Finite Group Databasebeta

← #18006320

Subgroups — #18006320

Order 4736.

494 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×#11924557C211yesmaximal, characteristic, complemented
2#14558202C211yesmaximal, characteristic, complemented
3#14558182C211yesmaximal, characteristic, complemented
4#14557904C211yesmaximal, characteristic, complemented
5#14557762C211yesmaximal, characteristic, complemented
6#14557759C211yesmaximal, characteristic, complemented
7#14557741C211yesmaximal, characteristic, complemented
8#14557726C211yesmaximal, characteristic, complemented
9#14557695C211yesmaximal, characteristic, complemented
10#14557694C211yesmaximal, characteristic, complemented
11#14557678C211yesmaximal, characteristic, complemented
12#14557675C211yesmaximal, characteristic, complemented
13SD16×Dic37C211yesmaximal, characteristic, complemented
14C8×C22⋊D37C211yesmaximal, characteristic, complemented
15C2×#135×C37C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×#10596964C2211yescharacteristic
18#11924557—24no—
19C2×#10596942C2211yescharacteristic
20C2×#10596930C2211yescharacteristic
21C2×#10596940C2211yescharacteristic
22C2×#10596941C2211yescharacteristic
23C2×#10596939C2211yescharacteristic
24C2×C8×D37C2211yescharacteristic
25#11924534C2211yescharacteristic
26#11924532—21no—
27#11924532C2211yescharacteristic
28#11924519—21no—
29#11924517—21no—
30#11924515C2211yescharacteristic
31#11924512C2211yescharacteristic
32#11924510—21no—
33#11924510C2211yescharacteristic
34#11924508—21no—
35#11924507—21no—
36#11924507C2211yescharacteristic
37Q8×Dic37C2211yescharacteristic
38D4×Dic37C2211yescharacteristic
39C4×C22⋊D37—21no—
40C4×C22⋊D37C2211yescharacteristic
41C2×#10596936—21no—
42#11924468C2211yescharacteristic
43#11924465C2211yescharacteristic
44#11924461C2211yescharacteristic
45#11924460C2211yescharacteristic
46#11924460C2211yescharacteristic
47#11924458C2211yescharacteristic
48#11924457C2211yescharacteristic
49#11924457C2211yescharacteristic
50C22⋊#64436C2211yescharacteristic
51#11924448C2211yescharacteristic
52C8×Dic37C2211yescharacteristic
53C2×#41×C37C2211yescharacteristic
54C2×#41×C37C2211yescharacteristic
55#135×C37—24no—
56C2×Q16×C37C2211yescharacteristic
57C2×SD16×C37C2211yescharacteristic
58C2×SD16×C37C2211yescharacteristic
59C2×D8×C37C2211yescharacteristic
60C22×C8×C37C2211yescharacteristic
61#41×C37—22no—
62#41×C37—22no—
63#41×C37—41no—
64#41×C37—41no—
65C2×Q8×C37C2311yescharacteristic
66C2×Q8×C37C2311yescharacteristic
67C2×D4×C37—21no—
68C2×D4×C37—21no—
69C2×D4×C37C2311yescharacteristic
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
80C22×Dic37—21no—
81C22×Dic37—21no—
82#10596966—22no—
83#10596966—41no—
84#10596964—22no—
85#10596964—41no—
86C2×D148—21no—
87C2×D148C2311yescharacteristic
88C2×C4×D37—21no—
89C2×C4×D37C2311yescharacteristic
90C2×Dic74C2311yescharacteristic
91Q16×C37—22no—
92SD16×C37—22no—
93SD16×C37D414yescomplemented
94D8×C37—22no—
95C2×C8×C37—22no—
96C2×C8×C37C2311yescharacteristic
97C2×C8×C37C2311yescharacteristic
98C22⋊Dic37—21no—
99C22⋊Dic37—21no—
100C22⋊Dic37—21no—
101C22⋊Dic37D411yescharacteristic
102#10596942—22no—
