Finite Group Databasebeta

← #49168932

Subgroups — #49168932

Order 37504.

430 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036676C211yesmaximal, characteristic, complemented
2C4×#17989801C211yesmaximal, characteristic, complemented
3#34036455C211yesmaximal, characteristic, complemented
4#34036451C211yesmaximal, characteristic, complemented
5#34036413C211yesmaximal, characteristic, complemented
6#34036407C211yesmaximal, characteristic, complemented
7#34036328C211yesmaximal, characteristic, complemented
8#34036322C211yesmaximal, characteristic, complemented
9#34036275C211yesmaximal, characteristic, complemented
10#34036271C211yesmaximal, characteristic, complemented
11#34036239C211yesmaximal, characteristic, complemented
12#34036231C211yesmaximal, characteristic, complemented
13#34036229C211yesmaximal, characteristic, complemented
14#34036184C211yesmaximal, characteristic, complemented
15#442×C293C211yesmaximal, characteristic, complemented
16C2×#17989802—21no—
17C2×#17989801C2211yescharacteristic
18C2×#17989791C2211yescharacteristic
19C2×#17989790C2211yescharacteristic
20C2×#17989787C2211yescharacteristic
21#22627623C2211yescharacteristic
22#22627620C2211yescharacteristic
23#22627610—21no—
24#22627599C2211yescharacteristic
25#22627597—21no—
26#22627595C2211yescharacteristic
27C4×Dic586C2211yescharacteristic
28#22627589C2211yescharacteristic
29C4×D1172C2211yescharacteristic
30D4×Dic293C2211yescharacteristic
31C4×C22⋊D293—21no—
32C4×C22⋊D293—21no—
33#22627584—21no—
34#22627582C2211yescharacteristic
35#22627580—21no—
36C2×C4×Dic293—21no—
37C42×D293C2211yescharacteristic
38#22627558C2211yescharacteristic
39#22627557C2211yescharacteristic
40#22627555C2211yescharacteristic
41#22627553C2211yescharacteristic
42#22627553C2211yescharacteristic
43#22627549C2211yescharacteristic
44#22627547C2211yescharacteristic
45#22627546C2211yescharacteristic
46#22627545C2211yescharacteristic
47#22627545C2211yescharacteristic
48#22627544C2211yescharacteristic
49#22627536C2211yescharacteristic
50#22627536C2211yescharacteristic
51#22627535C2211yescharacteristic
52C2×D8×C293C2211yescharacteristic
53C4×D4×C293C2211yescharacteristic
54C4×D4×C293C2211yescharacteristic
55#106×C293C2211yescharacteristic
56#102×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58#97×C293C2211yescharacteristic
59#17989802—44no—
60#17989801—22no—
61#17989801—22no—
62C2×Dic586—21no—
63C2×Dic586C2311yescharacteristic
64C2×D1172—21no—
65C2×D1172C2311yescharacteristic
66C2×C22⋊D293—21no—
67C2×C22⋊D293—21no—
68C2×C22⋊D293—21no—
69C2×C22⋊D293—21no—
70C22×Dic293—21no—
71C22×Dic293—21no—
72C2×C4×D293—21no—
73C2×C4×D293D411yescharacteristic
74C2×C4×D293D411yescharacteristic
75C2×C4×D293C2311yescharacteristic
76#17989791—22no—
77#17989790—22no—
78#17989787—22no—
79C2×#14556873C2311yescharacteristic
80C2×#14556873C2311yescharacteristic
81C4⋊Dic293C2311yescharacteristic
82C4⋊Dic293C2311yescharacteristic
83#17989781—21no—
84#17989781—21no—
85#17989781—21no—
86C22⋊Dic293—21no—
87C22⋊Dic293—21no—
88#17989779—21no—
89#17989779—21no—
90#17989779—21no—
91C4×Dic293—21no—
92C4×Dic293—21no—
93C4×Dic293—21no—
94C4×Dic293D411yescharacteristic
95C4×Dic293D411yescharacteristic
