Finite Group Databasebeta

← #49175519

Subgroups — #49175519

Order 37504.

502 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22627711C211yesmaximal, characteristic, complemented
2C2×D293⋊M16C211yesmaximal, characteristic, complemented
3#34037163C211yesmaximal, characteristic, complemented
4#34037162C211yesmaximal, characteristic, complemented
5#34037161C211yesmaximal, characteristic, complemented
6#34037159C211yesmaximal, characteristic, complemented
7#34037159C211yesmaximal, characteristic, complemented
8#34037158C211yesmaximal, characteristic, complemented
9#34037157C211yesmaximal, characteristic, complemented
10#34037156C211yesmaximal, characteristic, complemented
11#34037135C211yesmaximal, characteristic, complemented
12#34037102C211yesmaximal, characteristic, complemented
13C2×#22627681C211yesmaximal, characteristic, complemented
14#34037093C211yesmaximal, characteristic, complemented
15#34036637C211yesmaximal, characteristic
16#22627711—24no—
17C2×#17989812C2211yescharacteristic
18C2×#17989812C2211yescharacteristic
19C2×#17989812C2211yescharacteristic, complemented
20D293⋊M16—24no—
21C2×#17989811C2211yescharacteristic
22C2×#17989811C2211yescharacteristic
23C2×#17989811C2211yescharacteristic, complemented
24C2×D293⋊C8C2211yescharacteristic
25C2×D293⋊C8C2211yescharacteristic
26C2×D293⋊C8C2211yescharacteristic, complemented
27C22×#14556880C2211yescharacteristic
28C22×#14556880C2211yescharacteristic
29C22×#14556880C2211yescharacteristic, complemented
30#22627691C2211yescharacteristic, complemented
31#22627691C2211yescharacteristic, complemented
32C4⋊#14556880C2211yescharacteristic, complemented
33C4⋊#14556880C2211yescharacteristic, complemented
34#22627681C2211yescharacteristic
35#22627681C2211yescharacteristic
36#22627681C2211yescharacteristic
37#22627681C2211yescharacteristic
38#22627681C2211yescharacteristic, complemented
39#22627681C2211yescharacteristic, complemented
40C22⋊#14556880C2211yescharacteristic, complemented
41C22⋊#14556880C2211yescharacteristic, complemented
42#22627679C2211yescharacteristic, complemented
43#22627679C2211yescharacteristic, complemented
44C4×#14556880C2211yescharacteristic, complemented
45C4×#14556880C2211yescharacteristic, complemented
46C2×#17989801C2211yescharacteristic
47C22×C4×D293C2211yescharacteristic
48#22627607C411yescharacteristic
49#22627602C411yescharacteristic
50#22627602C411yescharacteristic
51#22627597C411yescharacteristic
52#22627597C411yescharacteristic
53#22627594C411yescharacteristic
54#22627592C411yescharacteristic
55#22627586C2211yescharacteristic
56#22627586C2211yescharacteristic
57#22627584C2211yescharacteristic
58#22627584C2211yescharacteristic
59#22627580C2211yescharacteristic
60#123×C293C411yescharacteristic
61#17989812—22no—
62#17989812—22no—
63#17989812—22no—
64#17989811—22no—
65#17989811—22no—
66#17989811D414yescomplemented
67D293⋊C8—22no—
68D293⋊C8—22no—
69D293⋊C8—22no—
70C2×#14556880—22no—
