Finite Group Databasebeta

← #33084121

Subgroups — #33084121

Order 18688.

1222 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988639C212yesmaximal
2C43×D73C211yesmaximal, characteristic
3#22609786C212yesmaximal, complemented
4#22609784C211yesmaximal, characteristic, complemented
5#22609694C212yesmaximal
6#22609692C212yesmaximal
7#22609675C212yesmaximal, complemented
8#97×Dic73C212yesmaximal, complemented
9C73×#1767C211yesmaximal, characteristic, complemented
10C2×C42×D73C412yes—
11C2×C42×D73C412yes—
12C2×C42×D73C2211yescharacteristic
13C2×C42×D73C2211yescharacteristic
14C2×C42×D73C2211yescharacteristic
15#17988639C4116yescomplemented
16C2×C4⋊#10596831C2212yes—
17C2×#14556503C2214yes—
18C2×#14556502C2212yes—
19C2×#14556501C2214yes—
20C2×C8×Dic73C2214yes—
21C42×Dic73C412yes—
22C42×Dic73C412yes—
23C42×Dic73C2211yescharacteristic
24C42×Dic73C2211yescharacteristic
25C42×Dic73C2211yescharacteristic
26#17988342C2212yes—
27#17988341C2214yes—
28C2×C4⋊C8×C73C2212yes—
29C2×#97×C73C2212yes—
30C43×C73C2211yescharacteristic
31#336×C73C2212yes—
32C22×C4×D73C2×C412yes—
33C22×C4×D73C2×C412yes—
34C22×C4×D73C2×C411yescharacteristic
35C22×C4×D73C2×C411yescharacteristic
36C22×C4×D73C2311yescharacteristic
37C22×#10596831C2314yes—
38C2×C4×Dic73C2×C412yes—
39C2×C4×Dic73C2×C412yes—
40C2×C4×Dic73C2×C412yes—
41C2×C4×Dic73C2×C412yes—
42C2×C4×Dic73C2×C412yes—
43C2×C4×Dic73C2×C412yes—
44C2×C4×Dic73C2×C412yes—
45C2×C4×Dic73C2×C411yescharacteristic
46C2×C4×Dic73C2×C411yescharacteristic
47C2×C4×Dic73C2×C412yes—
48C2×C4×Dic73C2311yescharacteristic
49C2×C4×Dic73C2311yescharacteristic
50C2×C4×Dic73C2311yescharacteristic
51C42×D73—28no—
52C42×D73—28no—
53C42×D73—24no—
54C42×D73—22no—
55C42×D73—22no—
56C42×D73C2×C418yes—
57C4⋊#10596831C2×C418yescomplemented
58#14556503C2×C4116yes—
59#14556502—24no—
60#14556501—28no—
61C8×Dic73C2×C4116yescomplemented
62C22×C8×C73C2314yes—
63C2×C42×C73C2×C412yes—
64C2×C42×C73C2×C412yes—
65C2×C42×C73C2311yescharacteristic
66C2×C42×C73C2311yescharacteristic
67C2×C42×C73C2311yescharacteristic
68C4⋊C8×C73C2×C418yescomplemented
69#97×C73—24no—
70C23×D73C22×C411yescharacteristic
71C22×Dic73C22×C411yescharacteristic
72C22×Dic73C22×C412yes—
73C22×Dic73C22×C412yes—
74C22×Dic73C22×C411yescharacteristic
75C22×Dic73C22×C411yescharacteristic
76C2×C4×D73—24no—
77C2×C4×D73—24no—
78C2×C4×D73—24no—
79C2×C4×D73—24no—
80C2×C4×D73—22no—
81C2×C4×D73—21no—
82C2×C4×D73—21no—
83C2×C4×D73—24no—
84C2×C4×D73—24no—
85C2×C4×D73—24no—
86C2×C4×D73C4214yes—
87C2×C4×D73C4214yes—
88C2×C4×D73M1618yes—
89C2×C4×D73C22×C414yes—
90C2×#10596831—24no—
91C2×#10596831—24no—
92C2×#10596831C22×C418yes—
93C4×Dic73—24no—
94C4×Dic73—24no—
95C4×Dic73—21no—
96C4×Dic73—21no—
97C4×Dic73—24no—
98C4×Dic73—24no—
99C4×Dic73—24no—
100C4×Dic73—24no—
101C4×Dic73—24no—
102C4×Dic73C4214yes—
103C4×Dic73C4214yes—
104C4×Dic73M1618yes—
105C4×Dic73C22×C414yes—
106C4×Dic73#4114yes—
107C22×C4×C73C22×C411yescharacteristic
108C22×C4×C73C22×C412yes—
109C22×C4×C73C22×C412yes—
110C22×C4×C73C22×C411yescharacteristic
111C22×C4×C73C2411yescharacteristic
112C2×C8×C73—24no—
