Finite Group Databasebeta

← #33090025

Subgroups — #33090025

Order 18688.

1562 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623264C211yesmaximal, characteristic
2C2×#17988603C212yesmaximal, complemented
3C22×#14556517C212yesmaximal, complemented
4#22612415C211yesmaximal, characteristic, complemented
5#22610850C218yesmaximal, complemented
6C73×#2873C211yesmaximal, characteristic, complemented
7C22×#11924028C2212yes—
8#17989168—22no—
9#17989163C414yescomplemented
10#17989156C414yescomplemented
11#17989149—22no—
12#17989137C2214yes—
13#17989099—24no—
14C2×#14556550C2211yescharacteristic
15C22×C4×Dic73C2211yescharacteristic
16#17988603—28no—
17C2×#14556517—28no—
18C2×#14556517C2218yescomplemented
19C2×#14556517C2218yescomplemented
20#17988486—22no—
21#17988462—22no—
22C4×C4⋊Dic73C2214yescomplemented
23C22×M16×C73C2212yes—
24C2×#117×C73C2211yescharacteristic
25#405×C73—24no—
26C4×M16×C73C2214yescomplemented
27C2×#11924028—22no—
28C2×#11924028—22no—
29C2×#11924028—24no—
30C2×#11924028—24no—
31C2×#11924028—24no—
32C2×#11924028—24no—
33C2×#11924028C2×C414yes—
34C2×#11924028C2314yes—
35C22×Dic146C2×C412yes—
36C22×D292C2×C412yes—
37C22×C22⋊D73—22no—
38C23×Dic73—21no—
39C22×C4×D73—22no—
40#14556591C2×C414yescomplemented
41#14556588C2×C414yescomplemented
42#14556579C2×C418yescomplemented
43#14556575—28no—
44#14556571—28no—
45#14556566—28no—
46#14556565—28no—
47#14556561—28no—
48C4×D292—28no—
49#14556550—24no—
50C2×C4⋊Dic73—24no—
51C2×C4⋊Dic73—21no—
52C2×C22⋊Dic73—21no—
53C2×C4×Dic73—24no—
54C2×C4×Dic73—21no—
55C2×C4×Dic73C2312yes—
56C2×C4×Dic73C2312yes—
57#14556517—216no—
58#14556517—216no—
59#14556498—24no—
60C23×C4×C73C2311yescharacteristic
61C2×M16×C73—22no—
62C2×M16×C73—24no—
63C2×M16×C73D418yescomplemented
64C2×M16×C73C2314yes—
65C22×C8×C73—22no—
66#117×C73C2×C414yes—
67#117×C73D414yes—
68C2×C4⋊C4×C73D412yes—
69C2×C22⋊C4×C73D412yes—
70C2×C42×C73C2312yes—
71#97×C73—24no—
72C4×C8×C73—24no—
73C23×D73—22no—
74#11924028—28no—
75#11924028—28no—
76#11924028—24no—
77#11924028—24no—
78#11924028—24no—
79#11924028—24no—
80#11924028—44no—
81#11924028—44no—
82#11924028—44no—
83#11924028—44no—
84C2×Dic146—24no—
85C2×Dic146—24no—
86C2×Dic146—22no—
87C2×Dic146C22×C414yes—
88C2×D292—24no—
89C2×D292—24no—
90C2×D292—22no—
91C2×D292—28no—
92C2×D292C22×C414yes—
93C2×C22⋊D73—24no—
94C2×C22⋊D73—24no—
95C2×C22⋊D73—44no—
96C2×C22⋊D73—44no—
97C22×Dic73—22no—
98C22×Dic73—22no—
99C22×Dic73—22no—
100C22×Dic73—44no—
101C22×Dic73—42no—
102C2×C4×D73—24no—
103C2×C4×D73—24no—
104C2×C4×D73—44no—
105C2×C4×D73—44no—
106C4⋊Dic73—28no—
107C4⋊Dic73—48no—
108C4⋊Dic73—42no—
109C22⋊Dic73—42no—
110#11924005—216no—
111C4×Dic73—24no—
112C4×Dic73—24no—
113C4×Dic73—42no—
114C24×C73C2×D411yescharacteristic
115C22×C4×C73C22×C412yes—
116C22×C4×C73C2×D412yes—
117C22×C4×C73C2×D414yes—
118C22×C4×C73C2×D411yescharacteristic
119C22×C4×C73C2×D414yes—
120C22×C4×C73#4114yes—
121C22×C4×C73C2411yescharacteristic
122M16×C73—28no—
123M16×C73—24no—
124M16×C73C2×D418yes—
125C2×C8×C73—28no—
126C2×C8×C73—24no—
127C4⋊C4×C73C22⋊C418yes—
128C22⋊C4×C73C22⋊C418yes—
129C42×C73C22×C414yes—
130C42×C73C2×D414yes—
