Finite Group Databasebeta

← C2×#22620459 #33955605

Subgroups — C2×#22620459 #33955605

Order 18688.

1854 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989218C212yesmaximal
2#22620459C2116yesmaximal, direct product factor
3C2×#17988994C214yesmaximal, complemented
4C2×#17988987C212yesmaximal, complemented
5C2×#17988984C212yesmaximal, complemented
6C2×#17988627C212yesmaximal
7C2×#17988625C211yesmaximal, characteristic
8C2×#17988542C211yesmaximal, characteristic
9C22×#106×C73C211yesmaximal, characteristic
10C22×#11924012C2211yescharacteristic
11#17989218—28no—
12#17989218C22116yes—
13C2×#14556590—22no—
14C2×#14556590C2214yes—
15C2×#14556582—22no—
16C2×#14556582C2214yes—
17C2×#14556570—24no—
18C2×#14556550C2212yes—
19C2×#14556550C2211yescharacteristic
20#17988994C22132yescomplemented
21#17988987C22116yescomplemented
22#17988984C22116yescomplemented
23#17988627C22116yes—
24#17988625C2218yes—
25C2×#14556525C2212yes—
26C2×#14556524C2214yes—
27C2×#14556523C2211yescharacteristic
28C2×#14556523C2211yescharacteristic
29C2×#14556522C2214yes—
30#17988542C2218yes—
31C2×#14556501C2212yes—
32C2×C8×Dic73C2212yes—
33C23×C8×C73C2211yescharacteristic
34C22×C4⋊C4×C73C2212yes—
35C2×#106×C73C2212yes—
36C2×#106×C73C2212yes—
37C2×#106×C73C2218yes—
38C22×Dic146—24no—
39C2×#11924012Q818yescomplemented
40C2×#11924012C2314yes—
41C22×#10596831C2312yes—
42#14556590—216no—
43#14556590—28no—
44#14556590C23116yes—
45#14556582—216no—
46#14556582—28no—
47#14556582C23116yes—
48#14556570—232no—
49#14556550—24no—
50#14556550D414yes—
51#14556550C2318yes—
52#14556550C2314yes—
53C2×C4⋊Dic73—24no—
54C2×C4⋊Dic73D412yes—
55C2×C4⋊Dic73C2312yes—
56C2×C4⋊Dic73C2312yes—
57C2×#11924007—24no—
58C2×#11924007—24no—
59C2×C22⋊Dic73—22no—
60C2×C22⋊Dic73D412yes—
61C2×C4×Dic73—22no—
62C2×C4×Dic73C2312yes—
63#14556525C2318yes—
64#14556524C23116yes—
65#14556523C2314yes—
66#14556523C2314yes—
67#14556522C23116yes—
68#14556501C2318yes—
69C8×Dic73C2318yes—
70C23×C4×C73—22no—
71C23×C4×C73C2311yescharacteristic
72C22×C8×C73Q818yescomplemented
73C22×C8×C73C2311yescharacteristic
74C22×C8×C73C2311yescharacteristic
75C22×C8×C73C2314yes—
76C2×C4⋊C4×C73—22no—
77C2×C4⋊C4×C73—24no—
78C2×C4⋊C4×C73C2314yes—
79C2×C4⋊C4×C73C2318yes—
80#106×C73C2318yes—
81#106×C73C2318yes—
82C2×Dic146—216no—
83C2×Dic146—88no—
84C22×Dic73—22no—
85C22×Dic73—22no—
86C22×Dic73C2×D414yes—
87#11924012C2×Q8116yescomplemented
88C2×#10596831C2×Q818yes—
89C2×#10596831C2414yes—
90C4⋊Dic73—22no—
91C4⋊Dic73—22no—
92C4⋊Dic73—216no—
93C4⋊Dic73C2×D418yes—
94C4⋊Dic73C2414yes—
95C4⋊Dic73C2414yes—
96#11924007—216no—
97#11924007—216no—
98C22⋊Dic73—28no—
99C22⋊Dic73C2×D418yes—
100C4×Dic73—28no—
101C4×Dic73C2×D414yes—
102C4×Dic73C2414yes—
103C24×C73C2×D411yescharacteristic
104C22×C4×C73—24no—
105C22×C4×C73—28no—
106C22×C4×C73—84no—
107C22×C4×C73C2×D411yescharacteristic
