Finite Group Databasebeta

← #33001986

Subgroups — #33001986

Order 18688.

468 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 95 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#22612500C211yesmaximal, characteristic
2C2×#17988385C212yesmaximal
3#22609925C212yesmaximal
4#22608058C211yesmaximal, characteristic
5C73×#1394C211yesmaximal, characteristic
6C2×#14556589C2211yescharacteristic
7C2×Q8×Dic73C2211yescharacteristic
8C2×#14556556C411yescharacteristic
9#17988610—22no—
10C2×#14556510C2212yes—
11#17988493C411yescharacteristic
12#17988484—22no—
13#17988456C411yescharacteristic
14#17988438—22no—
15C42×Dic73C411yescharacteristic
16#17988385—24no—
17#17988355—22no—
18C2×#101×C73C2212yes—
19#391×C73C2211yescharacteristic
20C22×Dic146C2×C411yescharacteristic
21C2×#11924012—22no—
22#14556589—22no—
23#14556589D412yes—
24#14556589Q812yes—
25Q8×Dic73—41no—
26Q8×Dic73—41no—
27#14556556—41no—
28#14556556—41no—
29C2×C4⋊Dic73C2×C411yescharacteristic
30C2×C4⋊Dic73D412yes—
31C2×#11924007—22no—
32C2×#11924007—21no—
33C2×#11924007—22no—
34C2×C4×Dic73—21no—
35C2×C4×Dic73—21no—
36C2×C4×Dic73—21no—
37C2×C4×Dic73C2×C411yescharacteristic
38C2×C4×Dic73C2×C411yescharacteristic
39C2×C4×Dic73D412yes—
40#14556520—42no—
41#14556520—42no—
42#14556510—22no—
43#14556510—22no—
44#14556498—22no—
45C22×Q8×C73C2311yescharacteristic
46C2×M16×C73—22no—
47C2×C4⋊C4×C73C2×C411yescharacteristic
48C2×C42×C73C2×C411yescharacteristic
49#101×C73—22no—
50#101×C73—22no—
51#95×C73—22no—
52C2×Dic146—21no—
53C2×Dic146—41no—
54C2×Dic146—41no—
55C2×Dic146C4⋊C412yes—
56C22×Dic73—21no—
57C22×Dic73—21no—
58C22×Dic73C22⋊C411yescharacteristic
59C22×Dic73C22⋊C412yes—
60C22×Dic73C22⋊C411yescharacteristic
61#11924012—42no—
62#11924012—42no—
63C2×#10596831—42no—
64C4⋊Dic73—41no—
65C4⋊Dic73—42no—
66#11924007—24no—
67#11924007—24no—
68#11924007—44no—
69#11924007—42no—
70C4×Dic73—24no—
71C4×Dic73—21no—
72C4×Dic73—22no—
73C4×Dic73—22no—
74C4×Dic73—21no—
75C4×Dic73—21no—
76C4×Dic73—42no—
77C4×Dic73—41no—
78C4×Dic73—41no—
79C4×Dic73C4⋊C412yes—
80C2×Q8×C73—41no—
81C2×Q8×C73—41no—
82C2×Q8×C73C2×D411yescharacteristic
83C2×Q8×C73C2×Q811yescharacteristic
84C2×Q8×C73#4112yes—
85C22×C4×C73—21no—
86C22×C4×C73—21no—
87C22×C4×C73C22×C411yescharacteristic
88C22×C4×C73C2×D412yes—
89M16×C73—42no—
90M16×C73—42no—
91C2×C8×C73—42no—
92C4⋊C4×C73—41no—
93C42×C73—41no—
94C23×C73C2×C22⋊C411yescharacteristic
95Q8×C73—41no—
96Q8×C73—41no—
97Q8×C73—42no—
98C2×C4×C73—21no—
99C2×C4×C73—22no—
100C2×C4×C73—21no—
101C2×C4×C73—22no—
102C2×C4×C73—22no—
103C2×C4×C73—41no—
104C2×C4×C73—41no—
105C2×C4×C73—42no—
106C2×C4×C73—41no—
107C2×C4×C73C2×C4⋊C411yescharacteristic
108C2×C4×C73#11711yescharacteristic
109C2×C4×C73#12112yes—
110C2×C4×C73C22⋊Q812yes—
111C2×Dic73—22no—
112C2×Dic73—22no—
113C2×Dic73—22no—
114C2×Dic73—22no—
115C2×Dic73—22no—
116C2×Dic73—21no—
117C2×Dic73—22no—
118C2×Dic73—41no—
119C2×Dic73—41no—
120C2×Dic73—41no—
121C2×Dic73—42no—
122C2×Dic73#9911yescharacteristic
123C2×Dic73#9911yescharacteristic
124Dic146—42no—
125Dic146—42no—
126C8×C73—82no—
127#10596831—82no—
128C22×C73—21no—
129C22×C73—21no—
130C22×C73#38011yescharacteristic
131C22×C73C2×#9911yescharacteristic
132C22×C73#41011yescharacteristic
133C4×C73—22no—
134C4×C73—21no—
135C4×C73—21no—
136C4×C73—22no—
137C4×C73—42no—
138C4×C73—81no—
139Dic73—24no—
140Dic73—21no—
141Dic73—42no—
142Dic73—41no—
143Dic73—42no—
144Dic73#35612yescomplemented
