Finite Group Databasebeta

← #31807464

Subgroups — #31807464

Order 17792.

348 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 71 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#22581751C211yesmaximal, characteristic
2C2×#17984873C211yesmaximal, characteristic, complemented
3#22580970C211yesmaximal, characteristic, complemented
4#22580962C211yesmaximal, characteristic, complemented
5#22580926C211yesmaximal, characteristic, complemented
6#22580723C211yesmaximal, characteristic, complemented
7#536×C139C211yesmaximal, characteristic, complemented
8C2×#14555785C2211yescharacteristic
9#17984873—22no—
10#17984873—22no—
11#17984873—21no—
12#17984872—21no—
13#17984868—21no—
14#17984867—21no—
15#17984862—22no—
16C2×#14555775—21no—
17C2×#14555772—21no—
18C2×#14555769C2211yescharacteristic
19C2×#14555769C2211yescharacteristic
20#17984801C2211yescharacteristic
21#17984769—22no—
22#17984766—22no—
23#17984756—22no—
24C2×#41×C139C2211yescharacteristic
25C22×Q8×C139C2211yescharacteristic
26C4⋊Q8×C139—21no—
27#124×C139—21no—
28#123×C139—22no—
29C22⋊Q8×C139—22no—
30#117×C139C2211yescharacteristic
31#14555785—21no—
32#14555785—21no—
33#14555785—21no—
34#14555785—21no—
35C2×Dic278D411yescharacteristic
36C2×D556D411yescharacteristic
37C2×C22⋊D139—21no—
38C2×C4×D139—21no—
39#14555775—24no—
40#14555775—22no—
41#14555773—22no—
42#14555772—24no—
43#14555772—22no—
44#14555770—22no—
45#14555769—21no—
46#14555769—21no—
47#14555769—21no—
48#14555769D412yes—
49C2×C139⋊C8—21no—
50C2×C139⋊C8D412yes—
51C4⋊Dic139—21no—
52C22⋊Dic139—21no—
53C4×Dic139—21no—
54#41×C139—21no—
55#41×C139—21no—
56#41×C139—21no—
57#41×C139—21no—
58C2×Q8×C139—21no—
59C2×Q8×C139—21no—
60C2×Q8×C139—21no—
61C2×Q8×C139—21no—
62C2×Q8×C139—21no—
63C2×Q8×C139D412yes—
64C2×Q8×C139D411yescharacteristic
65C2×D4×C139—21no—
66C2×D4×C139D411yescharacteristic
67C22×C4×C139—21no—
68C22×C4×C139—21no—
69C22×C4×C139C2311yescharacteristic
70C4⋊C4×C139—24no—
71C4⋊C4×C139—21no—
72C22⋊C4×C139—24no—
73C22⋊C4×C139D412yes—
74C42×C139—21no—
75C22×D139—21no—
76Dic278—21no—
77Dic278—21no—
78D556—21no—
79D556—21no—
80C22⋊D139—41no—
81C22⋊D139—41no—
82C2×Dic139—21no—
83C2×Dic139—41no—
84C4×D139—41no—
85C4×D139—41no—
86C139⋊C8—22no—
87C139⋊C8—22no—
88C23×C139—21no—
89C23×C139C2×D411yescharacteristic
90Q8×C139—22no—
91Q8×C139—21no—
92Q8×C139—22no—
93Q8×C139—21no—
94Q8×C139—41no—
95Q8×C139—41no—
96D4×C139—21no—
97D4×C139—21no—
98D4×C139—41no—
99D4×C139—41no—
100C2×C4×C139—22no—
101C2×C4×C139—22no—
102C2×C4×C139—21no—
103C2×C4×C139—41no—
104C2×C4×C139—41no—
105C2×C4×C139—41no—
106C2×C4×C139—41no—
107C2×C4×C139C2×D411yescharacteristic
108C2×C4×C139C2×D411yescharacteristic
109C2×C4×C139C2×D411yescharacteristic
110C2×C4×C139C2×D411yescharacteristic
111C2×C4×C139C2×D411yescharacteristic
112C2×C4×C139#4111yescharacteristic
113C22×C139—41no—
114C22×C139—42no—
115C22×C139—41no—
116C22×C139#12011yescharacteristic
117C22×C139#12111yescharacteristic
118C22×C139#12711yescharacteristic
119C2×D139—41no—
120C2×D139—81no—
121C4×C139—42no—
122C4×C139—41no—
123C4×C139—42no—
124C4×C139#12011yescharacteristic
125C4×C139#12011yescharacteristic
126C4×C139#12111yescharacteristic
127C4×C139#12111yescharacteristic
128Dic139—41no—
129Dic139—81no—
130C2×C139—21no—
131C2×C139—21no—
