Finite Group Databasebeta

← #49169016

Subgroups — #49169016

Order 37504.

370 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#34036750C211yesmaximal, characteristic
2#34036606C211yesmaximal, characteristic, complemented
3#34036471C211yesmaximal, characteristic, complemented
4#34036454C211yesmaximal, characteristic
5#34036425C211yesmaximal, characteristic, complemented
6#34036415C211yesmaximal, characteristic, complemented
7#34036352C211yesmaximal, characteristic, complemented
8#34036352C211yesmaximal, characteristic, complemented
9#34036287C211yesmaximal, characteristic, complemented
10#34036270C211yesmaximal, characteristic
11#34036237C211yesmaximal, characteristic, complemented
12#34036231C211yesmaximal, characteristic, complemented
13C4×Dic1172C211yesmaximal, characteristic, complemented
14C4×#17989791C211yesmaximal, characteristic, complemented
15#433×C293C211yesmaximal, characteristic, complemented
16C22×Dic586C2211yescharacteristic
17C2×Dic1172C2211yescharacteristic
18C2×Dic1172C2211yescharacteristic
19C2×#17989791C2211yescharacteristic
20C2×#17989791C2211yescharacteristic
21#22627624C2211yescharacteristic
22#22627619—21no—
23#22627612C2211yescharacteristic
24#22627610—21no—
25#22627606—21no—
26#22627603C2211yescharacteristic
27#22627602—21no—
28#22627598C2211yescharacteristic
29C4×Dic586C2211yescharacteristic
30C4×Dic586C2211yescharacteristic
31C4×Dic586C2211yescharacteristic
32C4×Dic586C2211yescharacteristic
33C4×Dic586C2211yescharacteristic
34#22627589—21no—
35#22627589—21no—
36C4×D1172C2211yescharacteristic
37#22627583C2211yescharacteristic
38#22627580—21no—
39#22627580—21no—
40#22627558C2211yescharacteristic
41#22627558C2211yescharacteristic
42#22627556C2211yescharacteristic
43#22627556C2211yescharacteristic
44#22627549C2211yescharacteristic
45#22627549C2211yescharacteristic
46#22627549C2211yescharacteristic
47#22627549C2211yescharacteristic
48#22627549C2211yescharacteristic
49#22627549C2211yescharacteristic
50#22627546C2211yescharacteristic
51#22627546C2211yescharacteristic
52#117×C293C2211yescharacteristic
53C4⋊C8×C293C2211yescharacteristic
54C4⋊C8×C293C2211yescharacteristic
55C22⋊C8×C293C2211yescharacteristic
56C22⋊C8×C293C2211yescharacteristic
57#97×C293C2211yescharacteristic
58C4×C8×C293C2211yescharacteristic
59C2×Dic586—22no—
60C2×Dic586—22no—
61C2×Dic586—21no—
62C2×Dic586—21no—
63C2×Dic586C2311yescharacteristic
64C2×Dic586C2311yescharacteristic
65C2×Dic586C2311yescharacteristic
66C2×D1172C2311yescharacteristic
67C2×C22⋊D293—21no—
68C22×Dic293—21no—
69C2×C4×D293—21no—
70Dic1172—22no—
71Dic1172—22no—
72#17989791—22no—
73#17989791—22no—
74C4⋊Dic293—21no—
75C4⋊Dic293C2311yescharacteristic
76C4⋊Dic293C2311yescharacteristic
77C4⋊Dic293C2311yescharacteristic
78C4⋊Dic293C2311yescharacteristic
79#17989781—21no—
80#17989781—21no—
81#17989781—21no—
82#17989781—21no—
83#17989781—21no—
84#17989781—21no—
85C22⋊Dic293—21no—
86C22⋊Dic293—21no—
87#17989779—21no—
88#17989779—21no—
89#17989779—21no—
90#17989779—21no—
