Finite Group Databasebeta

← C2×#22620443 #33955587

Subgroups — C2×#22620443 #33955587

Order 18688.

1942 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989140C212yesmaximal
2#22620443C2116yesmaximal, direct product factor
3C2×#17988991C212yesmaximal, complemented
4C2×#17988988C212yesmaximal, complemented
5C2×#17988987C212yesmaximal, complemented
6C2×#17988984C212yesmaximal, complemented
7C2×#17988625C211yesmaximal, characteristic
8C2×#17988623C212yesmaximal
9C22×C8×Dic73C211yesmaximal, characteristic
10C2×#427×C73C211yesmaximal, characteristic
11C23×#10596831C2211yescharacteristic
12#17989140—28no—
13#17989140C22116yes—
14C2×#14556590C2214yes—
15C2×#14556582C2214yes—
16C2×#14556568—24no—
17C2×C4×Dic146—24no—
18C2×#14556550C2212yes—
19C22×C4×Dic73C2211yescharacteristic
20#17988991C22116yescomplemented
21#17988988C22116yescomplemented
22#17988987C22116yescomplemented
23#17988984C22116yescomplemented
24#17988625C2218yes—
25#17988623C22116yes—
26C2×#14556525C2212yes—
27C2×#14556524C2214yes—
28C2×#14556523C2212yes—
29C2×#14556522C2214yes—
30C2×C8×Dic73C2211yescharacteristic
31C2×C8×Dic73C2211yescharacteristic
32C2×C8×Dic73C2211yescharacteristic
33C2×C8×Dic73C2211yescharacteristic
34C2×C8×Dic73C2218yes—
35C23×C8×C73C2211yescharacteristic
36C2×#117×C73C2212yes—
37#427×C73C2218yes—
38C2×#107×C73C2212yes—
39C2×#106×C73C2212yes—
40C22×Dic146—24no—
41C23×Dic73D412yes—
42C22×#10596831Q818yescomplemented
43C22×#10596831C2311yescharacteristic
44C22×#10596831C2311yescharacteristic
45C22×#10596831C2314yes—
46#14556590—28no—
47#14556590C23116yes—
48#14556582—28no—
49#14556582C23116yes—
50#14556568—232no—
51C4×Dic146—232no—
52#14556550—24no—
53#14556550C2318yes—
54C2×C4⋊Dic73—24no—
55C2×C4⋊Dic73C2314yes—
56C2×#11924007—24no—
57C2×#11924007—24no—
58C2×C22⋊Dic73—22no—
59C2×C4×Dic73—22no—
60C2×C4×Dic73D414yes—
61C2×C4×Dic73D412yes—
62C2×C4×Dic73C2311yescharacteristic
63C2×C4×Dic73C2314yes—
64C2×C4×Dic73C2311yescharacteristic
65#14556525C2318yes—
66#14556524C23116yes—
67#14556523C2318yes—
68#14556522C23116yes—
69C8×Dic73C2314yes—
70C8×Dic73C2314yes—
71C8×Dic73C2314yes—
72C8×Dic73C2314yes—
73C23×C4×C73C2311yescharacteristic
74C22×C8×C73Q818yescomplemented
75C22×C8×C73C2311yescharacteristic
76C22×C8×C73C2311yescharacteristic
77C22×C8×C73C2314yes—
78#117×C73—24no—
79#117×C73C2318yes—
80C2×C4⋊C4×C73C2314yes—
81C2×C22⋊C4×C73—22no—
82C2×C42×C73—22no—
83#107×C73C2318yes—
84#106×C73C2318yes—
85C2×Dic146—216no—
86C2×Dic146—416no—
87C22×Dic73—28no—
88C22×Dic73—24no—
89C22×Dic73C2×D412yes—
90C22×Dic73C2×D418yes—
91C22×Dic73C2×D412yes—
92C2×#10596831C2×Q814yes—
93C2×#10596831C2×Q814yes—
94C2×#10596831C2×Q8116yescomplemented
95C2×#10596831C2412yes—
96C2×#10596831C2412yes—
97C4⋊Dic73—24no—
98C4⋊Dic73—216no—
99C4⋊Dic73C2418yes—
100#11924007—216no—
101#11924007—216no—
102C22⋊Dic73—28no—
103C4×Dic73—28no—
104C4×Dic73C2×D418yes—
105C4×Dic73C2×D412yes—
106C4×Dic73C2×D412yes—
107C4×Dic73C2412yes—
108C4×Dic73C2412yes—
109C24×C73C2×D411yescharacteristic
