Finite Group Databasebeta

← #49175523

Subgroups — #49175523

Order 37504.

544 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
1C2×D293⋊M16C211yesmaximal, characteristic, complemented
2C22×#17989811C211yesmaximal, characteristic, complemented
3#34037162C212yesmaximal, complemented
4#34037161C212yesmaximal, complemented
5#34037158C212yesmaximal, complemented
6#34037156C212yesmaximal, complemented
7#34037132C211yesmaximal, characteristic, complemented
8#34037101C211yesmaximal, characteristic, complemented
9#34037099C211yesmaximal, characteristic, complemented
10C4×#17989811C211yesmaximal, characteristic, complemented
11C2×#22627584C211yesmaximal, characteristic
12C2×#17989812C2212yescomplemented
13D293⋊M16—24no—
14C2×#17989811—24no—
15C2×#17989811C2211yescharacteristic
16C2×#17989811C2211yescharacteristic
17C2×#17989811C2211yescharacteristic
18C2×#17989811C2211yescharacteristic
19C2×#17989811C2212yescomplemented
20C2×D293⋊C8C2212yescomplemented
21C22×#14556880C2212yescomplemented
22#22627691C2212yescomplemented
23C4⋊#14556880C2212yescomplemented
24#22627681C2212yescomplemented
25#22627681C2212yescomplemented
26C22⋊#14556880C2212yescomplemented
27C22⋊#14556880C2212yescomplemented
28#22627679C2212yescomplemented
29C4×#14556880C2212yescomplemented
30C22×C22⋊D293C411yescharacteristic
31C23×Dic293C2211yescharacteristic
32C22×C4×D293C2211yescharacteristic
33#22627584C411yescharacteristic
34#22627584C411yescharacteristic
35#22627584C411yescharacteristic
36#22627584C411yescharacteristic
37#22627584C2211yescharacteristic
38#22627584C2211yescharacteristic
39#22627584C2211yescharacteristic
40#22627584C2211yescharacteristic
41C2×#17989781C411yescharacteristic
42C2×#17989779C411yescharacteristic
43C2×C4×Dic293C2211yescharacteristic
44C2×C22⋊C4×C293C411yescharacteristic
45#17989812—24no—
46#17989811—24no—
47#17989811—22no—
48#17989811—22no—
49#17989811—22no—
50#17989811D414yescomplemented
51D293⋊C8—24no—
52C2×#14556880—24no—
53C2×#14556880C2312yes—
54C2×#14556880C2312yes—
55C2×#14556880C2312yes—
56C2×#14556880C2312yes—
57C23×D293C2×C411yescharacteristic
58C2×C22⋊D293—24no—
59C2×C22⋊D293C2×C411yescharacteristic
60C2×C22⋊D293C2×C411yescharacteristic
61C2×C22⋊D293C2×C411yescharacteristic
62C2×C22⋊D293C2×C411yescharacteristic
63C22×Dic293—22no—
64C22×Dic293—22no—
65C22×Dic293C2×C411yescharacteristic
66C22×Dic293C2×C411yescharacteristic
67C22×Dic293C2×C411yescharacteristic
68C22×Dic293C2×C411yescharacteristic
69C22×Dic293C2311yescharacteristic
70C22×Dic293C2311yescharacteristic
71C22×Dic293C2311yescharacteristic
72C2×C4×D293—22no—
73C2×C4×D293—22no—
74C2×C4×D293C2×C411yescharacteristic
75C2×C4×D293C2×C411yescharacteristic
76C2×C4×D293C2311yescharacteristic
77C2×C4×D293C2311yescharacteristic
78#17989781C2×C411yescharacteristic
79#17989781C2×C411yescharacteristic
80#17989781C2×C411yescharacteristic
81#17989781C2×C411yescharacteristic
82#17989779C2×C411yescharacteristic
83#17989779C2×C411yescharacteristic
84#17989779C2×C411yescharacteristic
85#17989779C2×C411yescharacteristic
86C4×Dic293C2×C411yescharacteristic
87C4×Dic293C2×C411yescharacteristic
88C4×Dic293C2311yescharacteristic
89C4×Dic293C2311yescharacteristic
90C24×C293C2×C411yescharacteristic
91C22×C4×C293C2×C411yescharacteristic
92C22×C4×C293C2×C411yescharacteristic
93C22⋊C4×C293C2×C411yescharacteristic
94C22⋊C4×C293C2×C411yescharacteristic
95C22⋊C4×C293C2×C411yescharacteristic
