Finite Group Databasebeta

← #33091096

Subgroups — #33091096

Order 18688.

1430 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×#17989137C211yesmaximal, characteristic
2C2×#17988644C211yesmaximal, characteristic, complemented
3#22610883C212yesmaximal, complemented
4#22610858C212yesmaximal, complemented
5#22610253C214yesmaximal, complemented
6#22609759C214yesmaximal, complemented
7C4×#117×C73C211yesmaximal, characteristic, complemented
8C22×#11924028—21no—
9#17989137—24no—
10#17989137C418yescomplemented
11C2×#14556591C2211yescharacteristic
12C2×#14556588C2211yescharacteristic
13C2×#14556579—21no—
14C2×#14556565—21no—
15C2×#14556565C2212yes—
16C2×C4×D292—21no—
17C2×C4×D292C2212yes—
18#17988644—24no—
19C2×C4⋊#10596831C2212yes—
20C2×#14556511C2218yes—
21C2×C22⋊#10596831C2212yes—
22C2×#14556502C2212yes—
23#17988349C2218yes—
24C2×#117×C73C2212yes—
25C22×C42×C73C2211yescharacteristic
26C4×C4⋊C4×C73C2212yes—
27C4×C4⋊C4×C73C2212yes—
28C4×C22⋊C4×C73—21no—
29C4×C22⋊C4×C73—21no—
30#376×C73—21no—
31C43×C73—21no—
32C2×#11924028—28no—
33C2×#11924028—48no—
34C22×Dic146—21no—
35C22×D292—21no—
36C22×D292—21no—
37C22×D292C2312yes—
38C22×C22⋊D73—22no—
39C22×C4×D73—22no—
40C22×#10596831C2314yes—
41#14556591—22no—
42#14556591C2×C414yes—
43#14556588—22no—
44#14556588C2×C414yes—
45#14556579—28no—
46#14556565—28no—
47#14556565—24no—
48#14556565C2×C418yes—
49C4×D292—28no—
50C4×D292—24no—
51C4×D292C2×C418yes—
52C2×C4⋊Dic73—21no—
53C2×C4⋊Dic73C2312yes—
54C2×#11924005—22no—
55C2×#11924005—22no—
56C4⋊#10596831—24no—
57#14556511—216no—
58C22⋊#10596831—24no—
59#14556502—24no—
60C23×C4×C73D411yescharacteristic
61C23×C4×C73D411yescharacteristic
62C23×C4×C73C2311yescharacteristic
63#117×C73—28no—
64C2×C4⋊C4×C73C2314yes—
65C2×C22⋊C4×C73—22no—
66C2×C42×C73—22no—
67C2×C42×C73—22no—
68C2×C42×C73—22no—
69C2×C42×C73C2×C414yes—
70C2×C42×C73D411yescharacteristic
71C2×C42×C73D411yescharacteristic
72C2×C42×C73D414yes—
73C2×C42×C73C2311yescharacteristic
74C2×C42×C73C2311yescharacteristic
75#95×C73—22no—
76#95×C73—22no—
77C23×D73—22no—
78#11924028—432no—
79C2×Dic146—24no—
80C2×Dic146—44no—
81C2×D292—28no—
82C2×D292—24no—
83C2×D292—24no—
84C2×D292—22no—
85C2×D292—44no—
86C2×D292—44no—
87C2×D292C22×C414yes—
88C2×C22⋊D73—28no—
89C2×C22⋊D73—48no—
90C22×Dic73—22no—
91C2×C4×D73—28no—
92C2×C4×D73—48no—
93C2×#10596831—24no—
94C2×#10596831—28no—
95C4⋊Dic73—24no—
96C4⋊Dic73—22no—
97C4⋊Dic73C22×C414yes—
98#11924005—28no—
99#11924005—28no—
100C24×C73C2×D411yescharacteristic
101C22×C4×C73—24no—
102C22×C4×C73—24no—
103C22×C4×C73—24no—
104C22×C4×C73—42no—
105C22×C4×C73C22⋊C414yes—
106C22×C4×C73C22⋊C414yes—
107C22×C4×C73C22×C412yes—
108C22×C4×C73C2×D411yescharacteristic
109C22×C4×C73C2×D411yescharacteristic
110C22×C4×C73C2×D411yescharacteristic
111C22×C4×C73C2×D411yescharacteristic
112C22×C4×C73C2×D411yescharacteristic
113C22×C4×C73C2×D412yes—
114C22×C4×C73C2411yescharacteristic
115C4⋊C4×C73—24no—
116C4⋊C4×C73#4118yescomplemented
117C22⋊C4×C73—28no—
118C42×C73—28no—
119C42×C73—44no—
120C42×C73—44no—
121C42×C73C22⋊C414yes—
122C42×C73C22⋊C414yes—
123C42×C73C22×C412yes—
