Finite Group Databasebeta

← #49170747

Subgroups — #49170747

Order 37504.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036780C211yesmaximal, characteristic, complemented
2#34036767C211yesmaximal, characteristic, complemented
3#34036490C211yesmaximal, characteristic, complemented
4#34036458C211yesmaximal, characteristic, complemented
5#34036447C211yesmaximal, characteristic, complemented
6#34036417C211yesmaximal, characteristic, complemented
7#34036382C211yesmaximal, characteristic, complemented
8#34036361C211yesmaximal, characteristic, complemented
9#34036347C211yesmaximal, characteristic, complemented
10#34036274C211yesmaximal, characteristic, complemented
11#34036264C211yesmaximal, characteristic, complemented
12#34036238C211yesmaximal, characteristic, complemented
13#34036198C211yesmaximal, characteristic, complemented
14#102×D293C211yesmaximal, characteristic, complemented
15#417×C293C211yesmaximal, characteristic, complemented
16C2×#17989802—21no—
17C2×D4×D293C2211yescharacteristic
18C2×#17989789C2211yescharacteristic, complemented
19C2×D2344C2211yescharacteristic
20C2×#17989787C2211yescharacteristic
21C2×C8×D293C2211yescharacteristic
22#22627623C2211yescharacteristic, complemented
23#22627613C2211yescharacteristic
24#22627609—21no—
25#22627607—21no—
26#22627607—21no—
27#22627602—21no—
28#22627600C2211yescharacteristic
29#22627599C2211yescharacteristic
30#22627598C2211yescharacteristic
31#22627598C2211yescharacteristic, complemented
32#22627596—21no—
33#22627592—21no—
34D4×Dic293C2211yescharacteristic
35#22627586C2211yescharacteristic, complemented
36C4×C22⋊D293C2211yescharacteristic
37C4⋊C4×D293C2211yescharacteristic
38C2×#17989779—21no—
39#22627556C2211yescharacteristic, complemented
40#22627555C2211yescharacteristic, complemented
41#22627555C2211yescharacteristic, complemented
42#22627553C2211yescharacteristic, complemented
43#22627548C2211yescharacteristic, complemented
44#22627546C2211yescharacteristic
45#22627546C2211yescharacteristic, complemented
46#22627545C2211yescharacteristic
47#22627544C2211yescharacteristic
48#22627544C2211yescharacteristic
49C22⋊#14556873C2211yescharacteristic, complemented
50#22627536C2211yescharacteristic
51#22627534C2211yescharacteristic, complemented
52C2×#41×C293C2211yescharacteristic
53C2×M16×C293C2211yescharacteristic, complemented
54C2×C4⋊C4×C293C2211yescharacteristic, complemented
55#103×C293C2211yescharacteristic, complemented
56#103×C293C2211yescharacteristic, complemented
57#102×C293C2211yescharacteristic
58#102×C293C2211yescharacteristic
59C23×D293—21no—
60#17989802—44no—
61C2×Dic586—21no—
62C2×D1172—21no—
63C2×D1172C2311yescharacteristic
64C2×D1172C2311yescharacteristic
65C2×C22⋊D293—21no—
66C2×C22⋊D293—21no—
67C2×C22⋊D293—21no—
68C2×C22⋊D293D411yescharacteristic
69D4×D293—22no—
70D4×D293—41no—
71C22×Dic293—21no—
72C2×C4×D293—21no—
73C2×C4×D293—21no—
74C2×C4×D293C2311yescharacteristic
75#17989789—41no—
76D2344—41no—
77#17989787—22no—
78C2×#14556873C2311yescharacteristic
79C2×#14556873C2311yescharacteristic
80C8×D293—41no—
81C4⋊Dic293C2311yescharacteristic
82C4⋊Dic293C2311yescharacteristic
83#17989781—21no—
84#17989781—21no—
85#17989781—21no—
86#17989781D411yescharacteristic
87C22⋊Dic293—21no—
88C22⋊Dic293D411yescharacteristic
89#17989779—21no—
90#17989779—21no—
91#17989779—21no—
92#17989779—21no—
93#17989779—21no—
94#17989779—21no—
95#17989779—21no—
96#17989779D411yescharacteristic
97C4×Dic293C2311yescharacteristic
98#41×C293—22no—
99#41×C293—41no—
100C2×Q8×C293C2311yescharacteristic
101C2×D4×C293—21no—
