Finite Group Databasebeta

← #32975124

Subgroups — #32975124

Order 18688.

338 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 79 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#22617922C211yesmaximal, characteristic
2#22611489C211yesmaximal, characteristic
3#22611409C211yesmaximal, characteristic
4#22611404C211yesmaximal, characteristic
5#22607755C211yesmaximal, characteristic
6#22607753C211yesmaximal, characteristic
7C73×#1271C211yesmaximal, characteristic
8C2×#14556525—21no—
9C2×#14556523—21no—
10#17988527—21no—
11#17988526—21no—
12#17988525—21no—
13#17988485C2211yescharacteristic
14#17988485C2211yescharacteristic
15#17988474—21no—
16#17988473—21no—
17#17988468—21no—
18#17988457C2211yescharacteristic
19#17988350—21no—
20#17988350—21no—
21#17988349—21no—
22#17988349—21no—
23#17988342C2211yescharacteristic
24#389×C73C2211yescharacteristic
25#336×C73C2211yescharacteristic
26#336×C73C2211yescharacteristic
27C22×#10596831—21no—
28C2×C4⋊Dic73—21no—
29C2×C4⋊Dic73—21no—
30C2×C4⋊Dic73—21no—
31C2×C4⋊Dic73D411yescharacteristic
32C2×C4⋊Dic73D411yescharacteristic
33C2×C4⋊Dic73D411yescharacteristic
34C2×C4⋊Dic73D411yescharacteristic
35C2×#11924007—21no—
36C2×#11924007—21no—
37C2×C4×Dic73—21no—
38#14556525—42no—
39#14556523—42no—
40#14556498—21no—
41#14556498—21no—
42#14556498—21no—
43#14556498—21no—
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47#14556498—21no—
48#14556498—21no—
49C22×C8×C73—21no—
50C22×C8×C73—21no—
51C2×C4⋊C4×C73—21no—
52C2×C4⋊C4×C73D411yescharacteristic
53C2×C4⋊C4×C73D411yescharacteristic
54C2×C42×C73C2311yescharacteristic
55#95×C73—21no—
56C22×Dic73—21no—
57C22×Dic73—21no—
58C22×Dic73—21no—
59C22×Dic73—21no—
60C22×Dic73—41no—
61C2×#10596831—41no—
62C2×#10596831—41no—
63C2×#10596831—41no—
64C4⋊Dic73—21no—
65C4⋊Dic73—21no—
66C4⋊Dic73—21no—
67C4⋊Dic73—21no—
68C4⋊Dic73—41no—
69C4⋊Dic73—41no—
70C4⋊Dic73—42no—
71C4⋊Dic73—41no—
72C4⋊Dic73—41no—
73C4⋊Dic73—41no—
74C4⋊Dic73—41no—
75#11924007—41no—
76#11924007—41no—
77#11924007—41no—
78#11924007—41no—
79C4×Dic73—81no—
80C22×C4×C73—21no—
81C22×C4×C73—21no—
82C22×C4×C73C2×D411yescharacteristic
83C22×C4×C73C2×D411yescharacteristic
84C22×C4×C73C2×D411yescharacteristic
85C2×C8×C73—22no—
86C2×C8×C73—22no—
87C2×C8×C73—41no—
88C2×C8×C73—41no—
89C2×C8×C73—41no—
90C2×C8×C73—41no—
91C4⋊C4×C73—21no—
92C4⋊C4×C73—21no—
93C4⋊C4×C73—41no—
94C4⋊C4×C73—41no—
95C4⋊C4×C73—41no—
96C42×C73—41no—
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#13511yescharacteristic
111C2×C4×C73#13511yescharacteristic
112C2×C4×C73#13511yescharacteristic
113C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
114C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
115C2×C4×C73#13711yescharacteristic
116C2×Dic73—41no—
117C2×Dic73—41no—
118C2×Dic73—41no—
119C2×Dic73—41no—
120C2×Dic73—41no—
121C2×Dic73—41no—
122C2×Dic73—41no—
123C2×Dic73—41no—
124C2×Dic73—41no—
125C2×Dic73—41no—
126C2×Dic73—41no—
127C2×Dic73—41no—
128C2×Dic73—81no—
129C2×Dic73—81no—
130C2×Dic73—81no—
131C8×C73—42no—
132C8×C73—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—
149Dic73—81no—
150Dic73—81no—
151Dic73—81no—
152Dic73—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#2810—731no—
163#2099—731no—
164#2084—731no—
165#2083—731no—
166#1271—731no—
167#1271—731no—
168#1271D7311yescharacteristic
