Finite Group Databasebeta

← #49169387

Subgroups — #49169387

Order 37504.

364 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036683C211yesmaximal, characteristic, complemented
2#34036661C211yesmaximal, characteristic
3#34036536C211yesmaximal, characteristic, complemented
4#34036520C211yesmaximal, characteristic, complemented
5#34036496C211yesmaximal, characteristic, complemented
6#34036487C211yesmaximal, characteristic, complemented
7#34036388C211yesmaximal, characteristic, complemented
8#34036386C211yesmaximal, characteristic, complemented
9#34036374C211yesmaximal, characteristic
10#34036372C211yesmaximal, characteristic
11C4×Dic1172C211yesmaximal, characteristic, complemented
12C4×#17989792C211yesmaximal, characteristic, complemented
13C4×#17989790C211yesmaximal, characteristic, complemented
14C4×#17989785C211yesmaximal, characteristic, complemented
15C4×SD16×C293C211yesmaximal, characteristic, complemented
16C2×Dic1172C2211yescharacteristic
17C2×#17989792C2211yescharacteristic
18C2×#17989790C2211yescharacteristic
19C2×#17989785C2211yescharacteristic
20C2×#17989785C2211yescharacteristic
21#22627623C2211yescharacteristic
22#22627622C2211yescharacteristic
23#22627617—21no—
24#22627615C2211yescharacteristic
25#22627614—21no—
26#22627611C2211yescharacteristic
27#22627606—21no—
28#22627604C2211yescharacteristic
29#22627604C2211yescharacteristic
30#22627602—21no—
31#22627600C2211yescharacteristic
32#22627595C2211yescharacteristic
33C4×Dic586—21no—
34C4×Dic586C2211yescharacteristic
35C4×Dic586C2211yescharacteristic
36C4×C22⋊D293—21no—
37#22627583—21no—
38#22627581—21no—
39C42×D293C2211yescharacteristic
40#22627558C2211yescharacteristic
41#22627557C2211yescharacteristic
42#22627555C2211yescharacteristic
43#22627549C2211yescharacteristic
44#22627549C2211yescharacteristic
45#22627548C2211yescharacteristic
46#22627547C2211yescharacteristic
47#22627547C2211yescharacteristic
48#22627545C2211yescharacteristic
49#22627534C2211yescharacteristic
50#22627534C2211yescharacteristic
51C4×#14556873C2211yescharacteristic
52C2×SD16×C293C2211yescharacteristic
53C4×Q8×C293C2211yescharacteristic
54C4×D4×C293C2211yescharacteristic
55#106×C293C2211yescharacteristic
56#103×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58C4×C8×C293C2211yescharacteristic
59C2×Dic586—21no—
60C2×Dic586C2311yescharacteristic
61C2×Dic586C2311yescharacteristic
62C2×C22⋊D293—21no—
63C2×C4×D293D411yescharacteristic
64C2×C4×D293D411yescharacteristic
65C2×C4×D293C2311yescharacteristic
66Dic1172—22no—
67#17989792—22no—
68#17989790—22no—
69#17989785—22no—
70#17989785—22no—
71C2×#14556873C2311yescharacteristic
72C2×#14556873C2311yescharacteristic
73C4⋊Dic293—21no—
74C4⋊Dic293—21no—
75C4⋊Dic293—21no—
76C4⋊Dic293C2311yescharacteristic
77C4⋊Dic293C2311yescharacteristic
78#17989781—21no—
79#17989781—21no—
80#17989781—21no—
81#17989781—21no—
82#17989781—21no—
83#17989781—21no—
84#17989781—21no—
85C22⋊Dic293—21no—
86C22⋊Dic293—21no—
87C22⋊Dic293—21no—
