Finite Group Databasebeta

← #33008647

Subgroups — #33008647

Order 18688.

1342 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988455C211yesmaximal, characteristic
2C2×C4×C4⋊Dic73C211yesmaximal, characteristic
3#22608196C212yesmaximal
4#22608188C212yesmaximal
5#22608165C214yesmaximal
6#22608161C212yesmaximal
7#22608158C212yesmaximal
8C2×#376×C73C211yesmaximal, characteristic
9C22×C4⋊Dic73C2212yes—
10C22×C4⋊Dic73C2214yes—
11C22×C4×Dic73C2212yes—
12#17988455—24no—
13C4×C4⋊Dic73—24no—
14C2×#14556498C2211yescharacteristic
15C2×#14556498C2212yes—
16C2×#14556498C2214yes—
17C2×#14556498C2214yes—
18C2×#14556498C2211yescharacteristic
19C2×#14556498C2212yes—
20C2×#14556498C2212yes—
21C2×#14556498C2214yes—
22C22×C42×C73C2212yes—
23C22×C42×C73C2211yescharacteristic
24#376×C73C418yescomplemented
25C2×#95×C73C2212yes—
26C2×#95×C73C2211yescharacteristic
27C2×#95×C73C2211yescharacteristic
28C23×Dic73C2312yes—
29C23×Dic73C2312yes—
30C23×Dic73C2314yes—
31C2×C4⋊Dic73—28no—
32C2×C4⋊Dic73—28no—
33C2×C4⋊Dic73—24no—
34C2×C4⋊Dic73—28no—
35C2×C4⋊Dic73—44no—
36C2×C4×Dic73—24no—
37C2×C4×Dic73—42no—
38C2×C4×Dic73—42no—
39#14556498—28no—
40#14556498—24no—
41#14556498—22no—
42#14556498—22no—
43#14556498—24no—
44#14556498—24no—
45#14556498—28no—
46#14556498—44no—
47C23×C4×C73C2312yes—
48C23×C4×C73C2311yescharacteristic
49C23×C4×C73C2311yescharacteristic
50C23×C4×C73C2311yescharacteristic
51C23×C4×C73C2312yes—
52C2×C42×C73—28no—
53C2×C42×C73C2×C418yes—
54C2×C42×C73C2×C414yes—
55C2×C42×C73D414yes—
56C2×C42×C73Q814yes—
57#95×C73C2×C414yes—
58#95×C73C2×C418yes—
59#95×C73C2×C414yes—
60C22×Dic73—24no—
61C22×Dic73—24no—
62C22×Dic73—24no—
63C22×Dic73—24no—
64C22×Dic73—24no—
65C22×Dic73—24no—
66C22×Dic73—22no—
67C22×Dic73—22no—
68C22×Dic73—24no—
69C22×Dic73—24no—
70C22×Dic73—24no—
71C22×Dic73—24no—
72C22×Dic73—22no—
73C22×Dic73—22no—
74C22×Dic73—22no—
75C22×Dic73—22no—
76C22×Dic73#4118yes—
77C4⋊Dic73—216no—
78C4⋊Dic73—416no—
79C4×Dic73—48no—
80C24×C73C2411yescharacteristic
81C22×C4×C73—24no—
82C22×C4×C73—24no—
83C22×C4×C73—24no—
84C22×C4×C73—21no—
85C22×C4×C73—21no—
86C22×C4×C73—22no—
87C22×C4×C73—21no—
88C22×C4×C73—21no—
89C22×C4×C73—22no—
90C22×C4×C73—24no—
91C22×C4×C73—24no—
92C22×C4×C73—22no—
93C22×C4×C73—22no—
94C22×C4×C73C22×C414yes—
95C22×C4×C73C22×C412yes—
96C22×C4×C73C22×C412yes—
97C22×C4×C73C22×C412yes—
98C22×C4×C73C22×C414yes—
99C22×C4×C73C2×D412yes—
100C22×C4×C73C2×D412yes—
101C22×C4×C73C2×D412yes—
102C22×C4×C73C2×Q812yes—
103C22×C4×C73C2×Q812yes—
104C22×C4×C73C2×Q812yes—
105C22×C4×C73#4118yes—
106C42×C73—216no—
107C42×C73C4⋊C4116yescomplemented
108C23×C73C23×C411yescharacteristic
109C23×C73C22×D411yescharacteristic
110C23×C73C22×Q811yescharacteristic
111C23×C73C2×#4114yes—
112C23×C73C2×#4114yes—
113C23×C73H(5,𝔽2)11yescharacteristic
114C23×C73H(5,𝔽2)11yescharacteristic
115C23×C732−1+411yescharacteristic
116C23×C732−1+411yescharacteristic
117C2×C4×C73—24no—
118C2×C4×C73—24no—
119C2×C4×C73—24no—
120C2×C4×C73—22no—
121C2×C4×C73—22no—
122C2×C4×C73—24no—
