Finite Group Databasebeta

← #49168929

Subgroups — #49168929

Order 37504.

430 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036674C211yesmaximal, characteristic, complemented
2#41×Dic293C211yesmaximal, characteristic, complemented
3#34036454C211yesmaximal, characteristic, complemented
4#34036450C211yesmaximal, characteristic, complemented
5#34036412C211yesmaximal, characteristic, complemented
6#34036407C211yesmaximal, characteristic, complemented
7#34036327C211yesmaximal, characteristic, complemented
8#34036322C211yesmaximal, characteristic, complemented
9#34036274C211yesmaximal, characteristic, complemented
10#34036241C211yesmaximal, characteristic, complemented
11#34036238C211yesmaximal, characteristic, complemented
12#34036232C211yesmaximal, characteristic, complemented
13#34036230C211yesmaximal, characteristic, complemented
14#34036183C211yesmaximal, characteristic, complemented
15#449×C293C211yesmaximal, characteristic, complemented
16C2×#17989801—21no—
17C2×#17989789C2211yescharacteristic
18C2×#17989787C2211yescharacteristic
19#22627623C2211yescharacteristic
20#22627620C2211yescharacteristic
21#22627610—21no—
22#22627598C2211yescharacteristic
23#22627596—21no—
24Q8×Dic293C2211yescharacteristic
25Q8×Dic293C2211yescharacteristic
26D4×Dic293—21no—
27D4×Dic293—21no—
28D4×Dic293C2211yescharacteristic
29D4×Dic293C2211yescharacteristic
30D4×Dic293C2211yescharacteristic
31#22627586C2211yescharacteristic
32#22627584—21no—
33#22627583—21no—
34#22627583C2211yescharacteristic
35C2×C4×Dic293—21no—
36C2×C4×Dic293C2211yescharacteristic
37#22627558C2211yescharacteristic
38#22627557C2211yescharacteristic
39#22627556C2211yescharacteristic
40#22627555C2211yescharacteristic
41#22627553C2211yescharacteristic
42#22627553C2211yescharacteristic
43#22627548C2211yescharacteristic
44#22627546C2211yescharacteristic
45#22627546C2211yescharacteristic
46#22627545C2211yescharacteristic
47#22627545C2211yescharacteristic
48#22627545C2211yescharacteristic
49C22⋊#14556873C2211yescharacteristic
50#22627534C2211yescharacteristic
51#22627534C2211yescharacteristic
52C2×#41×C293C2211yescharacteristic
53C2×SD16×C293C2211yescharacteristic
54C2×D8×C293C2211yescharacteristic
55#121×C293C2211yescharacteristic
56#103×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58C22⋊C8×C293C2211yescharacteristic
59#17989801—44no—
60C2×Dic586—21no—
61C2×D1172C2311yescharacteristic
62C2×C22⋊D293—21no—
63C2×C22⋊D293—21no—
64C2×C22⋊D293—21no—
65C22×Dic293—21no—
66C22×Dic293—21no—
67C22×Dic293—21no—
68C22×Dic293D411yescharacteristic
69C22×Dic293D411yescharacteristic
70C2×C4×D293—21no—
71#17989789—22no—
72#17989787—22no—
73C2×#14556873C2311yescharacteristic
74C2×#14556873C2311yescharacteristic
75C4⋊Dic293—21no—
76C4⋊Dic293—21no—
77C4⋊Dic293C2311yescharacteristic
78C4⋊Dic293C2311yescharacteristic
79C4⋊Dic293C2311yescharacteristic
80#17989781—21no—
81C22⋊Dic293—21no—
82C22⋊Dic293—21no—
83C22⋊Dic293—21no—
84C22⋊Dic293—21no—
85#17989779—21no—
86#17989779—21no—
87C4×Dic293—21no—
88C4×Dic293—21no—
89C4×Dic293—21no—
90C4×Dic293D411yescharacteristic
91C4×Dic293D411yescharacteristic
92C4×Dic293C2311yescharacteristic
93C4×Dic293C2311yescharacteristic
94#41×C293—22no—
95#41×C293—22no—