102C2×D4×C293C2311yescharacteristic
103C22×C4×C293—21no—
104C22×C4×C293—21no—
105C22×C4×C293C2311yescharacteristic
106M16×C293—41no—
107C2×C8×C293C2311yescharacteristic
108C2×C8×C293C2311yescharacteristic
109C4⋊C4×C293—21no—
110C4⋊C4×C293C2311yescharacteristic
111C4⋊C4×C293C2311yescharacteristic
112C22×D293—21no—
113C22×D293—21no—
114C22×D293—42no—
115C22×D293—42no—
116C22×D293—81no—
117C22×D293C2×D411yescharacteristic
118Dic586—42no—
119D1172—21no—
120D1172—21no—
121D1172—21no—
122D1172—21no—
123D1172—42no—
124C22⋊D293—22no—
125C22⋊D293—42no—
126C22⋊D293—42no—
127C22⋊D293—81no—
128C2×Dic293—21no—
129C2×Dic293—21no—
130C2×Dic293—81no—
131C2×Dic293C2×D411yescharacteristic
132C2×Dic293C2×D411yescharacteristic
133C2×Dic293C2×D411yescharacteristic
134C4×D293—21no—
135C4×D293—21no—
136C4×D293—42no—
137C4×D293—42no—
138#14556873—21no—
139#14556873—21no—
140C23×C293—21no—
141C23×C293C2×D411yescharacteristic
142Q8×C293—21no—
143Q8×C293—21no—
144D4×C293—21no—
145D4×C293—42no—
146D4×C293#4112yescomplemented
147C2×C4×C293—21no—
148C2×C4×C293—21no—
149C2×C4×C293—21no—
150C2×C4×C293—21no—
151C2×C4×C293—21no—
152C2×C4×C293—42no—
153C2×C4×C293—42no—
154C2×C4×C293C2×D411yescharacteristic
155C2×C4×C293C2411yescharacteristic
156C8×C293—21no—
157C8×C293—21no—
158C22×C293—21no—
159C22×C293—22no—
160C22×C293—21no—
161C22×C293—21no—
162C22×C293—41no—
163C22×C293—41no—
164C22×C293C22×D411yescharacteristic
165C2×D293—21no—
166C2×D293—21no—
167C2×D293—41no—
168C2×D293—41no—
169C2×D293—41no—
170C2×D293—41no—
171C2×D293—41no—
172C2×D293—41no—
173C2×D293—84no—
174C2×D293AGL(1,ℤ/8)12yes—
175C4×C293—21no—
176C4×C293—41no—
177C4×C293—41no—
178C4×C293—41no—
179C4×C293C2×#4111yescharacteristic
180C4×C293H(5,𝔽2)11yescharacteristic
181Dic293—21no—
182Dic293—21no—
183Dic293—21no—
184Dic293—41no—
185Dic293—41no—
186C2×C293—42no—
187C2×C293—41no—
188C2×C293#54611yescharacteristic
189C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C293#57711yescharacteristic
191D293—22no—
192D293—81no—
193D293—81no—
194C293#330611yescharacteristic, complemented, Sylow
195#3306—2931nomaximal, Sylow
196#547—2931no—
197#546—2931no—
198#489—2931no—
199#483—2931no—
200#481—2931no—
201#476—2931no—
202#469—2931no—
203#465—2931no—
204#463—2931no—
205#449—2931no—
206#447—2931no—
207#442—2931no—
208#435—2931no—
209#417D29311yescharacteristic, complemented
210C2×#102—2931no—
211C2×#41—5861no—
212C2×#41C2×D29311yescharacteristic
213C22×D4—2931no—
214C2×SD16—2931no—
215C2×D8—2931no—
216C2×D8—2931no—
217C2×M16C2×D29311yescharacteristic, complemented
218C22×C8—2931no—
219C4⋊Q8—2931no—
220#124—2931no—
221#123—5861no—
222#123—5861no—
223#123—5861no—
224C22⋊Q8—2931no—
225C22⋊Q8—5861no—
226#121—2931no—
227#121—2931no—
228#121—2931no—
229#121—5861no—
230#120—5861no—
231C4×D4—2931no—
232C4×D4—2931no—
233C4×D4—2931no—
234C2×C4⋊C4—2931no—
235C2×C4⋊C4C2×D29311yescharacteristic, complemented
236C2×C22⋊C4—5861no—
237#106—2931no—
238#106—2931no—
239#106—2931no—
240C4⋊C8—2931no—
241#103—2931no—
242#103C2×D29311yescharacteristic, complemented
243#103C2×D29311yescharacteristic, complemented
244#102—2931no—
245#102—2931no—
246#102—2931no—
247#102—2931no—
248#102—2931no—
249#102C2×D29311yescharacteristic
250#102C2×D29311yescharacteristic
251C22⋊C8—2931no—
252C22⋊C8—2931no—
253#97—2931no—
254C24—5861no—
255#41—22no—
256#41—41no—
257#41—11724no—
258C2×Q8—5861no—
259C2×Q8C22×D29311yescharacteristic
260C2×D4—21no—
261C2×D4—2931no—
262C2×D4—2931no—
263C2×D4—2931no—
264C2×D4—5861no—
265C2×D4—5861no—
266C2×D4—5861no—
267C2×D4—5862no—
268C2×D4—5861no—
269C2×D4—11721no—
