Finite Group Databasebeta

← #33012640

Subgroups — #33012640

Order 18688.

1934 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556579C211yesmaximal, characteristic
2C2×C4×C4⋊Dic73C211yesmaximal, characteristic, complemented
3#22608201C212yesmaximal, complemented
4#22608177C214yesmaximal, complemented
5#22608171C212yesmaximal
6#22608167C214yesmaximal, complemented
7C2×#383×C73C211yesmaximal, characteristic, complemented
8C23×Dic146C2211yescharacteristic
9C23×D292C2211yescharacteristic
10C2×#14556579—24no—
11C2×#14556579—24no—
12C2×#14556579C418yescomplemented
13C22×C4⋊Dic73C2212yes—
14C22×#11924005C2212yes—
15C22×#11924005C2212yes—
16C22×#11924005C2218yes—
17C22×C4×Dic73C2212yes—
18C4×C4⋊Dic73—24no—
19C2×#14556498C2212yes—
20C2×#14556498C2218yes—
21C22×C42×C73C2211yescharacteristic
22#383×C73—24no—
23C2×#95×C73C2212yes—
24C2×#95×C73C2212yes—
25C2×#95×C73C2212yes—
26C24×D73C2312yes—
27C22×Dic146—22no—
28C22×Dic146—22no—
29C22×Dic146—44no—
30C22×Dic146C2×C414yes—
31C22×D292—22no—
32C22×D292—22no—
33C22×D292—44no—
34C22×D292C2×C414yes—
35C23×Dic73C2312yes—
36C23×Dic73C2314yes—
37#14556579—232no—
38C2×C4⋊Dic73—28no—
39C2×C4⋊Dic73—24no—
40C2×#11924005—216no—
41C2×#11924005—24no—
42C2×#11924005—24no—
43C2×#11924005—24no—
44C2×#11924005—24no—
45C2×#11924005—48no—
46C2×#11924005—48no—
47C2×#11924005C2×C418yes—
48C2×#11924005C2×C418yes—
49C2×C4×Dic73—24no—
50C2×C4×Dic73—44no—
51#14556498—24no—
52#14556498—48no—
53C23×C4×C73C2314yes—
54C23×C4×C73C2311yescharacteristic
55C23×C4×C73C2311yescharacteristic
56C23×C4×C73C2311yescharacteristic
57C2×C42×C73C2×C414yes—
58C2×C42×C73D414yes—
59C2×C42×C73D414yes—
60#95×C73—24no—
61#95×C73—24no—
62#95×C73—24no—
63C23×D73—22no—
64C23×D73—22no—
65C23×D73—28no—
66C23×D73—24no—
67C23×D73—28no—
68C23×D73—24no—
69C23×D73C22×C414yes—
70C2×Dic146—28no—
71C2×Dic146—48no—
72C2×Dic146—48no—
73C2×Dic146—48no—
74C2×D292—28no—
75C2×D292—48no—
76C2×D292—48no—
77C2×D292—48no—
78C22×Dic73—24no—
79C22×Dic73—22no—
80C22×Dic73—22no—
81C22×Dic73—24no—
82C22×Dic73—28no—
83C22×Dic73—28no—
84C22×Dic73—28no—
85C22×Dic73C22×C414yes—
86C22×Dic73#4118yes—
87C4⋊Dic73—216no—
88#11924005—216no—
89#11924005—216no—
90#11924005—432no—
91C4×Dic73—48no—
92C24×C73C2411yescharacteristic
93C22×C4×C73—24no—
94C22×C4×C73—22no—
95C22×C4×C73—24no—
96C22×C4×C73—22no—
97C22×C4×C73—24no—
98C22×C4×C73—28no—
99C22×C4×C73—28no—
100C22×C4×C73—24no—
101C22×C4×C73—24no—
102C22×C4×C73C22×C412yes—
103C22×C4×C73C22×C412yes—
104C22×C4×C73C22×C412yes—
105C22×C4×C73C2×D412yes—
106C22×C4×C73C2×D412yes—
107C22×C4×C73C2×D412yes—
108C22×C4×C73C2×D412yes—
109C22×C4×C73C2×D412yes—
110C22×C4×C73C2×D412yes—
111C42×C73C22⋊C4116yescomplemented
112C23×C73C23×C411yescharacteristic
113C23×C73C22×D411yescharacteristic
114C23×C73C22×D411yescharacteristic
115C23×C73C2×#4114yes—
116C23×C73H(5,𝔽2)14yes—
117C23×C73H(5,𝔽2)12yes—
118C23×C732−1+412yes—
119C22×D73—24no—
120C22×D73—28no—
121C22×D73—28no—
122C22×D73—28no—
123C22×D73—44no—
124C22×D73—44no—
125C22×D73—44no—
126C22×D73—44no—
