Finite Group Databasebeta

← #49169019

Subgroups — #49169019

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#34036753C211yesmaximal, characteristic
2#34036605C211yesmaximal, characteristic, complemented
3#34036472C211yesmaximal, characteristic, complemented
4#34036456C211yesmaximal, characteristic
5#34036411C211yesmaximal, characteristic, complemented
6#34036352C211yesmaximal, characteristic, complemented
7#34036351C211yesmaximal, characteristic, complemented
8#34036286C211yesmaximal, characteristic, complemented
9#34036269C211yesmaximal, characteristic
10#34036233C211yesmaximal, characteristic, complemented
11#34036228C211yesmaximal, characteristic, complemented
12#34036223C211yesmaximal, characteristic, complemented
13#34036214C211yesmaximal, characteristic, complemented
14#34036189C211yesmaximal, characteristic, complemented
15#477×C293C211yesmaximal, characteristic, complemented
16C2×Q8×D293C2211yescharacteristic
17C2×Dic1172C2211yescharacteristic
18C2×#17989792C2211yescharacteristic
19C2×#17989791C2211yescharacteristic
20C2×#17989789C2211yescharacteristic
21#22627619—21no—
22#22627613—21no—
23#22627612C2211yescharacteristic
24#22627609—21no—
25#22627604C2211yescharacteristic
26#22627600—21no—
27#22627599C2211yescharacteristic
28Q8×Dic293C2211yescharacteristic
29C4×Dic586—21no—
30C4×Dic586C2211yescharacteristic
31#22627589—21no—
32#22627589C2211yescharacteristic
33#22627589C2211yescharacteristic
34#22627586C2211yescharacteristic
35#22627582—21no—
36#22627582C2211yescharacteristic
37#22627581—21no—
38#22627581C2211yescharacteristic
39#22627555C2211yescharacteristic
40#22627555C2211yescharacteristic
41C4⋊#14556873C2211yescharacteristic
42#22627549C2211yescharacteristic
43#22627547C2211yescharacteristic
44#22627547C2211yescharacteristic
45#22627547C2211yescharacteristic
46#22627546C2211yescharacteristic
47#22627544C2211yescharacteristic
48#22627536C2211yescharacteristic
49#22627536C2211yescharacteristic
50#22627534C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52C4⋊Q8×C293C2211yescharacteristic
53C4×Q8×C293C2211yescharacteristic
54#107×C293C2211yescharacteristic
55#107×C293C2211yescharacteristic
56C4⋊C8×C293C2211yescharacteristic
57#103×C293C2211yescharacteristic
58#103×C293C2211yescharacteristic
59C2×Dic586—21no—
60C2×Dic586C2311yescharacteristic
61C2×Dic586C2311yescharacteristic
62Q8×D293—22no—
63Q8×D293—22no—
64C2×D1172—21no—
65C2×D1172C2311yescharacteristic
66C2×C4×D293—21no—
67C2×C4×D293—21no—
68C2×C4×D293C2311yescharacteristic
69Dic1172—22no—
70#17989792—22no—
71#17989791—22no—
72#17989789—22no—
73C2×#14556873C2311yescharacteristic
74C2×#14556873C2311yescharacteristic
75C4⋊Dic293—21no—
76C4⋊Dic293—21no—
77C4⋊Dic293C2311yescharacteristic
78#17989781—21no—
79#17989781—21no—
80#17989781—21no—
81#17989781D411yescharacteristic
82#17989781D411yescharacteristic
83#17989779—21no—
84#17989779—21no—
85#17989779—21no—
86#17989779—21no—
87#17989779—21no—
88#17989779—21no—
89#17989779D411yescharacteristic
90#17989779D411yescharacteristic
91C4×Dic293—21no—
92C4×Dic293—21no—
93C4×Dic293—21no—
94C4×Dic293—21no—
95C4×Dic293—21no—
96C4×Dic293C2311yescharacteristic
97C2×Q8×C293—21no—
98C2×Q8×C293C2311yescharacteristic
99C2×C8×C293C2311yescharacteristic
100C2×C8×C293C2311yescharacteristic
101C4⋊C4×C293—21no—
102C4⋊C4×C293—21no—
103C4⋊C4×C293C2311yescharacteristic
104C4⋊C4×C293C2311yescharacteristic
105C4⋊C4×C293C2311yescharacteristic
106C42×C293—21no—
107C42×C293C2311yescharacteristic
108C22×D293—21no—
109C22×D293C2×D411yescharacteristic
110Dic586—24no—
111Dic586—21no—
112Dic586—21no—
113Dic586—21no—
114Dic586#4112yes—
115D1172—21no—
116D1172—21no—
117D1172—81no—
118C2×Dic293—21no—
119C2×Dic293—21no—
120C2×Dic293—21no—
121C2×Dic293C2×D411yescharacteristic
122C2×Dic293C2×D411yescharacteristic
123C2×Dic293C2×D411yescharacteristic
124C4×D293—24no—
125C4×D293—21no—
126C4×D293—21no—
127C4×D293—81no—
128#14556873—21no—
129#14556873—21no—
130Q8×C293—21no—
131Q8×C293—81no—
132Q8×C293#4112yes—
133C2×C4×C293—21no—
134C2×C4×C293—21no—
135C2×C4×C293—21no—
136C2×C4×C293—21no—
137C2×C4×C293C2×D411yescharacteristic
138C2×C4×C293C2×D411yescharacteristic
139C2×C4×C293C2411yescharacteristic
140C8×C293—21no—
141C8×C293—21no—