110C22×C4×C73—24no—
111C22×C4×C73C2×D412yes—
112C22×C4×C73C2×D411yescharacteristic
113C22×C4×C73C2×Q814yes—
114C22×C4×C73C2×Q814yes—
115C22×C4×C73C2411yescharacteristic
116C22×C4×C73C2412yes—
117C2×C8×C73C2×Q814yes—
118C2×C8×C73C2×Q814yes—
119C2×C8×C73C2×Q8116yescomplemented
120C2×C8×C73C2412yes—
121C2×C8×C73C2412yes—
122C4⋊C4×C73—24no—
123C4⋊C4×C73C2418yes—
124C22⋊C4×C73—28no—
125C42×C73—28no—
126C23×C73—24no—
127C23×C73C4⋊Q814yes—
128C23×C73C22×D412yes—
129C23×C73C22×D411yescharacteristic
130C2×C4×C73—28no—
131C2×C4×C73—48no—
132C2×C4×C73C4⋊Q818yes—
133C2×C4×C73C4⋊Q814yes—
134C2×C4×C73C22×D412yes—
135C2×C4×C73C22×D411yescharacteristic
136C2×C4×C73C22×Q812yes—
137C2×C4×C73C22×Q814yes—
138C2×C4×C73C22×Q812yes—
139C2×C4×C73C22×Q814yes—
140C2×C4×C73C2511yescharacteristic
141C2×Dic73—24no—
142C2×Dic73—216no—
143C2×Dic73—28no—
144C2×Dic73—48no—
145C2×Dic73#13518yes—
146C2×Dic73C22×D414yes—
147C2×Dic73C22×D414yes—
148Dic146—432no—
149C8×C73C22×Q814yes—
150C8×C73C22×Q814yes—
151#10596831C22×Q814yes—
152#10596831C22×Q814yes—
153C22×C73—28no—
154C22×C73—24no—
155C22×C73C2×C4⋊Q814yes—
156C22×C73C2×C4⋊Q812yes—
157C22×C73C2×#13514yes—
158C22×C73C23×D411yescharacteristic
159C4×C73—48no—
160C4×C73C2×C4⋊Q814yes—
161C4×C73C2×C4⋊Q812yes—
162C4×C73C23×Q811yescharacteristic
163C4×C73C23×Q811yescharacteristic
164Dic73—24no—
165Dic73—48no—
166Dic73C2×#13518yes—
167C2×#3160—731nomaximal, Sylow
168C2×C73—24no—
169C2×C73#316014yescomplemented
170C2×C73C22×C4⋊Q811yescharacteristic
171C2×C73C22×#13512yes—
172C2×#533—732no—
173#3160—7316no—
174C2×#500—732no—
175C2×#499—732no—
176C2×#499—732no—
177C2×#498—732no—
178C2×#427—731no—
179C2×#427—732no—
180C2×#427D7311yescharacteristic
181C22×C4×C8—731no—
182C73C2×#316011yescharacteristic, complemented, Sylow
183C23×C8—731no—
184C23×C8C2×D7311yescharacteristic
185#533—7316no—
186#533—1468no—
187C2×C4⋊Q8—734no—
188C2×#125—734no—
189C2×C22⋊Q8—1464no—
190C2×C4×Q8—1464no—
191C2×#117—732no—
192C2×#117C2×D7312yes—
193C22×C42—731no—
194#500—7316no—
195#499—7316no—
196#499—7316no—
197#498—7316no—
198#427—738no—
199#427—7316no—
200#427C2×D7318yes—
201C2×#107—732no—
202C2×#107—734no—
203C2×#107C2×D7312yes—
204C2×#106—732no—
205C2×#106—734no—
206C2×#106C2×D7312yes—
207C2×C4×C8—731no—
208C2×C4×C8—731no—
209C2×C4×C8—731no—
210C2×C4×C8—731no—
211C2×C4×C8—738no—
212C22×Q8—1464no—
213C23×C4—732no—
214C23×C4C22×D7311yescharacteristic
215C22×C8—738no—
216C22×C8—731no—
217C22×C8—731no—
218C22×C8—734no—
219C22×C8Dic14618yescomplemented
220C22×C8C22×D7311yescharacteristic
221C22×C8C22×D7311yescharacteristic
222C22×C8C22×D7314yes—
223C4⋊Q8—7316no—
224C4⋊Q8—1468no—
225#125—7316no—
226#125—1468no—
227C22⋊Q8—14632no—
228C4×Q8—14632no—
229#117—24no—
230#117—738no—
231#117—1464no—
232#117C22×D7318yes—
233C2×C4⋊C4—734no—
234C2×C4⋊C4—1464no—
235C2×C4⋊C4—1464no—
236C2×C4⋊C4—1464no—
237C2×C4⋊C4C22×D7314yes—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—1462no—
240C2×C42—22no—
241C2×C42—734no—
