Finite Group Databasebeta

← #49168913

Subgroups — #49168913

Order 37504.

380 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036683C211yesmaximal, characteristic
2C4×Q8×D293C211yesmaximal, characteristic
3#34036461C211yesmaximal, characteristic
4#34036458C211yesmaximal, characteristic
5#34036413C211yesmaximal, characteristic, complemented
6#34036412C211yesmaximal, characteristic, complemented
7#34036338C211yesmaximal, characteristic, complemented
8#34036337C211yesmaximal, characteristic, complemented
9#34036286C211yesmaximal, characteristic
10#34036283C211yesmaximal, characteristic
11#34036237C211yesmaximal, characteristic, complemented
12#34036234C211yesmaximal, characteristic, complemented
13#34036234C211yesmaximal, characteristic, complemented
14#34036184C211yesmaximal, characteristic
15#441×C293C211yesmaximal, characteristic, complemented
16C2×Q8×D293C2211yescharacteristic
17C2×Dic1172C2211yescharacteristic
18C2×#17989792C2211yescharacteristic
19C2×#17989792C2211yescharacteristic
20#22627623C2211yescharacteristic
21#22627622C2211yescharacteristic
22#22627614—21no—
23#22627604C2211yescharacteristic
24#22627602—21no—
25#22627600C2211yescharacteristic
26Q8×Dic293C2211yescharacteristic
27C4×Dic586—21no—
28C4×Dic586—21no—
29C4×Dic586C2211yescharacteristic
30C4×Dic586C2211yescharacteristic
31#22627589—21no—
32#22627589C2211yescharacteristic
33#22627581—21no—
34C4⋊C4×D293—21no—
35C4⋊C4×D293C2211yescharacteristic
36C42×D293—21no—
37C42×D293C2211yescharacteristic
38#22627556C2211yescharacteristic
39#22627555C2211yescharacteristic
40#22627555C2211yescharacteristic
41#22627553C2211yescharacteristic
42#22627553C2211yescharacteristic
43#22627549C2211yescharacteristic
44#22627549C2211yescharacteristic
45#22627548C2211yescharacteristic
46#22627548C2211yescharacteristic
47#22627547C2211yescharacteristic
48#22627547C2211yescharacteristic
49#22627536C2211yescharacteristic
50#22627536C2211yescharacteristic
51#22627535C2211yescharacteristic
52C2×Q16×C293C2211yescharacteristic
53C4×Q8×C293C2211yescharacteristic
54C4×Q8×C293C2211yescharacteristic
55#106×C293C2211yescharacteristic
56#103×C293C2211yescharacteristic
57#103×C293C2211yescharacteristic
58#97×C293C2211yescharacteristic
59C2×Dic586—21no—
60C2×Dic586—21no—
61C2×Dic586C2311yescharacteristic
62C2×Dic586C2311yescharacteristic
63Q8×D293—22no—
64Q8×D293—22no—
65C2×C4×D293—21no—
66C2×C4×D293—21no—
67C2×C4×D293D411yescharacteristic
68C2×C4×D293D411yescharacteristic
69C2×C4×D293C2311yescharacteristic
70Dic1172—22no—
71#17989792—22no—
72#17989792—22no—
73C2×#14556873C2311yescharacteristic
74C2×#14556873C2311yescharacteristic
75C4⋊Dic293—21no—
76C4⋊Dic293—21no—
77C4⋊Dic293C2311yescharacteristic
78C4⋊Dic293C2311yescharacteristic
79#17989781—21no—
80#17989781—21no—
81#17989781—21no—
82#17989781—21no—
83#17989781—21no—
84#17989781—21no—
85#17989781—21no—
86#17989781—21no—
87#17989779—21no—
88#17989779—21no—
89C4×Dic293—21no—
90C4×Dic293—21no—
91C4×Dic293—21no—
92C4×Dic293—21no—
93C4×Dic293D411yescharacteristic
94C4×Dic293D411yescharacteristic
95C4×Dic293C2311yescharacteristic
96C2×Q8×C293C2311yescharacteristic
97C2×Q8×C293C2311yescharacteristic
98Q16×C293—22no—
99C2×C8×C293C2311yescharacteristic
100C2×C8×C293C2311yescharacteristic
101C4⋊C4×C293—21no—
102C4⋊C4×C293—21no—
103C4⋊C4×C293C2311yescharacteristic
104C4⋊C4×C293C2311yescharacteristic
105C42×C293—21no—
106C42×C293—21no—
107C42×C293C2311yescharacteristic
108C22×D293C2×D411yescharacteristic
109Dic586—24no—
110Dic586—21no—
111Dic586—21no—
112Dic586—21no—
113Dic586—42no—
114Dic586#4112yes—
115C2×Dic293—21no—
116C2×Dic293—21no—
117C2×Dic293—21no—
118C2×Dic293—21no—
119C2×Dic293C2×D411yescharacteristic
120C2×Dic293C2×D411yescharacteristic
121C2×Dic293C2×D411yescharacteristic
122C4×D293—24no—
123C4×D293—22no—
124C4×D293—21no—
125C4×D293—21no—
126C4×D293—22no—
127C4×D293—42no—
128#14556873—21no—
129#14556873—21no—
130Q8×C293—21no—
131Q8×C293—21no—
132Q8×C293—21no—
133Q8×C293#4112yes—
134C2×C4×C293—21no—
135C2×C4×C293—21no—
136C2×C4×C293—21no—
137C2×C4×C293—21no—
138C2×C4×C293C2×D411yescharacteristic
139C2×C4×C293C2×D411yescharacteristic
140C2×C4×C293C2411yescharacteristic
141C8×C293—21no—
