Finite Group Databasebeta

← #32983841

Subgroups — #32983841

Order 18688.

518 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 111 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#22618972C211yesmaximal, characteristic
2#22615285C211yesmaximal, characteristic
3#22608359C212yesmaximal, complemented
4#22607791C212yesmaximal, complemented
5C73×#1800C211yesmaximal, characteristic
6C2×C4×Dic146C2211yescharacteristic
7#17988665—24no—
8#17988640C2212yes—
9#17988551—22no—
10#17988523C412yes—
11#17988499C412yes—
12#17988490—21no—
13#17988483—21no—
14#17988460—22no—
15#17988453C2211yescharacteristic
16#17988317—24no—
17C2×C4×D4×C73C2211yescharacteristic
18#423×C73C2212yes—
19C2×#100×C73—21no—
20#343×C73—21no—
21C22×Dic146C2×C411yescharacteristic
22C2×#11924012—24no—
23C4×Dic146—22no—
24C4×Dic146—22no—
25C2×C4⋊Dic73—21no—
26C2×C4⋊Dic73C2×C411yescharacteristic
27C2×#11924007—22no—
28C2×#11924007—21no—
29C2×C22⋊Dic73—22no—
30C2×C22⋊Dic73—22no—
31C2×C4×Dic73—21no—
32C4⋊#10596831—22no—
33C22⋊#10596831—24no—
34C22⋊#10596831—22no—
35C4×#10596831D414yes—
36#14556498—22no—
37#14556498—21no—
38#14556498C2×C412yes—
39C22×D4×C73D411yescharacteristic
40C23×C4×C73D412yes—
41C2×M16×C73—22no—
42C4×D4×C73—22no—
43C4×D4×C73—22no—
44C2×C4⋊C4×C73D411yescharacteristic
45C2×C22⋊C4×C73C2×C412yes—
46C2×C42×C73C2311yescharacteristic
47C4⋊C8×C73—22no—
48C4⋊C8×C73—22no—
49#100×C73—42no—
50C2×Dic146—22no—
51C2×Dic146—42no—
52C22×Dic73—21no—
53C22×Dic73—22no—
54C22×Dic73—21no—
55#11924012—84no—
56C2×#10596831—24no—
57C4⋊Dic73—22no—
58C4⋊Dic73—41no—
59C4⋊Dic73—41no—
60#11924007—41no—
61#11924007—41no—
62#11924007—82no—
63C22⋊Dic73—44no—
64C22⋊Dic73—82no—
65C4×Dic73—42no—
66C24×C73C22⋊C412yes—
67C2×D4×C73—22no—
68C2×D4×C73—21no—
69C2×D4×C73—22no—
70C2×D4×C73—21no—
71C22×C4×C73—22no—
72C22×C4×C73—22no—
73C22×C4×C73—82no—
74C22×C4×C73C22⋊C412yes—
75C22×C4×C73C22×C411yescharacteristic
76C22×C4×C73C2×D411yescharacteristic
77C22×C4×C73C2×D411yescharacteristic
78M16×C73—42no—
79M16×C73—42no—
80C2×C8×C73—42no—
81C4⋊C4×C73—22no—
82C22⋊C4×C73—24no—
83C42×C73C2×D412yes—
84C42×C73#4112yes—
85C23×C73—22no—
86C23×C73—22no—
87C23×C73—22no—
88C23×C73—42no—
89C23×C73—42no—
90C23×C73C2×C22⋊C411yescharacteristic
91D4×C73—42no—
92D4×C73—42no—
93C2×C4×C73—22no—
94C2×C4×C73—41no—
95C2×C4×C73—41no—
96C2×C4×C73—44no—
97C2×C4×C73—42no—
98C2×C4×C73—82no—
99C2×C4×C73C4×D412yes—
100C2×C4×C73#12011yescharacteristic
101C2×C4×C73#12112yes—
102C2×C4×C73#12311yescharacteristic
103C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
104C2×C4×C73#13712yes—
105C2×C4×C73#13711yescharacteristic
106C2×Dic73—22no—
107C2×Dic73—41no—
108C2×Dic73—41no—
109C2×Dic73—42no—
110C2×Dic73—41no—
111C2×Dic73—42no—
112C2×Dic73—41no—
113C2×Dic73—41no—
114C2×Dic73—42no—
115Dic146—24no—
116Dic146—42no—
117C8×C73—82no—
118#10596831—44no—
119C22×C73—21no—
120C22×C73—21no—
121C22×C73—44no—
122C22×C73—42no—
123C22×C73—42no—
124C22×C73—42no—
125C22×C73—82no—
126C22×C73#38611yescharacteristic
127C22×C73#41711yescharacteristic
128C22×C73#41911yescharacteristic
129C4×C73—22no—
130C4×C73—21no—
131C4×C73—21no—
132C4×C73—42no—
133C4×C73#46812yes—
134C4×C73#47012yes—
135Dic73—42no—
136Dic73—82no—
137Dic73—81no—
138#9487—731nomaximal, Sylow
139C2×C73—21no—
140C2×C73—21no—
141C2×C73—82no—
142C2×C73#189111yescharacteristic
