Finite Group Databasebeta

← #18010596

Subgroups — #18010596

Order 4736.

370 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558602C211yesmaximal, characteristic, complemented
2D37⋊#104C211yesmaximal, characteristic, complemented
3#14558525C211yesmaximal, characteristic, complemented
4#14558485C211yesmaximal, characteristic, complemented
5#14558412C211yesmaximal, characteristic, complemented
6#14558405C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×D37C211yesmaximal, characteristic
8D37⋊M16C2211yescharacteristic
9Q8×#3866—21no—
10D4×#3866—22no—
11D4×#3866—21no—
12#11924615—21no—
13#11924615C2211yescharacteristic
14C2×C4⋊#3866—21no—
15C2×C4⋊#3866C2211yescharacteristic
16C2×C22⋊#3866—22no—
17C2×C4×#3866C2211yescharacteristic
18#11924601—21no—
19#11924600—21no—
20#11924598—21no—
21#11924598—21no—
22#41×D37C2211yescharacteristic
23C2×D4×D37C2211yescharacteristic
24#11924564C411yescharacteristic, complemented
25#11924563—21no—
26#11924562C411yescharacteristic, complemented
27#11924561C411yescharacteristic, complemented
28#11924560—21no—
29SD16×D37—21no—
30D8×D37—21no—
31M16×D37C2211yescharacteristic
32AGL(1,ℤ/8)×C37C411yescharacteristic, complemented
33C23×D37—21no—
34C22×#3866—21no—
35C22×#3866—22no—
36C22×#3866D412yes—
37#41×C37C2×C411yescharacteristic
38C2×D4×C37C2×C411yescharacteristic, complemented
39C2×C22⋊D37—21no—
40#10596966D411yescharacteristic
41Q8×D37D411yescharacteristic
42#10596964—21no—
43#10596964D411yescharacteristic
44D4×D37—21no—
45D4×D37—21no—
46D4×D37—21no—
47D4×D37—21no—
48D4×D37—21no—
49D4×D37D411yescharacteristic
50#10596962—21no—
51#10596962C2×C411yescharacteristic
52C2×D148C2×C411yescharacteristic, complemented
53C2×C4×D37—21no—
54C2×C4×D37C2311yescharacteristic
55C22⋊#3866—22no—
56C22⋊#3866—21no—
57C22⋊#3866—44no—
58#10596957—21no—
59C4⋊#3866—22no—
60C4⋊#3866—21no—
61C4⋊#3866—21no—
62C4⋊#3866D411yescharacteristic
63C4⋊#3866D411yescharacteristic
64C4×#3866—22no—
65C4×#3866—21no—
66C4×#3866—21no—
67C4×#3866—21no—
68#10596953—21no—
69D37⋊C8—21no—
70SD16×C37—21no—
71D8×C37—21no—
72M16×C37C2×C411yescharacteristic, complemented
73#10596941—21no—
74#10596940—21no—
75#10596939—21no—
76#10596939—21no—
77#10596934C2×C411yescharacteristic, complemented
78D296—21no—
79#10596930—21no—
80#10596929—21no—
81C8×D37—21no—
82C23×C37—21no—
83C22×D37—21no—
84C22×D37—21no—
85C22×D37—42no—
86C22×D37—42no—
87C22×D37—41no—
88C22×D37—41no—
89C22×D37C2×D411yescharacteristic
90C2×#3866—22no—
91C2×#3866—21no—
92C2×#3866—22no—
93C2×#3866—21no—
94C2×#3866—41no—
95C2×#3866—41no—
96C2×#3866—42no—
97C2×#3866—82no—
98Q8×C37C22⋊C411yescharacteristic, complemented
99D4×C37—21no—
100D4×C37—21no—
