Finite Group Databasebeta

← #49169056

Subgroups — #49169056

Order 37504.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036609C211yesmaximal, characteristic, complemented
2#34036457C211yesmaximal, characteristic, complemented
3#34036445C211yesmaximal, characteristic, complemented
4#34036416C211yesmaximal, characteristic, complemented
5#34036411C211yesmaximal, characteristic, complemented
6#34036348C211yesmaximal, characteristic, complemented
7#34036341C211yesmaximal, characteristic, complemented
8#34036289C211yesmaximal, characteristic, complemented
9#34036272C211yesmaximal, characteristic
10#34036239C211yesmaximal, characteristic, complemented
11#34036234C211yesmaximal, characteristic, complemented
12C4×#17989789C211yesmaximal, characteristic, complemented
13C4×#17989790C211yesmaximal, characteristic, complemented
14#34036190C211yesmaximal, characteristic, complemented
15#542×C293C211yesmaximal, characteristic, complemented
16C2×#17989802C2211yescharacteristic
17C2×#17989792C2211yescharacteristic
18C2×#17989790C2211yescharacteristic
19C2×#17989789C2211yescharacteristic
20C2×#17989787C2211yescharacteristic
21C4×Dic586C2211yescharacteristic
22C4×Dic586C2211yescharacteristic
23C4×D1172C2211yescharacteristic
24C4×D1172C2211yescharacteristic
25#22627584—21no—
26#22627584—21no—
27#22627582—21no—
28C2×C4⋊Dic293C2211yescharacteristic
29C4⋊C4×D293—21no—
30#22627555C2211yescharacteristic
31#22627555C2211yescharacteristic
32#22627555C2211yescharacteristic
33#22627555C2211yescharacteristic
34C4⋊#14556873C2211yescharacteristic
35C4⋊#14556873C2211yescharacteristic
36#22627548C2211yescharacteristic
37#22627548C2211yescharacteristic
38#22627547C2211yescharacteristic
39#22627547C2211yescharacteristic
40#22627545C2211yescharacteristic
41#22627545C2211yescharacteristic
42#22627544C2211yescharacteristic
43#22627544C2211yescharacteristic
44C22⋊#14556873C2211yescharacteristic
45C22⋊#14556873C2211yescharacteristic
46#22627535C2211yescharacteristic
47C4×#14556873C2211yescharacteristic
48C4⋊Q8×C293C2211yescharacteristic
49#126×C293—21no—
50#124×C293—21no—
51#124×C293C2211yescharacteristic
52#123×C293—21no—
53C22⋊Q8×C293—21no—
54C22⋊Q8×C293C2211yescharacteristic
55#121×C293C2211yescharacteristic
56C4×Q8×C293C2211yescharacteristic
57C4×D4×C293C2211yescharacteristic
58#117×C293C2211yescharacteristic
59#17989802—22no—
60#17989802—22no—
61C2×Dic586C2311yescharacteristic
62C2×D1172C2311yescharacteristic
63C2×C22⋊D293—21no—
64C22×Dic293—21no—
65C2×C4×D293—21no—
66C2×C4×D293—21no—
67C2×C4×D293—21no—
68#17989792—22no—
69#17989790—22no—
70#17989789—22no—
71#17989787—22no—
72C2×#14556873C2311yescharacteristic
73C2×#14556873C2311yescharacteristic
74C2×#14556873C2311yescharacteristic
75C2×#14556873C2311yescharacteristic
76C4⋊Dic293—21no—
77C4⋊Dic293C2311yescharacteristic
78C4⋊Dic293C2311yescharacteristic
79#17989781—21no—
80#17989781—21no—
81#17989779—21no—
82#17989779—21no—
83C4×Dic293—21no—
84C4×Dic293—21no—
85C2×Q8×C293—21no—
86C2×Q8×C293C2311yescharacteristic
87C2×D4×C293—21no—