242C2×C42—732no—
243C2×C42—731no—
244C2×C42—731no—
245C2×C42—734no—
246C2×C42—1462no—
247#107—738no—
248#107—7316no—
249#107C22×D7318yes—
250#106—738no—
251#106—7316no—
252#106C22×D7318yes—
253C4×C8—734no—
254C4×C8—734no—
255C4×C8—734no—
256C4×C8—734no—
257C24D4×D7311yescharacteristic
258C2×Q8—29216no—
259C2×Q8—14616no—
260C22×C4—24no—
261C22×C4—732no—
262C22×C4—732no—
263C22×C4—738no—
264C22×C4—1464no—
265C22×C4—1468no—
266C22×C4D4×D7312yes—
267C22×C4D4×D7311yescharacteristic
268C22×C4Q8×D7314yes—
269C22×C4C2×Dic14614yes—
270C22×C4C23×D7311yescharacteristic
271C22×C4C23×D7312yes—
272C2×C8—734no—
273C2×C8—734no—
274C2×C8—7316no—
275C2×C8—732no—
276C2×C8—732no—
277C2×C8C2×Dic14614yes—
278C2×C8C2×Dic14614yes—
279C2×C8C2×Dic146116yescomplemented
280C2×C8C23×D7312yes—
281C2×C8C23×D7312yes—
282C4⋊C4—24no—
283C4⋊C4—738no—
284C4⋊C4—14616no—
285C4⋊C4—14616no—
286C4⋊C4—14616no—
287C4⋊C4—1464no—
288C4⋊C4C23×D7318yes—
289C22⋊C4—28no—
290C22⋊C4—1468no—
291C42—28no—
292C42—738no—
293C42—732no—
294C42—732no—
295C42—732no—
296C42—732no—
297C42—1468no—
298C23—24no—
299C23#1455659014yes—
300C23C2×D4×D7312yes—
301C23C2×D4×D7311yescharacteristic
302Q8—29232no—
303C2×C4—28no—
304C2×C4—48no—
305C2×C4—2928no—
306C2×C4—734no—
307C2×C4—738no—
308C2×C4—734no—
309C2×C4—1468no—
310C2×C4—14616no—
311C2×C4—1464no—
312C2×C4#1455659018yes—
313C2×C4#1455659014yes—
314C2×C4C2×D4×D7312yes—
315C2×C4C2×D4×D7311yescharacteristic
316C2×C4C2×Q8×D7314yes—
317C2×C4C2×Q8×D7312yes—
318C2×C4C22×Dic14612yes—
319C2×C4C22×Dic14614yes—
320C2×C4C24×D7311yescharacteristic
321C8—734no—
322C8—734no—
323C8C22×Dic14614yes—
324C8C22×Dic14614yes—
325C22—28no—
326C22—24no—
327C22C2×#1455659014yes—
328C22C2×#1455659012yes—
329C22#135×D7314yes—
330C22C22×D4×D7311yescharacteristic
331C4—48no—
332C4—2928no—
333C4—738no—
334C4—1464no—
335C4C2×#1455659012yes—
336C4C2×#1455659014yes—
337C4C22×Q8×D7311yescharacteristic
338C4C23×Dic14611yescharacteristic
339C2—24no—
340C2#2262044314yesdirect product factor
341C2C22×#1455659011yescharacteristic
342C2C2×#135×D7312yes—
subgroupG/H
centerC22×C4D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#427×C73C2
socleC23×C73C22×D4
prime radicalC24×C73C2×D4
hypercenterC2×#427D73
hypocenterC73C2×#3160
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
2. #22620443C2direct (N × H)
3. C2×#17988991C2semidirect
4. C2×#17988988C2semidirect
5. C2×#17988987C2semidirect
6. C2×#17988984C2semidirect
20. #17988991C22semidirect
21. #17988988C22semidirect
22. #17988987C22semidirect
23. #17988984C22semidirect
42. C22×#10596831Q8semidirect
74. C22×C8×C73Q8semidirect
94. C2×#10596831C2×Q8semidirect
119. C2×C8×C73C2×Q8semidirect
169. C2×C73#3160semidirect
182. C73C2×#3160semidirect
219. C22×C8Dic146semidirect
279. C2×C8C2×Dic146semidirect
340. C2#22620443direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891402
#226204432
C2×#179889912
C2×#179889882
C2×#179889872
C2×#179889842
C2×#179886252
C2×#179886232
C22×C8×Dic732
C2×#427×C732
C2×#316073