Finite Group Databasebeta

← C2×#22622945 #33966922

Subgroups — C2×#22622945 #33966922

Order 18688.

2086 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989323C212yesmaximal, complemented
2#22622945C2116yesmaximal, direct product factor
3C2×#17988970C212yesmaximal, complemented
4C2×#17988784C212yesmaximal, complemented
5C2×#17988800C214yesmaximal, complemented
6C2×C8×Dic146C211yesmaximal, characteristic, complemented
7C2×C4×Dic292C211yesmaximal, characteristic, complemented
8C2×D8×Dic73C212yesmaximal, complemented
9C2×#493×C73C211yesmaximal, characteristic
10C22×Dic292C2211yescharacteristic
11C22×#11924016C2214yes—
12#17989323—28no—
13#17989323C22116yescomplemented
14C2×#14556578—22no—
15C2×#14556578C2214yes—
16C2×#14556572—24no—
17C2×C4×Dic146C2212yes—
18C2×C4×Dic146C2211yescharacteristic
19C2×D4×Dic73—22no—
20C2×D4×Dic73C2214yes—
21#17988970C22116yescomplemented
22#17988800C22132yescomplemented
23#17988784C22116yescomplemented
24C8×Dic146C2218yescomplemented
25C4×Dic292C2218yescomplemented
26D8×Dic73C22116yescomplemented
27C2×#14556525C2211yescharacteristic
28C2×C4⋊#10596831C2211yescharacteristic
29C2×#14556520C2212yes—
30C2×#14556516C2212yes—
31C2×#14556512C2214yes—
32C2×C8×Dic73C2212yes—
33C22×D8×C73C2212yes—
34C22×D8×C73C2212yes—
35C2×#127×C73C2212yes—
36#493×C73C2218yes—
37C2×C4×C8×C73C2211yescharacteristic
38C22×Dic146D411yescharacteristic
39C22×Dic146C2312yes—
40C23×Dic73—24no—
41C2×Dic292—24no—
42C2×Dic292C2314yes—
43C2×#11924016—48no—
44C2×#11924016C23116yes—
45C22×#10596831C2312yes—
46#14556578—216no—
47#14556578—28no—
48#14556578C23116yes—
49#14556572—232no—
50C4×Dic146—24no—
51C4×Dic146D414yes—
52C4×Dic146C2318yes—
53C4×Dic146C2314yes—
54D4×Dic73—216no—
55D4×Dic73—28no—
56D4×Dic73C23116yes—
57C2×C4⋊Dic73D411yescharacteristic
58C2×C4⋊Dic73C2312yes—
59C2×#11924007—22no—
60C2×#11924007D412yes—
61C2×C22⋊Dic73—24no—
62C2×C22⋊Dic73—24no—
63C2×C22⋊Dic73—24no—
64C2×C4×Dic73—22no—
65C2×C4×Dic73C2312yes—
66#14556525C2314yes—
67C4⋊#10596831C2314yes—
68#14556520C2318yes—
69#14556516C2318yes—
70#14556512C23116yes—
71C8×Dic73C2318yes—
72C22×D4×C73—22no—
73C22×D4×C73—22no—
74C22×D4×C73C2314yes—
75C2×D8×C73—28no—
76C2×D8×C73—44no—
77C2×D8×C73C2318yes—
78C2×D8×C73C2318yes—
79C22×C8×C73C2311yescharacteristic
80C22×C8×C73C2311yescharacteristic
81#127×C73—24no—
82#127×C73C2318yes—
83C2×C42×C73C2311yescharacteristic
84C4×C8×C73C2314yes—
85C2×Dic146—24no—
86C2×Dic146—24no—
87C2×Dic146—24no—
88C2×Dic146—22no—
89C2×Dic146C2×D414yes—
90C2×Dic146C2414yes—
91C22×Dic73—22no—
92C22×Dic73—22no—
93C22×Dic73—216no—
94C22×Dic73—88no—
95C22×Dic73C2×D412yes—
96C22×Dic73C2×D412yes—
97Dic292—28no—
98#11924016—416no—
99C2×#10596831—24no—
100C2×#10596831C2414yes—
101C4⋊Dic73—22no—
102C4⋊Dic73C2×D414yes—
103C4⋊Dic73C2414yes—
104#11924007—28no—
105#11924007C2×D418yes—
106C22⋊Dic73—216no—
107C22⋊Dic73—216no—
108C22⋊Dic73—216no—
109C4×Dic73—28no—
110C4×Dic73C2×D414yes—
111C4×Dic73C2414yes—
112C24×C73—24no—
113C2×D4×C73—24no—
114C2×D4×C73—28no—
115C2×D4×C73—28no—
116C2×D4×C73—28no—
117C2×D4×C73—28no—
118C2×D4×C73—48no—
119C2×D4×C73—84no—
