Finite Group Databasebeta

← #49169339

Subgroups — #49169339

Order 37504.

412 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036681C211yesmaximal, characteristic, complemented
2#34036674C211yesmaximal, characteristic
3#34036526C211yesmaximal, characteristic, complemented
4#34036500C211yesmaximal, characteristic, complemented
5#34036478C211yesmaximal, characteristic, complemented
6#34036474C211yesmaximal, characteristic, complemented
7#34036360C211yesmaximal, characteristic, complemented
8#34036358C211yesmaximal, characteristic, complemented
9#34036356C211yesmaximal, characteristic, complemented
10#34036220C211yesmaximal, characteristic, complemented
11SD16×Dic293C211yesmaximal, characteristic, complemented
12#34036216C211yesmaximal, characteristic, complemented
13#34036214C211yesmaximal, characteristic, complemented
14C2×C8×Dic293C211yesmaximal, characteristic, complemented
15#465×C293C211yesmaximal, characteristic, complemented
16C2×#17989801—21no—
17C2×#17989791C2211yescharacteristic
18C2×#17989790C2211yescharacteristic
19C2×#17989789C2211yescharacteristic
20C22×#14556873C2211yescharacteristic
21#22627623C2211yescharacteristic
22#22627623C2211yescharacteristic
23#22627622C2211yescharacteristic
24#22627620C2211yescharacteristic
25#22627614—21no—
26#22627610—21no—
27#22627603C2211yescharacteristic
28#22627601—21no—
29#22627598C2211yescharacteristic
30#22627596—21no—
31Q8×Dic293C2211yescharacteristic
32#22627589—21no—
33#22627589C2211yescharacteristic
34D4×Dic293C2211yescharacteristic
35#22627586C2211yescharacteristic
36#22627584—21no—
37#22627580—21no—
38C2×C4×Dic293C2211yescharacteristic
39#22627556C2211yescharacteristic
40#22627555C2211yescharacteristic
41#22627555C2211yescharacteristic
42#22627549C2211yescharacteristic
43#22627548C2211yescharacteristic
44#22627547C2211yescharacteristic
45#22627546C2211yescharacteristic
46#22627545C2211yescharacteristic
47#22627544C2211yescharacteristic
48C8×Dic293C2211yescharacteristic
49C8×Dic293C2211yescharacteristic
50C8×Dic293C2211yescharacteristic
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×Dic586C2311yescharacteristic
63C2×D1172C2311yescharacteristic
64C2×C22⋊D293—21no—
65C2×C22⋊D293—21no—
66C2×C22⋊D293—21no—
67C22×Dic293—21no—
68C22×Dic293D411yescharacteristic
69C22×Dic293D411yescharacteristic
70C2×C4×D293—21no—
71#17989791—22no—
72#17989790—22no—
73#17989789—22no—
74C2×#14556873—22no—
75C2×#14556873C2311yescharacteristic
76C2×#14556873C2311yescharacteristic
77C4⋊Dic293—21no—
78C4⋊Dic293C2311yescharacteristic
79C4⋊Dic293C2311yescharacteristic
80#17989781—21no—
81#17989781—21no—
82#17989781—21no—
83#17989781—21no—
84#17989781—21no—
85#17989781—21no—
86C22⋊Dic293—21no—
87C22⋊Dic293—21no—
88#17989779—21no—
89#17989779—21no—
90C4×Dic293—21no—
91C4×Dic293—21no—
92C4×Dic293D411yescharacteristic
93C4×Dic293D411yescharacteristic
94C4×Dic293C2311yescharacteristic
95C4×Dic293C2311yescharacteristic
96C2×Q8×C293C2311yescharacteristic
97C2×D4×C293—21no—
98C2×D4×C293C2311yescharacteristic
99C22×C4×C293C2311yescharacteristic