91C4×Dic293—21no—
92C4×Dic293—21no—
93C4×Dic293—21no—
94C4×Dic293—21no—
95C4×Dic293—21no—
96C4×Dic293—21no—
97C22×C4×C293C2311yescharacteristic
98C2×C8×C293C2311yescharacteristic
99C2×C8×C293C2311yescharacteristic
100C2×C8×C293C2311yescharacteristic
101C2×C8×C293C2311yescharacteristic
102C4⋊C4×C293D411yescharacteristic
103C4⋊C4×C293D411yescharacteristic
104C22⋊C4×C293D411yescharacteristic
105C22⋊C4×C293D411yescharacteristic
106C42×C293C2311yescharacteristic
107C42×C293C2311yescharacteristic
108C22×D293—21no—
109Dic586—24no—
110Dic586—21no—
111Dic586—21no—
112Dic586—21no—
113Dic586—21no—
114Dic586—81no—
115Dic586#4112yes—
116Dic586#4112yes—
117D1172—21no—
118D1172—21no—
119C22⋊D293—81no—
120C2×Dic293—24no—
121C2×Dic293—21no—
122C2×Dic293—21no—
123C2×Dic293—21no—
124C2×Dic293—21no—
125C2×Dic293—21no—
126C2×Dic293—21no—
127C2×Dic293—21no—
128C4×D293—81no—
129C23×C293C2×D411yescharacteristic
130C2×C4×C293—21no—
131C2×C4×C293—21no—
132C2×C4×C293C2×D411yescharacteristic
133C2×C4×C293C2×D411yescharacteristic
134C2×C4×C293C2×D411yescharacteristic
135C2×C4×C293C2×D411yescharacteristic
136C2×C4×C293C2×D411yescharacteristic
137C2×C4×C293C2411yescharacteristic
138C8×C293—21no—
139C8×C293—21no—
140C8×C293—21no—
141C8×C293—21no—
142C22×C293—21no—
143C22×C293—21no—
144C22×C293—21no—
145C22×C293C22×D411yescharacteristic
146C2×D293—41no—
147C2×D293—41no—
148C2×D293—41no—
149C4×C293—21no—
150C4×C293—21no—
151C4×C293—21no—
152C4×C293—21no—
153C4×C293—21no—
154C4×C293C2×#4111yescharacteristic
155C4×C293C2×#4111yescharacteristic
156Dic293—22no—
157Dic293—22no—
158Dic293—41no—
159Dic293—41no—
160Dic293—41no—
161Dic293—41no—
162Dic293—41no—
163C2×C293—41no—
164C2×C293#52511yescharacteristic
165C2×C293#57711yescharacteristic
166C2×C293#57811yescharacteristic
167D293—81no—
168C293#312111yescharacteristic, complemented, Sylow
169#3121—2931nomaximal, Sylow
170#542—2931no—
171#519—2931no—
172#485—2931no—
173#482—2931no—
174#477—2931no—
175#475—2931no—
176#464—2931no—
177#464—2931no—
178#451—2931no—
179#448—2931no—
180#441—2931no—
181#440—2931no—
182C4×Q16—2931no—
183C4×SD16—2931no—
184#433D29311yescharacteristic, complemented
185C22×Q8—2931no—
186C2×Q16—2931no—
187C2×Q16—2931no—
188C2×SD16—2931no—
189C2×SD16—2931no—
190C4⋊Q8—2931no—
191#126—5861no—
192#124—2931no—
193#124—5861no—
194#123—5861no—
195C22⋊Q8—2931no—
196C22⋊Q8—5861no—
197#121—2931no—
198C4×Q8—2931no—
199C4×Q8—2931no—
200C4×Q8—2931no—
201C4×Q8—2931no—
202C4×Q8—2931no—
203C4×Q8—5861no—
204C4×Q8—5861no—
205C4×D4—2931no—
206#117—2931no—
207#117—5861no—
208#117—5861no—
209#117C2×D29311yescharacteristic
210#107—2931no—
211#107—2931no—
212#106—2931no—
213#106—2931no—
214C4⋊C8C2×D29311yescharacteristic
215C4⋊C8C2×D29311yescharacteristic
216#103—2931no—
217#103—2931no—
218#103—2931no—
219#103—2931no—
220#103—2931no—
221#103—2931no—
222#102—2931no—
223#102—2931no—
224C22⋊C8C2×D29311yescharacteristic
225C22⋊C8C2×D29311yescharacteristic
226#97C2×D29311yescharacteristic
227C4×C8C2×D29311yescharacteristic
