Finite Group Databasebeta

← #49170758

Subgroups — #49170758

Order 37504.

394 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036832C211yesmaximal, characteristic, complemented
2#34036783C211yesmaximal, characteristic, complemented
3#34036499C211yesmaximal, characteristic, complemented
4#34036472C211yesmaximal, characteristic, complemented
5#34036461C211yesmaximal, characteristic, complemented
6#34036376C211yesmaximal, characteristic, complemented
7#34036359C211yesmaximal, characteristic, complemented
8#34036335C211yesmaximal, characteristic, complemented
9#34036275C211yesmaximal, characteristic, complemented
10#34036275C211yesmaximal, characteristic, complemented
11#34036239C211yesmaximal, characteristic, complemented
12#34036199C211yesmaximal, characteristic, complemented
13#34036127C211yesmaximal, characteristic, complemented
14#34036122C211yesmaximal, characteristic, complemented
15#478×C293C211yesmaximal, characteristic, complemented
16C2×#17989801C2211yescharacteristic
17C2×#17989801C2211yescharacteristic
18C2×#17989791C2211yescharacteristic
19C2×#17989791C2211yescharacteristic
20C2×#17989787C2211yescharacteristic
21C2×#17989785C2211yescharacteristic
22C2×C8×D293C2211yescharacteristic
23#22627624C2211yescharacteristic
24#22627619—21no—
25#22627609—21no—
26#22627608—21no—
27#22627608—21no—
28#22627604C2211yescharacteristic
29#22627604C2211yescharacteristic
30#22627599—21no—
31#22627599C2211yescharacteristic
32#22627599C2211yescharacteristic
33#22627598—21no—
34C4×D1172C2211yescharacteristic
35C4×D1172C2211yescharacteristic
36#22627586—21no—
37#22627582C2211yescharacteristic
38C2×C4⋊Dic293—21no—
39C4⋊C4×D293C2211yescharacteristic
40#22627555C2211yescharacteristic
41#22627549C2211yescharacteristic
42#22627549C2211yescharacteristic
43#22627547C2211yescharacteristic
44#22627547C2211yescharacteristic
45#22627547C2211yescharacteristic
46#22627547C2211yescharacteristic
47#22627545C2211yescharacteristic
48#22627544C2211yescharacteristic
49#22627536C2211yescharacteristic
50#22627536C2211yescharacteristic
51#22627535C2211yescharacteristic
52#125×C293C2211yescharacteristic
53C4×D4×C293C2211yescharacteristic
54#107×C293C2211yescharacteristic
55#106×C293C2211yescharacteristic
56C4⋊C8×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58#102×C293C2211yescharacteristic
59#17989801—22no—
60#17989801—22no—
61#17989801—41no—
62#17989801—41no—
63C2×Dic586C2311yescharacteristic
64C2×Dic586C2311yescharacteristic
65C2×D1172—21no—
66C2×D1172—21no—
67C2×D1172D411yescharacteristic
68C2×D1172C2311yescharacteristic
69C2×C22⋊D293—21no—
70C2×C22⋊D293—21no—
71C22×Dic293—21no—
72C22×Dic293—21no—
73C2×C4×D293—21no—
74C2×C4×D293—21no—
75C2×C4×D293C2311yescharacteristic
76C2×C4×D293C2311yescharacteristic
77#17989791—41no—
78#17989791—41no—
79#17989787—22no—
80#17989785—41no—
81C2×#14556873C2311yescharacteristic
82C2×#14556873C2311yescharacteristic
83C8×D293—41no—
84C4⋊Dic293—21no—
85C4⋊Dic293—21no—
86C4⋊Dic293—21no—
87C4⋊Dic293—21no—
88C4⋊Dic293D411yescharacteristic
89C4⋊Dic293C2311yescharacteristic
90#17989781—21no—
91#17989779—21no—
92#17989779—21no—
93#17989779—21no—
94#17989779—21no—