145#12802—731nomaximal, Sylow
146C2×C73—21no—
147C2×C73—21no—
148C2×C73#179911yescharacteristic
149C2×C73C2×#35611yescharacteristic
150C2×C73#213211yescharacteristic
151C4×C4⋊Q8—731no—
152C2×#356—732no—
153#1801—732no—
154#1394—731no—
155#1394D7311yescharacteristic
156C73#1280211yescharacteristic, complemented, Sylow
157C2×C4⋊Q8—731no—
158C2×C4×Q8—731no—
159C2×C4×Q8—731no—
160#423—1462no—
161C2×#101—732no—
162C2×#101C2×D7312yes—
163#391—731no—
164#391C2×D7311yescharacteristic
165#389—1462no—
166#384—731no—
167C4×C4⋊C4—1462no—
168C43—731no—
169#356—1464no—
170#343—1462no—
171C22×Q8—731no—
172C22×Q8C22×D7311yescharacteristic
173C2×M16—22no—
174C2×M16—1462no—
175C4⋊Q8—732no—
176C4⋊Q8—732no—
177C4⋊Q8—1462no—
178C4×Q8—2921no—
179C4×Q8—2921no—
180C4×Q8—2921no—
181C4×Q8—2921no—
182C2×C4⋊C4—731no—
183C2×C4⋊C4—732no—
184C2×C4⋊C4—1461no—
185C2×C4⋊C4—1462no—
186C2×C4⋊C4—1462no—
187C2×C4⋊C4C4×D7311yescharacteristic
188C2×C42—731no—
189C2×C42—731no—
190C2×C42—732no—
191C2×C42—1461no—
192C2×C42—1461no—
193C2×C42—1461no—
194C2×C42C4×D7311yescharacteristic
195C4⋊C8—2922no—
196C4⋊C8—2922no—
197#101—22no—
198#101—22no—
199#101—1462no—
200#101—1462no—
201#95—22no—
202#95—1462no—
203C2×Q8—41no—
204C2×Q8—41no—
205C2×Q8—2921no—
206C2×Q8—2921no—
207C2×Q8—732no—
208C2×Q8—1461no—
209C2×Q8D4×D7311yescharacteristic
210C2×Q8Q8×D7311yescharacteristic
211C2×Q8#1192402812yes—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—732no—
215C22×C4—731no—
216C22×C4—731no—
217C22×C4—1461no—
218C22×C4—1461no—
219C22×C4C2×C4×D7311yescharacteristic
220C22×C4D4×D7312yes—
221M16—42no—
222M16—42no—
223M16—2922no—
224M16—2922no—
225C2×C8—42no—
226C2×C8—2922no—
227C4⋊C4—41no—
228C4⋊C4—2921no—
229C4⋊C4—2922no—
230C4⋊C4—2924no—
231C4⋊C4—2922no—
232C4⋊C4—1464no—
233C4⋊C4—1464no—
234C42—41no—
235C42—2921no—
236C42—2921no—
237C42—2922no—
238C42—732no—
239C42—1462no—
240C42—1462no—
241C42—1461no—
242C42—1461no—
243C42—1464no—
244C42—1461no—
245C23C22⋊C4×D7311yescharacteristic
246Q8—41no—
247Q8—41no—
248Q8—42no—
249Q8—2922no—
250Q8—2922no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—2921no—
261C2×C4—2921no—
262C2×C4—2921no—
263C2×C4—2922no—
264C2×C4—731no—
265C2×C4—731no—
266C2×C4—1462no—
267C2×C4—1461no—
268C2×C4—1462no—
269C2×C4—1462no—
270C2×C4—1462no—
271C2×C4—1462no—
272C2×C4—1462no—
273C2×C4C4⋊C4×D7311yescharacteristic
274C2×C4#1455654811yescharacteristic
275C2×C4#1455656412yes—
276C2×C4#1455656912yes—
277C8—82no—
278C8—5842no—
279C22—21no—
280C22—21no—
281C22#1798844611yescharacteristic
282C22#99×D7311yescharacteristic
283C22#1798855911yescharacteristic
284C4—22no—
285C4—21no—
286C4—21no—
287C4—22no—
288C4—42no—
289C4—81no—
290C4—2921no—
291C4—2922no—
292C4—2922no—
293C4—732no—
294C4—1464no—
295C4—1461no—
296C2—21no—
297C2—21no—
298C2#2260991811yescharacteristic
299C2#356×D7311yescharacteristic
300C2#2261161311yescharacteristic
subgroupG/H
centerC22#99×D73
commutatorC22×C4×C73C22×C4
FrattiniC22×Q8C22×D73
FittingC73×#1394C2
socleC22×C73C2×#99
prime radicalC23×C73C2×C22⋊C4
cosocleC22×Q8×C73C23
hypercenter#1394D73
hypocenterC73#12802
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1394

Complements

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

NH ≅ G/Ntype
144. Dic73#356semidirect
156. C73#12802semidirect

Maximal subgroups

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

subgroupindex
#226125002
C2×#179883852
#226099252
#226080582
C73×#13942
#1280273