228C2×Q8—2931no—
229C2×Q8—2931no—
230C2×Q8—2931no—
231C2×Q8—5862no—
232C2×Q8—5862no—
233C2×Q8—5861no—
234C2×Q8—5861no—
235C2×D4—2931no—
236C2×D4—5861no—
237C22×C4—5861no—
238C22×C4—5861no—
239C22×C4C22×D29311yescharacteristic
240Q16—5862no—
241Q16—5862no—
242SD16—5862no—
243SD16—5862no—
244C2×C8C22×D29311yescharacteristic
245C2×C8C22×D29311yescharacteristic
246C2×C8C22×D29311yescharacteristic
247C2×C8C22×D29311yescharacteristic
248C4⋊C4—2931no—
249C4⋊C4—2931no—
250C4⋊C4—2931no—
251C4⋊C4—2931no—
252C4⋊C4—5861no—
253C4⋊C4—5861no—
254C4⋊C4—5861no—
255C4⋊C4—5861no—
256C4⋊C4—5861no—
257C4⋊C4—5861no—
258C4⋊C4—5861no—
259C4⋊C4D117211yescharacteristic
260C4⋊C4D117211yescharacteristic
261C22⋊C4—5861no—
262C22⋊C4—5861no—
263C22⋊C4—5861no—
264C22⋊C4—5861no—
265C22⋊C4—5861no—
266C22⋊C4—5861no—
267C22⋊C4D117211yescharacteristic
268C22⋊C4D117211yescharacteristic
269C42—5861no—
270C42—5861no—
271C42—5861no—
272C42—5861no—
273C42—5861no—
274C42—5861no—
275C42C22×D29311yescharacteristic
276C42C22×D29311yescharacteristic
277C23—5861no—
278C23C2×D117211yescharacteristic
279Q8—2932no—
280Q8—2932no—
281Q8—23441no—
282Q8—5864no—
283Q8—5861no—
284Q8—5861no—
285Q8—5861no—
286Q8—5861no—
287D4—23441no—
288D4—5861no—
289D4—5861no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—23441no—
293C2×C4—5864no—
294C2×C4—5861no—
295C2×C4—5861no—
296C2×C4—5861no—
297C2×C4—5861no—
298C2×C4—5861no—
299C2×C4—5861no—
300C2×C4—5861no—
301C2×C4C2×D117211yescharacteristic
302C2×C4C2×D117211yescharacteristic
303C2×C4C2×D117211yescharacteristic
304C2×C4C2×D117211yescharacteristic
305C2×C4C2×D117211yescharacteristic
306C2×C4C23×D29311yescharacteristic
307C8—21no—
308C8—21no—
309C8—21no—
310C8—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—11721no—
315C22—11721no—
316C22—11721no—
317C22C22×D117211yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—5862no—
324C4—5862no—
325C4—11721no—
326C4—11721no—
327C4—11721no—
328C4—11721no—
329C4—11721no—
330C4#41×D29311yescharacteristic
331C4#41×D29311yescharacteristic
332C2—41no—
333C2—23441no—
334C2#3403664111yescharacteristic
335C2#3403694111yescharacteristic
336C2#3403694611yescharacteristic
subgroupG/H
centerC22C22×D1172
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#433×C293C2
socleC22×C293C22×D4
prime radical#22627598C22
hypercenter#433D293
hypocenterC293#3121
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #34036606C2semidirect
3. #34036471C2semidirect
5. #34036425C2semidirect
6. #34036415C2semidirect
7. #34036352C2semidirect
8. #34036352C2semidirect
9. #34036287C2semidirect
11. #34036237C2semidirect
12. #34036231C2semidirect
13. C4×Dic1172C2semidirect
14. C4×#17989791C2semidirect
15. #433×C293C2semidirect
168. C293#3121semidirect
184. #433D293semidirect

Maximal subgroups

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

subgroupindex
#340367502
#340366062
#340364712
#340364542
#340364252
#340364152
#340363522
#340362872
#340362702
#340362372
#340362312
C4×Dic11722
C4×#179897912
#433×C2932
#3121293