Finite Group Databasebeta

← #49170733

Subgroups — #49170733

Order 37504.

408 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036842C211yesmaximal, characteristic, complemented
2#34036797C211yesmaximal, characteristic, complemented
3#34036474C211yesmaximal, characteristic, complemented
4#34036455C211yesmaximal, characteristic, complemented
5#34036423C211yesmaximal, characteristic, complemented
6#34036366C211yesmaximal, characteristic, complemented
7#34036363C211yesmaximal, characteristic, complemented
8#34036323C211yesmaximal, characteristic, complemented
9#34036276C211yesmaximal, characteristic, complemented
10#34036275C211yesmaximal, characteristic, complemented
11#34036216C211yesmaximal, characteristic, complemented
12#34036192C211yesmaximal, characteristic, complemented
13#34036123C211yesmaximal, characteristic, complemented
14#34036122C211yesmaximal, characteristic, complemented
15#482×C293C211yesmaximal, characteristic, complemented
16C2×#17989802C2211yescharacteristic
17C2×#17989801C2211yescharacteristic
18C2×#17989791C2211yescharacteristic
19C2×D2344C2211yescharacteristic
20C2×#17989787C2211yescharacteristic
21C22×#14556873C2211yescharacteristic
22C2×C8×D293C2211yescharacteristic
23#22627623C2211yescharacteristic
24#22627620—21no—
25#22627620C2211yescharacteristic
26#22627612—21no—
27#22627610—21no—
28#22627599C2211yescharacteristic
29#22627599C2211yescharacteristic
30#22627598C2211yescharacteristic
31#22627597—21no—
32#22627597—21no—
33#22627596—21no—
34#22627589C2211yescharacteristic
35#22627586C2211yescharacteristic
36C4×C22⋊D293C2211yescharacteristic
37#22627584—21no—
38#22627582C2211yescharacteristic
39#22627581—21no—
40#22627557C2211yescharacteristic
41#22627553C2211yescharacteristic
42#22627549C2211yescharacteristic
43#22627547C2211yescharacteristic
44#22627547C2211yescharacteristic
45#22627546C2211yescharacteristic
46#22627545C2211yescharacteristic
47#22627544C2211yescharacteristic
48#22627544C2211yescharacteristic
49#22627544C2211yescharacteristic
50#22627536C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52#121×C293C2211yescharacteristic
53#117×C293C2211yescharacteristic
54#107×C293C2211yescharacteristic
55#106×C293C2211yescharacteristic
56#102×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58C22⋊C8×C293C2211yescharacteristic
59#17989802—22no—
60#17989802—41no—
61#17989801—22no—
62#17989801—41no—
63C2×Dic586—21no—
64C2×Dic586C2311yescharacteristic
65C2×D1172—21no—
66C2×D1172—21no—
67C2×D1172C2311yescharacteristic
68C2×D1172C2311yescharacteristic
69C2×C22⋊D293—21no—
70C2×C22⋊D293—21no—
71C2×C22⋊D293—21no—
72C2×C22⋊D293—21no—
73C2×C22⋊D293—21no—
74C2×C22⋊D293D411yescharacteristic
75C22×Dic293—21no—
76C2×C4×D293—21no—
77C2×C4×D293—21no—
78C2×C4×D293C2311yescharacteristic
79#17989791—22no—
80D2344—41no—
81#17989787—41no—
82C2×#14556873—41no—
83C2×#14556873C2311yescharacteristic
84C2×#14556873C2311yescharacteristic
85C8×D293—41no—
86C4⋊Dic293C2311yescharacteristic
87#17989781—21no—
88#17989781—21no—
89#17989781D411yescharacteristic
90C22⋊Dic293D411yescharacteristic
91#17989779—21no—
92#17989779—21no—
93#17989779—21no—
94#17989779—21no—
95#17989779—21no—
96#17989779D411yescharacteristic