88#17989779—21no—
89#17989779—21no—
90#17989779—21no—
91C4×Dic293—21no—
92C4×Dic293—21no—
93C4×Dic293D411yescharacteristic
94C4×Dic293D411yescharacteristic
95C4×Dic293C2311yescharacteristic
96C2×Q8×C293C2311yescharacteristic
97C2×D4×C293C2311yescharacteristic
98C22×C4×C293—21no—
99SD16×C293—22no—
100C2×C8×C293C2311yescharacteristic
101C2×C8×C293C2311yescharacteristic
102C4⋊C4×C293—21no—
103C4⋊C4×C293C2311yescharacteristic
104C4⋊C4×C293C2311yescharacteristic
105C22⋊C4×C293—21no—
106C42×C293—21no—
107C42×C293C2311yescharacteristic
108C22×D293C2×D411yescharacteristic
109Dic586—21no—
110Dic586—21no—
111Dic586—21no—
112Dic586—21no—
113Dic586—42no—
114C22⋊D293—42no—
115C2×Dic293—21no—
116C2×Dic293—21no—
117C2×Dic293—21no—
118C2×Dic293—21no—
119C2×Dic293C2×D411yescharacteristic
120C2×Dic293C2×D411yescharacteristic
121C2×Dic293C2×D411yescharacteristic
122C4×D293—22no—
123C4×D293—21no—
124C4×D293—21no—
125C4×D293—41no—
126#14556873—21no—
127#14556873#4112yes—
128C23×C293—21no—
129Q8×C293—21no—
130Q8×C293—21no—
131D4×C293—21no—
132D4×C293—21no—
133C2×C4×C293—21no—
134C2×C4×C293—21no—
135C2×C4×C293—21no—
136C2×C4×C293—42no—
137C2×C4×C293C2×D411yescharacteristic
138C2×C4×C293C2×D411yescharacteristic
139C2×C4×C293C2411yescharacteristic
140C8×C293—21no—
141C8×C293#4112yes—
142C22×C293—41no—
143C22×C293—41no—
144C22×C293—41no—
145C22×C293C22×D411yescharacteristic
146C2×D293—21no—
147C2×D293—21no—
148C2×D293—21no—
149C4×C293—21no—
150C4×C293—41no—
151C4×C293—41no—
152C4×C293—41no—
153C4×C293#13712yes—
154C4×C293C2×#4111yescharacteristic
155C4×C293C2×#4111yescharacteristic
156Dic293—21no—
157Dic293—21no—
158Dic293—21no—
159Dic293—41no—
160Dic293—41no—
161Dic293—41no—
162Dic293—41no—
163C2×C293—81no—
164C2×C293#53211yescharacteristic
165C2×C293C2×#13711yescharacteristic
166C2×C293#57511yescharacteristic
167D293—41no—
168C293#317211yescharacteristic, complemented, Sylow
169#3172—2931nomaximal, Sylow
170#533—2931no—
171#529—2931no—
172#501—2931no—
173#497—2931no—
174#491—2931no—
175#489—2931no—
176#470—2931no—
177#470—2931no—
178#468—2931no—
179#468—2931no—
180C4×Q16—2931no—
181C4×Q16—2931no—
182C4×SD16—2931no—
183C4×SD16D29311yescharacteristic, complemented
184C4×M16—2931no—
185C2×Q16—2931no—
186C2×Q16—2931no—
187C2×SD16—2931no—
188C2×SD16C2×D29311yescharacteristic
189C2×M16—2931no—
190C2×M16—2931no—
191C4⋊Q8—2931no—
192C4⋊Q8—2931no—
193#126—5861no—
194#125—2931no—
195#125—5861no—
196#124—2931no—
197#123—5861no—
198C22⋊Q8—2931no—
199C22⋊Q8—2931no—
200C22⋊Q8—2931no—
201C22⋊Q8—5861no—
202#121—2931no—
203C4×Q8—2931no—
204C4×Q8—2931no—
205C4×Q8—5861no—
206C4×Q8C2×D29311yescharacteristic
207C4×D4—5861no—
208C4×D4C2×D29311yescharacteristic
209#117—5861no—
210#117—5861no—
211C2×C42—2931no—
212#107—2931no—
213#107—2931no—
214#106—2931no—
215#106C2×D29311yescharacteristic
216#103—2931no—
217#103—2931no—
218#103—2931no—
219#103—2931no—
220#103—2931no—
221#103C2×D29311yescharacteristic
222#102—2931no—
223#102C2×D29311yescharacteristic
224#97—2931no—