124C42×C73C22×C412yes—
125C42×C73C2×D412yes—
126C42×C73C2×D412yes—
127C23×C73—22no—
128C23×C73—22no—
129C23×C73—22no—
130C23×C73C2×C22⋊C412yes—
131C23×C73C22×D411yescharacteristic
132C22×D73—24no—
133C22×D73—44no—
134C22×D73—44no—
135C22×D73—44no—
136C2×C4×C73—22no—
137C2×C4×C73—22no—
138C2×C4×C73—22no—
139C2×C4×C73—22no—
140C2×C4×C73—24no—
141C2×C4×C73—24no—
142C2×C4×C73—28no—
143C2×C4×C73—28no—
144C2×C4×C73—44no—
145C2×C4×C73—44no—
146C2×C4×C73—44no—
147C2×C4×C73C2×C22⋊C412yes—
148C2×C4×C73C2×C22⋊C412yes—
149C2×C4×C73C2×C22⋊C412yes—
150C2×C4×C73C2×C22⋊C412yes—
151C2×C4×C73C2×C22⋊C412yes—
152C2×C4×C73AGL(1,ℤ/8)14yes—
153C2×C4×C73C23×C411yescharacteristic
154C2×C4×C73C22×D411yescharacteristic
155C2×C4×C73C2×#4114yes—
156C22⋊D73—416no—
157C2×Dic73—24no—
158C2×Dic73—44no—
159D292—28no—
160D292—48no—
161D292—44no—
162D292—48no—
163C4×D73—416no—
164Dic146—48no—
165#10596831—44no—
166C22×C73—22no—
167C22×C73—22no—
168C22×C73—22no—
169C22×C73—44no—
170C22×C73C22×C22⋊C411yescharacteristic
171C22×C73#52512yes—
172C22×C73C2×AGL(1,ℤ/8)12yes—
173C22×C73#57512yes—
174C2×D73—44no—
175C2×D73—44no—
176C2×D73—44no—
177C2×D73—88no—
178C4×C73—22no—
179C4×C73—22no—
180C4×C73—22no—
181C4×C73—22no—
182C4×C73—48no—
183C4×C73#41814yes—
184C4×C73C4×#4112yes—
185C4×C73#53212yes—
186Dic73—44no—
187#21393—731nomaximal, Sylow
188C2×C73—42no—
189C2×C73#229711yescharacteristic
190C2×C73C2×#41811yescharacteristic
191C2×C73#289611yescharacteristic
192C2×C73#311514yes—
193D73—84no—
194C2×#532—731no—
195C2×#432—731no—
196C4×#117D7311yescharacteristic, complemented
197#1988—732no—
198#1982—732no—
199#1875—734no—
200#1762—734no—
201C73#2139311yescharacteristic, complemented, Sylow
202C22×#41—1461no—
203#532—738no—
204#532—1464no—
205C2×C4⋊Q8—731no—
206C2×#127—731no—
207C2×#124—1461no—
208C2×#121—732no—
209C2×#121—1461no—
210C2×C4×D4—732no—
211C2×C4×D4—1461no—
212C2×#117C2×D7312yes—
213C22×C42C2×D7311yescharacteristic
214#432—1464no—
215C2×C4⋊C8—732no—
216C2×#102—738no—
217C2×C22⋊C8—732no—
218C2×#97—732no—
219C4×C4⋊C4C2×D7312yes—
220C4×C4⋊C4C2×D7312yes—
221C4×C22⋊C4—21no—
222C4×C22⋊C4—21no—
223#376—21no—
224C43—21no—
225#340—738no—
226C2×#41—2928no—
227C2×#41—1468no—
228C22×Q8—1461no—
229C22×D4—732no—
230C22×D4—1462no—
231C22×D4—1461no—
232C22×D4—1461no—
233C23×C4—1462no—
234C23×C4C22⋊D7311yescharacteristic
235C23×C4C22⋊D7311yescharacteristic
236C23×C4C22×D7311yescharacteristic
237C22×C8—734no—
238C4⋊Q8—734no—
239C4⋊Q8—1462no—
240#127—734no—
241#127—1462no—
242#124—1468no—
243#121—738no—
244#121—1468no—
245#121—1464no—
246C4×D4—738no—
247C4×D4—1468no—
248C4×D4—1464no—
249#117—28no—
250C2×C4⋊C4—732no—
251C2×C4⋊C4—1461no—
252C2×C4⋊C4C22×D7314yes—
253C2×C22⋊C4—22no—
254C2×C22⋊C4—1462no—
255C2×C22⋊C4—1462no—
256C2×C42—22no—
257C2×C42—22no—
258C2×C42—22no—
259C2×C42C4×D7314yes—
260C2×C42D29214yes—
261C2×C42C22⋊D7311yescharacteristic
262C2×C42C22⋊D7311yescharacteristic
263C2×C42C22×D7311yescharacteristic
264C2×C42C22×D7311yescharacteristic
265C4⋊C8—1464no—
266#102—14616no—
267C22⋊C8—1464no—
268#97—1464no—
269#95—22no—
270#95—22no—
271C24—1462no—