169C73#780311yescharacteristic, complemented, Sylow
170C2×#107—1461no—
171C2×#106—1461no—
172#400—1461no—
173#400—1461no—
174#400—1461no—
175#389—731no—
176#389—731no—
177#389C2×D7311yescharacteristic
178#387—1461no—
179#387—1461no—
180#387—1461no—
181#384—731no—
182#340—1461no—
183#340—1461no—
184#340—1461no—
185#340—1461no—
186#336—731no—
187#336C2×D7311yescharacteristic
188#336C2×D7311yescharacteristic
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—1461no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—731no—
194C2×C4⋊C4—731no—
195C2×C4⋊C4—731no—
196C2×C4⋊C4—731no—
197C2×C4⋊C4—1461no—
198C2×C4⋊C4—1461no—
199C2×C4⋊C4—1461no—
200C2×C4⋊C4—1461no—
201C2×C4⋊C4—1461no—
202C2×C4⋊C4D29211yescharacteristic
203C2×C4⋊C4D29211yescharacteristic
204C2×C42—1461no—
205C2×C42C22×D7311yescharacteristic
206#107—2922no—
207#106—2922no—
208#95—21no—
209#95—1461no—
210#95—1461no—
211#95—1461no—
212#95—1461no—
213#95—1461no—
214#95—1461no—
215#95—1461no—
216#95—1461no—
217#95—1461no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—2921no—
221C22×C4—1461no—
222C22×C4—1461no—
223C22×C4—1461no—
224C22×C4—1461no—
225C22×C4D4×D7311yescharacteristic
226C22×C4D4×D7311yescharacteristic
227C22×C4C2×D29211yescharacteristic
228C2×C8—22no—
229C2×C8—22no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—2921no—
235C2×C8—2921no—
236C2×C8—2921no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—2921no—
243C4⋊C4—2921no—
244C4⋊C4—2922no—
245C4⋊C4—2921no—
246C4⋊C4—2921no—
247C4⋊C4—2921no—
248C4⋊C4—2921no—
249C4⋊C4—2921no—
250C4⋊C4—2921no—
251C4⋊C4—2921no—
252C4⋊C4—2921no—
253C4⋊C4—1461no—
254C4⋊C4—1461no—
255C4⋊C4—1461no—
256C4⋊C4—1461no—
257C42—41no—
258C42—5841no—
259C23#1455656111yescharacteristic
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—2921no—
273C2×C4—2921no—
274C2×C4—2921no—
275C2×C4—2921no—
276C2×C4—2921no—
277C2×C4—2921no—
278C2×C4—2921no—
279C2×C4—2921no—
280C2×C4—2921no—
281C2×C4—2921no—
282C2×C4—2921no—
283C2×C4—2921no—
284C2×C4—5841no—
285C2×C4—5841no—
286C2×C4—5841no—
287C2×C4#1455661211yescharacteristic
288C2×C4#1455661311yescharacteristic
289C2×C4#1455661411yescharacteristic
290C2×C4#1455661511yescharacteristic
291C2×C4#1455661811yescharacteristic
292C2×C4#1455662411yescharacteristic
293C8—42no—
294C8—42no—
295C8—5841no—
296C22#1798873311yescharacteristic
297C22#1798873511yescharacteristic
298C22#1798875111yescharacteristic
299C22#1798876211yescharacteristic
300C22#1798877111yescharacteristic
301C22#1798877111yescharacteristic
302C22#1798877811yescharacteristic
303C4—21no—
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—81no—
310C4—81no—
311C4—5841no—
312C4—5841no—
313C4—5841no—
314C4—5841no—
315C4—11681no—
316C2#2260892911yescharacteristic
317C2#2260893111yescharacteristic
318C2#2260896411yescharacteristic
319C2#2260904211yescharacteristic
320C2#2260919011yescharacteristic
321C2#2260920411yescharacteristic
322C2#2260926011yescharacteristic
subgroupG/H
centerC23#14556561
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1271C2
socle, prime radicalC23×C73#120
hypercenter#1271D73
hypocenterC73#7803
LCSG ▷ C2×C42×C73 ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

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
#226179222
#226114892
#226114092
#226114042
#226077552
#226077532
C73×#12712
#780373