270C2×D4C22×D29311yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—2931no—
274C22×C4—5861no—
275C22×C4—5861no—
276C22×C4—5861no—
277C22×C4C22×D29311yescharacteristic
278SD16—11721no—
279D8—5862no—
280D8—11721no—
281M16—41no—
282C2×C8—2931no—
283C2×C8—2931no—
284C2×C8—11721no—
285C2×C8C22×D29311yescharacteristic
286C2×C8C22×D29311yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—2931no—
289C4⋊C4—2931no—
290C4⋊C4—2931no—
291C4⋊C4—5861no—
292C4⋊C4—5861no—
293C4⋊C4—5861no—
294C4⋊C4C22×D29311yescharacteristic
295C4⋊C4C22×D29311yescharacteristic
296C22⋊C4—2931no—
297C22⋊C4—2931no—
298C22⋊C4—5861no—
299C22⋊C4—5861no—
300C22⋊C4—5861no—
301C22⋊C4—5861no—
302C22⋊C4—5861no—
303C22⋊C4—5861no—
304C22⋊C4—5861no—
305C22⋊C4—5861no—
306C42—2931no—
307C23—21no—
308C23—2931no—
309C23—23441no—
310C23—5861no—
311C23—5861no—
312C23—11722no—
313C23—11722no—
314C23D4×D29311yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—11722no—
318D4—21no—
319D4—42no—
320D4—23441no—
321D4—5862no—
322D4—5861no—
323D4—5861no—
324D4—5861no—
325D4—5861no—
326D4—11722no—
327D4—11722no—
328D4—11722no—
329D4#1798980212yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—2931no—
338C2×C4—2931no—
339C2×C4—2931no—
340C2×C4—23441no—
341C2×C4—5861no—
342C2×C4—5861no—
343C2×C4—5861no—
344C2×C4—5861no—
345C2×C4—11722no—
346C2×C4—11722no—
347C2×C4D4×D29311yescharacteristic
348C2×C4C23×D29311yescharacteristic
349C8—21no—
350C8—21no—
351C8—5861no—
352C8—5861no—
353C22—21no—
354C22—22no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—2932no—
360C22—23444no—
361C22—5861no—
362C22—5861no—
363C22—11721no—
364C22—11721no—
365C22—11721no—
366C22—11721no—
367C22—11721no—
368C22—11721no—
369C22C2×D4×D29311yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—5861no—
375C4—5861no—
376C4—5861no—
377C4—11721no—
378C4—11721no—
379C4C2×#1798980211yescharacteristic
380C4#2262766911yescharacteristic
381C2—41no—
382C2—42no—
383C2—23441no—
384C2—23441no—
385C2—5862no—
386C2#3403676911yescharacteristic
387C2AGL(1,ℤ/8)×D29311yescharacteristic
388C2#3403693811yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#417×C293C2
socleC22×C293C22×D4
hypercenter#417D293
hypocenterC293#3306
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #34036780C2semidirect
2. #34036767C2semidirect
3. #34036490C2semidirect
4. #34036458C2semidirect
5. #34036447C2semidirect
6. #34036417C2semidirect
7. #34036382C2semidirect
8. #34036361C2semidirect
9. #34036347C2semidirect
10. #34036274C2semidirect
11. #34036264C2semidirect
12. #34036238C2semidirect
13. #34036198C2semidirect
14. #102×D293C2semidirect
15. #417×C293C2semidirect
18. C2×#17989789C22semidirect
22. #22627623C22semidirect
31. #22627598C22semidirect
35. #22627586C22semidirect
39. #22627556C22semidirect
40. #22627555C22semidirect
41. #22627555C22semidirect
42. #22627553C22semidirect
43. #22627548C22semidirect
45. #22627546C22semidirect
49. C22⋊#14556873C22semidirect
51. #22627534C22semidirect
53. C2×M16×C293C22semidirect
54. C2×C4⋊C4×C293C22semidirect
55. #103×C293C22semidirect
56. #103×C293C22semidirect
146. D4×C293#41semidirect
194. C293#3306semidirect
209. #417D293semidirect
217. C2×M16C2×D293semidirect
235. C2×C4⋊C4C2×D293semidirect
242. #103C2×D293semidirect
243. #103C2×D293semidirect
329. D4#17989802semidirect

Maximal subgroups

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

subgroupindex
#340367802
#340367672
#340364902
#340364582
#340364472
#340364172
#340363822
#340363612
#340363472
#340362742
#340362642
#340362382
#340361982
#102×D2932
#417×C2932
#3306293