Finite Group Databasebeta

← #32975121

Subgroups — #32975121

Order 18688.

338 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 83 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#22611489C211yesmaximal, characteristic
2#22611407C211yesmaximal, characteristic
3#22611402C211yesmaximal, characteristic
4#22607754C211yesmaximal, characteristic
5#22607754C211yesmaximal, characteristic
6#22607754C211yesmaximal, characteristic
7C73×#2810C211yesmaximal, characteristic
8C2×#14556524—21no—
9C2×#14556522—21no—
10#17988457C2211yescharacteristic
11#17988349—21no—
12#17988349—21no—
13#17988349—21no—
14#17988349—21no—
15#17988342C2211yescharacteristic
16#17988342C2211yescharacteristic
17#17988342C2211yescharacteristic
18#400×C73—21no—
19#400×C73—21no—
20#400×C73—21no—
21#389×C73C2211yescharacteristic
22#389×C73C2211yescharacteristic
23#389×C73C2211yescharacteristic
24#387×C73—21no—
25#387×C73—21no—
26#387×C73—21no—
27C22×#10596831—21no—
28C22×#10596831—21no—
29C22×#10596831—21no—
30C2×C4⋊Dic73—21no—
31C2×C4⋊Dic73—21no—
32C2×C4⋊Dic73—21no—
33#14556524—42no—
34#14556522—42no—
35C2×C4⋊C4×C73—21no—
36C2×C4⋊C4×C73—21no—
37C2×C4⋊C4×C73—21no—
38C2×C4⋊C4×C73D411yescharacteristic
39C2×C4⋊C4×C73D411yescharacteristic
40C2×C4⋊C4×C73D411yescharacteristic
41C2×C4⋊C4×C73D411yescharacteristic
42C2×C4⋊C4×C73D411yescharacteristic
43C2×C4⋊C4×C73D411yescharacteristic
44C2×C42×C73—21no—
45C2×C42×C73C2311yescharacteristic
46#95×C73—21no—
47#95×C73—21no—
48#95×C73—21no—
49#95×C73—21no—
50#95×C73—21no—
51#95×C73—21no—
52#95×C73—21no—
53#95×C73—21no—
54#95×C73—21no—
55#95×C73—21no—
56C22×Dic73—41no—
57C2×#10596831—22no—
58C2×#10596831—22no—
59C2×#10596831—41no—
60C2×#10596831—41no—
61C2×#10596831—41no—
62C2×#10596831—41no—
63C2×#10596831—41no—
64C2×#10596831—41no—
65C2×#10596831—41no—
66C4⋊Dic73—42no—
67C4⋊Dic73—41no—
68C4⋊Dic73—41no—
69C4⋊Dic73—41no—
70C4⋊Dic73—41no—
71C22×C4×C73—21no—
72C22×C4×C73—21no—
73C22×C4×C73—21no—
74C22×C4×C73—21no—
75C22×C4×C73—21no—
76C22×C4×C73—21no—
77C22×C4×C73C2×D411yescharacteristic
78C22×C4×C73C2×D411yescharacteristic
79C22×C4×C73C2×D411yescharacteristic
80C4⋊C4×C73—21no—
81C4⋊C4×C73—21no—
82C4⋊C4×C73—21no—
83C4⋊C4×C73—21no—
84C4⋊C4×C73—21no—
85C4⋊C4×C73—21no—
86C4⋊C4×C73—41no—
87C4⋊C4×C73—41no—
88C4⋊C4×C73—41no—
89C4⋊C4×C73—41no—
90C4⋊C4×C73—41no—
91C4⋊C4×C73—41no—
92C4⋊C4×C73—41no—
93C4⋊C4×C73—41no—
94C4⋊C4×C73—41no—
95C42×C73—41no—
96C42×C73—81no—
97C23×C73#12011yescharacteristic
98C2×C4×C73—21no—
99C2×C4×C73—21no—
100C2×C4×C73—21no—
101C2×C4×C73—21no—
102C2×C4×C73—21no—
103C2×C4×C73—21no—
104C2×C4×C73—41no—
105C2×C4×C73—41no—
106C2×C4×C73—41no—
107C2×C4×C73—41no—
108C2×C4×C73—41no—
109C2×C4×C73—41no—
110C2×C4×C73—41no—
111C2×C4×C73—41no—
112C2×C4×C73—41no—
113C2×C4×C73—41no—
114C2×C4×C73—41no—
115C2×C4×C73—41no—
116C2×C4×C73—41no—
117C2×C4×C73—41no—
118C2×C4×C73—41no—
119C2×C4×C73—41no—
120C2×C4×C73—41no—
121C2×C4×C73—41no—
122C2×C4×C73#13511yescharacteristic
123C2×C4×C73#13511yescharacteristic
124C2×C4×C73#13511yescharacteristic
125C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C73#13711yescharacteristic
128C2×Dic73—81no—
129C2×Dic73—81no—
130C2×Dic73—81no—
131#10596831—42no—
132#10596831—42no—
133#10596831—81no—
134C22×C73#44911yescharacteristic
135C22×C73#44911yescharacteristic
136C22×C73#45211yescharacteristic
137C22×C73#45411yescharacteristic
138C22×C73#45611yescharacteristic
139C22×C73#45611yescharacteristic
140C22×C73#45811yescharacteristic
141C4×C73—21no—
