Finite Group Databasebeta

← C2×#22615802 #33252778

Subgroups — C2×#22615802 #33252778

Order 18688.

2894 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×#14556583C211yesmaximal, characteristic, complemented
2C22×C4×D292C211yesmaximal, characteristic
3#22615802C2116yesmaximal, direct product factor
4C2×#17988524C212yesmaximal, complemented
5C2×#17988519C212yesmaximal, complemented
6C2×#17988514C212yesmaximal, complemented
7C2×#17988505C212yesmaximal
8C2×#17988461C214yesmaximal, complemented
9C2×#383×C73C211yesmaximal, characteristic, complemented
10C23×D292C2211yescharacteristic
11C23×C4×D73C2212yes—
12C2×#14556583—28no—
13C2×#14556583C2218yescomplemented
14C2×C4×D292—28no—
15C2×C4×D292C2218yes—
16C22×C4⋊Dic73C2211yescharacteristic
17C22×C4⋊Dic73C2211yescharacteristic
18C22×C4⋊Dic73C2211yescharacteristic
19C22×C4⋊Dic73C2214yes—
20C22×#11924007C2212yes—
21C22×#11924007C2212yes—
22C22×#11924005C2214yes—
23C22×#11924005C2212yes—
24C22×#11924005C2214yes—
25#17988524C22116yescomplemented
26#17988519C22116yescomplemented
27#17988514C22116yescomplemented
28#17988505C22116yes—
29#17988461C22132yescomplemented
30C2×#14556498C2214yes—
31C22×C42×C73C2211yescharacteristic
32#383×C73C2218yescomplemented
33C2×#95×C73C2212yes—
34C2×#95×C73C2212yes—
35C2×#95×C73C2212yes—
36C24×D73C2312yes—
37C22×D292—28no—
38C22×D292—24no—
39C22×D292C2314yes—
40C23×Dic73C2312yes—
41C23×Dic73C2312yes—
42C23×Dic73C2312yes—
43C22×C4×D73—28no—
44C22×C4×D73—48no—
45C22×C4×D73C2318yes—
46#14556583—232no—
47C4×D292—232no—
48C2×C4⋊Dic73—24no—
49C2×C4⋊Dic73—24no—
50C2×C4⋊Dic73—24no—
51C2×C4⋊Dic73—48no—
52C2×C4⋊Dic73C2314yes—
53C2×C4⋊Dic73C2314yes—
54C2×C4⋊Dic73C2314yes—
55C2×C4⋊Dic73C23116yes—
56C2×#11924007—28no—
57C2×#11924007—28no—
58C2×#11924007C2318yes—
59C2×#11924007C2318yes—
60C2×#11924005—216no—
61C2×#11924005—28no—
62C2×#11924005—48no—
63C2×#11924005C23116yes—
64C2×#11924005C2318yes—
65C2×#11924005C23116yes—
66#14556498C23116yes—
67C23×C4×C73C2314yes—
68C23×C4×C73C2311yescharacteristic
69C23×C4×C73C2311yescharacteristic
70C23×C4×C73C2311yescharacteristic
71C2×C42×C73D418yes—
72C2×C42×C73C2314yes—
73#95×C73C2318yes—
74#95×C73C2318yes—
75#95×C73C2318yes—
76C23×D73—24no—
77C23×D73—24no—
78C23×D73—28no—
79C23×D73—28no—
80C23×D73#4118yes—
81C23×D73C2414yes—
82C2×D292—232no—
83C2×D292—216no—
84C2×D292—28no—
85C22×Dic73—24no—
86C22×Dic73—24no—
87C22×Dic73—24no—
88C22×Dic73—28no—
89C22×Dic73—24no—
90C22×Dic73—24no—
91C22×Dic73—28no—
92C22×Dic73C2414yes—
93C22×Dic73C2414yes—
94C22×Dic73C2414yes—
95C2×C4×D73—216no—
96C2×C4×D73—416no—
97C2×C4×D73—432no—
98C4⋊Dic73—28no—
99C4⋊Dic73—28no—
100C4⋊Dic73—28no—
101C4⋊Dic73—416no—
102#11924007—216no—
103#11924007—216no—
104#11924005—232no—
105#11924005—216no—
106#11924005—416no—
107C24×C73C2411yescharacteristic
108C22×C4×C73—24no—
109C22×C4×C73—24no—
110C22×C4×C73—24no—
111C22×C4×C73—28no—
112C22×C4×C73—28no—
113C22×C4×C73—28no—
114C22×C4×C73C2×D414yes—
115C22×C4×C73C2×D414yes—
116C22×C4×C73C2×D414yes—
117C22×C4×C73C2418yes—
118C22×C4×C73C2412yes—
119C22×C4×C73C2412yes—
120C22×C4×C73C2412yes—