120C2×D4×C73C2418yes—
121C22×C4×C73C2×D411yescharacteristic
122C22×C4×C73C2×D411yescharacteristic
123C22×C4×C73C2411yescharacteristic
124D8×C73—216no—
125D8×C73—48no—
126C2×C8×C73—22no—
127C2×C8×C73#4114yes—
128C2×C8×C73C2412yes—
129C2×C8×C73C2412yes—
130C42×C73C2×D412yes—
131C42×C73C2412yes—
132C23×C73—28no—
133C23×C73—48no—
134C23×C73—48no—
135C23×C73—48no—
136C23×C73C22×D411yescharacteristic
137D4×C73—28no—
138D4×C73—28no—
139D4×C73—48no—
140D4×C73—416no—
141D4×C73—88no—
142C2×C4×C73—22no—
143C2×C4×C73#13514yes—
144C2×C4×C73C22×D412yes—
145C2×C4×C73C22×D411yescharacteristic
146C2×C4×C73C22×D412yes—
147C2×C4×C73C2×#4112yes—
148C2×C4×C73H(5,𝔽2)12yes—
149C2×C4×C73C2511yescharacteristic
150C2×Dic73—24no—
151C2×Dic73—24no—
152C2×Dic73—24no—
153C2×Dic73—24no—
154C2×Dic73—44no—
155C2×Dic73—44no—
156C2×Dic73—816no—
157C2×Dic73C22×D414yes—
158C2×Dic73C22×D414yes—
159Dic146—28no—
160Dic146—24no—
161Dic146—24no—
162Dic146—44no—
163C8×C73—22no—
164C8×C73C2×#4114yes—
165#10596831—24no—
166C22×C73—48no—
167C22×C73—48no—
168C22×C73—48no—
169C22×C73—816no—
170C22×C73#55012yes—
171C22×C73C2×#13512yes—
172C22×C73#57612yes—
173C22×C73C23×D411yescharacteristic
174C4×C73—22no—
175C4×C73#55012yes—
176C4×C73C2×#13514yes—
177C4×C73C22×#4111yescharacteristic
178C4×C73C2×H(5,𝔽2)11yescharacteristic
179Dic73—24no—
180Dic73—24no—
181Dic73—44no—
182Dic73—44no—
183C2×#3396—731nomaximal, Sylow
184C2×C73—88no—
185C2×C73#339614yescomplemented
186C2×C73C2×#55011yescharacteristic
187C2×C73C22×#13511yescharacteristic
188C2×C73C2×#57611yescharacteristic
189C2×#559—732no—
190#3396—7316no—
191C2×#495—732no—
192C2×#493D7311yescharacteristic
193C2×#460—732no—
194C2×#463—734no—
195C2×C8×Q8—731no—
196C2×C4×Q16—731no—
197C2×C4×D8—732no—
198C73C2×#339611yescharacteristic, complemented, Sylow
199C22×Q16—731no—
200C22×SD16—734no—
201C22×D8C2×D7312yes—
202C22×D8C2×D7312yes—
203#559—7316no—
204#559—1468no—
205C2×#127C2×D7312yes—
206C2×#124—734no—
207C2×#124—1462no—
208C2×#123—1464no—
209C2×C4×Q8—731no—
210C2×C4×Q8—732no—
211C2×C4×D4—734no—
212C2×C4×D4—1462no—
213#495—7316no—
214#493C2×D7318yes—
215#463—7332no—
216#460—7316no—
217C8×Q8—738no—
218C4×Q16—738no—
219C4×D8—7316no—
220C2×#107—731no—
221C2×C4⋊C8—732no—
222C2×C4⋊C8—731no—
223C2×#103—732no—
224C2×#102—734no—
225C2×C4×C8—732no—
226C2×C4×C8C2×D7311yescharacteristic
227C22×Q8—731no—
228C22×Q8—732no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4C22×D7314yes—
232C23×C4—1464no—
233C2×Q16—734no—
234C2×Q16—1464no—
235C2×SD16—2928no—
236C2×SD16—7316no—
237C2×D8—28no—
238C2×D8—44no—
239C2×D8C22×D7318yes—
240C2×D8C22×D7318yes—
241C22×C8—732no—
242C22×C8C22×D7311yescharacteristic
243C22×C8C22×D7311yescharacteristic
244#127—24no—
245#127C22×D7318yes—
246#124—7316no—
247#124—1468no—
248#124—14616no—
249#123—14632no—
250C4×Q8—734no—
251C4×Q8—734no—
252C4×Q8—738no—
253C4×Q8—1464no—
254C4×D4—7316no—
255C4×D4—1468no—
256C4×D4—14616no—
257C2×C4⋊C4—731no—
258C2×C4⋊C4—732no—
259C2×C4⋊C4—732no—
260C2×C4⋊C4—1462no—
261C2×C22⋊C4—1464no—
262C2×C22⋊C4—1464no—
263C2×C22⋊C4—1464no—
264C2×C42—732no—
265C2×C42—1462no—
