Finite Group Databasebeta

← #49171448

Subgroups — #49171448

Order 37504.

362 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036862C211yesmaximal, characteristic, complemented
2#34036835C211yesmaximal, characteristic, complemented
3#34036486C211yesmaximal, characteristic, complemented
4#34036482C211yesmaximal, characteristic, complemented
5#34036474C211yesmaximal, characteristic, complemented
6#34036428C211yesmaximal, characteristic, complemented
7#34036423C211yesmaximal, characteristic, complemented
8#34036345C211yesmaximal, characteristic, complemented
9#34036343C211yesmaximal, characteristic, complemented
10#34036323C211yesmaximal, characteristic
11#34036253C211yesmaximal, characteristic, complemented
12#34036216C211yesmaximal, characteristic, complemented
13#34036211C211yesmaximal, characteristic, complemented
14C4×#17989787C211yesmaximal, characteristic, complemented
15#478×C293C211yesmaximal, characteristic, complemented
16C2×#17989791C2211yescharacteristic
17C2×D2344C2211yescharacteristic
18C2×#17989787C2211yescharacteristic
19#22627623C2211yescharacteristic
20#22627620C2211yescharacteristic
21#22627615C2211yescharacteristic
22#22627612C2211yescharacteristic
23#22627611C2211yescharacteristic
24#22627610—21no—
25#22627607—21no—
26#22627606—21no—
27#22627604—21no—
28#22627602—21no—
29#22627602—21no—
30C4×Dic586C2211yescharacteristic
31#22627589C2211yescharacteristic
32C4×D1172C2211yescharacteristic
33#22627586C2211yescharacteristic
34#22627586C2211yescharacteristic
35#22627586C2211yescharacteristic
36C4×C22⋊D293—21no—
37C4⋊C4×D293—21no—
38#22627557C2211yescharacteristic
39#22627553C2211yescharacteristic
40#22627553C2211yescharacteristic
41#22627549C2211yescharacteristic
42#22627547C2211yescharacteristic
43#22627547C2211yescharacteristic
44#22627546C2211yescharacteristic
45#22627545C2211yescharacteristic
46#22627544C2211yescharacteristic
47#22627544C2211yescharacteristic
48#22627544C2211yescharacteristic
49C4×#14556873C2211yescharacteristic
50C8×Dic293C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52#125×C293C2211yescharacteristic
53C4×D4×C293C2211yescharacteristic
54#107×C293C2211yescharacteristic
55#106×C293C2211yescharacteristic
56C4⋊C8×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58#102×C293C2211yescharacteristic
59C2×Dic586—21no—
60C2×Dic586D411yescharacteristic
61C2×Dic586C2311yescharacteristic
62C2×D1172C2311yescharacteristic
63C2×D1172C2311yescharacteristic
64C2×C22⋊D293—21no—
65C2×C22⋊D293—21no—
66C2×C4×D293—21no—
67C2×C4×D293—21no—
68C2×C4×D293—21no—
69C2×C4×D293—21no—
70#17989791—22no—
71D2344—22no—
72#17989787—22no—
73C2×#14556873C2311yescharacteristic
74C2×#14556873C2311yescharacteristic
75C4⋊Dic293—21no—
76C4⋊Dic293D411yescharacteristic
77C4⋊Dic293C2311yescharacteristic
78#17989781—21no—
79#17989781—21no—
80#17989781—21no—
81#17989781D411yescharacteristic
82#17989781D411yescharacteristic
83C22⋊Dic293—21no—
84C22⋊Dic293—21no—
