Finite Group Databasebeta

← #49170637

Subgroups — #49170637

Order 37504.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036825C211yesmaximal, characteristic, complemented
2#34036775C211yesmaximal, characteristic, complemented
3#34036484C211yesmaximal, characteristic, complemented
4#34036465C211yesmaximal, characteristic, complemented
5#34036454C211yesmaximal, characteristic, complemented
6#34036430C211yesmaximal, characteristic, complemented
7#34036365C211yesmaximal, characteristic, complemented
8#34036358C211yesmaximal, characteristic, complemented
9#34036345C211yesmaximal, characteristic, complemented
10#34036276C211yesmaximal, characteristic, complemented
11#34036265C211yesmaximal, characteristic, complemented
12C4×D2344C211yesmaximal, characteristic, complemented
13#34036126C211yesmaximal, characteristic, complemented
14C2×#22627546C211yesmaximal, characteristic, complemented
15C8×D4×C293C211yesmaximal, characteristic, complemented
16C2×#17989802C2211yescharacteristic
17C22×D1172C2211yescharacteristic
18C2×#17989791C2211yescharacteristic, complemented
19C2×D2344C2211yescharacteristic
20C2×D2344C2211yescharacteristic
21#22627619—21no—
22#22627616C2211yescharacteristic, complemented
23#22627612C2211yescharacteristic
24#22627609—21no—
25#22627606—21no—
26#22627603C2211yescharacteristic
27#22627598C2211yescharacteristic
28#22627598C2211yescharacteristic
29#22627598C2211yescharacteristic, complemented
30#22627597—21no—
31#22627596—21no—
32#22627592—21no—
33C4×D1172C2211yescharacteristic
34C4×D1172C2211yescharacteristic, complemented
35#22627584—21no—
36#22627583C2211yescharacteristic, complemented
37C2×C4⋊Dic293C2211yescharacteristic
38C22⋊C4×D293—21no—
39#22627558C2211yescharacteristic, complemented
40#22627558C2211yescharacteristic, 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
52C22×C8×C293C2211yescharacteristic
53C22×C8×C293C2211yescharacteristic, complemented
54C4×D4×C293C2211yescharacteristic
55C4⋊C8×C293C2211yescharacteristic, complemented
56C22⋊C8×C293C2211yescharacteristic
57C22⋊C8×C293C2211yescharacteristic, complemented
58C4×C8×C293C2211yescharacteristic, complemented
59C23×D293—21no—
60#17989802—22no—
61#17989802—41no—
62C2×Dic586C2311yescharacteristic
63C2×D1172—22no—
64C2×D1172—21no—
65C2×D1172—41no—
66C2×D1172C2311yescharacteristic
67C2×D1172C2311yescharacteristic
68C2×D1172C2311yescharacteristic
69C2×C22⋊D293—21no—
70C2×C22⋊D293—21no—
71C2×C22⋊D293—21no—
72C2×C22⋊D293—21no—
73C22×Dic293—21no—
74C2×C4×D293—21no—
75C2×C4×D293—21no—
76C2×C4×D293—21no—
77#17989791—41no—
78D2344—22no—
79D2344—41no—
80C4⋊Dic293—21no—
81C4⋊Dic293C2311yescharacteristic
82C4⋊Dic293C2311yescharacteristic
83C4⋊Dic293C2311yescharacteristic
84C4⋊Dic293C2311yescharacteristic
85#17989781—21no—
86#17989781—21no—
87#17989781—21no—
88C22⋊Dic293—21no—
89C22⋊Dic293—21no—
90#17989779—21no—
91#17989779—21no—
92#17989779—21no—
93#17989779—21no—
94#17989779—21no—
95#17989779—21no—
96#17989779—21no—
97C4×Dic293—21no—
98C2×D4×C293D411yescharacteristic
99C22×C4×C293C2311yescharacteristic
100C22×C4×C293C2311yescharacteristic
101C2×C8×C293—41no—
102C2×C8×C293—41no—
103C2×C8×C293C2311yescharacteristic
104C2×C8×C293C2311yescharacteristic
105C2×C8×C293C2311yescharacteristic
106C2×C8×C293C2311yescharacteristic
107C4⋊C4×C293D411yescharacteristic
108C22⋊C4×C293D411yescharacteristic
109C22⋊C4×C293D411yescharacteristic
110C42×C293C2311yescharacteristic
111C22×D293—21no—
