Finite Group Databasebeta

← C2×#14539316 #17903949

Subgroups — C2×#14539316 #17903949

Order 4352.

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×#11763437C212yesmaximal
2#14539316C2116yesmaximal, direct product factor
3C2×#11763217C214yesmaximal, complemented
4C2×#11763209C212yesmaximal, complemented
5C2×#11763206C212yesmaximal, complemented
6C2×#11762852C212yesmaximal
7C22×#10587488C211yesmaximal, characteristic
8C2×#11762764C211yesmaximal, characteristic
9C2×C17×#427C211yesmaximal, characteristic
10C22×#63223C2211yescharacteristic
11#11763437—28no—
12#11763437C22116yes—
13C2×#10587555—22no—
14C2×#10587574C2214yes—
15C2×#10587556—22no—
16C2×#10587576C2214yes—
17C2×#10587564—24no—
18C2×#10587612C2211yescharacteristic
19C22×C4⋊Dic17C2212yes—
20#11763217C22132yescomplemented
21#11763209C22116yescomplemented
22#11763206C22116yescomplemented
23#11762852C22116yes—
24C2×#10587478C2214yes—
25C2×#10587488C2212yes—
26C2×#10587488C2212yes—
27C2×#10587488C2218yes—
28C2×#10587479C2214yes—
29#11762764C2218yes—
30C2×#10587486C2212yes—
31C2×C8×Dic17C2212yes—
32C23×C8×C17C2211yescharacteristic
33C2×C17×#117C2212yes—
34C17×#427C2218yes—
35C2×C17×#107C2212yes—
36C2×C17×#106C2211yescharacteristic
37C2×C17×#106C2211yescharacteristic
38C23×C4×C17C2311yescharacteristic
39C23×Dic17—22no—
40C22×Dic34—24no—
41C22×C8×C17Q818yescomplemented
42C22×C8×C17C2311yescharacteristic
43C22×C8×C17C2311yescharacteristic
44C22×C8×C17C2314yes—
45C17×#117—24no—
46C17×#117C2318yes—
47C2×C4⋊C4×C17C2312yes—
48C2×C4⋊C4×C17C2312yes—
49C2×C22⋊C4×C17—22no—
50C2×C42×C17—22no—
51C2×C22⋊Dic17D412yes—
52#10587612D414yes—
53#10587612C2314yes—
54C2×C4⋊Dic17—22no—
55C2×C4⋊Dic17—24no—
56C2×C4⋊Dic17—24no—
57C2×C4⋊Dic17D412yes—
58C2×C4⋊Dic17C2314yes—
59C2×C4⋊Dic17C2318yes—
60C2×#63225—24no—
61C2×#63225—24no—
62C2×C4×Dic17C2312yes—
63C2×#63223Q818yescomplemented
64C2×#63223C2314yes—
65C22×#3622C2312yes—
66#10587576—28no—
67#10587576C23116yes—
68#10587574—28no—
69#10587574C23116yes—
70#10587564—232no—
71#10587556—216no—
72#10587555—216no—
73C17×#107C2318yes—
74C17×#106C2314yes—
75C17×#106C2314yes—
76#10587488C2318yes—
77#10587488C2318yes—
78#10587486C2318yes—
79C8×Dic17C2318yes—
80#10587479C23116yes—
81#10587478C23116yes—
82C24×C17C2×D411yescharacteristic
83C22×C4×C17—22no—
84C22×C4×C17—22no—
85C22×C4×C17C2×D411yescharacteristic
86C22×C4×C17C2×D412yes—
87C22×C4×C17C2×Q814yes—
88C22×C4×C17C2×Q814yes—
89C22×C4×C17C2411yescharacteristic
90C22×C4×C17C2412yes—
91C22×Dic17—24no—
92C22×Dic17—28no—
93C22×Dic17—84no—
94C22×Dic17C2×D414yes—
95C2×Dic34—216no—
96C2×Dic34—88no—
97C2×C8×C17C2×Q814yes—
98C2×C8×C17C2×Q814yes—
99C2×C8×C17C2×Q8116yescomplemented
100C2×C8×C17C2412yes—
101C2×C8×C17C2412yes—
102C4⋊C4×C17—22no—
103C4⋊C4×C17—22no—
104C4⋊C4×C17C2414yes—
105C4⋊C4×C17C2414yes—
106C22⋊C4×C17—28no—
