Finite Group Databasebeta

← #33060889

Subgroups — #33060889

Order 18688.

870 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 870 conjugacy classes of subgroups — too many to draw. Only its 191 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#22623741C211yesmaximal, characteristic
2#22621082C212yesmaximal
3#22608972C218yesmaximal
4#22608429C212yesmaximal
5#22608255C211yesmaximal, characteristic
6C73×#2568C211yesmaximal, characteristic
7Q8×Dic146—22no—
8#17989316—22no—
9#17989313—24no—
10#17989218—21no—
11#17989218C2214yes—
12#17989144—22no—
13#17989144C2212yes—
14#17989065—21no—
15#17988990—22no—
16#17988939—22no—
17#17988922C2218yes—
18#17988879—24no—
19#17988640C2212yes—
20#17988323C2218yes—
21#17988313C2214yes—
22C2×C4⋊Q8×C73C2211yescharacteristic
23C2×C4×Q8×C73C2211yescharacteristic
24#400×C73C2214yes—
25#391×C73—21no—
26#391×C73—22no—
27#382×C73—21no—
28C4×C4⋊C4×C73C2211yescharacteristic
29#14556591—22no—
30#14556591—22no—
31#14556591D412yes—
32#14556591D412yes—
33#14556590—24no—
34#14556590—28no—
35#14556583—24no—
36#14556583—22no—
37#14556582—24no—
38#14556582—28no—
39#14556570—22no—
40#14556570—24no—
41#14556570C2314yes—
42Q8×Dic73—24no—
43Q8×Dic73—24no—
44C4×Dic146—24no—
45C4×Dic146—24no—
46C4×Dic146—22no—
47C4×Dic146D414yes—
48#14556550—24no—
49#14556550—22no—
50#14556524—28no—
51C4⋊#10596831—22no—
52#14556514—28no—
53C22⋊#10596831C2314yes—
54C4×#10596831—22no—
55C22×Q8×C73—21no—
56C22×Q8×C73D411yescharacteristic
57C4⋊Q8×C73—22no—
58C4⋊Q8×C73—22no—
59C4×Q8×C73—22no—
60C4×Q8×C73—22no—
61C2×C4⋊C4×C73—21no—
62C2×C4⋊C4×C73—21no—
63C2×C4⋊C4×C73D411yescharacteristic
64C2×C4⋊C4×C73C2312yes—
65C2×C4⋊C4×C73C2312yes—
66C2×C42×C73—21no—
67C2×C42×C73D412yes—
68C2×C42×C73C2311yescharacteristic
69#95×C73—24no—
70#95×C73—24no—
71#95×C73C2312yes—
72C2×Dic146—22no—
73C2×Dic146—24no—
74C2×Dic146C2×D414yes—
75C2×#10596831—24no—
76C4⋊Dic73—24no—
77C4⋊Dic73—24no—
78C4⋊Dic73—24no—
79C4⋊Dic73—22no—
80C4⋊Dic73—22no—
81C4⋊Dic73—22no—
82C4⋊Dic73C2×D414yes—
83#11924007—28no—
84#11924007—24no—
85#11924007—24no—
86C22⋊Dic73—24no—
87C4×Dic73—28no—
88C4×Dic73—24no—
89C2×Q8×C73—22no—
90C2×Q8×C73—22no—
91C2×Q8×C73—44no—
92C2×Q8×C73—41no—
93C2×Q8×C73—41no—
94C2×Q8×C73Q1614yes—
95C22×C4×C73—22no—
96C22×C4×C73—22no—
97C22×C4×C73C2×D411yescharacteristic
98C22×C4×C73C2×D412yes—
99C22×C4×C73C2×D412yes—
100C22×C4×C73C2×D411yescharacteristic
101C22×C4×C73C2411yescharacteristic
102C4⋊C4×C73—22no—
103C4⋊C4×C73—24no—
104C4⋊C4×C73—24no—
105C4⋊C4×C73—42no—
106C4⋊C4×C73—42no—
107C42×C73—22no—
108C42×C73—22no—
109C42×C73—42no—
110C42×C73C2×D412yes—
111C42×C73C2×D412yes—
112C23×C73C22×D411yescharacteristic
113Q8×C73—28no—
114Q8×C73—82no—
115Q8×C73—82no—
116C2×C4×C73—22no—
117C2×C4×C73—22no—
118C2×C4×C73—22no—
119C2×C4×C73—22no—
120C2×C4×C73—41no—
121C2×C4×C73—42no—
122C2×C4×C73—42no—
123C2×C4×C73—42no—
124C2×C4×C73—44no—
125C2×C4×C73—42no—
126C2×C4×C73—42no—
127C2×C4×C73#12011yescharacteristic
128C2×C4×C73#12012yes—
129C2×C4×C73#12011yescharacteristic
130C2×C4×C73C2×Q1614yes—
131C2×C4×C73C2×Q1612yes—
132C2×C4×C73#13712yes—
133C2×C4×C73C22×D412yes—
134C2×Dic73—24no—
135C2×Dic73—24no—
136Dic146—44no—
137Dic146—44no—
138Dic146—84no—
139#10596831—44no—
140C22×C73—21no—
141C22×C73—21no—
142C22×C73C2×#12011yescharacteristic
143C22×C73C22×Q1611yescharacteristic
144C22×C73C2×#13711yescharacteristic
145C4×C73—24no—
146C4×C73—21no—
147C4×C73—22no—
148C4×C73—42no—
149C4×C73—82no—
150C4×C73—82no—
151C4×C73#45114yes—
152C4×C73#45412yes—
153Dic73—44no—
154Dic73—44no—
155#18411—731nomaximal, Sylow
156C2×C73—21no—
157C2×C73—21no—
158C2×C73C2×#45111yescharacteristic
159C2×C73C2×#45411yescharacteristic
