Finite Group Databasebeta

← #49168971

Subgroups — #49168971

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#34036603C211yesmaximal, characteristic, complemented
3#34036471C211yesmaximal, characteristic, complemented
4#34036454C211yesmaximal, characteristic, complemented
5#34036420C211yesmaximal, characteristic, complemented
6#34036410C211yesmaximal, characteristic, complemented
7#34036345C211yesmaximal, characteristic, complemented
8#34036345C211yesmaximal, characteristic, complemented
9#34036282C211yesmaximal, characteristic, complemented
10#34036265C211yesmaximal, characteristic
11#34036242C211yesmaximal, characteristic, complemented
12#34036231C211yesmaximal, characteristic, complemented
13C4×#17989791C211yesmaximal, characteristic, complemented
14C4×D2344C211yesmaximal, characteristic, complemented
15#433×C293C211yesmaximal, characteristic, complemented
16C22×D1172C2211yescharacteristic
17C2×#17989791C2211yescharacteristic
18C2×#17989791C2211yescharacteristic
19C2×D2344C2211yescharacteristic
20C2×D2344C2211yescharacteristic
21#22627624C2211yescharacteristic, complemented
22#22627619—21no—
23#22627612C2211yescharacteristic, complemented
24#22627610—21no—
25#22627606—21no—
26#22627603C2211yescharacteristic
27#22627602—21no—
28#22627598C2211yescharacteristic
29C4×Dic586C2211yescharacteristic, complemented
30C4×D1172C2211yescharacteristic
31C4×D1172C2211yescharacteristic
32C4×D1172C2211yescharacteristic
33C4×D1172C2211yescharacteristic
34C4×D1172C2211yescharacteristic, complemented
35#22627586—21no—
36#22627586—21no—
37#22627583C2211yescharacteristic
38C22⋊C4×D293—21no—
39C22⋊C4×D293—21no—
40#22627558C2211yescharacteristic, complemented
41#22627558C2211yescharacteristic, complemented
42#22627556C2211yescharacteristic, complemented
43#22627556C2211yescharacteristic, complemented
44#22627549C2211yescharacteristic, complemented
45#22627549C2211yescharacteristic, complemented
46#22627546C2211yescharacteristic
47#22627546C2211yescharacteristic
48#22627546C2211yescharacteristic
49#22627546C2211yescharacteristic
50#22627546C2211yescharacteristic, complemented
51#22627546C2211yescharacteristic, complemented
52#117×C293C2211yescharacteristic
53C4⋊C8×C293C2211yescharacteristic, complemented
54C4⋊C8×C293C2211yescharacteristic, complemented
55C22⋊C8×C293C2211yescharacteristic
56C22⋊C8×C293C2211yescharacteristic
57#97×C293C2211yescharacteristic, complemented
58C4×C8×C293C2211yescharacteristic, complemented
59C23×D293—21no—
60C2×Dic586—21no—
61C2×Dic586C2311yescharacteristic
62C2×D1172—22no—
63C2×D1172—22no—
64C2×D1172—21no—
65C2×D1172C2311yescharacteristic
66C2×D1172C2311yescharacteristic
67C2×D1172C2311yescharacteristic
68C2×C22⋊D293—21no—
69C2×C4×D293—21no—
70C2×C4×D293—21no—
71C2×C4×D293—21no—
72C2×C4×D293—21no—
73C2×C4×D293—21no—
74#17989791—22no—
75#17989791—22no—
76D2344—22no—
77D2344—22no—
78C4⋊Dic293—21no—
79C4⋊Dic293C2311yescharacteristic
80C4⋊Dic293C2311yescharacteristic
81C4⋊Dic293C2311yescharacteristic
82C4⋊Dic293C2311yescharacteristic
83#17989781—21no—
84#17989781—21no—
85C22⋊Dic293—21no—
86C22⋊Dic293—21no—
87#17989779—21no—
88#17989779—21no—
89#17989779—21no—
90#17989779—21no—
91#17989779—21no—
92#17989779—21no—