107C42×C17—28no—
108C22⋊Dic17C2×D418yes—
109C4⋊Dic17—28no—
110C4⋊Dic17—24no—
111C4⋊Dic17—216no—
112C4⋊Dic17C2×D418yes—
113C4⋊Dic17C2418yes—
114#63225—216no—
115#63225—216no—
116C4×Dic17C2×D414yes—
117C4×Dic17C2414yes—
118#63223C2×Q8116yescomplemented
119C2×#3622C2×Q818yes—
120C2×#3622C2414yes—
121C2×#3163—171nomaximal, Sylow
122C23×C17—24no—
123C23×C17C4⋊Q814yes—
124C23×C17C22×D412yes—
125C23×C17C22×D411yescharacteristic
126C2×C4×C17—24no—
127C2×C4×C17—24no—
128C2×C4×C17—44no—
129C2×C4×C17—44no—
130C2×C4×C17C4⋊Q818yes—
131C2×C4×C17C4⋊Q814yes—
132C2×C4×C17C22×D412yes—
133C2×C4×C17C22×D411yescharacteristic
134C2×C4×C17C22×Q812yes—
135C2×C4×C17C22×Q814yes—
136C2×C4×C17C22×Q812yes—
137C2×C4×C17C22×Q814yes—
138C2×C4×C17C2511yescharacteristic
139C2×Dic17—28no—
140C2×Dic17—28no—
141C2×Dic17—48no—
142C2×Dic17—88no—
143C2×Dic17C22×D418yes—
144Dic34—816no—
145C8×C17C22×Q814yes—
146C8×C17C22×Q814yes—
147#3622C22×Q818yes—
148C2×#544—172no—
149#3163—1716no—
150C2×#501—174no—
151C2×#499—172no—
152C2×#498—172no—
153C2×#428—172no—
154C2×#427D1711yescharacteristic
155C22×#106—171no—
156C2×#405—171no—
157C22×C17—28no—
158C22×C17—24no—
159C22×C17C2×C4⋊Q814yes—
160C22×C17C2×C4⋊Q812yes—
161C22×C17#57714yes—
162C22×C17C23×D411yescharacteristic
163C4×C17—44no—
164C4×C17—44no—
165C4×C17C2×C4⋊Q814yes—
166C4×C17C2×C4⋊Q812yes—
167C4×C17C23×Q811yescharacteristic
168C4×C17C23×Q811yescharacteristic
169Dic17—28no—
170Dic17—48no—
171C22×M16—171no—
172C23×C8C2×D1711yescharacteristic
173#544—1716no—
174#544—348no—
175C2×C4⋊Q8—174no—
176C2×C4⋊Q8—342no—
177C2×#125—174no—
178C2×#125—342no—
179C2×C22⋊Q8—344no—
180C2×#117—171no—
181C2×#117C2×D1712yes—
182C22×C4⋊C4—172no—
183#501—1732no—
184#499—1716no—
185#498—1716no—
186#428—1716no—
187#427C2×D1718yes—
188C2×#107—174no—
189C2×#107C2×D1712yes—
190C2×#106—172no—
191C2×#106—172no—
192C2×#106—178no—
193C2×#106—174no—
194C2×#106C2×D1711yescharacteristic
195C2×#106C2×D1711yescharacteristic
196#405—178no—
197C2×#97—172no—
198C2×C4×C8—172no—
199C2×C17—24no—
200C2×C17#316314yescomplemented
201C2×C17C22×C4⋊Q811yescharacteristic
202C2×C17C2×#57712yes—
203C22×Q8—344no—
204C23×C4—342no—
205C23×C4C22×D1711yescharacteristic
206C2×M16—178no—
207C2×M16—174no—
208C22×C8—172no—
209C22×C8Dic3418yescomplemented
210C22×C8C22×D1711yescharacteristic
211C22×C8C22×D1711yescharacteristic
212C22×C8C22×D1714yes—
213C4⋊Q8—1716no—
214C4⋊Q8—3416no—
215C4⋊Q8—348no—
216#125—1716no—
217#125—3416no—
218#125—348no—
219C22⋊Q8—3432no—
220#117—24no—
221#117—174no—
222#117—174no—
223#117C22×D1718yes—
224C2×C4⋊C4—172no—
225C2×C4⋊C4—174no—
226C2×C4⋊C4—178no—
227C2×C4⋊C4—344no—
228C2×C4⋊C4—344no—
229C2×C4⋊C4—344no—
230C2×C4⋊C4—342no—
231C2×C4⋊C4—344no—
232C2×C4⋊C4C22×D1712yes—
233C2×C4⋊C4C22×D1712yes—
234C2×C22⋊C4—22no—
235C2×C22⋊C4—172no—
236C2×C42—22no—
