Finite Group Databasebeta

← C2×#22626065 #34022205

Subgroups — C2×#22626065 #34022205

Order 18688.

1878 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989591C211yesmaximal, characteristic, complemented
2C22×#14556655C214yesmaximal, complemented
3C2×C42×#64408C211yesmaximal, characteristic, complemented
4#22626065C218yesmaximal, direct product factor
5C2×#17989135C211yesmaximal, characteristic
6C22×#11924038C2212yes—
7C22×C4×#64408—22no—
8C22×C4×#64408C2212yes—
9#17989591—22no—
10#17989591C2214yescomplemented
11C2×C4⋊#10596833—22no—
12C2×#14556655—216no—
13C2×#14556655C22116yescomplemented
14C42×#64408—22no—
15C42×#64408C2214yescomplemented
16C22×#11924027C2212yes—
17#17989135—22no—
18#17989135—22no—
19#17989135C414yescomplemented
20#17989135C2214yes—
21C2×#14556591C411yescharacteristic, complemented
22C2×#14556578C412yescomplemented
23C2×#14556562—22no—
24C2×D4×Dic73—22no—
25C2×C42×D73C2211yescharacteristic
26C2×#127×C73C411yescharacteristic, complemented
27C23×#64408—22no—
28C2×#11924038—22no—
29C2×#11924038—28no—
30C2×#11924038C2314yes—
31C22×#10596833—22no—
32C2×C4×#64408—216no—
33C2×C4×#64408—28no—
34C2×C4×#64408—22no—
35C2×C4×#64408—24no—
36C2×C4×#64408D418yescomplemented
37C2×C4×#64408C2314yes—
38C4⋊#10596833—28no—
39#14556655—232no—
40C2×#11924027—22no—
41C2×#11924027—22no—
42C2×#11924027—28no—
43C2×#11924027—28no—
44C2×#11924027C2×C414yes—
45C2×#11924027C2314yes—
46C22×Dic146C2×C412yes—
47C22×C22⋊D73—22no—
48C23×Dic73—22no—
49C22×C4×D73D412yes—
50C22×C4×D73C2311yescharacteristic
51#14556591—22no—
52#14556591C2×C414yescomplemented
53#14556578—24no—
54#14556578C2×C418yescomplemented
55#14556562—28no—
56#14556562—28no—
57D4×Dic73—28no—
58D4×Dic73—28no—
59C2×C4⋊Dic73—22no—
60C2×C22⋊Dic73—24no—
61C2×C4×Dic73C2×C411yescharacteristic
62C2×C4×Dic73D412yes—
63C42×D73C2×C412yes—
64C42×D73D412yes—
65C42×D73D412yes—
66C42×D73C2312yes—
67C22×D4×C73—22no—
68C22×D4×C73C2×C412yes—
69#127×C73—22no—
70#127×C73C2×C414yescomplemented
71C2×C42×C73C2×C411yescharacteristic
72C22×#64408—216no—
73C22×#64408—28no—
74C22×#64408—24no—
75#11924038—28no—
76#11924038—44no—
77C2×#10596833—24no—
78C2×#10596833—44no—
79C4×#64408—232no—
80C4×#64408—28no—
81C4×#64408—24no—
82C4×#64408C2×D418yescomplemented
83C23×D73C2×D411yescharacteristic
84#11924027—216no—
85#11924027—28no—
86#11924027—28no—
87#11924027—48no—
88#11924027—44no—
89#11924027—44no—
90C2×Dic146—28no—
91C2×Dic146—22no—
92C2×Dic146C22×C414yes—
93C2×C22⋊D73—24no—
94C2×C22⋊D73—24no—
95C2×C22⋊D73—48no—
96C22×Dic73—22no—
97C22×Dic73—24no—
98C22×Dic73—24no—
99C22×Dic73—44no—
100C22×Dic73—44no—
101C22×Dic73C22⋊C412yes—
102C22×Dic73C2×D411yescharacteristic
103C2×C4×D73—28no—
104C2×C4×D73C22⋊C414yes—
105C2×C4×D73C22×C411yescharacteristic
106C2×C4×D73C2×D414yes—
107C2×C4×D73C2×D414yes—
108C2×C4×D73C2×D411yescharacteristic
109C2×C4×D73C2×D411yescharacteristic
110C2×C4×D73#4114yes—
111C2×C4×D73C2411yescharacteristic
112C4⋊Dic73—28no—
113C22⋊Dic73—216no—
114C4×Dic73C22⋊C414yes—
115C4×Dic73C22⋊C412yes—
116C4×Dic73C22×C412yes—
117C4×Dic73C2×D414yes—
118C24×C73—22no—
119C2×D4×C73—22no—
120C2×D4×C73—28no—
121C2×D4×C73—28no—
122C2×D4×C73—48no—
123C2×D4×C73C22×C414yes—
124C22×C4×C73C22⋊C412yes—
