Finite Group Databasebeta

← #34008346

Subgroups — #34008346

Order 18688.

1646 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
1C2×#17989529C212yesmaximal
2C2×#17989461C214yesmaximal, complemented
3C23×C8×D73C211yesmaximal, characteristic
4C22×C4⋊#64408C2214yes—
5C22×C22⋊#64408—22no—
6#17989529—24no—
7#17989529C418yescomplemented
8C2×(C2×#64408)⋊C4—22no—
9#17989461—28no—
10C23×C4×D73C2211yescharacteristic
11C23×#10596831C411yescharacteristic, complemented
12C22×C8×D73—24no—
13C22×C8×D73—28no—
14C22×C8×D73C412yescomplemented
15C22×C8×D73C2212yes—
16C23×C8×C73C411yescharacteristic, complemented
17C23×#64408—24no—
18C2×C4⋊#64408—28no—
19C2×C4⋊#64408—24no—
20C2×C4⋊#64408—28no—
21C2×C4⋊#64408C2×C418yes—
22C2×C22⋊#64408—28no—
23C2×C22⋊#64408—44no—
24C2×C22⋊#64408—44no—
25(C2×#64408)⋊C4—28no—
26C24×D73D411yescharacteristic
27C23×Dic73Q811yescharacteristic
28C22×C4×D73—24no—
29C22×C4×D73—24no—
30C22×C4×D73C2×C414yes—
31C22×C4×D73C2×C411yescharacteristic
32C22×C4×D73D414yes—
33C22×C4×D73D411yescharacteristic
34C22×C4×D73Q811yescharacteristic
35C22×C4×D73C2311yescharacteristic
36C22×#10596831—24no—
37C22×#10596831—22no—
38C22×#10596831C2×C412yes—
39C2×C8×D73—232no—
40C2×C8×D73—24no—
41C2×C8×D73—24no—
42C2×C8×D73—24no—
43C2×C8×D73—24no—
44C2×C8×D73—24no—
45C2×C8×D73D418yes—
46C23×C4×C73C2×C411yescharacteristic
47C22×C8×C73—22no—
48C22×C8×C73—24no—
49C22×C8×C73C2×C412yes—
50C22×#64408—28no—
51C22×#64408—48no—
52C22×#64408—44no—
53C22×#64408—44no—
54C22×#64408—48no—
55C4⋊#64408—216no—
56C4⋊#64408—44no—
57C4⋊#64408—44no—
58C22⋊#64408—416no—
59C23×D73—24no—
60C23×D73—24no—
61C23×D73C22⋊C414yes—
62C23×D73C4⋊C411yescharacteristic
63C23×D73D812yes—
64C23×D73SD1614yes—
65C23×D73Q1612yes—
66C23×D73C2×D411yescharacteristic
67C22×Dic73—24no—
68C22×Dic73C4⋊C411yescharacteristic
69C22×Dic73C4⋊C414yes—
70C22×Dic73C2×Q811yescharacteristic
71C2×C4×D73—24no—
72C2×C4×D73—22no—
73C2×C4×D73—22no—
74C2×C4×D73—24no—
75C2×C4×D73—216no—
76C2×C4×D73—28no—
77C2×C4×D73—28no—
78C2×C4×D73C4212yes—
79C2×C4×D73C22⋊C414yes—
80C2×C4×D73C22⋊C412yes—
81C2×C4×D73C4⋊C414yes—
82C2×C4×D73C22×C412yes—
83C2×C4×D73C2×D414yes—
84C2×C4×D73C2×D412yes—
85C2×C4×D73#4114yes—
86C2×#10596831—28no—
87C2×#10596831—22no—
88C2×#10596831—22no—
89C2×#10596831C22⋊C414yescomplemented
90C8×D73—216no—
91C8×D73—216no—
92C24×C73C4⋊C411yescharacteristic
93C22×C4×C73—22no—
94C22×C4×C73—22no—
95C22×C4×C73C4212yes—
96C22×C4×C73C22⋊C412yes—
97C22×C4×C73C4⋊C411yescharacteristic
98C22×C4×C73C22×C411yescharacteristic
99C2×C8×C73—28no—
100C2×C8×C73—22no—
101C2×C8×C73—22no—
102C2×C8×C73C22⋊C414yescomplemented
103C23×C73—22no—
104C23×C73—22no—
105C23×C73#9512yes—
106C23×C73#10612yes—
107C23×C73#10712yes—
108C23×C73C2×C4⋊C411yescharacteristic
109C22×D73—22no—
110C22×D73—22no—
111C22×D73—28no—
112C22×D73—28no—
113C22×D73—216no—
114C22×D73—28no—
115C22×D73—28no—
116C22×D73#9512yes—
117C22×D73#10218yes—
118C22×D73#10318yes—
119C22×D73#10612yes—
120C22×D73#10712yes—
121C22×D73C2×C22⋊C412yes—
122C22×D73#12114yes—
123C22×D73C2×D811yescharacteristic
124C22×D73C2×SD1612yes—