237C2×C42—172no—
238#107—1716no—
239#107C22×D1718yes—
240#106—178no—
241#106—178no—
242#106—1716no—
243#106C22×D1714yes—
244#106C22×D1714yes—
245#97—178no—
246C4×C8—178no—
247C17C2×#316311yescharacteristic, complemented, Sylow
248C24D4×D1711yescharacteristic
249C2×Q8—3416no—
250C2×Q8—1368no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—174no—
254C22×C4—344no—
255C22×C4—348no—
256C22×C4—1364no—
257C22×C4C2×Dic3414yes—
258C22×C4D4×D1712yes—
259C22×C4D4×D1711yescharacteristic
260C22×C4Q8×D1714yes—
261C22×C4C23×D1712yes—
262C22×C4C23×D1711yescharacteristic
263M16—1716no—
264C2×C8—178no—
265C2×C8—174no—
266C2×C8C2×Dic3414yes—
267C2×C8C2×Dic3414yes—
268C2×C8C2×Dic34116yescomplemented
269C2×C8C23×D1712yes—
270C2×C8C23×D1712yes—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—178no—
274C4⋊C4—178no—
275C4⋊C4—3416no—
276C4⋊C4—3416no—
277C4⋊C4—3416no—
278C4⋊C4—348no—
279C4⋊C4—344no—
280C4⋊C4C23×D1714yes—
281C4⋊C4C23×D1714yes—
282C22⋊C4—28no—
283C22⋊C4—178no—
284C42—28no—
285C42—174no—
286C42—174no—
287C23—24no—
288C23#1058757414yes—
289C23C2×D4×D1712yes—
290C23C2×D4×D1711yescharacteristic
291Q8—13616no—
292C2×C4—24no—
293C2×C4—24no—
294C2×C4—44no—
295C2×C4—44no—
296C2×C4—178no—
297C2×C4—348no—
298C2×C4—348no—
299C2×C4—688no—
300C2×C4—1368no—
301C2×C4#1058757418yes—
302C2×C4#1058757414yes—
303C2×C4C22×Dic3412yes—
304C2×C4C22×Dic3414yes—
305C2×C4C2×D4×D1712yes—
306C2×C4C2×D4×D1711yescharacteristic
307C2×C4C2×Q8×D1712yes—
308C2×C4C2×Q8×D1714yes—
309C2×C4C24×D1711yescharacteristic
310C8—178no—
311C8C22×Dic3414yes—
312C8C22×Dic3414yes—
313C22—28no—
314C22—24no—
315C22C2×#1058757414yes—
316C22C2×#1058757412yes—
317C22#1176361614yes—
318C22C22×D4×D1711yescharacteristic
319C4—44no—
320C4—44no—
321C4—348no—
322C4—688no—
323C4C2×#1058757412yes—
324C4C2×#1058757414yes—
325C4C22×Q8×D1711yescharacteristic
326C4C23×Dic3411yescharacteristic
327C2—24no—
328C2#1453931614yesdirect product factor
329C2C22×#1058757411yescharacteristic
330C2C2×#1176361612yes—
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#427C2
socleC23×C17C22×D4
prime radicalC24×C17C2×D4
hypercenterC2×#427D17
hypocenterC17C2×#3163
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
2. #14539316C2direct (N × H)
3. C2×#11763217C2semidirect
4. C2×#11763209C2semidirect
5. C2×#11763206C2semidirect
20. #11763217C22semidirect
21. #11763209C22semidirect
22. #11763206C22semidirect
41. C22×C8×C17Q8semidirect
63. C2×#63223Q8semidirect
99. C2×C8×C17C2×Q8semidirect
118. #63223C2×Q8semidirect
200. C2×C17#3163semidirect
209. C22×C8Dic34semidirect
247. C17C2×#3163semidirect
268. C2×C8C2×Dic34semidirect
328. C2#14539316direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634372
#145393162
C2×#117632172
C2×#117632092
C2×#117632062
C2×#117628522
C22×#105874882
C2×#117627642
C2×C17×#4272
C2×#316317