125C22×C4×C73C22×C411yescharacteristic
126C42×C73C22⋊C412yes—
127C42×C73C22×C412yes—
128C23×C73—24no—
129C23×C73—44no—
130C23×C73—48no—
131C23×C73C2×C22⋊C411yescharacteristic
132C22×D73—24no—
133C22×D73C2×C22⋊C411yescharacteristic
134C22×D73#12114yes—
135C22×D73C22×D411yescharacteristic
136C2×#64408—216no—
137C2×#64408—232no—
138C2×#64408—28no—
139D4×C73—28no—
140D4×C73—44no—
141D4×C73—416no—
142C2×C4×C73#10418yescomplemented
143C2×C4×C73C2×C22⋊C411yescharacteristic
144C2×C4×C73C2×C22⋊C414yes—
145C2×C4×C73C4×D414yes—
146C2×C4×C73C23×C411yescharacteristic
147C22⋊D73—48no—
148C22⋊D73—48no—
149C2×Dic73—24no—
150C2×Dic73—24no—
151C2×Dic73—44no—
152C2×Dic73—44no—
153C2×Dic73—44no—
154C2×Dic73—48no—
155C2×Dic73C2×C22⋊C414yes—
156C2×Dic73C2×C22⋊C411yescharacteristic
157C2×Dic73#12412yes—
158C2×Dic73#12712yes—
159C2×Dic73C22×D411yescharacteristic
160C4×D73—28no—
161C4×D73—28no—
162C4×D73C4×D414yes—
163C4×D73#12114yes—
164C4×D73#12412yes—
165C4×D73#12712yes—
166C4×D73C22×D412yes—
167C4×D73C2×#4112yes—
168Dic146—28no—
169Dic146—44no—
170#10596833—44no—
171C22×C73—48no—
172C22×C73—44no—
173C22×C73—88no—
174C22×C73#39012yes—
175C22×C73C2×#10414yes—
176C22×C73C22×C22⋊C411yescharacteristic
177C2×D73—22no—
178C2×D73—22no—
179C2×D73—28no—
180C2×D73#39012yes—
181C2×D73C2×#12112yes—
182#64408—216no—
183C4×C73#39012yes—
184C4×C73C2×#10418yescomplemented
185C4×C73C2×C4×D412yes—
186Dic73—24no—
187Dic73—44no—
188Dic73#39012yes—
189Dic73C2×#12411yescharacteristic
190Dic73C2×#12711yescharacteristic
191C2×#1962—731nomaximal, Sylow
192C2×C73—84no—
193C2×C73#196214yescomplemented
194C2×C73C2×#39011yescharacteristic
195C2×C73C22×#10412yes—
196D73—22no—
197D73—22no—
198C2×#532—731no—
199C2×#423—731no—
200C22×#104—734no—
201C2×C43—731no—
202#1962—738no—
203C73C2×#196211yescharacteristic, complemented, Sylow
204C22×#41—732no—
205C22×M16—732no—
206#532—734no—
207#532—734no—
208#532—1462no—
209#532—1462no—
210C2×C4⋊Q8—731no—
211C2×#127#6440811yescharacteristic, complemented
212C2×#124—732no—
213C2×#121—1462no—
214C2×C4×D4—1462no—
215C22×C42—731no—
216C22×C42—732no—
217C22×C42—1462no—
218#423—734no—
219#423—1462no—
220C2×C4⋊C8—1462no—
221C2×#104—7316no—
222C2×#104—14616no—
223C43—734no—
224C43—1462no—
225C2×#41—734no—
226C2×#41—734no—
227C2×#41—1468no—
228C2×#41—1468no—
229C2×#41—1462no—
230C2×#41—1462no—
231C22×Q8—732no—
232C22×D4—22no—
233C22×D4—1462no—
234C22×D4C2×#6440812yes—
235C23×C4—731no—
236C23×C4—732no—
237C23×C4—1462no—
238C23×C4—1462no—
239C2×M16—734no—
240C2×M16—1468no—
241C2×M16—1462no—
242C22×C8—1462no—
243C4⋊Q8—734no—
244C4⋊Q8—1462no—
245#127—22no—
246#127C2×#6440814yescomplemented
247#124—738no—
248#124—1464no—
249#121—1468no—
250#121—1468no—
251C4×D4—1468no—
252C4×D4—1468no—
253C2×C4⋊C4—1462no—
254C2×C22⋊C4—1464no—
255C2×C42—732no—
256C2×C42—731no—
257C2×C42—732no—
258C2×C42—732no—
259C2×C42—732no—
260C2×C42—732no—
261C2×C42—734no—
262C2×C42—738no—
263C2×C42—1468no—
264C2×C42—1462no—
265C2×C42—1464no—
266C2×C42—14616no—
267C2×C42C2×#6440811yescharacteristic
268C4⋊C8—1468no—
269#104—14632no—
270C24—22no—
271C24—731no—
272#41—2928no—
273#41—2924no—
274#41—2924no—
275#41—1468no—
276#41—1468no—
277#41—14616no—
278C2×Q8—734no—
279C2×Q8—1468no—
