Finite Group Databasebeta

← #18004264

Subgroups — #18004264

Order 4736.

484 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924557C211yesmaximal, characteristic, complemented
2C2×#11924544C211yesmaximal, characteristic, complemented
3#14558113C211yesmaximal, characteristic, complemented
4#14558112C211yesmaximal, characteristic, complemented
5#14557780C211yesmaximal, characteristic, complemented
6#14557779C211yesmaximal, characteristic, complemented
7#14557776C211yesmaximal, characteristic, complemented
8#14557773C211yesmaximal, characteristic, complemented
9#14557772C211yesmaximal, characteristic, complemented
10#14557768C211yesmaximal, characteristic, complemented
11#14557767C211yesmaximal, characteristic, complemented
12#107×D37C211yesmaximal, characteristic, complemented
13#14557533C211yesmaximal, characteristic, complemented
14#14557531C211yesmaximal, characteristic, complemented
15C37×#468C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×#10596962C2211yescharacteristic
18C2×#10596964C2211yescharacteristic
19#11924557—24no—
20C2×#10596942C2211yescharacteristic
21C2×#10596930C2211yescharacteristic
22C2×#10596939C2211yescharacteristic
23#11924544—24no—
24C2×#10596929C2211yescharacteristic
25C2×#10596929C2211yescharacteristic
26C22×#64436C2211yescharacteristic
27C2×C8×D37C2211yescharacteristic
28C2×C8×D37C2211yescharacteristic
29#11924516C2211yescharacteristic
30#11924515C2211yescharacteristic
31#11924514—21no—
32#11924513—21no—
33#11924512C2211yescharacteristic
34#11924511—21no—
35#11924511C2211yescharacteristic
36#11924510C2211yescharacteristic
37#11924509—21no—
38#11924509—21no—
39#11924509—21no—
40#11924508—21no—
41#11924507—21no—
42#11924507C2211yescharacteristic
43C4⋊C4×D37C2211yescharacteristic
44C4⋊C4×D37C2211yescharacteristic
45#11924470C2211yescharacteristic
46#11924469C2211yescharacteristic
47#11924469C2211yescharacteristic
48#11924461C2211yescharacteristic
49#11924460C2211yescharacteristic
50#11924459C2211yescharacteristic
51#11924458C2211yescharacteristic
52#11924457C2211yescharacteristic
53#11924456C2211yescharacteristic
54C2×SD16×C37C2211yescharacteristic
55C2×M16×C37C2211yescharacteristic
56C22⋊Q8×C37C2211yescharacteristic
57#121×C37C2211yescharacteristic
58#107×C37C2211yescharacteristic
59#103×C37C2211yescharacteristic
60#102×C37C2211yescharacteristic
61C2×Q8×C37C2311yescharacteristic
62C2×D4×C37—21no—
63C2×D4×C37C2311yescharacteristic
64C22×C4×C37C2311yescharacteristic
65C2×C22⋊D37—21no—
66C2×C22⋊D37—21no—
67C2×C22⋊D37—21no—
68C2×C22⋊D37D411yescharacteristic
69C2×C22⋊D37D411yescharacteristic
70C22×Dic37—21no—
71#10596966—22no—
72#10596966—22no—
73#10596964—22no—
74#10596964—22no—
75#10596962—22no—
76#10596962—22no—
77C2×D148—21no—
78C2×D148—21no—
79C2×D148D411yescharacteristic
80C2×D148C2311yescharacteristic
81C2×C4×D37—21no—
82C2×C4×D37—21no—
83C2×C4×D37—21no—
84C2×C4×D37C2311yescharacteristic
85C2×C4×D37C2311yescharacteristic
86C2×Dic74D411yescharacteristic
87C2×Dic74C2311yescharacteristic
88SD16×C37—22no—
89M16×C37—22no—
90C2×C8×C37C2311yescharacteristic
91C2×C8×C37C2311yescharacteristic
92C4⋊C4×C37—21no—
93C4⋊C4×C37C2311yescharacteristic
94C4⋊C4×C37C2311yescharacteristic
95C22⋊C4×C37—21no—
96C22⋊C4×C37—21no—
97C22⋊Dic37—21no—
98C22⋊Dic37—21no—
