Finite Group Databasebeta

← #49168969

Subgroups — #49168969

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#34036750C211yesmaximal, characteristic, complemented
2#34036470C211yesmaximal, characteristic, complemented
3#34036453C211yesmaximal, characteristic, complemented
4#34036419C211yesmaximal, characteristic, complemented
5#34036409C211yesmaximal, characteristic, complemented
6#34036344C211yesmaximal, characteristic, complemented
7#34036344C211yesmaximal, characteristic, complemented
8#34036280C211yesmaximal, characteristic, complemented
9#34036263C211yesmaximal, characteristic
10#34036239C211yesmaximal, characteristic, complemented
11#34036229C211yesmaximal, characteristic, complemented
12C4×#17989790C211yesmaximal, characteristic, complemented
13C4×#17989787C211yesmaximal, characteristic, complemented
14#34036190C211yesmaximal, characteristic, complemented
15#518×C293C211yesmaximal, characteristic, complemented
16C2×#17989790C2211yescharacteristic
17C2×#17989790C2211yescharacteristic
18C2×#17989787C2211yescharacteristic
19C2×#17989787C2211yescharacteristic
20#22627624C2211yescharacteristic, complemented
21#22627619—21no—
22#22627612C2211yescharacteristic, complemented
23#22627610—21no—
24#22627606—21no—
25#22627603C2211yescharacteristic
26#22627602—21no—
27#22627598C2211yescharacteristic
28C4×Dic586C2211yescharacteristic, complemented
29C4×D1172C2211yescharacteristic, complemented
30#22627557C2211yescharacteristic, complemented
31#22627557C2211yescharacteristic, complemented
32#22627555C2211yescharacteristic, complemented
33#22627555C2211yescharacteristic, complemented
34C4⋊#14556873C2211yescharacteristic, complemented
35C4⋊#14556873C2211yescharacteristic, complemented
36#22627547C2211yescharacteristic, complemented
37#22627547C2211yescharacteristic, complemented
38#22627545C2211yescharacteristic
39#22627545C2211yescharacteristic
40#22627545C2211yescharacteristic
41#22627545C2211yescharacteristic
42#22627544C2211yescharacteristic, complemented
43#22627544C2211yescharacteristic, complemented
44C22⋊#14556873C2211yescharacteristic
45C22⋊#14556873C2211yescharacteristic
46#22627535C2211yescharacteristic, complemented
47C4×#14556873C2211yescharacteristic, complemented
48C22×D4×C293C2211yescharacteristic
49C4×D4×C293—21no—
50C4×D4×C293—21no—
51C4×D4×C293C2211yescharacteristic
52C4×D4×C293C2211yescharacteristic
53C4×D4×C293C2211yescharacteristic
54C4×D4×C293C2211yescharacteristic
55#117×C293C2211yescharacteristic
56#117×C293C2211yescharacteristic
57C2×C22⋊C4×C293—21no—
58C2×C22⋊C4×C293—21no—
59C2×Dic586—21no—
60C2×Dic586C2311yescharacteristic
61C2×D1172C2311yescharacteristic
62C2×C22⋊D293—21no—
63C2×C4×D293—21no—
64#17989790—22no—
65#17989790—22no—
66#17989787—22no—
67#17989787—22no—
68C2×#14556873C2311yescharacteristic
69C2×#14556873C2311yescharacteristic
70C2×#14556873C2311yescharacteristic
71C2×#14556873C2311yescharacteristic
72C4⋊Dic293—21no—
73C4⋊Dic293C2311yescharacteristic
74C4⋊Dic293C2311yescharacteristic
75#17989781—21no—
76#17989781—21no—
77C22⋊Dic293—21no—
78#17989779—21no—
79#17989779—21no—
80#17989779—21no—
81#17989779—21no—
82C4×Dic293—21no—
83C24×C293—21no—
84C2×D4×C293—22no—
85C2×D4×C293—22no—
86C2×D4×C293—21no—
87C2×D4×C293C2311yescharacteristic