96C4×Dic293C2311yescharacteristic
97C2×D4×C293C2311yescharacteristic
98C2×D4×C293C2311yescharacteristic
99C22×C4×C293—21no—
100C22×C4×C293—21no—
101D8×C293—22no—
102C2×C8×C293C2311yescharacteristic
103C2×C8×C293C2311yescharacteristic
104C4⋊C4×C293C2311yescharacteristic
105C4⋊C4×C293C2311yescharacteristic
106C22⋊C4×C293—21no—
107C22⋊C4×C293—21no—
108C42×C293C2311yescharacteristic
109C22×D293—21no—
110C22×D293C2×D411yescharacteristic
111Dic586—21no—
112Dic586—42no—
113Dic586#4112yescomplemented
114D1172—21no—
115D1172—21no—
116D1172—42no—
117C22⋊D293—24no—
118C22⋊D293—42no—
119C22⋊D293—42no—
120C22⋊D293—42no—
121C2×Dic293—24no—
122C2×Dic293—21no—
123C2×Dic293—21no—
124C2×Dic293—21no—
125C2×Dic293—42no—
126C2×Dic293C2×D411yescharacteristic
127C2×Dic293C2×D411yescharacteristic
128C2×Dic293C2×D411yescharacteristic
129C4×D293—21no—
130C4×D293—21no—
131C4×D293—22no—
132C4×D293—41no—
133C4×D293—42no—
134#14556873—21no—
135#14556873—21no—
136C23×C293—21no—
137C23×C293—21no—
138D4×C293—21no—
139D4×C293—21no—
140D4×C293—21no—
141D4×C293#4112yescomplemented
142C2×C4×C293—21no—
143C2×C4×C293—21no—
144C2×C4×C293—42no—
145C2×C4×C293—42no—
146C2×C4×C293C2×D411yescharacteristic
147C2×C4×C293C2×D411yescharacteristic
148C2×C4×C293C2411yescharacteristic
149C8×C293—21no—
150C8×C293—21no—
151C22×C293—22no—
152C22×C293—41no—
153C22×C293—41no—
154C22×C293—41no—
155C22×C293—41no—
156C22×C293—41no—
157C22×C293C22×D411yescharacteristic
158C2×D293—21no—
159C2×D293—21no—
160C2×D293—21no—
161C2×D293—41no—
162C2×D293—41no—
163C2×D293—41no—
164C4×C293—21no—
165C4×C293—21no—
166C4×C293—41no—
167C4×C293—41no—
168C4×C293C2×#4111yescharacteristic
169C4×C293C2×#4111yescharacteristic
170Dic293—21no—
171Dic293—22no—
172Dic293—21no—
173Dic293—41no—
174Dic293—41no—
175Dic293AGL(1,ℤ/8)12yes—
176C2×C293—42no—
177C2×C293—81no—
178C2×C293#52511yescharacteristic
179C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
180C2×C293#57511yescharacteristic
181D293—41no—
182D293—81no—
183C293#311511yescharacteristic, complemented, Sylow
184#3115—2931nomaximal, Sylow
185#532—2931no—
186C4×#41—2931no—
187#482—2931no—
188#482—2931no—
189#475—2931no—
190#474—2931no—
191#460—2931no—
192#459—2931no—
193#449—2931no—
194#449—2931no—
195#442—2931no—
196#442D29311yescharacteristic, complemented
197#440—2931no—
198#440—2931no—
199#432—2931no—
200C2×#41—2931no—
201C2×#41—5861no—
202C2×SD16—2931no—
203C2×SD16—2931no—
204C2×D8—2931no—
205C2×D8C2×D29311yescharacteristic
206C4⋊Q8—2931no—
207#127—2931no—
208#124—5861no—
209#121—2931no—
210#121—2931no—
211#121—5861no—
212C4×Q8—2931no—
213C4×Q8—2931no—
214C4×D4—2931no—
215C4×D4—2931no—
216C4×D4—5861no—
217C4×D4—5861no—
218C4×D4—5861no—
219C4×D4C2×D29311yescharacteristic
220C4×D4C2×D29311yescharacteristic
221#117—2931no—
222#117—5861no—
223C2×C42—2931no—
224C2×C42—5861no—
225#107—2931no—
226#107—2931no—
227#106—2931no—
228#106C2×D29311yescharacteristic
229C4⋊C8—2931no—
230C4⋊C8—2931no—
231#103—2931no—
232#103—2931no—
233#102—2931no—
234#102—2931no—
235#102—2931no—
236#102—2931no—
237#102C2×D29311yescharacteristic
238#102C2×D29311yescharacteristic
239C22⋊C8—2931no—
240C22⋊C8—2931no—
241#97—2931no—