95#17989779—21no—
96#17989779—21no—
97#17989779D411yescharacteristic
98#17989779D411yescharacteristic
99C4×Dic293—21no—
100C2×D4×C293C2311yescharacteristic
101C22×C4×C293—21no—
102C2×C8×C293C2311yescharacteristic
103C2×C8×C293C2311yescharacteristic
104C4⋊C4×C293—21no—
105C4⋊C4×C293—21no—
106C4⋊C4×C293C2311yescharacteristic
107C4⋊C4×C293C2311yescharacteristic
108C4⋊C4×C293C2311yescharacteristic
109C22⋊C4×C293—21no—
110C42×C293C2311yescharacteristic
111C22×D293—21no—
112C22×D293C2×D411yescharacteristic
113C22×D293C2×D411yescharacteristic
114Dic586—21no—
115Dic586—21no—
116Dic586—21no—
117Dic586—21no—
118D1172—21no—
119D1172—21no—
120D1172—41no—
121D1172—42no—
122D1172—81no—
123C22⋊D293—42no—
124C22⋊D293—42no—
125C2×Dic293—21no—
126C2×Dic293—21no—
127C2×Dic293—21no—
128C2×Dic293—42no—
129C2×Dic293—42no—
130C2×Dic293C2×D411yescharacteristic
131C2×Dic293C2×D411yescharacteristic
132C4×D293—21no—
133C4×D293—21no—
134C4×D293—21no—
135C4×D293—21no—
136C4×D293—81no—
137C4×D293—81no—
138#14556873—21no—
139#14556873—21no—
140C23×C293—21no—
141D4×C293—21no—
142D4×C293#4112yes—
143C2×C4×C293—21no—
144C2×C4×C293—21no—
145C2×C4×C293—21no—
146C2×C4×C293—42no—
147C2×C4×C293C2×D411yescharacteristic
148C2×C4×C293C2×D411yescharacteristic
149C2×C4×C293C2411yescharacteristic
150C8×C293—21no—
151C8×C293—21no—
152C22×C293—22no—
153C22×C293—41no—
154C22×C293—41no—
155C22×C293C22×D411yescharacteristic
156C2×D293—21no—
157C2×D293—21no—
158C2×D293—21no—
159C2×D293—21no—
160C2×D293—21no—
161C2×D293—21no—
162C2×D293—41no—
163C2×D293—41no—
164C2×D293—41no—
165C4×C293—21no—
166C4×C293—21no—
167C4×C293—41no—
168C4×C293—41no—
169C4×C293—41no—
170C4×C293C2×#4111yescharacteristic
171C4×C293H(5,𝔽2)11yescharacteristic
172Dic293—21no—
173Dic293—21no—
174Dic293—41no—
175Dic293—41no—
176Dic293—41no—
177C2×C293—42no—
178C2×C293#54611yescharacteristic
179C2×C293#57511yescharacteristic
180C2×C293#57711yescharacteristic
181D293—41no—
182D293—41no—
183D293—81no—
184C293#330711yescharacteristic, complemented, Sylow
185#3307—2931nomaximal, Sylow
186#553—2931no—
187#547—2931no—
188#491—2931no—
189#485—2931no—
190#483—2931no—
191#478D29311yescharacteristic, complemented
192#468—2931no—
193#465—2931no—
194#461—2931no—
195#449—2931no—
196#449—2931no—
197#442—2931no—
198#435—2931no—
199#417—2931no—
200#416—2931no—
201C2×#41—2931no—
202C2×#41—2931no—
203C2×SD16—2931no—
204C2×SD16—2931no—
205C2×D8—2931no—
206C2×M16—2931no—
207C22×C8—2931no—
208C4⋊Q8—2931no—
209#126—5861no—
210#125C2×D29311yescharacteristic
211#123—5861no—
212#123—5861no—
213#123—5861no—
214C22⋊Q8—2931no—
215C22⋊Q8—2931no—
216#121—2931no—
217#121—2931no—
218#121—5861no—
219#121—5861no—
220C4×D4—2931no—
221C4×D4—2931no—
222C4×D4—5861no—
223C4×D4C2×D29311yescharacteristic
224#117—2931no—
225C2×C4⋊C4—2931no—
226C2×C4⋊C4—5861no—
227#107C2×D29311yescharacteristic
228#106—2931no—
229#106C2×D29311yescharacteristic
230C4⋊C8C2×D29311yescharacteristic
231#103—2931no—
232#103—2931no—
233#103—2931no—
234#103—2931no—
235#103—2931no—
236#103—2931no—
237#102—2931no—
238#102—2931no—
239#102C2×D29311yescharacteristic
240#102C2×D29311yescharacteristic
241C22⋊C8—2931no—