101D4×C37—21no—
102D4×C37C22⋊C411yescharacteristic, complemented
103C2×C4×C37—21no—
104C2×C4×C37C22×C411yescharacteristic
105C22⋊D37—21no—
106C22⋊D37—21no—
107C22⋊D37—21no—
108C22⋊D37—41no—
109C22⋊D37—41no—
110C2×Dic37—21no—
111C2×Dic37#4111yescharacteristic
112D148—21no—
113D148—21no—
114D148—21no—
115D148C22⋊C411yescharacteristic, complemented
116C4×D37—21no—
117C4×D37—21no—
118C4×D37—21no—
119C4×D37C2×D411yescharacteristic
120C4×D37C2×D411yescharacteristic
121C4×D37C2×D411yescharacteristic
122C4×D37#4111yescharacteristic
123Dic74—21no—
124Dic74C22⋊C411yescharacteristic, complemented
125#64438—41no—
126C8×C37—21no—
127#64436—21no—
128C22×C37—21no—
129C22×C37—42no—
130C22×C37—41no—
131C22×C37C4×D411yescharacteristic
132C2×D37—21no—
133C2×D37—21no—
134C2×D37—21no—
135C2×D37—41no—
136C2×D37—41no—
137C2×D37—42no—
138C2×D37—41no—
139C2×D37—82no—
140C2×D37—81no—
141C2×D37—81no—
142C2×D37#12011yescharacteristic
143C2×D37#12111yescharacteristic
144#3866—42no—
145#3866—42no—
146#3866—41no—
147#3866—41no—
148C4×C37—21no—
149C4×C37C2×C22⋊C411yescharacteristic
150C4×C37C4×D411yescharacteristic
151Dic37—21no—
152Dic37#12111yescharacteristic
153Dic37#12311yescharacteristic
154#1883—371nomaximal, Sylow
155C2×C37—21no—
156C2×C37—41no—
157C2×C37—81no—
158C2×C37#38611yescharacteristic
159D37—21no—
160D37—41no—
161D37—81no—
162D37#45311yescharacteristic
163D37#45411yescharacteristic
164C2×AGL(1,ℤ/8)—371no—
165#520—371no—
166C2×#104—371no—
167#418—371no—
168#390—371no—
169#343—371no—
170#339—371no—
171C37#188311yescharacteristic, complemented, Sylow
172C2×#41—371no—
173C22×D4—371no—
174AGL(1,ℤ/8)—371no—
175AGL(1,ℤ/8)—371no—
176AGL(1,ℤ/8)—371no—
177AGL(1,ℤ/8)—741no—
178AGL(1,ℤ/8)—741no—
179AGL(1,ℤ/8)#386611yescharacteristic, complemented
180C2×SD16—741no—
181C2×D8—741no—
182C2×M16—371no—
183C2×M16—371no—
184C4×Q8—741no—
185C4×D4—742no—
186C4×D4—741no—
187#117—371no—
188#117—741no—
189C2×C4⋊C4—371no—
190C2×C4⋊C4—741no—
191C2×C22⋊C4—742no—
192C2×C42—371no—
193#104—741no—
194#104—741no—
195#102—741no—
196#102—741no—
197C24—741no—
198#41—371no—
199#41—371no—
200#41—371no—
201#41—741no—
202#41—741no—
203#41C2×#386611yescharacteristic
204C2×Q8—371no—
205C2×D4—371no—
206C2×D4—371no—
207C2×D4—741no—
208C2×D4—741no—
209C2×D4—741no—
210C2×D4—741no—
211C2×D4—741no—
212C2×D4—741no—
213C2×D4C2×#386611yescharacteristic, complemented
214C22×C4—371no—
215C22×C4—372no—
216C22×C4—741no—
217C22×C4—742no—
218C22×C4—741no—
219SD16—21no—
220SD16—741no—
221SD16—741no—
222SD16—741no—
223D8—21no—
224D8—741no—
225D8—741no—
226D8—741no—
227M16—371no—
228M16—741no—
229M16—741no—
230M16—741no—
231M16C2×#386611yescharacteristic, complemented