96C2×Q8×C293C2311yescharacteristic
97C2×D4×C293—21no—
98C2×D4×C293—21no—
99C2×D4×C293C2311yescharacteristic
100C2×D4×C293C2311yescharacteristic
101C22×C4×C293—21no—
102C22×C4×C293C2311yescharacteristic
103SD16×C293—22no—
104D8×C293—22no—
105C2×C8×C293C2311yescharacteristic
106C2×C8×C293C2311yescharacteristic
107C4⋊C4×C293C2311yescharacteristic
108C22⋊C4×C293—21no—
109C22×D293—21no—
110Dic586—42no—
111D1172—21no—
112D1172—21no—
113C22⋊D293—42no—
114C22⋊D293—42no—
115C22⋊D293—42no—
116C2×Dic293—22no—
117C2×Dic293—21no—
118C2×Dic293—21no—
119C2×Dic293—21no—
120C2×Dic293—41no—
121C2×Dic293—42no—
122C2×Dic293—42no—
123C2×Dic293—42no—
124C2×Dic293C2×D411yescharacteristic
125C2×Dic293C2×D411yescharacteristic
126C2×Dic293C2×D411yescharacteristic
127C2×Dic293C2×D411yescharacteristic
128C4×D293—42no—
129#14556873—21no—
130#14556873—21no—
131C23×C293—21no—
132C23×C293—21no—
133C23×C293C2×D411yescharacteristic
134Q8×C293—21no—
135Q8×C293#4112yescomplemented
136D4×C293—24no—
137D4×C293—21no—
138D4×C293—21no—
139D4×C293—21no—
140D4×C293—42no—
141D4×C293#4112yescomplemented
142C2×C4×C293—24no—
143C2×C4×C293—21no—
144C2×C4×C293—21no—
145C2×C4×C293—21no—
146C2×C4×C293—21no—
147C2×C4×C293C2×D411yescharacteristic
148C2×C4×C293C2411yescharacteristic
149C8×C293—21no—
150C8×C293—21no—
151C22×C293—21no—
152C22×C293—22no—
153C22×C293—21no—
154C22×C293—21no—
155C22×C293—41no—
156C22×C293—41no—
157C22×C293—41no—
158C22×C293—41no—
159C22×C293—41no—
160C22×C293C22×D411yescharacteristic
161C2×D293—41no—
162C2×D293—41no—
163C2×D293—41no—
164C4×C293—21no—
165C4×C293—22no—
166C4×C293—41no—
167C4×C293C2×#4111yescharacteristic
168C4×C293C2×#4111yescharacteristic
169Dic293—21no—
170Dic293—21no—
171Dic293—21no—
172Dic293—41no—
173Dic293—41no—
174Dic293—41no—
175Dic293AGL(1,ℤ/8)12yes—
176C2×C293—41no—
177C2×C293—42no—
178C2×C293—81no—
179C2×C293#52511yescharacteristic
180C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
181C2×C293#57511yescharacteristic
182D293—81no—
183C293#311511yescharacteristic, complemented, Sylow
184#3115—2931nomaximal, Sylow
185#532—2931no—
186C4×#41—2931no—
187#482—2931no—
188#482—2931no—
189#475—2931no—
190#474—2931no—
191#460—2931no—
192#459—2931no—
193#449—2931no—
194#449D29311yescharacteristic, complemented
195#442—2931no—
196#442—2931no—
197#440—2931no—
198#440—2931no—
199#432—2931no—
200C2×#41—5861no—
201C2×#41C2×D29311yescharacteristic
202C2×SD16—2931no—
203C2×SD16C2×D29311yescharacteristic
204C2×D8—2931no—
205C2×D8C2×D29311yescharacteristic
206C4⋊Q8—2931no—
207#127—2931no—
208#124—5861no—
209#121—2931no—
210#121—5861no—
211#121C2×D29311yescharacteristic
212C4×Q8—2931no—
213C4×Q8—2931no—
214C4×D4—2931no—
215C4×D4—2931no—
216C4×D4—2931no—
217C4×D4—2931no—
218C4×D4—5861no—
219C4×D4—5861no—
220C4×D4—5861no—
221#117—2931no—
222#117—5861no—
223C2×C42—2931no—
224C2×C42—5861no—
225#107—2931no—
226#107—2931no—
227#106—2931no—
228#106—2931no—
229C4⋊C8—2931no—
230C4⋊C8—2931no—
231#103—2931no—
232#103C2×D29311yescharacteristic
233#102—2931no—
234#102—2931no—
235#102—2931no—
236#102—2931no—
237#102—2931no—
238#102C2×D29311yescharacteristic
239C22⋊C8—2931no—
240C22⋊C8C2×D29311yescharacteristic
241#97—2931no—
242#97—2931no—
243#41—22no—