142C8×C293—21no—
143C22×C293C22×D411yescharacteristic
144C2×D293—21no—
145C2×D293—21no—
146C2×D293#13712yes—
147C4×C293—22no—
148C4×C293—21no—
149C4×C293—21no—
150C4×C293—41no—
151C4×C293—41no—
152C4×C293—41no—
153C4×C293C2×#4111yescharacteristic
154C4×C293C2×#4111yescharacteristic
155Dic293—22no—
156Dic293—21no—
157Dic293—21no—
158Dic293—41no—
159Dic293—41no—
160Dic293—41no—
161Dic293#13712yes—
162C2×C293#52511yescharacteristic
163C2×C293C2×#13711yescharacteristic
164C2×C293C2×#13711yescharacteristic
165D293—22no—
166C293#311311yescharacteristic, complemented, Sylow
167#3113—2931nomaximal, Sylow
168#533—2931no—
169C2×C4×Q8—2931no—
170#483—2931no—
171#483—2931no—
172#475—2931no—
173#475—2931no—
174#462—2931no—
175#462—2931no—
176#451—2931no—
177#451—2931no—
178#441—2931no—
179#441—2931no—
180#441—2931no—
181#441D29311yescharacteristic, complemented
182#432—2931no—
183C22×Q8—2931no—
184C2×Q16—2931no—
185C2×Q16—2931no—
186C2×Q16—2931no—
187C2×Q16C2×D29311yescharacteristic
188C4⋊Q8—2931no—
189C4⋊Q8—2931no—
190#125—5861no—
191C22⋊Q8—2931no—
192C22⋊Q8—2931no—
193C22⋊Q8—5861no—
194C4×Q8—2931no—
195C4×Q8—2931no—
196C4×Q8—2931no—
197C4×Q8—2931no—
198C4×Q8—5861no—
199C4×Q8—5861no—
200C4×Q8—5861no—
201C4×Q8C2×D29311yescharacteristic
202C4×Q8C2×D29311yescharacteristic
203#117—5861no—
204C2×C4⋊C4—2931no—
205C2×C4⋊C4—5861no—
206C2×C42—2931no—
207C2×C42—5861no—
208#106—2931no—
209#106—2931no—
210#106—2931no—
211#106C2×D29311yescharacteristic
212C4⋊C8—2931no—
213C4⋊C8—2931no—
214#103—2931no—
215#103—2931no—
216#103—2931no—
217#103—2931no—
218#103—2931no—
219#103—2931no—
220#103C2×D29311yescharacteristic
221#103C2×D29311yescharacteristic
222C22⋊C8—2931no—
223C22⋊C8—2931no—
224#97—2931no—
225#97C2×D29311yescharacteristic
226C2×Q8—2931no—
227C2×Q8—2931no—
228C2×Q8—5861no—
229C2×Q8—5861no—
230C2×Q8—5862no—
231C2×Q8—5862no—
232C2×Q8C22×D29311yescharacteristic
233C2×Q8C22×D29311yescharacteristic
234C22×C4—2931no—
235C22×C4—2931no—
236C22×C4—2931no—
237C22×C4—5861no—
238C22×C4—5861no—
239Q16—22no—
240Q16—5862no—
241Q16—5862no—
242Q16—5862no—
243C2×C8—2931no—
244C2×C8—2931no—
245C2×C8C22×D29311yescharacteristic
246C2×C8C22×D29311yescharacteristic
247C4⋊C4—21no—
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—5861no—
264C22⋊C4—5861no—
265C42—21no—
266C42—21no—
267C42—2931no—
268C42—2931no—
269C42—2931no—
270C42—5861no—
271C42—5861no—
272C42—5861no—
273C42—5861no—
274C42C22×D29311yescharacteristic
275C23—2931no—
276Q8—21no—
277Q8—21no—
278Q8—21no—
279Q8—2932no—
280Q8—5864no—
281Q8—5861no—
282Q8—5861no—
283Q8—5861no—
284Q8—11722no—
285Q8#1798980212yes—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—2931no—
291C2×C4—2931no—
292C2×C4—2931no—
293C2×C4—5862no—
294C2×C4—5862no—
295C2×C4—5864no—
296C2×C4—5861no—
297C2×C4—5861no—
298C2×C4—5861no—
299C2×C4—5861no—
300C2×C4—5861no—
301C2×C4—5861no—
302C2×C4—11722no—
303C2×C4D4×D29311yescharacteristic
304C2×C4D4×D29311yescharacteristic
305C2×C4C23×D29311yescharacteristic
306C8—21no—
307C8—21no—
308C8—5861no—
309C8—5861no—
310C22—2932no—
311C22—5861no—
312C22—5861no—
313C22C2×D4×D29311yescharacteristic
314C4—22no—
315C4—21no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—2932no—
321C4—5861no—
322C4—5862no—
323C4—5861no—
324C4—11721no—
325C4—11721no—
326C4—11721no—
327C4#41×D29311yescharacteristic
328C4C2×#1798980211yescharacteristic
329C2—5862no—
330C2#3403663811yescharacteristic
331C2#137×D29311yescharacteristic
332C2#137×D29311yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#441×C293C2
socleC22×C293C22×D4
prime radicalC22×D293C2×D4
hypercenter#441D293
hypocenterC293#3113
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
5. #34036413C2semidirect
6. #34036412C2semidirect
7. #34036338C2semidirect
8. #34036337C2semidirect
11. #34036237C2semidirect
12. #34036234C2semidirect
13. #34036234C2semidirect
15. #441×C293C2semidirect
166. C293#3113semidirect
181. #441D293semidirect

Maximal subgroups

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

subgroupindex
#340366832
C4×Q8×D2932
#340364612
#340364582
#340364132
#340364122
#340363382
#340363372
#340362862
#340362832
#340362372
#340362342
#340361842
#441×C2932
#3113293