88C2×D4×C293C2311yescharacteristic
89C22×C4×C293—21no—
90C22×C4×C293C2311yescharacteristic
91C4⋊C4×C293—21no—
92C4⋊C4×C293—21no—
93C4⋊C4×C293—21no—
94C4⋊C4×C293D411yescharacteristic
95C4⋊C4×C293D411yescharacteristic
96C4⋊C4×C293C2311yescharacteristic
97C4⋊C4×C293C2311yescharacteristic
98C22⋊C4×C293—21no—
99C22⋊C4×C293—21no—
100C22⋊C4×C293—21no—
101C22⋊C4×C293—21no—
102C22⋊C4×C293—21no—
103C22⋊C4×C293D411yescharacteristic
104C22⋊C4×C293D411yescharacteristic
105C42×C293—21no—
106C42×C293C2311yescharacteristic
107C42×C293C2311yescharacteristic
108C22×D293—21no—
109Dic586—21no—
110Dic586#4112yes—
111D1172—21no—
112D1172#4112yes—
113C22⋊D293—24no—
114C2×Dic293—21no—
115C2×Dic293—21no—
116C2×Dic293—21no—
117C2×Dic293—81no—
118C4×D293—24no—
119C4×D293—81no—
120C4×D293—81no—
121#14556873—21no—
122#14556873—21no—
123#14556873—21no—
124#14556873—21no—
125C23×C293—21no—
126C23×C293C2×D411yescharacteristic
127Q8×C293—21no—
128Q8×C293—21no—
129Q8×C293—81no—
130D4×C293—21no—
131D4×C293—21no—
132D4×C293—81no—
133C2×C4×C293—21no—
134C2×C4×C293—21no—
135C2×C4×C293—21no—
136C2×C4×C293—21no—
137C2×C4×C293—21no—
138C2×C4×C293—81no—
139C2×C4×C293C2×D411yescharacteristic
140C2×C4×C293C2×D411yescharacteristic
141C2×C4×C293C2×D411yescharacteristic
142C2×C4×C293C2×D411yescharacteristic
143C2×C4×C293C2×D411yescharacteristic
144C2×C4×C293C2411yescharacteristic
145C22×C293—21no—
146C22×C293—21no—
147C22×C293—21no—
148C22×C293—41no—
149C22×C293—41no—
150C22×C293—41no—
151C22×C293C22×D411yescharacteristic
152C2×D293—22no—
153C2×D293—41no—
154C2×D293—41no—
155C4×C293—21no—
156C4×C293—21no—
157C4×C293—21no—
158C4×C293—21no—
159C4×C293—21no—
160C4×C293—41no—
161C4×C293—41no—
162C4×C293—41no—
163C4×C293C2×#4111yescharacteristic
164C4×C293C2×#4111yescharacteristic
165Dic293—22no—
166Dic293—41no—
167Dic293—41no—
168C2×C293—41no—
169C2×C293—81no—
170C2×C293#52511yescharacteristic
171C2×C293#57711yescharacteristic
172C2×C293#57711yescharacteristic
173D293—42no—
174C293#312511yescharacteristic, complemented, Sylow
175#3125—2931nomaximal, Sylow
176#542D29311yescharacteristic, complemented
177#520—2931no—
178#483—2931no—
179#481—2931no—
180#476—2931no—
181#475—2931no—
182#464—2931no—
183#463—2931no—
184#452—2931no—
185#449—2931no—
186#442—2931no—
187#441—2931no—
188C4×SD16—2931no—
189C4×SD16—2931no—
190#433—2931no—
191C2×#41—2931no—
192C2×Q16—2931no—
193C2×SD16—2931no—
194C2×SD16—2931no—
195C2×D8—2931no—
196C4⋊Q8C2×D29311yescharacteristic
197#126—21no—
198#124—21no—
199#124C2×D29311yescharacteristic
200#123—21no—
201C22⋊Q8—21no—
202C22⋊Q8C2×D29311yescharacteristic
203#121C2×D29311yescharacteristic
204C4×Q8—2931no—
205C4×Q8—2931no—
206C4×Q8C2×D29311yescharacteristic
207C4×D4—2931no—
208C4×D4—2931no—
209C4×D4—5861no—
210C4×D4—5861no—
211C4×D4C2×D29311yescharacteristic
212#117—5861no—
213#117C2×D29311yescharacteristic
214C2×C4⋊C4—2931no—
215C2×C4⋊C4—5861no—
216#106—2931no—
217#106—2931no—
218#106—2931no—
219#106—2931no—
220C4⋊C8—2931no—
221C4⋊C8—2931no—
222#103—2931no—
223#103—2931no—
224#103—2931no—
225#103—2931no—
