Finite Group Databasebeta

← #49171517

Subgroups — #49171517

Order 37504.

382 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036856C211yesmaximal, characteristic, complemented
2#34036800C211yesmaximal, characteristic
3#34036495C211yesmaximal, characteristic, complemented
4#34036492C211yesmaximal, characteristic, complemented
5#34036474C211yesmaximal, characteristic, complemented
6#34036428C211yesmaximal, characteristic, complemented
7#34036408C211yesmaximal, characteristic, complemented
8#34036330C211yesmaximal, characteristic, complemented
9#34036328C211yesmaximal, characteristic, complemented
10#34036328C211yesmaximal, characteristic, complemented
11#34036258C211yesmaximal, characteristic, complemented
12#34036229C211yesmaximal, characteristic, complemented
13#34036228C211yesmaximal, characteristic, complemented
14#34036216C211yesmaximal, characteristic, complemented
15#478×C293C211yesmaximal, characteristic, complemented
16C2×#17989802—21no—
17C2×#17989791C2211yescharacteristic
18C2×#17989791C2211yescharacteristic
19C2×#17989790C2211yescharacteristic
20#22627623—21no—
21#22627623C2211yescharacteristic
22#22627621C2211yescharacteristic
23#22627620C2211yescharacteristic
24#22627620C2211yescharacteristic
25#22627615C2211yescharacteristic
26#22627614—21no—
27#22627614—21no—
28#22627598—21no—
29#22627597—21no—
30#22627597—21no—
31C4×Dic586C2211yescharacteristic
32C4×Dic586C2211yescharacteristic
33#22627589—21no—
34#22627589C2211yescharacteristic
35#22627589C2211yescharacteristic
36#22627586C2211yescharacteristic
37#22627586C2211yescharacteristic
38#22627557C2211yescharacteristic
39#22627553C2211yescharacteristic
40#22627553C2211yescharacteristic
41#22627547C2211yescharacteristic
42#22627546C2211yescharacteristic
43#22627546C2211yescharacteristic
44#22627545C2211yescharacteristic
45#22627544C2211yescharacteristic
46#22627544C2211yescharacteristic
47#22627544C2211yescharacteristic
48#22627544C2211yescharacteristic
49#22627535C2211yescharacteristic
50#22627534C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52#125×C293C2211yescharacteristic
53C4×D4×C293C2211yescharacteristic
54#107×C293C2211yescharacteristic
55#106×C293C2211yescharacteristic
56C4⋊C8×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58#102×C293C2211yescharacteristic
59#17989802—44no—
60C2×Dic586—21no—
61C2×Dic586D411yescharacteristic
62C2×Dic586C2311yescharacteristic
63C2×D1172—21no—
64C2×D1172—21no—
65C2×D1172C2311yescharacteristic
66C2×D1172C2311yescharacteristic
67C2×C22⋊D293—21no—
68C2×C22⋊D293—21no—
69C2×C22⋊D293—21no—
70C2×C22⋊D293—21no—
71C2×C4×D293—21no—
72C2×C4×D293—21no—
73#17989791—22no—
74#17989791—22no—
75#17989790—22no—
76C2×#14556873C2311yescharacteristic
77C2×#14556873C2311yescharacteristic
78C4⋊Dic293—21no—
79C4⋊Dic293D411yescharacteristic
80C4⋊Dic293C2311yescharacteristic
81#17989781—21no—
82#17989781—21no—
83#17989781—21no—
84#17989781—21no—
85#17989781—21no—
86#17989781D411yescharacteristic
87#17989781D411yescharacteristic
88#17989779—21no—
89#17989779—21no—