108C22×C4×C73C2×D412yes—
109C22×C4×C73C2×Q814yes—
110C22×C4×C73C2×Q814yes—
111C22×C4×C73C2411yescharacteristic
112C22×C4×C73C2412yes—
113C2×C8×C73C2×Q814yes—
114C2×C8×C73C2×Q814yes—
115C2×C8×C73C2×Q8116yescomplemented
116C2×C8×C73C2412yes—
117C2×C8×C73C2412yes—
118C4⋊C4×C73—28no—
119C4⋊C4×C73—24no—
120C4⋊C4×C73C2418yes—
121C23×C73—24no—
122C23×C73C4⋊Q814yes—
123C23×C73C22×D412yes—
124C23×C73C22×D411yescharacteristic
125C2×C4×C73—28no—
126C2×C4×C73—48no—
127C2×C4×C73—88no—
128C2×C4×C73C4⋊Q818yes—
129C2×C4×C73C4⋊Q814yes—
130C2×C4×C73C22×D412yes—
131C2×C4×C73C22×D411yescharacteristic
132C2×C4×C73C22×Q812yes—
133C2×C4×C73C22×Q814yes—
134C2×C4×C73C22×Q812yes—
135C2×C4×C73C22×Q814yes—
136C2×C4×C73C2511yescharacteristic
137C2×Dic73—28no—
138C2×Dic73—24no—
139C2×Dic73—24no—
140C2×Dic73—44no—
141C2×Dic73—44no—
142C2×Dic73C22×D418yes—
143Dic146—816no—
144C8×C73C22×Q814yes—
145C8×C73C22×Q814yes—
146#10596831C22×Q818yes—
147C22×C73—28no—
148C22×C73—24no—
149C22×C73C2×C4⋊Q814yes—
150C22×C73C2×C4⋊Q812yes—
151C22×C73#57714yes—
152C22×C73C23×D411yescharacteristic
153C4×C73—48no—
154C4×C73C2×C4⋊Q814yes—
155C4×C73C2×C4⋊Q812yes—
156C4×C73C23×Q811yescharacteristic
157C4×C73C23×Q811yescharacteristic
158Dic73—28no—
159Dic73—44no—
160Dic73—44no—
161C2×#3163—731nomaximal, Sylow
162C2×C73—24no—
163C2×C73#316314yescomplemented
164C2×C73C22×C4⋊Q811yescharacteristic
165C2×C73C2×#57712yes—
166C2×#544—732no—
167#3163—7316no—
168C2×#501—734no—
169C2×#499—732no—
170C2×#498—732no—
171C2×#428—732no—
172C2×#427—731no—
173C22×#106D7311yescharacteristic
174C2×#405—731no—
175C73C2×#316311yescharacteristic, complemented, Sylow
176C22×M16—731no—
177C23×C8C2×D7311yescharacteristic
178#544—7316no—
179#544—1468no—
180C2×C4⋊Q8—734no—
181C2×C4⋊Q8—1462no—
182C2×#125—734no—
183C2×#125—1462no—
184C2×C22⋊Q8—1464no—
185C2×#117—731no—
186C2×#117—732no—
187C22×C4⋊C4C2×D7312yes—
188#501—7332no—
189#499—7316no—
190#498—7316no—
191#428—7316no—
192#427—738no—
193C2×#107—732no—
194C2×#107—734no—
195C2×#106—731no—
196C2×#106—731no—
197C2×#106—734no—
198C2×#106C2×D7312yes—
199C2×#106C2×D7312yes—
200C2×#106C2×D7318yes—
201#405—738no—
202C2×#97—732no—
203C2×C4×C8—732no—
204C22×Q8—1464no—
205C23×C4—22no—
206C23×C4C22×D7311yescharacteristic
207C2×M16—738no—
208C2×M16—734no—
209C22×C8—732no—
210C22×C8Dic14618yescomplemented
211C22×C8C22×D7311yescharacteristic
212C22×C8C22×D7311yescharacteristic
213C22×C8C22×D7314yes—
214C4⋊Q8—7316no—
215C4⋊Q8—1468no—
216C4⋊Q8—14616no—
217#125—7316no—
218#125—1468no—
219#125—14616no—
220C22⋊Q8—14632no—
221#117—734no—
222#117—734no—
223#117—738no—
224#117—1464no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—24no—
227C2×C4⋊C4—732no—
228C2×C4⋊C4—732no—
229C2×C4⋊C4—732no—
230C2×C4⋊C4—1464no—
231C2×C4⋊C4—1464no—
232C2×C4⋊C4—1464no—
233C2×C4⋊C4C22×D7314yes—
234C2×C4⋊C4C22×D7318yes—