272C24C2×C22⋊D7311yescharacteristic
273#41—29232no—
274C2×Q8—2924no—
275C2×Q8—1464no—
276C2×D4—2924no—
277C2×D4—2928no—
278C2×D4—2924no—
279C2×D4—734no—
280C2×D4—1468no—
281C2×D4—1464no—
282C2×D4—1464no—
283C2×D4—1462no—
284C2×D4—1468no—
285C22×C4—24no—
286C22×C4—24no—
287C22×C4—24no—
288C22×C4—42no—
289C22×C4—2928no—
290C22×C4—1462no—
291C22×C4—1468no—
292C22×C4#1192400514yes—
293C22×C4#1192400514yes—
294C22×C4C2×C4×D7312yes—
295C22×C4C2×C22⋊D7311yescharacteristic
296C22×C4C2×C22⋊D7311yescharacteristic
297C22×C4C2×C22⋊D7311yescharacteristic
298C22×C4C2×C22⋊D7311yescharacteristic
299C22×C4C2×C22⋊D7311yescharacteristic
300C22×C4C2×D29212yes—
301C22×C4C23×D7311yescharacteristic
302C2×C8—1464no—
303C2×C8—1468no—
304C4⋊C4—24no—
305C4⋊C4—734no—
306C4⋊C4—1464no—
307C4⋊C4—1462no—
308C4⋊C4#1192402818yescomplemented
309C22⋊C4—28no—
310C22⋊C4—1468no—
311C22⋊C4—1468no—
312C42—28no—
313C42—44no—
314C42—44no—
315C42#1192400514yes—
316C42#1192400514yes—
317C42C2×C4×D7312yes—
318C42C2×C4×D7312yes—
319C42C2×D29212yes—
320C42C2×D29212yes—
321C23—22no—
322C23—22no—
323C23—22no—
324C23—2924no—
325C23—2924no—
326C23—2924no—
327C23—1464no—
328C23C2×#1192400512yes—
329C23C22×C22⋊D7311yescharacteristic
330Q8—2928no—
331D4—2928no—
332D4—29216no—
333D4—2924no—
334D4—2928no—
335D4—1468no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—28no—
343C2×C4—28no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—44no—
347C2×C4—29216no—
348C2×C4—2924no—
349C2×C4—1464no—
350C2×C4C2×#1192400512yes—
351C2×C4C2×#1192400512yes—
352C2×C4C2×#1192400512yes—
353C2×C4C2×#1192400512yes—
354C2×C4C2×#1192400512yes—
355C2×C4#1455661614yes—
356C2×C4C22×C4×D7311yescharacteristic
357C2×C4C22×D29211yescharacteristic
358C2×C4C2×#1192402814yes—
359C8—2924no—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—44no—
364C22—2924no—
365C22—2924no—
366C22—2924no—
367C22—5848no—
368C22C22×#1192400511yescharacteristic
369C22#1798909812yes—
370C22C2×#1455661612yes—
371C22#1798938512yes—
372C4—22no—
373C4—22no—
374C4—22no—
375C4—22no—
376C4—48no—
377C4—2924no—
378C4#1798859114yes—
379C4C4×#1192402812yes—
380C4#1798913712yes—
381C2—42no—
382C2—5844no—
383C2#2261242111yescharacteristic
384C2C2×#1798859111yescharacteristic
385C2#2261844811yescharacteristic
386C2#2262008214yes—
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC4×#117×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989137C2
cosocleC22×C4×C73C24
hypercenterC4×#117D73
hypocenterC73#21393
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#117

Complements

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

NH ≅ G/Ntype
2. C2×#17988644C2semidirect
3. #22610883C2semidirect
4. #22610858C2semidirect
5. #22610253C2semidirect
6. #22609759C2semidirect
7. C4×#117×C73C2semidirect
10. #17989137C4semidirect
116. C4⋊C4×C73#41semidirect
196. C4×#117D73semidirect
201. C73#21393semidirect
308. C4⋊C4#11924028semidirect

Maximal subgroups

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

subgroupindex
C2×#179891372
C2×#179886442
#226108832
#226108582
#226102532
#226097592
C4×#117×C732
#2139373