Finite Group Databasebeta

← #49170689

Subgroups — #49170689

Order 37504.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036825C211yesmaximal, characteristic, complemented
2#34036788C211yesmaximal, characteristic, complemented
3#34036484C211yesmaximal, characteristic, complemented
4#34036471C211yesmaximal, characteristic, complemented
5#34036448C211yesmaximal, characteristic, complemented
6#34036437C211yesmaximal, characteristic, complemented
7#34036365C211yesmaximal, characteristic, complemented
8#34036358C211yesmaximal, characteristic, complemented
9#34036345C211yesmaximal, characteristic, complemented
10#34036276C211yesmaximal, characteristic, complemented
11#34036270C211yesmaximal, characteristic, complemented
12C4×#17989791C211yesmaximal, characteristic, complemented
13#34036126C211yesmaximal, characteristic, complemented
14C2×#22627549C211yesmaximal, characteristic, complemented
15C8×D4×C293C211yesmaximal, characteristic, complemented
16C2×#17989802C2211yescharacteristic
17C22×Dic586C2211yescharacteristic
18C2×#17989791C2211yescharacteristic
19C2×#17989791C2211yescharacteristic
20C2×D2344C2211yescharacteristic
21#22627619—21no—
22#22627616C2211yescharacteristic
23#22627612C2211yescharacteristic
24#22627610—21no—
25#22627606—21no—
26#22627603C2211yescharacteristic
27#22627602—21no—
28#22627598C2211yescharacteristic
29#22627598C2211yescharacteristic
30#22627598C2211yescharacteristic
31#22627596—21no—
32#22627596—21no—
33C4×Dic586C2211yescharacteristic
34C4×D1172C2211yescharacteristic
35#22627584—21no—
36#22627584—21no—
37#22627583C2211yescharacteristic
38C2×C4⋊Dic293C2211yescharacteristic
39#22627558C2211yescharacteristic
40#22627556C2211yescharacteristic
41#22627556C2211yescharacteristic
42#22627549C2211yescharacteristic
43#22627549C2211yescharacteristic
44#22627549C2211yescharacteristic
45#22627549C2211yescharacteristic
46#22627549C2211yescharacteristic
47#22627549C2211yescharacteristic
48#22627546C2211yescharacteristic
49#22627546C2211yescharacteristic
50#22627546C2211yescharacteristic
51#22627546C2211yescharacteristic
52C22×C8×C293C2211yescharacteristic
53C22×C8×C293C2211yescharacteristic
54C4×D4×C293C2211yescharacteristic
55C4⋊C8×C293C2211yescharacteristic
56C22⋊C8×C293C2211yescharacteristic
57C22⋊C8×C293C2211yescharacteristic
58C4×C8×C293C2211yescharacteristic
59#17989802—22no—
60#17989802—41no—
61C2×Dic586—22no—
62C2×Dic586—21no—
63C2×Dic586—41no—
64C2×Dic586C2311yescharacteristic
65C2×Dic586C2311yescharacteristic
66C2×D1172C2311yescharacteristic
67C2×D1172C2311yescharacteristic
68C2×C22⋊D293—21no—
69C2×C22⋊D293—21no—
70C2×C22⋊D293—21no—
71C2×C22⋊D293—21no—
72C22×Dic293—21no—
73C22×Dic293—21no—
74C2×C4×D293—21no—
75C2×C4×D293—21no—
76#17989791—22no—
77#17989791—41no—
78D2344—41no—
79C4⋊Dic293—21no—
80C4⋊Dic293C2311yescharacteristic
81C4⋊Dic293C2311yescharacteristic
82C4⋊Dic293C2311yescharacteristic
83C4⋊Dic293C2311yescharacteristic
84#17989781—21no—
85#17989781—21no—
86#17989781—21no—
87#17989781—21no—
88C22⋊Dic293—21no—
89C22⋊Dic293—21no—
90#17989779—21no—
91#17989779—21no—
92#17989779—21no—
93#17989779—21no—
94#17989779—21no—
95#17989779—21no—
96C4×Dic293—21no—
97C4×Dic293—21no—
98C2×D4×C293D411yescharacteristic
