Finite Group Databasebeta

← #49170357

Subgroups — #49170357

Order 37504.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22627656C211yesmaximal, characteristic, complemented
2C2×Q16×D293C211yesmaximal, characteristic, complemented
3Q8×D1172C211yesmaximal, characteristic, complemented
4#34036791C211yesmaximal, characteristic
5#34036523C211yesmaximal, characteristic, complemented
6#34036388C211yesmaximal, characteristic, complemented
7#34036359C211yesmaximal, characteristic, complemented
8#34036351C211yesmaximal, characteristic, complemented
9#34036339C211yesmaximal, characteristic, complemented
10#34036294C211yesmaximal, characteristic, complemented
11#34036286C211yesmaximal, characteristic, complemented
12#34036286C211yesmaximal, characteristic, complemented
13#34036269C211yesmaximal, characteristic, complemented
14#34036202C211yesmaximal, characteristic, complemented
15#441×C293C211yesmaximal, characteristic, complemented
16C2×#17989803C2211yescharacteristic
17C2×Q8×D293C2211yescharacteristic
18C2×Q8×D293C2211yescharacteristic
19C2×Q8×D293C2211yescharacteristic
20#22627656—24no—
21C2×Dic1172C2211yescharacteristic
22C2×Dic1172C2211yescharacteristic
23C2×#17989792C2211yescharacteristic
24C2×#17989792C2211yescharacteristic
25C2×#17989792C2211yescharacteristic
26Q16×D293—24no—
27C2×#17989791C2211yescharacteristic
28C2×#17989791C2211yescharacteristic
29C2×#17989789C2211yescharacteristic
30C2×#17989785C2211yescharacteristic
31C2×C8×D293C2211yescharacteristic
32#22627624—21no—
33#22627624C2211yescharacteristic
34#22627612—21no—
35#22627612C2211yescharacteristic
36#22627604—21no—
37#22627604—21no—
38#22627604—21no—
39#22627604C2211yescharacteristic
40#22627604C2211yescharacteristic
41#22627604C2211yescharacteristic
42#22627599—21no—
43#22627599C2211yescharacteristic
44C4×D1172—21no—
45C4×D1172—21no—
46C4×D1172C2211yescharacteristic
47C4⋊#14556873C2211yescharacteristic
48#22627547C2211yescharacteristic
49#22627547C2211yescharacteristic
50#22627547C2211yescharacteristic
51#22627544C2211yescharacteristic
52#22627536C2211yescharacteristic
53#22627536C2211yescharacteristic
54C2×Q16×C293C2211yescharacteristic
55C4×Q8×C293C2211yescharacteristic
56C4×Q8×C293C2211yescharacteristic
57#106×C293C2211yescharacteristic
58#103×C293C2211yescharacteristic
59#103×C293C2211yescharacteristic
60#97×C293C2211yescharacteristic
61#17989803—22no—
62#17989803—41no—
63C2×Dic586—21no—
64C2×Dic586—21no—
65C2×Dic586—21no—
66C2×Dic586C2311yescharacteristic
67C2×Dic586C2311yescharacteristic
68C2×Dic586C2311yescharacteristic
69Q8×D293—22no—
70Q8×D293—22no—
71Q8×D293—22no—
72Q8×D293—41no—
73Q8×D293—41no—
74Q8×D293—41no—
75C2×D1172—21no—
76C2×D1172—21no—
77C2×D1172D411yescharacteristic
78C2×D1172C2311yescharacteristic
79C2×C4×D293—21no—
80C2×C4×D293—21no—
81C2×C4×D293—21no—
82C2×C4×D293—21no—
83C2×C4×D293C2311yescharacteristic
84C2×C4×D293C2311yescharacteristic
85Dic1172—22no—
86Dic1172—41no—
87#17989792—22no—
88#17989792—22no—
89#17989792—22no—
90#17989791—22no—
91#17989791—41no—
92#17989789—22no—
93#17989785—22no—
94C2×#14556873C2311yescharacteristic
95C2×#14556873C2311yescharacteristic
96C8×D293—22no—
97C4⋊Dic293—21no—
98C4⋊Dic293—21no—
99C4⋊Dic293—21no—
100C4⋊Dic293—21no—
101C4⋊Dic293—21no—
102C4⋊Dic293D411yescharacteristic
103#17989779—21no—
104#17989779—21no—
105#17989779—21no—
106#17989779—21no—