225#97—2931no—
226C4×C8—2931no—
227C4×C8C2×D29311yescharacteristic
228C2×Q8—2931no—
229C2×Q8—2931no—
230C2×Q8—5861no—
231C2×Q8C22×D29311yescharacteristic
232C2×D4—5861no—
233C2×D4C22×D29311yescharacteristic
234C22×C4—21no—
235C22×C4—2931no—
236C22×C4—2931no—
237C22×C4—2931no—
238Q16—5862no—
239Q16—5862no—
240SD16—22no—
241SD16—5862no—
242M16—5862no—
243M16—5862no—
244C2×C8—2931no—
245C2×C8—2931no—
246C2×C8C22×D29311yescharacteristic
247C2×C8C22×D29311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—2931no—
250C4⋊C4—2931no—
251C4⋊C4—5861no—
252C4⋊C4—5861no—
253C4⋊C4—5861no—
254C4⋊C4—5861no—
255C4⋊C4—5861no—
256C4⋊C4—5861no—
257C4⋊C4—5861no—
258C4⋊C4—5861no—
259C4⋊C4—5861no—
260C4⋊C4—5861no—
261C4⋊C4C22×D29311yescharacteristic
262C4⋊C4C22×D29311yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—5861no—
265C22⋊C4—5861no—
266C22⋊C4—5861no—
267C22⋊C4—5861no—
268C22⋊C4—5861no—
269C22⋊C4—5861no—
270C42—21no—
271C42—2931no—
272C42—2931no—
273C42—2931no—
274C42—5861no—
275C42—5861no—
276C42C22×D29311yescharacteristic
277C23—21no—
278C23—2931no—
279Q8—21no—
280Q8—21no—
281Q8—5861no—
282Q8—5861no—
283Q8—5861no—
284Q8—5861no—
285Q8—11722no—
286D4—21no—
287D4—21no—
288D4—11722no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—42no—
293C2×C4—2931no—
294C2×C4—2931no—
295C2×C4—2931no—
296C2×C4—5862no—
297C2×C4—5861no—
298C2×C4—5861no—
299C2×C4—5861no—
300C2×C4—5861no—
301C2×C4—5861no—
302C2×C4—5861no—
303C2×C4—11721no—
304C2×C4D4×D29311yescharacteristic
305C2×C4D4×D29311yescharacteristic
306C2×C4C23×D29311yescharacteristic
307C8—21no—
308C8—2932no—
309C8—5861no—
310C8#1798980212yes—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—5861no—
315C22—5861no—
316C22—5861no—
317C22C2×D4×D29311yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—5861no—
323C4—5861no—
324C4—5861no—
325C4—11721no—
326C4—11721no—
327C4—11721no—
328C4—11721no—
329C4#2262765312yes—
330C4#41×D29311yescharacteristic
331C4C2×#1798980211yescharacteristic
332C2—81no—
333C2—11721no—
334C2#3403667611yescharacteristic
335C2C2×#2262765311yescharacteristic
336C2#3403692611yescharacteristic
subgroupG/H
centerC2×C4D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC4×SD16×C293C2
socleC22×C293C22×D4
prime radical#22627595C22
hypercenterC4×SD16D293
hypocenterC293#3172
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #34036683C2semidirect
3. #34036536C2semidirect
4. #34036520C2semidirect
5. #34036496C2semidirect
6. #34036487C2semidirect
7. #34036388C2semidirect
8. #34036386C2semidirect
11. C4×Dic1172C2semidirect
12. C4×#17989792C2semidirect
13. C4×#17989790C2semidirect
14. C4×#17989785C2semidirect
15. C4×SD16×C293C2semidirect
168. C293#3172semidirect
183. C4×SD16D293semidirect

Maximal subgroups

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

subgroupindex
#340366832
#340366612
#340365362
#340365202
#340364962
#340364872
#340363882
#340363862
#340363742
#340363722
C4×Dic11722
C4×#179897922
C4×#179897902
C4×#179897852
C4×SD16×C2932
#3172293