Finite Group Databasebeta

← #32975289

Subgroups — #32975289

Order 18688.

494 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 87 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#22611469C211yesmaximal, characteristic, complemented
2#22611464C212yesmaximal, complemented
3#22607757C211yesmaximal, characteristic, complemented
4#22607752C212yesmaximal, complemented
5C73×#2733C211yesmaximal, characteristic
6C2×#14556524—21no—
7C2×#14556522—22no—
8C2×#14556515—21no—
9C2×#14556512—22no—
10#17988457C2211yescharacteristic
11#17988342C2212yes—
12#17988342C2211yescharacteristic
13C2×#124×C73—21no—
14#394×C73—21no—
15#392×C73—22no—
16#391×C73C2211yescharacteristic
17#390×C73C2212yes—
18#388×C73—22no—
19C22×#10596831—22no—
20C22×#10596831—21no—
21C2×C4⋊Dic73—22no—
22C2×C4⋊Dic73—21no—
23#14556524—42no—
24#14556522—44no—
25#14556515—42no—
26#14556512—44no—
27C22×Q8×C73D411yescharacteristic
28C22×D4×C73—21no—
29C22×D4×C73—21no—
30C22×D4×C73D412yes—
31#124×C73—42no—
32#124×C73—42no—
33C2×C4⋊C4×C73D412yes—
34C2×C4⋊C4×C73D411yescharacteristic
35C2×C22⋊C4×C73—22no—
36C2×C22⋊C4×C73—22no—
37C2×C22⋊C4×C73—22no—
38C2×C22⋊C4×C73—22no—
39C2×C42×C73—21no—
40C2×C42×C73C2311yescharacteristic
41#95×C73—21no—
42#95×C73—22no—
43C22×Dic73—41no—
44C2×#10596831—24no—
45C2×#10596831—22no—
46C2×#10596831—42no—
47C2×#10596831—41no—
48C2×#10596831—42no—
49C2×#10596831—41no—
50C4⋊Dic73—42no—
51C4⋊Dic73—41no—
52C4⋊Dic73—42no—
53C4⋊Dic73—41no—
54C24×C73—22no—
55C2×Q8×C73—21no—
56C2×Q8×C73—41no—
57C2×Q8×C73—41no—
58C2×Q8×C73SD1612yes—
59C2×D4×C73—22no—
60C2×D4×C73—22no—
61C2×D4×C73—42no—
62C2×D4×C73—42no—
63C2×D4×C73—42no—
64C2×D4×C73—81no—
65C2×D4×C73—81no—
66C2×D4×C73—82no—
67C2×D4×C73—81no—
68C22×C4×C73—21no—
69C22×C4×C73—21no—
70C22×C4×C73—22no—
71C22×C4×C73C2×D411yescharacteristic
72C22×C4×C73C2×D412yes—
73C4⋊C4×C73—42no—
74C4⋊C4×C73—41no—
75C22⋊C4×C73—44no—
76C22⋊C4×C73—42no—
77C22⋊C4×C73—42no—
78C22⋊C4×C73—42no—
79C22⋊C4×C73—42no—
80C22⋊C4×C73—82no—
81C42×C73—41no—
82C42×C73—42no—
83C23×C73—42no—
84C23×C73—42no—
85C23×C73—42no—
86C23×C73—42no—
87C23×C73—42no—
88C23×C73—42no—
89C23×C73—42no—
90C23×C73#12011yescharacteristic
91Q8×C73—42no—
92Q8×C73—81no—
93D4×C73—44no—
94D4×C73—82no—
95D4×C73—84no—
96D4×C73—84no—
97C2×C4×C73—22no—
98C2×C4×C73—21no—
99C2×C4×C73—22no—
100C2×C4×C73—21no—
101C2×C4×C73—22no—
102C2×C4×C73—41no—
103C2×C4×C73—41no—
104C2×C4×C73—42no—
105C2×C4×C73—42no—
106C2×C4×C73—42no—
107C2×C4×C73—42no—
108C2×C4×C73—41no—
109C2×C4×C73C2×SD1611yescharacteristic
110C2×C4×C73#13512yes—
111C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
112C2×C4×C73#13712yes—
113C2×Dic73—81no—
114C2×Dic73—82no—
115#10596831—42no—
116#10596831—44no—
117C22×C73—82no—
118C22×C73—82no—
119C22×C73—82no—
120C22×C73—82no—
121C22×C73—82no—
122C22×C73—82no—
123C22×C73—82no—
124C22×C73#45011yescharacteristic
125C22×C73#45212yes—
126C22×C73#45311yescharacteristic
127C22×C73#45312yes—
128C22×C73#45811yescharacteristic
129C4×C73—21no—
130C4×C73—21no—
131C4×C73—22no—
132C4×C73—22no—
133C4×C73—42no—
134C4×C73—82no—
135C4×C73—81no—
136Dic73—161no—
137#7830—731nomaximal, Sylow
138C2×C73—162no—
139C2×C73#161311yescharacteristic
140C2×C73#161812yes—
