Finite Group Databasebeta

← #49168973

Subgroups — #49168973

Order 37504.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036751C211yesmaximal, characteristic, complemented
2#34036601C211yesmaximal, characteristic, complemented
3#34036468C211yesmaximal, characteristic, complemented
4#34036456C211yesmaximal, characteristic, complemented
5#34036417C211yesmaximal, characteristic, complemented
6#34036408C211yesmaximal, characteristic, complemented
7#34036347C211yesmaximal, characteristic, complemented
8#34036346C211yesmaximal, characteristic, complemented
9#34036278C211yesmaximal, characteristic, complemented
10#34036264C211yesmaximal, characteristic
11#34036242C211yesmaximal, characteristic, complemented
12C4×#17989789C211yesmaximal, characteristic, complemented
13C4×#17989787C211yesmaximal, characteristic, complemented
14#34036191C211yesmaximal, characteristic, complemented
15#440×C293C211yesmaximal, characteristic, complemented
16C2×D4×D293C2211yescharacteristic
17C2×#17989789C2211yescharacteristic
18C2×D2344C2211yescharacteristic
19C2×#17989787C2211yescharacteristic
20#22627623C2211yescharacteristic, complemented
21#22627618—21no—
22#22627613C2211yescharacteristic, complemented
23#22627612—21no—
24#22627609—21no—
25#22627602—21no—
26#22627600C2211yescharacteristic
27#22627599C2211yescharacteristic
28C4×D1172C2211yescharacteristic
29C4×D1172C2211yescharacteristic, complemented
30D4×Dic293C2211yescharacteristic
31#22627586C2211yescharacteristic
32C4×C22⋊D293—21no—
33#22627584—21no—
34#22627582C2211yescharacteristic
35#22627581C2211yescharacteristic
36C2×#17989779—21no—
37C22⋊C4×D293—21no—
38#22627557C2211yescharacteristic, complemented
39#22627556C2211yescharacteristic, complemented
40#22627555C2211yescharacteristic, complemented
41#22627553C2211yescharacteristic, complemented
42#22627553C2211yescharacteristic, complemented
43#22627548C2211yescharacteristic, complemented
44#22627546C2211yescharacteristic
45#22627546C2211yescharacteristic, complemented
46#22627545C2211yescharacteristic
47#22627544C2211yescharacteristic
48#22627544C2211yescharacteristic, complemented
49#22627536C2211yescharacteristic
50#22627536C2211yescharacteristic
51C4×#14556873C2211yescharacteristic, complemented
52C2×SD16×C293C2211yescharacteristic
53C4×Q8×C293C2211yescharacteristic, complemented
54C4×D4×C293C2211yescharacteristic
55#107×C293C2211yescharacteristic, complemented
56#103×C293C2211yescharacteristic, complemented
57#102×C293C2211yescharacteristic
58#97×C293C2211yescharacteristic, complemented
59C23×D293—21no—
60C2×Dic586—21no—
61C2×D1172—21no—
62C2×D1172C2311yescharacteristic
63C2×D1172C2311yescharacteristic
64C2×C22⋊D293—21no—
65D4×D293—22no—
66D4×D293—22no—
67C22×Dic293—21no—
68C2×C4×D293—21no—
69C2×C4×D293—21no—
70C2×C4×D293—21no—
71C2×C4×D293C2311yescharacteristic
72#17989789—22no—
73D2344—22no—
74#17989787—22no—
75C2×#14556873C2311yescharacteristic
76C2×#14556873C2311yescharacteristic
77C4⋊Dic293C2311yescharacteristic
78C4⋊Dic293C2311yescharacteristic
79#17989781—21no—
80#17989781—21no—
81#17989781D411yescharacteristic
82#17989781D411yescharacteristic
83C22⋊Dic293—21no—
84#17989779—21no—
85#17989779—21no—
86#17989779—21no—
87#17989779—21no—
88#17989779—21no—
89#17989779—21no—
90#17989779—21no—