280C2×Q8—1462no—
281C2×D4—28no—
282C2×D4—22no—
283C2×D4—28no—
284C2×D4—48no—
285C2×D4—2928no—
286C2×D4—1464no—
287C2×D4—1464no—
288C2×D4C22×#6440814yes—
289C22×C4—2924no—
290C22×C4—2924no—
291C22×C4—731no—
292C22×C4—731no—
293C22×C4—731no—
294C22×C4—731no—
295C22×C4—731no—
296C22×C4—734no—
297C22×C4—734no—
298C22×C4—732no—
299C22×C4—734no—
300C22×C4—734no—
301C22×C4—1464no—
302C22×C4—1464no—
303C22×C4—1462no—
304C22×C4—1464no—
305C22×C4—1468no—
306C22×C4—14616no—
307C22×C4—1468no—
308C22×C4C22⋊#6440812yes—
309C22×C4C22×#6440811yescharacteristic
310M16—2924no—
311M16—1468no—
312C2×C8—2924no—
313C2×C8—1464no—
314C4⋊C4—1468no—
315C22⋊C4—14616no—
316C42—732no—
317C42—734no—
318C42—732no—
319C42—734no—
320C42—738no—
321C42—1464no—
322C42—1468no—
323C42—14632no—
324C42C22⋊#6440812yes—
325C42C22×#6440812yes—
326C23—24no—
327C23—44no—
328C23—48no—
329C23—731no—
330C23—731no—
331C23—734no—
332C23—1464no—
333C23C2×C22⋊#6440811yescharacteristic
334Q8—2924no—
335Q8—1468no—
336D4—28no—
337D4—44no—
338D4—416no—
339D4—2928no—
340D4—2928no—
341C2×C4—2924no—
342C2×C4—2924no—
343C2×C4—2924no—
344C2×C4—2928no—
345C2×C4—731no—
346C2×C4—731no—
347C2×C4—732no—
348C2×C4—732no—
349C2×C4—732no—
350C2×C4—732no—
351C2×C4—734no—
352C2×C4—734no—
353C2×C4—732no—
354C2×C4—732no—
355C2×C4—734no—
356C2×C4—1464no—
357C2×C4—1468no—
358C2×C4—14616no—
359C2×C4—14632no—
360C2×C4—1464no—
361C2×C4—1468no—
362C2×C4—1468no—
363C2×C4#1455665518yescomplemented
364C2×C4C2×C22⋊#6440811yescharacteristic
365C2×C4C2×C22⋊#6440814yes—
366C2×C4D4×#6440814yes—
367C2×C4C23×#6440811yescharacteristic
368C8—2924no—
369C22—44no—
370C22—48no—
371C22—88no—
372C22—732no—
373C22—732no—
374C22—1468no—
375C22—1462no—
376C22—1462no—
377C22#1798953912yes—
378C22C2×#1455665514yes—
379C22C22×C22⋊#6440811yescharacteristic
380C4—2924no—
381C4—731no—
382C4—731no—
383C4—732no—
384C4—14616no—
385C4—1464no—
386C4#1798953912yes—
387C4C2×#1455665518yescomplemented
388C4C2×D4×#6440812yes—
389C2—84no—
390C2—1462no—
391C2—1462no—
392C2#2262606514yesdirect product factor
393C2C2×#1798953911yescharacteristic
394C2C22×#1455665512yes—
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
FittingC2×#127×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC2×#17989135C2
cosocleC2×C4×D73C24
hypercenterC2×#127#64408
hypocenterC73C2×#1962
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#17989591C2semidirect
2. C22×#14556655C2semidirect
3. C2×C42×#64408C2semidirect
4. #22626065C2direct (N × H)
10. #17989591C22semidirect
13. C2×#14556655C22semidirect
15. C42×#64408C22semidirect
19. #17989135C4semidirect
21. C2×#14556591C4semidirect
22. C2×#14556578C4semidirect
26. C2×#127×C73C4semidirect
36. C2×C4×#64408D4semidirect
52. #14556591C2×C4semidirect
54. #14556578C2×C4semidirect
70. #127×C73C2×C4semidirect
82. C4×#64408C2×D4semidirect
142. C2×C4×C73#104semidirect
184. C4×C73C2×#104semidirect
193. C2×C73#1962semidirect
203. C73C2×#1962semidirect
211. C2×#127#64408semidirect
246. #127C2×#64408semidirect
363. C2×C4#14556655semidirect
387. C4C2×#14556655semidirect
392. C2#22626065direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179895912
C22×#145566552
C2×C42×#644082
#226260652
C2×#179891352
C2×#196273