107#17989779—21no—
108#17989779—21no—
109#17989779D411yescharacteristic
110#17989779D411yescharacteristic
111C2×Q8×C293C2311yescharacteristic
112C2×Q8×C293C2311yescharacteristic
113Q16×C293D414yescomplemented
114C2×C8×C293C2311yescharacteristic
115C2×C8×C293C2311yescharacteristic
116C4⋊C4×C293—21no—
117C4⋊C4×C293—21no—
118C4⋊C4×C293C2311yescharacteristic
119C4⋊C4×C293C2311yescharacteristic
120C42×C293—21no—
121C42×C293—21no—
122C42×C293C2311yescharacteristic
123C22×D293—21no—
124C22×D293C2×D411yescharacteristic
125C22×D293C2×D411yescharacteristic
126Dic586—21no—
127Dic586—21no—
128Dic586—21no—
129Dic586—21no—
130Dic586—21no—
131Dic586—21no—
132Dic586—42no—
133Dic586—42no—
134Dic586—42no—
135D1172—22no—
136D1172—21no—
137D1172—21no—
138D1172—42no—
139D1172—42no—
140C2×Dic293—21no—
141C2×Dic293—21no—
142C2×Dic293—21no—
143C2×Dic293C2×D411yescharacteristic
144C2×Dic293C2×D411yescharacteristic
145C4×D293—21no—
146C4×D293—21no—
147C4×D293—21no—
148C4×D293—21no—
149C4×D293—42no—
150C4×D293—42no—
151C4×D293—42no—
152C4×D293—42no—
153#14556873—21no—
154#14556873—21no—
155Q8×C293—21no—
156Q8×C293—21no—
157Q8×C293C2×D412yes—
158Q8×C293C2×D412yes—
159C2×C4×C293—21no—
160C2×C4×C293—21no—
161C2×C4×C293—21no—
162C2×C4×C293—21no—
163C2×C4×C293C2×D411yescharacteristic
164C2×C4×C293C2×D411yescharacteristic
165C2×C4×C293C2411yescharacteristic
166C8×C293—21no—
167C8×C293C2×D412yes—
168C22×C293C22×D411yescharacteristic
169C2×D293—21no—
170C2×D293—21no—
171C2×D293—21no—
172C2×D293—21no—
173C2×D293—21no—
174C2×D293—41no—
175C2×D293—41no—
176C2×D293—41no—
177C2×D293#13712yescomplemented
178C4×C293—22no—
179C4×C293—22no—
180C4×C293—21no—
181C4×C293—21no—
182C4×C293—41no—
183C4×C293—41no—
184C4×C293C22×D411yescharacteristic
185C4×C293H(5,𝔽2)11yescharacteristic
186Dic293—21no—
187Dic293—21no—
188Dic293—41no—
189Dic293—41no—
190Dic293—41no—
191C2×C293D4211yescharacteristic
192C2×C293C2×#13711yescharacteristic
193C2×C293#57811yescharacteristic
194D293—22no—
195D293—41no—
196D293—81no—
197C293#327011yescharacteristic, complemented, Sylow
198#3270—2931nomaximal, Sylow
199C2×#137—2931no—
200C22×Q16—2931no—
201D4×Q8—2931no—
202#548—2931no—
203#497—2931no—
204#470—2931no—
205#465—2931no—
206#464—2931no—
207#462—2931no—
208#452—2931no—
209#451—2931no—
210#451—2931no—
211#448—2931no—
212#441D29311yescharacteristic, complemented
213#435—2931no—
214C2×#41—2931no—
215C22×Q8—2931no—
216C22×Q8—2931no—
217C22×Q8—2931no—
218#137—5864no—
219C2×Q16—2931no—
220C2×Q16—2931no—
221C2×Q16—2931no—
222C2×Q16—2931no—
223C2×Q16—2931no—
224C2×Q16—5864no—
225C2×Q16C2×D29311yescharacteristic
226C2×SD16—2931no—
227C2×SD16—2931no—
228C2×SD16—2931no—
229C2×M16—2931no—
230C22×C8—2931no—
231C4⋊Q8—2931no—
232C4⋊Q8—5861no—
233#124—2931no—
234#124—5861no—
235C22⋊Q8—2931no—
236C22⋊Q8—2931no—
237C22⋊Q8—2931no—
238C22⋊Q8—5861no—
239C22⋊Q8—5861no—
240C22⋊Q8—5861no—
241#121—2931no—
242#121—5861no—
243C4×Q8C2×D29311yescharacteristic
244C4×Q8C2×D29311yescharacteristic
245C4×D4—2931no—
246C4×D4—5861no—
247C4×D4—5861no—
248#106C2×D29311yescharacteristic
249C4⋊C8—2931no—
250#103—2931no—
251#103—2931no—
252#103—2931no—
253#103C2×D29311yescharacteristic
254#103C2×D29311yescharacteristic
255#102—2931no—
256C22⋊C8—2931no—
257C22⋊C8—2931no—
258#97C2×D29311yescharacteristic
259#41—5862no—
260#41—11721no—
261C2×Q8—2931no—
262C2×Q8—2931no—
263C2×Q8—2931no—