121C42×C73C2×D4116yes—
122C23×C73C22×D412yes—
123C23×C73C2×#4114yes—
124C23×C73H(5,𝔽2)14yes—
125C23×C732−1+414yes—
126C23×C73C2511yescharacteristic
127C22×D73—216no—
128C22×D73—232no—
129C22×D73—24no—
130C22×D73—24no—
131C22×D73—28no—
132C22×D73—28no—
133C22×D73—48no—
134C22×D73—48no—
135C22×D73—416no—
136C22×D73C2×#4118yes—
137C2×C4×C73—28no—
138C2×C4×C73—28no—
139C2×C4×C73—28no—
140C2×C4×C73—24no—
141C2×C4×C73—24no—
142C2×C4×C73—24no—
143C2×C4×C73—28no—
144C2×C4×C73—28no—
145C2×C4×C73—28no—
146C2×C4×C73—416no—
147C2×C4×C73C22×D414yes—
148C2×C4×C73C22×D414yes—
149C2×C4×C73C22×D414yes—
150C2×Dic73—24no—
151C2×Dic73—24no—
152C2×Dic73—24no—
153C2×Dic73—28no—
154C2×Dic73—24no—
155C2×Dic73—24no—
156C2×Dic73—28no—
157C2×Dic73—48no—
158C2×Dic73—48no—
159C2×Dic73—48no—
160D292—232no—
161C4×D73—432no—
162C22×C73#52514yes—
163C22×C73#53514yes—
164C22×C73#53614yes—
165C22×C73#539116yes—
166C22×C73C23×D411yescharacteristic
167C22×C73C22×#4112yes—
168C22×C73C2×H(5,𝔽2)12yes—
169C22×C73C2×2−1+412yes—
170C2×D73—28no—
171C2×D73—216no—
172C2×D73—432no—
173C2×D73—44no—
174C2×D73—44no—
175C2×D73—48no—
176C4×C73—24no—
177C4×C73—24no—
178C4×C73—24no—
179C4×C73—48no—
180Dic73—44no—
181Dic73—44no—
182Dic73—44no—
183C2×#2633—731nomaximal, Sylow
184C2×C73#263318yescomplemented
185C2×C73C2×#52511yescharacteristic
186C2×C73C2×#53511yescharacteristic
187C2×C73C2×#53611yescharacteristic
188C2×C73C2×#53914yes—
189D73—48no—
190C22×#125—731no—
191C22×C4×D4—731no—
192#2633—7316no—
193C2×#399—732no—
194C2×#398—732no—
195C2×#397—732no—
196C2×#394—732no—
197C2×#385—734no—
198C2×#383D7311yescharacteristic, complemented
199C73C2×#263311yescharacteristic, complemented, Sylow
200C23×D4—731no—
201C24×C4—732no—
202C2×#125—738no—
203C2×#125—1468no—
204C2×C4×D4—738no—
205C2×C4×D4—1468no—
206C22×C4⋊C4—734no—
207C22×C4⋊C4—732no—
208C22×C4⋊C4—731no—
209C22×C4⋊C4—731no—
210C22×C4⋊C4—731no—
211C22×C4⋊C4—732no—
212C22×C22⋊C4—734no—
213C22×C22⋊C4—734no—
214C22×C22⋊C4—732no—
215C22×C42C2×D7311yescharacteristic
216#399—7316no—
217#398—7316no—
218#397—7316no—
219#394—7316no—
220#385—7332no—
221#383C2×D7318yescomplemented
222C2×#95—734no—
223C2×#95C2×D7312yes—
224C2×#95C2×D7312yes—
225C2×#95C2×D7312yes—
226C25—732no—
227C22×D4—734no—
228C22×D4—1468no—
229C22×D4—1464no—
230C23×C4—2928no—
231C23×C4—738no—
232C23×C4—732no—
233C23×C4—732no—
234C23×C4—732no—
235C23×C4—1468no—
236C23×C4C22×D7314yes—
237C23×C4C22×D7311yescharacteristic
238C23×C4C22×D7311yescharacteristic
239C23×C4C22×D7311yescharacteristic
240#125—14632no—
241C4×D4—14632no—
242C2×C4⋊C4—2928no—
243C2×C4⋊C4—7316no—
244C2×C4⋊C4—734no—
245C2×C4⋊C4—738no—
246C2×C4⋊C4—738no—
247C2×C4⋊C4—734no—
248C2×C4⋊C4—734no—
249C2×C4⋊C4—1464no—
250C2×C4⋊C4—1468no—
251C2×C4⋊C4—1468no—
252C2×C4⋊C4—1464no—
253C2×C4⋊C4—1464no—
254C2×C22⋊C4—2928no—
255C2×C22⋊C4—7316no—
256C2×C22⋊C4—738no—
257C2×C22⋊C4—7316no—
258C2×C22⋊C4—14616no—
259C2×C22⋊C4—1468no—
260C2×C42D29218yes—
261C2×C42C22×D7314yes—
262#95—7316no—
263#95C22×D7318yes—
264#95C22×D7318yes—
265#95C22×D7318yes—
266C24—738no—
267C24—734no—
268C24—1464no—
269C24—1464no—