266C2×C42C22×D7311yescharacteristic
267#107—734no—
268C4⋊C8—738no—
269C4⋊C8—734no—
270#103—738no—
271#102—7316no—
272C4×C8—738no—
273C4×C8C22×D7314yes—
274C24—24no—
275C2×Q8—734no—
276C2×Q8—734no—
277C2×Q8—1464no—
278C2×Q8—1464no—
279C2×Q8—1464no—
280C2×Q8—1462no—
281C2×D4—24no—
282C2×D4—28no—
283C2×D4—28no—
284C2×D4—28no—
285C2×D4—28no—
286C2×D4—48no—
287C2×D4—84no—
288C2×D4C23×D7318yes—
289C22×C4—5848no—
290C22×C4—732no—
291C22×C4—732no—
292C22×C4—1462no—
293C22×C4—1462no—
294C22×C4—14616no—
295C22×C4D4×D7311yescharacteristic
296C22×C4D4×D7311yescharacteristic
297C22×C4C23×D7311yescharacteristic
298Q16—1468no—
299SD16—29216no—
300D8—216no—
301D8—48no—
302C2×C8—22no—
303C2×C8—734no—
304C2×C8—1464no—
305C2×C8#1192402714yes—
306C2×C8C23×D7312yes—
307C2×C8C23×D7312yes—
308C4⋊C4—738no—
309C4⋊C4—734no—
310C4⋊C4—734no—
311C4⋊C4—1468no—
312C4⋊C4—1462no—
313C22⋊C4—14616no—
314C22⋊C4—14616no—
315C22⋊C4—14616no—
316C42—734no—
317C42—734no—
318C42—1468no—
319C42D4×D7312yes—
320C42C23×D7312yes—
321C23—28no—
322C23—48no—
323C23—48no—
324C23—48no—
325C23C2×D4×D7311yescharacteristic
326Q8—2924no—
327Q8—1464no—
328Q8—1464no—
329Q8—1468no—
330D4—28no—
331D4—28no—
332D4—48no—
333D4—416no—
334D4—88no—
335C2×C4—22no—
336C2×C4—2924no—
337C2×C4—2924no—
338C2×C4—58416no—
339C2×C4—734no—
340C2×C4—734no—
341C2×C4—1464no—
342C2×C4—1464no—
343C2×C4—1464no—
344C2×C4—1464no—
345C2×C4#1455661014yes—
346C2×C4C2×D4×D7312yes—
347C2×C4C2×D4×D7311yescharacteristic
348C2×C4C2×D4×D7312yes—
349C2×C4C2×#1192402712yes—
350C2×C4#1455663612yes—
351C2×C4C24×D7311yescharacteristic
352C8—22no—
353C8—1464no—
354C8C2×#1192402714yes—
355C22—48no—
356C22—48no—
357C22—48no—
358C22—816no—
359C22#1798925712yes—
360C22C2×#1455661012yes—
361C22#1798938812yes—
362C22C22×D4×D7311yescharacteristic
363C4—22no—
364C4—2924no—
365C4—2924no—
366C4—1464no—
367C4—1464no—
368C4#1798925712yes—
369C4C2×#1455661014yes—
370C4C22×#1192402711yescharacteristic
371C4C2×#1455663611yescharacteristic
372C2—88no—
373C2#2262294514yesdirect product factor
374C2C2×#1798925711yescharacteristic
375C2C22×#1455661011yescharacteristic
376C2C2×#1798938811yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
Fitting, prime radicalC2×#493×C73C2
socleC23×C73C22×D4
hypercenterC2×#493D73
hypocenterC73C2×#3396
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#493

Complements

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

NH ≅ G/Ntype
1. C2×#17989323C2semidirect
2. #22622945C2direct (N × H)
3. C2×#17988970C2semidirect
4. C2×#17988784C2semidirect
5. C2×#17988800C2semidirect
6. C2×C8×Dic146C2semidirect
7. C2×C4×Dic292C2semidirect
8. C2×D8×Dic73C2semidirect
13. #17989323C22semidirect
21. #17988970C22semidirect
22. #17988800C22semidirect
23. #17988784C22semidirect
24. C8×Dic146C22semidirect
25. C4×Dic292C22semidirect
26. D8×Dic73C22semidirect
185. C2×C73#3396semidirect
198. C73C2×#3396semidirect
373. C2#22622945direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893232
#226229452
C2×#179889702
C2×#179887842
C2×#179888002
C2×C8×Dic1462
C2×C4×Dic2922
C2×D8×Dic732
C2×#493×C732
C2×#339673