99#10596942—22no—
100#10596939—22no—
101#10596938—21no—
102#10596938—21no—
103#10596938—21no—
104#10596938—21no—
105C4⋊Dic37—21no—
106C4⋊Dic37C2311yescharacteristic
107C4⋊Dic37C2311yescharacteristic
108#10596936—21no—
109#10596936—21no—
110#10596936—21no—
111#10596936—21no—
112C2×#64436—22no—
113C2×#64436C2311yescharacteristic
114C2×#64436C2311yescharacteristic
115#10596930—22no—
116#10596929—22no—
117#10596929—22no—
118C8×D37—22no—
119C8×D37D414yescomplemented
120C23×C37—21no—
121C23×C37C2×D411yescharacteristic
122C22×D37—21no—
123C22×D37C2×D411yescharacteristic
124C22×D37C2×D411yescharacteristic
125Q8×C37—21no—
126Q8×C37—21no—
127D4×C37—21no—
128D4×C37—21no—
129D4×C37—81no—
130C2×C4×C37—21no—
131C2×C4×C37—21no—
132C2×C4×C37—21no—
133C2×C4×C37—21no—
134C2×C4×C37—21no—
135C2×C4×C37C2×D411yescharacteristic
136C2×C4×C37C2411yescharacteristic
137C22⋊D37—22no—
138C22⋊D37—22no—
139C22⋊D37—42no—
140C22⋊D37—81no—
141C22⋊D37—81no—
142C2×Dic37—21no—
143C2×Dic37—21no—
144C2×Dic37—21no—
145C2×Dic37—42no—
146C2×Dic37C2×D411yescharacteristic
147C2×Dic37C2×D411yescharacteristic
148D148—22no—
149D148—21no—
150D148—21no—
151D148—42no—
152D148—81no—
153C4×D37—21no—
154C4×D37—21no—
155C4×D37—42no—
156C4×D37—81no—
157C4×D37—81no—
158C4×D37C2×D412yes—
159C4×D37#4112yes—
160Dic74—22no—
161Dic74—21no—
162Dic74—21no—
163C8×C37—21no—
164C8×C37C2×D412yes—
165#64436—21no—
166#64436C2×D412yes—
167C22×C37—21no—
168C22×C37—21no—
169C22×C37—21no—
170C22×C37—41no—
171C22×C37—41no—
172C22×C37—41no—
173C22×C37C22×D411yescharacteristic
174C2×D37—21no—
175C2×D37—21no—
176C2×D37—21no—
177C2×D37—21no—
178C2×D37—21no—
179C2×D37—41no—
180C2×D37—41no—
181C2×D37—41no—
182C2×D37#12112yes—
183C4×C37—21no—
184C4×C37—41no—
185C4×C37—41no—
186C4×C37—41no—
187C4×C37C22×D411yescharacteristic
188C4×C37C2×#4111yescharacteristic
189Dic37—21no—
190Dic37—41no—
191Dic37—41no—
192Dic37—41no—
193Dic37#12112yes—
194#3061—371nomaximal, Sylow
195C2×C37—41no—
196C2×C37—81no—
197C2×C37C2×#12111yescharacteristic
198C2×C37#57611yescharacteristic
199C2×C37#57811yescharacteristic
200D37—22no—
201D37—41no—
202D37—81no—
203C2×#135—371no—
204C2×#131—371no—
205#537—371no—
206#537—371no—
207#468—371no—
208#468—371no—
209#468—371no—
210#468D3711yescharacteristic, complemented
211#467—371no—
212#467—371no—
213#466—371no—
214#466—371no—
215C2×#107—371no—
216#417—371no—
217#417—371no—
218C37#306111yescharacteristic, complemented, Sylow
219C2×#41—371no—
220C2×#41—371no—
221C2×#41—371no—
222#135—744no—
223C2×Q16—371no—
224C2×SD16—371no—
225C2×SD16C2×D3711yescharacteristic
226C2×D8—371no—
227#131—744no—
228C2×M16—371no—
229C2×M16—371no—
230C2×M16C2×D3711yescharacteristic
231C22×C8—371no—
232C22×C8—371no—
233C22×C8—371no—
234C22⋊Q8—371no—
235C22⋊Q8—371no—
236C22⋊Q8—371no—
237C22⋊Q8—741no—
238C22⋊Q8—741no—
239C22⋊Q8C2×D3711yescharacteristic
240#121—371no—
241#121—371no—
242#121—371no—
243#121—741no—
244#121—741no—
245#121—741no—
246#121—741no—
247#121—741no—
248#121—741no—
249#121C2×D3711yescharacteristic
250C2×C4⋊C4—371no—
251C2×C4⋊C4—371no—
252#107—371no—
253#107—371no—
254#107—371no—
255#107C2×D3711yescharacteristic
256#103—371no—
257#103—371no—
258#103—371no—
259#103C2×D3711yescharacteristic
260#102—371no—
261#102—371no—
262#102—371no—
