Finite Group Databasebeta

← #18006175

Subgroups — #18006175

Order 4736.

488 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924559C211yesmaximal, characteristic, complemented
2#14558202C211yesmaximal, characteristic, complemented
3#14558194C211yesmaximal, characteristic, complemented
4#14557919C211yesmaximal, characteristic, complemented
5#14557786C211yesmaximal, characteristic, complemented
6#14557759C211yesmaximal, characteristic, complemented
7#14557757C211yesmaximal, characteristic, complemented
8#14557731C211yesmaximal, characteristic, complemented
9#14557694C211yesmaximal, characteristic, complemented
10#14557678C211yesmaximal, characteristic, complemented
11#14557677C211yesmaximal, characteristic, complemented
12#14557672C211yesmaximal, characteristic, complemented
13#14557640C211yesmaximal, characteristic, complemented
14#14557602C211yesmaximal, characteristic, complemented
15C2×#137×C37C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×#10596966C2211yescharacteristic
18#11924559—24no—
19C2×#10596941C2211yescharacteristic
20C2×#10596941C2211yescharacteristic
21C2×#10596941C2211yescharacteristic
22C2×D296C2211yescharacteristic
23C2×#10596939C2211yescharacteristic
24C2×C8×D37C2211yescharacteristic
25#11924532—21no—
26#11924532C2211yescharacteristic
27#11924525—21no—
28#11924525C2211yescharacteristic
29#11924512—21no—
30#11924512C2211yescharacteristic
31#11924510—21no—
32#11924510—21no—
33#11924510C2211yescharacteristic
34#11924510C2211yescharacteristic
35#11924507—21no—
36#11924507C2211yescharacteristic
37Q8×Dic37C2211yescharacteristic
38Q8×Dic37C2211yescharacteristic
39C4×C22⋊D37—21no—
40C4×C22⋊D37—21no—
41C4×C22⋊D37C2211yescharacteristic
42#11924468C2211yescharacteristic
43#11924465C2211yescharacteristic
44#11924460C2211yescharacteristic
45#11924460C2211yescharacteristic
46#11924460C2211yescharacteristic
47#11924458C2211yescharacteristic
48#11924458C2211yescharacteristic
49#11924457C2211yescharacteristic
50C22⋊#64436C2211yescharacteristic
51#11924448C2211yescharacteristic
52#11924446C2211yescharacteristic
53C2×#41×C37C2211yescharacteristic
54C22×Q8×C37C2211yescharacteristic
55#137×C37—24no—
56C2×Q16×C37C2211yescharacteristic
57C2×Q16×C37C2211yescharacteristic
58C2×SD16×C37C2211yescharacteristic
59C2×SD16×C37C2211yescharacteristic
60C2×M16×C37C2211yescharacteristic
61#41×C37—22no—
62#41×C37—41no—
63C2×Q8×C37—21no—
64C2×Q8×C37—22no—
65C2×Q8×C37—41no—
66C2×Q8×C37C2311yescharacteristic
67C2×Q8×C37C2311yescharacteristic
68C2×Q8×C37C2311yescharacteristic
69C2×D4×C37—21no—
70C2×D4×C37C2311yescharacteristic
71C22×C4×C37—21no—
72C22×C4×C37—21no—
73C22×C4×C37C2311yescharacteristic
74C2×C22⋊D37—21no—
75C2×C22⋊D37—21no—
76C2×C22⋊D37—21no—
77C2×C22⋊D37—21no—
78C2×C22⋊D37—21no—
79C2×C22⋊D37D411yescharacteristic
80#10596966—22no—
81#10596966—22no—
82#10596966—41no—
83#10596966—41no—
84C2×D148—21no—
85C2×D148—21no—
86C2×D148C2311yescharacteristic
87C2×D148C2311yescharacteristic
88C2×C4×D37—21no—
89C2×C4×D37—21no—
90C2×C4×D37C2311yescharacteristic
91Q16×C37—22no—
92Q16×C37D414yescomplemented
93SD16×C37—22no—
94SD16×C37—22no—
95M16×C37—22no—
96C2×C8×C37C2311yescharacteristic
97C2×C8×C37C2311yescharacteristic
98C22⋊Dic37—21no—
99C22⋊Dic37D411yescharacteristic
100#10596941—22no—
101#10596941—22no—