88C2×D4×C293C2311yescharacteristic
89C22×C4×C293—21no—
90C22×C4×C293—21no—
91C22×C4×C293—21no—
92C22×C4×C293—21no—
93C22×C4×C293C2311yescharacteristic
94C4⋊C4×C293D411yescharacteristic
95C4⋊C4×C293D411yescharacteristic
96C4⋊C4×C293C2311yescharacteristic
97C4⋊C4×C293C2311yescharacteristic
98C22⋊C4×C293—21no—
99C22⋊C4×C293—21no—
100C22⋊C4×C293—21no—
101C22⋊C4×C293—21no—
102C22⋊C4×C293—21no—
103C22⋊C4×C293D411yescharacteristic
104C22⋊C4×C293D411yescharacteristic
105C42×C293—21no—
106C42×C293C2311yescharacteristic
107C42×C293C2311yescharacteristic
108C22×D293—21no—
109Dic586—21no—
110Dic586—21no—
111Dic586—81no—
112D1172—21no—
113D1172—21no—
114C22⋊D293—81no—
115C2×Dic293—21no—
116C2×Dic293—21no—
117C2×Dic293—21no—
118C4×D293—81no—
119#14556873—21no—
120#14556873—21no—
121#14556873—21no—
122#14556873—21no—
123C23×C293—24no—
124C23×C293—21no—
125C23×C293—21no—
126C23×C293—81no—
127C23×C293—81no—
128C23×C293C2×D411yescharacteristic
129D4×C293—24no—
130D4×C293—21no—
131D4×C293—21no—
132D4×C293#4112yes—
133D4×C293#4112yes—
134C2×C4×C293—21no—
135C2×C4×C293—21no—
136C2×C4×C293—21no—
137C2×C4×C293—21no—
138C2×C4×C293—81no—
139C2×C4×C293—81no—
140C2×C4×C293—81no—
141C2×C4×C293—81no—
142C2×C4×C293C2×D411yescharacteristic
143C2×C4×C293C2×D411yescharacteristic
144C2×C4×C293C2×D411yescharacteristic
145C2×C4×C293C2×D411yescharacteristic
146C2×C4×C293C2×D411yescharacteristic
147C2×C4×C293C2411yescharacteristic
148C22×C293—21no—
149C22×C293—22no—
150C22×C293—22no—
151C22×C293—21no—
152C22×C293—21no—
153C22×C293—41no—
154C22×C293—41no—
155C22×C293—41no—
156C22×C293—41no—
157C22×C293—84no—
158C22×C293C22×D411yescharacteristic
159C2×D293—41no—
160C2×D293—41no—
161C2×D293—41no—
162C4×C293—21no—
163C4×C293—21no—
164C4×C293—21no—
165C4×C293—21no—
166C4×C293—21no—
167C4×C293—41no—
168C4×C293—41no—
169C4×C293C2×#4111yescharacteristic
170C4×C293C2×#4111yescharacteristic
171Dic293—41no—
172Dic293—41no—
173Dic293—41no—
174C2×C293—41no—
175C2×C293—42no—
176C2×C293—42no—
177C2×C293#52511yescharacteristic
178C2×C293#57611yescharacteristic
179C2×C293#57711yescharacteristic
180D293—81no—
181C293#311811yescharacteristic, complemented, Sylow
182#3118—2931nomaximal, Sylow
183#542—2931no—
184#518D29311yescharacteristic, complemented
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#440—2931no—
195C4×SD16—2931no—
196C4×D8—2931no—
197#433—2931no—
198C22×D4C2×D29311yescharacteristic
199C2×SD16—2931no—
200C2×SD16—2931no—
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×Q8—2931no—
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—2931no—
215C4×D4C2×D29311yescharacteristic
216C4×D4C2×D29311yescharacteristic
217C4×D4C2×D29311yescharacteristic
218C4×D4C2×D29311yescharacteristic
219#117C2×D29311yescharacteristic
220#117C2×D29311yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223#107—2931no—
224#107—2931no—
225#106—2931no—
226#106—2931no—
227C4⋊C8—2931no—
228C4⋊C8—2931no—
229#103—2931no—
230#103—2931no—
231#102—2931no—
232#102—2931no—
233#102—2931no—
234#102—2931no—
235#102—2931no—
236#102—2931no—
237C22⋊C8—2931no—
238C22⋊C8—2931no—
239#97—2931no—
240C4×C8—2931no—
241C24—21no—
242C2×Q8—2931no—
243C2×Q8—5861no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—2931no—
