Finite Group Databasebeta

← #32974247

Subgroups — #32974247

Order 18688.

436 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14556583C211yesmaximal, characteristic
2#22609784C211yesmaximal, characteristic
3#22607755C212yesmaximal
4#22607753C212yesmaximal
5C73×#1767C211yesmaximal, characteristic
6C2×#14556583C411yescharacteristic
7C2×C4⋊#10596831—21no—
8C2×#14556502—21no—
9#17988485C2211yescharacteristic
10#17988485C2211yescharacteristic
11#17988471—21no—
12#17988471—21no—
13#17988453C411yescharacteristic
14C4×#11924007—21no—
15C4×#11924007—21no—
16C4×C4⋊Dic73C411yescharacteristic
17C4×C4⋊Dic73C411yescharacteristic
18#17988342C2212yes—
19C2×C4⋊C8×C73—21no—
20C2×#97×C73—21no—
21C43×C73C2211yescharacteristic
22#336×C73C2212yes—
23C22×#10596831—22no—
24#14556583—22no—
25#14556583—22no—
26C2×C4⋊Dic73C2×C411yescharacteristic
27C2×C4⋊Dic73C2×C411yescharacteristic
28C2×C4⋊Dic73C2×C411yescharacteristic
29C2×C4⋊Dic73C2×C411yescharacteristic
30C2×#11924007—21no—
31C2×#11924007—21no—
32C2×#11924007—21no—
33C2×#11924007—21no—
34C2×C4×Dic73—21no—
35C2×C4×Dic73—21no—
36C4⋊#10596831—24no—
37#14556502—42no—
38#14556498—21no—
39#14556498—21no—
40#14556498—21no—
41#14556498—21no—
42#14556498—21no—
43#14556498—21no—
44C22×C8×C73—22no—
45C2×C42×C73C2×C411yescharacteristic
46C2×C42×C73C2×C411yescharacteristic
47C2×C42×C73D411yescharacteristic
48C2×C42×C73D411yescharacteristic
49C2×C42×C73D411yescharacteristic
50C2×C42×C73D411yescharacteristic
51C2×C42×C73C2311yescharacteristic
52C4⋊C8×C73—24no—
53#97×C73—42no—
54C22×Dic73—21no—
55C22×Dic73—21no—
56C22×Dic73—21no—
57C22×Dic73—21no—
58C2×#10596831—24no—
59C2×#10596831—42no—
60C2×#10596831—42no—
61C4⋊Dic73—21no—
62C4⋊Dic73—21no—
63C4⋊Dic73—41no—
64C4⋊Dic73—41no—
65C4⋊Dic73M1612yes—
66C4⋊Dic73M1612yes—
67#11924007—24no—
68#11924007—24no—
69#11924007—41no—
70#11924007—41no—
71#11924007—41no—
72#11924007—41no—
73C4×Dic73—42no—
74C4×Dic73—42no—
75C22×C4×C73C22⋊C411yescharacteristic
76C22×C4×C73C22⋊C411yescharacteristic
77C22×C4×C73C22⋊C411yescharacteristic
78C22×C4×C73C22⋊C411yescharacteristic
79C22×C4×C73C22×C411yescharacteristic
80C22×C4×C73C2×D411yescharacteristic
81C22×C4×C73C2×D411yescharacteristic
82C2×C8×C73—24no—
83C2×C8×C73—42no—
84C2×C8×C73—42no—
85C42×C73—22no—
86C42×C73—22no—
87C42×C73—22no—
88C42×C73—21no—
89C42×C73—21no—
90C42×C73—21no—
91C42×C73—21no—
92C42×C73—21no—
93C42×C73—21no—
94C42×C73—41no—
95C23×C73C2×C22⋊C411yescharacteristic
96C2×C4×C73—21no—
97C2×C4×C73—21no—
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—21no—
105C2×C4×C73—21no—
106C2×C4×C73—21no—
107C2×C4×C73—21no—
108C2×C4×C73—21no—
109C2×C4×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73#10112yes—
112C2×C4×C73#10412yes—
113C2×C4×C73#10412yes—
114C2×C4×C73C2×M1611yescharacteristic
115C2×C4×C73C2×M1611yescharacteristic
116C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
118C2×C4×C73#13711yescharacteristic
119C2×C4×C73#13711yescharacteristic
120C2×Dic73—22no—
121C2×Dic73—22no—
122C2×Dic73—41no—
123C2×Dic73—41no—
124C2×Dic73—41no—
125C2×Dic73—41no—
126C2×Dic73—41no—
127C2×Dic73—41no—
128C2×Dic73—41no—
129C2×Dic73—41no—
130C2×Dic73—41no—
131C2×Dic73—41no—
132C8×C73—44no—
133#10596831—44no—
134C22×C73#40711yescharacteristic
135C22×C73#41011yescharacteristic
136C22×C73C2×#10111yescharacteristic
137C22×C73#41711yescharacteristic
138C22×C73#41711yescharacteristic
139C22×C73C2×#10411yescharacteristic
140C22×C73C2×#10411yescharacteristic
141C4×C73—21no—
142C4×C73—21no—
143C4×C73—21no—
144C4×C73—21no—
145C4×C73—21no—
146C4×C73—21no—
147C4×C73—41no—
148C4×C73—41no—
149C4×C73—41no—
150C4×C73#33014yes—
151Dic73—42no—
152Dic73—42no—
153Dic73—81no—
154Dic73—81no—
155#7636—731nomaximal, Sylow