71C2×#14556880—22no—
72C2×#14556880—22no—
73C2×#14556880C2311yescharacteristic
74C2×#14556880C2311yescharacteristic
75C2×#14556880C2311yescharacteristic
76C2×#14556880C2311yescharacteristic
77C2×#14556880C2311yescharacteristic
78C2×#14556880C2311yescharacteristic
79C2×#14556880C2311yescharacteristic
80C2×#14556880C2311yescharacteristic
81C23×D293C2×C411yescharacteristic
82#17989801—22no—
83#17989801—22no—
84C2×Dic586C2×C411yescharacteristic
85C2×D1172C2×C411yescharacteristic
86C2×D1172C2×C411yescharacteristic
87C2×C22⋊D293C2×C411yescharacteristic
88C2×C22⋊D293C2×C411yescharacteristic
89C2×C22⋊D293C2×C411yescharacteristic
90C2×C22⋊D293C2×C411yescharacteristic
91C22×Dic293C2311yescharacteristic
92C22×Dic293C2311yescharacteristic
93C2×C4×D293—22no—
94C2×C4×D293—22no—
95C2×C4×D293C2×C411yescharacteristic
96C2×C4×D293C2×C411yescharacteristic
97C2×C4×D293C2311yescharacteristic
98C2×C4×D293C2311yescharacteristic
99C2×C4×D293C2311yescharacteristic
100#17989781C2×C411yescharacteristic
101#17989781C2×C411yescharacteristic
102#17989781C2×C411yescharacteristic
103#17989781C2×C411yescharacteristic
104C22⋊Dic293C2×C411yescharacteristic
105#17989779C2×C411yescharacteristic
106#17989779C2×C411yescharacteristic
107#17989779C2×C411yescharacteristic
108#17989779C2×C411yescharacteristic
109#17989779C2×C411yescharacteristic
110#17989779C2×C411yescharacteristic
111C4×Dic293C2311yescharacteristic
112C4×Dic293C2311yescharacteristic
113C2×D4×C293C2×C411yescharacteristic
114C22×C4×C293C2×C411yescharacteristic
115C4⋊C4×C293C2×C411yescharacteristic
116C4⋊C4×C293C2×C411yescharacteristic
117C22⋊C4×C293C2×C411yescharacteristic
118C22⋊C4×C293C2×C411yescharacteristic
119C22⋊C4×C293C2×C411yescharacteristic
120#14556880—21no—
121#14556880—21no—
122#14556880—21no—
123#14556880—21no—
124#14556880—21no—
125#14556880—21no—
126#14556880C2×D412yes—
127#14556880C2×D412yes—
128C22×D293—22no—
129C22×D293—22no—
130C22×D293—41no—
131C22×D293C22×C411yescharacteristic
132C22×D293C22×C411yescharacteristic
133C22×D293C22×C411yescharacteristic
134Dic586—22no—
135D1172—22no—
136D1172—41no—
137C22⋊D293—22no—
138C22⋊D293—22no—
139C22⋊D293—22no—
140C22⋊D293—41no—
141C2×Dic293—21no—
142C2×Dic293—21no—
143C2×Dic293C22×C411yescharacteristic
144C2×Dic293C22×C411yescharacteristic
145C2×Dic293C22×C411yescharacteristic
146C2×Dic293C22×C411yescharacteristic
147C2×Dic293C2×D412yes—
148C2×Dic293#4112yes—
149C2×Dic293C2411yescharacteristic
150C4×D293—22no—
151C4×D293—22no—
152C4×D293—21no—
153C4×D293—21no—
154C4×D293—21no—
155C4×D293—21no—
156C4×D293—21no—
157C4×D293—21no—
158C23×C293C22×C411yescharacteristic
159C23×C293C22×C411yescharacteristic
160D4×C293—22no—
161C2×C4×C293—22no—
162C2×C4×C293C22×C411yescharacteristic
163C2×C4×C293C22×C411yescharacteristic
164C2×C4×C293C22×C411yescharacteristic
165C2×C4×C293C22×C411yescharacteristic
166C2×C4×C293C22×C411yescharacteristic
167C22×C293—21no—
168C22×C293—21no—
169C22×C293—21no—
