Finite Group Databasebeta

← #49168898

Subgroups — #49168898

Order 37504.

392 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036666C211yesmaximal, characteristic, complemented
2C4×#17989801C211yesmaximal, characteristic, complemented
3#34036469C211yesmaximal, characteristic, complemented
4#34036456C211yesmaximal, characteristic, complemented
5#34036435C211yesmaximal, characteristic, complemented
6#34036427C211yesmaximal, characteristic, complemented
7#34036354C211yesmaximal, characteristic, complemented
8#34036346C211yesmaximal, characteristic, complemented
9#34036288C211yesmaximal, characteristic, complemented
10#34036275C211yesmaximal, characteristic
11#34036239C211yesmaximal, characteristic, complemented
12#34036234C211yesmaximal, characteristic, complemented
13#34036231C211yesmaximal, characteristic, complemented
14#34036184C211yesmaximal, characteristic, complemented
15#440×C293C211yesmaximal, characteristic, complemented
16C2×#17989801C2211yescharacteristic
17C2×#17989792C2211yescharacteristic
18C2×#17989791C2211yescharacteristic
19C2×#17989787C2211yescharacteristic
20#22627619—21no—
21#22627615C2211yescharacteristic
22#22627613C2211yescharacteristic
23#22627609—21no—
24#22627600C2211yescharacteristic
25#22627599C2211yescharacteristic
26C4×Dic586C2211yescharacteristic
27#22627589C2211yescharacteristic
28C4×D1172—21no—
29C4×D1172C2211yescharacteristic
30D4×Dic293C2211yescharacteristic
31C4×C22⋊D293—21no—
32#22627584—21no—
33#22627582C2211yescharacteristic
34#22627581—21no—
35#22627580—21no—
36C2×C4×Dic293—21no—
37C42×D293C2211yescharacteristic
38#22627558C2211yescharacteristic
39#22627555C2211yescharacteristic
40#22627555C2211yescharacteristic
41#22627553C2211yescharacteristic
42#22627553C2211yescharacteristic
43#22627549C2211yescharacteristic
44#22627548C2211yescharacteristic
45#22627547C2211yescharacteristic
46#22627546C2211yescharacteristic
47#22627545C2211yescharacteristic
48#22627544C2211yescharacteristic
49#22627536C2211yescharacteristic
50#22627536C2211yescharacteristic
51#22627535C2211yescharacteristic
52C2×SD16×C293C2211yescharacteristic
53C4×Q8×C293C2211yescharacteristic
54C4×D4×C293C2211yescharacteristic
55#107×C293C2211yescharacteristic
56#103×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58#97×C293C2211yescharacteristic
59#17989801—22no—
60#17989801—22no—
61C2×Dic586C2311yescharacteristic
62C2×D1172—21no—
63C2×D1172C2311yescharacteristic
64C2×C22⋊D293—21no—
65C22×Dic293—21no—
66C22×Dic293—21no—
67C2×C4×D293—21no—
68C2×C4×D293D411yescharacteristic
69C2×C4×D293D411yescharacteristic
70C2×C4×D293C2311yescharacteristic
71#17989792—22no—
72#17989791—22no—
73#17989787—22no—
74C2×#14556873C2311yescharacteristic
75C2×#14556873C2311yescharacteristic
76C4⋊Dic293—21no—
77C4⋊Dic293C2311yescharacteristic
78C4⋊Dic293C2311yescharacteristic
79#17989781—21no—
80#17989781—21no—
81#17989781—21no—
82#17989781—21no—
83C22⋊Dic293—21no—
84#17989779—21no—
85#17989779—21no—
86#17989779—21no—
87#17989779—21no—
88#17989779—21no—
89#17989779—21no—
90C4×Dic293—21no—