97C4×Dic293—21no—
98C4×Dic293—21no—
99C4×Dic293C2311yescharacteristic
100C2×D4×C293—21no—
101C2×D4×C293C2311yescharacteristic
102C22×C4×C293C2311yescharacteristic
103C2×C8×C293C2311yescharacteristic
104C2×C8×C293C2311yescharacteristic
105C4⋊C4×C293C2311yescharacteristic
106C4⋊C4×C293C2311yescharacteristic
107C4⋊C4×C293C2311yescharacteristic
108C22⋊C4×C293—21no—
109C22⋊C4×C293—21no—
110C42×C293—21no—
111C22×D293—21no—
112C22×D293—21no—
113C22×D293C2×D411yescharacteristic
114Dic586—21no—
115Dic586—81no—
116Dic586#4112yes—
117D1172—21no—
118D1172—21no—
119D1172—21no—
120D1172—21no—
121D1172—81no—
122D1172—81no—
123C22⋊D293—22no—
124C22⋊D293—42no—
125C22⋊D293—42no—
126C22⋊D293—42no—
127C22⋊D293—81no—
128C22⋊D293—81no—
129C2×Dic293—21no—
130C2×Dic293—21no—
131C2×Dic293—42no—
132C2×Dic293C2×D411yescharacteristic
133C2×Dic293C2×D411yescharacteristic
134C2×Dic293C2×D411yescharacteristic
135C4×D293—21no—
136C4×D293—21no—
137C4×D293—42no—
138C4×D293—42no—
139#14556873—21no—
140#14556873—21no—
141C23×C293—21no—
142C23×C293C2×D411yescharacteristic
143D4×C293—21no—
144D4×C293—21no—
145D4×C293—81no—
146C2×C4×C293—21no—
147C2×C4×C293—21no—
148C2×C4×C293—21no—
149C2×C4×C293—21no—
150C2×C4×C293—21no—
151C2×C4×C293C2×D411yescharacteristic
152C2×C4×C293C2411yescharacteristic
153C8×C293—21no—
154C8×C293—21no—
155C22×C293—21no—
156C22×C293—21no—
157C22×C293—21no—
158C22×C293—41no—
159C22×C293—41no—
160C22×C293—41no—
161C22×C293C22×D411yescharacteristic
162C2×D293—21no—
163C2×D293—21no—
164C2×D293—21no—
165C2×D293—41no—
166C2×D293—41no—
167C2×D293—41no—
168C2×D293—41no—
169C2×D293—41no—
170C2×D293—41no—
171C4×C293—21no—
172C4×C293—41no—
173C4×C293—41no—
174C4×C293—41no—
175C4×C293C2×#4111yescharacteristic
176C4×C293H(5,𝔽2)11yescharacteristic
177Dic293—21no—
178Dic293—22no—
179Dic293—21no—
180Dic293—41no—
181Dic293#13512yes—
182C2×C293—41no—
183C2×C293—81no—
184C2×C293#54611yescharacteristic
185C2×C293C2×#13511yescharacteristic
186C2×C293#57611yescharacteristic
187D293—41no—
188D293—81no—
189D293—81no—
190C293#330511yescharacteristic, complemented, Sylow
191#3305—2931nomaximal, Sylow
192#555—2931no—
193#550—2931no—
194#486—2931no—
195#482—2931no—
196#482D29311yescharacteristic, complemented
197#477—2931no—
198#466—2931no—
199#466—2931no—
200#459—2931no—
201#449—2931no—
202#449—2931no—
203C4×SD16—2931no—
204C8×D4—2931no—
205#416—2931no—
206#416—2931no—
207C2×#41—2931no—
208C2×#41—2931no—
209C2×SD16—2931no—
210C2×D8—2931no—
211C2×D8—2931no—
212C22×C8—2931no—
213C22×C8—2931no—
214C4⋊Q8—2931no—
215#127—2931no—
216#127—5861no—
217#124—5861no—
218#124—5861no—
219#121—2931no—
220#121—2931no—
221#121—2931no—
222#121—5861no—
223#121—5861no—
224#121—5861no—
225#121C2×D29311yescharacteristic
226C4×Q8—2931no—
227C4×D4—2931no—
228C4×D4—2931no—
229C4×D4—5861no—
230#117—2931no—
231#117—5861no—
232#117C2×D29311yescharacteristic
233#107—2931no—
234#107C2×D29311yescharacteristic
235#106C2×D29311yescharacteristic
236C4⋊C8—2931no—
237#103—2931no—
238#103—2931no—
239#103—2931no—
240#102—2931no—
241#102—2931no—
242#102—2931no—
243#102—2931no—
244#102—2931no—
245#102C2×D29311yescharacteristic
246#102C2×D29311yescharacteristic