264C2×Q8—5861no—
265C2×Q8—5861no—
266C2×Q8—5861no—
267C2×Q8—5862no—
268C2×Q8—5862no—
269C2×Q8—5862no—
270C2×Q8—11721no—
271C2×Q8—11721no—
272C2×Q8—11721no—
273C2×Q8C22×D29311yescharacteristic
274C2×Q8C22×D29311yescharacteristic
275C2×D4—2931no—
276C2×D4—2931no—
277C2×D4—5861no—
278C2×D4—5861no—
279C22×C4—2931no—
280C22×C4—2931no—
281C22×C4—5861no—
282C22×C4—5861no—
283C22×C4—5861no—
284C22×C4—5861no—
285Q16—5862no—
286Q16—5862no—
287Q16—5862no—
288Q16—5862no—
289Q16—11721no—
290Q16D117214yescomplemented
291SD16—5862no—
292SD16—5862no—
293SD16—11721no—
294M16—5862no—
295C2×C8—2931no—
296C2×C8—2931no—
297C2×C8—5862no—
298C2×C8C22×D29311yescharacteristic
299C2×C8C22×D29311yescharacteristic
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—2931no—
303C4⋊C4—5861no—
304C4⋊C4—5861no—
305C4⋊C4—5861no—
306C4⋊C4—5861no—
307C4⋊C4—5861no—
308C4⋊C4C22×D29311yescharacteristic
309C4⋊C4C22×D29311yescharacteristic
310C22⋊C4—2931no—
311C22⋊C4—2931no—
312C22⋊C4—5861no—
313C22⋊C4—5861no—
314C22⋊C4—5861no—
315C22⋊C4—5861no—
316C22⋊C4—5861no—
317C22⋊C4—5861no—
318C42—21no—
319C42—21no—
320C42C22×D29311yescharacteristic
321C23—2931no—
322C23—2931no—
323C23—5861no—
324Q8—21no—
325Q8—21no—
326Q8—5861no—
327Q8—5861no—
328Q8—5861no—
329Q8—5861no—
330Q8—5861no—
331Q8—5861no—
332Q8—11722no—
333Q8—11722no—
334Q8—11722no—
335Q8C2×D117212yes—
336Q8C2×D117212yes—
337D4—5862no—
338D4—5861no—
339D4—5861no—
340D4—11722no—
341D4—11722no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—2931no—
347C2×C4—2931no—
348C2×C4—5861no—
349C2×C4—5861no—
350C2×C4—5861no—
351C2×C4—5861no—
352C2×C4—5861no—
353C2×C4—5861no—
354C2×C4—5861no—
355C2×C4—11722no—
356C2×C4—11722no—
357C2×C4—11722no—
358C2×C4—11722no—
359C2×C4D4×D29311yescharacteristic
360C2×C4D4×D29311yescharacteristic
361C2×C4C23×D29311yescharacteristic
362C8—21no—
363C8—5861no—
364C8—5861no—
365C8C2×D117212yes—
366C22—2932no—
367C22—5861no—
368C22—5861no—
369C22—5861no—
370C22—5861no—
371C22—5861no—
372C22—11721no—
373C22—11721no—
374C22—11721no—
375C22C2×D4×D29311yescharacteristic
376C4—22no—
377C4—22no—
378C4—21no—
379C4—21no—
380C4—41no—
381C4—41no—
382C4—5861no—
383C4—5861no—
384C4—11721no—
385C4—11721no—
386C4—11721no—
387C4C22×D117211yescharacteristic
388C4#2262767011yescharacteristic
389C2—23441no—
390C2—5862no—
391C2—11721no—
392C2D4×D117211yescharacteristic
393C2#137×D29311yescharacteristic
394C2#3403694511yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#441×C293C2
socleC22×C293C22×D4
prime radical#34036791C2
hypercenter#441D293
hypocenterC293#3270
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. C2×#22627656C2semidirect
2. C2×Q16×D293C2semidirect
3. Q8×D1172C2semidirect
5. #34036523C2semidirect
6. #34036388C2semidirect
7. #34036359C2semidirect
8. #34036351C2semidirect
9. #34036339C2semidirect
10. #34036294C2semidirect
11. #34036286C2semidirect
12. #34036286C2semidirect
13. #34036269C2semidirect
14. #34036202C2semidirect
15. #441×C293C2semidirect
113. Q16×C293D4semidirect
177. C2×D293#137semidirect
197. C293#3270semidirect
212. #441D293semidirect
290. Q16D1172semidirect

Maximal subgroups

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

subgroupindex
C2×#226276562
C2×Q16×D2932
Q8×D11722
#340367912
#340365232
#340363882
#340363592
#340363512
#340363392
#340362942
#340362862
#340362692
#340362022
#441×C2932
#3270293