112C22×D293—21no—
113C22×D293—21no—
114C22×D293—42no—
115C22×D293—42no—
116C22×D293—81no—
117Dic586—21no—
118Dic586—21no—
119D1172—21no—
120D1172—21no—
121D1172—21no—
122D1172—21no—
123D1172—21no—
124D1172—42no—
125D1172#4112yes—
126C22⋊D293—42no—
127C22⋊D293—42no—
128C22⋊D293—81no—
129C22⋊D293—81no—
130C2×Dic293—21no—
131C2×Dic293—21no—
132C2×Dic293—21no—
133C2×Dic293—21no—
134C2×Dic293—21no—
135C2×Dic293—81no—
136C4×D293—42no—
137C4×D293—81no—
138C4×D293—81no—
139C23×C293C2×D411yescharacteristic
140C23×C293C2×D411yescharacteristic
141D4×C293—22no—
142C2×C4×C293—21no—
143C2×C4×C293—21no—
144C2×C4×C293—21no—
145C2×C4×C293—21no—
146C2×C4×C293C2×D411yescharacteristic
147C2×C4×C293C2×D411yescharacteristic
148C2×C4×C293C2×D411yescharacteristic
149C2×C4×C293C2×D411yescharacteristic
150C2×C4×C293C2411yescharacteristic
151C8×C293—21no—
152C8×C293—21no—
153C8×C293—21no—
154C8×C293—21no—
155C22×C293—21no—
156C22×C293—21no—
157C22×C293—21no—
158C22×C293—21no—
159C22×C293—21no—
160C22×C293#13512yes—
161C22×C293C22×D411yescharacteristic
162C2×D293—22no—
163C2×D293—41no—
164C2×D293—41no—
165C2×D293—41no—
166C2×D293—41no—
167C2×D293—41no—
168C2×D293—41no—
169C2×D293—41no—
170C2×D293—41no—
171C2×D293—84no—
172C4×C293—21no—
173C4×C293—21no—
174C4×C293—21no—
175C4×C293—21no—
176C4×C293C2×#4111yescharacteristic
177C4×C293H(5,𝔽2)11yescharacteristic
178Dic293—41no—
179Dic293—41no—
180Dic293—41no—
181Dic293—41no—
182Dic293—41no—
183C2×C293—22no—
184C2×C293—41no—
185C2×C293#54611yescharacteristic
186C2×C293C2×#13511yescharacteristic
187C2×C293#57611yescharacteristic
188D293—42no—
189D293—81no—
190D293—81no—
191C293#329711yescharacteristic, complemented, Sylow
192#3297—2931nomaximal, Sylow
193#553—2931no—
194#546—2931no—
195#488—2931no—
196#484—2931no—
197#482—2931no—
198#478—2931no—
199#466—2931no—
200#465—2931no—
201#463—2931no—
202#449—2931no—
203#447—2931no—
204C4×D8—2931no—
205C8×D4D29311yescharacteristic, complemented
206#416—2931no—
207C2×#102—2931no—
208C2×#41—2931no—
209C22×D4—2931no—
210C2×SD16—2931no—
211C2×D8—2931no—
212C2×D8—2931no—
213C22×C8C2×D29311yescharacteristic
214C22×C8C2×D29311yescharacteristic, complemented
215#126—5861no—
216#125—2931no—
217#124—2931no—
218#123—5861no—
219#123—5861no—
220C22⋊Q8—2931no—
221#121—2931no—
222#121—2931no—
223#121—2931no—
224#121—5861no—
225#121—5861no—
226#120—5861no—
227C4×D4—2931no—
228C4×D4—2931no—
229C4×D4—5861no—
230C4×D4C2×D29311yescharacteristic
231#117—2931no—
232C2×C4⋊C4—2931no—
233C2×C22⋊C4—5861no—
234#107—2931no—
235#107—2931no—
236#106—2931no—
237C4⋊C8C2×D29311yescharacteristic, complemented
238#103—2931no—
239#103—2931no—
240#103—2931no—
241#102—2931no—
242#102—2931no—
243#102—2931no—
244#102—2931no—
245#102—2931no—
246#102—2931no—
247#102—2931no—
248C22⋊C8C2×D29311yescharacteristic
249C22⋊C8C2×D29311yescharacteristic, complemented
250C4×C8C2×D29311yescharacteristic, complemented
251C24—5861no—
252#41—5862no—
253#41—11721no—
254C2×Q8—2931no—
255C2×D4—2931no—
256C2×D4—2931no—
257C2×D4—2931no—
258C2×D4—5862no—
259C2×D4—5861no—
260C2×D4—5861no—
261C2×D4—5861no—
262C2×D4—5861no—
263C2×D4—5861no—
264C2×D4—11721no—
265C2×D4D117211yescharacteristic
266C22×C4—5861no—
267C22×C4—5861no—
268C22×C4—5861no—
269C22×C4—5861no—
270C22×C4C22×D29311yescharacteristic
271C22×C4C22×D29311yescharacteristic
272SD16—11721no—
273D8—5862no—
274D8—11721no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8C22×D29311yescharacteristic