125C22×D73C2×Q1611yescharacteristic
126C22×D73#13514yes—
127C2×#64408—48no—
128C2×#64408—48no—
129C2×#64408—48no—
130C2×#64408—88no—
131C2×#64408—88no—
132C2×C4×C73—22no—
133C2×C4×C73—24no—
134C2×C4×C73—22no—
135C2×C4×C73—22no—
136C2×C4×C73#9512yes—
137C2×C4×C73C2×C4211yescharacteristic
138C2×C4×C73C2×C22⋊C412yes—
139C2×C4×C73C2×C22⋊C411yescharacteristic
140C2×C4×C73#11712yes—
141C2×Dic73—22no—
142C2×Dic73—28no—
143C2×Dic73#9512yes—
144C2×Dic73C2×C4⋊C412yes—
145C2×Dic73C22⋊Q814yes—
146C4×D73—28no—
147C4×D73—24no—
148C4×D73—22no—
149C4×D73—22no—
150C4×D73—28no—
151C4×D73C4×D418yes—
152C4×D73#12014yes—
153C4×D73#12314yes—
154C8×C73—24no—
155#10596831—24no—
156C22×C73—24no—
157C22×C73—24no—
158C22×C73—22no—
159C22×C73—22no—
160C22×C73#34014yescomplemented
161C22×C73C2×#9511yescharacteristic
162C22×C73#38012yes—
163C22×C73C2×#10611yescharacteristic
164C22×C73C2×#10711yescharacteristic
165C22×C73#42712yes—
166C2×D73—24no—
167C2×D73—24no—
168C2×D73—22no—
169C2×D73—22no—
170C2×D73—216no—
171C2×D73—216no—
172C2×D73#34014yescomplemented
173C2×D73#38614yes—
174C2×D73C2×#10212yes—
175C2×D73C2×#10312yes—
176C2×D73#41614yes—
177C2×D73#46518yes—
178C2×D73#46614yes—
179C2×D73#46714yes—
180#64408—88no—
181C4×C73—22no—
182C4×C73C4×C22⋊C412yes—
183C4×C73#37911yescharacteristic
184C4×C73#38111yescharacteristic
185Dic73—22no—
186Dic73#38514yes—
187#10721—731nomaximal, Sylow
188C2×C73—24no—
189C2×C73C22⋊#9511yescharacteristic
190C2×C73C2×#34011yescharacteristic
191C2×C73#173511yescharacteristic
192C2×C73#180712yes—
193C2×C73#180812yes—
194D73—24no—
195D73#189214yes—
196D73#189314yes—
197C24×C8—731no—
198C2×#380—732no—
199C2×#340—734no—
200C73#1072111yescharacteristic, complemented, Sylow
201C24×C4—731no—
202C23×C8—732no—
203C23×C8—731no—
204C23×C8—732no—
205C23×C8—1468no—
206C23×C8—1464no—
207C23×C8#6440811yescharacteristic, complemented
208C22×C4⋊C4—734no—
209C22×C22⋊C4—1462no—
210#380—738no—
211#380—1464no—
212C2×#95—1462no—
213#340—1468no—
214C25—731no—
215C23×C4—731no—
216C23×C4—731no—
217C23×C4—734no—
218C23×C4—734no—
219C23×C4—731no—
220C23×C4—731no—
221C23×C4—731no—
222C23×C4—1464no—
223C23×C4—1464no—
224C23×C4—1464no—
225C23×C4C2×#6440811yescharacteristic
226C22×C8—22no—
227C22×C8—24no—
228C22×C8—732no—
229C22×C8—738no—
230C22×C8—1464no—
231C22×C8—1464no—
232C22×C8—1464no—
233C22×C8—1464no—
234C22×C8—14632no—
235C22×C8—1464no—
236C22×C8—1462no—
237C22×C8—1464no—
238C22×C8C2×#6440812yes—
239C2×C4⋊C4—738no—
240C2×C4⋊C4—1464no—
241C2×C4⋊C4—1468no—
242C2×C4⋊C4—1468no—
243C2×C22⋊C4—2924no—
244C2×C22⋊C4—2924no—
245C2×C22⋊C4—1468no—
246#95—1468no—
247C24—731no—
248C24—734no—
249C24—734no—
250C24—732no—
251C24—732no—
252C24—731no—
253C24—1464no—
254C24—1464no—
255C24C4⋊#6440811yescharacteristic
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—2924no—
259C22×C4—2924no—
260C22×C4—2928no—
261C22×C4—2928no—
262C22×C4—731no—
263C22×C4—732no—
264C22×C4—734no—
265C22×C4—732no—
266C22×C4—734no—
267C22×C4—734no—
268C22×C4—731no—
269C22×C4—734no—
270C22×C4—734no—
271C22×C4—732no—
272C22×C4—732no—
273C22×C4—1468no—
274C22×C4—1464no—