142C4×C73—21no—
143C4×C73—21no—
144C4×C73—21no—
145C4×C73—21no—
146C4×C73—21no—
147C4×C73—81no—
148C4×C73—81no—
149C4×C73—81no—
150C4×C73—81no—
151C4×C73—81no—
152C4×C73—81no—
153Dic73—161no—
154#7803—731nomaximal, Sylow
155C2×C73#160911yescharacteristic
156C2×C73#160911yescharacteristic
157C2×C73#161511yescharacteristic
158C2×C73#162811yescharacteristic
159C2×C73#165011yescharacteristic
160C2×C73#165211yescharacteristic
161C2×C73#166311yescharacteristic
162#2810D7311yescharacteristic
163#2099—731no—
164#2084—731no—
165#2083—731no—
166#1271—731no—
167#1271—731no—
168#1271—731no—
169C73#780311yescharacteristic, complemented, Sylow
170C2×#107—1461no—
171C2×#106—1461no—
172#400—21no—
173#400—21no—
174#400—21no—
175#389C2×D7311yescharacteristic
176#389C2×D7311yescharacteristic
177#389C2×D7311yescharacteristic
178#387—21no—
179#387—21no—
180#387—21no—
181#384—731no—
182#340—1461no—
183#340—1461no—
184#340—1461no—
185#340—1461no—
186#336—731no—
187#336—731no—
188#336—731no—
189C22×C8—1461no—
190C22×C8—1461no—
191C22×C8—1461no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—1461no—
196C2×C4⋊C4—1461no—
197C2×C4⋊C4—1461no—
198C2×C4⋊C4C22⋊D7311yescharacteristic
199C2×C4⋊C4C22⋊D7311yescharacteristic
200C2×C4⋊C4C22⋊D7311yescharacteristic
201C2×C4⋊C4C22⋊D7311yescharacteristic
202C2×C4⋊C4C22⋊D7311yescharacteristic
203C2×C4⋊C4C22⋊D7311yescharacteristic
204C2×C42—21no—
205C2×C42C22×D7311yescharacteristic
206#107—2922no—
207#106—2922no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—2921no—
225C22×C4C2×C22⋊D7311yescharacteristic
226C22×C4C2×C22⋊D7311yescharacteristic
227C22×C4C2×C22⋊D7311yescharacteristic
228C2×C8—2921no—
229C2×C8—2921no—
230C2×C8—2921no—
231C2×C8—2921no—
232C2×C8—2921no—
233C2×C8—2921no—
234C2×C8—2921no—
235C2×C8—1462no—
236C2×C8—1462no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—2922no—
253C4⋊C4—2921no—
254C4⋊C4—2921no—
255C4⋊C4—2921no—
256C4⋊C4—2921no—
257C42—41no—
258C42—81no—
259C23#1455656011yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—5841no—
285C2×C4—5841no—
286C2×C4—5841no—
287C2×C4#1455661111yescharacteristic
288C2×C4#1455661111yescharacteristic
289C2×C4#1455661111yescharacteristic
290C2×C4#1455661611yescharacteristic
291C2×C4#1455661611yescharacteristic
292C2×C4#1455662111yescharacteristic
293C8—2922no—
294C8—2922no—
295C8—5841no—
296C22#1798873211yescharacteristic
297C22#1798873211yescharacteristic
298C22#1798874911yescharacteristic
299C22#1798876011yescharacteristic
300C22#1798877011yescharacteristic
301C22#1798877011yescharacteristic
302C22#1798877711yescharacteristic
303C4—21no—
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—81no—
310C4—81no—
311C4—81no—
312C4—81no—
313C4—81no—
314C4—81no—
315C4—11681no—
316C2#2260892811yescharacteristic
317C2#2260892811yescharacteristic
318C2#2260896211yescharacteristic
319C2#2260904111yescharacteristic
320C2#2260918711yescharacteristic
321C2#2260920111yescharacteristic
322C2#2260925911yescharacteristic
subgroupG/H
centerC23#14556560
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#2810C2
socle, prime radicalC23×C73#120
hypercenter#2810D73
hypocenterC73#7803
LCSG ▷ C2×C42×C73 ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2810

Complements

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

NH ≅ G/Ntype
169. C73#7803semidirect

Maximal subgroups

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

subgroupindex
#226114892
#226114072
#226114022
#226077542
C73×#28102
#780373