Finite Group Databasebeta

← #49171504

Subgroups — #49171504

Order 37504.

372 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036851C211yesmaximal, characteristic, complemented
2D4×Dic586C211yesmaximal, characteristic, complemented
3#34036490C211yesmaximal, characteristic, complemented
4#34036489C211yesmaximal, characteristic, complemented
5#34036478C211yesmaximal, characteristic, complemented
6#34036424C211yesmaximal, characteristic, complemented
7#34036423C211yesmaximal, characteristic, complemented
8#34036408C211yesmaximal, characteristic, complemented
9#34036346C211yesmaximal, characteristic
10#34036344C211yesmaximal, characteristic
11#34036332C211yesmaximal, characteristic, complemented
12#34036257C211yesmaximal, characteristic, complemented
13#34036226C211yesmaximal, characteristic, complemented
14#34036209C211yesmaximal, characteristic
15#440×C293C211yesmaximal, characteristic, complemented
16C22×Dic586—21no—
17C2×#17989790C2211yescharacteristic
18C2×#17989787C2211yescharacteristic
19#22627624C2211yescharacteristic
20#22627623C2211yescharacteristic
21#22627623C2211yescharacteristic
22#22627622C2211yescharacteristic
23#22627619—21no—
24#22627618—21no—
25#22627613C2211yescharacteristic
26#22627612C2211yescharacteristic
27#22627603—21no—
28#22627602—21no—
29#22627601—21no—
30#22627601—21no—
31C4×Dic586C2211yescharacteristic
32#22627589C2211yescharacteristic
33D4×Dic293C2211yescharacteristic
34D4×Dic293C2211yescharacteristic
35#22627586C2211yescharacteristic
36#22627581—21no—
37#22627557C2211yescharacteristic
38#22627557C2211yescharacteristic
39C4⋊#14556873C2211yescharacteristic
40#22627553C2211yescharacteristic
41#22627553C2211yescharacteristic
42#22627549C2211yescharacteristic
43#22627549C2211yescharacteristic
44#22627548C2211yescharacteristic
45#22627548C2211yescharacteristic
46#22627547C2211yescharacteristic
47#22627546C2211yescharacteristic
48#22627546C2211yescharacteristic
49#22627544C2211yescharacteristic
50#22627534C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52C2×SD16×C293C2211yescharacteristic
53C4×Q8×C293C2211yescharacteristic
54C4×D4×C293C2211yescharacteristic
55#107×C293C2211yescharacteristic
56#103×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58#97×C293C2211yescharacteristic
59C2×Dic586—21no—
60C2×Dic586—21no—
61C2×Dic586—21no—
62C2×Dic586—44no—
63C2×Dic586D411yescharacteristic
64C2×Dic586C2311yescharacteristic
65C2×D1172C2311yescharacteristic
66C22×Dic293—21no—
67C22×Dic293—21no—
68C2×C4×D293—21no—
69#17989790—22no—
70#17989787—22no—
71C2×#14556873C2311yescharacteristic
72C2×#14556873C2311yescharacteristic
73C4⋊Dic293—21no—
74C4⋊Dic293D411yescharacteristic
75C4⋊Dic293C2311yescharacteristic
76C4⋊Dic293C2311yescharacteristic
77#17989781—21no—
78#17989781—21no—
79#17989781—21no—
80#17989781—21no—
81#17989781—21no—
82#17989781D411yescharacteristic
83#17989781D411yescharacteristic
84C22⋊Dic293—21no—
85C22⋊Dic293—21no—