91#17989779—21no—
92#17989779D411yescharacteristic
93#17989779D411yescharacteristic
94C4×Dic293—21no—
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×D293—24no—
110C22×D293—21no—
111C22×D293—81no—
112C22×D293—81no—
113C22×D293C2×D411yescharacteristic
114Dic586—81no—
115D1172—21no—
116D1172—21no—
117D1172—21no—
118D1172—81no—
119D1172#4112yes—
120C22⋊D293—24no—
121C2×Dic293—21no—
122C2×Dic293—21no—
123C2×Dic293—81no—
124C2×Dic293C2×D411yescharacteristic
125C2×Dic293C2×D411yescharacteristic
126C2×Dic293C2×D411yescharacteristic
127C4×D293—21no—
128C4×D293—21no—
129C4×D293—81no—
130C4×D293—81no—
131C4×D293—81no—
132#14556873—21no—
133#14556873—21no—
134C23×C293—21no—
135Q8×C293—21no—
136Q8×C293—21no—
137D4×C293—21no—
138D4×C293#4112yes—
139C2×C4×C293—21no—
140C2×C4×C293—21no—
141C2×C4×C293—21no—
142C2×C4×C293—81no—
143C2×C4×C293C2×D411yescharacteristic
144C2×C4×C293C2×D411yescharacteristic
145C2×C4×C293C2411yescharacteristic
146C8×C293—21no—
147C8×C293—21no—
148C22×C293—22no—
149C22×C293—41no—
150C22×C293—41no—
151C22×C293C22×D411yescharacteristic
152C2×D293—21no—
153C2×D293—22no—
154C2×D293—21no—
155C2×D293—21no—
156C2×D293—41no—
157C2×D293—41no—
158C2×D293—41no—
159C2×D293—41no—
160C2×D293—41no—
161C2×D293—84no—
162C4×C293—21no—
163C4×C293—21no—
164C4×C293—41no—
165C4×C293—41no—
166C4×C293—41no—
167C4×C293C2×#4111yescharacteristic
168C4×C293C2×#4111yescharacteristic
169Dic293—21no—
170Dic293—21no—
171Dic293—21no—
172Dic293—41no—
173Dic293—41no—
174C2×C293—42no—
175C2×C293#52511yescharacteristic
176C2×C293#57611yescharacteristic
177C2×C293#57711yescharacteristic
178D293—41no—
179D293—42no—
180D293—81no—
181C293#311811yescharacteristic, complemented, Sylow
182#3118—2931nomaximal, Sylow
183#542—2931no—
184#518—2931no—
185#485—2931no—
186#482—2931no—
187#476—2931no—
188#474—2931no—
189#463—2931no—
190#463—2931no—
191#450—2931no—
192#447—2931no—
193#442—2931no—
194#440D29311yescharacteristic, complemented
195C4×SD16—2931no—
196C4×D8—2931no—
197#433—2931no—
198C22×D4—2931no—
199C2×SD16—2931no—
200C2×SD16C2×D29311yescharacteristic
201C2×D8—2931no—
202C2×D8—2931no—
203C4⋊Q8—2931no—
204#126—5861no—
205#124—2931no—
206#124—5861no—
207#123—5861no—
208C22⋊Q8—2931no—
209C22⋊Q8—5861no—
210#121—2931no—
211C4×Q8C2×D29311yescharacteristic, complemented
212C4×D4—2931no—
213C4×D4—2931no—
214C4×D4—2931no—
215C4×D4—2931no—
216C4×D4—5861no—
217C4×D4—5861no—
218C4×D4C2×D29311yescharacteristic
219#117—2931no—
220#117—2931no—
221C2×C22⋊C4—5861no—
222C2×C22⋊C4—5861no—
223#107—2931no—
224#107C2×D29311yescharacteristic, complemented
225#106—2931no—
226#106—2931no—
227C4⋊C8—2931no—
228C4⋊C8—2931no—
229#103—2931no—
230#103C2×D29311yescharacteristic, complemented
231#102—2931no—
232#102—2931no—
233#102—2931no—
234#102—2931no—
235#102—2931no—
236#102C2×D29311yescharacteristic
237C22⋊C8—2931no—
238C22⋊C8—2931no—
239#97C2×D29311yescharacteristic, complemented
240C4×C8—2931no—
241C24—5861no—
242C2×Q8—5861no—
243C2×Q8C22×D29311yescharacteristic
244C2×D4—2931no—
245C2×D4—2931no—
246C2×D4—5861no—
247C2×D4—5861no—
248C2×D4—5862no—
249C2×D4—5862no—
250C2×D4C22×D29311yescharacteristic
251C22×C4—21no—
252C22×C4—2931no—
253C22×C4—5861no—
254C22×C4—5861no—
255C22×C4—5861no—
256C22×C4—5861no—
257SD16—22no—
258SD16—5862no—
259D8—5862no—