123C2×C4×C73—24no—
124C2×C4×C73—24no—
125C2×C4×C73—24no—
126C2×C4×C73—24no—
127C2×C4×C73—22no—
128C2×C4×C73—22no—
129C2×C4×C73—22no—
130C2×C4×C73—22no—
131C2×C4×C73—28no—
132C2×C4×C73—28no—
133C2×C4×C73—24no—
134C2×C4×C73—24no—
135C2×C4×C73—24no—
136C2×C4×C73—44no—
137C2×C4×C73—44no—
138C2×C4×C73C2×C4⋊C414yes—
139C2×C4×C73C2×C4⋊C414yes—
140C2×C4×C73C2×C4⋊C414yes—
141C2×C4×C73#11718yes—
142C2×Dic73—28no—
143C2×Dic73—28no—
144C2×Dic73—28no—
145C2×Dic73—44no—
146C2×Dic73—44no—
147C2×Dic73—44no—
148C2×Dic73—44no—
149C2×Dic73—42no—
150C2×Dic73—42no—
151C2×Dic73—42no—
152C2×Dic73—42no—
153C2×Dic73—42no—
154C2×Dic73—42no—
155C2×Dic73—44no—
156C2×Dic73—44no—
157C2×Dic73—44no—
158C2×Dic73—44no—
159C22×C73C22×C4⋊C411yescharacteristic
160C22×C73C2×#11712yes—
161C22×C73C4×#4112yes—
162C22×C73#52011yescharacteristic
163C22×C73#52011yescharacteristic
164C22×C73#52512yes—
165C22×C73#53212yes—
166C22×C73#53312yes—
167C22×C73#53312yes—
168C22×C73#53511yescharacteristic
169C22×C73#53611yescharacteristic
170C22×C73#54411yescharacteristic
171C22×C73#54411yescharacteristic
172C22×C73#55114yes—
173C22×C73#55214yes—
174C22×C73#55314yes—
175C22×C73#55614yes—
176C4×C73—24no—
177C4×C73—28no—
178C4×C73—24no—
179C4×C73—24no—
180C4×C73—44no—
181Dic73—48no—
182Dic73—82no—
183Dic73—82no—
184#13952—731nomaximal, Sylow
185C2×C73#228511yescharacteristic
186C2×C73#229611yescharacteristic
187C2×C73#231711yescharacteristic
188C2×C73#234312yes—
189C2×C73#234712yes—
190C2×C73#260312yes—
191C2×C73#260412yes—
192C2×C73#260512yes—
193C2×C73#260612yes—
194C2×#383—731no—
195C2×C4×C4⋊C4—731no—
196C2×#376D7311yescharacteristic
197#1444—732no—
198#1442—732no—
199#1436—734no—
200C4⋊#95—732no—
201#1434—732no—
202C73#1395211yescharacteristic, complemented, Sylow
203C22×C4⋊C4—734no—
204C22×C4⋊C4—732no—
205C22×C42—732no—
206C22×C42C2×D7312yes—
207C22×C42C2×D7311yescharacteristic
208#383—1464no—
209C4×C4⋊C4—1464no—
210#376Dic7318yescomplemented
211C2×#95—734no—
212C2×#95—731no—
213C2×#95—732no—
214C2×#95—734no—
215C2×#95—734no—
216C2×#95—731no—
217C2×#95—732no—
218C2×#95—732no—
219C2×#95C2×D7312yes—
220C2×#95C2×D7311yescharacteristic
221C2×#95C2×D7311yescharacteristic
222C23×C4—734no—
223C23×C4—732no—
224C23×C4—732no—
225C23×C4C22×D7312yes—
226C23×C4C22×D7311yescharacteristic
227C23×C4C22×D7311yescharacteristic
228C23×C4C22×D7311yescharacteristic
229C23×C4C22×D7312yes—
230C2×C4⋊C4—2924no—
231C2×C4⋊C4—1468no—
232C2×C4⋊C4—1468no—
233C2×C4⋊C4—1468no—
234C2×C4⋊C4—1464no—
235C2×C42—28no—
236C2×C42—2922no—
237C2×C42—2922no—
238C2×C42—1464no—
239C2×C42Dic14614yes—
240C2×C42D29214yes—
241C2×C42C2×Dic7318yes—
242C2×C42C2×Dic7314yes—
243#95—2924no—
244#95—1468no—
245#95—1464no—
246#95—1462no—
247#95—1462no—
248#95—1464no—
249#95—1464no—
250#95—1468no—
251#95C2×Dic7314yes—
252#95C2×Dic7318yes—
253#95C2×Dic7314yes—
254C24C23×D7311yescharacteristic
255C22×C4—24no—
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—24no—
265C22×C4—24no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—738no—
