D116C2311yescharacteristic
73C2×C4×D29—21no—
74C2×C4×D29—21no—
75C2×C4×D29—21no—
76C2×Dic58C2311yescharacteristic
77C4⋊C4×C29—21no—
78C4⋊C4×C29—21no—
79C4⋊C4×C29D411yescharacteristic
80C4⋊C4×C29D411yescharacteristic
81C4⋊C4×C29C2311yescharacteristic
82C4⋊C4×C29C2311yescharacteristic
83C22⋊C4×C29—21no—
84C22⋊C4×C29—21no—
85C22⋊C4×C29—21no—
86C22⋊C4×C29—21no—
87C22⋊C4×C29D411yescharacteristic
88C22⋊C4×C29D411yescharacteristic
89C42×C29C2311yescharacteristic
90C42×C29C2311yescharacteristic
91#90783—22no—
92#90783—22no—
93#90782—22no—
94#90782—22no—
95#90781—21no—
96#90781—21no—
97C4⋊Dic29—21no—
98C4⋊Dic29C2311yescharacteristic
99C4⋊Dic29C2311yescharacteristic
100#90779—21no—
101#90779—21no—
102C4×Dic29—21no—
103C4×Dic29—21no—
104C2×#6597C2311yescharacteristic
105C2×#6597C2311yescharacteristic
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108C23×C29—21no—
109C23×C29—21no—
110C23×C29C2×D411yescharacteristic
111C22×D29—21no—
112D4×C29—21no—
113D4×C29—21no—
114D4×C29—21no—
115D4×C29—21no—
116D4×C29—81no—
117D4×C29—81no—
118D4×C29—81no—
119D4×C29—81no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29—81no—
125C2×C4×C29—81no—
126C2×C4×C29C2×D411yescharacteristic
127C2×C4×C29C2×D411yescharacteristic
128C2×C4×C29C2×D411yescharacteristic
129C2×C4×C29C2×D411yescharacteristic
130C2×C4×C29C2×D411yescharacteristic
131C2×C4×C29C2411yescharacteristic
132C22⋊D29—24no—
133C2×Dic29—21no—
134C2×Dic29—21no—
135C2×Dic29—21no—
136C2×Dic29—81no—
137D116—21no—
138D116#4112yes—
139C4×D29—24no—
140C4×D29—81no—
141C4×D29—81no—
142Dic58—21no—
143Dic58#4112yes—
144#6597—21no—
145#6597—21no—
146#6597—21no—
147#6597—21no—
148#3119—291nomaximal, Sylow
149C22×C29—21no—
150C22×C29—21no—
151C22×C29—21no—
152C22×C29—41no—
153C22×C29—41no—
154C22×C29—41no—
155C22×C29—41no—
156C22×C29—41no—
157C22×C29—41no—
158C22×C29C22×D411yescharacteristic
159C2×D29—22no—
160C2×D29—41no—
161C2×D29—41no—
162C4×C29—21no—
163C4×C29—21no—
164C4×C29—21no—
165C4×C29—21no—
166C4×C29—21no—
167C4×C29—41no—
168C4×C29—41no—
169C4×C29C2×#4111yescharacteristic
170C4×C29C2×#4111yescharacteristic
171Dic29—22no—
172Dic29—41no—
173Dic29—41no—
174#540D2911yescharacteristic, complemented
175#520—291no—
176#481—291no—
177#480—291no—
178#479—291no—
179#478—291no—
180#460—291no—
181#459—291no—
182#449—291no—
183#449—291no—
184#442—291no—
185#440—291no—
186C4×SD16—291no—
187C4×D8—291no—
188#433—291no—
189C2×C29—41no—
190C2×C29—81no—
191C2×C29—81no—
192C2×C29#52511yescharacteristic
193C2×C29#57611yescharacteristic
194C2×C29#57711yescharacteristic
195D29—42no—
196C2×#41—291no—
197C2×SD16—291no—
198C2×SD16—291no—
199C2×D8—291no—
200C2×D8—291no—
201#127C2×D2911yescharacteristic
202#125C2×D2911yescharacteristic
203#123—21no—
204#123—21no—
205#121—21no—
206#121—21no—
207#121C2×D2911yescharacteristic
208#121C2×D2911yescharacteristic
209C4×Q8—291no—
210C4×Q8—291no—
211C4×D4—291no—
212C4×D4—291no—
213C4×D4—581no—
214C4×D4—581no—
215C4×D4C2×D2911yescharacteristic
216C4×D4C2×D2911yescharacteristic
217#117—581no—
218#117C2×D2911yescharacteristic
219C2×C4⋊C4—291no—
220C2×C4⋊C4—581no—
221#107—291no—
222#107—291no—
