Finite Group Databasebeta

← #49170748

Subgroups — #49170748

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#34036783C211yesmaximal, characteristic, complemented
2#34036775C211yesmaximal, characteristic, complemented
3#34036489C211yesmaximal, characteristic, complemented
4#34036460C211yesmaximal, characteristic, complemented
5#34036448C211yesmaximal, characteristic, complemented
6#34036420C211yesmaximal, characteristic, complemented
7#34036382C211yesmaximal, characteristic, complemented
8#34036358C211yesmaximal, characteristic, complemented
9#34036345C211yesmaximal, characteristic, complemented
10#34036276C211yesmaximal, characteristic, complemented
11#34036265C211yesmaximal, characteristic, complemented
12#34036242C211yesmaximal, characteristic, complemented
13#34036131C211yesmaximal, characteristic, complemented
14C2×#22627546C211yesmaximal, characteristic, complemented
15#435×C293C211yesmaximal, characteristic, complemented
16C2×#17989802C2211yescharacteristic
17C2×#17989801—21no—
18C22×D1172C2211yescharacteristic
19C2×#17989791C2211yescharacteristic, complemented
20C2×D2344C2211yescharacteristic
21C2×D2344C2211yescharacteristic
22#22627624C2211yescharacteristic, complemented
23#22627612C2211yescharacteristic
24#22627609—21no—
25#22627608—21no—
26#22627608—21no—
27#22627604—21no—
28#22627603C2211yescharacteristic
29#22627598C2211yescharacteristic
30#22627598C2211yescharacteristic
31#22627598C2211yescharacteristic, complemented
32#22627597—21no—
33#22627592—21no—
34C4×D1172C2211yescharacteristic
35C4×D1172C2211yescharacteristic, complemented
36C2×C4⋊Dic293C2211yescharacteristic
37C2×C4⋊Dic293C2211yescharacteristic, complemented
38C22⋊C4×D293—21no—
39#22627556C2211yescharacteristic, complemented
40#22627556C2211yescharacteristic, complemented
41#22627556C2211yescharacteristic, complemented
42#22627549C2211yescharacteristic, complemented
43#22627549C2211yescharacteristic, complemented
44#22627549C2211yescharacteristic, complemented
45#22627546C2211yescharacteristic
46#22627546C2211yescharacteristic
47#22627546C2211yescharacteristic
48#22627546C2211yescharacteristic
49#22627546C2211yescharacteristic
50#22627546C2211yescharacteristic
51#22627546C2211yescharacteristic, complemented
52C2×M16×C293C2211yescharacteristic, complemented
53C22×C8×C293C2211yescharacteristic
54C4×D4×C293C2211yescharacteristic
55C4⋊C8×C293C2211yescharacteristic, complemented
56C22⋊C8×C293C2211yescharacteristic
57C22⋊C8×C293C2211yescharacteristic, complemented
58#97×C293C2211yescharacteristic, complemented
59C23×D293—21no—
60#17989802—22no—
61#17989802—41no—
62#17989801—44no—
63C2×Dic586—21no—
64C2×Dic586C2311yescharacteristic
65C2×D1172—22no—
66C2×D1172—21no—
67C2×D1172—41no—
68C2×D1172C2311yescharacteristic
69C2×D1172C2311yescharacteristic
70C2×D1172C2311yescharacteristic
71C2×C22⋊D293—21no—
72C2×C22⋊D293—21no—
73C2×C22⋊D293—21no—
74C2×C22⋊D293—21no—
75C22×Dic293—21no—
76C22×Dic293—21no—
77C2×C4×D293—21no—
78C2×C4×D293—21no—
79C2×C4×D293—21no—
80#17989791—41no—
81D2344—22no—
82D2344—41no—
83C4⋊Dic293—21no—
84C4⋊Dic293—21no—
85C4⋊Dic293—21no—
86C4⋊Dic293C2311yescharacteristic
87C4⋊Dic293C2311yescharacteristic
88C4⋊Dic293C2311yescharacteristic
89C4⋊Dic293C2311yescharacteristic
90#17989781—21no—
91C22⋊Dic293—21no—
92#17989779—21no—
93#17989779—21no—
94#17989779—21no—
95#17989779—21no—
96#17989779—21no—
97#17989779—21no—
98#17989779—21no—
99C2×D4×C293D411yescharacteristic
100C22×C4×C293C2311yescharacteristic