131C23×C73—42no—
132C23×C73C2×C22⋊C412yes—
133C23×C73#12412yes—
134C23×C73#12712yes—
135C23×C73C22×D411yescharacteristic
136C22×D73—24no—
137C22×D73—44no—
138C22×D73—84no—
139C2×C4×C73—44no—
140C2×C4×C73C2×C22⋊C418yes—
141C2×C4×C73C2×C22⋊C412yes—
142C2×C4×C73C4×D414yes—
143C2×C4×C73C4×D414yes—
144C2×C4×C73#12114yes—
145C2×C4×C73#12114yes—
146C2×C4×C73#12412yes—
147C2×C4×C73#12712yes—
148C2×C4×C73C23×C411yescharacteristic
149C2×C4×C73C22×D411yescharacteristic
150C2×C4×C73C22×D412yes—
151C2×C4×C73C2×#4112yes—
152C22⋊D73—44no—
153C22⋊D73—44no—
154C22⋊D73—48no—
155C2×Dic73—24no—
156C2×Dic73—24no—
157C2×Dic73—42no—
158C2×Dic73—48no—
159C2×Dic73—42no—
160C2×Dic73—44no—
161C2×Dic73—44no—
162C2×Dic73—42no—
163D292—24no—
164D292—24no—
165D292—44no—
166D292—88no—
167C4×D73—44no—
168C4×D73—44no—
169C4×D73—48no—
170Dic146—24no—
171Dic146—24no—
172Dic146—44no—
173C8×C73—28no—
174C22×C73—22no—
175C22×C73—24no—
176C22×C73—42no—
177C22×C73—42no—
178C22×C73#39014yes—
179C22×C73C22×C22⋊C411yescharacteristic
180C22×C73C2×#12411yescharacteristic
181C22×C73C2×#12711yescharacteristic
182C2×D73—48no—
183C2×D73—44no—
184C2×D73—88no—
185C4×C73—28no—
186C4×C73#39014yes—
187C4×C73C2×C4×D412yes—
188C4×C73C2×#12112yes—
189Dic73—44no—
190Dic73—44no—
191Dic73—82no—
192#21253—731nomaximal, Sylow
193C2×C73—21no—
194C2×C73—24no—
195C2×C73—21no—
196C2×C73C2×#39011yescharacteristic
197C2×C73#290112yes—
198D73—84no—
199#3449—731no—
200C2×#421—732no—
201C22×#104—732no—
202#2873D7311yescharacteristic, complemented
203#2296—731no—
204#1980—738no—
205C73#2125311yescharacteristic, complemented, Sylow
206C22×#41—732no—
207C22×M16C2×D7312yes—
208#537—1462no—
209#536—734no—
210#535—734no—
211#534—1462no—
212#532—734no—
213#525—1464no—
214C2×#117—731no—
215C2×#117C2×D7311yescharacteristic
216C22×C42—731no—
217#421—1468no—
218C2×#104—738no—
219C2×#104—738no—
220C2×#104—1468no—
221#405—24no—
222C4×M16C2×D7314yescomplemented
223#389—1462no—
224#385—1462no—
225C4×C4⋊C4—734no—
226C2×#41—734no—
227C2×#41—734no—
228C2×#41—1464no—
229C2×#41—1464no—
230C2×#41—1464no—
231C2×#41—1464no—
232C2×#41—1462no—
233C2×#41—1462no—
234C22×Q8—732no—
235C22×D4—732no—
236C22×D4—1462no—
237C23×C4—1461no—
238C23×C4—1462no—
239C23×C4C22×D7311yescharacteristic
240C2×M16—22no—
241C2×M16—24no—
242C2×M16D29218yescomplemented
243C2×M16C22×D7314yes—
244C22×C8—22no—
245C4⋊Q8—734no—
246#127—734no—
247#124—738no—
248#123—1468no—
249C22⋊Q8—1468no—
250#121—1468no—
251#121—1468no—
252#120—1468no—
253C4×D4—1468no—
254#117—1464no—
255#117C4×D7314yes—
256#117C22⋊D7314yes—
257C2×C4⋊C4—1461no—
258C2×C4⋊C4—1464no—
259C2×C4⋊C4D29212yes—
260C2×C22⋊C4—1461no—
261C2×C22⋊C4D29212yes—
262C2×C42—732no—
263C2×C42—732no—
264C2×C42—1461no—
265C2×C42—1464no—
266C2×C42C22×D7312yes—
267#104—14616no—
268#104—14616no—
269#97—24no—
270C4×C8—24no—
271#95—1464no—
272C24—1462no—
273C24C2×D29211yescharacteristic
274#41—2924no—
275#41—2924no—
276#41—2924no—
277#41—2924no—
278#41—1468no—
279#41—1468no—
280#41—1464no—
281#41—1464no—
282#41—1464no—
283#41—1464no—
284C2×Q8—734no—
285C2×Q8—1464no—
286C2×Q8—1464no—
287C2×Q8—1462no—
288C2×D4—2924no—
