Finite Group Databasebeta

← #33060883

Subgroups — #33060883

Order 18688.

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

normal subgroups only

This group has 906 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#22621075C212yesmaximal
3#22608938C218yesmaximal
4#22608429C212yesmaximal
5#22608255C211yesmaximal, characteristic
6C73×#2546C211yesmaximal, characteristic
7Q8×Dic146—22no—
8#17989316—22no—
9#17989313—24no—
10#17989218—21no—
11#17989218C2214yes—
12#17989144—22no—
13#17989144C2212yes—
14#17989065—21no—
15#17988983—22no—
16#17988939—22no—
17#17988917C2218yes—
18#17988869—24no—
19#17988640C2212yes—
20#17988323C2218yes—
21#17988313C2214yes—
22C2×C4⋊Q8×C73—21no—
23C2×C4⋊Q8×C73C2211yescharacteristic
24C2×C4×Q8×C73C2211yescharacteristic
25#398×C73C2214yes—
26#391×C73—21no—
27#389×C73—22no—
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#14556522—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—44no—
60C4×Q8×C73—22no—
61C4×Q8×C73—22no—
62C2×C4⋊C4×C73—21no—
63C2×C4⋊C4×C73—21no—
64C2×C4⋊C4×C73—24no—
65C2×C4⋊C4×C73D411yescharacteristic
66C2×C4⋊C4×C73C2312yes—
67C2×C4⋊C4×C73C2312yes—
68C2×C42×C73—21no—
69C2×C42×C73D412yes—
70C2×C42×C73C2311yescharacteristic
71#95×C73—24no—
72#95×C73C2312yes—
73C2×Dic146—22no—
74C2×Dic146—24no—
75C2×Dic146C2×D414yes—
76C2×#10596831—24no—
77C4⋊Dic73—24no—
78C4⋊Dic73—24no—
79C4⋊Dic73—24no—
80C4⋊Dic73—22no—
81C4⋊Dic73—22no—
82C4⋊Dic73—22no—
83C4⋊Dic73C2×D414yes—
84#11924007—28no—
85#11924007—24no—
86#11924007—24no—
87C22⋊Dic73—24no—
88C4×Dic73—28no—
89C4×Dic73—24no—
90C2×Q8×C73—22no—
91C2×Q8×C73—22no—
92C2×Q8×C73—42no—
93C2×Q8×C73—42no—
94C2×Q8×C73—42no—
95C2×Q8×C73SD1614yes—
96C22×C4×C73—22no—
97C22×C4×C73—22no—
98C22×C4×C73C2×D411yescharacteristic
99C22×C4×C73C2×D412yes—
100C22×C4×C73C2×D412yes—
101C22×C4×C73C2×D411yescharacteristic
102C22×C4×C73C2411yescharacteristic
103C4⋊C4×C73—24no—
104C4⋊C4×C73—22no—
105C4⋊C4×C73—24no—
106C4⋊C4×C73—24no—
107C4⋊C4×C73—41no—
108C4⋊C4×C73—41no—
109C4⋊C4×C73—48no—
110C42×C73—22no—
111C42×C73—22no—
112C42×C73—42no—
113C42×C73C2×D412yes—
114C42×C73C2×D412yes—
115C23×C73C22×D411yescharacteristic
116Q8×C73—28no—
117Q8×C73—84no—
118C2×C4×C73—22no—
119C2×C4×C73—22no—
120C2×C4×C73—22no—
121C2×C4×C73—24no—
122C2×C4×C73—22no—
123C2×C4×C73—41no—
124C2×C4×C73—42no—
125C2×C4×C73—42no—
126C2×C4×C73—42no—
127C2×C4×C73—42no—
128C2×C4×C73—42no—
129C2×C4×C73—42no—
130C2×C4×C73#12011yescharacteristic
131C2×C4×C73#12012yes—
132C2×C4×C73#12011yescharacteristic
133C2×C4×C73C2×SD1614yes—
134C2×C4×C73C2×SD1612yes—
135C2×C4×C73#13712yes—
136C2×C4×C73C22×D412yes—
137C2×Dic73—24no—
138C2×Dic73—24no—
139Dic146—44no—
140Dic146—44no—
141Dic146—84no—
142#10596831—44no—
143C22×C73—21no—
144C22×C73—21no—
145C22×C73C2×#12011yescharacteristic
146C22×C73C22×SD1611yescharacteristic
147C22×C73C2×#13711yescharacteristic
148C4×C73—24no—
149C4×C73—21no—
150C4×C73—22no—
151C4×C73—44no—
152C4×C73—42no—
153C4×C73—82no—
154C4×C73#44814yes—
155C4×C73#45612yes—
156Dic73—44no—
157Dic73—44no—
158#18410—731nomaximal, Sylow
159C2×C73—21no—
160C2×C73—21no—
161C2×C73C2×#44811yescharacteristic
162C2×C73C2×#45611yescharacteristic
163C2×C73#302811yescharacteristic
164#3502—731no—
165#3229—732no—
166#2546D7311yescharacteristic
167#1611—738no—
168#1503—732no—
169#1461—731no—
170C73#1841011yescharacteristic, complemented, Sylow
171Q82—1462no—
172#557—1464no—
173#557—1462no—
174#544—734no—
