Finite Group Databasebeta

← #49170645

Subgroups — #49170645

Order 37504.

420 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#34036792C211yesmaximal, characteristic, complemented
2#34036779C211yesmaximal, characteristic
3#34036478C211yesmaximal, characteristic, complemented
4#34036461C211yesmaximal, characteristic, complemented
5#34036457C211yesmaximal, characteristic, complemented
6#34036413C211yesmaximal, characteristic, complemented
7#34036357C211yesmaximal, characteristic, complemented
8#34036332C211yesmaximal, characteristic, complemented
9#34036267C211yesmaximal, characteristic, complemented
10#34036266C211yesmaximal, characteristic, complemented
11#34036220C211yesmaximal, characteristic, complemented
12C8×C22⋊D293C211yesmaximal, characteristic, complemented
13C2×#22627549C211yesmaximal, characteristic, complemented
14#103×D293C211yesmaximal, characteristic, complemented
15#465×C293C211yesmaximal, characteristic, complemented
16C2×#17989801—21no—
17C22×Dic586C2211yescharacteristic
18C2×Q8×D293C2211yescharacteristic
19C2×#17989790C2211yescharacteristic
20C2×#17989790C2211yescharacteristic
21C2×C8×D293C2211yescharacteristic
22#22627623—21no—
23#22627623C2211yescharacteristic
24#22627622C2211yescharacteristic
25#22627606—21no—
26#22627605—21no—
27#22627604C2211yescharacteristic
28#22627602—21no—
29#22627601—21no—
30#22627601—21no—
31#22627595C2211yescharacteristic
32#22627589C2211yescharacteristic
33D4×Dic293C2211yescharacteristic
34C4×C22⋊D293C2211yescharacteristic
35#22627584—21no—
36C2×C4⋊Dic293C2211yescharacteristic
37C4⋊C4×D293C2211yescharacteristic
38#22627555C2211yescharacteristic
39#22627555C2211yescharacteristic
40#22627553C2211yescharacteristic
41#22627549C2211yescharacteristic
42#22627549C2211yescharacteristic
43#22627549C2211yescharacteristic
44#22627549C2211yescharacteristic
45#22627548C2211yescharacteristic
46#22627548C2211yescharacteristic
47#22627547C2211yescharacteristic
48#22627547C2211yescharacteristic
49C22⋊#14556873C2211yescharacteristic
50#22627536C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52C2×SD16×C293C2211yescharacteristic
53C22×C8×C293C2211yescharacteristic
54C22⋊Q8×C293C2211yescharacteristic
55#121×C293C2211yescharacteristic
56#106×C293C2211yescharacteristic
57#103×C293C2211yescharacteristic
58#102×C293C2211yescharacteristic
59#17989801—44no—
60C2×Dic586—21no—
61C2×Dic586—21no—
62C2×Dic586—22no—
63C2×Dic586—21no—
64C2×Dic586—41no—
65C2×Dic586C2311yescharacteristic
66C2×Dic586C2311yescharacteristic
67Q8×D293—22no—
68Q8×D293—41no—
69C2×C22⋊D293—21no—
70C2×C22⋊D293D411yescharacteristic
71C22×Dic293—21no—
72C22×Dic293—21no—
73C22×Dic293—21no—
74C2×C4×D293—21no—
75C2×C4×D293—21no—
76C2×C4×D293C2311yescharacteristic
77#17989790—22no—
78#17989790—41no—
79C2×#14556873C2311yescharacteristic
80C2×#14556873C2311yescharacteristic
81C8×D293—41no—
82C4⋊Dic293—21no—
83C4⋊Dic293—21no—
84C4⋊Dic293C2311yescharacteristic
85C4⋊Dic293C2311yescharacteristic
86#17989781—21no—
87#17989781—21no—
88#17989781—21no—
89#17989781—21no—
90#17989781—21no—
91#17989781D411yescharacteristic
92C22⋊Dic293—21no—
93C22⋊Dic293—21no—
94C22⋊Dic293D411yescharacteristic
95#17989779—21no—