102#10596941—41no—
103#10596939—41no—
104#10596938—21no—
105#10596938—21no—
106#10596938—21no—
107#10596938—21no—
108#10596938—21no—
109#10596938D411yescharacteristic
110C4⋊Dic37—21no—
111C4⋊Dic37—21no—
112C4⋊Dic37C2311yescharacteristic
113C4⋊Dic37C2311yescharacteristic
114#10596936—21no—
115#10596936D411yescharacteristic
116C4×Dic37—21no—
117C4×Dic37—21no—
118C4×Dic37C2311yescharacteristic
119C2×#64436C2311yescharacteristic
120C2×#64436C2311yescharacteristic
121D296—22no—
122C8×D37—22no—
123C23×C37—21no—
124C23×C37C2×D411yescharacteristic
125C22×D37—21no—
126C22×D37—21no—
127C22×D37C2×D411yescharacteristic
128Q8×C37—21no—
129Q8×C37—21no—
130Q8×C37—21no—
131Q8×C37—21no—
132Q8×C37—42no—
133Q8×C37C2×D412yes—
134Q8×C37C2×D412yes—
135D4×C37—21no—
136D4×C37—21no—
137D4×C37—42no—
138C2×C4×C37—21no—
139C2×C4×C37—21no—
140C2×C4×C37—21no—
141C2×C4×C37—21no—
142C2×C4×C37—21no—
143C2×C4×C37—42no—
144C2×C4×C37—42no—
145C2×C4×C37C2×D411yescharacteristic
146C2×C4×C37C2411yescharacteristic
147C22⋊D37—41no—
148C22⋊D37—42no—
149C22⋊D37—42no—
150C22⋊D37—81no—
151C22⋊D37—81no—
152C22⋊D37—81no—
153C2×Dic37—21no—
154C2×Dic37—21no—
155C2×Dic37C2×D411yescharacteristic
156C2×Dic37C2×D411yescharacteristic
157C2×Dic37C2×D411yescharacteristic
158D148—21no—
159D148—21no—
160D148—21no—
161D148—21no—
162D148—42no—
163D148—42no—
164C4×D37—21no—
165C4×D37—21no—
166C4×D37—42no—
167C4×D37—42no—
168C8×C37—21no—
169C8×C37C2×D412yes—
170#64436—21no—
171#64436—21no—
172C22×C37—21no—
173C22×C37—21no—
174C22×C37—21no—
175C22×C37—41no—
176C22×C37—41no—
177C22×C37—41no—
178C22×C37C22×D411yescharacteristic
179C2×D37—21no—
180C2×D37—21no—
181C2×D37—21no—
182C2×D37—41no—
183C2×D37—41no—
184C2×D37—41no—
185C2×D37—41no—
186C2×D37—41no—
187C2×D37—41no—
188C4×C37—22no—
189C4×C37—22no—
190C4×C37—21no—
191C4×C37—41no—
192C4×C37C22×D411yescharacteristic
193C4×C37H(5,𝔽2)11yescharacteristic
194Dic37—21no—
195Dic37—21no—
196Dic37—21no—
197Dic37—41no—
198Dic37—41no—
199#3271—371nomaximal, Sylow
200C2×C37—41no—
201C2×C37—81no—
202C2×C37D4211yescharacteristic
203C2×C37#57511yescharacteristic
204C2×C37#57711yescharacteristic
205D37—41no—
206D37—81no—
207D37—81no—
208C2×#137D3711yescharacteristic, complemented
209C2×#135—371no—
210#550—371no—
211#548—371no—
212#496—371no—
213#469—371no—
214#465—371no—
215#464—371no—
216#460—371no—
217#452—371no—
218#449—371no—
219#449—371no—
220#448—371no—
221#441—371no—
222#435—371no—
223C37#327111yescharacteristic, complemented, Sylow
224C2×#41—371no—
225C2×#41—371no—
226C2×#41C2×D3711yescharacteristic
227C22×Q8C2×D3711yescharacteristic
228#137—24no—
229#135—744no—
230C2×Q16C2×D3711yescharacteristic
231C2×Q16C2×D3711yescharacteristic
232C2×SD16—371no—
233C2×SD16—371no—
234C2×SD16—371no—
235C2×SD16C2×D3711yescharacteristic
236C2×SD16C2×D3711yescharacteristic
237C2×D8—371no—
238C2×D8—371no—
239C2×M16C2×D3711yescharacteristic
240C22×C8—371no—
241#127—371no—
242#127—741no—
243#124—371no—
244#124—741no—
245C22⋊Q8—371no—
246C22⋊Q8—741no—
247#121—371no—
248#121—371no—
249#121—371no—
250#121—741no—
251#121—741no—
252#121—741no—
253C4×Q8—371no—
254C4×Q8—371no—
255C4×D4—371no—
256C4×D4—741no—
257C4×D4—741no—
258#106—371no—
259C4⋊C8—371no—
260#103—371no—
261#103—371no—
262#103—371no—
263#102—371no—
264#102—371no—
265#102—371no—
266C22⋊C8—371no—