141C2×C73#163112yes—
142C2×C73#163411yescharacteristic
143C2×C73#165511yescharacteristic
144#2733D7311yescharacteristic
145#2095—731no—
146#2094—732no—
147#1272—731no—
148#1270—732no—
149C73#783011yescharacteristic, complemented, Sylow
150C2×#124—21no—
151C2×#107—1461no—
152C2×#106—1462no—
153C2×#103—1461no—
154C2×#102—1462no—
155#394—21no—
156#392—22no—
157#391C2×D7311yescharacteristic
158#390C2×D7312yes—
159#388—22no—
160#384—731no—
161#336—732no—
162#336—731no—
163C22×Q8C22⋊D7311yescharacteristic
164C22×D4—21no—
165C22×D4—21no—
166C22×D4C22⋊D7312yes—
167C22×C8—1462no—
168C22×C8—1461no—
169#124—42no—
170#124—42no—
171C2×C4⋊C4—1462no—
172C2×C4⋊C4—1461no—
173C2×C4⋊C4C22⋊D7312yes—
174C2×C4⋊C4C22⋊D7311yescharacteristic
175C2×C22⋊C4—22no—
176C2×C22⋊C4—22no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—22no—
179C2×C42—21no—
180C2×C42C22×D7311yescharacteristic
181#107—2922no—
182#106—2924no—
183#103—2922no—
184#102—2924no—
185#95—21no—
186#95—22no—
187C24—22no—
188C2×Q8—21no—
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8#1192401612yes—
192C2×D4—22no—
193C2×D4—22no—
194C2×D4—42no—
195C2×D4—42no—
196C2×D4—42no—
197C2×D4—81no—
198C2×D4—81no—
199C2×D4—82no—
200C2×D4—81no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—2921no—
205C22×C4C2×C22⋊D7311yescharacteristic
206C22×C4C2×C22⋊D7312yes—
207C2×C8—2922no—
208C2×C8—2921no—
209C2×C8—2922no—
210C2×C8—2921no—
211C2×C8—1464no—
212C2×C8—1462no—
213C4⋊C4—42no—
214C4⋊C4—41no—
215C4⋊C4—2922no—
216C4⋊C4—2921no—
217C4⋊C4—2922no—
218C4⋊C4—2921no—
219C22⋊C4—44no—
220C22⋊C4—42no—
221C22⋊C4—42no—
222C22⋊C4—42no—
223C22⋊C4—42no—
224C22⋊C4—82no—
225C42—41no—
226C42—42no—
227C23—42no—
228C23—42no—
229C23—42no—
230C23—42no—
231C23—42no—
232C23—42no—
233C23—42no—
234C23#1455656011yescharacteristic
235Q8—42no—
236Q8—81no—
237D4—44no—
238D4—82no—
239D4—84no—
240D4—84no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—5841no—
254C2×C4—5842no—
255C2×C4C2×#1192401611yescharacteristic
256C2×C4#1455661112yes—
257C2×C4#1455661711yescharacteristic
258C2×C4#1455662112yes—
259C8—2922no—
260C8—2924no—
261C22—82no—
262C22—82no—
263C22—82no—
264C22—82no—
265C22—82no—
266C22—82no—
267C22—82no—
268C22#1798873811yescharacteristic
269C22#1798874912yes—
270C22#1798875511yescharacteristic
271C22#1798875512yes—
272C22#1798877711yescharacteristic
273C4—21no—
274C4—21no—
275C4—22no—
276C4—22no—
277C4—42no—
278C4—81no—
279C4—82no—
280C4—11681no—
281C2—162no—
282C2#2260895111yescharacteristic
283C2#2260897912yes—
284C2#2260905812yes—
285C2#2260907611yescharacteristic
286C2#2260922011yescharacteristic
subgroupG/H
centerC23#14556560
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
Fitting, prime radicalC73×#2733C2
socleC23×C73#120
hypercenter#2733D73
hypocenterC73#7830
LCSG ▷ C2×C42×C73 ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2733

Complements

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

NH ≅ G/Ntype
1. #22611469C2semidirect
2. #22611464C2semidirect
3. #22607757C2semidirect
4. #22607752C2semidirect
149. C73#7830semidirect

Maximal subgroups

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

subgroupindex
#226114692
#226114642
#226077572
#226077522
C73×#27332
#783073