242C22⋊C8—2931no—
243#97—2931no—
244#41—5862no—
245#41—5862no—
246#41—11721no—
247#41—11721no—
248C2×Q8—2931no—
249C2×Q8—2931no—
250C2×D4—2931no—
251C2×D4—2931no—
252C2×D4—5861no—
253C2×D4—5861no—
254C2×D4—5861no—
255C2×D4—5861no—
256C2×D4C22×D29311yescharacteristic
257C22×C4—21no—
258C22×C4—2931no—
259C22×C4—2931no—
260C22×C4—5861no—
261C22×C4—5861no—
262C22×C4—5861no—
263C22×C4—5861no—
264SD16—11721no—
265SD16—11721no—
266D8—5862no—
267M16—11721no—
268C2×C8—2931no—
269C2×C8—2931no—
270C2×C8—11721no—
271C2×C8C22×D29311yescharacteristic
272C2×C8C22×D29311yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—2931no—
276C4⋊C4—2931no—
277C4⋊C4—5861no—
278C4⋊C4—5861no—
279C4⋊C4—5861no—
280C4⋊C4—5861no—
281C4⋊C4—5861no—
282C4⋊C4C22×D29311yescharacteristic
283C4⋊C4C22×D29311yescharacteristic
284C4⋊C4C22×D29311yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—2931no—
287C22⋊C4—2931no—
288C22⋊C4—5861no—
289C22⋊C4—5861no—
290C22⋊C4—5861no—
291C22⋊C4—5861no—
292C22⋊C4—5861no—
293C22⋊C4—5861no—
294C42—5861no—
295C42C22×D29311yescharacteristic
296C23—21no—
297C23—2931no—
298C23—2931no—
299C23—5861no—
300Q8—5861no—
301Q8—5861no—
302Q8—5861no—
303Q8—5861no—
304D4—21no—
305D4—23441no—
306D4—5861no—
307D4—5861no—
308D4—11721no—
309D4—11722no—
310D4—11722no—
311D4—11722no—
312D4#1798980312yes—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—42no—
317C2×C4—2931no—
318C2×C4—2931no—
319C2×C4—23441no—
320C2×C4—23441no—
321C2×C4—5861no—
322C2×C4—5861no—
323C2×C4—5861no—
324C2×C4—5861no—
325C2×C4—5861no—
326C2×C4—5861no—
327C2×C4—5861no—
328C2×C4—11722no—
329C2×C4—11722no—
330C2×C4D4×D29311yescharacteristic
331C2×C4D4×D29311yescharacteristic
332C2×C4C23×D29311yescharacteristic
333C8—21no—
334C8—21no—
335C8—5861no—
336C8—5861no—
337C22—22no—
338C22—41no—
339C22—41no—
340C22—5861no—
341C22—5861no—
342C22—5861no—
343C22—5861no—
344C22—5861no—
345C22—5861no—
346C22—11721no—
347C22—11721no—
348C22—11721no—
349C22C2×D4×D29311yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—5861no—
356C4—5861no—
357C4—11721no—
358C4—11721no—
359C4—11721no—
360C4C2×#1798980311yescharacteristic
361C4#2262767011yescharacteristic
362C2—42no—
363C2—23441no—
364C2—11721no—
365C2—11721no—
366C2#3403677011yescharacteristic
367C2#3403692511yescharacteristic
368C2#3403693611yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#478×C293C2
socleC22×C293C22×D4
hypercenter#478D293
hypocenterC293#3307
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. #34036832C2semidirect
2. #34036783C2semidirect
3. #34036499C2semidirect
4. #34036472C2semidirect
5. #34036461C2semidirect
6. #34036376C2semidirect
7. #34036359C2semidirect
8. #34036335C2semidirect
9. #34036275C2semidirect
10. #34036275C2semidirect
11. #34036239C2semidirect
12. #34036199C2semidirect
13. #34036127C2semidirect
14. #34036122C2semidirect
15. #478×C293C2semidirect
184. C293#3307semidirect
191. #478D293semidirect

Maximal subgroups

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

subgroupindex
#340368322
#340367832
#340364992
#340364722
#340364612
#340363762
#340363592
#340363352
#340362752
#340362392
#340361992
#340361272
#340361222
#478×C2932
#3307293