101C22×C4×C293C2311yescharacteristic
102M16×C293—41no—
103C2×C8×C293—41no—
104C2×C8×C293C2311yescharacteristic
105C2×C8×C293C2311yescharacteristic
106C2×C8×C293C2311yescharacteristic
107C2×C8×C293C2311yescharacteristic
108C4⋊C4×C293D411yescharacteristic
109C22⋊C4×C293D411yescharacteristic
110C22⋊C4×C293D411yescharacteristic
111C42×C293C2311yescharacteristic
112C22×D293—21no—
113C22×D293—21no—
114C22×D293—21no—
115C22×D293—42no—
116C22×D293—42no—
117C22×D293—81no—
118Dic586—21no—
119Dic586—21no—
120Dic586—42no—
121D1172—21no—
122D1172—21no—
123D1172—21no—
124D1172—21no—
125D1172—21no—
126D1172—42no—
127D1172#4112yescomplemented
128C22⋊D293—42no—
129C22⋊D293—42no—
130C22⋊D293—42no—
131C22⋊D293—81no—
132C2×Dic293—21no—
133C2×Dic293—21no—
134C2×Dic293—21no—
135C2×Dic293—21no—
136C2×Dic293—21no—
137C2×Dic293—42no—
138C2×Dic293—42no—
139C4×D293—42no—
140C4×D293—42no—
141C4×D293—81no—
142C23×C293C2×D411yescharacteristic
143C23×C293C2×D411yescharacteristic
144D4×C293—22no—
145C2×C4×C293—21no—
146C2×C4×C293—21no—
147C2×C4×C293—21no—
148C2×C4×C293—21no—
149C2×C4×C293C2×D411yescharacteristic
150C2×C4×C293C2×D411yescharacteristic
151C2×C4×C293C2×D411yescharacteristic
152C2×C4×C293C2×D411yescharacteristic
153C2×C4×C293C2411yescharacteristic
154C8×C293—21no—
155C8×C293—21no—
156C8×C293—21no—
157C8×C293—21no—
158C22×C293—21no—
159C22×C293—21no—
160C22×C293—21no—
161C22×C293—21no—
162C22×C293—21no—
163C22×C293AGL(1,ℤ/8)12yes—
164C22×C293C22×D411yescharacteristic
165C2×D293—22no—
166C2×D293—41no—
167C2×D293—41no—
168C2×D293—41no—
169C2×D293—41no—
170C2×D293—41no—
171C2×D293—41no—
172C2×D293—41no—
173C2×D293—41no—
174C2×D293—84no—
175C4×C293—21no—
176C4×C293—21no—
177C4×C293—21no—
178C4×C293—21no—
179C4×C293C2×#4111yescharacteristic
180C4×C293H(5,𝔽2)11yescharacteristic
181Dic293—41no—
182Dic293—41no—
183Dic293—41no—
184Dic293—41no—
185Dic293—41no—
186C2×C293—22no—
187C2×C293—41no—
188C2×C293#54611yescharacteristic
189C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C293#57711yescharacteristic
191D293—42no—
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#435D29311yescharacteristic, complemented
209#417—2931no—
210C2×#102—2931no—
211C2×#41—2931no—
212C2×#41—5861no—
213C22×D4—2931no—
214C2×SD16—2931no—
215C2×D8—2931no—
216C2×D8—2931no—
217C2×M16C2×D29311yescharacteristic, complemented
218C22×C8C2×D29311yescharacteristic
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×D4C2×D29311yescharacteristic
234C2×C4⋊C4—2931no—
235C2×C4⋊C4—2931no—
236C2×C22⋊C4—5861no—
237#106—2931no—
238#106—2931no—
239#106—2931no—
240C4⋊C8C2×D29311yescharacteristic, complemented
241#103—2931no—
242#103—2931no—
243#103—2931no—
244#102—2931no—
245#102—2931no—
246#102—2931no—
247#102—2931no—
248#102—2931no—
249#102—2931no—
250#102—2931no—
251C22⋊C8C2×D29311yescharacteristic
252C22⋊C8C2×D29311yescharacteristic, complemented
253#97C2×D29311yescharacteristic, complemented
254C24—5861no—
255#41—5862no—
256#41—11721no—
257#41—11724no—
258C2×Q8—2931no—
259C2×Q8—5861no—
260C2×D4—2931no—
261C2×D4—2931no—
262C2×D4—2931no—
263C2×D4—5862no—
264C2×D4—5861no—
265C2×D4—5861no—
266C2×D4—5861no—
267C2×D4—5861no—
268C2×D4—5861no—
269C2×D4—11721no—
270C2×D4D117211yescharacteristic
271C22×C4—5861no—
272C22×C4—5861no—
273C22×C4—5861no—
274C22×C4—5861no—
275C22×C4—5861no—
276C22×C4C22×D29311yescharacteristic
277C22×C4C22×D29311yescharacteristic
278SD16—11721no—
279D8—5862no—
280D8—11721no—
281M16—41no—
282C2×C8—41no—
283C2×C8C22×D29311yescharacteristic