143C2×C73#189411yescharacteristic
144C2×C73#191111yescharacteristic
145#2975—731no—
146#2580—731no—
147#1800D7311yescharacteristic
148#1487—732no—
149#1286—732no—
150C73#948711yescharacteristic, complemented, Sylow
151C2×C4×Q8—731no—
152C2×C4×D4C2×D7311yescharacteristic
153#436—1464no—
154#431—732no—
155#423C2×D7312yes—
156C2×#100—21no—
157#407—1462no—
158#399—732no—
159#393—732no—
160#390—1461no—
161#389—1461no—
162#385—1462no—
163#382—731no—
164#343—21no—
165Q8⋊C8—1464no—
166C22×Q8—731no—
167C22×D4C22⋊D7311yescharacteristic
168C23×C4D29212yes—
169C2×M16—22no—
170C2×M16—1464no—
171C4×Q8—1462no—
172C4×Q8—1462no—
173C4×D4—22no—
174C4×D4—22no—
175C2×C4⋊C4—731no—
176C2×C4⋊C4—1461no—
177C2×C4⋊C4—1461no—
178C2×C4⋊C4—1462no—
179C2×C4⋊C4C22⋊D7311yescharacteristic
180C2×C22⋊C4—1462no—
181C2×C22⋊C4—1462no—
182C2×C22⋊C4C4×D7312yes—
183C2×C42—1461no—
184C2×C42C22×D7311yescharacteristic
185C4⋊C8—22no—
186C4⋊C8—22no—
187C4⋊C8—1462no—
188#100—42no—
189C22⋊C8—1464no—
190C22⋊C8—1462no—
191C4×C8—734no—
192#95—732no—
193#95—1462no—
194#95—1461no—
195C24#1192400512yes—
196C2×Q8—2922no—
197C2×Q8—1462no—
198C2×D4—22no—
199C2×D4—21no—
200C2×D4—22no—
201C2×D4—21no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—82no—
205C22×C4—1462no—
206C22×C4—1461no—
207C22×C4—1461no—
208C22×C4#1192400512yes—
209C22×C4C2×C4×D7311yescharacteristic
210C22×C4C2×C22⋊D7311yescharacteristic
211C22×C4C2×D29211yescharacteristic
212M16—42no—
213M16—42no—
214M16—5844no—
215C2×C8—42no—
216C2×C8—1464no—
217C4⋊C4—22no—
218C4⋊C4—2921no—
219C4⋊C4—2921no—
220C4⋊C4—2921no—
221C4⋊C4—2921no—
222C4⋊C4—5842no—
223C4⋊C4—1462no—
224C22⋊C4—24no—
225C22⋊C4—2924no—
226C22⋊C4—5842no—
227C42—2922no—
228C42D4×D7312yes—
229C42#1192402712yes—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—42no—
234C23—42no—
235C23C2×#1192400511yescharacteristic
236Q8—2922no—
237Q8—1464no—
238D4—42no—
239D4—42no—
240C2×C4—22no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—44no—
244C2×C4—42no—
245C2×C4—82no—
246C2×C4—2921no—
247C2×C4—2921no—
248C2×C4—2922no—
249C2×C4—2921no—
250C2×C4—2922no—
251C2×C4—2921no—
252C2×C4—2921no—
253C2×C4—2922no—
254C2×C4—1462no—
255C2×C4#1455655112yes—
256C2×C4#1455656111yescharacteristic
257C2×C4#1455656312yes—
258C2×C4#1455657511yescharacteristic
259C2×C4#1455661711yescharacteristic
260C2×C4#1455662112yes—
261C2×C4#1455662211yescharacteristic
262C8—82no—
263C8—2924no—
264C22—21no—
265C22—21no—
266C22—44no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—82no—
271C22#1798846411yescharacteristic
272C22#1798858611yescharacteristic
273C22#1798859511yescharacteristic
274C4—21no—
275C4—21no—
276C4—22no—
277C4—42no—
278C4—2922no—
279C4—5842no—
280C4—5841no—
281C4#1798883112yes—
282C4#1798884312yes—
283C2—21no—
284C2—21no—
285C2—82no—
286C2#2261034711yescharacteristic
287C2#2261036211yescharacteristic
288C2#2261046111yescharacteristic
subgroupG/H
centerC22#17988464
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1800C2
socleC22×C73#386
prime radicalC22×D4×C73D4
cosocleC2×C42×C73C23
hypercenter#1800D73
hypocenterC73#9487
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
3. #22608359C2semidirect
4. #22607791C2semidirect
150. C73#9487semidirect

Maximal subgroups

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

subgroupindex
#226189722
#226152852
#226083592
#226077912
C73×#18002
#948773