85#17989779—21no—
86#17989779—21no—
87#17989779—21no—
88#17989779—21no—
89#17989779—21no—
90#17989779—21no—
91C4×Dic293—21no—
92C4×Dic293C2311yescharacteristic
93C4×Dic293C2311yescharacteristic
94C2×D4×C293C2311yescharacteristic
95C22×C4×C293—21no—
96C2×C8×C293C2311yescharacteristic
97C2×C8×C293C2311yescharacteristic
98C4⋊C4×C293—21no—
99C4⋊C4×C293—21no—
100C4⋊C4×C293C2311yescharacteristic
101C4⋊C4×C293C2311yescharacteristic
102C4⋊C4×C293C2311yescharacteristic
103C22⋊C4×C293—21no—
104C42×C293C2311yescharacteristic
105C22×D293—21no—
106C22×D293—21no—
107Dic586—22no—
108Dic586—21no—
109Dic586—21no—
110Dic586—81no—
111D1172—21no—
112D1172—21no—
113D1172—21no—
114D1172#4112yes—
115C22⋊D293—42no—
116C22⋊D293—81no—
117C2×Dic293—21no—
118C2×Dic293—21no—
119C2×Dic293C2×D411yescharacteristic
120C2×Dic293C2×D411yescharacteristic
121C2×Dic293C2×D411yescharacteristic
122C2×Dic293C2×D411yescharacteristic
123C4×D293—42no—
124C4×D293—81no—
125C4×D293—81no—
126C4×D293—81no—
127#14556873—21no—
128#14556873—21no—
129C23×C293—21no—
130D4×C293—21no—
131D4×C293—21no—
132C2×C4×C293—21no—
133C2×C4×C293—21no—
134C2×C4×C293—21no—
135C2×C4×C293—81no—
136C2×C4×C293C2×D411yescharacteristic
137C2×C4×C293C2×D411yescharacteristic
138C2×C4×C293C2411yescharacteristic
139C8×C293—21no—
140C8×C293—21no—
141C22×C293—41no—
142C22×C293—41no—
143C22×C293—41no—
144C22×C293C22×D411yescharacteristic
145C2×D293—22no—
146C2×D293—41no—
147C2×D293—41no—
148C2×D293—41no—
149C2×D293—41no—
150C2×D293—41no—
151C4×C293—21no—
152C4×C293—21no—
153C4×C293—41no—
154C4×C293—41no—
155C4×C293—41no—
156C4×C293C2×#4111yescharacteristic
157C4×C2932−1+411yescharacteristic
158Dic293—21no—
159Dic293—21no—
160Dic293—21no—
161Dic293—41no—
162Dic293—41no—
163Dic293#13512yes—
164C2×C293—81no—
165C2×C293#54811yescharacteristic
166C2×C293C2×#13511yescharacteristic
167C2×C293#57611yescharacteristic
168D293—42no—
169D293—81no—
170C293#336111yescharacteristic, complemented, Sylow
171#3361—2931nomaximal, Sylow
172#559—2931no—
173#554—2931no—
174#488—2931no—
175#488—2931no—
176#486—2931no—
177#478—2931no—
178#478D29311yescharacteristic, complemented
179#477—2931no—
180#463—2931no—
181#463—2931no—
182#459—2931no—
183C8×Q8—2931no—
184C4×SD16—2931no—
185C4×D8—2931no—
186C4×D8—2931no—
187C2×SD16—2931no—
188C2×D8—2931no—
189C2×D8—2931no—
190C4⋊Q8—2931no—
191#127—2931no—
192#125—2931no—
193#125C2×D29311yescharacteristic
194#124—2931no—
195#124—2931no—
196#124—5861no—
197#123—5861no—
198#123—5861no—
199C22⋊Q8—5861no—
200C22⋊Q8—5861no—
201C22⋊Q8—5861no—
202C4×Q8—2931no—
203C4×Q8—2931no—
204C4×D4—2931no—
205C4×D4—2931no—
206C4×D4—2931no—
207C4×D4—2931no—
208C4×D4—5861no—
209C4×D4C2×D29311yescharacteristic
210C2×C4⋊C4—5861no—
211#107—2931no—
212#107C2×D29311yescharacteristic
213#106C2×D29311yescharacteristic
214C4⋊C8—2931no—
215C4⋊C8—2931no—
216C4⋊C8C2×D29311yescharacteristic
217#103—2931no—
218#103—2931no—
219#103—2931no—
220#102—2931no—