90C4×Dic293—21no—
91C4×Dic293—21no—
92C4×Dic293—21no—
93C4×Dic293C2311yescharacteristic
94C4×Dic293C2311yescharacteristic
95C2×D4×C293C2311yescharacteristic
96C22×C4×C293—21no—
97C2×C8×C293C2311yescharacteristic
98C2×C8×C293C2311yescharacteristic
99C4⋊C4×C293—21no—
100C4⋊C4×C293—21no—
101C4⋊C4×C293C2311yescharacteristic
102C4⋊C4×C293C2311yescharacteristic
103C4⋊C4×C293C2311yescharacteristic
104C22⋊C4×C293—21no—
105C42×C293C2311yescharacteristic
106C22×D293—21no—
107C22×D293—21no—
108Dic586—21no—
109Dic586—22no—
110Dic586—42no—
111Dic586#4112yescomplemented
112D1172—21no—
113D1172—21no—
114D1172—21no—
115D1172—21no—
116D1172—42no—
117D1172—81no—
118C22⋊D293—42no—
119C22⋊D293—42no—
120C22⋊D293—81no—
121C22⋊D293—81no—
122C2×Dic293—21no—
123C2×Dic293—21no—
124C2×Dic293C2×D411yescharacteristic
125C2×Dic293C2×D411yescharacteristic
126C2×Dic293C2×D411yescharacteristic
127C2×Dic293C2×D411yescharacteristic
128C4×D293—42no—
129C4×D293—42no—
130#14556873—21no—
131#14556873—21no—
132C23×C293—21no—
133D4×C293—21no—
134D4×C293—21no—
135C2×C4×C293—21no—
136C2×C4×C293—21no—
137C2×C4×C293—21no—
138C2×C4×C293—42no—
139C2×C4×C293C2×D411yescharacteristic
140C2×C4×C293C2×D411yescharacteristic
141C2×C4×C293C2411yescharacteristic
142C8×C293—21no—
143C8×C293—21no—
144C22×C293—41no—
145C22×C293—41no—
146C22×C293—41no—
147C22×C293C22×D411yescharacteristic
148C2×D293—41no—
149C2×D293—41no—
150C2×D293—41no—
151C2×D293—41no—
152C2×D293—41no—
153C2×D293—41no—
154C4×C293—21no—
155C4×C293—21no—
156C4×C293—41no—
157C4×C293—41no—
158C4×C293—41no—
159C4×C293C2×#4111yescharacteristic
160C4×C2932−1+411yescharacteristic
161Dic293—22no—
162Dic293—21no—
163Dic293—21no—
164Dic293—21no—
165Dic293—41no—
166Dic293AGL(1,ℤ/8)12yes—
167C2×C293—81no—
168C2×C293#54811yescharacteristic
169C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
170C2×C293#57711yescharacteristic
171D293—81no—
172D293—81no—
173C293#336811yescharacteristic, complemented, Sylow
174#3368—2931nomaximal, Sylow
175#557—2931no—
176#550—2931no—
177#490—2931no—
178#490—2931no—
179#486—2931no—
180#478—2931no—
181#478D29311yescharacteristic, complemented
182#474—2931no—
183#460—2931no—
184#460—2931no—
185#460—2931no—
186#446—2931no—
187#440—2931no—
188#440—2931no—
189C4×SD16—2931no—
190C2×#41—5861no—
191C2×SD16—2931no—
192C2×SD16—2931no—
193C2×SD16—2931no—
194C4⋊Q8—2931no—
195C4⋊Q8—5861no—
196#127—2931no—
197#127—2931no—
198#127—2931no—
199#125—2931no—
200#125—5861no—
201#125—5861no—
202#125C2×D29311yescharacteristic
203#121—5861no—
204#121—5861no—
205#121—5861no—
206C4×Q8—2931no—
207C4×Q8—2931no—
208C4×Q8—2931no—
209C4×Q8—2931no—
210C4×Q8—5861no—
211C4×D4—2931no—
212C4×D4—2931no—
213C4×D4C2×D29311yescharacteristic
214#107—2931no—
215#107C2×D29311yescharacteristic
216#106C2×D29311yescharacteristic
217C4⋊C8—2931no—
218C4⋊C8—2931no—
219C4⋊C8C2×D29311yescharacteristic
220#103—2931no—
221#102—2931no—
222#102—2931no—
223#102—2931no—
224#102—2931no—
225#102—2931no—
226#102—2931no—
227#102—2931no—
228#102C2×D29311yescharacteristic