263#102C2×D3711yescharacteristic
264#41—742no—
265#41—742no—
266#41—742no—
267#41—742no—
268#41—742no—
269#41—742no—
270C2×Q8—371no—
271C2×Q8—371no—
272C2×Q8C22×D3711yescharacteristic
273C2×D4—21no—
274C2×D4—371no—
275C2×D4—371no—
276C2×D4—371no—
277C2×D4—371no—
278C2×D4—741no—
279C2×D4—741no—
280C2×D4—741no—
281C2×D4—741no—
282C2×D4—741no—
283C2×D4C22×D3711yescharacteristic
284C22×C4—371no—
285C22×C4—371no—
286C22×C4—741no—
287C22×C4—741no—
288C22×C4—741no—
289C22×C4—741no—
290C22×C4C22×D3711yescharacteristic
291Q16—742no—
292SD16—22no—
293SD16—742no—
294D8—742no—
295M16—22no—
296M16—742no—
297M16—742no—
298C2×C8—371no—
299C2×C8—374no—
300C2×C8—371no—
301C2×C8—742no—
302C2×C8—742no—
303C2×C8C22×D3711yescharacteristic
304C2×C8C22×D3711yescharacteristic
305C4⋊C4—21no—
306C4⋊C4—371no—
307C4⋊C4—371no—
308C4⋊C4—741no—
309C4⋊C4—741no—
310C4⋊C4—741no—
311C4⋊C4—741no—
312C4⋊C4—741no—
313C4⋊C4C22×D3711yescharacteristic
314C4⋊C4C22×D3711yescharacteristic
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—741no—
318C22⋊C4—741no—
319C22⋊C4—741no—
320C22⋊C4—741no—
321C22⋊C4—741no—
322C22⋊C4—741no—
323C23—21no—
324C23—371no—
325C23—371no—
326C23—741no—
327C23D4×D3711yescharacteristic
328Q8—21no—
329Q8—21no—
330Q8—742no—
331Q8—741no—
332Q8—741no—
333D4—21no—
334D4—21no—
335D4—81no—
336D4—2961no—
337D4—2961no—
338D4—2961no—
339D4—742no—
340D4—742no—
341D4—742no—
342D4—741no—
343D4—741no—
344D4—1482no—
345D4—1482no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—371no—
352C2×C4—372no—
353C2×C4—372no—
354C2×C4—371no—
355C2×C4—2961no—
356C2×C4—2961no—
357C2×C4—741no—
358C2×C4—741no—
359C2×C4—741no—
360C2×C4—741no—
361C2×C4—741no—
362C2×C4—1482no—
363C2×C4—1482no—
364C2×C4D4×D3711yescharacteristic
365C2×C4C23×D3711yescharacteristic
366C8—21no—
367C8—372no—
368C8—741no—
369C8D4×D3712yes—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—372no—
377C22—741no—
378C22—741no—
379C22—741no—
380C22—741no—
381C22—741no—
382C22—1481no—
383C22—1481no—
384C22—1481no—
385C22C2×D4×D3711yescharacteristic
386C4—21no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—372no—
391C4—741no—
392C4—1481no—
393C4—1481no—
394C4—1481no—
395C4C2×D4×D3711yescharacteristic
396C4#41×D3711yescharacteristic
397C2—41no—
398C2—81no—
399C2—2961no—
400C2—742no—
401C2—1481no—
402C2#121×D3711yescharacteristic
403C2#1455833711yescharacteristic
404C2#1455834911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#468C2
socleC22×C37C22×D4
hypercenter#468D37
hypocenterC37#3061
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#11924557C2semidirect
2. C2×#11924544C2semidirect
3. #14558113C2semidirect
4. #14558112C2semidirect
5. #14557780C2semidirect
6. #14557779C2semidirect
7. #14557776C2semidirect
8. #14557773C2semidirect
9. #14557772C2semidirect
10. #14557768C2semidirect
11. #14557767C2semidirect
12. #107×D37C2semidirect
13. #14557533C2semidirect
14. #14557531C2semidirect
15. C37×#468C2semidirect
119. C8×D37D4semidirect
210. #468D37semidirect
218. C37#3061semidirect

Maximal subgroups

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

subgroupindex
C2×#119245572
C2×#119245442
#145581132
#145581122
#145577802
#145577792
#145577762
#145577732
#145577722
#145577682
#145577672
#107×D372
#145575332
#145575312
C37×#4682
#306137