113C2×C8×C73—24no—
114C2×C8×C73C22×C418yes—
115C42×C73—24no—
116C42×C73—24no—
117C42×C73—22no—
118C42×C73C22×C414yes—
119C42×C73#4112yes—
120C42×C73#4112yes—
121C23×C73C23×C411yescharacteristic
122C22×D73—21no—
123C22×D73—21no—
124C22×D73—22no—
125C22×D73C2×C4212yes—
126C22×D73C2×M1614yes—
127C2×C4×C73—22no—
128C2×C4×C73—22no—
129C2×C4×C73—22no—
130C2×C4×C73—22no—
131C2×C4×C73—22no—
132C2×C4×C73C2×C4212yes—
133C2×C4×C73C2×C4212yes—
134C2×C4×C73#11714yes—
135C2×C4×C73C2×M1614yes—
136C2×C4×C73C2×M1614yes—
137C2×C4×C73C23×C412yes—
138C2×C4×C73C2×#4112yes—
139C2×C4×C73C2×#4111yescharacteristic
140C2×C4×C73C2×#4111yescharacteristic
141C2×Dic73—21no—
142C2×Dic73—22no—
143C2×Dic73—21no—
144C2×Dic73—22no—
145C2×Dic73—22no—
146C2×Dic73—22no—
147C2×Dic73C2×C4212yes—
148C2×Dic73C2×C4212yes—
149C2×Dic73C2×C4212yes—
150C2×Dic73#11714yes—
151C2×Dic73C2×M1614yes—
152C2×Dic73C2×M1614yes—
153C2×Dic73C2×M1614yes—
154C4×D73—216no—
155C4×D73—216no—
156C4×D73—24no—
157C4×D73—24no—
158C4×D73—28no—
159C4×D73#97116yescomplemented
160C8×C73—28no—
161#10596831—28no—
162C22×C73C22×C4211yescharacteristic
163C22×C73C2×#11711yescharacteristic
164C22×C73C2×#11711yescharacteristic
165C22×C73C22×M1612yes—
166C22×C73C22×M1612yes—
167C2×D73—22no—
168C2×D73—24no—
169C2×D73—24no—
170C2×D73—22no—
171C2×D73C2×#9714yes—
172C4×C73—22no—
173C4×C73—24no—
174C4×C73—24no—
175C4×C73C2×#9714yes—
176C4×C73C4×#4112yes—
177C4×C73C4×#4112yes—
178Dic73—24no—
179Dic73—24no—
180Dic73—22no—
181Dic73C2×#9714yes—
182Dic73C4×M1614yes—
183#20463—731nomaximal, Sylow
184C2×C73C4×#11711yescharacteristic
185C2×C73C22×#9711yescharacteristic
186C2×C73C2×C4×M1611yescharacteristic
187C2×C73#292012yes—
188C2×C73#292012yes—
189D73—24no—
190C2×#431—732no—
191C2×C43—731no—
192#1767—732no—
193#1767—731no—
194#1767D7311yescharacteristic, complemented
195#1749—732no—
196#1749—732no—
197#1744—732no—
198C4×#97—732no—
199C73#2046311yescharacteristic, complemented, Sylow
200C22×C42—731no—
201C22×C42—732no—
202C22×C42—732no—
203C22×C42—731no—
204C22×C42—731no—
205#431—7316no—
206C2×C4⋊C8—732no—
207C2×C4⋊C8C2×D7312yes—
208C2×C22⋊C8—734no—
209C2×#97—734no—
210C2×#97—732no—
211C2×#97C2×D7312yes—
212C2×C4×C8—734no—
213C43—732no—
214C43—732no—
215C43—731no—
216C43—731no—
217C43—731no—
218C43C2×D7311yescharacteristic
219#336—734no—
220#336—732no—
221#336C2×D7312yes—
222C23×C4—731no—
223C23×C4—731no—
224C23×C4—731no—
225C23×C4—732no—
226C23×C4—732no—
227C22×C8—734no—
228C22×C8C22×D7314yes—
229C2×C42—731no—
230C2×C42—731no—
231C2×C42—732no—
232C2×C42—731no—
233C2×C42—731no—
234C2×C42—738no—
235C2×C42—732no—
236C2×C42—732no—
237C2×C42—732no—
238C2×C42—732no—
239C2×C42—732no—
240C2×C42—732no—
241C2×C42—732no—
242C2×C42—731no—
243C2×C42—1468no—
244C2×C42—1464no—
245C2×C42—1468no—
246C2×C42—1462no—
247C2×C42—1462no—
248C2×C42C4×D7312yes—
249C2×C42C4×D7312yes—
250C2×C42C22×D7311yescharacteristic
251C2×C42C22×D7311yescharacteristic
252C2×C42C22×D7311yescharacteristic
253C4⋊C8—738no—
254C4⋊C8C4×D7318yescomplemented
255C22⋊C8—7316no—
256#97—24no—
257#97—1468no—
258#97—1464no—