96C22⋊C4×C293C2×C411yescharacteristic
97#14556880—22no—
98#14556880—22no—
99#14556880—22no—
100#14556880C2×D414yescomplemented
101C22×D293—22no—
102C22×D293—22no—
103C22×D293—41no—
104C22×D293C22×C411yescharacteristic
105C22×D293C22×C411yescharacteristic
106C22⋊D293—22no—
107C22⋊D293—22no—
108C22⋊D293—22no—
109C22⋊D293M1614yescomplemented
110C2×Dic293—22no—
111C2×Dic293—22no—
112C2×Dic293—22no—
113C2×Dic293—22no—
114C2×Dic293—21no—
115C2×Dic293—21no—
116C2×Dic293—21no—
117C2×Dic293—21no—
118C2×Dic293C22×C411yescharacteristic
119C2×Dic293C22×C411yescharacteristic
120C2×Dic293C22×C411yescharacteristic
121C2×Dic293C22×C411yescharacteristic
122C2×Dic293C22×C411yescharacteristic
123C2×Dic293C2×D412yes—
124C2×Dic293#4112yes—
125C2×Dic293C2411yescharacteristic
126C4×D293—22no—
127C4×D293—22no—
128C4×D293—21no—
129C4×D293—21no—
130C4×D293—21no—
131C4×D293—21no—
132C23×C293—22no—
133C23×C293—22no—
134C23×C293—41no—
135C23×C293C22×C411yescharacteristic
136C23×C293C22×C411yescharacteristic
137C23×C293C22×C411yescharacteristic
138C2×C4×C293—22no—
139C2×C4×C293—41no—
140C2×C4×C293C22×C411yescharacteristic
141C2×C4×C293C22×C411yescharacteristic
142C2×C4×C293C22×C411yescharacteristic
143C2×C4×C293C22×C411yescharacteristic
144C22×C293—21no—
145C22×C293—21no—
146C22×C293—21no—
147C22×C293—21no—
148C22×C293—21no—
149C22×C293—21no—
150C22×C293—21no—
151C22×C293—44no—
152C22×C293C4×D412yes—
153C22×C293C2×M1612yescomplemented
154C22×C293C23×C411yescharacteristic
155C2×D293—21no—
156C2×D293—21no—
157C2×D293—21no—
158C2×D293—21no—
159C2×D293—21no—
160C2×D293—44no—
161C2×D293C2×M1612yescomplemented
162C4×C293—21no—
163C4×C293—21no—
164C4×C293—21no—
165C4×C293—21no—
166Dic293—21no—
167Dic293—21no—
168Dic293—21no—
169Dic293C4×D412yes—
170Dic293C2×M1612yescomplemented
171Dic293C22×D411yescharacteristic
172Dic293C2×#4111yescharacteristic
173C2×C293—22no—
174C2×C293—22no—
175C2×C293—41no—
176C2×C293C2×C4×D411yescharacteristic
177C2×C293C22×M1611yescharacteristic
178C2×C293#56811yescharacteristic
179D293—22no—
180D293—41no—
181C293D4×M1611yescharacteristic, complemented, Sylow
182D4×M16—2931nomaximal, Sylow
183C22×M16—2931no—
184C22×M16—2931no—
185C2×C4×D4—2931no—
186#436—2932no—
187#435—2932no—
188#435—2932no—
189C8×D4—2932no—
190#423—2931no—
191#407—2931no—
192#407—2931no—
193C4×M16—2931no—
194C22×D4—2931no—
195C23×C4—2931no—
196C23×C4—2931no—
197C2×M16—2931no—
198C2×M16—2931no—
199C2×M16—2931no—
200C2×M16—2932no—
201C2×M16—2932no—
202C2×M16—2931no—
203C2×M16—5864no—
204C2×M16—5864no—
205C22×C8—2932no—
206C22×C8—2932no—
207C4×D4—2931no—
208C4×D4—2931no—
209C4×D4—2931no—
210C4×D4—2931no—
211C4×D4—2931no—
212C4×D4—2931no—
213C4×D4—2931no—
214C4×D4—2931no—
215C2×C4⋊C4—2931no—
216C2×C22⋊C4—2931no—
217C2×C22⋊C4#1192407811yescharacteristic
218C2×C42—2931no—
219C4⋊C8—2932no—
220C4⋊C8—2932no—
221C22⋊C8—2932no—
222C22⋊C8—2932no—
223C22⋊C8—2932no—
224C22⋊C8—2932no—
225#97—2932no—
226C4×C8—2932no—
227C24—2931no—
228C24C2×#1192407811yescharacteristic
229C2×D4—2931no—
230C2×D4—2931no—
231C2×D4—2931no—
232C2×D4—2931no—
233C2×D4—5864no—
234C22×C4—2931no—
235C22×C4—2931no—
236C22×C4—2931no—
237C22×C4—2931no—
238C22×C4—2931no—
239C22×C4—2931no—
240C22×C4—2931no—
241C22×C4—2931no—
242C22×C4—2931no—
243C22×C4—2931no—
244C22×C4—2931no—
245C22×C4—5862no—
246C22×C4—5862no—
247C22×C4—5862no—
248C22×C4—5862no—
249C22×C4C2×#1192407811yescharacteristic