132C2×C139—21no—
133C2×C139—81no—
134C2×C139#39211yescharacteristic
135D139—81no—
136C139#200911yescharacteristic, complemented, Sylow
137#2009—1391nomaximal, Sylow
138#575—1391no—
139C2×#137—1391no—
140#536D13911yescharacteristic, complemented
141#421—1391no—
142#419—1391no—
143#410—1391no—
144#344—1391no—
145C2×#41—1391no—
146C2×#41C2×D13911yescharacteristic
147C22×Q8C2×D13911yescharacteristic
148#137—2781no—
149#137—2782no—
150#137—2781no—
151#137—2782no—
152AGL(1,ℤ/8)—2781no—
153AGL(1,ℤ/8)—2781no—
154#135—2782no—
155C2×Q16—2781no—
156C2×SD16—2781no—
157C2×M16—1391no—
158C2×M16—1391no—
159C4⋊Q8—21no—
160#124—21no—
161#123—22no—
162C22⋊Q8—22no—
163#117—1391no—
164#117C2×D13911yescharacteristic
165#104—2782no—
166#103—2782no—
167#99—2782no—
168#41—21no—
169#41—21no—
170#41—21no—
171#41—21no—
172#41—2781no—
173#41—2781no—
174#41—2781no—
175#41—2781no—
176C2×Q8—21no—
177C2×Q8—21no—
178C2×Q8—21no—
179C2×Q8—21no—
180C2×Q8—21no—
181C2×Q8—1391no—
182C2×Q8C22⋊D13912yes—
183C2×Q8C22⋊D13911yescharacteristic
184C2×D4—21no—
185C2×D4—2781no—
186C2×D4—1391no—
187C2×D4C22⋊D13911yescharacteristic
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—2781no—
191C22×C4C22×D13911yescharacteristic
192Q16—2784no—
193Q16—2782no—
194SD16—2782no—
195SD16—2784no—
196SD16—2782no—
197D8—2782no—
198M16—2781no—
199M16—2781no—
200M16—2781no—
201M16—1392no—
202C2×C8—2781no—
203C2×C8—1392no—
204C4⋊C4—24no—
205C4⋊C4—21no—
206C4⋊C4—2781no—
207C22⋊C4—24no—
208C22⋊C4—2781no—
209C22⋊C4C22⋊D13912yes—
210C42—21no—
211C42—2781no—
212C23—21no—
213C23—2781no—
214C23C2×C22⋊D13911yescharacteristic
215Q8—22no—
216Q8—21no—
217Q8—22no—
218Q8—21no—
219Q8—41no—
220Q8—41no—
221Q8—2781no—
222Q8—2781no—
223D4—21no—
224D4—21no—
225D4—41no—
226D4—41no—
227D4—2781no—
228D4—2781no—
229D4—5561no—
230D4—5561no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—2781no—
239C2×C4—5561no—
240C2×C4—5561no—
241C2×C4—5561no—
242C2×C4D4×D13911yescharacteristic
243C2×C4D4×D13911yescharacteristic
244C2×C4D4×D13911yescharacteristic
245C2×C4C2×C22⋊D13911yescharacteristic
246C2×C4C2×C22⋊D13911yescharacteristic
247C2×C4#1455578411yescharacteristic
248C8—2782no—
249C8—2782no—
250C22—41no—
251C22—42no—
252C22—41no—
253C22—5561no—
254C22—11121no—
255C22#1798481111yescharacteristic
256C22#1798481311yescharacteristic
257C22#1798483811yescharacteristic
258C4—42no—
259C4—41no—
260C4—42no—
261C4—5561no—
262C4—11121no—
263C4#1798481011yescharacteristic
264C4#1798481011yescharacteristic
265C4#1798481411yescharacteristic
266C4#1798481411yescharacteristic
267C2—21no—
268C2—21no—
269C2—21no—
270C2—81no—
271C2—11121no—
272C2#2258086111yescharacteristic
subgroupG/H
centerC2#22580861
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#536×C139C2
socleC2×C139#392
prime radical#22581751C2
hypercenter#536D139
hypocenterC139#2009
LCSG ▷ C22×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
2. C2×#17984873C2semidirect
3. #22580970C2semidirect
4. #22580962C2semidirect
5. #22580926C2semidirect
6. #22580723C2semidirect
7. #536×C139C2semidirect
136. C139#2009semidirect
140. #536D139semidirect

Maximal subgroups

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

subgroupindex
#225817512
C2×#179848732
#225809702
#225809622
#225809262
#225807232
#536×C1392
#2009139