Finite Group Databasebeta

← #18006152

Subgroups — #18006152

Order 4736.

478 conjugacy classes of subgroups.

The subgroup lattice has 404 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#14558188C211yesmaximal, characteristic, complemented
4#14557928C211yesmaximal, characteristic, complemented
5#14557777C211yesmaximal, characteristic, complemented
6#14557772C211yesmaximal, characteristic, complemented
7#14557745C211yesmaximal, characteristic, complemented
8#14557743C211yesmaximal, characteristic, complemented
9#14557695C211yesmaximal, characteristic, complemented
10#14557693C211yesmaximal, characteristic, complemented
11#14557689C211yesmaximal, characteristic, complemented
12#14557676C211yesmaximal, characteristic, complemented
13#14557631C211yesmaximal, 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×#10596942C2211yescharacteristic
23C2×#10596942C2211yescharacteristic
24C2×#10596940C2211yescharacteristic
25C2×#10596940C2211yescharacteristic
26C2×#10596941C2211yescharacteristic
27C2×#10596941C2211yescharacteristic
28C2×#10596939C2211yescharacteristic
29C2×#10596934C2211yescharacteristic
30C22×#64436C2211yescharacteristic
31#11924536C2211yescharacteristic
32#11924518—21no—
33#11924518—21no—
34#11924515C2211yescharacteristic
35#11924515C2211yescharacteristic
36#11924507—21no—
37C4×D148C2211yescharacteristic
38C4⋊C4×D37—21no—
39#11924469C2211yescharacteristic
40C4⋊#64436C2211yescharacteristic
41#11924460C2211yescharacteristic
42#11924460C2211yescharacteristic
43#11924459C2211yescharacteristic
44#11924459C2211yescharacteristic
45#11924457C2211yescharacteristic
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—
78#10596962—22no—
79#10596962—22no—
80#10596962—41no—
81#10596962—41no—
82C2×D148C2311yescharacteristic
83C2×C4×D37—21no—
84C2×C4×D37—21no—
85C2×C4×D37—21no—
86C2×Dic74C2311yescharacteristic
87C2×Dic74C2311yescharacteristic
88C4⋊C4×C37—21no—
89C4⋊C4×C37—21no—
90C4⋊C4×C37D411yescharacteristic
91C4⋊C4×C37C2311yescharacteristic
92C22⋊C4×C37—21no—
93C22⋊C4×C37—21no—
94C22⋊C4×C37—21no—
95C22⋊C4×C37—21no—
96C22⋊C4×C37D411yescharacteristic
97C22⋊C4×C37D411yescharacteristic
98C42×C37—21no—
99C42×C37C2311yescharacteristic
100C22⋊Dic37—21no—
101C22⋊Dic37—21no—
102#10596942—22no—
103#10596942—22no—
104#10596942—22no—
105#10596942—41no—
106#10596941—22no—
107#10596941D414yescomplemented
108#10596940—22no—
109#10596940—41no—
110#10596939—22no—
111#10596938—21no—
112C4⋊Dic37—21no—
113C4⋊Dic37—21no—
114C4⋊Dic37C2311yescharacteristic
115#10596936—21no—
116#10596936—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—
127Q8×C37—21no—
128Q8×C37—21no—
129Q8×C37—21no—
130Q8×C37—42no—
131Q8×C37C2×D412yes—
132D4×C37—21no—
133D4×C37—21no—
134D4×C37—41no—
135D4×C37—42no—
136D4×C37—42no—
137C2×C4×C37—21no—
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—42no—
145C2×C4×C37—42no—
146C2×C4×C37C2×D411yescharacteristic
147C2×C4×C37C2×D411yescharacteristic
148C2×C4×C37C2×D411yescharacteristic
149C2×C4×C37C2×D411yescharacteristic
150C2×C4×C37C2411yescharacteristic
151C22⋊D37—42no—
152C22⋊D37—42no—
153C2×Dic37—21no—
154C2×Dic37—21no—
155C2×Dic37—21no—
156D148—21no—
157D148C2×D412yes—
158C4×D37—42no—
159C4×D37—42no—
160C4×D37—42no—
161Dic74—21no—
162Dic74—21no—
163Dic74—21no—
164Dic74—21no—
165#64436—21no—
166#64436—21no—
167#64436—21no—
168#64436C2×D412yes—
169C22×C37—21no—
170C22×C37—21no—
171C22×C37—21no—
172C22×C37—21no—
173C22×C37—21no—
174C22×C37—21no—
175C22×C37—41no—
176C22×C37—41no—
177C22×C37—41no—
178C22×C37C22×D411yescharacteristic
179C2×D37—22no—
180C2×D37—41no—
181C2×D37—41no—
182C4×C37—21no—
183C4×C37—21no—
184C4×C37—22no—
185C4×C37—21no—
186C4×C37—21no—
187C4×C37—41no—
188C4×C37—41no—
189C4×C37C22×D411yescharacteristic
190C4×C37H(5,𝔽2)11yescharacteristic
191Dic37—41no—
192Dic37—41no—
193Dic37—41no—
194#3269—371nomaximal, Sylow
195C2×C37—41no—
196C2×C37—41no—
197C2×C37—81no—
198C2×C37D4211yescharacteristic
199C2×C37#57511yescharacteristic
200C2×C37#57811yescharacteristic
201D37—42no—
202C2×#137—371no—
203C2×#135—371no—
204#548D3711yescharacteristic, complemented
205#547—371no—
206#497—371no—
207#468—371no—
208#467—371no—
209#463—371no—
210#462—371no—
