Finite Group Databasebeta

← C2×#14537382 #17897995

Subgroups — C2×#14537382 #17897995

Order 4352.

2766 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587634C211yesmaximal, characteristic
2C2×#11763292C211yesmaximal, characteristic
3#14537382C2116yesmaximal, direct product factor
4C2×#11762852C213yesmaximal, complemented
5C2×#11762849C213yesmaximal, complemented
6C2×#11762845C213yesmaximal, complemented
7C22×#10587478C213yesmaximal, complemented
8C2×C17×#520C211yesmaximal, characteristic
9C2×#10587634C4116yescomplemented
10C2×#10587634C2218yes—
11C22×#63223C2213yes—
12C23×#3622C2213yes—
13#11763292—24no—
14#11763292C2218yes—
15C2×Q8×Dic17—21no—
16C2×D4×Dic17—23no—
17C2×#10587612C2213yes—
18C22×C4⋊Dic17C2213yes—
19#11762852C22124yescomplemented
20#11762849C22124yescomplemented
21#11762845C22124yescomplemented
22C2×#10587478C2213yes—
23C2×#10587478C2216yes—
24C2×#10587478C2211yescharacteristic
25C2×#10587478C22124yescomplemented
26C2×#10587479C2213yes—
27C2×#10587479C2213yes—
28C22×#41×C17C2211yescharacteristic
29C17×#520—24no—
30C17×#520C2218yes—
31C2×C4×Q8×C17—21no—
32C2×C4×D4×C17—23no—
33C2×C17×#117C2213yes—
34C22×C4⋊C4×C17C2213yes—
35C2×#41×C17C2×C418yes—
36C2×#41×C17D414yes—
37C2×#41×C17Q818yes—
38C2×#41×C17C2314yes—
39C22×Q8×C17D411yescharacteristic
40C22×D4×C17D413yes—
41C23×C4×C17—23no—
42C23×C4×C17C2313yes—
43C23×Dic17—23no—
44C4×Q8×C17—28no—
45C4×D4×C17—224no—
46C17×#117—26no—
47C17×#117C23112yes—
48C2×C4⋊C4×C17—23no—
49C2×C4⋊C4×C17—26no—
50C2×C4⋊C4×C17C2313yes—
51C2×C4⋊C4×C17C23112yes—
52C2×C4⋊C4×C17C2311yescharacteristic
53C2×C22⋊C4×C17—23no—
54C2×C42×C17—23no—
55C2×C22⋊Dic17—23no—
56#10587634C2×C4164yescomplemented
57Q8×Dic17—28no—
58D4×Dic17—224no—
59#10587612—26no—
60#10587612C23112yes—
61C2×C4⋊Dic17—23no—
62C2×C4⋊Dic17—26no—
63C2×C4⋊Dic17C2313yes—
64C2×C4⋊Dic17C23112yes—
65C2×C4⋊Dic17C2311yescharacteristic
66C2×C4×Dic17—23no—
67C2×#63223C2×C4124yescomplemented
68C2×#63223C23112yes—
69C22×#3622C2×C4124yescomplemented
70C22×#3622C2311yescharacteristic
71C22×#3622C2313yes—
72C22×#3622C23112yes—
73#10587479C23112yes—
74#10587479C23112yes—
75#10587478C23112yes—
76#10587478C23124yes—
77#10587478C2314yes—
78C24×C17C2×D413yes—
79#41×C17C4⋊C4132yes—
80#41×C17C22×C4116yes—
81#41×C17C2×Q8116yes—
82C2×Q8×C17C4⋊C418yes—
83C2×Q8×C17C2×D414yes—
84C2×D4×C17C4⋊C4124yes—
85C2×D4×C17C2×D4112yes—
86C22×C4×C17—23no—
87C22×C4×C17—21no—
88C22×C4×C17—212no—
89C22×C4×C17—86no—
90C22×C4×C17C22×C4112yes—
91C22×C4×C17C2×D413yes—
92C22×C4×C17C2×D416yes—
93C22×C4×C17C2×Q8112yes—
94C22×C4×C17C2411yescharacteristic
95C22×C4×C17C2416yes—
96C22×Dic17—23no—
97C22×Dic17—21no—
98C22×Dic17—212no—
99C22×Dic17—86no—
100C4⋊C4×C17—23no—
101C4⋊C4×C17—212no—
102C4⋊C4×C17—21no—
103C4⋊C4×C17C2416yes—
104C4⋊C4×C17C2412yes—
105C22⋊C4×C17—212no—
106C42×C17—212no—
107C22⋊Dic17—212no—
108C4⋊Dic17—23no—
109C4⋊Dic17—212no—
110C4⋊Dic17—21no—
111C4⋊Dic17C2416yes—