270C24—1468no—
271C24—1468no—
272C24C23×D7311yescharacteristic
273C2×D4—14616no—
274C2×D4—14632no—
275C2×D4—1468no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—28no—
280C22×C4—28no—
281C22×C4—28no—
282C22×C4—29232no—
283C22×C4—29216no—
284C22×C4—734no—
285C22×C4—734no—
286C22×C4—734no—
287C22×C4—1464no—
288C22×C4—1464no—
289C22×C4—1464no—
290C22×C4—1468no—
291C22×C4—1464no—
292C22×C4—1464no—
293C22×C4—1468no—
294C22×C4—14616no—
295C22×C4C2×D29214yes—
296C22×C4C2×D29214yes—
297C22×C4C2×D29214yes—
298C22×C4C23×D7318yes—
299C22×C4C23×D7312yes—
300C22×C4C23×D7312yes—
301C22×C4C23×D7312yes—
302C4⋊C4—29216no—
303C4⋊C4—14616no—
304C4⋊C4—14616no—
305C4⋊C4—1468no—
306C4⋊C4—1468no—
307C4⋊C4—1468no—
308C22⋊C4—29216no—
309C22⋊C4—14632no—
310C22⋊C4—14616no—
311C42C2×D292116yes—
312C23—2928no—
313C23—2928no—
314C23—29216no—
315C23—738no—
316C23—1464no—
317C23—1464no—
318C23—1468no—
319C23—1468no—
320C23—14632no—
321C23—14616no—
322C23C22×D29212yes—
323C23#41×D7314yes—
324C23#1455663714yes—
325C23#1455663814yes—
326C23C24×D7311yescharacteristic
327D4—14632no—
328C2×C4—28no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—28no—
332C2×C4—24no—
333C2×C4—28no—
334C2×C4—28no—
335C2×C4—28no—
336C2×C4—28no—
337C2×C4—416no—
338C2×C4—29232no—
339C2×C4—2928no—
340C2×C4—2928no—
341C2×C4—2928no—
342C2×C4—1464no—
343C2×C4—1464no—
344C2×C4—1464no—
345C2×C4—1468no—
346C2×C4—1464no—
347C2×C4—1464no—
348C2×C4—1468no—
349C2×C4C22×D29214yes—
350C2×C4C22×D29214yes—
351C2×C4C22×D29214yes—
352C22—2924no—
353C22—2924no—
354C22—2928no—
355C22—29232no—
356C22—14616no—
357C22—1468no—
358C22#1798909914yes—
359C22#1798915614yes—
360C22#1798916314yes—
361C22#17989178116yes—
362C22C23×D29211yescharacteristic
363C22C2×#41×D7312yes—
364C22C2×#1455663712yes—
365C22C2×#1455663812yes—
366C4—24no—
367C4—24no—
368C4—24no—
369C4—48no—
370C4—2924no—
371C4—2924no—
372C4—2924no—
373C2—2928no—
374C2#2261580218yesdirect product factor
375C2C2×#1798909911yescharacteristic
376C2C2×#1798915611yescharacteristic
377C2C2×#1798916311yescharacteristic
378C2C2×#1798917814yes—
subgroupG/H
centerC24C23×D73
commutator, cosocleC23×C73C25
FrattiniC23C24×D73
FittingC2×#383×C73C2
socleC24×C73C24
prime radicalC23×D292C22
hypercenterC2×#383D73
hypocenterC73C2×#2633
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#383

Complements

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

NH ≅ G/Ntype
1. C22×#14556583C2semidirect
3. #22615802C2direct (N × H)
4. C2×#17988524C2semidirect
5. C2×#17988519C2semidirect
6. C2×#17988514C2semidirect
8. C2×#17988461C2semidirect
9. C2×#383×C73C2semidirect
13. C2×#14556583C22semidirect
25. #17988524C22semidirect
26. #17988519C22semidirect
27. #17988514C22semidirect
29. #17988461C22semidirect
32. #383×C73C22semidirect
184. C2×C73#2633semidirect
198. C2×#383D73semidirect
199. C73C2×#2633semidirect
221. #383C2×D73semidirect
374. C2#22615802direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145565832
C22×C4×D2922
#226158022
C2×#179885242
C2×#179885192
C2×#179885142
C2×#179885052
C2×#179884612
C2×#383×C732
C2×#263373