259C4×C8—7316no—
260C24—731no—
261C22×C4—731no—
262C22×C4—731no—
263C22×C4—734no—
264C22×C4—738no—
265C22×C4—731no—
266C22×C4—732no—
267C22×C4—732no—
268C22×C4—734no—
269C22×C4—734no—
270C22×C4—1464no—
271C22×C4—1464no—
272C22×C4—1464no—
273C22×C4—1464no—
274C22×C4—1464no—
275C22×C4—1464no—
276C22×C4—1464no—
277C22×C4—1462no—
278C22×C4—1461no—
279C22×C4—1461no—
280C22×C4C2×C4×D7311yescharacteristic
281C22×C4C2×C4×D7312yes—
282C22×C4C2×C4×D7312yes—
283C22×C4C2×C4×D7311yescharacteristic
284C22×C4C23×D7311yescharacteristic
285C2×C8—24no—
286C2×C8—24no—
287C2×C8—738no—
288C2×C8—1464no—
289C2×C8—1464no—
290C2×C8C2×C4×D7318yes—
291C42—24no—
292C42—24no—
293C42—22no—
294C42—734no—
295C42—734no—
296C42—738no—
297C42—734no—
298C42—734no—
299C42—1464no—
300C42—1464no—
301C42—1464no—
302C42—1464no—
303C42—1464no—
304C42—1464no—
305C42—1464no—
306C42—1461no—
307C42—1461no—
308C42C2×C4×D7314yes—
309C42#1192402712yes—
310C42#1192402912yes—
311C23—732no—
312C23—734no—
313C23—1461no—
314C23—1461no—
315C23—1462no—
316C23C22×C4×D7311yescharacteristic
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—732no—
323C2×C4—732no—
324C2×C4—734no—
325C2×C4—734no—
326C2×C4—7316no—
327C2×C4—732no—
328C2×C4—734no—
329C2×C4—734no—
330C2×C4—1468no—
331C2×C4—14616no—
332C2×C4—14616no—
333C2×C4—1461no—
334C2×C4—1461no—
335C2×C4—1462no—
336C2×C4—1462no—
337C2×C4—1462no—
338C2×C4—1462no—
339C2×C4—1464no—
340C2×C4—1464no—
341C2×C4C42×D7312yes—
342C2×C4C42×D7312yes—
343C2×C4#1455654914yes—
344C2×C4M16×D7314yes—
345C2×C4M16×D7314yes—
346C2×C4C22×C4×D7312yes—
347C2×C4#41×D7312yes—
348C2×C4C2×#1192402711yescharacteristic
349C2×C4C2×#1192402911yescharacteristic
350C8—28no—
351C8—1468no—
352C22—734no—
353C22—1462no—
354C22—1464no—
355C22—1464no—
356C22—1462no—
357C22C2×C42×D7311yescharacteristic
358C22#117×D7311yescharacteristic
359C22C2×#1455654911yescharacteristic
360C22C2×M16×D7312yes—
361C22C2×M16×D7312yes—
362C4—24no—
363C4—24no—
364C4—22no—
365C4—734no—
366C4—734no—
367C4—1462no—
368C4—1464no—
369C4—1464no—
370C4#97×D7314yes—
371C4C4×#1192402712yes—
372C4C4×#1192402912yes—
373C2—1464no—
374C2C4×#1455654911yescharacteristic
375C2C2×#97×D7311yescharacteristic
376C2C4×M16×D7311yescharacteristic
377C2#2261856112yes—
378C2#2261856312yes—
subgroupG/H
center, FrattiniC22×C4C23×D73
commutatorC22×C73C22×C42
FittingC73×#1767C2
socleC23×C73C23×C4
prime radicalC23×D73C22×C4
cosocleC22×C4×C73C24
hypercenter#1767D73
hypocenterC73#20463
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1767

Complements

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

NH ≅ G/Ntype
3. #22609786C2semidirect
4. #22609784C2semidirect
7. #22609675C2semidirect
8. #97×Dic73C2semidirect
9. C73×#1767C2semidirect
15. #17988639C4semidirect
57. C4⋊#10596831C2×C4semidirect
61. C8×Dic73C2×C4semidirect
68. C4⋊C8×C73C2×C4semidirect
159. C4×D73#97semidirect
194. #1767D73semidirect
199. C73#20463semidirect
254. C4⋊C8C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179886392
C43×D732
#226097862
#226097842
#226096942
#226096922
#226096752
#97×Dic732
C73×#17672
#2046373