226#102—2931no—
227#102—2931no—
228#102—2931no—
229#102—2931no—
230C22⋊C8—2931no—
231C22⋊C8—2931no—
232#97—2931no—
233C4×C8—2931no—
234#41—5862no—
235#41—5862no—
236C2×Q8—21no—
237C2×Q8—2931no—
238C2×Q8C22×D29311yescharacteristic
239C2×D4—21no—
240C2×D4—2931no—
241C2×D4—5861no—
242C2×D4C22×D29311yescharacteristic
243C22×C4—21no—
244C22×C4—5861no—
245C22×C4—5861no—
246C22×C4—5861no—
247C22×C4—5861no—
248C22×C4C22×D29311yescharacteristic
249Q16—5862no—
250SD16—5862no—
251SD16—5862no—
252D8—5862no—
253C2×C8—2931no—
254C2×C8—2931no—
255C2×C8—2931no—
256C2×C8—2931no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—2931no—
261C4⋊C4—2931no—
262C4⋊C4—5861no—
263C4⋊C4—5861no—
264C4⋊C4—5861no—
265C4⋊C4C22⋊D29311yescharacteristic
266C4⋊C4C22⋊D29311yescharacteristic
267C4⋊C4C22×D29311yescharacteristic
268C4⋊C4C22×D29311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—5861no—
275C22⋊C4—5861no—
276C22⋊C4C22⋊D29311yescharacteristic
277C22⋊C4C22⋊D29311yescharacteristic
278C42—21no—
279C42—5861no—
280C42—5861no—
281C42C22×D29311yescharacteristic
282C42C22×D29311yescharacteristic
283C23—21no—
284C23—5861no—
285C23C2×C22⋊D29311yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—81no—
289Q8—2932no—
290Q8—5861no—
291D4—21no—
292D4—21no—
293D4—81no—
294D4—2932no—
295D4—5864no—
296D4—5861no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—23441no—
304C2×C4—23441no—
305C2×C4—23441no—
306C2×C4—5864no—
307C2×C4—5861no—
308C2×C4—5861no—
309C2×C4—5861no—
310C2×C4C2×C22⋊D29311yescharacteristic
311C2×C4C2×C22⋊D29311yescharacteristic
312C2×C4C2×C22⋊D29311yescharacteristic
313C2×C4C2×C22⋊D29311yescharacteristic
314C2×C4C2×C22⋊D29311yescharacteristic
315C2×C4C23×D29311yescharacteristic
316C8—5861no—
317C8—5861no—
318C8—5861no—
319C8—5861no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—5862no—
327C22—11721no—
328C22—11721no—
329C22C22×C22⋊D29311yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—5862no—
339C4—11721no—
340C4—11721no—
341C4#41×D29311yescharacteristic
342C4#41×D29311yescharacteristic
343C2—41no—
344C2—81no—
345C2—11722no—
346C2#3403663611yescharacteristic
347C2#3403693711yescharacteristic
348C2#3403694011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#542×C293C2
socleC22×C293C22×D4
prime radical#34036272C2
hypercenter#542D293
hypocenterC293#3125
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #34036609C2semidirect
2. #34036457C2semidirect
3. #34036445C2semidirect
4. #34036416C2semidirect
5. #34036411C2semidirect
6. #34036348C2semidirect
7. #34036341C2semidirect
8. #34036289C2semidirect
10. #34036239C2semidirect
11. #34036234C2semidirect
12. C4×#17989789C2semidirect
13. C4×#17989790C2semidirect
14. #34036190C2semidirect
15. #542×C293C2semidirect
174. C293#3125semidirect
176. #542D293semidirect

Maximal subgroups

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

subgroupindex
#340366092
#340364572
#340364452
#340364162
#340364112
#340363482
#340363412
#340362892
#340362722
#340362392
#340362342
C4×#179897892
C4×#179897902
#340361902
#542×C2932
#3125293