Finite Group Databasebeta

← C2×#22611640 #33238879

Subgroups — C2×#22611640 #33238879

Order 18688.

1214 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556610C211yesmaximal, characteristic
2C22×#14556530C211yesmaximal, characteristic, complemented
3C2×#107×D73C211yesmaximal, characteristic, complemented
4#22611640C218yesmaximal, direct product factor
5C2×#17988392C211yesmaximal, characteristic, complemented
6C2×#17988390C211yesmaximal, characteristic, complemented
7C2×#17988388C211yesmaximal, characteristic, complemented
8C2×#357×C73C211yesmaximal, characteristic, complemented
9C22×#11924027—21no—
10C2×#14556610—22no—
11C2×#14556610—24no—
12C2×#14556610C418yescomplemented
13C2×#14556610C2214yes—
14C22×Dic292C2211yescharacteristic
15C22×#11924016—21no—
16C22×C8×D73C2211yescharacteristic
17C2×C4⋊C4×D73—21no—
18C2×#14556530—24no—
19C2×#14556530C2214yescomplemented
20C22×#11924003C2211yescharacteristic
21C2×#14556525C2211yescharacteristic
22C2×#14556524—21no—
23#107×D73—22no—
24#107×D73C2214yescomplemented
25#17988392C2214yescomplemented
26#17988390C2214yescomplemented
27#17988388C2214yescomplemented
28C22×D8×C73C2211yescharacteristic
29C22×C16×C73C2211yescharacteristic
30C2×#107×C73C2211yescharacteristic
31#357×C73C2214yescomplemented
32C2×#11924027—28no—
33C2×#11924027—24no—
34C2×#11924027—42no—
35C2×#11924027—44no—
36C22×Dic146—21no—
37C22×C22⋊D73—41no—
38C23×Dic73—41no—
39C22×C4×D73—41no—
40C22×C4×D73D411yescharacteristic
41#14556610—216no—
42#14556610—28no—
43#14556610C2×C4116yescomplemented
44C2×Dic292—21no—
45C2×Dic292—22no—
46C2×Dic292C2×C414yescomplemented
47C2×Dic292C2312yes—
48C2×#11924016—28no—
49C2×#11924016—24no—
50C22×#10596831D411yescharacteristic
51C2×C8×D73C2×C414yes—
52C2×C8×D73D412yes—
53C2×C8×D73D414yes—
54C2×C8×D73C2312yes—
55C2×C4⋊Dic73—21no—
56C2×#11924007—41no—
57C4⋊C4×D73—24no—
58C4⋊C4×D73—42no—
59#14556530—28no—
60C2×#11924003—22no—
61C2×#11924003C2312yes—
62#14556525—21no—
63#14556525C2312yes—
64#14556524—24no—
65C22×D4×C73—21no—
66C2×D8×C73—21no—
67C2×D8×C73—22no—
68C2×D8×C73C2×C414yescomplemented
69C2×D8×C73C2312yes—
70C22×C8×C73C2311yescharacteristic
71C2×C4⋊C4×C73—21no—
72C2×C16×C73—22no—
73C2×C16×C73C2312yes—
74#107×C73—21no—
75#107×C73C2312yes—
76C23×D73D811yescharacteristic
77#11924027—216no—
78#11924027—416no—
79#11924027—48no—
80C2×Dic146—24no—
81C2×Dic146—22no—
82C2×Dic146—41no—
83C2×Dic146—42no—
84C2×C22⋊D73—48no—
85C2×C22⋊D73—44no—
86C22×Dic73—41no—
87C22×Dic73—48no—
88C22×Dic73—44no—
89C22×Dic73—41no—
90C22×Dic73D811yescharacteristic
91C2×C4×D73—44no—
92C2×C4×D73—84no—
93C2×C4×D73C22⋊C414yes—
94C2×C4×D73D812yes—
95C2×C4×D73SD1614yes—
96C2×C4×D73C2×D412yes—
97Dic292—24no—
98Dic292—22no—
99Dic292C22×C414yescomplemented
100#11924016—216no—
101C2×#10596831C22⋊C414yes—
102C2×#10596831C2×D412yes—
103C8×D73C22⋊C418yes—
104C8×D73C22×C414yes—
105C8×D73C2×D414yes—
106C4⋊Dic73—22no—
107C4⋊Dic73—41no—
108#11924007—44no—
109#11924003—22no—
110C24×C73—41no—
111C2×D4×C73—24no—
112C2×D4×C73—22no—
113C2×D4×C73—41no—
114C2×D4×C73—42no—
115C22×C4×C73—41no—
116C22×C4×C73C2×D411yescharacteristic
117D8×C73—24no—
118D8×C73—22no—
119D8×C73C22×C414yescomplemented
120C2×C8×C73C22×C412yes—