175#544—1461no—
176#533—732no—
177#533—1462no—
178C2×C4⋊Q8—21no—
179C2×C4⋊Q8C2×D7311yescharacteristic
180#519—1461no—
181C2×C4×Q8C2×D7311yescharacteristic
182#498—1462no—
183#487—1462no—
184#483—738no—
185#475—1464no—
186#431—732no—
187#398C2×D7314yes—
188#391—21no—
189#389—22no—
190C4×C4⋊C4C2×D7311yescharacteristic
191#328—738no—
192#324—734no—
193C22×Q8—21no—
194C22×Q8C22⋊D7311yescharacteristic
195C4⋊Q8—22no—
196C4⋊Q8—22no—
197C4⋊Q8—44no—
198C4⋊Q8—732no—
199C4⋊Q8—732no—
200C4⋊Q8—1462no—
201C4⋊Q8—1462no—
202C4⋊Q8—1468no—
203C4⋊Q8—1464no—
204#125—1464no—
205#125—1468no—
206#125—1464no—
207#125—1462no—
208C22⋊Q8—734no—
209C22⋊Q8—1462no—
210C22⋊Q8—1464no—
211C4×Q8—22no—
212C4×Q8—22no—
213C4×Q8—734no—
214C4×Q8—1464no—
215C4×Q8—1464no—
216C4×Q8—1464no—
217C4×Q8—1464no—
218C4×Q8—1462no—
219#117—1462no—
220#117—1464no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—24no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4C22⋊D7311yescharacteristic
225C2×C4⋊C4C22×D7312yes—
226C2×C4⋊C4C22×D7312yes—
227C2×C42—21no—
228C2×C42C22⋊D7312yes—
229C2×C42C22×D7311yescharacteristic
230#106—1468no—
231C4⋊C8—1462no—
232#103—1468no—
233C22⋊C8—734no—
234C4×C8—1462no—
235#95—24no—
236#95C22×D7312yes—
237C2×Q8—22no—
238C2×Q8—22no—
239C2×Q8—42no—
240C2×Q8—42no—
241C2×Q8—42no—
242C2×Q8—734no—
243C2×Q8—1464no—
244C2×Q8—1462no—
245C2×Q8#1192401614yes—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4C2×C22⋊D7311yescharacteristic
249C22×C4C2×C22⋊D7312yes—
250C22×C4C2×C22⋊D7312yes—
251C22×C4C2×C22⋊D7311yescharacteristic
252C22×C4C23×D7311yescharacteristic
253C2×C8—1464no—
254C4⋊C4—24no—
255C4⋊C4—22no—
256C4⋊C4—24no—
257C4⋊C4—24no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—48no—
261C4⋊C4—734no—
262C4⋊C4—1468no—
263C4⋊C4—1464no—
264C4⋊C4—1464no—
265C4⋊C4—1464no—
266C4⋊C4—1464no—
267C4⋊C4—1462no—
268C4⋊C4—1462no—
269C4⋊C4—1462no—
270C4⋊C4—1464no—
271C22⋊C4—1464no—
272C42—22no—
273C42—22no—
274C42—42no—
275C42—1468no—
276C42—1464no—
277C42D4×D7312yes—
278C42D4×D7312yes—
279C23C22×C22⋊D7311yescharacteristic
280Q8—28no—
281Q8—84no—
282Q8—2924no—
283Q8—2924no—
284Q8—5844no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—24no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—1464no—
298C2×C4—1464no—
299C2×C4#1455655911yescharacteristic
300C2×C4#1455655912yes—
301C2×C4#1455655911yescharacteristic
302C2×C4C2×#1192401614yes—
303C2×C4C2×#1192401612yes—
304C2×C4#1455662112yes—
305C2×C4C2×D4×D7312yes—
306C8—2924no—
307C22—21no—
308C22—21no—
309C22C2×#1455655911yescharacteristic
310C22C22×#1192401611yescharacteristic
311C22C2×#1455662111yescharacteristic
312C4—21no—
313C4—22no—
314C4—24no—
315C4—44no—
316C4—42no—
317C4—82no—
318C4—2924no—
319C4—2924no—
320C4#1798872514yes—
321C4#1798876912yes—
322C2—21no—
323C2—21no—
324C2C2×#1798872511yescharacteristic
325C2C2×#1798876911yescharacteristic
326C2#2261933611yescharacteristic
subgroupG/H
centerC22C2×#14556559
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#2546C2
socleC22×C73C2×#120
prime radicalC23×C73C22×D4
hypercenter#2546D73
hypocenterC73#18410
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2546

Complements

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

NH ≅ G/Ntype
170. C73#18410semidirect

Maximal subgroups

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

subgroupindex
#226237412
#226210752
#226089382
#226084292
#226082552
C73×#25462
#1841073