142C22×C293C22×D411yescharacteristic
143C2×D293—21no—
144C2×D293—21no—
145C2×D293—21no—
146C2×D293—41no—
147C2×D293—41no—
148C2×D293—41no—
149C4×C293—22no—
150C4×C293—21no—
151C4×C293—21no—
152C4×C293—41no—
153C4×C293—41no—
154C4×C293—41no—
155C4×C293C2×#4111yescharacteristic
156C4×C293C2×#4111yescharacteristic
157Dic293—22no—
158Dic293—21no—
159Dic293—21no—
160Dic293—21no—
161Dic293—41no—
162Dic293—41no—
163C2×C293#52511yescharacteristic
164C2×C293#57711yescharacteristic
165C2×C293#57811yescharacteristic
166D293—41no—
167D293—81no—
168C293#312111yescharacteristic, complemented, Sylow
169#3121—2931nomaximal, Sylow
170#542—2931no—
171#519—2931no—
172#485—2931no—
173#482—2931no—
174#477D29311yescharacteristic, complemented
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#433—2931no—
185C22×Q8—2931no—
186C2×Q16—2931no—
187C2×Q16—2931no—
188C2×SD16—2931no—
189C2×SD16—2931no—
190C4⋊Q8C2×D29311yescharacteristic
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—5861no—
203C4×Q8—5861no—
204C4×Q8C2×D29311yescharacteristic
205C4×D4—2931no—
206#117—2931no—
207#117—2931no—
208#117—5861no—
209#117—5861no—
210#107C2×D29311yescharacteristic
211#107C2×D29311yescharacteristic
212#106—2931no—
213#106—2931no—
214C4⋊C8—2931no—
215C4⋊C8C2×D29311yescharacteristic
216#103—2931no—
217#103—2931no—
218#103—2931no—
219#103—2931no—
220#103C2×D29311yescharacteristic
221#103C2×D29311yescharacteristic
222#102—2931no—
223#102—2931no—
224C22⋊C8—2931no—
225C22⋊C8—2931no—
226#97—2931no—
227C4×C8—2931no—
228C2×Q8—21no—
229C2×Q8—2931no—
230C2×Q8—2931no—
231C2×Q8—5861no—
232C2×Q8—5862no—
233C2×Q8—5862no—
234C2×Q8C22×D29311yescharacteristic
235C2×D4—2931no—
236C2×D4—5861no—
237C22×C4—2931no—
238C22×C4—5861no—
239C22×C4—5861no—
240Q16—5862no—
241Q16—5862no—
242SD16—5862no—
243SD16—5862no—
244C2×C8—2931no—
245C2×C8—2931no—
246C2×C8C22×D29311yescharacteristic
247C2×C8C22×D29311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
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⋊C4C22×D29311yescharacteristic
259C4⋊C4C22×D29311yescharacteristic
260C4⋊C4C22×D29311yescharacteristic
261C22⋊C4—2931no—
262C22⋊C4—2931no—
263C22⋊C4—5861no—
264C22⋊C4—5861no—
265C22⋊C4—5861no—
266C22⋊C4—5861no—
267C22⋊C4—5861no—
268C22⋊C4—5861no—
269C42—21no—
270C42—2931no—
271C42—5861no—
272C42—5861no—
273C42—5861no—
274C42—5861no—
275C42—5861no—
276C42C22×D29311yescharacteristic
277C23—2931no—
278C23—5861no—
279Q8—21no—
280Q8—81no—
281Q8—2932no—
282Q8—5864no—
283Q8—5861no—
284Q8—5861no—
285Q8—5861no—
286Q8#1798980312yes—
287D4—23441no—
288D4—5861no—
289D4—5861no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—2931no—
295C2×C4—2931no—
296C2×C4—2931no—
297C2×C4—23441no—
298C2×C4—5864no—
299C2×C4—5861no—
300C2×C4—5861no—
301C2×C4—5861no—
302C2×C4—5861no—
303C2×C4—5861no—
304C2×C4D4×D29311yescharacteristic
305C2×C4D4×D29311yescharacteristic
306C2×C4C23×D29311yescharacteristic
307C8—21no—
308C8—21no—
309C8—5861no—
310C8—5861no—
311C22—5861no—
312C22—5861no—
313C22—5861no—
314C22—11721no—
315C22—11721no—
316C22—11721no—
317C22C2×D4×D29311yescharacteristic
318C4—22no—
319C4—21no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—5861no—
325C4—5862no—
326C4—5861no—
327C4—5861no—
328C4—11721no—
329C4—11721no—
330C4#41×D29311yescharacteristic
331C4C2×#1798980311yescharacteristic
332C2—23441no—
333C2—11721no—
334C2#3403664211yescharacteristic
335C2#3403693911yescharacteristic
336C2#3403694211yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#477×C293C2
socleC22×C293C22×D4
prime radical#22627599C22
hypercenter#477D293
hypocenterC293#3121
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
2. #34036605C2semidirect
3. #34036472C2semidirect
5. #34036411C2semidirect
6. #34036352C2semidirect
7. #34036351C2semidirect
8. #34036286C2semidirect
10. #34036233C2semidirect
11. #34036228C2semidirect
12. #34036223C2semidirect
13. #34036214C2semidirect
14. #34036189C2semidirect
15. #477×C293C2semidirect
168. C293#3121semidirect
174. #477D293semidirect

Maximal subgroups

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

subgroupindex
#340367532
#340366052
#340364722
#340364562
#340364112
#340363522
#340363512
#340362862
#340362692
#340362332
#340362282
#340362232
#340362142
#340361892
#477×C2932
#3121293