91C4×Dic293—21no—
92C4×Dic293—21no—
93C4×Dic293D411yescharacteristic
94C4×Dic293D411yescharacteristic
95C4×Dic293C2311yescharacteristic
96C2×Q8×C293C2311yescharacteristic
97C2×D4×C293C2311yescharacteristic
98C22×C4×C293—21no—
99SD16×C293—22no—
100C2×C8×C293C2311yescharacteristic
101C2×C8×C293C2311yescharacteristic
102C4⋊C4×C293—21no—
103C4⋊C4×C293C2311yescharacteristic
104C4⋊C4×C293C2311yescharacteristic
105C22⋊C4×C293—21no—
106C42×C293—21no—
107C42×C293C2311yescharacteristic
108C22×D293—21no—
109C22×D293C2×D411yescharacteristic
110Dic586—21no—
111Dic586#4112yes—
112D1172—21no—
113D1172—21no—
114D1172—42no—
115C22⋊D293—24no—
116C2×Dic293—24no—
117C2×Dic293—21no—
118C2×Dic293—21no—
119C2×Dic293—21no—
120C2×Dic293—42no—
121C2×Dic293C2×D411yescharacteristic
122C2×Dic293C2×D411yescharacteristic
123C2×Dic293C2×D411yescharacteristic
124C4×D293—21no—
125C4×D293—21no—
126C4×D293—41no—
127C4×D293—41no—
128C4×D293—42no—
129#14556873—21no—
130#14556873—21no—
131C23×C293—21no—
132Q8×C293—21no—
133Q8×C293—21no—
134D4×C293—21no—
135D4×C293#4112yes—
136C2×C4×C293—21no—
137C2×C4×C293—21no—
138C2×C4×C293—21no—
139C2×C4×C293—42no—
140C2×C4×C293C2×D411yescharacteristic
141C2×C4×C293C2×D411yescharacteristic
142C2×C4×C293C2411yescharacteristic
143C8×C293—21no—
144C8×C293—21no—
145C22×C293—22no—
146C22×C293—41no—
147C22×C293—41no—
148C22×C293C22×D411yescharacteristic
149C2×D293—21no—
150C2×D293—21no—
151C2×D293—21no—
152C2×D293—41no—
153C2×D293—41no—
154C2×D293—41no—
155C4×C293—21no—
156C4×C293—21no—
157C4×C293—41no—
158C4×C293—41no—
159C4×C293—41no—
160C4×C293C2×#4111yescharacteristic
161C4×C293C2×#4111yescharacteristic
162Dic293—21no—
163Dic293—22no—
164Dic293—21no—
165Dic293—21no—
166Dic293—41no—
167Dic293—41no—
168C2×C293—42no—
169C2×C293#52511yescharacteristic
170C2×C293#57511yescharacteristic
171C2×C293#57511yescharacteristic
172D293—41no—
173D293—81no—
174C293#311111yescharacteristic, complemented, Sylow
175#3111—2931nomaximal, Sylow
176#529—2931no—
177C4×#41—2931no—
178#485—2931no—
179#482—2931no—
180#479—2931no—
181#478—2931no—
182#464—2931no—
183#463—2931no—
184#452—2931no—
185#449—2931no—
186#442—2931no—
187#441—2931no—
188#440—2931no—
189#440D29311yescharacteristic, complemented
190#432—2931no—
191C2×#41—2931no—
192C2×Q16—2931no—
193C2×SD16—2931no—
194C2×SD16C2×D29311yescharacteristic
195C2×D8—2931no—
196#126—5861no—
197#125—2931no—
198#124—2931no—
199#123—5861no—
200C22⋊Q8—2931no—
201#121—2931no—
202C4×Q8—2931no—
203C4×Q8—2931no—
204C4×Q8C2×D29311yescharacteristic
205C4×D4—2931no—
206C4×D4—2931no—
207C4×D4—5861no—
208C4×D4—5861no—
209C4×D4—5861no—
210C4×D4C2×D29311yescharacteristic
211#117—2931no—
212#117—5861no—
213#117—5861no—
214C2×C42—2931no—
215C2×C42—5861no—
216#107—2931no—
217#107C2×D29311yescharacteristic
218#106—2931no—
219#106—2931no—
220C4⋊C8—2931no—
221C4⋊C8—2931no—
222#103—2931no—
223#103—2931no—
224#103—2931no—
225#103C2×D29311yescharacteristic
226#102—2931no—
227#102—2931no—
228#102—2931no—
229#102C2×D29311yescharacteristic
230C22⋊C8—2931no—
231C22⋊C8—2931no—