99C22×C4×C293C2311yescharacteristic
100C22×C4×C293C2311yescharacteristic
101C2×C8×C293—41no—
102C2×C8×C293—41no—
103C2×C8×C293C2311yescharacteristic
104C2×C8×C293C2311yescharacteristic
105C2×C8×C293C2311yescharacteristic
106C2×C8×C293C2311yescharacteristic
107C4⋊C4×C293D411yescharacteristic
108C22⋊C4×C293D411yescharacteristic
109C22⋊C4×C293D411yescharacteristic
110C42×C293C2311yescharacteristic
111C22×D293—21no—
112C22×D293—21no—
113Dic586—21no—
114Dic586—21no—
115Dic586—21no—
116Dic586—42no—
117Dic586#4112yes—
118D1172—21no—
119D1172—21no—
120D1172—21no—
121D1172—21no—
122C22⋊D293—42no—
123C22⋊D293—42no—
124C22⋊D293—42no—
125C22⋊D293—81no—
126C2×Dic293—21no—
127C2×Dic293—21no—
128C2×Dic293—21no—
129C2×Dic293—21no—
130C2×Dic293—21no—
131C2×Dic293—21no—
132C2×Dic293—42no—
133C2×Dic293—81no—
134C4×D293—42no—
135C4×D293—81no—
136C23×C293C2×D411yescharacteristic
137C23×C293C2×D411yescharacteristic
138D4×C293—22no—
139C2×C4×C293—21no—
140C2×C4×C293—21no—
141C2×C4×C293—21no—
142C2×C4×C293—21no—
143C2×C4×C293C2×D411yescharacteristic
144C2×C4×C293C2×D411yescharacteristic
145C2×C4×C293C2×D411yescharacteristic
146C2×C4×C293C2×D411yescharacteristic
147C2×C4×C293C2411yescharacteristic
148C8×C293—21no—
149C8×C293—21no—
150C8×C293—21no—
151C8×C293—21no—
152C22×C293—21no—
153C22×C293—21no—
154C22×C293—21no—
155C22×C293—21no—
156C22×C293—21no—
157C22×C293#13512yes—
158C22×C293C22×D411yescharacteristic
159C2×D293—41no—
160C2×D293—41no—
161C2×D293—41no—
162C2×D293—41no—
163C2×D293—41no—
164C2×D293—41no—
165C4×C293—21no—
166C4×C293—21no—
167C4×C293—21no—
168C4×C293—21no—
169C4×C293C2×#4111yescharacteristic
170C4×C293H(5,𝔽2)11yescharacteristic
171Dic293—22no—
172Dic293—41no—
173Dic293—41no—
174Dic293—41no—
175Dic293—41no—
176Dic293—41no—
177C2×C293—22no—
178C2×C293—41no—
179C2×C293#54611yescharacteristic
180C2×C293C2×#13511yescharacteristic
181C2×C293#57711yescharacteristic
182D293—81no—
183D293—81no—
184C293#330111yescharacteristic, complemented, Sylow
185#3301—2931nomaximal, Sylow
186#553—2931no—
187#548—2931no—
188#488—2931no—
189#485—2931no—
190#481—2931no—
191#479—2931no—
192#466—2931no—
193#465—2931no—
194#463—2931no—
195#449—2931no—
196#448—2931no—
197C4×SD16—2931no—
198C8×D4D29311yescharacteristic, complemented
199#416—2931no—
200C2×#103—2931no—
201C2×#41—2931no—
202C22×Q8—2931no—
203C2×SD16—2931no—
204C2×SD16—2931no—
205C2×D8—2931no—
206C22×C8C2×D29311yescharacteristic
207C22×C8C2×D29311yescharacteristic
208#126—5861no—
209#125—2931no—
210#124—2931no—
211#124—5861no—
212#123—5861no—
213C22⋊Q8—2931no—
214C22⋊Q8—5861no—
215#121—2931no—
216#121—2931no—
217#121—2931no—
218#121—5861no—
219#121—5861no—
220C4×Q8—2931no—
221C4×D4—2931no—
222C4×D4—5861no—
223C4×D4—5861no—
224C4×D4C2×D29311yescharacteristic
225#117—2931no—
226C2×C4⋊C4—2931no—
227#107—2931no—
228#106—2931no—
229#106—2931no—
230C4⋊C8C2×D29311yescharacteristic
231#103—2931no—
232#103—2931no—
233#103—2931no—
234#103—2931no—
235#103—2931no—
236#103—2931no—
237#102—2931no—
238#102—2931no—
239#102—2931no—
240#102—2931no—
241C22⋊C8C2×D29311yescharacteristic
242C22⋊C8C2×D29311yescharacteristic
243C4×C8C2×D29311yescharacteristic
244#41—5862no—
245#41—11721no—
246C2×Q8—2931no—