170C22×C293—21no—
171C22×C293—21no—
172C22×C293C4×D412yes—
173C22×C293C23×C411yescharacteristic
174C2×D293—21no—
175C2×D293—21no—
176C2×D293—21no—
177C2×D293—21no—
178C2×D293—21no—
179C2×D293—21no—
180C2×D293—21no—
181C2×D293—21no—
182C2×D293—44no—
183C2×D293#13112yescomplemented
184C4×C293—21no—
185C4×C293—21no—
186C4×C293—21no—
187C4×C293—21no—
188C4×C293—21no—
189Dic293—21no—
190Dic293—21no—
191Dic293—21no—
192Dic293C4×D412yes—
193Dic293C22×D411yescharacteristic
194Dic293C2×#4111yescharacteristic
195C2×C293—22no—
196C2×C293—41no—
197C2×C293C2×C4×D411yescharacteristic
198C2×C293C2×#13111yescharacteristic
199C2×C293#56811yescharacteristic
200D293—22no—
201D293—41no—
202D293—41no—
203C293#293311yescharacteristic, complemented, Sylow
204#2933—2931nomaximal, Sylow
205C2×#131—2931no—
206C22×M16—2931no—
207#525—2931no—
208#436—2931no—
209#436—2931no—
210#435—2931no—
211#435—2931no—
212#435—2931no—
213#435—2931no—
214C8×D4—2931no—
215C8×D4—2931no—
216#424—2931no—
217#408—2931no—
218C2×C22⋊C8—2931no—
219#405—2931no—
220C2×#41—2931no—
221C23×C4—2931no—
222#131—5864no—
223C2×M16—2931no—
224C2×M16—2931no—
225C2×M16—2931no—
226C2×M16—2931no—
227C2×M16—2931no—
228C2×M16—2931no—
229C2×M16—5864no—
230C22×C8—2931no—
231C22×C8—2931no—
232C22×C8—2931no—
233C22×C8—2931no—
234C22×C8—2931no—
235C22×C8—2931no—
236#123—2931no—
237#123#1192407811yescharacteristic
238C22⋊Q8—2931no—
239C22⋊Q8—2931no—
240#121—2931no—
241#121—2931no—
242#120—2931no—
243#120—2931no—
244C4×D4—2931no—
245C4×D4—2931no—
246C4×D4—2931no—
247C4×D4—2931no—
248#117—2931no—
249C4⋊C8—2931no—
250C4⋊C8—2931no—
251C4⋊C8—2931no—
252C4⋊C8—2931no—
253C22⋊C8—2931no—
254C22⋊C8—2931no—
255C22⋊C8—2931no—
256C22⋊C8—2931no—
257C22⋊C8—2931no—
258C22⋊C8—2931no—
259C22⋊C8—2931no—
260C22⋊C8—2931no—
261#97—2931no—
262#97—2931no—
263C4×C8—2931no—
264C4×C8—2931no—
265C24—2931no—
266#41—5862no—
267#41—5862no—
268C2×Q8—2931no—
269C2×D4—2931no—
270C2×D4—2931no—
271C2×D4—2931no—
272C2×D4—2931no—
273C2×D4—2931no—
274C2×D4—2931no—
275C2×D4C2×#1192407811yescharacteristic
276C22×C4—2931no—
277C22×C4—2931no—
278C22×C4—2931no—
279C22×C4—2931no—
280C22×C4—2931no—
281C22×C4—2931no—
282C22×C4—2931no—
283C22×C4—5862no—
284C22×C4—5862no—
285C22×C4C2×#1192407811yescharacteristic
286M16—2934no—
287M16—5862no—
288M16—5862no—
289M16—5862no—
290M16—5862no—
291M16—5862no—
292C2×C8—2931no—
293C2×C8—2931no—
294C2×C8—2931no—
295C2×C8—2931no—
296C2×C8—2931no—
297C2×C8—2931no—
298C2×C8—2931no—
299C2×C8—2931no—
300C2×C8—5862no—
301C2×C8—5862no—
302C2×C8—5862no—
303C2×C8—5862no—
304C2×C8—5862no—
305C2×C8—5862no—
306C4⋊C4—2931no—
307C4⋊C4—2931no—
308C4⋊C4—2931no—
309C4⋊C4—2931no—
310C4⋊C4C2×#1192407811yescharacteristic
311C4⋊C4C2×#1192407811yescharacteristic
312C22⋊C4—2931no—
313C22⋊C4—2931no—
314C22⋊C4—2931no—
315C22⋊C4—2931no—
316C22⋊C4—2931no—
317C22⋊C4—2931no—
318C22⋊C4—2931no—
319C22⋊C4C2×#1192407811yescharacteristic
320C22⋊C4C2×#1192407811yescharacteristic