232#97—2931no—
233#97C2×D29311yescharacteristic
234#41—5862no—
235#41—5862no—
236C2×Q8—2931no—
237C2×Q8C22×D29311yescharacteristic
238C2×D4—2931no—
239C2×D4—5861no—
240C2×D4—5861no—
241C2×D4C22×D29311yescharacteristic
242C22×C4—21no—
243C22×C4—2931no—
244C22×C4—2931no—
245C22×C4—2931no—
246C22×C4—5861no—
247C22×C4—5861no—
248C22×C4—5861no—
249Q16—5862no—
250SD16—22no—
251SD16—5862no—
252D8—5862no—
253C2×C8—2931no—
254C2×C8—2931no—
255C2×C8C22×D29311yescharacteristic
256C2×C8C22×D29311yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—2931no—
259C4⋊C4—2931no—
260C4⋊C4—5861no—
261C4⋊C4—5861no—
262C4⋊C4—5861no—
263C4⋊C4—5861no—
264C4⋊C4—5861no—
265C4⋊C4C22×D29311yescharacteristic
266C4⋊C4C22×D29311yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—5861no—
269C22⋊C4—5861no—
270C22⋊C4—5861no—
271C22⋊C4—5861no—
272C22⋊C4—5861no—
273C22⋊C4—5861no—
274C22⋊C4—5861no—
275C42—21no—
276C42—2931no—
277C42—2931no—
278C42—2931no—
279C42—5861no—
280C42—5861no—
281C42—5861no—
282C42C22×D29311yescharacteristic
283C23—21no—
284C23—2931no—
285C23—5861no—
286Q8—21no—
287Q8—21no—
288Q8—2932no—
289Q8—5861no—
290D4—21no—
291D4—5864no—
292D4—5861no—
293D4—5861no—
294D4—11722no—
295D4#1798980212yes—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—42no—
300C2×C4—2931no—
301C2×C4—2931no—
302C2×C4—2931no—
303C2×C4—5864no—
304C2×C4—5861no—
305C2×C4—5861no—
306C2×C4—5861no—
307C2×C4—5861no—
308C2×C4—5861no—
309C2×C4—11721no—
310C2×C4—11721no—
311C2×C4—11722no—
312C2×C4—11722no—
313C2×C4D4×D29311yescharacteristic
314C2×C4D4×D29311yescharacteristic
315C2×C4C23×D29311yescharacteristic
316C8—21no—
317C8—21no—
318C8—5861no—
319C8—5861no—
320C22—22no—
321C22—41no—
322C22—41no—
323C22—5861no—
324C22—5861no—
325C22—5861no—
326C22—11721no—
327C22—11721no—
328C22—11721no—
329C22C2×D4×D29311yescharacteristic
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—5861no—
336C4—5862no—
337C4—5861no—
338C4—5861no—
339C4—11721no—
340C4—11721no—
341C4#41×D29311yescharacteristic
342C4C2×#1798980211yescharacteristic
343C2—42no—
344C2—23441no—
345C2—11721no—
346C2#3403663811yescharacteristic
347C2#3403692511yescharacteristic
348C2#3403692811yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#440×C293C2
socleC22×C293C22×D4
prime radical#34036275C2
hypercenter#440D293
hypocenterC293#3111
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. #34036666C2semidirect
2. C4×#17989801C2semidirect
3. #34036469C2semidirect
4. #34036456C2semidirect
5. #34036435C2semidirect
6. #34036427C2semidirect
7. #34036354C2semidirect
8. #34036346C2semidirect
9. #34036288C2semidirect
11. #34036239C2semidirect
12. #34036234C2semidirect
13. #34036231C2semidirect
14. #34036184C2semidirect
15. #440×C293C2semidirect
174. C293#3111semidirect
189. #440D293semidirect

Maximal subgroups

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

subgroupindex
#340366662
C4×#179898012
#340364692
#340364562
#340364352
#340364272
#340363542
#340363462
#340362882
#340362752
#340362392
#340362342
#340362312
#340361842
#440×C2932
#3111293