103#10596941—41no—
104#10596940—41no—
105#10596939—22no—
106#10596938—21no—
107#10596938—21no—
108#10596938D411yescharacteristic
109C4⋊Dic37—21no—
110C4⋊Dic37C2311yescharacteristic
111C4⋊Dic37C2311yescharacteristic
112#10596936—21no—
113#10596936—21no—
114#10596936—21no—
115#10596936—21no—
116#10596936D411yescharacteristic
117C4×Dic37—21no—
118C4×Dic37C2311yescharacteristic
119C2×#64436C2311yescharacteristic
120C2×#64436C2311yescharacteristic
121#10596930—22no—
122C8×D37—22no—
123C23×C37—21no—
124C23×C37—21no—
125C23×C37C2×D411yescharacteristic
126C22×D37—21no—
127C22×D37C2×D411yescharacteristic
128Q8×C37—21no—
129Q8×C37—21no—
130Q8×C37—21no—
131Q8×C37C2×D412yes—
132D4×C37—21no—
133D4×C37—21no—
134D4×C37—21no—
135D4×C37—42no—
136D4×C37—42no—
137D4×C37C2×D412yes—
138C2×C4×C37—21no—
139C2×C4×C37—21no—
140C2×C4×C37—21no—
141C2×C4×C37—21no—
142C2×C4×C37—42no—
143C2×C4×C37—42no—
144C2×C4×C37C2×D411yescharacteristic
145C2×C4×C37C2411yescharacteristic
146C22⋊D37—22no—
147C22⋊D37—42no—
148C22⋊D37—42no—
149C22⋊D37—81no—
150C22⋊D37—81no—
151C22⋊D37—81no—
152C2×Dic37—21no—
153C2×Dic37—21no—
154C2×Dic37—21no—
155C2×Dic37—42no—
156C2×Dic37—42no—
157C2×Dic37C2×D411yescharacteristic
158C2×Dic37C2×D411yescharacteristic
159C2×Dic37C2×D411yescharacteristic
160D148—21no—
161D148—21no—
162D148—42no—
163C4×D37—21no—
164C4×D37—21no—
165C4×D37—42no—
166Dic74—21no—
167Dic74—21no—
168C8×C37—21no—
169C8×C37C2×D412yes—
170#64436—21no—
171#64436—21no—
172C22×C37—22no—
173C22×C37—21no—
174C22×C37—21no—
175C22×C37—21no—
176C22×C37—41no—
177C22×C37—41no—
178C22×C37—41no—
179C22×C37—41no—
180C22×C37—41no—
181C22×C37C22×D411yescharacteristic
182C2×D37—21no—
183C2×D37—21no—
184C2×D37—21no—
185C2×D37—41no—
186C2×D37—41no—
187C2×D37—41no—
188C4×C37—22no—
189C4×C37—21no—
190C4×C37—41no—
191C4×C37C22×D411yescharacteristic
192C4×C37H(5,𝔽2)11yescharacteristic
193Dic37—21no—
194Dic37—21no—
195Dic37—41no—
196Dic37—41no—
197Dic37—41no—
198Dic37#13512yescomplemented
199#3284—371nomaximal, Sylow
200C2×C37—41no—
201C2×C37—42no—
202C2×C37—81no—
203C2×C37D4211yescharacteristic
204C2×C37C2×#13511yescharacteristic
205C2×C37#57711yescharacteristic
206D37—41no—
207D37—81no—
208C2×#135—371no—
209C2×#135D3711yescharacteristic, complemented
210#550—371no—
211#547—371no—
212#492—371no—
213#465—371no—
214#465—371no—
215#462—371no—
216#459—371no—
217#452—371no—
218#452—371no—
219#449—371no—
220#449—371no—
221C4×SD16—371no—
222C8×D4—371no—
223C37#328411yescharacteristic, complemented, Sylow
224C2×#41—371no—
225C2×#41—371no—
226C2×#41C2×D3711yescharacteristic
227C2×#41C2×D3711yescharacteristic
228#135—24no—
229#135—744no—
230C2×Q16—371no—
231C2×Q16C2×D3711yescharacteristic
232C2×SD16—371no—
233C2×SD16—371no—
234C2×SD16—371no—
235C2×SD16C2×D3711yescharacteristic
236C2×SD16C2×D3711yescharacteristic
237C2×D8—371no—
238C2×D8C2×D3711yescharacteristic
239C22×C8—371no—
240C22×C8C2×D3711yescharacteristic
241C4⋊Q8—371no—
242#127—371no—
243#127—741no—
244#123—741no—
245#123—741no—
246C22⋊Q8—371no—
247C22⋊Q8—371no—
248#121—371no—
249#121—371no—
250#121—741no—
251#121—741no—
252#121—741no—
253C4×Q8—371no—
254C4×D4—371no—