250C22×C4C2×#1192407811yescharacteristic
251M16—2934no—
252M16—5864no—
253M16—5864no—
254M16—5862no—
255M16—5862no—
256M16—5862no—
257C2×C8—2932no—
258C2×C8—2932no—
259C2×C8—2932no—
260C2×C8—2932no—
261C2×C8—5864no—
262C2×C8—5864no—
263C4⋊C4—2931no—
264C4⋊C4—2931no—
265C4⋊C4—2931no—
266C4⋊C4—2931no—
267C22⋊C4—2931no—
268C22⋊C4—2931no—
269C22⋊C4—2931no—
270C22⋊C4—2931no—
271C22⋊C4C2×#1192407811yescharacteristic
272C22⋊C4C2×#1192407811yescharacteristic
273C22⋊C4C2×#1192407811yescharacteristic
274C22⋊C4C2×#1192407811yescharacteristic
275C42—2931no—
276C42—2931no—
277C42—2931no—
278C42—2931no—
279C23—22no—
280C23—22no—
281C23—41no—
282C23—2931no—
283C23—2931no—
284C23—5862no—
285C23—5862no—
286C23—11721no—
287C23C22×#1192407811yescharacteristic
288C23C22×#1192407811yescharacteristic
289C23C22×#1192407811yescharacteristic
290D4—2934no—
291D4—5862no—
292D4—5862no—
293D4—5862no—
294C2×C4—22no—
295C2×C4—41no—
296C2×C4—2932no—
297C2×C4—2932no—
298C2×C4—2931no—
299C2×C4—2931no—
300C2×C4—2931no—
301C2×C4—2931no—
302C2×C4—2931no—
303C2×C4—2931no—
304C2×C4—5861no—
305C2×C4—5861no—
306C2×C4—5861no—
307C2×C4—5861no—
308C2×C4—5862no—
309C2×C4—5862no—
310C2×C4—5861no—
311C2×C4—5861no—
312C2×C4—5861no—
313C2×C4—5861no—
314C2×C4—5862no—
315C2×C4—5862no—
316C2×C4—5862no—
317C2×C4—5862no—
318C2×C4C22×#1192407811yescharacteristic
319C2×C4C22×#1192407811yescharacteristic
320C2×C4C22×#1192407811yescharacteristic
321C2×C4C22×#1192407811yescharacteristic
322C8—2934no—
323C8—5862no—
324C8—5862no—
325C8—5862no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—44no—
334C22—2932no—
335C22—5861no—
336C22—5861no—
337C22—5861no—
338C22—5861no—
339C22—5861no—
340C22—11724no—
341C22D4×#1192407812yes—
342C22D293⋊M1612yescomplemented
343C22C23×#1192407811yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—2931no—
349C4—2931no—
350C4—2932no—
351C4—2932no—
352C4—5861no—
353C4—5861no—
354C4—5861no—
355C2—22no—
356C2—22no—
357C2—41no—
358C2—5862no—
359C2—11721no—
360C2C2×D4×#1192407811yescharacteristic
361C2C2×D293⋊M1611yescharacteristic
362C2#3403720711yescharacteristic
subgroupG/H
center, FrattiniC22C23×#11924078
commutator, socleC22×C293C23×C4
FittingC2×C22⋊C4×C293C4
prime radicalC22×C22⋊D293C4
cosocleC2×Dic293C24
hypercenterC2×C22⋊C4#11924078
hypocenterC293D4×M16
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×D293⋊M16C2semidirect
2. C22×#17989811C2semidirect
3. #34037162C2semidirect
4. #34037161C2semidirect
5. #34037158C2semidirect
6. #34037156C2semidirect
7. #34037132C2semidirect
8. #34037101C2semidirect
9. #34037099C2semidirect
10. C4×#17989811C2semidirect
12. C2×#17989812C22semidirect
19. C2×#17989811C22semidirect
20. C2×D293⋊C8C22semidirect
21. C22×#14556880C22semidirect
22. #22627691C22semidirect
23. C4⋊#14556880C22semidirect
24. #22627681C22semidirect
25. #22627681C22semidirect
26. C22⋊#14556880C22semidirect
27. C22⋊#14556880C22semidirect
28. #22627679C22semidirect
29. C4×#14556880C22semidirect
50. #17989811D4semidirect
100. #14556880C2×D4semidirect
109. C22⋊D293M16semidirect
153. C22×C293C2×M16semidirect
161. C2×D293C2×M16semidirect
170. Dic293C2×M16semidirect
181. C293D4×M16semidirect
342. C22D293⋊M16semidirect

Maximal subgroups

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

subgroupindex
C2×D293⋊M162
C22×#179898112
#340371622
#340371612
#340371582
#340371562
#340371322
#340371012
#340370992
C4×#179898112
C2×#226275842
D4×M16293