127C22×D73—42no—
128C22×D73—42no—
129C22×D73—44no—
130C22×D73—48no—
131C22×D73—48no—
132C22×D73—416no—
133C2×C4×C73—24no—
134C2×C4×C73—24no—
135C2×C4×C73—24no—
136C2×C4×C73—24no—
137C2×C4×C73—24no—
138C2×C4×C73—22no—
139C2×C4×C73—24no—
140C2×C4×C73—24no—
141C2×C4×C73—22no—
142C2×C4×C73—24no—
143C2×C4×C73—44no—
144C2×C4×C73—44no—
145C2×C4×C73—44no—
146C2×C4×C73—48no—
147C2×C4×C73—48no—
148C2×C4×C73C2×C22⋊C414yes—
149C2×C4×C73C2×C22⋊C414yes—
150C2×C4×C73C2×C22⋊C414yes—
151C2×Dic73—24no—
152C2×Dic73—28no—
153C2×Dic73—28no—
154C2×Dic73—216no—
155C2×Dic73—44no—
156C2×Dic73—44no—
157C2×Dic73—44no—
158C2×Dic73—44no—
159C2×Dic73—48no—
160D292—416no—
161Dic146—416no—
162C22×C73C22×C22⋊C411yescharacteristic
163C22×C73C4×#4112yes—
164C22×C73#51812yes—
165C22×C73#52012yes—
166C22×C73#52512yes—
167C22×C73#53212yes—
168C22×C73#53512yes—
169C22×C73#53512yes—
170C22×C73#53511yescharacteristic
171C22×C73#53611yescharacteristic
172C22×C73#53712yes—
173C22×C73#53818yes—
174C22×C73#54218yes—
175C2×D73—44no—
176C2×D73—44no—
177C2×D73—416no—
178C2×D73—44no—
179C2×D73—84no—
180C2×D73—84no—
181C2×D73—88no—
182C4×C73—24no—
183C4×C73—24no—
184C4×C73—24no—
185C4×C73—84no—
186Dic73—44no—
187Dic73—48no—
188#14288—731nomaximal, Sylow
189C2×C73#229711yescharacteristic
190C2×C73#230911yescharacteristic
191C2×C73#231111yescharacteristic
192C2×C73#233714yes—
193C2×C73#263112yes—
194C2×C73#263212yes—
195C2×C73#266214yes—
196D73—84no—
197C22×#124—731no—
198C2×#383D7311yescharacteristic, complemented
199C2×C4×C4⋊C4—731no—
200#1446—732no—
201#1439—734no—
202#1438—732no—
203#1437—734no—
204C73#1428811yescharacteristic, complemented, Sylow
205C23×Q8—731no—
206C23×D4—731no—
207C2×#124—738no—
208C2×#124—1464no—
209C2×#124—1464no—
210C22×C4⋊C4—732no—
211C22×C22⋊C4—738no—
212C22×C22⋊C4—732no—
213C22×C22⋊C4—732no—
214C22×C42—732no—
215C22×C42C2×D7311yescharacteristic
216#383—24no—
217C4×C4⋊C4—1464no—
218C2×#95—738no—
219C2×#95—732no—
220C2×#95C2×D7312yes—
221C2×#95C2×D7312yes—
222C2×#95C2×D7312yes—
223C25—732no—
224C22×Q8—2924no—
225C22×Q8—734no—
226C22×Q8—1462no—
227C22×Q8—1462no—
228C22×D4—2924no—
229C22×D4—734no—
230C22×D4—1462no—
231C22×D4—1462no—
232C23×C4—734no—
233C23×C4—732no—
234C23×C4C22×D7314yes—
235C23×C4C22×D7311yescharacteristic
236C23×C4C22×D7311yescharacteristic
237C23×C4C22×D7311yescharacteristic
238#124—14632no—
239C2×C4⋊C4—1468no—
240C2×C4⋊C4—1464no—
241C2×C22⋊C4—2928no—
242C2×C22⋊C4—2928no—
243C2×C22⋊C4—738no—
244C2×C22⋊C4—738no—
245C2×C22⋊C4—14616no—
246C2×C22⋊C4—1464no—
247C2×C22⋊C4—1464no—
248C2×C22⋊C4—1464no—
249C2×C22⋊C4—1464no—
250C2×C42—2924no—
251C2×C42—1464no—
252C2×C42C4×D7314yes—
253C2×C42D29214yes—
254C2×C42C22⋊D7314yes—
255#95—24no—
256#95—24no—
257#95—24no—
258#95—2928no—
259#95—1464no—
260C24—734no—
261C24—1462no—
262C24—1462no—
263C24—1468no—
264C24—1464no—
265C24—1468no—
266C24—1464no—
267C24C23×D7311yescharacteristic
268C2×Q8—2928no—
269C2×Q8—2928no—
270C2×Q8—2928no—
271C2×Q8—1468no—
272C2×D4—2928no—
273C2×D4—2928no—
274C2×D4—2928no—