232C2×C8—741no—
233C2×C8—741no—
234C4⋊C4—371no—
235C4⋊C4—371no—
236C4⋊C4—741no—
237C4⋊C4—741no—
238C4⋊C4—742no—
239C22⋊C4—741no—
240C22⋊C4—742no—
241C22⋊C4—1484no—
242C42—741no—
243C42—741no—
244C42—741no—
245C42—742no—
246C23—21no—
247C23—371no—
248C23—741no—
249C23—741no—
250C23—1481no—
251C23—1481no—
252C23—1482no—
253C23—1482no—
254Q8—371no—
255Q8—741no—
256Q8C22⋊#386611yescharacteristic, complemented
257D4—21no—
258D4—21no—
259D4—21no—
260D4—371no—
261D4—741no—
262D4—741no—
263D4—741no—
264D4—741no—
265D4—741no—
266D4—741no—
267D4—1481no—
268D4—1481no—
269D4C22⋊#386611yescharacteristic, complemented
270C2×C4—21no—
271C2×C4—371no—
272C2×C4—371no—
273C2×C4—371no—
274C2×C4—371no—
275C2×C4—371no—
276C2×C4—2962no—
277C2×C4—741no—
278C2×C4—741no—
279C2×C4—741no—
280C2×C4—741no—
281C2×C4—741no—
282C2×C4—741no—
283C2×C4—742no—
284C2×C4—742no—
285C2×C4—1481no—
286C2×C4—1481no—
287C2×C4—1482no—
288C2×C4C22×#386611yescharacteristic
289C8—21no—
290C8—741no—
291C8—1481no—
292C22—21no—
293C22—42no—
294C22—41no—
295C22—371no—
296C22—371no—
297C22—2961no—
298C22—2961no—
299C22—2962no—
300C22—741no—
301C22—741no—
302C22—741no—
303C22—1482no—
304C22—1481no—
305C22—1481no—
306C22—1481no—
307C22D4×#386611yescharacteristic
308C4—21no—
309C4—371no—
310C4—371no—
311C4—741no—
312C4—1481no—
313C4—1482no—
314C4—1481no—
315C4—1482no—
316C4C2×C22⋊#386611yescharacteristic
317C4D4×#386611yescharacteristic
318C2—21no—
319C2—41no—
320C2—81no—
321C2—371no—
322C2—371no—
323C2—2961no—
324C2—741no—
325C2—1481no—
326C2#1455848111yescharacteristic
subgroupG/H
centerC2#14558481
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingAGL(1,ℤ/8)×C37C4
socleC2×C37#386
prime radicalAGL(1,ℤ/8)×D37C2
cosocleC2×C4×D37C23
hypercenterAGL(1,ℤ/8)#3866
hypocenterC37#1883
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #14558602C2semidirect
2. D37⋊#104C2semidirect
3. #14558525C2semidirect
4. #14558485C2semidirect
5. #14558412C2semidirect
6. #14558405C2semidirect
24. #11924564C4semidirect
26. #11924562C4semidirect
27. #11924561C4semidirect
32. AGL(1,ℤ/8)×C37C4semidirect
38. C2×D4×C37C2×C4semidirect
52. C2×D148C2×C4semidirect
72. M16×C37C2×C4semidirect
77. #10596934C2×C4semidirect
98. Q8×C37C22⋊C4semidirect
102. D4×C37C22⋊C4semidirect
115. D148C22⋊C4semidirect
124. Dic74C22⋊C4semidirect
171. C37#1883semidirect
179. AGL(1,ℤ/8)#3866semidirect
213. C2×D4C2×#3866semidirect
231. M16C2×#3866semidirect
256. Q8C22⋊#3866semidirect
269. D4C22⋊#3866semidirect

Maximal subgroups

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

subgroupindex
#145586022
D37⋊#1042
#145585252
#145584852
#145584122
#145584052
AGL(1,ℤ/8)×D372
#188337