121C2×C8×C73C2×D411yescharacteristic
122C2×C8×C73C2×D412yes—
123C2×C8×C73C2411yescharacteristic
124C4⋊C4×C73—22no—
125C4⋊C4×C73—41no—
126C16×C73—22no—
127C23×C73—42no—
128C23×C73—44no—
129C23×C73—82no—
130C23×C73—82no—
131C23×C73C2×D811yescharacteristic
132C22×D73—22no—
133C22×D73—22no—
134C22×D73#10214yes—
135C22×D73C2×D812yes—
136D4×C73—24no—
137D4×C73—42no—
138D4×C73—44no—
139C2×C4×C73—42no—
140C2×C4×C73—82no—
141C2×C4×C73C2×C22⋊C412yes—
142C2×C4×C73C2×D811yescharacteristic
143C2×C4×C73C2×SD1612yes—
144C2×C4×C73C22×D411yescharacteristic
145C22⋊D73—416no—
146C2×Dic73—42no—
147C2×Dic73—44no—
148C2×Dic73—416no—
149C2×Dic73—42no—
150C2×Dic73—82no—
151C2×Dic73#10214yes—
152C2×Dic73C2×D812yes—
153C4×D73—88no—
154C4×D73#10218yes—
155C4×D73C2×C22⋊C414yes—
156C4×D73C2×SD1614yes—
157Dic146—24no—
158Dic146—42no—
159Dic146—44no—
160C8×C73C2×C22⋊C412yes—
161C8×C73C23×C411yescharacteristic
162C8×C73C22×D411yescharacteristic
163#10596831C2×C22⋊C414yes—
164C22×C73—44no—
165C22×C73—82no—
166C22×C73—82no—
167C22×C73—88no—
168C22×C73C2×#10212yes—
169C22×C73#50912yes—
170C22×C73#51012yes—
171C22×C73C22×D811yescharacteristic
172C2×D73—22no—
173C2×D73—22no—
174C2×D73—28no—
175C2×D73C2×#10214yes—
176C4×C73—82no—
177C4×C73C2×#10212yes—
178C4×C73C22×C22⋊C411yescharacteristic
179C4×C73C22×SD1611yescharacteristic
180Dic73—44no—
181Dic73—82no—
182Dic73C2×#10214yes—
183C2×#2139—731nomaximal, Sylow
184C2×C73—84no—
185C2×C73#213914yescomplemented
186C2×C73C22×#10211yescharacteristic
187C2×C73C2×#50911yescharacteristic
188C2×C73C2×#51011yescharacteristic
189D73—24no—
190C22×#135—731no—
191C22×M32—731no—
192C22×#107—731no—
193#2139—738no—
194C2×#358—731no—
195C2×#358—731no—
196C2×#357—731no—
197C2×#357D7311yescharacteristic, complemented
198C73C2×#213911yescharacteristic, complemented, Sylow
199C22×#41—1461no—
200C2×#135—738no—
201C2×#135—734no—
202C2×#135—1462no—
203C2×#135—1464no—
204C22×Q16—731no—
205C22×SD16—1461no—
206C22×D8C2×D7311yescharacteristic
207C23×C8—731no—
208C22×C4⋊C4—1461no—
209C2×M32—734no—
210C2×M32—1464no—
211C22×C16—731no—
212C22×C16C2×D7311yescharacteristic
213C2×#107—731no—
214C2×#107—734no—
215C2×#107—1462no—
216C2×#107—1461no—
217C2×#107C2×D7311yescharacteristic
218#358—734no—
219#358—734no—
220#357—734no—
221#357C2×D7314yescomplemented
222C2×#41—2922no—
223C2×#41—2924no—
224C2×#41—1468no—
225C2×#41—1464no—
226C22×Q8—1461no—
227C22×D4—21no—
228C22×D4—2921no—
229C23×C4—2921no—
230C23×C4—2921no—
231C23×C4—731no—
232#135—7316no—
233#135—14616no—
234#135—1468no—
235C2×Q16—734no—
236C2×Q16—732no—
237C2×Q16—1461no—
238C2×Q16—1462no—
239C2×SD16—1468no—
240C2×SD16—1464no—
241C2×D8—21no—
242C2×D8—22no—
243C2×D8C4×D7314yescomplemented
244C2×D8C22×D7312yes—
245C22×C8—731no—
246C22×C8—734no—
247C22×C8—732no—
248C22×C8—734no—
249C22×C8—732no—
250C22×C8C22×D7311yescharacteristic
251C2×C4⋊C4—21no—
252C2×C4⋊C4—2922no—
253C2×C4⋊C4—2921no—
254C2×C4⋊C4—1464no—
255C2×C4⋊C4—1461no—
256M32—1468no—
257C2×C16—22no—
258C2×C16—732no—
259C2×C16—1462no—
260C2×C16C22×D7312yes—
261#107—21no—
262#107—732no—
263#107—1464no—
264#107—1461no—
265#107C22×D7312yes—
266C24—41no—
267C24—731no—
268#41—29216no—
269#41—2928no—
270#41—14616no—