284C2×C8C22×D29311yescharacteristic
285C2×C8C22×D29311yescharacteristic
286C2×C8C22×D29311yescharacteristic
287C4⋊C4—2931no—
288C4⋊C4—2931no—
289C4⋊C4—2931no—
290C4⋊C4—2931no—
291C4⋊C4—5861no—
292C4⋊C4—5861no—
293C4⋊C4—5861no—
294C4⋊C4—5861no—
295C4⋊C4D117211yescharacteristic
296C22⋊C4—5861no—
297C22⋊C4—5861no—
298C22⋊C4—5861no—
299C22⋊C4—5861no—
300C22⋊C4—5861no—
301C22⋊C4—5861no—
302C22⋊C4—5861no—
303C22⋊C4—5861no—
304C22⋊C4D117211yescharacteristic
305C22⋊C4D117211yescharacteristic
306C42C22×D29311yescharacteristic
307C23—23441no—
308C23—5861no—
309C23—5861no—
310C23—5861no—
311C23—11722no—
312C23—11722no—
313C23C2×D117211yescharacteristic
314C23C2×D117211yescharacteristic
315Q8—5861no—
316Q8—5861no—
317Q8—11722no—
318D4—22no—
319D4—2932no—
320D4—23441no—
321D4—5861no—
322D4—5861no—
323D4—5861no—
324D4—5861no—
325D4—5861no—
326D4—11722no—
327D4—11722no—
328D4—11722no—
329D4—11722no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—23441no—
335C2×C4—5861no—
336C2×C4—5861no—
337C2×C4—5861no—
338C2×C4—5861no—
339C2×C4—5861no—
340C2×C4—11722no—
341C2×C4—11722no—
342C2×C4—11722no—
343C2×C4—11722no—
344C2×C4C2×D117211yescharacteristic
345C2×C4C2×D117211yescharacteristic
346C2×C4C2×D117211yescharacteristic
347C2×C4C2×D117211yescharacteristic
348C2×C4C23×D29311yescharacteristic
349C8—21no—
350C8—21no—
351C8—21no—
352C8—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—23444no—
359C22—5862no—
360C22—11721no—
361C22—11721no—
362C22—11721no—
363C22—11721no—
364C22—11721no—
365C22—11721no—
366C22—11721no—
367C22—11721no—
368C22#2262765212yes—
369C22C22×D117211yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—11721no—
375C4—11721no—
376C4—11721no—
377C4—11721no—
378C4—11721no—
379C4#41×D29311yescharacteristic
380C4#2262766911yescharacteristic
381C2—22no—
382C2—41no—
383C2—23441no—
384C2—23441no—
385C2—11722no—
386C2#3403677411yescharacteristic
387C2C2×#2262765211yescharacteristic
388C2#3403694111yescharacteristic
subgroupG/H
centerC22C22×D1172
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#435×C293C2
socleC22×C293C22×D4
hypercenter#435D293
hypocenterC293#3306
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #34036783C2semidirect
2. #34036775C2semidirect
3. #34036489C2semidirect
4. #34036460C2semidirect
5. #34036448C2semidirect
6. #34036420C2semidirect
7. #34036382C2semidirect
8. #34036358C2semidirect
9. #34036345C2semidirect
10. #34036276C2semidirect
11. #34036265C2semidirect
12. #34036242C2semidirect
13. #34036131C2semidirect
14. C2×#22627546C2semidirect
15. #435×C293C2semidirect
19. C2×#17989791C22semidirect
22. #22627624C22semidirect
31. #22627598C22semidirect
35. C4×D1172C22semidirect
37. C2×C4⋊Dic293C22semidirect
39. #22627556C22semidirect
40. #22627556C22semidirect
41. #22627556C22semidirect
42. #22627549C22semidirect
43. #22627549C22semidirect
44. #22627549C22semidirect
51. #22627546C22semidirect
52. C2×M16×C293C22semidirect
55. C4⋊C8×C293C22semidirect
57. C22⋊C8×C293C22semidirect
58. #97×C293C22semidirect
127. D1172#41semidirect
194. C293#3306semidirect
208. #435D293semidirect
217. C2×M16C2×D293semidirect
240. C4⋊C8C2×D293semidirect
252. C22⋊C8C2×D293semidirect
253. #97C2×D293semidirect

Maximal subgroups

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

subgroupindex
#340367832
#340367752
#340364892
#340364602
#340364482
#340364202
#340363822
#340363582
#340363452
#340362762
#340362652
#340362422
#340361312
C2×#226275462
#435×C2932
#3306293