260D8—5862no—
261C2×C8—2931no—
262C2×C8—2931no—
263C2×C8C22×D29311yescharacteristic
264C2×C8C22×D29311yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—2931no—
267C4⋊C4—2931no—
268C4⋊C4—2931no—
269C4⋊C4—2931no—
270C4⋊C4—5861no—
271C4⋊C4—5861no—
272C4⋊C4C22×D29311yescharacteristic
273C4⋊C4C22×D29311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—2931no—
276C22⋊C4—2931no—
277C22⋊C4—5861no—
278C22⋊C4—5861no—
279C22⋊C4—5861no—
280C22⋊C4—5861no—
281C22⋊C4—5861no—
282C22⋊C4—5861no—
283C22⋊C4—5861no—
284C22⋊C4—5861no—
285C22⋊C4—5861no—
286C42—21no—
287C42—2931no—
288C42—5861no—
289C42C22×D29311yescharacteristic
290C23—21no—
291C23—2931no—
292C23—23441no—
293C23—23441no—
294C23—5864no—
295C23—5861no—
296C23—5861no—
297Q8—21no—
298Q8—21no—
299Q8—23441no—
300D4—21no—
301D4—2932no—
302D4—23441no—
303D4—5864no—
304D4—5861no—
305D4—5861no—
306D4—5861no—
307D4#1798980212yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—2931no—
313C2×C4—2931no—
314C2×C4—2931no—
315C2×C4—23441no—
316C2×C4—23441no—
317C2×C4—23441no—
318C2×C4—23441no—
319C2×C4—5861no—
320C2×C4—5861no—
321C2×C4—5861no—
322C2×C4—5861no—
323C2×C4D4×D29311yescharacteristic
324C2×C4D4×D29311yescharacteristic
325C2×C4C23×D29311yescharacteristic
326C8—21no—
327C8—21no—
328C8—5861no—
329C8—5861no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—23444no—
334C22—5861no—
335C22—5862no—
336C22—5861no—
337C22—5861no—
338C22—11721no—
339C22—11721no—
340C22—11721no—
341C22—11721no—
342C22—11721no—
343C22C2×D4×D29311yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—5861no—
350C4—5861no—
351C4—5861no—
352C4—11721no—
353C4—11721no—
354C4#41×D29311yescharacteristic
355C4C2×#1798980211yescharacteristic
356C2—42no—
357C2—23441no—
358C2—11721no—
359C2—11722no—
360C2#3403663811yescharacteristic
361C2#3403693311yescharacteristic
362C2#3403693811yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#440×C293C2
socleC22×C293C22×D4
prime radical#34036264C2
hypercenter#440D293
hypocenterC293#3118
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. #34036751C2semidirect
2. #34036601C2semidirect
3. #34036468C2semidirect
4. #34036456C2semidirect
5. #34036417C2semidirect
6. #34036408C2semidirect
7. #34036347C2semidirect
8. #34036346C2semidirect
9. #34036278C2semidirect
11. #34036242C2semidirect
12. C4×#17989789C2semidirect
13. C4×#17989787C2semidirect
14. #34036191C2semidirect
15. #440×C293C2semidirect
20. #22627623C22semidirect
22. #22627613C22semidirect
29. C4×D1172C22semidirect
38. #22627557C22semidirect
39. #22627556C22semidirect
40. #22627555C22semidirect
41. #22627553C22semidirect
42. #22627553C22semidirect
43. #22627548C22semidirect
45. #22627546C22semidirect
48. #22627544C22semidirect
51. C4×#14556873C22semidirect
53. C4×Q8×C293C22semidirect
55. #107×C293C22semidirect
56. #103×C293C22semidirect
58. #97×C293C22semidirect
181. C293#3118semidirect
194. #440D293semidirect
211. C4×Q8C2×D293semidirect
224. #107C2×D293semidirect
230. #103C2×D293semidirect
239. #97C2×D293semidirect

Maximal subgroups

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

subgroupindex
#340367512
#340366012
#340364682
#340364562
#340364172
#340364082
#340363472
#340363462
#340362782
#340362642
#340362422
C4×#179897892
C4×#179897872
#340361912
#440×C2932
#3118293