100SD16×C293—22no—
101C2×C8×C293—22no—
102C2×C8×C293C2311yescharacteristic
103C2×C8×C293C2311yescharacteristic
104C4⋊C4×C293—21no—
105C4⋊C4×C293C2311yescharacteristic
106C4⋊C4×C293C2311yescharacteristic
107C22⋊C4×C293—21no—
108C22⋊C4×C293—21no—
109C22×D293—21no—
110Dic586—21no—
111Dic586—21no—
112Dic586—42no—
113Dic586—42no—
114D1172—21no—
115D1172—21no—
116C22⋊D293—42no—
117C22⋊D293—42no—
118C22⋊D293—42no—
119C2×Dic293—22no—
120C2×Dic293—21no—
121C2×Dic293—21no—
122C2×Dic293—21no—
123C2×Dic293—42no—
124C2×Dic293SD1614yescomplemented
125C2×Dic293C2×D411yescharacteristic
126C2×Dic293C2×D411yescharacteristic
127C2×Dic293C2×D411yescharacteristic
128C2×Dic293C2×D411yescharacteristic
129C4×D293—42no—
130#14556873—21no—
131#14556873#4112yescomplemented
132C23×C293—21no—
133C23×C293C2×D411yescharacteristic
134Q8×C293—21no—
135Q8×C293—21no—
136D4×C293—21no—
137D4×C293—21no—
138D4×C293—42no—
139C2×C4×C293—21no—
140C2×C4×C293—21no—
141C2×C4×C293—21no—
142C2×C4×C293—21no—
143C2×C4×C293—21no—
144C2×C4×C293C2×D411yescharacteristic
145C2×C4×C293C2411yescharacteristic
146C8×C293—21no—
147C8×C293#4112yescomplemented
148C22×C293—21no—
149C22×C293—21no—
150C22×C293—41no—
151C22×C293—41no—
152C22×C293—41no—
153C22×C293C2×SD1612yes—
154C22×C293C22×D411yescharacteristic
155C2×D293—41no—
156C2×D293—41no—
157C2×D293—41no—
158C4×C293—21no—
159C4×C293—41no—
160C4×C293—41no—
161C4×C293—41no—
162C4×C293C2×#4111yescharacteristic
163C4×C293C2×#4111yescharacteristic
164Dic293—21no—
165Dic293—41no—
166Dic293—41no—
167Dic293—41no—
168Dic293C2×SD1612yes—
169Dic293C2×SD1612yes—
170Dic293#13512yes—
171C2×C293—22no—
172C2×C293—81no—
173C2×C293#53211yescharacteristic
174C2×C293C22×SD1611yescharacteristic
175C2×C293C2×#13511yescharacteristic
176D293—81no—
177C293#316711yescharacteristic, complemented, Sylow
178#3167—2931nomaximal, Sylow
179#533—2931no—
180#532—2931no—
181#498—2931no—
182#492—2931no—
183#487—2931no—
184#486—2931no—
185#465—2931no—
186#465—2931no—
187#465—2931no—
188#465D29311yescharacteristic, complemented
189C4×SD16—2931no—
190C4×SD16—2931no—
191C4×SD16—2931no—
192C4×SD16—2931no—
193C2×C4×C8—2931no—
194C2×#41—5861no—
195C2×SD16—2931no—
196C2×SD16—2931no—
197C2×SD16—2931no—
198C2×SD16C2×D29311yescharacteristic
199C22×C8—2931no—
200C22×C8C2×D29311yescharacteristic
201C4⋊Q8—2931no—
202C4⋊Q8—2931no—
203C4⋊Q8—2931no—
204#127—2931no—
205#125—5861no—
206#124—5861no—
207C22⋊Q8—2931no—
208C22⋊Q8—5861no—
209C22⋊Q8C2×D29311yescharacteristic
210#121—2931no—
211#121—5861no—
212#121C2×D29311yescharacteristic
213C4×Q8—2931no—
214C4×Q8—2931no—
215C4×Q8—5861no—
216C4×D4—2931no—
217C4×D4—2931no—
218C4×D4—5861no—
219#117—5861no—
220C2×C42—2931no—
221#106—2931no—
222#106—2931no—
223#106—2931no—
224#106C2×D29311yescharacteristic
225#103—2931no—
226#103—2931no—
227#103—2931no—
228#103C2×D29311yescharacteristic
229#102—2931no—
230#102—2931no—
231#102—2931no—
232#102C2×D29311yescharacteristic
233C4×C8—2931no—
234C4×C8—2931no—
235C4×C8—2931no—
236C4×C8—2931no—
237#41—11724no—
238C2×Q8—2931no—
239C2×Q8—5861no—