271C2×Q8—2921no—
272C2×Q8—2922no—
273C2×Q8—1464no—
274C2×Q8—1462no—
275C2×D4—24no—
276C2×D4—22no—
277C2×D4—41no—
278C2×D4—42no—
279C2×D4—2928no—
280C2×D4—2924no—
281C22×C4—41no—
282C22×C4—2924no—
283C22×C4—2921no—
284C22×C4—2928no—
285C22×C4—2924no—
286C22×C4—2921no—
287C22×C4—5844no—
288C22×C4—731no—
289C22×C4—734no—
290C22×C4—732no—
291C22×C4—734no—
292C22×C4—732no—
293C22×C4D4×D7311yescharacteristic
294Q16—734no—
295Q16—1464no—
296Q16—1462no—
297SD16—14616no—
298D8—24no—
299D8—22no—
300D8C2×C4×D7314yescomplemented
301C2×C8—734no—
302C2×C8—732no—
303C2×C8—738no—
304C2×C8—734no—
305C2×C8—734no—
306C2×C8C2×C4×D7312yes—
307C2×C8D4×D7311yescharacteristic
308C2×C8D4×D7312yes—
309C2×C8C23×D7311yescharacteristic
310C4⋊C4—22no—
311C4⋊C4—41no—
312C4⋊C4—2924no—
313C4⋊C4—2921no—
314C4⋊C4—1462no—
315C16—22no—
316C16—1462no—
317C23—44no—
318C23—42no—
319C23—82no—
320C23—82no—
321C23—734no—
322C23—732no—
323C23—1462no—
324C23—1462no—
325C23D8×D7311yescharacteristic
326Q8—2924no—
327Q8—2922no—
328Q8—1464no—
329D4—24no—
330D4—44no—
331D4—42no—
332D4—29216no—
333C2×C4—42no—
334C2×C4—82no—
335C2×C4—2924no—
336C2×C4—2922no—
337C2×C4—29216no—
338C2×C4—2922no—
339C2×C4—5848no—
340C2×C4—5842no—
341C2×C4—734no—
342C2×C4—732no—
343C2×C4—734no—
344C2×C4—738no—
345C2×C4—734no—
346C2×C4C22⋊C4×D7312yes—
347C2×C4D8×D7311yescharacteristic
348C2×C4SD16×D7312yes—
349C2×C4C2×D4×D7311yescharacteristic
350C8—734no—
351C8C22⋊C4×D7312yes—
352C8C22×C4×D7311yescharacteristic
353C8C2×D4×D7311yescharacteristic
354C22—44no—
355C22—82no—
356C22—82no—
357C22—88no—
358C22—734no—
359C22—1462no—
360C22—1462no—
361C22—1468no—
362C22#102×D7312yes—
363C22#1798902112yes—
364C22#1798902612yes—
365C22C2×D8×D7311yescharacteristic
366C4—82no—
367C4—2924no—
368C4—5842no—
369C4—734no—
370C4#102×D7312yes—
371C4C2×C22⋊C4×D7311yescharacteristic
372C4C2×SD16×D7311yescharacteristic
373C2—84no—
374C2—1464no—
375C2#2261164014yesdirect product factor
376C2C2×#102×D7311yescharacteristic
377C2C2×#1798902111yescharacteristic
378C2C2×#1798902611yescharacteristic
subgroupG/H
centerC23D8×D73
commutatorC8×C73C23×C4
FrattiniC2×C8C23×D73
FittingC2×#357×C73C2
socleC23×C73C2×D8
prime radicalC22×#14556610C2
cosocleC2×C8×C73C24
hypercenterC2×#357D73
hypocenterC73C2×#2139
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C22×#14556530C2semidirect
3. C2×#107×D73C2semidirect
4. #22611640C2direct (N × H)
5. C2×#17988392C2semidirect
6. C2×#17988390C2semidirect
7. C2×#17988388C2semidirect
8. C2×#357×C73C2semidirect
12. C2×#14556610C4semidirect
19. C2×#14556530C22semidirect
24. #107×D73C22semidirect
25. #17988392C22semidirect
26. #17988390C22semidirect
27. #17988388C22semidirect
31. #357×C73C22semidirect
43. #14556610C2×C4semidirect
46. C2×Dic292C2×C4semidirect
68. C2×D8×C73C2×C4semidirect
99. Dic292C22×C4semidirect
119. D8×C73C22×C4semidirect
185. C2×C73#2139semidirect
197. C2×#357D73semidirect
198. C73C2×#2139semidirect
221. #357C2×D73semidirect
243. C2×D8C4×D73semidirect
300. D8C2×C4×D73semidirect
375. C2#22611640direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145566102
C22×#145565302
C2×#107×D732
#226116402
C2×#179883922
C2×#179883902
C2×#179883882
C2×#357×C732
C2×#213973