223#106—291no—
224#106—291no—
225C4⋊C8—291no—
226C4⋊C8—291no—
227#103—291no—
228#103—291no—
229#102—291no—
230#102—291no—
231#102—291no—
232#102—291no—
233#102—291no—
234#102—291no—
235C22⋊C8—291no—
236C22⋊C8—291no—
237#97—291no—
238C4×C8—291no—
239C29#311911yescharacteristic, complemented, Sylow
240#41—582no—
241#41—582no—
242C2×Q8—291no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—291no—
248C2×D4—581no—
249C2×D4C22×D2911yescharacteristic
250C2×D4C22×D2911yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—581no—
254C22×C4—581no—
255C22×C4—581no—
256C22×C4—581no—
257C22×C4C22×D2911yescharacteristic
258SD16—582no—
259SD16—582no—
260D8—582no—
261D8—582no—
262C2×C8—291no—
263C2×C8—291no—
264C2×C8—291no—
265C2×C8—291no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—291no—
269C4⋊C4—291no—
270C4⋊C4—581no—
271C4⋊C4—581no—
272C4⋊C4—581no—
273C4⋊C4C22⋊D2911yescharacteristic
274C4⋊C4C22⋊D2911yescharacteristic
275C4⋊C4C22×D2911yescharacteristic
276C4⋊C4C22×D2911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C22⋊C4C22⋊D2911yescharacteristic
284C22⋊C4C22⋊D2911yescharacteristic
285C42—581no—
286C42—581no—
287C42C22×D2911yescharacteristic
288C42C22×D2911yescharacteristic
289C23—21no—
290C23—21no—
291C23—581no—
292C23C2×C22⋊D2911yescharacteristic
293Q8—292no—
294Q8—581no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—81no—
301D4—81no—
302D4—81no—
303D4—292no—
304D4—584no—
305D4—581no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—584no—
313C2×C4—581no—
314C2×C4—581no—
315C2×C4—581no—
316C2×C4—2321no—
317C2×C4—2321no—
318C2×C4—2321no—
319C2×C4C2×C22⋊D2911yescharacteristic
320C2×C4C2×C22⋊D2911yescharacteristic
321C2×C4C2×C22⋊D2911yescharacteristic
322C2×C4C2×C22⋊D2911yescharacteristic
323C2×C4C2×C22⋊D2911yescharacteristic
324C2×C4C23×D2911yescharacteristic
325C8—581no—
326C8—581no—
327C8—581no—
328C8—581no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—582no—
339C22—1161no—
340C22—1161no—
341C22C22×C22⋊D2911yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—582no—
350C4—1161no—
351C4—1161no—
352C4#41×D2911yescharacteristic
353C4#41×D2911yescharacteristic
354C2—41no—
355C2—81no—
356C2—81no—
357C2—1162no—
358C2#1427167011yescharacteristic
359C2#1427196611yescharacteristic
360C2#1427197411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#540C2
socleC22×C29C22×D4
hypercenter#540D29
hypocenterC29#3119
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #14271643C2semidirect
2. #14271479C2semidirect
3. #14271474C2semidirect
4. #14271467C2semidirect
5. #14271460C2semidirect
6. #14271360C2semidirect
7. #14271355C2semidirect
8. #14271306C2semidirect
9. #14271306C2semidirect
10. #14271273C2semidirect
11. #14271263C2semidirect
12. C4×#90783C2semidirect
13. C4×#90782C2semidirect
14. #14271224C2semidirect
15. C29×#540C2semidirect
174. #540D29semidirect
239. C29#3119semidirect

Maximal subgroups

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

subgroupindex
#142716432
#142714792
#142714742
#142714672
#142714602
#142713602
#142713552
#142713062
#142712732
#142712632
C4×#907832
C4×#907822
#142712242
C29×#5402
#311929