278C2×C8C22×D29311yescharacteristic
279C2×C8C22×D29311yescharacteristic
280C2×C8C22×D29311yescharacteristic
281C4⋊C4—2931no—
282C4⋊C4—2931no—
283C4⋊C4—2931no—
284C4⋊C4—2931no—
285C4⋊C4—5861no—
286C4⋊C4—5861no—
287C4⋊C4—5861no—
288C4⋊C4—5861no—
289C4⋊C4D117211yescharacteristic
290C22⋊C4—5861no—
291C22⋊C4—5861no—
292C22⋊C4—5861no—
293C22⋊C4—5861no—
294C22⋊C4—5861no—
295C22⋊C4—5861no—
296C22⋊C4—5861no—
297C22⋊C4—5861no—
298C22⋊C4—5861no—
299C22⋊C4D117211yescharacteristic
300C22⋊C4D117211yescharacteristic
301C42—5861no—
302C42C22×D29311yescharacteristic
303C23—23441no—
304C23—5861no—
305C23—5861no—
306C23—5861no—
307C23—11722no—
308C23—11722no—
309C23C2×D117211yescharacteristic
310C23C2×D117211yescharacteristic
311Q8—5861no—
312Q8—5861no—
313D4—22no—
314D4—2932no—
315D4—23441no—
316D4—23441no—
317D4—5861no—
318D4—5861no—
319D4—5861no—
320D4—5861no—
321D4—5861no—
322D4—11722no—
323D4—11722no—
324D4—11722no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—23441no—
330C2×C4—23441no—
331C2×C4—23441no—
332C2×C4—5861no—
333C2×C4—5861no—
334C2×C4—5861no—
335C2×C4—5861no—
336C2×C4—5861no—
337C2×C4—11722no—
338C2×C4C2×D117211yescharacteristic
339C2×C4C2×D117211yescharacteristic
340C2×C4C2×D117211yescharacteristic
341C2×C4C2×D117211yescharacteristic
342C2×C4C23×D29311yescharacteristic
343C8—21no—
344C8—21no—
345C8—21no—
346C8—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—23444no—
353C22—5862no—
354C22—11721no—
355C22—11721no—
356C22—11721no—
357C22—11721no—
358C22—11721no—
359C22—11721no—
360C22—11721no—
361C22—11721no—
362C22#2262764612yes—
363C22C22×D117211yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—11721no—
369C4—11721no—
370C4—11721no—
371C4—11721no—
372C4—11721no—
373C4#41×D29311yescharacteristic
374C4#2262766911yescharacteristic
375C2—22no—
376C2—41no—
377C2—23441no—
378C2—23441no—
379C2—11722no—
380C2#3403677411yescharacteristic
381C2C2×#2262764611yescharacteristic
382C2#3403693411yescharacteristic
subgroupG/H
centerC22C22×D1172
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC8×D4×C293C2
socleC22×C293C22×D4
hypercenterC8×D4D293
hypocenterC293#3297
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #34036825C2semidirect
2. #34036775C2semidirect
3. #34036484C2semidirect
4. #34036465C2semidirect
5. #34036454C2semidirect
6. #34036430C2semidirect
7. #34036365C2semidirect
8. #34036358C2semidirect
9. #34036345C2semidirect
10. #34036276C2semidirect
11. #34036265C2semidirect
12. C4×D2344C2semidirect
13. #34036126C2semidirect
14. C2×#22627546C2semidirect
15. C8×D4×C293C2semidirect
18. C2×#17989791C22semidirect
22. #22627616C22semidirect
29. #22627598C22semidirect
34. C4×D1172C22semidirect
36. #22627583C22semidirect
39. #22627558C22semidirect
40. #22627558C22semidirect
41. #22627556C22semidirect
42. #22627549C22semidirect
43. #22627549C22semidirect
44. #22627549C22semidirect
51. #22627546C22semidirect
53. C22×C8×C293C22semidirect
55. C4⋊C8×C293C22semidirect
57. C22⋊C8×C293C22semidirect
58. C4×C8×C293C22semidirect
191. C293#3297semidirect
205. C8×D4D293semidirect
214. C22×C8C2×D293semidirect
237. C4⋊C8C2×D293semidirect
249. C22⋊C8C2×D293semidirect
250. C4×C8C2×D293semidirect

Maximal subgroups

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

subgroupindex
#340368252
#340367752
#340364842
#340364652
#340364542
#340364302
#340363652
#340363582
#340363452
#340362762
#340362652
C4×D23442
#340361262
C2×#226275462
C8×D4×C2932
#3297293