156C2×C73#146711yescharacteristic
157C2×C73#148911yescharacteristic
158C2×C73#148911yescharacteristic
159C2×C73#150911yescharacteristic
160C2×C73#150911yescharacteristic
161C2×C73C2×#33011yescharacteristic
162C2×C73#156111yescharacteristic
163C4×#125—731no—
164#1767—731no—
165#1767D7311yescharacteristic
166#1271—732no—
167#1271—732no—
168C73#763611yescharacteristic, complemented, Sylow
169C2×#125—731no—
170C2×C4⋊C8—21no—
171C2×C4⋊C8—1461no—
172C2×#97—21no—
173C2×#97—1461no—
174#389—731no—
175#389—731no—
176#387—1461no—
177#387—1461no—
178#382—731no—
179C4×C4⋊C4—731no—
180C4×C4⋊C4—731no—
181C4×C4⋊C4—1461no—
182C4×C4⋊C4—1461no—
183C43C2×D7311yescharacteristic
184#336—732no—
185#336C2×D7312yes—
186C22×C8—22no—
187C22×C8—1462no—
188#125—1462no—
189#125—1462no—
190C2×C4⋊C4—731no—
191C2×C4⋊C4—731no—
192C2×C4⋊C4—731no—
193C2×C4⋊C4—731no—
194C2×C4⋊C4—1461no—
195C2×C4⋊C4—1461no—
196C2×C4⋊C4—1461no—
197C2×C4⋊C4—1461no—
198C2×C42—1461no—
199C2×C42—1461no—
200C2×C42C4×D7311yescharacteristic
201C2×C42C4×D7311yescharacteristic
202C2×C42D29211yescharacteristic
203C2×C42D29211yescharacteristic
204C2×C42C22⋊D7311yescharacteristic
205C2×C42C22⋊D7311yescharacteristic
206C2×C42C22×D7311yescharacteristic
207C4⋊C8—24no—
208C4⋊C8—1464no—
209#97—42no—
210#97—2922no—
211#95—1461no—
212#95—1461no—
213#95—1461no—
214#95—1461no—
215#95—1461no—
216#95—1461no—
217C22×C4—1461no—
218C22×C4—1461no—
219C22×C4—1461no—
220C22×C4—1461no—
221C22×C4#1192400511yescharacteristic
222C22×C4#1192400511yescharacteristic
223C22×C4#1192400511yescharacteristic
224C22×C4#1192400511yescharacteristic
225C22×C4C2×C4×D7311yescharacteristic
226C22×C4C2×C22⋊D7311yescharacteristic
227C22×C4C2×D29211yescharacteristic
228C2×C8—24no—
229C2×C8—42no—
230C2×C8—42no—
231C2×C8—2922no—
232C2×C8—2922no—
233C2×C8—1464no—
234C4⋊C4—2921no—
235C4⋊C4—2921no—
236C4⋊C4—2921no—
237C4⋊C4—2921no—
238C4⋊C4—2921no—
239C4⋊C4—2921no—
240C4⋊C4—732no—
241C4⋊C4—732no—
242C4⋊C4—1464no—
243C4⋊C4—1464no—
244C4⋊C4—1461no—
245C4⋊C4—1461no—
246C42—22no—
247C42—22no—
248C42—22no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—41no—
256C42—2922no—
257C42—2922no—
258C23C2×#1192400511yescharacteristic
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
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—1462no—
285C2×C4—1462no—
286C2×C4#1455650912yes—
287C2×C4#1455651712yes—
288C2×C4#1455651912yes—
289C2×C4M16×D7311yescharacteristic
290C2×C4M16×D7311yescharacteristic
291C2×C4#1455661711yescharacteristic
292C2×C4#1455661911yescharacteristic
293C2×C4#1455662211yescharacteristic
294C2×C4#1455662411yescharacteristic
295C8—44no—
296C8—2924no—
297C22#1798855011yescharacteristic
298C22#1798856011yescharacteristic
299C22C2×#1455650911yescharacteristic
300C22#1798858611yescharacteristic
301C22#1798858911yescharacteristic
302C22C2×#1455651711yescharacteristic
303C22C2×#1455651911yescharacteristic
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—21no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—2922no—
314C4—2922no—
315C4—5841no—
316C4—5841no—
317C4#1798832814yes—
318C2#2260827411yescharacteristic
319C2#2260836811yescharacteristic
320C2#2260837111yescharacteristic
321C2#2260845411yescharacteristic
322C2#2260845711yescharacteristic
323C2C2×#1798832811yescharacteristic
324C2#2260866811yescharacteristic
subgroupG/H
centerC23C2×#11924005
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1767C2
socle, prime radicalC23×C73C2×C22⋊C4
cosocleC2×C42×C73C23
hypercenter#1767D73
hypocenterC73#7636
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
168. C73#7636semidirect

Maximal subgroups

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

subgroupindex
C4×#145565832
#226097842
#226077552
#226077532
C73×#17672
#763673