Finite Group Databasebeta

← #18006182

Subgroups — #18006182

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×#11924567C211yesmaximal, characteristic, complemented
2C2×#11924556C211yesmaximal, characteristic, complemented
3#14558204C211yesmaximal, characteristic, complemented
4#14557923C211yesmaximal, characteristic, complemented
5#14557784C211yesmaximal, characteristic, complemented
6#14557764C211yesmaximal, characteristic, complemented
7#14557752C211yesmaximal, characteristic, complemented
8#14557733C211yesmaximal, characteristic, complemented
9#14557693C211yesmaximal, characteristic, complemented
10#14557678C211yesmaximal, characteristic, complemented
11#14557676C211yesmaximal, characteristic, complemented
12#14557672C211yesmaximal, characteristic, complemented
13#14557638C211yesmaximal, characteristic, complemented
14#14557605C211yesmaximal, characteristic, complemented
15C37×#548C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C2×#10596962C2211yescharacteristic
18#11924567—24no—
19#11924556—24no—
20C2×#10596942C2211yescharacteristic
21C2×#10596942C2211yescharacteristic
22C2×#10596940C2211yescharacteristic
23C2×#10596941C2211yescharacteristic
24C2×#10596941C2211yescharacteristic
25C2×#10596941C2211yescharacteristic
26C2×#10596941C2211yescharacteristic
27C2×#10596939C2211yescharacteristic
28C2×#10596939C2211yescharacteristic
29C2×#10596934C2211yescharacteristic
30C22×#64436C2211yescharacteristic
31#11924533C2211yescharacteristic
32#11924532—21no—
33#11924510C2211yescharacteristic
34#11924510C2211yescharacteristic
35#11924509—21no—
36#11924509—21no—
37C4×Dic74C2211yescharacteristic
38#11924498—21no—
39#11924467C2211yescharacteristic
40C4⋊#64436C2211yescharacteristic
41#11924460C2211yescharacteristic
42#11924460C2211yescharacteristic
43#11924459C2211yescharacteristic
44#11924457C2211yescharacteristic
45#11924456C2211yescharacteristic
46#11924456C2211yescharacteristic
47C22⋊#64436C2211yescharacteristic
48C22⋊#64436C2211yescharacteristic
49#11924447C2211yescharacteristic
50C2×#41×C37C2211yescharacteristic
51C22×Q8×C37C2211yescharacteristic
52#124×C37—21no—
53#124×C37C2211yescharacteristic
54C22⋊Q8×C37—21no—
55C22⋊Q8×C37C2211yescharacteristic
56#121×C37—21no—
57#121×C37C2211yescharacteristic
58C4×Q8×C37C2211yescharacteristic
59C4×D4×C37—21no—
60C4×D4×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×D4×C37—21no—
69C2×D4×C37—21no—
70C2×D4×C37D411yescharacteristic
71C2×D4×C37C2311yescharacteristic
72C22×C4×C37—21no—
73C22×C4×C37—21no—
74C22×C4×C37C2311yescharacteristic
75C22×C4×C37C2311yescharacteristic
76C2×C22⋊D37—21no—
77C2×C22⋊D37—21no—
78C2×C22⋊D37—21no—
79C2×C22⋊D37—21no—
80#10596962—22no—
81#10596962—22no—
82#10596962—41no—
83#10596962—41no—
84C2×D148—21no—
85C2×D148—21no—
86C2×D148C2311yescharacteristic
87C2×D148C2311yescharacteristic
88C2×C4×D37—21no—
89C2×C4×D37—21no—
90C2×Dic74C2311yescharacteristic
91C4⋊C4×C37—21no—
92C4⋊C4×C37—21no—
93C4⋊C4×C37D411yescharacteristic
94C4⋊C4×C37C2311yescharacteristic
95C22⋊C4×C37—21no—
96C22⋊C4×C37—21no—