244#41—22no—
245#41—11724no—
246C2×Q8—5861no—
247C2×Q8C22×D29311yescharacteristic
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—2931no—
251C2×D4—5861no—
252C2×D4—5861no—
253C2×D4—5861no—
254C2×D4C22×D29311yescharacteristic
255C2×D4C22×D29311yescharacteristic
256C22×C4—21no—
257C22×C4—2931no—
258C22×C4—2931no—
259C22×C4—5861no—
260C22×C4—5861no—
261C22×C4—5861no—
262C22×C4—5861no—
263C22×C4C22×D29311yescharacteristic
264SD16—22no—
265SD16—5862no—
266D8—22no—
267D8—5862no—
268C2×C8—2931no—
269C2×C8—2931no—
270C2×C8C22×D29311yescharacteristic
271C2×C8C22×D29311yescharacteristic
272C4⋊C4—2931no—
273C4⋊C4—2931no—
274C4⋊C4—2931no—
275C4⋊C4—5861no—
276C4⋊C4—5861no—
277C4⋊C4—5861no—
278C4⋊C4C22×D29311yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—5861no—
281C22⋊C4—5861no—
282C22⋊C4—5861no—
283C22⋊C4—5861no—
284C22⋊C4—5861no—
285C22⋊C4—5861no—
286C42—2931no—
287C42—2931no—
288C42—2931no—
289C42—2931no—
290C42—5861no—
291C42—5861no—
292C42—5861no—
293C23—21no—
294C23—21no—
295C23—5861no—
296C23D4×D29311yescharacteristic
297Q8—21no—
298Q8—11722no—
299Q8#1798980112yescomplemented
300D4—24no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—42no—
305D4—5861no—
306D4—5861no—
307D4—11722no—
308D4—11722no—
309D4—11722no—
310D4#1798980112yescomplemented
311C2×C4—24no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—2931no—
317C2×C4—2931no—
318C2×C4—2931no—
319C2×C4—2931no—
320C2×C4—5862no—
321C2×C4—5861no—
322C2×C4—5861no—
323C2×C4—5861no—
324C2×C4—11722no—
325C2×C4—11722no—
326C2×C4—11721no—
327C2×C4—11722no—
328C2×C4—11722no—
329C2×C4D4×D29311yescharacteristic
330C2×C4C23×D29311yescharacteristic
331C8—21no—
332C8—21no—
333C8—5861no—
334C8—5861no—
335C22—21no—
336C22—22no—
337C22—21no—
338C22—21no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—11721no—
345C22—11721no—
346C22—11721no—
347C22C2×D4×D29311yescharacteristic
348C4—21no—
349C4—22no—
350C4—41no—
351C4—2932no—
352C4—5861no—
353C4—5861no—
354C4—5861no—
355C4—11721no—
356C4—11721no—
357C4—11721no—
358C4C2×#1798980111yescharacteristic
359C4C2×#1798980111yescharacteristic
360C2—41no—
361C2—42no—
362C2—81no—
363C2—23441no—
364C2#3403663511yescharacteristic
365C2AGL(1,ℤ/8)×D29311yescharacteristic
366C2#3403692611yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#449×C293C2
socleC22×C293C22×D4
hypercenter#449D293
hypocenterC293#3115
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #34036674C2semidirect
2. #41×Dic293C2semidirect
3. #34036454C2semidirect
4. #34036450C2semidirect
5. #34036412C2semidirect
6. #34036407C2semidirect
7. #34036327C2semidirect
8. #34036322C2semidirect
9. #34036274C2semidirect
10. #34036241C2semidirect
11. #34036238C2semidirect
12. #34036232C2semidirect
13. #34036230C2semidirect
14. #34036183C2semidirect
15. #449×C293C2semidirect
135. Q8×C293#41semidirect
141. D4×C293#41semidirect
183. C293#3115semidirect
194. #449D293semidirect
299. Q8#17989801semidirect
310. D4#17989801semidirect

Maximal subgroups

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

subgroupindex
#340366742
#41×Dic2932
#340364542
#340364502
#340364122
#340364072
#340363272
#340363222
#340362742
#340362412
#340362382
#340362322
#340362302
#340361832
#449×C2932
#3115293