93#17989779—21no—
94#17989779—21no—
95C4×Dic293—21no—
96C4×Dic293—21no—
97C22×C4×C293C2311yescharacteristic
98C2×C8×C293C2311yescharacteristic
99C2×C8×C293C2311yescharacteristic
100C2×C8×C293C2311yescharacteristic
101C2×C8×C293C2311yescharacteristic
102C4⋊C4×C293D411yescharacteristic
103C4⋊C4×C293D411yescharacteristic
104C22⋊C4×C293D411yescharacteristic
105C22⋊C4×C293D411yescharacteristic
106C42×C293C2311yescharacteristic
107C42×C293C2311yescharacteristic
108C22×D293—21no—
109C22×D293—21no—
110C22×D293—24no—
111C22×D293—21no—
112C22×D293—81no—
113C22×D293—81no—
114Dic586—21no—
115Dic586—21no—
116Dic586—81no—
117D1172—24no—
118D1172—21no—
119D1172—21no—
120D1172—21no—
121D1172—21no—
122D1172#4112yes—
123D1172#4112yes—
124C22⋊D293—81no—
125C2×Dic293—21no—
126C2×Dic293—21no—
127C2×Dic293—21no—
128C2×Dic293—21no—
129C2×Dic293—21no—
130C4×D293—81no—
131C4×D293—81no—
132C4×D293—81no—
133C4×D293—81no—
134C4×D293—81no—
135C23×C293C2×D411yescharacteristic
136C2×C4×C293—21no—
137C2×C4×C293—21no—
138C2×C4×C293C2×D411yescharacteristic
139C2×C4×C293C2×D411yescharacteristic
140C2×C4×C293C2×D411yescharacteristic
141C2×C4×C293C2×D411yescharacteristic
142C2×C4×C293C2×D411yescharacteristic
143C2×C4×C293C2411yescharacteristic
144C8×C293—21no—
145C8×C293—21no—
146C8×C293—21no—
147C8×C293—21no—
148C22×C293—21no—
149C22×C293—21no—
150C22×C293—21no—
151C22×C293C22×D411yescharacteristic
152C2×D293—22no—
153C2×D293—22no—
154C2×D293—41no—
155C2×D293—41no—
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—21no—
165C4×C293—21no—
166C4×C293—21no—
167C4×C293C2×#4111yescharacteristic
168C4×C293C2×#4111yescharacteristic
169Dic293—41no—
170Dic293—41no—
171Dic293—41no—
172Dic293—41no—
173Dic293—41no—
174C2×C293—41no—
175C2×C293#52511yescharacteristic
176C2×C293#57611yescharacteristic
177C2×C293#57711yescharacteristic
178D293—42no—
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#440—2931no—
195C4×SD16—2931no—
196C4×D8—2931no—
197#433D29311yescharacteristic, complemented
198C22×D4—2931no—
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—2931no—
213C4×D4—2931no—
214C4×D4—2931no—
215C4×D4—2931no—
216C4×D4—2931no—
217C4×D4—5861no—
218C4×D4—5861no—
219#117—2931no—
220#117C2×D29311yescharacteristic
221C2×C22⋊C4—5861no—
222C2×C22⋊C4—5861no—
223#107—2931no—
224#107—2931no—
225#106—2931no—
226#106—2931no—
227C4⋊C8C2×D29311yescharacteristic, complemented
228C4⋊C8C2×D29311yescharacteristic, complemented
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⋊C8C2×D29311yescharacteristic
238C22⋊C8C2×D29311yescharacteristic
239#97C2×D29311yescharacteristic, complemented
240C4×C8C2×D29311yescharacteristic, complemented
241C24—5861no—
242C2×Q8—2931no—
243C2×Q8—5861no—
244C2×D4—2931no—
245C2×D4—2931no—
246C2×D4—2931no—
247C2×D4—5862no—
248C2×D4—5862no—
249C2×D4—5861no—
250C2×D4—5861no—
251C22×C4—5861no—
252C22×C4—5861no—
253C22×C4—5861no—
254C22×C4—5861no—
255C22×C4—5861no—
256C22×C4C22×D29311yescharacteristic
257SD16—5862no—
258SD16—5862no—
259D8—5862no—
260D8—5862no—
261C2×C8C22×D29311yescharacteristic
262C2×C8C22×D29311yescharacteristic
263C2×C8C22×D29311yescharacteristic
264C2×C8C22×D29311yescharacteristic
265C4⋊C4—2931no—
266C4⋊C4—2931no—
267C4⋊C4—2931no—