97C22⋊C4×C37—21no—
98C22⋊C4×C37—21no—
99C22⋊C4×C37D411yescharacteristic
100C22⋊C4×C37D411yescharacteristic
101C42×C37—21no—
102C42×C37C2311yescharacteristic
103#10596942—22no—
104#10596942D414yescomplemented
105#10596941—22no—
106#10596941—22no—
107#10596941—22no—
108#10596941—41no—
109#10596940—22no—
110#10596939—22no—
111#10596939—41no—
112#10596938—21no—
113#10596938—21no—
114C4⋊Dic37C2311yescharacteristic
115#10596936—21no—
116C4×Dic37—21no—
117#10596934—22no—
118C2×#64436—22no—
119C2×#64436C2311yescharacteristic
120C2×#64436C2311yescharacteristic
121C2×#64436C2311yescharacteristic
122C2×#64436C2311yescharacteristic
123C23×C37—21no—
124C23×C37C2×D411yescharacteristic
125C23×C37C2×D411yescharacteristic
126C22×D37—21no—
127C22×D37—21no—
128Q8×C37—21no—
129Q8×C37—21no—
130Q8×C37—21no—
131Q8×C37—42no—
132Q8×C37C2×D412yes—
133D4×C37—21no—
134D4×C37—21no—
135D4×C37—41no—
136D4×C37—42no—
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—21no—
144C2×C4×C37—21no—
145C2×C4×C37—42no—
146C2×C4×C37—42no—
147C2×C4×C37C2×D411yescharacteristic
148C2×C4×C37C2×D411yescharacteristic
149C2×C4×C37C2×D411yescharacteristic
150C2×C4×C37C2×D411yescharacteristic
151C2×C4×C37C2411yescharacteristic
152C22⋊D37—42no—
153C22⋊D37—42no—
154C22⋊D37—81no—
155C22⋊D37—81no—
156C2×Dic37—21no—
157C2×Dic37—21no—
158D148—21no—
159D148—21no—
160D148—21no—
161D148—21no—
162D148—42no—
163D148—81no—
164C4×D37—42no—
165C4×D37—42no—
166Dic74—21no—
167Dic74C2×D412yes—
168#64436—21no—
169#64436—21no—
170#64436—21no—
171#64436C2×D412yes—
172C22×C37—21no—
173C22×C37—21no—
174C22×C37—21no—
175C22×C37—21no—
176C22×C37—21no—
177C22×C37—21no—
178C22×C37—41no—
179C22×C37—41no—
180C22×C37—41no—
181C22×C37C22×D411yescharacteristic
182C2×D37—41no—
183C2×D37—41no—
184C2×D37—41no—
185C2×D37—41no—
186C2×D37—41no—
187C2×D37—41no—
188C4×C37—21no—
189C4×C37—21no—
190C4×C37—22no—
191C4×C37—21no—
192C4×C37—21no—
193C4×C37—41no—
194C4×C37—41no—
195C4×C37C22×D411yescharacteristic
196C4×C37H(5,𝔽2)11yescharacteristic
197Dic37—22no—
198Dic37—41no—
199#3271—371nomaximal, Sylow
200C2×C37—41no—
201C2×C37—41no—
202C2×C37—81no—
203C2×C37D4211yescharacteristic
204C2×C37#57511yescharacteristic
205C2×C37#57711yescharacteristic
206D37—81no—
207D37—81no—
208C2×#137—371no—
209C2×#135—371no—
210#550—371no—
211#548D3711yescharacteristic, complemented
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—744no—
229#135—744no—
230C2×Q16—371no—
231C2×Q16—371no—
232C2×SD16—371no—
233C2×SD16—371no—
234C2×SD16—371no—
235C2×SD16—371no—
236C2×SD16—371no—
237C2×D8—371no—
238C2×D8—371no—
239C2×M16—371no—
240C22×C8—371no—
241#127—371no—
242#127—741no—
243#124—21no—
244#124C2×D3711yescharacteristic
245C22⋊Q8—21no—
246C22⋊Q8C2×D3711yescharacteristic
247#121—21no—
248#121—371no—
249#121—371no—
250#121—741no—
251#121—741no—
252#121C2×D3711yescharacteristic
253C4×Q8—371no—
254C4×Q8C2×D3711yescharacteristic
255C4×D4—21no—
256C4×D4—741no—
257C4×D4C2×D3711yescharacteristic
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×Q8—371no—
279C2×Q8C22×D3711yescharacteristic