112C4⋊Dic17C2412yes—
113C4×Dic17—212no—
114#63223C22×C4148yescomplemented
115C2×#3622C22×C414yes—
116C2×#3622C22×C4112yes—
117C2×#3622C22×C4148yescomplemented
118C2×#3622C2412yes—
119C2×#3622C2416yes—
120C2×#2913—171nomaximal, Sylow
121C23×C17—26no—
122C23×C17—26no—
123C23×C17C2×C4⋊C4112yes—
124C23×C17C22×D416yes—
125C23×C17C22×D411yescharacteristic
126Q8×C17C2×C4⋊C4116yes—
127D4×C17C2×C4⋊C4148yes—
128C2×C4×C17—22no—
129C2×C4×C17—26no—
130C2×C4×C17—46no—
131C2×C4×C17—42no—
132C2×C4×C17—812no—
133C2×C4×C17C2×C4⋊C4112yes—
134C2×C4×C17C2×C4⋊C4124yes—
135C2×C4×C17C23×C412yes—
136C2×C4×C17C23×C4112yes—
137C2×C4×C17C22×D416yes—
138C2×C4×C17C22×D411yescharacteristic
139C2×C4×C17C22×Q812yes—
140C2×C4×C17C22×Q8112yes—
141C2×C4×C17C2511yescharacteristic
142C2×Dic17—22no—
143C2×Dic17—26no—
144C2×Dic17—46no—
145C2×Dic17—42no—
146C2×Dic17—812no—
147#3622C23×C414yes—
148#3622C23×C4112yes—
149C22×#131—171no—
150C2×#520—171no—
151C2×#520D1711yescharacteristic
152#2913—1716no—
153C2×#428—173no—
154C2×#428—173no—
155C2×#427—173no—
156C22×#107—173no—
157C22×C17—224no—
158C22×C17—26no—
159C22×C17—26no—
160C22×C17C22×C4⋊C4112yes—
161C22×C17C22×C4⋊C412yes—
162C22×C17#57612yes—
163C22×C17#57812yes—
164C22×C17C23×D411yescharacteristic
165C4×C17—46no—
166C4×C17—42no—
167C4×C17C22×C4⋊C412yes—
168C4×C17C22×C4⋊C4112yes—
169C4×C17C24×C411yescharacteristic
170C4×C17C23×Q811yescharacteristic
171Dic17—46no—
172Dic17—42no—
173C22×#41C2×D1711yescharacteristic
174C2×#131—1716no—
175C2×#131—178no—
176C22×M16—173no—
177C23×C8—173no—
178#520—24no—
179#520—178no—
180#520—344no—
181#520C2×D1718yes—
182C2×C4×Q8—21no—
183C2×C4×Q8—341no—
184C2×C4×D4—23no—
185C2×C4×D4—343no—
186C2×#117—173no—
187C2×#117C2×D1713yes—
188C22×C4⋊C4—173no—
189C22×C4⋊C4C2×D1713yes—
190#428—1724no—
191#428—1724no—
192#427—1724no—
193C2×#107—173no—
194C2×#107—176no—
195C2×#107—1724no—
196C2×#107—171no—
197C2×#106—173no—
198C2×#106—173no—
199C2×C17—212no—
200C2×C17#291314yescomplemented
201C2×C17C23×C4⋊C411yescharacteristic
202C2×C17C2×#57611yescharacteristic
203C2×C17C2×#57811yescharacteristic
204C2×#41Dic3418yes—
205C2×#41C4×D1718yes—
206C2×#41C22⋊D1714yes—
207C2×#41C22×D1714yes—
208C22×Q8C22⋊D1711yescharacteristic
209C22×D4C22⋊D1713yes—
210C23×C4—23no—
211C23×C4—343no—
212C23×C4C22×D1713yes—
213#131—1764no—
214C2×M16—1724no—
215C2×M16—1712no—
216C22×C8—1724no—
217C22×C8—171no—
218C22×C8—173no—
219C22×C8—1712no—
220C4×Q8—28no—
221C4×Q8—348no—
222C4×D4—224no—
223C4×D4—3424no—
224#117—26no—
225#117—1712no—
226#117—346no—
227#117C22×D17112yes—
228C2×C4⋊C4—23no—
229C2×C4⋊C4—26no—
230C2×C4⋊C4—173no—
231C2×C4⋊C4—1712no—
232C2×C4⋊C4—171no—
233C2×C4⋊C4—343no—
234C2×C4⋊C4—346no—
235C2×C4⋊C4C22×D1713yes—
236C2×C4⋊C4C22×D17112yes—
237C2×C4⋊C4C22×D1711yescharacteristic
238C2×C22⋊C4—23no—
239C2×C22⋊C4—343no—
240C2×C42—23no—
241C2×C42—343no—
242#107—1712no—
243#107—1724no—
244#107—174no—
245#106—1712no—