275C22×C4—14616no—
276C22×C4—1468no—
277C22×C4—1464no—
278C22×C4—1468no—
279C22×C4—1464no—
280C22×C4—1462no—
281C22×C4—1462no—
282C22×C4C4×#6440812yes—
283C22×C4C22⋊#6440812yes—
284C22×C4C4⋊#6440811yescharacteristic
285C22×C4C22×#6440811yescharacteristic
286C2×C8—28no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—734no—
290C2×C8—14616no—
291C2×C8—14616no—
292C2×C8—1468no—
293C2×C8—1462no—
294C2×C8—1462no—
295C2×C8C22⋊#6440814yescomplemented
296C4⋊C4—2924no—
297C4⋊C4—2924no—
298C4⋊C4—14616no—
299C22⋊C4—29216no—
300C23—22no—
301C23—22no—
302C23—732no—
303C23—734no—
304C23—732no—
305C23—731no—
306C23—731no—
307C23—734no—
308C23—738no—
309C23—738no—
310C23—732no—
311C23—732no—
312C23—732no—
313C23—1468no—
314C23—14616no—
315C23—1468no—
316C23—1468no—
317C23—1468no—
318C23—1462no—
319C23—1462no—
320C23(C2×#64408)⋊C412yes—
321C23#1455665912yes—
322C23#1455666012yes—
323C23C2×C4⋊#6440811yescharacteristic
324C2×C4—22no—
325C2×C4—24no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—2928no—
329C2×C4—2928no—
330C2×C4—2928no—
331C2×C4—5848no—
332C2×C4—5848no—
333C2×C4—732no—
334C2×C4—734no—
335C2×C4—738no—
336C2×C4—734no—
337C2×C4—734no—
338C2×C4—732no—
339C2×C4—1468no—
340C2×C4—1468no—
341C2×C4—1468no—
342C2×C4—1462no—
343C2×C4—1464no—
344C2×C4—1462no—
345C2×C4—1462no—
346C2×C4(C2×#64408)⋊C412yes—
347C2×C4C2×C4×#6440811yescharacteristic
348C2×C4C2×C22⋊#6440812yes—
349C2×C4C2×C22⋊#6440811yescharacteristic
350C2×C4#1455667012yes—
351C8—24no—
352C8—1464no—
353C22—24no—
354C22—24no—
355C22—22no—
356C22—22no—
357C22—738no—
358C22—734no—
359C22—734no—
360C22—732no—
361C22—732no—
362C22—734no—
363C22—734no—
364C22—734no—
365C22—14616no—
366C22—14616no—
367C22—1464no—
368C22—1464no—
369C22—1462no—
370C22—1462no—
371C22#1798946114yescomplemented
372C22C2×(C2×#64408)⋊C411yescharacteristic
373C22#1798952912yes—
374C22C2×#1455665911yescharacteristic
375C22C2×#1455666011yescharacteristic
376C22#1798959712yes—
377C4—22no—
378C4—5848no—
379C4—734no—
380C4—1462no—
381C4C4×C22⋊#6440812yes—
382C4#1798952811yescharacteristic
383C4#1798953011yescharacteristic
384C2—24no—
385C2—734no—
386C2—734no—
387C2—1464no—
388C2#2262510511yescharacteristic
389C2C2×#1798946111yescharacteristic
390C2#2262561711yescharacteristic
391C2#2262580712yes—
392C2#2262580812yes—
subgroupG/H
centerC23C2×C4⋊#64408
commutatorC2×C4×C73C2×C42
FrattiniC22×C4C22×#64408
FittingC23×C8×C73C4
socleC23×C73C2×C4⋊C4
prime radicalC24×D73D4
cosocleC22×C4×D73C23
hypercenterC23×C8#64408
hypocenterC73#10721
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
2. C2×#17989461C2semidirect
7. #17989529C4semidirect
11. C23×#10596831C4semidirect
14. C22×C8×D73C4semidirect
16. C23×C8×C73C4semidirect
89. C2×#10596831C22⋊C4semidirect
102. C2×C8×C73C22⋊C4semidirect
160. C22×C73#340semidirect
172. C2×D73#340semidirect
200. C73#10721semidirect
207. C23×C8#64408semidirect
295. C2×C8C22⋊#64408semidirect
371. C22#17989461semidirect

Maximal subgroups

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

subgroupindex
C2×#179895292
C2×#179894612
C23×C8×D732
#1072173