280C2×Q8C22×D3711yescharacteristic
281C2×D4—21no—
282C2×D4—21no—
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×D4C22⋊D3711yescharacteristic
292C2×D4C22×D3711yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—741no—
296C22×C4—741no—
297C22×C4C22×D3711yescharacteristic
298C22×C4C22×D3711yescharacteristic
299Q16—374no—
300Q16—742no—
301SD16—742no—
302SD16—742no—
303SD16—742no—
304SD16—742no—
305SD16—1481no—
306D8—742no—
307D8—1481no—
308M16—742no—
309C2×C8—371no—
310C2×C8—371no—
311C2×C8—371no—
312C2×C8—371no—
313C2×C8—742no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—371no—
317C4⋊C4—741no—
318C4⋊C4C22⋊D3711yescharacteristic
319C4⋊C4C22×D3711yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—741no—
325C22⋊C4—741no—
326C22⋊C4C22⋊D3711yescharacteristic
327C22⋊C4C22⋊D3711yescharacteristic
328C42—21no—
329C42—741no—
330C42C22×D3711yescharacteristic
331C23—21no—
332C23—741no—
333C23—741no—
334C23C2×C22⋊D3711yescharacteristic
335C23C2×C22⋊D3711yescharacteristic
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—42no—
340Q8—372no—
341Q8—741no—
342Q8D4×D3712yes—
343D4—21no—
344D4—21no—
345D4—41no—
346D4—42no—
347D4—42no—
348D4—2961no—
349D4—2961no—
350D4—2961no—
351D4—741no—
352D4—741no—
353D4—741no—
354D4—741no—
355D4—1482no—
356D4—1482no—
357D4—1482no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—741no—
368C2×C4—741no—
369C2×C4—1482no—
370C2×C4—1482no—
371C2×C4C2×C22⋊D3711yescharacteristic
372C2×C4C2×C22⋊D3711yescharacteristic
373C2×C4C2×C22⋊D3711yescharacteristic
374C2×C4C2×C22⋊D3711yescharacteristic
375C2×C4C23×D3711yescharacteristic
376C8—372no—
377C8—741no—
378C8—741no—
379C8—741no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—1481no—
390C22—1481no—
391C22—1481no—
392C22—1481no—
393C22—1481no—
394C22—1481no—
395C22C22×C22⋊D3711yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—22no—
401C4—41no—
402C4—41no—
403C4—742no—
404C4—1481no—
405C4C2×D4×D3711yescharacteristic
406C4#1192458111yescharacteristic
407C2—41no—
408C2—41no—
409C2—81no—
410C2—2961no—
411C2—2961no—
412C2D4×C22⋊D3711yescharacteristic
413C2#1455833111yescharacteristic
414C2#1455834111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#548C2
socleC22×C37C22×D4
hypercenter#548D37
hypocenterC37#3271
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#11924567C2semidirect
2. C2×#11924556C2semidirect
3. #14558204C2semidirect
4. #14557923C2semidirect
5. #14557784C2semidirect
6. #14557764C2semidirect
7. #14557752C2semidirect
8. #14557733C2semidirect
9. #14557693C2semidirect
10. #14557678C2semidirect
11. #14557676C2semidirect
12. #14557672C2semidirect
13. #14557638C2semidirect
14. #14557605C2semidirect
15. C37×#548C2semidirect
104. #10596942D4semidirect
211. #548D37semidirect
223. C37#3271semidirect

Maximal subgroups

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

subgroupindex
C2×#119245672
C2×#119245562
#145582042
#145579232
#145577842
#145577642
#145577522
#145577332
#145576932
#145576782
#145576762
#145576722
#145576382
#145576052
C37×#5482
#327137