211#452—371no—
212#452—371no—
213#451—371no—
214#449—371no—
215#440—371no—
216#435—371no—
217C37#326911yescharacteristic, complemented, Sylow
218C2×#41—371no—
219C2×#41—371no—
220C2×#41C2×D3711yescharacteristic
221C22×Q8C2×D3711yescharacteristic
222#137—744no—
223#135—744no—
224C2×Q16—371no—
225C2×Q16—371no—
226C2×Q16—371no—
227C2×Q16—371no—
228C2×SD16—371no—
229C2×SD16—371no—
230C2×SD16—371no—
231C2×SD16—371no—
232C2×D8—371no—
233C2×M16—371no—
234C22×C8—371no—
235C4⋊Q8—371no—
236#124—21no—
237#124C2×D3711yescharacteristic
238#123—741no—
239#123—741no—
240C22⋊Q8—21no—
241C22⋊Q8—371no—
242C22⋊Q8—371no—
243C22⋊Q8C2×D3711yescharacteristic
244#121—21no—
245#121—741no—
246#121C2×D3711yescharacteristic
247C4×Q8C2×D3711yescharacteristic
248C4×D4—21no—
249C4×D4—371no—
250C4×D4C2×D3711yescharacteristic
251C2×C4⋊C4—741no—
252#107—371no—
253C4⋊C8—371no—
254#103—371no—
255#103—371no—
256#103—371no—
257#103—371no—
258#102—371no—
259#102—371no—
260C22⋊C8—371no—
261C22⋊C8—371no—
262#97—371no—
263#41—22no—
264#41—41no—
265#41—742no—
266#41—742no—
267#41—1481no—
268#41—1481no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—371no—
273C2×Q8—371no—
274C2×Q8C22×D3711yescharacteristic
275C2×Q8C22×D3711yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—371no—
279C2×D4—741no—
280C2×D4—741no—
281C2×D4C22⋊D3711yescharacteristic
282C2×D4C22×D3711yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—741no—
286C22×C4—741no—
287C22×C4—741no—
288C22×C4C22×D3711yescharacteristic
289C22×C4C22×D3711yescharacteristic
290Q16—742no—
291Q16—742no—
292Q16—742no—
293Q16—1481no—
294SD16—374no—
295SD16—742no—
296SD16—742no—
297SD16—1481no—
298D8—742no—
299M16—742no—
300C2×C8—371no—
301C2×C8—371no—
302C2×C8—371no—
303C2×C8—371no—
304C2×C8—742no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—371no—
308C4⋊C4—741no—
309C4⋊C4—741no—
310C4⋊C4—741no—
311C4⋊C4—741no—
312C4⋊C4C22⋊D3711yescharacteristic
313C4⋊C4C22×D3711yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—21no—
318C22⋊C4—741no—
319C22⋊C4—741no—
320C22⋊C4—741no—
321C22⋊C4C22⋊D3711yescharacteristic
322C22⋊C4C22⋊D3711yescharacteristic
323C42—21no—
324C42C22×D3711yescharacteristic
325C23—21no—
326C23—741no—
327C23C2×C22⋊D3711yescharacteristic
328C23C2×C22⋊D3711yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—42no—
333Q8—741no—
334Q8—741no—
335Q8—741no—
336Q8—741no—
337Q8D4×D3712yes—
338D4—21no—
339D4—21no—
340D4—41no—
341D4—42no—
342D4—42no—
343D4—372no—
344D4—741no—
345D4—1482no—
346D4—1482no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—741no—
357C2×C4—741no—
358C2×C4—741no—
359C2×C4—1482no—
360C2×C4—1482no—
361C2×C4—1482no—
362C2×C4C2×C22⋊D3711yescharacteristic
363C2×C4C2×C22⋊D3711yescharacteristic
364C2×C4C2×C22⋊D3711yescharacteristic
365C2×C4C2×C22⋊D3711yescharacteristic
366C2×C4C23×D3711yescharacteristic
367C8—372no—
368C8—741no—
369C8—741no—
370C8—741no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—742no—
381C22—1481no—
382C22—1481no—
383C22C22×C22⋊D3711yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—22no—
389C4—41no—
390C4—41no—
391C4—1481no—
392C4—1481no—
393C4—1481no—
394C4C2×D4×D3711yescharacteristic
395C4#1192458111yescharacteristic
396C2—41no—
397C2—41no—
398C2—81no—
399C2—1482no—
400C2D4×C22⋊D3711yescharacteristic
401C2#1455833111yescharacteristic
402C2#1455834811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#548C2
socleC22×C37C22×D4
hypercenter#548D37
hypocenterC37#3269
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. #14558188C2semidirect
4. #14557928C2semidirect
5. #14557777C2semidirect
6. #14557772C2semidirect
7. #14557745C2semidirect
8. #14557743C2semidirect
9. #14557695C2semidirect
10. #14557693C2semidirect
11. #14557689C2semidirect
12. #14557676C2semidirect
13. #14557631C2semidirect
14. #14557605C2semidirect
15. C37×#548C2semidirect
107. #10596941D4semidirect
204. #548D37semidirect
217. C37#3269semidirect

Maximal subgroups

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

subgroupindex
C2×#119245672
C2×#119245562
#145581882
#145579282
#145577772
#145577722
#145577452
#145577432
#145576952
#145576932
#145576892
#145576762
#145576312
#145576052
C37×#5482
#326937