289C2×D4—2924no—
290C2×D4—734no—
291C2×D4—1464no—
292C2×D4—1464no—
293C2×D4—1462no—
294C2×D4—1468no—
295C2×D4—1464no—
296C2×D4—1464no—
297C22×C4—2922no—
298C22×C4—2924no—
299C22×C4—2924no—
300C22×C4—2924no—
301C22×C4—1462no—
302C22×C4—1462no—
303C22×C4—1462no—
304C22×C4—1464no—
305C22×C4—1464no—
306C22×C4C2×C4×D7312yes—
307C22×C4C2×C22⋊D7312yes—
308C22×C4C2×D29214yes—
309C22×C4C2×D29211yescharacteristic
310C22×C4C2×D29214yes—
311C22×C4#1192402814yes—
312C22×C4C23×D7311yescharacteristic
313M16—28no—
314M16—24no—
315M16C2×D29218yes—
316C2×C8—28no—
317C2×C8—24no—
318C4⋊C4—2928no—
319C4⋊C4—2922no—
320C4⋊C4—1468no—
321C4⋊C4#1192400518yes—
322C22⋊C4—2922no—
323C22⋊C4—14616no—
324C22⋊C4#1192400518yes—
325C42—2922no—
326C42—1464no—
327C42—1464no—
328C42C2×C4×D7314yes—
329C42C2×C22⋊D7314yes—
330C23—42no—
331C23—2924no—
332C23—5844no—
333C23—1464no—
334C23C2×#1192400512yes—
335C23#1455657912yes—
336C23#1455658812yes—
337C23C22×D29211yescharacteristic
338Q8—2924no—
339Q8—1464no—
340Q8—1464no—
341D4—2924no—
342D4—2928no—
343D4—2924no—
344D4—2924no—
345D4—5848no—
346D4—1464no—
347D4—1464no—
348C2×C4—44no—
349C2×C4—2922no—
350C2×C4—2928no—
351C2×C4—2922no—
352C2×C4—2924no—
353C2×C4—2928no—
354C2×C4—2924no—
355C2×C4—2924no—
356C2×C4—2924no—
357C2×C4—2922no—
358C2×C4—1464no—
359C2×C4—1464no—
360C2×C4C2×#1192400518yes—
361C2×C4C2×#1192400512yes—
362C2×C4C4×D29214yes—
363C2×C4C4×D29214yes—
364C2×C4#1455656514yes—
365C2×C4#1455656514yes—
366C2×C4#1455657912yes—
367C2×C4#1455658812yes—
368C2×C4C22×C4×D7311yescharacteristic
369C2×C4C22×C22⋊D7311yescharacteristic
370C2×C4C22×D29212yes—
371C2×C4C2×#1192402812yes—
372C8—28no—
373C22—22no—
374C22—24no—
375C22—42no—
376C22—42no—
377C22—2928no—
378C22—2924no—
379C22—5848no—
380C22#1798848914yes—
381C22C22×#1192400511yescharacteristic
382C22C2×#1455657911yescharacteristic
383C22C2×#1455658811yescharacteristic
384C4—28no—
385C4—2924no—
386C4—2924no—
387C4—5842no—
388C4#1798848914yes—
389C4C2×C4×D29212yes—
390C4C2×#1455656512yes—
391C2—21no—
392C2—24no—
393C2—21no—
394C2—5844no—
395C2C2×#1798848911yescharacteristic
396C2#2261847612yes—
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2873C2
socleC22×C73C22×C22⋊C4
prime radical#22623264C2
cosocleC22×C4×C73C24
hypercenter#2873D73
hypocenterC73#21253
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×#117 ◁ #2873

Complements

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

NH ≅ G/Ntype
2. C2×#17988603C2semidirect
3. C22×#14556517C2semidirect
4. #22612415C2semidirect
5. #22610850C2semidirect
6. C73×#2873C2semidirect
9. #17989163C4semidirect
10. #17989156C4semidirect
18. C2×#14556517C22semidirect
19. C2×#14556517C22semidirect
22. C4×C4⋊Dic73C22semidirect
26. C4×M16×C73C22semidirect
40. #14556591C2×C4semidirect
41. #14556588C2×C4semidirect
42. #14556579C2×C4semidirect
63. C2×M16×C73D4semidirect
202. #2873D73semidirect
205. C73#21253semidirect
222. C4×M16C2×D73semidirect
242. C2×M16D292semidirect

Maximal subgroups

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

subgroupindex
#226232642
C2×#179886032
C22×#145565172
#226124152
#226108502
C73×#28732
#2125373