160C2×C73#302811yescharacteristic
161#3502—731no—
162#3230—732no—
163#2568D7311yescharacteristic
164#1617—738no—
165#1503—732no—
166#1461—731no—
167C73#1841111yescharacteristic, complemented, Sylow
168Q82—1462no—
169#557—1464no—
170#557—1462no—
171#544—734no—
172#544—1461no—
173#533—732no—
174#533—1462no—
175C2×C4⋊Q8C2×D7311yescharacteristic
176#519—1461no—
177C2×C4×Q8C2×D7311yescharacteristic
178#500—1462no—
179#487—1462no—
180#484—738no—
181#477—1464no—
182#431—732no—
183#400C2×D7314yes—
184#391—21no—
185#391—22no—
186#382—21no—
187C4×C4⋊C4C2×D7311yescharacteristic
188#328—738no—
189#324—734no—
190C22×Q8—21no—
191C22×Q8C22⋊D7311yescharacteristic
192C4⋊Q8—22no—
193C4⋊Q8—22no—
194C4⋊Q8—732no—
195C4⋊Q8—732no—
196C4⋊Q8—1462no—
197C4⋊Q8—1462no—
198C4⋊Q8—1468no—
199C4⋊Q8—1464no—
200#125—1464no—
201#125—1468no—
202#125—1464no—
203#125—1462no—
204C22⋊Q8—734no—
205C22⋊Q8—1462no—
206C22⋊Q8—1464no—
207C4×Q8—22no—
208C4×Q8—22no—
209C4×Q8—734no—
210C4×Q8—1464no—
211C4×Q8—1464no—
212C4×Q8—1464no—
213C4×Q8—1464no—
214C4×Q8—1462no—
215#117—1462no—
216#117—1464no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4C22⋊D7311yescharacteristic
220C2×C4⋊C4C22×D7312yes—
221C2×C4⋊C4C22×D7312yes—
222C2×C42—21no—
223C2×C42C22⋊D7312yes—
224C2×C42C22×D7311yescharacteristic
225#107—1468no—
226C4⋊C8—1462no—
227#103—1468no—
228C22⋊C8—734no—
229C4×C8—1462no—
230#95—24no—
231#95—24no—
232#95C22×D7312yes—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8—44no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—734no—
239C2×Q8—1464no—
240C2×Q8—1462no—
241C2×Q8#1192401814yes—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4C2×C22⋊D7311yescharacteristic
245C22×C4C2×C22⋊D7312yes—
246C22×C4C2×C22⋊D7312yes—
247C22×C4C2×C22⋊D7311yescharacteristic
248C22×C4C23×D7311yescharacteristic
249C2×C8—1464no—
250C4⋊C4—22no—
251C4⋊C4—24no—
252C4⋊C4—24no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—734no—
256C4⋊C4—1468no—
257C4⋊C4—1464no—
258C4⋊C4—1464no—
259C4⋊C4—1464no—
260C4⋊C4—1464no—
261C4⋊C4—1462no—
262C4⋊C4—1462no—
263C4⋊C4—1462no—
264C4⋊C4—1464no—
265C22⋊C4—1464no—
266C42—22no—
267C42—22no—
268C42—42no—
269C42—1468no—
270C42—1464no—
271C42D4×D7312yes—
272C42D4×D7312yes—
273C23C22×C22⋊D7311yescharacteristic
274Q8—28no—
275Q8—82no—
276Q8—82no—
277Q8—2924no—
278Q8—2924no—
279Q8—5844no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—41no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—44no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—1464no—
292C2×C4—1464no—
293C2×C4#1455655911yescharacteristic
294C2×C4#1455655912yes—
295C2×C4#1455655911yescharacteristic
296C2×C4C2×#1192401814yes—
297C2×C4C2×#1192401812yes—
298C2×C4#1455662112yes—
299C2×C4C2×D4×D7312yes—
300C8—2924no—
301C22—21no—
302C22—21no—
303C22C2×#1455655911yescharacteristic
304C22C22×#1192401811yescharacteristic
305C22C2×#1455662111yescharacteristic
306C4—21no—
307C4—22no—
308C4—24no—
309C4—42no—
310C4—82no—
311C4—82no—
312C4—2924no—
313C4—2924no—
314C4#1798874214yes—
315C4#1798875912yes—
316C2—21no—
317C2—21no—
318C2C2×#1798874211yescharacteristic
319C2C2×#1798875911yescharacteristic
320C2#2261933611yescharacteristic
subgroupG/H
centerC22C2×#14556559
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#2568C2
socleC22×C73C2×#120
prime radicalC23×C73C22×D4
hypercenter#2568D73
hypocenterC73#18411
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2568

Complements

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

NH ≅ G/Ntype
167. C73#18411semidirect

Maximal subgroups

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

subgroupindex
#226237412
#226210822
#226089722
#226084292
#226082552
C73×#25682
#1841173