275C2×D4—1468no—
276C22×C4—24no—
277C22×C4—22no—
278C22×C4—24no—
279C22×C4—22no—
280C22×C4—24no—
281C22×C4—28no—
282C22×C4—28no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—734no—
286C22×C4—738no—
287C22×C4—1462no—
288C22×C4—1464no—
289C22×C4—1462no—
290C22×C4—1464no—
291C22×C4—1468no—
292C22×C4—1468no—
293C22×C4—1468no—
294C22×C4C2×C4×D7312yes—
295C22×C4C2×C4×D7312yes—
296C22×C4C2×C4×D7312yes—
297C22×C4C2×C22⋊D7312yes—
298C22×C4C2×C22⋊D7312yes—
299C22×C4C2×C22⋊D7312yes—
300C22×C4C2×D29212yes—
301C22×C4C2×D29212yes—
302C22×C4C2×D29212yes—
303C4⋊C4—14616no—
304C22⋊C4—29232no—
305C22⋊C4—14616no—
306C22⋊C4—14616no—
307C42—2928no—
308C42#11924005116yescomplemented
309C23—2924no—
310C23—2924no—
311C23—2924no—
312C23—2922no—
313C23—2922no—
314C23—2924no—
315C23—2928no—
316C23—2928no—
317C23—29216no—
318C23—2924no—
319C23—1464no—
320C23—1468no—
321C23—1468no—
322C23—1468no—
323C23C22×C4×D7311yescharacteristic
324C23C22×C22⋊D7311yescharacteristic
325C23C22×D29211yescharacteristic
326C23#41×D7314yes—
327C23#1455663714yes—
328C23#1455663712yes—
329C23#1455663812yes—
330Q8—29216no—
331D4—29216no—
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—22no—
335C2×C4—24no—
336C2×C4—22no—
337C2×C4—24no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—48no—
346C2×C4—48no—
347C2×C4—2924no—
348C2×C4—2924no—
349C2×C4—2924no—
350C2×C4—2924no—
351C2×C4—2928no—
352C2×C4—14616no—
353C2×C4—1464no—
354C2×C4—1468no—
355C2×C4—1468no—
356C2×C4C2×#1192400514yes—
357C2×C4C2×#1192400514yes—
358C2×C4C2×#1192400514yes—
359C22—29216no—
360C22—2924no—
361C22—2924no—
362C22—2924no—
363C22—5848no—
364C22—5844no—
365C22—5844no—
366C22C22×#1192400511yescharacteristic
367C22#1798905512yes—
368C22#1798906112yes—
369C22#1798906712yes—
370C22#1798909912yes—
371C22#1798913312yes—
372C22#1798915112yes—
373C22#1798915612yes—
374C22#1798915611yescharacteristic
375C22#1798916311yescharacteristic
376C22#1798916512yes—
377C22#1798917618yes—
378C22#1798920318yes—
379C4—24no—
380C4—24no—
381C4—24no—
382C4—84no—
383C4—2924no—
384C4—2928no—
385C2—5844no—
386C2#2261241911yescharacteristic
387C2#2261251111yescharacteristic
388C2#2261251911yescharacteristic
389C2#2261274114yes—
390C2#2261578612yes—
391C2#2261579412yes—
392C2#2261607114yes—
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC2×#383×C73C2
socle, cosocleC24×C73C24
prime radicalC23×D292C22
hypercenterC2×#383D73
hypocenterC73#14288
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#383

Complements

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

NH ≅ G/Ntype
2. C2×C4×C4⋊Dic73C2semidirect
3. #22608201C2semidirect
4. #22608177C2semidirect
6. #22608167C2semidirect
7. C2×#383×C73C2semidirect
12. C2×#14556579C4semidirect
111. C42×C73C22⋊C4semidirect
198. C2×#383D73semidirect
204. C73#14288semidirect
308. C42#11924005semidirect

Maximal subgroups

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

subgroupindex
C22×#145565792
C2×C4×C4⋊Dic732
#226082012
#226081772
#226081712
#226081672
C2×#383×C732
#1428873