221#102—2931no—
222#102—2931no—
223#102—2931no—
224#102—2931no—
225#102C2×D29311yescharacteristic
226#102C2×D29311yescharacteristic
227C4×C8—2931no—
228C4×C8—2931no—
229C4×C8—2931no—
230C2×Q8—2931no—
231C2×Q8—2931no—
232C2×Q8—5861no—
233C2×D4—2931no—
234C2×D4—2931no—
235C2×D4—5861no—
236C2×D4—5861no—
237C2×D4C22×D29311yescharacteristic
238C22×C4—21no—
239C22×C4—5861no—
240C22×C4—5861no—
241C22×C4—5861no—
242C22×C4—5861no—
243SD16—5862no—
244D8—5862no—
245D8—5862no—
246C2×C8—2931no—
247C2×C8—2931no—
248C2×C8C22×D29311yescharacteristic
249C2×C8C22×D29311yescharacteristic
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—2931no—
253C4⋊C4—2931no—
254C4⋊C4—2931no—
255C4⋊C4—2931no—
256C4⋊C4—5861no—
257C4⋊C4—5861no—
258C4⋊C4—5861no—
259C4⋊C4—5861no—
260C4⋊C4C22×D29311yescharacteristic
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—
270C22⋊C4—5861no—
271C22⋊C4—5861no—
272C42—2931no—
273C42—2931no—
274C42—5861no—
275C42C22×D29311yescharacteristic
276C23—21no—
277C23—5861no—
278C23—5861no—
279Q8—23441no—
280Q8—5862no—
281Q8—5861no—
282Q8—5861no—
283D4—21no—
284D4—21no—
285D4—2932no—
286D4—23441no—
287D4—5861no—
288D4—5861no—
289D4—5861no—
290D4—11722no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—81no—
295C2×C4—2931no—
296C2×C4—2931no—
297C2×C4—2931no—
298C2×C4—2931no—
299C2×C4—23441no—
300C2×C4—23441no—
301C2×C4—23441no—
302C2×C4—5861no—
303C2×C4—5861no—
304C2×C4—11722no—
305C2×C4D4×D29311yescharacteristic
306C2×C4D4×D29311yescharacteristic
307C2×C4C23×D29311yescharacteristic
308C8—21no—
309C8—21no—
310C8—5861no—
311C8—5861no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—5862no—
316C22—11721no—
317C22—11721no—
318C22—11721no—
319C22—11721no—
320C22—11721no—
321C22C2×D4×D29311yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—2932no—
328C4—5861no—
329C4—5861no—
330C4—5861no—
331C4—11721no—
332C4—11721no—
333C4#41×D29311yescharacteristic
334C4#2262767211yescharacteristic
335C2—81no—
336C2—23441no—
337C2—11722no—
338C2#3403678911yescharacteristic
339C2#135×D29311yescharacteristic
340C2#3403693311yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#478×C293C2
socleC22×C293C22×D4
prime radical#34036323C2
hypercenter#478D293
hypocenterC293#3361
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. #34036862C2semidirect
2. #34036835C2semidirect
3. #34036486C2semidirect
4. #34036482C2semidirect
5. #34036474C2semidirect
6. #34036428C2semidirect
7. #34036423C2semidirect
8. #34036345C2semidirect
9. #34036343C2semidirect
11. #34036253C2semidirect
12. #34036216C2semidirect
13. #34036211C2semidirect
14. C4×#17989787C2semidirect
15. #478×C293C2semidirect
170. C293#3361semidirect
178. #478D293semidirect

Maximal subgroups

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

subgroupindex
#340368622
#340368352
#340364862
#340364822
#340364742
#340364282
#340364232
#340363452
#340363432
#340363232
#340362532
#340362162
#340362112
C4×#179897872
#478×C2932
#3361293