321C22⋊C4C2×#1192407811yescharacteristic
322C42—2931no—
323C42—2931no—
324C23—2931no—
325C23—2931no—
326C23—2931no—
327C23—5862no—
328C23—5862no—
329C23—11721no—
330C23C22×#1192407811yescharacteristic
331C23C22×#1192407811yescharacteristic
332Q8—5862no—
333D4—22no—
334D4—5862no—
335D4—5862no—
336D4—5862no—
337D4—5862no—
338D4—11721no—
339D4—11721no—
340C2×C4—22no—
341C2×C4—2932no—
342C2×C4—2932no—
343C2×C4—2931no—
344C2×C4—2931no—
345C2×C4—2931no—
346C2×C4—2931no—
347C2×C4—2931no—
348C2×C4—5861no—
349C2×C4—5861no—
350C2×C4—5861no—
351C2×C4—5861no—
352C2×C4—5861no—
353C2×C4—5862no—
354C2×C4—5862no—
355C2×C4—5861no—
356C2×C4—5861no—
357C2×C4—5861no—
358C2×C4C22×#1192407811yescharacteristic
359C2×C4C22×#1192407811yescharacteristic
360C2×C4C22×#1192407811yescharacteristic
361C2×C4C22×#1192407811yescharacteristic
362C2×C4C22×#1192407811yescharacteristic
363C8—2932no—
364C8—2932no—
365C8—5861no—
366C8—5861no—
367C8—5861no—
368C8—5861no—
369C8—5861no—
370C8—5861no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—2932no—
377C22—5861no—
378C22—5861no—
379C22—5861no—
380C22—5861no—
381C22—5861no—
382C22—5861no—
383C22—5861no—
384C22—5861no—
385C22—11724no—
386C22D4×#1192407812yes—
387C22C23×#1192407811yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—2931no—
394C4—2931no—
395C4—2932no—
396C4—5861no—
397C4—5861no—
398C4—5861no—
399C2—22no—
400C2—41no—
401C2—5862no—
402C2—11721no—
403C2—11721no—
404C2C2×D4×#1192407811yescharacteristic
405C2D293⋊#13111yescharacteristic
406C2#3403720811yescharacteristic
subgroupG/H
center, FrattiniC22C23×#11924078
commutator, socleC22×C293C23×C4
Fitting#123×C293C4
prime radical#34036637C2
cosocleC2×Dic293C24
hypercenter#123#11924078
hypocenterC293#2933
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×#22627711C2semidirect
2. C2×D293⋊M16C2semidirect
3. #34037163C2semidirect
4. #34037162C2semidirect
5. #34037161C2semidirect
6. #34037159C2semidirect
7. #34037159C2semidirect
8. #34037158C2semidirect
9. #34037157C2semidirect
10. #34037156C2semidirect
11. #34037135C2semidirect
12. #34037102C2semidirect
13. C2×#22627681C2semidirect
14. #34037093C2semidirect
19. C2×#17989812C22semidirect
23. C2×#17989811C22semidirect
26. C2×D293⋊C8C22semidirect
29. C22×#14556880C22semidirect
30. #22627691C22semidirect
31. #22627691C22semidirect
32. C4⋊#14556880C22semidirect
33. C4⋊#14556880C22semidirect
38. #22627681C22semidirect
39. #22627681C22semidirect
40. C22⋊#14556880C22semidirect
41. C22⋊#14556880C22semidirect
42. #22627679C22semidirect
43. #22627679C22semidirect
44. C4×#14556880C22semidirect
45. C4×#14556880C22semidirect
66. #17989811D4semidirect
183. C2×D293#131semidirect
203. C293#2933semidirect

Maximal subgroups

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

subgroupindex
C2×#226277112
C2×D293⋊M162
#340371632
#340371622
#340371612
#340371592
#340371582
#340371572
#340371562
#340371352
#340371022
C2×#226276812
#340370932
#340366372
#2933293