268C4⋊C4—2931no—
269C4⋊C4—5861no—
270C4⋊C4—5861no—
271C4⋊C4—5861no—
272C4⋊C4D117211yescharacteristic
273C4⋊C4D117211yescharacteristic
274C22⋊C4—5861no—
275C22⋊C4—5861no—
276C22⋊C4—5861no—
277C22⋊C4—5861no—
278C22⋊C4—5861no—
279C22⋊C4—5861no—
280C22⋊C4—5861no—
281C22⋊C4—5861no—
282C22⋊C4—5861no—
283C22⋊C4—5861no—
284C22⋊C4D117211yescharacteristic
285C22⋊C4D117211yescharacteristic
286C42—5861no—
287C42—5861no—
288C42C22×D29311yescharacteristic
289C42C22×D29311yescharacteristic
290C23—23441no—
291C23—23441no—
292C23—5864no—
293C23—5861no—
294C23—5861no—
295C23—5861no—
296C23C2×D117211yescharacteristic
297Q8—23441no—
298Q8—5861no—
299Q8—5861no—
300D4—2932no—
301D4—2932no—
302D4—23441no—
303D4—5864no—
304D4—5861no—
305D4—5861no—
306D4—5861no—
307D4—5861no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—23441no—
311C2×C4—23441no—
312C2×C4—23441no—
313C2×C4—23441no—
314C2×C4—23441no—
315C2×C4—5861no—
316C2×C4—5861no—
317C2×C4—5861no—
318C2×C4—5861no—
319C2×C4—5861no—
320C2×C4C2×D117211yescharacteristic
321C2×C4C2×D117211yescharacteristic
322C2×C4C2×D117211yescharacteristic
323C2×C4C2×D117211yescharacteristic
324C2×C4C2×D117211yescharacteristic
325C2×C4C23×D29311yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—23444no—
334C22—5862no—
335C22—5862no—
336C22—11721no—
337C22—11721no—
338C22—11721no—
339C22—11721no—
340C22—11721no—
341C22—11721no—
342C22—11721no—
343C22C22×D117211yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—11721no—
350C4—11721no—
351C4—11721no—
352C4—11721no—
353C4—11721no—
354C4#41×D29311yescharacteristic
355C4#41×D29311yescharacteristic
356C2—41no—
357C2—23441no—
358C2—11722no—
359C2—11722no—
360C2#3403664111yescharacteristic
361C2#3403693411yescharacteristic
362C2#3403694111yescharacteristic
subgroupG/H
centerC22C22×D1172
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#433×C293C2
socleC22×C293C22×D4
prime radical#34036265C2
hypercenter#433D293
hypocenterC293#3118
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #34036750C2semidirect
2. #34036603C2semidirect
3. #34036471C2semidirect
4. #34036454C2semidirect
5. #34036420C2semidirect
6. #34036410C2semidirect
7. #34036345C2semidirect
8. #34036345C2semidirect
9. #34036282C2semidirect
11. #34036242C2semidirect
12. #34036231C2semidirect
13. C4×#17989791C2semidirect
14. C4×D2344C2semidirect
15. #433×C293C2semidirect
21. #22627624C22semidirect
23. #22627612C22semidirect
29. C4×Dic586C22semidirect
34. C4×D1172C22semidirect
40. #22627558C22semidirect
41. #22627558C22semidirect
42. #22627556C22semidirect
43. #22627556C22semidirect
44. #22627549C22semidirect
45. #22627549C22semidirect
50. #22627546C22semidirect
51. #22627546C22semidirect
53. C4⋊C8×C293C22semidirect
54. C4⋊C8×C293C22semidirect
57. #97×C293C22semidirect
58. C4×C8×C293C22semidirect
181. C293#3118semidirect
197. #433D293semidirect
227. C4⋊C8C2×D293semidirect
228. C4⋊C8C2×D293semidirect
239. #97C2×D293semidirect
240. C4×C8C2×D293semidirect

Maximal subgroups

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

subgroupindex
#340367502
#340366032
#340364712
#340364542
#340364202
#340364102
#340363452
#340362822
#340362652
#340362422
#340362312
C4×#179897912
C4×D23442
#433×C2932
#3118293