248C2×D4—5861no—
249C2×D4C22×D29311yescharacteristic
250C2×D4C22×D29311yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—5861no—
256C22×C4C22×D29311yescharacteristic
257SD16—5862no—
258SD16—5862no—
259D8—5862no—
260D8—5862no—
261C2×C8—2931no—
262C2×C8—2931no—
263C2×C8—2931no—
264C2×C8—2931no—
265C4⋊C4—2931no—
266C4⋊C4—2931no—
267C4⋊C4—5861no—
268C4⋊C4—5861no—
269C4⋊C4—5861no—
270C4⋊C4C22⋊D29311yescharacteristic
271C4⋊C4C22⋊D29311yescharacteristic
272C4⋊C4C22×D29311yescharacteristic
273C4⋊C4C22×D29311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—5861no—
280C22⋊C4—5861no—
281C22⋊C4—5861no—
282C22⋊C4—5861no—
283C22⋊C4—5861no—
284C22⋊C4C22⋊D29311yescharacteristic
285C22⋊C4C22⋊D29311yescharacteristic
286C42—21no—
287C42—5861no—
288C42C22×D29311yescharacteristic
289C42C22×D29311yescharacteristic
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—5861no—
296C23C2×C22⋊D29311yescharacteristic
297Q8—23441no—
298Q8—5861no—
299Q8—5861no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—23441no—
304D4—5861no—
305D4—5861no—
306D4#1798980212yes—
307D4#1798980212yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—23441no—
317C2×C4—5861no—
318C2×C4—5861no—
319C2×C4—5861no—
320C2×C4C2×C22⋊D29311yescharacteristic
321C2×C4C2×C22⋊D29311yescharacteristic
322C2×C4C2×C22⋊D29311yescharacteristic
323C2×C4C2×C22⋊D29311yescharacteristic
324C2×C4C2×C22⋊D29311yescharacteristic
325C2×C4C23×D29311yescharacteristic
326C8—5861no—
327C8—5861no—
328C8—5861no—
329C8—5861no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—84no—
340C22—11721no—
341C22—11721no—
342C22—11721no—
343C22C22×C22⋊D29311yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—11721no—
352C4—11721no—
353C4—11721no—
354C4C2×#1798980211yescharacteristic
355C4C2×#1798980211yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—23441no—
360C2#3403664011yescharacteristic
361C2#3403693211yescharacteristic
362C2#3403694011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#518×C293C2
socleC22×C293C22×D4
prime radical#34036263C2
hypercenter#518D293
hypocenterC293#3118
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #34036750C2semidirect
2. #34036470C2semidirect
3. #34036453C2semidirect
4. #34036419C2semidirect
5. #34036409C2semidirect
6. #34036344C2semidirect
7. #34036344C2semidirect
8. #34036280C2semidirect
10. #34036239C2semidirect
11. #34036229C2semidirect
12. C4×#17989790C2semidirect
13. C4×#17989787C2semidirect
14. #34036190C2semidirect
15. #518×C293C2semidirect
20. #22627624C22semidirect
22. #22627612C22semidirect
28. C4×Dic586C22semidirect
29. C4×D1172C22semidirect
30. #22627557C22semidirect
31. #22627557C22semidirect
32. #22627555C22semidirect
33. #22627555C22semidirect
34. C4⋊#14556873C22semidirect
35. C4⋊#14556873C22semidirect
36. #22627547C22semidirect
37. #22627547C22semidirect
42. #22627544C22semidirect
43. #22627544C22semidirect
46. #22627535C22semidirect
47. C4×#14556873C22semidirect
181. C293#3118semidirect
184. #518D293semidirect

Maximal subgroups

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

subgroupindex
#340367502
#340364702
#340364532
#340364192
#340364092
#340363442
#340362802
#340362632
#340362392
#340362292
C4×#179897902
C4×#179897872
#340361902
#518×C2932
#3118293