96#17989779D411yescharacteristic
97C4×Dic293—21no—
98C4×Dic293C2311yescharacteristic
99C2×Q8×C293C2311yescharacteristic
100C2×D4×C293—21no—
101C2×D4×C293C2311yescharacteristic
102C22×C4×C293C2311yescharacteristic
103SD16×C293—41no—
104C2×C8×C293—41no—
105C2×C8×C293C2311yescharacteristic
106C2×C8×C293C2311yescharacteristic
107C4⋊C4×C293—21no—
108C4⋊C4×C293C2311yescharacteristic
109C4⋊C4×C293C2311yescharacteristic
110C22⋊C4×C293—21no—
111C22⋊C4×C293—21no—
112C22×D293C2×D411yescharacteristic
113Dic586—21no—
114Dic586—21no—
115Dic586—21no—
116Dic586—42no—
117Dic586—42no—
118Dic586—42no—
119Dic586#4112yescomplemented
120C22⋊D293—42no—
121C22⋊D293SD1614yescomplemented
122C2×Dic293—21no—
123C2×Dic293—21no—
124C2×Dic293—21no—
125C2×Dic293—21no—
126C2×Dic293—42no—
127C2×Dic293—42no—
128C2×Dic293—42no—
129C2×Dic293C2×D411yescharacteristic
130C2×Dic293C2×D411yescharacteristic
131C2×Dic293C2×D411yescharacteristic
132C4×D293—21no—
133C4×D293—21no—
134C4×D293—42no—
135C4×D293—42no—
136#14556873—21no—
137#14556873—21no—
138C23×C293—21no—
139C23×C293C2×D411yescharacteristic
140Q8×C293—21no—
141Q8×C293—21no—
142D4×C293—21no—
143D4×C293—21no—
144D4×C293—42no—
145C2×C4×C293—21no—
146C2×C4×C293—21no—
147C2×C4×C293—21no—
148C2×C4×C293—21no—
149C2×C4×C293—21no—
150C2×C4×C293C2×D411yescharacteristic
151C2×C4×C293C2411yescharacteristic
152C8×C293—21no—
153C8×C293—21no—
154C22×C293—21no—
155C22×C293—21no—
156C22×C293—41no—
157C22×C293—41no—
158C22×C293—41no—
159C22×C293C2×SD1612yes—
160C22×C293C22×D411yescharacteristic
161C2×D293—21no—
162C2×D293—21no—
163C2×D293C2×SD1612yes—
164C4×C293—21no—
165C4×C293—41no—
166C4×C293—41no—
167C4×C293—41no—
168C4×C293C2×#4111yescharacteristic
169C4×C293H(5,𝔽2)11yescharacteristic
170Dic293—21no—
171Dic293—22no—
172Dic293—21no—
173Dic293—41no—
174Dic293—41no—
175Dic293—41no—
176Dic293C2×SD1612yes—
177C2×C293—22no—
178C2×C293—81no—
179C2×C293#54611yescharacteristic
180C2×C293C22×SD1611yescharacteristic
181C2×C293#57811yescharacteristic
182D293—22no—
183C293#329811yescharacteristic, complemented, Sylow
184#3298—2931nomaximal, Sylow
185D4×Q8—2931no—
186#547—2931no—
187#487—2931no—
188#483—2931no—
189#483—2931no—
190#475—2931no—
191#465—2931no—
192#465D29311yescharacteristic, complemented
193#461—2931no—
194#448—2931no—
195#448—2931no—
196C4×SD16—2931no—
197C8×D4—2931no—
198C2×#103—2931no—
199C2×#103—2931no—
200C2×#41—5861no—
201C22×Q8—2931no—
202C22×Q8—2931no—
203C2×SD16—2931no—
204C2×SD16—2931no—
205C2×SD16C2×D29311yescharacteristic
206C22×C8—2931no—
207C22×C8C2×D29311yescharacteristic
208C4⋊Q8—2931no—
209C4⋊Q8—2931no—
210C4⋊Q8—5861no—
211#123—5861no—
212#123—5861no—
213C22⋊Q8—2931no—
214C22⋊Q8—5861no—
215C22⋊Q8—5861no—
216C22⋊Q8—5861no—
217C22⋊Q8C2×D29311yescharacteristic
218#121—2931no—
219#121C2×D29311yescharacteristic
220C4×Q8—2931no—
221C4×D4—2931no—
222C4×D4—2931no—
223C4×D4—5861no—
224C2×C4⋊C4—2931no—
225C2×C4⋊C4—2931no—
226#106—2931no—
227#106—2931no—
228#106C2×D29311yescharacteristic
229C4⋊C8—2931no—
230#103—2931no—
231#103—2931no—
232#103—2931no—
233#103—2931no—
234#103—2931no—
235#103—2931no—
236#103—2931no—
237#103—2931no—
238#103C2×D29311yescharacteristic
239#102C2×D29311yescharacteristic