86#17989779—21no—
87#17989779—21no—
88#17989779—21no—
89#17989779—21no—
90#17989779—21no—
91C4×Dic293—21no—
92C4×Dic293C2311yescharacteristic
93C4×Dic293C2311yescharacteristic
94C2×Q8×C293C2311yescharacteristic
95C2×D4×C293C2311yescharacteristic
96C22×C4×C293—21no—
97SD16×C293—22no—
98C2×C8×C293C2311yescharacteristic
99C2×C8×C293C2311yescharacteristic
100C4⋊C4×C293—21no—
101C4⋊C4×C293C2311yescharacteristic
102C4⋊C4×C293C2311yescharacteristic
103C22⋊C4×C293—21no—
104C42×C293—21no—
105C42×C293C2311yescharacteristic
106C22×D293—21no—
107Dic586—22no—
108Dic586—21no—
109Dic586—21no—
110Dic586—42no—
111Dic586—42no—
112Dic586—42no—
113D1172—21no—
114D1172—21no—
115C2×Dic293—21no—
116C2×Dic293—21no—
117C2×Dic293—21no—
118C2×Dic293—42no—
119C2×Dic293—42no—
120C2×Dic293C2×D411yescharacteristic
121C2×Dic293C2×D411yescharacteristic
122C2×Dic293C2×D411yescharacteristic
123C2×Dic293C2×D411yescharacteristic
124C4×D293—42no—
125#14556873—21no—
126#14556873—21no—
127C23×C293—21no—
128Q8×C293—21no—
129Q8×C293—21no—
130D4×C293—21no—
131D4×C293#4112yes—
132C2×C4×C293—21no—
133C2×C4×C293—21no—
134C2×C4×C293—21no—
135C2×C4×C293—42no—
136C2×C4×C293C2×D411yescharacteristic
137C2×C4×C293C2×D411yescharacteristic
138C2×C4×C293C2411yescharacteristic
139C8×C293—21no—
140C8×C293—21no—
141C22×C293—22no—
142C22×C293—41no—
143C22×C293—41no—
144C22×C293C22×D411yescharacteristic
145C2×D293—41no—
146C2×D293—41no—
147C2×D293—41no—
148C4×C293—21no—
149C4×C293—21no—
150C4×C293—41no—
151C4×C293—41no—
152C4×C293—41no—
153C4×C293C2×#4111yescharacteristic
154C4×C2932−1+411yescharacteristic
155Dic293—21no—
156Dic293—21no—
157Dic293—21no—
158Dic293—41no—
159Dic293—41no—
160Dic293—41no—
161Dic293AGL(1,ℤ/8)12yes—
162C2×C293—42no—
163C2×C293#54811yescharacteristic
164C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
165C2×C293#57811yescharacteristic
166D293—81no—
167C293#336711yescharacteristic, complemented, Sylow
168#3367—2931nomaximal, Sylow
169#556—2931no—
170D4×Q8—2931no—
171#489—2931no—
172#489—2931no—
173#487—2931no—
174#477—2931no—
175#477—2931no—
176#474—2931no—
177#463—2931no—
178#463—2931no—
179#461—2931no—
180#446—2931no—
181#440—2931no—
182#440D29311yescharacteristic, complemented
183C4×D8—2931no—
184C22×Q8—5861no—
185C2×SD16—2931no—
186C2×SD16C2×D29311yescharacteristic
187C2×D8—2931no—
188C4⋊Q8—2931no—
189C4⋊Q8—2931no—
190C4⋊Q8—2931no—
191C4⋊Q8—2931no—
192#126—5861no—
193#126—5861no—
194#124—2931no—
195#124—2931no—
196C22⋊Q8—5861no—
197C22⋊Q8—5861no—
198C22⋊Q8—5861no—
199C22⋊Q8—5861no—
200C4×Q8—2931no—
201C4×Q8—2931no—
202C4×Q8C2×D29311yescharacteristic
203C4×D4—2931no—
204C4×D4—2931no—
205C4×D4—2931no—
206C4×D4C2×D29311yescharacteristic
207#117—5861no—
208#107—2931no—
209#107—2931no—
210#107C2×D29311yescharacteristic
211C4⋊C8—2931no—
212C4⋊C8—2931no—
213C4⋊C8—2931no—
214#103—2931no—
215#103—2931no—
216#103—2931no—
217#103—2931no—
218#103—2931no—
219#103C2×D29311yescharacteristic
220#102—2931no—