267C22⋊C8—371no—
268#97—371no—
269#41—22no—
270#41—41no—
271#41—742no—
272#41—742no—
273#41—1481no—
274#41—1481no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8C22×D3711yescharacteristic
279C2×Q8C22×D3711yescharacteristic
280C2×Q8C22×D3711yescharacteristic
281C2×D4—21no—
282C2×D4—371no—
283C2×D4—371no—
284C2×D4—371no—
285C2×D4—741no—
286C2×D4—741no—
287C2×D4—741no—
288C2×D4—741no—
289C2×D4—741no—
290C2×D4—741no—
291C2×D4—741no—
292C2×D4C22×D3711yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—371no—
296C22×C4—741no—
297C22×C4—741no—
298C22×C4C22×D3711yescharacteristic
299Q16—22no—
300Q16C22⋊D3714yescomplemented
301SD16—22no—
302SD16—22no—
303SD16—742no—
304SD16—742no—
305SD16—1481no—
306D8—742no—
307D8—1481no—
308M16—22no—
309C2×C8—371no—
310C2×C8—371no—
311C2×C8—742no—
312C2×C8C22×D3711yescharacteristic
313C2×C8C22×D3711yescharacteristic
314C4⋊C4—371no—
315C4⋊C4—371no—
316C4⋊C4—371no—
317C4⋊C4—741no—
318C4⋊C4—741no—
319C4⋊C4—741no—
320C22⋊C4—371no—
321C22⋊C4—371no—
322C22⋊C4—741no—
323C22⋊C4—741no—
324C22⋊C4—741no—
325C22⋊C4—741no—
326C22⋊C4—741no—
327C22⋊C4—741no—
328C42—371no—
329C42—741no—
330C42—741no—
331C23—21no—
332C23—371no—
333C23—741no—
334C23—741no—
335C23D4×D3711yescharacteristic
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—21no—
340Q8—42no—
341Q8C2×C22⋊D3712yes—
342Q8C2×C22⋊D3712yes—
343D4—21no—
344D4—21no—
345D4—42no—
346D4—2961no—
347D4—2961no—
348D4—2961no—
349D4—741no—
350D4—741no—
351D4—741no—
352D4—741no—
353D4—1482no—
354D4—1482no—
355D4—1481no—
356D4—1482no—
357D4—1482no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—371no—
366C2×C4—371no—
367C2×C4—371no—
368C2×C4—741no—
369C2×C4—741no—
370C2×C4—741no—
371C2×C4—741no—
372C2×C4—1482no—
373C2×C4—1482no—
374C2×C4D4×D3711yescharacteristic
375C2×C4C23×D3711yescharacteristic
376C8—21no—
377C8—741no—
378C8—741no—
379C8C2×C22⋊D3712yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—741no—
387C22—741no—
388C22—741no—
389C22—1481no—
390C22—1481no—
391C22—1481no—
392C22—1481no—
393C22—1481no—
394C22—1481no—
395C22C2×D4×D3711yescharacteristic
396C4—21no—
397C4—22no—
398C4—22no—
399C4—41no—
400C4—741no—
401C4—741no—
402C4—741no—
403C4—1481no—
404C4—1481no—
405C4C22×C22⋊D3711yescharacteristic
406C4#1192458111yescharacteristic
407C2—41no—
408C2—81no—
409C2—2961no—
410C2—2961no—
411C2—1481no—
412C2D4×C22⋊D3711yescharacteristic
413C2#1455833211yescharacteristic
414C2#1455834211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#137×C37C2
socleC22×C37C22×D4
hypercenterC2×#137D37
hypocenterC37#3271
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#11924559C2semidirect
2. #14558202C2semidirect
3. #14558194C2semidirect
4. #14557919C2semidirect
5. #14557786C2semidirect
6. #14557759C2semidirect
7. #14557757C2semidirect
8. #14557731C2semidirect
9. #14557694C2semidirect
10. #14557678C2semidirect
11. #14557677C2semidirect
12. #14557672C2semidirect
13. #14557640C2semidirect
14. #14557602C2semidirect
15. C2×#137×C37C2semidirect
92. Q16×C37D4semidirect
208. C2×#137D37semidirect
223. C37#3271semidirect
300. Q16C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245592
#145582022
#145581942
#145579192
#145577862
#145577592
#145577572
#145577312
#145576942
#145576782
#145576772
#145576722
#145576402
#145576022
C2×#137×C372
#327137