255C4×D4—371no—
256C4×D4—741no—
257C2×C4⋊C4—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—
268C4×C8—371no—
269#41—22no—
270#41—22no—
271#41—41no—
272#41—41no—
273#41—742no—
274#41—742no—
275#41—1481no—
276#41—1481no—
277C2×Q8—371no—
278C2×Q8C22×D3711yescharacteristic
279C2×Q8C22×D3711yescharacteristic
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—371no—
283C2×D4—371no—
284C2×D4—741no—
285C2×D4—741no—
286C2×D4—741no—
287C2×D4—741no—
288C2×D4—741no—
289C2×D4—741no—
290C2×D4C22×D3711yescharacteristic
291C2×D4C22×D3711yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—371no—
295C22×C4—741no—
296C22×C4—741no—
297C22×C4—741no—
298C22×C4C22×D3711yescharacteristic
299Q16—22no—
300Q16—742no—
301SD16—22no—
302SD16—742no—
303SD16—1481no—
304SD16—1481no—
305SD16C22⋊D3714yescomplemented
306D8—22no—
307D8—742no—
308C2×C8—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—
320C4⋊C4—741no—
321C4⋊C4—741no—
322C22⋊C4—371no—
323C22⋊C4—371no—
324C22⋊C4—741no—
325C22⋊C4—741no—
326C22⋊C4—741no—
327C22⋊C4—741no—
328C22⋊C4—741no—
329C42—371no—
330C42—741no—
331C23—21no—
332C23—21no—
333C23—371no—
334C23—741no—
335C23D4×D3711yescharacteristic
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—741no—
340Q8—741no—
341Q8C2×C22⋊D3712yes—
342D4—21no—
343D4—21no—
344D4—21no—
345D4—42no—
346D4—42no—
347D4—2961no—
348D4—2961no—
349D4—2961no—
350D4—742no—
351D4—741no—
352D4—741no—
353D4—1482no—
354D4—1482no—
355D4—1482no—
356D4C2×C22⋊D3712yes—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—371no—
364C2×C4—371no—
365C2×C4—371no—
366C2×C4—741no—
367C2×C4—741no—
368C2×C4—741no—
369C2×C4—741no—
370C2×C4—741no—
371C2×C4—1482no—
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—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—741no—
390C22—741no—
391C22—741no—
392C22—1481no—
393C22—1481no—
394C22—1481no—
395C22C2×D4×D3711yescharacteristic
396C4—21no—
397C4—22no—
398C4—41no—
399C4—372no—
400C4—741no—
401C4—741no—
402C4—1481no—
403C4—1481no—
404C4—1481no—
405C4C22×C22⋊D3711yescharacteristic
406C4#1192458111yescharacteristic
407C2—41no—
408C2—42no—
409C2—81no—
410C2—2961no—
411C2—1481no—
412C2D4×C22⋊D3711yescharacteristic
413C2#135×D3711yescharacteristic
414C2#1455834011yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#135×C37C2
socleC22×C37C22×D4
hypercenterC2×#135D37
hypocenterC37#3284
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#11924557C2semidirect
2. #14558202C2semidirect
3. #14558182C2semidirect
4. #14557904C2semidirect
5. #14557762C2semidirect
6. #14557759C2semidirect
7. #14557741C2semidirect
8. #14557726C2semidirect
9. #14557695C2semidirect
10. #14557694C2semidirect
11. #14557678C2semidirect
12. #14557675C2semidirect
13. SD16×Dic37C2semidirect
14. C8×C22⋊D37C2semidirect
15. C2×#135×C37C2semidirect
93. SD16×C37D4semidirect
198. Dic37#135semidirect
209. C2×#135D37semidirect
223. C37#3284semidirect
305. SD16C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245572
#145582022
#145581822
#145579042
#145577622
#145577592
#145577412
#145577262
#145576952
#145576942
#145576782
#145576752
SD16×Dic372
C8×C22⋊D372
C2×#135×C372
#328437