221#102—2931no—
222#102—2931no—
223#102C2×D29311yescharacteristic
224#97—2931no—
225#97C2×D29311yescharacteristic
226C4×C8—2931no—
227C2×Q8—2931no—
228C2×Q8—2931no—
229C2×Q8—5861no—
230C2×Q8—5861no—
231C2×Q8—5861no—
232C2×Q8—11724no—
233C2×Q8C22×D29311yescharacteristic
234C2×D4—2931no—
235C2×D4C22×D29311yescharacteristic
236C22×C4—21no—
237C22×C4—5861no—
238C22×C4—5861no—
239C22×C4—5861no—
240SD16—22no—
241SD16—5862no—
242D8—5862no—
243C2×C8—2931no—
244C2×C8—2931no—
245C2×C8C22×D29311yescharacteristic
246C2×C8C22×D29311yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—2931no—
249C4⋊C4—2931no—
250C4⋊C4—2931no—
251C4⋊C4—2931no—
252C4⋊C4—2931no—
253C4⋊C4—5861no—
254C4⋊C4—5861no—
255C4⋊C4—5861no—
256C4⋊C4—5861no—
257C4⋊C4—5861no—
258C4⋊C4—5861no—
259C4⋊C4C22×D29311yescharacteristic
260C4⋊C4C22×D29311yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—5861no—
263C22⋊C4—5861no—
264C22⋊C4—5861no—
265C22⋊C4—5861no—
266C22⋊C4—5861no—
267C22⋊C4—5861no—
268C22⋊C4—5861no—
269C42—21no—
270C42—2931no—
271C42—2931no—
272C42—5861no—
273C42C22×D29311yescharacteristic
274C23—21no—
275C23—5861no—
276Q8—21no—
277Q8—21no—
278Q8—5862no—
279Q8—5861no—
280Q8—5861no—
281Q8—11722no—
282Q8—11722no—
283Q8—11722no—
284D4—21no—
285D4—5861no—
286D4—5861no—
287D4#1798980212yes—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—2931no—
293C2×C4—2931no—
294C2×C4—2931no—
295C2×C4—2931no—
296C2×C4—5861no—
297C2×C4—5861no—
298C2×C4—5861no—
299C2×C4—11722no—
300C2×C4—11722no—
301C2×C4—11722no—
302C2×C4D4×D29311yescharacteristic
303C2×C4D4×D29311yescharacteristic
304C2×C4C23×D29311yescharacteristic
305C8—21no—
306C8—21no—
307C8—5861no—
308C8—5861no—
309C22—22no—
310C22—41no—
311C22—41no—
312C22—11721no—
313C22—11721no—
314C22—11721no—
315C22C2×D4×D29311yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—2932no—
322C4—5861no—
323C4—5861no—
324C4—5861no—
325C4—11721no—
326C4—11721no—
327C4—11721no—
328C4C2×#1798980211yescharacteristic
329C4#2262767111yescharacteristic
330C2—42no—
331C2—23441no—
332C2#3403678811yescharacteristic
333C2AGL(1,ℤ/8)×D29311yescharacteristic
334C2#3403694511yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#440×C293C2
socleC22×C293C22×D4
prime radicalC2×#17989787C22
hypercenter#440D293
hypocenterC293#3367
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #34036851C2semidirect
2. D4×Dic586C2semidirect
3. #34036490C2semidirect
4. #34036489C2semidirect
5. #34036478C2semidirect
6. #34036424C2semidirect
7. #34036423C2semidirect
8. #34036408C2semidirect
11. #34036332C2semidirect
12. #34036257C2semidirect
13. #34036226C2semidirect
15. #440×C293C2semidirect
167. C293#3367semidirect
182. #440D293semidirect

Maximal subgroups

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

subgroupindex
#340368512
D4×Dic5862
#340364902
#340364892
#340364782
#340364242
#340364232
#340364082
#340363462
#340363442
#340363322
#340362572
#340362262
#340362092
#440×C2932
#3367293