247C22⋊C8—2931no—
248C22⋊C8C2×D29311yescharacteristic
249C4×C8—2931no—
250#41—5862no—
251#41—5862no—
252#41—11721no—
253#41—11721no—
254C2×Q8—2931no—
255C2×Q8—5861no—
256C2×D4—21no—
257C2×D4—2931no—
258C2×D4—2931no—
259C2×D4—2931no—
260C2×D4—5861no—
261C2×D4—5861no—
262C2×D4—5861no—
263C2×D4—5861no—
264C2×D4—5861no—
265C2×D4—5861no—
266C2×D4—5861no—
267C2×D4C22×D29311yescharacteristic
268C22×C4—2931no—
269C22×C4—5861no—
270C22×C4—5861no—
271C22×C4—5861no—
272C22×C4C22×D29311yescharacteristic
273SD16—5862no—
274D8—11721no—
275D8—11721no—
276C2×C8—2931no—
277C2×C8—2931no—
278C2×C8—11721no—
279C2×C8—11721no—
280C2×C8C22×D29311yescharacteristic
281C2×C8C22×D29311yescharacteristic
282C4⋊C4—2931no—
283C4⋊C4—2931no—
284C4⋊C4—5861no—
285C4⋊C4—5861no—
286C4⋊C4C22×D29311yescharacteristic
287C4⋊C4C22×D29311yescharacteristic
288C4⋊C4C22×D29311yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—2931no—
292C22⋊C4—2931no—
293C22⋊C4—5861no—
294C22⋊C4—5861no—
295C22⋊C4—5861no—
296C22⋊C4—5861no—
297C22⋊C4—5861no—
298C42—21no—
299C42—2931no—
300C42—5861no—
301C42—5861no—
302C23—21no—
303C23—2931no—
304C23—5861no—
305C23—5861no—
306C23D4×D29311yescharacteristic
307Q8—2932no—
308Q8—23441no—
309Q8—5861no—
310D4—21no—
311D4—21no—
312D4—81no—
313D4—23441no—
314D4—23441no—
315D4—23441no—
316D4—23441no—
317D4—5862no—
318D4—5861no—
319D4—5861no—
320D4—5861no—
321D4—5861no—
322D4—11722no—
323D4—11722no—
324D4—11722no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—2931no—
331C2×C4—2931no—
332C2×C4—2931no—
333C2×C4—5861no—
334C2×C4—5861no—
335C2×C4—5861no—
336C2×C4—5861no—
337C2×C4—11722no—
338C2×C4—11722no—
339C2×C4—11722no—
340C2×C4D4×D29311yescharacteristic
341C2×C4C23×D29311yescharacteristic
342C8—21no—
343C8—21no—
344C8—5861no—
345C8—5861no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—5861no—
353C22—5861no—
354C22—5861no—
355C22—11721no—
356C22—11721no—
357C22—11721no—
358C22—11721no—
359C22—11721no—
360C22—11721no—
361C22C2×D4×D29311yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—2932no—
367C4—5861no—
368C4—5862no—
369C4—5861no—
370C4—11721no—
371C4#41×D29311yescharacteristic
372C4#2262767011yescharacteristic
373C2—41no—
374C2—81no—
375C2—23441no—
376C2—23441no—
377C2—11721no—
378C2#3403677111yescharacteristic
379C2#135×D29311yescharacteristic
380C2#3403693311yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#482×C293C2
socleC22×C293C22×D4
hypercenter#482D293
hypocenterC293#3305
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #34036842C2semidirect
2. #34036797C2semidirect
3. #34036474C2semidirect
4. #34036455C2semidirect
5. #34036423C2semidirect
6. #34036366C2semidirect
7. #34036363C2semidirect
8. #34036323C2semidirect
9. #34036276C2semidirect
10. #34036275C2semidirect
11. #34036216C2semidirect
12. #34036192C2semidirect
13. #34036123C2semidirect
14. #34036122C2semidirect
15. #482×C293C2semidirect
190. C293#3305semidirect
196. #482D293semidirect

Maximal subgroups

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

subgroupindex
#340368422
#340367972
#340364742
#340364552
#340364232
#340363662
#340363632
#340363232
#340362762
#340362752
#340362162
#340361922
#340361232
#340361222
#482×C2932
#3305293