247C2×Q8—2931no—
248C2×Q8—5862no—
249C2×Q8—5861no—
250C2×Q8—11721no—
251C2×D4—2931no—
252C2×D4—2931no—
253C2×D4—5861no—
254C2×D4—5861no—
255C2×D4—5861no—
256C2×D4—5861no—
257C2×D4D117211yescharacteristic
258C22×C4—5861no—
259C22×C4—5861no—
260C22×C4—5861no—
261C22×C4—5861no—
262C22×C4C22×D29311yescharacteristic
263C22×C4C22×D29311yescharacteristic
264SD16—5862no—
265SD16—11721no—
266D8—11721no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8C22×D29311yescharacteristic
270C2×C8C22×D29311yescharacteristic
271C2×C8C22×D29311yescharacteristic
272C2×C8C22×D29311yescharacteristic
273C4⋊C4—2931no—
274C4⋊C4—2931no—
275C4⋊C4—2931no—
276C4⋊C4—2931no—
277C4⋊C4—5861no—
278C4⋊C4—5861no—
279C4⋊C4—5861no—
280C4⋊C4—5861no—
281C4⋊C4—5861no—
282C4⋊C4D117211yescharacteristic
283C22⋊C4—5861no—
284C22⋊C4—5861no—
285C22⋊C4—5861no—
286C22⋊C4—5861no—
287C22⋊C4—5861no—
288C22⋊C4—5861no—
289C22⋊C4—5861no—
290C22⋊C4—5861no—
291C22⋊C4D117211yescharacteristic
292C22⋊C4D117211yescharacteristic
293C42—5861no—
294C42—5861no—
295C42C22×D29311yescharacteristic
296C23—5861no—
297C23—5861no—
298C23C2×D117211yescharacteristic
299C23C2×D117211yescharacteristic
300Q8—2932no—
301Q8—5861no—
302Q8—5861no—
303Q8—5861no—
304Q8—11722no—
305D4—22no—
306D4—23441no—
307D4—5861no—
308D4—5861no—
309D4—5861no—
310D4—5861no—
311D4—11722no—
312D4—11722no—
313D4—11722no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—23441no—
319C2×C4—23441no—
320C2×C4—5861no—
321C2×C4—5861no—
322C2×C4—5861no—
323C2×C4—5861no—
324C2×C4—5861no—
325C2×C4—5861no—
326C2×C4—11722no—
327C2×C4—11722no—
328C2×C4C2×D117211yescharacteristic
329C2×C4C2×D117211yescharacteristic
330C2×C4C2×D117211yescharacteristic
331C2×C4C2×D117211yescharacteristic
332C2×C4C23×D29311yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—11721no—
343C22—11721no—
344C22—11721no—
345C22—11721no—
346C22—11721no—
347C22—11721no—
348C22#2262764612yes—
349C22C22×D117211yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—5862no—
355C4—11721no—
356C4—11721no—
357C4—11721no—
358C4—11721no—
359C4—11721no—
360C4#41×D29311yescharacteristic
361C4#2262766911yescharacteristic
362C2—22no—
363C2—41no—
364C2—23441no—
365C2—23441no—
366C2#3403677411yescharacteristic
367C2C2×#2262764611yescharacteristic
368C2#3403694111yescharacteristic
subgroupG/H
centerC22C22×D1172
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC8×D4×C293C2
socleC22×C293C22×D4
hypercenterC8×D4D293
hypocenterC293#3301
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #34036825C2semidirect
2. #34036788C2semidirect
3. #34036484C2semidirect
4. #34036471C2semidirect
5. #34036448C2semidirect
6. #34036437C2semidirect
7. #34036365C2semidirect
8. #34036358C2semidirect
9. #34036345C2semidirect
10. #34036276C2semidirect
11. #34036270C2semidirect
12. C4×#17989791C2semidirect
13. #34036126C2semidirect
14. C2×#22627549C2semidirect
15. C8×D4×C293C2semidirect
184. C293#3301semidirect
198. C8×D4D293semidirect

Maximal subgroups

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

subgroupindex
#340368252
#340367882
#340364842
#340364712
#340364482
#340364372
#340363652
#340363582
#340363452
#340362762
#340362702
C4×#179897912
#340361262
C2×#226275492
C8×D4×C2932
#3301293