240C2×Q8—5861no—
241C2×Q8C22×D29311yescharacteristic
242C2×D4—21no—
243C2×D4—2931no—
244C2×D4—5861no—
245C2×D4—5861no—
246C2×D4—5861no—
247C2×D4C22×D29311yescharacteristic
248C22×C4—2931no—
249C22×C4—2931no—
250C22×C4—5861no—
251C22×C4—5861no—
252C22×C4C22×D29311yescharacteristic
253SD16—22no—
254SD16—5862no—
255SD16—5862no—
256SD16—5862no—
257C2×C8—22no—
258C2×C8—2931no—
259C2×C8—2931no—
260C2×C8—5862no—
261C2×C8C22×D29311yescharacteristic
262C2×C8C22×D29311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—2931no—
265C4⋊C4—2931no—
266C4⋊C4—5861no—
267C4⋊C4—5861no—
268C4⋊C4—5861no—
269C4⋊C4—5861no—
270C4⋊C4—5861no—
271C4⋊C4—5861no—
272C4⋊C4—5861no—
273C4⋊C4C22×D29311yescharacteristic
274C4⋊C4C22×D29311yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—5861no—
278C22⋊C4—5861no—
279C22⋊C4—5861no—
280C22⋊C4—5861no—
281C42—2931no—
282C42—2931no—
283C42—2931no—
284C42—2931no—
285C42—5861no—
286C42—5861no—
287C23—21no—
288C23—5861no—
289C23D4×D29311yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—5861no—
293Q8—5861no—
294Q8—11722no—
295Q8—11722no—
296D4—21no—
297D4—21no—
298D4—42no—
299D4—5861no—
300D4—5861no—
301D4—11722no—
302D4—11722no—
303D4—11722no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—2934no—
310C2×C4—2931no—
311C2×C4—2931no—
312C2×C4—2931no—
313C2×C4—2931no—
314C2×C4—5862no—
315C2×C4—5861no—
316C2×C4—5861no—
317C2×C4—5861no—
318C2×C4—11722no—
319C2×C4—11722no—
320C2×C4D4×D29311yescharacteristic
321C2×C4C23×D29311yescharacteristic
322C8—21no—
323C8—2932no—
324C8—5861no—
325C8#1798980112yescomplemented
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—11721no—
332C22—11721no—
333C22—11721no—
334C22SD16×D29312yes—
335C22C2×D4×D29311yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—2932no—
341C4—2932no—
342C4—2932no—
343C4—5861no—
344C4—11721no—
345C4—11721no—
346C4—11721no—
347C4#41×D29311yescharacteristic
348C4C2×#1798980111yescharacteristic
349C2—22no—
350C2—81no—
351C2—23441no—
352C2#3403667411yescharacteristic
353C2C2×SD16×D29311yescharacteristic
354C2#135×D29311yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#465×C293C2
socleC22×C293C22×D4
prime radical#34036674C2
hypercenter#465D293
hypocenterC293#3167
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. #34036681C2semidirect
3. #34036526C2semidirect
4. #34036500C2semidirect
5. #34036478C2semidirect
6. #34036474C2semidirect
7. #34036360C2semidirect
8. #34036358C2semidirect
9. #34036356C2semidirect
10. #34036220C2semidirect
11. SD16×Dic293C2semidirect
12. #34036216C2semidirect
13. #34036214C2semidirect
14. C2×C8×Dic293C2semidirect
15. #465×C293C2semidirect
124. C2×Dic293SD16semidirect
131. #14556873#41semidirect
147. C8×C293#41semidirect
177. C293#3167semidirect
188. #465D293semidirect
325. C8#17989801semidirect

Maximal subgroups

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

subgroupindex
#340366812
#340366742
#340365262
#340365002
#340364782
#340364742
#340363602
#340363582
#340363562
#340362202
SD16×Dic2932
#340362162
#340362142
C2×C8×Dic2932
#465×C2932
#3167293