246#106—1712no—
247C17C2×#291311yescharacteristic, complemented, Sylow
248C24C2×C22⋊D1713yes—
249#41#63225132yes—
250#41C2×Dic34116yes—
251#41C2×C4×D17116yes—
252C2×Q8#6322518yes—
253C2×Q8C2×C22⋊D1714yes—
254C2×D4#63225124yes—
255C2×D4C2×C22⋊D17112yes—
256C22×C4—21no—
257C22×C4—23no—
258C22×C4—212no—
259C22×C4—86no—
260C22×C4—341no—
261C22×C4—343no—
262C22×C4—3412no—
263C22×C4—1366no—
264C22×C4C2×Dic34112yes—
265C22×C4C2×C4×D17112yes—
266C22×C4C2×C22⋊D1716yes—
267C22×C4C2×C22⋊D1713yes—
268C22×C4C23×D1716yes—
269C22×C4C23×D1711yescharacteristic
270M16—1748no—
271C2×C8—174no—
272C2×C8—1712no—
273C2×C8—1748no—
274C2×C8—176no—
275C2×C8—172no—
276C4⋊C4—23no—
277C4⋊C4—212no—
278C4⋊C4—21no—
279C4⋊C4—172no—
280C4⋊C4—176no—
281C4⋊C4—343no—
282C4⋊C4—3412no—
283C4⋊C4—341no—
284C4⋊C4C23×D1712yes—
285C4⋊C4C23×D1716yes—
286C22⋊C4—212no—
287C22⋊C4—3412no—
288C42—212no—
289C42—3412no—
290C23—26no—
291C23—26no—
292C23C2×#63225112yes—
293C23C22×C22⋊D1716yes—
294C23C22×C22⋊D1711yescharacteristic
295Q8C2×#63225116yes—
296D4C2×#63225148yes—
297C2×C4—22no—
298C2×C4—26no—
299C2×C4—46no—
300C2×C4—42no—
301C2×C4—812no—
302C2×C4—342no—
303C2×C4—346no—
304C2×C4—686no—
305C2×C4—682no—
306C2×C4—13612no—
307C2×C4C2×#63225112yes—
308C2×C4C2×#63225124yes—
309C2×C4C22×Dic3412yes—
310C2×C4C22×Dic34112yes—
311C2×C4C22×C4×D1712yes—
312C2×C4C22×C4×D17112yes—
313C2×C4C22×C22⋊D1716yes—
314C2×C4C22×C22⋊D1711yescharacteristic
315C2×C4C24×D1711yescharacteristic
316C8—174no—
317C8—1712no—
318C22—224no—
319C22—26no—
320C22—26no—
321C22C22×#63225112yes—
322C22C22×#6322512yes—
323C22#1176361212yes—
324C22#1176362412yes—
325C22C23×C22⋊D1711yescharacteristic
326C4—46no—
327C4—42no—
328C4—686no—
329C4—682no—
330C4C22×#6322512yes—
331C4C22×#63225112yes—
332C4C23×C4×D1711yescharacteristic
333C4C23×Dic3411yescharacteristic
334C2—212no—
335C2#1453738214yesdirect product factor
336C2C23×#6322511yescharacteristic
337C2C2×#1176361211yescharacteristic
338C2C2×#1176362411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC4×C17C24×C4
FrattiniC2×C4C24×D17
FittingC2×C17×#520C2
socleC23×C17C22×D4
prime radicalC22×#41×C17C22
cosocleC2×C4×C17C25
hypercenterC2×#520D17
hypocenterC17C2×#2913
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
3. #14537382C2direct (N × H)
4. C2×#11762852C2semidirect
5. C2×#11762849C2semidirect
6. C2×#11762845C2semidirect
7. C22×#10587478C2semidirect
9. C2×#10587634C4semidirect
19. #11762852C22semidirect
20. #11762849C22semidirect
21. #11762845C22semidirect
25. C2×#10587478C22semidirect
56. #10587634C2×C4semidirect
67. C2×#63223C2×C4semidirect
69. C22×#3622C2×C4semidirect
114. #63223C22×C4semidirect
117. C2×#3622C22×C4semidirect
200. C2×C17#2913semidirect
247. C17C2×#2913semidirect
335. C2#14537382direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105876342
C2×#117632922
#145373822
C2×#117628522
C2×#117628492
C2×#117628452
C22×#105874782
C2×C17×#5202
C2×#291317