240C22⋊C8—2931no—
241C22⋊C8—2931no—
242C4×C8—2931no—
243#41—11724no—
244C2×Q8—2931no—
245C2×Q8—2931no—
246C2×Q8—5861no—
247C2×Q8—5861no—
248C2×Q8—5862no—
249C2×Q8—5861no—
250C2×Q8—5862no—
251C2×Q8—11721no—
252C2×Q8—11721no—
253C2×Q8C22×D29311yescharacteristic
254C2×D4—21no—
255C2×D4—2931no—
256C2×D4—5861no—
257C2×D4C22×D29311yescharacteristic
258C22×C4—2931no—
259C22×C4—5861no—
260C22×C4—5861no—
261C22×C4—5861no—
262C22×C4—5861no—
263C22×C4—5861no—
264C22×C4C22×D29311yescharacteristic
265SD16—41no—
266SD16—5862no—
267SD16—11721no—
268C2×C8—41no—
269C2×C8—2931no—
270C2×C8—2931no—
271C2×C8—11721no—
272C2×C8C22×D29311yescharacteristic
273C2×C8C22×D29311yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—2931no—
276C4⋊C4—2931no—
277C4⋊C4—2931no—
278C4⋊C4—5861no—
279C4⋊C4—5861no—
280C4⋊C4—5861no—
281C4⋊C4—5861no—
282C4⋊C4—5861no—
283C4⋊C4—5861no—
284C4⋊C4—5861no—
285C4⋊C4C22×D29311yescharacteristic
286C4⋊C4C22×D29311yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—2931no—
290C22⋊C4—2931no—
291C22⋊C4—5861no—
292C22⋊C4—5861no—
293C22⋊C4—5861no—
294C42—2931no—
295C42—5861no—
296C23—21no—
297C23—2931no—
298C23D4×D29311yescharacteristic
299Q8—21no—
300Q8—21no—
301Q8—2932no—
302Q8—5861no—
303Q8—5861no—
304Q8—5861no—
305Q8—11722no—
306Q8—11722no—
307Q8—11722no—
308D4—21no—
309D4—21no—
310D4—42no—
311D4—2934no—
312D4—11722no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—2931no—
319C2×C4—2931no—
320C2×C4—2931no—
321C2×C4—5861no—
322C2×C4—5861no—
323C2×C4—5861no—
324C2×C4—5861no—
325C2×C4—5861no—
326C2×C4—5861no—
327C2×C4—11722no—
328C2×C4—11722no—
329C2×C4—11722no—
330C2×C4—11722no—
331C2×C4—11722no—
332C2×C4D4×D29311yescharacteristic
333C2×C4C23×D29311yescharacteristic
334C8—21no—
335C8—21no—
336C8—5861no—
337C8—5861no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—2932no—
344C22—5861no—
345C22—5861no—
346C22SD16×D29312yes—
347C22C2×D4×D29311yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—2932no—
353C4—5861no—
354C4—5862no—
355C4—5861no—
356C4—11721no—
357C4—11721no—
358C4—11721no—
359C4#41×D29311yescharacteristic
360C4#2262766911yescharacteristic
361C2—22no—
362C2—81no—
363C2—5862no—
364C2#3403676811yescharacteristic
365C2C2×SD16×D29311yescharacteristic
366C2#3403694311yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#465×C293C2
socleC22×C293C22×D4
prime radical#34036779C2
hypercenter#465D293
hypocenterC293#3298
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #34036792C2semidirect
3. #34036478C2semidirect
4. #34036461C2semidirect
5. #34036457C2semidirect
6. #34036413C2semidirect
7. #34036357C2semidirect
8. #34036332C2semidirect
9. #34036267C2semidirect
10. #34036266C2semidirect
11. #34036220C2semidirect
12. C8×C22⋊D293C2semidirect
13. C2×#22627549C2semidirect
14. #103×D293C2semidirect
15. #465×C293C2semidirect
119. Dic586#41semidirect
121. C22⋊D293SD16semidirect
183. C293#3298semidirect
192. #465D293semidirect

Maximal subgroups

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

subgroupindex
#340367922
#340367792
#340364782
#340364612
#340364572
#340364132
#340363572
#340363322
#340362672
#340362662
#340362202
C8×C22⋊D2932
C2×#226275492
#103×D2932
#465×C2932
#3298293