269C22×C4—1462no—
270C22×C4—1462no—
271C22×C4—1464no—
272C22×C4—1464no—
273C22×C4—1464no—
274C22×C4—1464no—
275C22×C4—1462no—
276C22×C4—1462no—
277C22×C4—1462no—
278C22×C4—1462no—
279C22×C4—1464no—
280C22×C4—1464no—
281C22×C4—1464no—
282C22×C4—1464no—
283C22×C4—1464no—
284C22×C4—1464no—
285C22×C4C22×Dic7314yes—
286C22×C4C22×Dic7312yes—
287C22×C4C22×Dic7312yes—
288C22×C4C22×Dic7312yes—
289C22×C4C22×Dic7314yes—
290C22×C4C2×D29212yes—
291C22×C4C2×D29212yes—
292C22×C4C2×D29212yes—
293C22×C4C2×Dic14612yes—
294C22×C4C2×Dic14612yes—
295C22×C4C2×Dic14612yes—
296C22×C4#1192402818yes—
297C4⋊C4—29216no—
298C4⋊C4—14616no—
299C42—216no—
300C42—2928no—
301C42C4⋊Dic73116yescomplemented
302C23C23×Dic7311yescharacteristic
303C23C22×D29211yescharacteristic
304C23C22×Dic14611yescharacteristic
305C23#41×D7314yes—
306C23C2×#1192402814yes—
307C23#1455663711yescharacteristic
308C23#1455663711yescharacteristic
309C23#1455663811yescharacteristic
310C23#1455663811yescharacteristic
311C2×C4—24no—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—28no—
319C2×C4—28no—
320C2×C4—24no—
321C2×C4—24no—
322C2×C4—24no—
323C2×C4—24no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—44no—
331C2×C4—44no—
332C2×C4—2924no—
333C2×C4—2924no—
334C2×C4—2924no—
335C2×C4—2924no—
336C2×C4—2922no—
337C2×C4—2922no—
338C2×C4—2922no—
339C2×C4—2922no—
340C2×C4—2924no—
341C2×C4—2924no—
342C2×C4—2924no—
343C2×C4—2924no—
344C2×C4—2922no—
345C2×C4—2922no—
346C2×C4—1468no—
347C2×C4—1468no—
348C2×C4—1468no—
349C2×C4C2×C4⋊Dic7314yes—
350C2×C4C2×C4⋊Dic7314yes—
351C2×C4C2×C4⋊Dic7314yes—
352C2×C4#1455655018yes—
353C22C22×C4⋊Dic7311yescharacteristic
354C22C2×#1455655012yes—
355C22#41×Dic7312yes—
356C22#1798907011yescharacteristic
357C22#1798907011yescharacteristic
358C22#1798909912yes—
359C22#1798913712yes—
360C22#1798914012yes—
361C22#1798914412yes—
362C22#1798915611yescharacteristic
363C22#1798916311yescharacteristic
364C22#1798921511yescharacteristic
365C22#1798921511yescharacteristic
366C22#1798926114yes—
367C22#1798927014yes—
368C22#1798928114yes—
369C22#1798930514yes—
370C4—28no—
371C4—24no—
372C4—24no—
373C4—24no—
374C4—44no—
375C4—2928no—
376C4—5842no—
377C4—5842no—
378C2#2261233811yescharacteristic
379C2#2261241511yescharacteristic
380C2#2261255411yescharacteristic
381C2#2261279112yes—
382C2#2261282412yes—
383C2#2261555812yes—
384C2#2261556912yes—
385C2#2261557912yes—
386C2#2261558812yes—
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC2×#376×C73C2
socle, prime radical, cosocleC24×C73C24
hypercenterC2×#376D73
hypocenterC73#13952
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#376

Complements

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

NH ≅ G/Ntype
24. #376×C73C4semidirect
107. C42×C73C4⋊C4semidirect
202. C73#13952semidirect
210. #376Dic73semidirect
301. C42C4⋊Dic73semidirect

Maximal subgroups

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

subgroupindex
C2×#179884552
C2×C4×C4⋊Dic732
#226081962
#226081882
#226081652
#226081612
#226081582
C2×#376×C732
#1395273