229#102C2×D29311yescharacteristic
230#97—2931no—
231#97—2931no—
232C4×C8—2931no—
233#41—11724no—
234C2×Q8—2931no—
235C2×Q8—2931no—
236C2×Q8—5861no—
237C2×D4—2931no—
238C2×D4—2931no—
239C2×D4—5861no—
240C2×D4—5861no—
241C2×D4—5861no—
242C2×D4—5861no—
243C2×D4—5861no—
244C2×D4—5861no—
245C2×D4C22×D29311yescharacteristic
246C22×C4—21no—
247C22×C4—5861no—
248C22×C4—5861no—
249SD16—5862no—
250SD16—5862no—
251SD16—5862no—
252C2×C8—2931no—
253C2×C8—2931no—
254C2×C8C22×D29311yescharacteristic
255C2×C8C22×D29311yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—2931no—
259C4⋊C4—2931no—
260C4⋊C4—2931no—
261C4⋊C4—2931no—
262C4⋊C4—5861no—
263C4⋊C4—5861no—
264C4⋊C4—5861no—
265C4⋊C4—5861no—
266C4⋊C4—5861no—
267C4⋊C4—5861no—
268C4⋊C4C22×D29311yescharacteristic
269C4⋊C4C22×D29311yescharacteristic
270C4⋊C4C22×D29311yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—5861no—
273C22⋊C4—5861no—
274C42—2931no—
275C42—2931no—
276C42—5861no—
277C42—5861no—
278C42—5861no—
279C42C22×D29311yescharacteristic
280C23—21no—
281C23—5861no—
282C23—5861no—
283Q8—2932no—
284Q8—5862no—
285Q8—5861no—
286Q8—11722no—
287D4—21no—
288D4—21no—
289D4—23441no—
290D4—23441no—
291D4—23441no—
292D4—5861no—
293D4—5861no—
294D4—5861no—
295D4—5861no—
296D4—11722no—
297D4—11722no—
298D4—11722no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—42no—
303C2×C4—2931no—
304C2×C4—2931no—
305C2×C4—2931no—
306C2×C4—2931no—
307C2×C4—5861no—
308C2×C4—5861no—
309C2×C4—11722no—
310C2×C4—11722no—
311C2×C4D4×D29311yescharacteristic
312C2×C4D4×D29311yescharacteristic
313C2×C4C23×D29311yescharacteristic
314C8—21no—
315C8—21no—
316C8—5861no—
317C8—5861no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—11721no—
322C22—11721no—
323C22—11721no—
324C22—11721no—
325C22—11721no—
326C22—11721no—
327C22C2×D4×D29311yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—2932no—
334C4—5862no—
335C4—5861no—
336C4—5861no—
337C4—5861no—
338C4—11721no—
339C4#41×D29311yescharacteristic
340C4#2262767211yescharacteristic
341C2—81no—
342C2—23441no—
343C2—23441no—
344C2#3403678911yescharacteristic
345C2AGL(1,ℤ/8)×D29311yescharacteristic
346C2#3403693611yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#478×C293C2
socleC22×C293C22×D4
prime radical#34036800C2
hypercenter#478D293
hypocenterC293#3368
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #34036856C2semidirect
3. #34036495C2semidirect
4. #34036492C2semidirect
5. #34036474C2semidirect
6. #34036428C2semidirect
7. #34036408C2semidirect
8. #34036330C2semidirect
9. #34036328C2semidirect
10. #34036328C2semidirect
11. #34036258C2semidirect
12. #34036229C2semidirect
13. #34036228C2semidirect
14. #34036216C2semidirect
15. #478×C293C2semidirect
111. Dic586#41semidirect
173. C293#3368semidirect
181. #478D293semidirect

Maximal subgroups

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

subgroupindex
#340368562
#340368002
#340364952
#340364922
#340364742
#340364282
#340364082
#340363302
#340363282
#340362582
#340362292
#340362282
#340362162
#478×C2932
#3368293