242#97C2×D29311yescharacteristic
243#41—5862no—
244#41—5862no—
245#41—11724no—
246C2×Q8—2931no—
247C2×Q8—5861no—
248C2×D4—2931no—
249C2×D4—5861no—
250C2×D4—5861no—
251C2×D4—5861no—
252C2×D4—5861no—
253C2×D4—5861no—
254C2×D4C22×D29311yescharacteristic
255C2×D4C22×D29311yescharacteristic
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—2931no—
259C22×C4—2931no—
260C22×C4—2931no—
261C22×C4—5861no—
262C22×C4—5861no—
263C22×C4—5861no—
264SD16—5862no—
265SD16—5862no—
266D8—22no—
267D8—5862no—
268C2×C8—2931no—
269C2×C8—2931no—
270C2×C8C22×D29311yescharacteristic
271C2×C8C22×D29311yescharacteristic
272C4⋊C4—2931no—
273C4⋊C4—2931no—
274C4⋊C4—5861no—
275C4⋊C4—5861no—
276C4⋊C4—5861no—
277C4⋊C4C22×D29311yescharacteristic
278C4⋊C4C22×D29311yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—5861no—
282C22⋊C4—5861no—
283C22⋊C4—5861no—
284C22⋊C4—5861no—
285C22⋊C4—5861no—
286C42—2931no—
287C42—2931no—
288C42—2931no—
289C42—5861no—
290C42—5861no—
291C42—5861no—
292C42C22×D29311yescharacteristic
293C23—21no—
294C23—21no—
295C23—2931no—
296C23—5861no—
297Q8—2932no—
298Q8—5861no—
299Q8—11722no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—5864no—
304D4—5861no—
305D4—5861no—
306D4—11722no—
307D4—11722no—
308D4—11722no—
309D4—11722no—
310D4#1798980212yescomplemented
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—2931no—
316C2×C4—2931no—
317C2×C4—2931no—
318C2×C4—5862no—
319C2×C4—5864no—
320C2×C4—5861no—
321C2×C4—5861no—
322C2×C4—5861no—
323C2×C4—5861no—
324C2×C4—5861no—
325C2×C4—11721no—
326C2×C4—11722no—
327C2×C4—11722no—
328C2×C4D4×D29311yescharacteristic
329C2×C4D4×D29311yescharacteristic
330C2×C4C23×D29311yescharacteristic
331C8—21no—
332C8—21no—
333C8—5861no—
334C8—5861no—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—5861no—
342C22—5861no—
343C22—5861no—
344C22—11721no—
345C22—11721no—
346C22—11721no—
347C22C2×D4×D29311yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—2932no—
353C4—5861no—
354C4—5862no—
355C4—5861no—
356C4—11721no—
357C4—11721no—
358C4#41×D29311yescharacteristic
359C4C2×#1798980211yescharacteristic
360C2—42no—
361C2—81no—
362C2—23441no—
363C2—11721no—
364C2#3403663811yescharacteristic
365C2AGL(1,ℤ/8)×D29311yescharacteristic
366C2#3403692511yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#442×C293C2
socleC22×C293C22×D4
hypercenter#442D293
hypocenterC293#3115
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #34036676C2semidirect
2. C4×#17989801C2semidirect
3. #34036455C2semidirect
4. #34036451C2semidirect
5. #34036413C2semidirect
6. #34036407C2semidirect
7. #34036328C2semidirect
8. #34036322C2semidirect
9. #34036275C2semidirect
10. #34036271C2semidirect
11. #34036239C2semidirect
12. #34036231C2semidirect
13. #34036229C2semidirect
14. #34036184C2semidirect
15. #442×C293C2semidirect
113. Dic586#41semidirect
141. D4×C293#41semidirect
183. C293#3115semidirect
196. #442D293semidirect
310. D4#17989802semidirect

Maximal subgroups

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

subgroupindex
#340366762
C4×#179898012
#340364552
#340364512
#340364132
#340364072
#340363282
#340363222
#340362752
#340362712
#340362392
#340362312
#340362292
#340361842
#442×C2932
#3115293