235C2×C22⋊C4—732no—
236C2×C22⋊C4—1462no—
237C2×C42—732no—
238C2×C42—1462no—
239#107—738no—
240#107—7316no—
241#106—734no—
242#106—734no—
243#106—7316no—
244#106C22×D7318yes—
245#106C22×D7318yes—
246#97—738no—
247C4×C8—738no—
248C24D4×D7311yescharacteristic
249C2×Q8—5848no—
250C2×Q8—14616no—
251C22×C4—24no—
252C22×C4—28no—
253C22×C4—84no—
254C22×C4—734no—
255C22×C4—1462no—
256C22×C4—1462no—
257C22×C4D4×D7312yes—
258C22×C4D4×D7311yescharacteristic
259C22×C4Q8×D7314yes—
260C22×C4C2×Dic14614yes—
261C22×C4C23×D7312yes—
262C22×C4C23×D7311yescharacteristic
263M16—7316no—
264C2×C8—738no—
265C2×C8—734no—
266C2×C8C2×Dic14614yes—
267C2×C8C2×Dic14614yes—
268C2×C8C2×Dic146116yescomplemented
269C2×C8C23×D7312yes—
270C2×C8C23×D7312yes—
271C4⋊C4—24no—
272C4⋊C4—28no—
273C4⋊C4—738no—
274C4⋊C4—734no—
275C4⋊C4—734no—
276C4⋊C4—14616no—
277C4⋊C4—14616no—
278C4⋊C4—14616no—
279C4⋊C4—1462no—
280C4⋊C4—1462no—
281C4⋊C4C23×D7318yes—
282C22⋊C4—738no—
283C22⋊C4—1468no—
284C42—734no—
285C42—734no—
286C42—1468no—
287C23—24no—
288C23#1455659014yes—
289C23C2×D4×D7312yes—
290C23C2×D4×D7311yescharacteristic
291Q8—58416no—
292C2×C4—28no—
293C2×C4—48no—
294C2×C4—88no—
295C2×C4—2924no—
296C2×C4—2924no—
297C2×C4—738no—
298C2×C4—1464no—
299C2×C4—1464no—
300C2×C4—1468no—
301C2×C4#1455659018yes—
302C2×C4#1455659014yes—
303C2×C4C2×D4×D7311yescharacteristic
304C2×C4C2×D4×D7312yes—
305C2×C4C2×Q8×D7312yes—
306C2×C4C2×Q8×D7314yes—
307C2×C4C22×Dic14612yes—
308C2×C4C22×Dic14614yes—
309C2×C4C24×D7311yescharacteristic
310C8—738no—
311C8C22×Dic14614yes—
312C8C22×Dic14614yes—
313C22—28no—
314C22—24no—
315C22C2×#1455659014yes—
316C22C2×#1455659012yes—
317C22#1798939314yes—
318C22C22×D4×D7311yescharacteristic
319C4—48no—
320C4—2924no—
321C4—2924no—
322C4—1468no—
323C4C2×#1455659012yes—
324C4C2×#1455659014yes—
325C4C22×Q8×D7311yescharacteristic
326C4C23×Dic14611yescharacteristic
327C2—24no—
328C2#2262045914yesdirect product factor
329C2C22×#1455659011yescharacteristic
330C2C2×#1798939312yes—
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC22×#106×C73C2
socleC23×C73C22×D4
prime radicalC24×C73C2×D4
hypercenterC22×#106D73
hypocenterC73C2×#3163
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
2. #22620459C2direct (N × H)
3. C2×#17988994C2semidirect
4. C2×#17988987C2semidirect
5. C2×#17988984C2semidirect
20. #17988994C22semidirect
21. #17988987C22semidirect
22. #17988984C22semidirect
39. C2×#11924012Q8semidirect
72. C22×C8×C73Q8semidirect
87. #11924012C2×Q8semidirect
115. C2×C8×C73C2×Q8semidirect
163. C2×C73#3163semidirect
175. C73C2×#3163semidirect
210. C22×C8Dic146semidirect
268. C2×C8C2×Dic146semidirect
328. C2#22620459direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892182
#226204592
C2×#179889942
C2×#179889872
C2×#179889842
C2×#179886272
C2×#179886252
C2×#179885422
C22×#106×C732
C2×#316373