Finite Group Databasebeta

← C2×#14545132 #17978428

Subgroups — C2×#14545132 #17978428

Order 4352.

658 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587535C211yesmaximal, characteristic
2C2×#11763819C211yesmaximal, characteristic
3#14545132C218yesmaximal, direct product factor
4C2×#11763734C212yesmaximal, complemented
5C2×#11763733C212yesmaximal, complemented
6C2×M32×D17C211yesmaximal, characteristic
7C22×#63243—21no—
8C2×#10587677—21no—
9C2×#10587535—21no—
10C2×#10587535—22no—
11C2×#10587535C2212yes—
12C2×#10587535C2214yes—
13#11763819—22no—
14#11763819C2214yes—
15C2×#10587534—21no—
16C2×#10587533C2211yescharacteristic
17C2×#10587533C2211yescharacteristic
18#11763734C2218yescomplemented
19#11763733C2218yescomplemented
20C22×C8×D17C2211yescharacteristic
21C2×#10587483C411yescharacteristic, complemented
22C2×#10587469C2212yes—
23M32×D17C414yescomplemented
24M32×D17C2214yes—
25C2×C16×D17C412yescomplemented
26C2×C17×M32C411yescharacteristic, complemented
27C22×C4×D17D411yescharacteristic
28C2×C22⋊#595—41no—
29C22×#3624—41no—
30#10587677—24no—
31#10587677—42no—
32C2×C4⋊#595—21no—
33C2×C4⋊#595—21no—
34C2×C4×#595—41no—
35C2×#63243—22no—
36C2×#63243—24no—
37C2×#63243—41no—
38C2×#63243—42no—
39C22×C8×C17C2×C411yescharacteristic
40C22×#3622Q811yescharacteristic
41C2×C8×D17C2×C411yescharacteristic
42C2×C8×D17C2×C412yes—
43C2×C8×D17D411yescharacteristic
44C2×C8×D17D412yes—
45C2×C8×D17Q811yescharacteristic
46C2×C8×D17Q812yes—
47C2×C8×D17C2312yes—
48C2×C8×D17C2311yescharacteristic
49#10587535—22no—
50#10587535—24no—
51#10587535C2314yes—
52#10587534—24no—
53#10587533—21no—
54#10587533—21no—
55#10587533C2312yes—
56#10587533C2312yes—
57C17×M32C2×C414yescomplemented
58C2×C16×C17C2×C412yes—
59#10587483C2×C414yescomplemented
60C2×#63214C2×C412yes—
61#10587469C2×C414yes—
62#10587469C2314yes—
63C16×D17C2×C418yescomplemented
64C23×D17SD1611yescharacteristic
65C22×#595—41no—
66C22×#595—41no—
67C22×C4×C17C4⋊C411yescharacteristic
68C22×Dic17SD1611yescharacteristic
69C2×C4×D17C4⋊C411yescharacteristic
70C2×C4×D17C4⋊C412yes—
71C2×C4×D17SD1611yescharacteristic
72C2×C4×D17SD1612yes—
73C2×C4×D17SD1611yescharacteristic
74C2×C4×D17SD1612yes—
75C2×C4×D17C2×D411yescharacteristic
76C2×C4×D17C2×D412yes—
77C22⋊#595—44no—
78C2×#3624—44no—
79C2×#3624—42no—
80C4⋊#595—22no—
81C4⋊#595—22no—
82C4⋊#595—41no—
83C4⋊#595—41no—
84C4×#595—44no—
85#63243—24no—
86#63243—42no—
87#63243—44no—
88C2×C8×C17C4⋊C411yescharacteristic
89C2×C8×C17C4⋊C412yes—
90C2×C8×C17C22×C411yescharacteristic
91C2×C8×C17C22×C412yes—
92C2×#3622C4⋊C411yescharacteristic
93C2×#3622C4⋊C412yes—
94C2×#3622C2×Q812yes—
95C2×#3622C2×Q811yescharacteristic
96C8×D17C4⋊C412yes—
97C8×D17C4⋊C412yes—
98C8×D17C4⋊C412yes—
99C8×D17C22×C412yes—
100C8×D17C22×C411yescharacteristic
101C8×D17C2×D411yescharacteristic
102C8×D17C2×D412yes—
103C8×D17C2×Q812yes—
104C8×D17C2×Q811yescharacteristic
105C8×D17C2411yescharacteristic
106C16×C17C22×C414yes—
107#63214C22×C414yes—
108C2×#2155—171nomaximal, Sylow
109C23×C17#10611yescharacteristic
110C22×D17—42no—
111C22×D17#10611yescharacteristic
112C22×D17#10612yes—
113C22×D17C2×SD1611yescharacteristic
114C22×D17C2×SD1612yes—
115C2×#595—42no—
116C2×#595—42no—
117C2×#595—82no—
118C2×#595—82no—
119C2×C4×C17#10612yes—
120C2×C4×C17#10611yescharacteristic
121C2×C4×C17C2×C4⋊C412yes—
122C2×C4×C17C2×C4⋊C411yescharacteristic
123C2×Dic17#10612yes—
124C2×Dic17#10611yescharacteristic
125C2×Dic17C2×SD1612yes—
126C2×Dic17C2×SD1611yescharacteristic
127C4×D17#10612yes—
128C4×D17#10612yes—
129C4×D17#10612yes—
130C4×D17C2×C4⋊C411yescharacteristic
131C4×D17C2×C4⋊C412yes—
132C4×D17C2×SD1611yescharacteristic
133C4×D17C2×SD1612yes—
134C4×D17C2×SD1612yes—
135C4×D17C2×SD1611yescharacteristic
136C4×D17C22×D411yescharacteristic
137#3624—44no—
138C8×C17C2×C4⋊C411yescharacteristic
139C8×C17C2×C4⋊C412yes—
140C8×C17C23×C411yescharacteristic
141#3622C2×C4⋊C412yes—
142#3622C2×C4⋊C411yescharacteristic
143#3622C22×Q811yescharacteristic
144C22×M32—171no—
145C22×#108—171no—
146C2×#427—171no—
147#2155—178no—
148C2×#365—172no—
149C2×#365—172no—
150C22×C17—22no—
151C22×C17C2×#10612yes—
152C22×C17C2×#10611yescharacteristic
153C2×D17—22no—
154C2×D17—22no—
155C2×D17—42no—
156C2×D17—42no—
157C2×D17C2×#10612yes—
158C2×D17C2×#10611yescharacteristic
159C2×D17C22×SD1611yescharacteristic
160#595—82no—
161#595—82no—
162C4×C17C2×#10612yes—
163C4×C17C2×#10611yescharacteristic
164C4×C17C22×C4⋊C411yescharacteristic
165Dic17C2×#10612yes—
166Dic17C2×#10611yescharacteristic
167Dic17C22×SD1611yescharacteristic
168C22×M16—341no—
169C23×C8—171no—
170C2×#117—341no—
171C2×M32—171no—
172C2×M32—174no—
173C2×M32—174no—
174C2×M32—172no—
175C2×M32#59511yescharacteristic, complemented
176C22×C16—172no—
177C2×#108—172no—
178C2×#108—174no—
179C2×#108—341no—
180C2×#108—342no—
181#427—174no—
182#427—342no—
183C2×#107—341no—
184C2×#106—171no—
185C2×#106—171no—
186#365—178no—
187#365—178no—
188C2×C17—22no—
189C2×C17#215512yescomplemented
190C2×C17C22×#10611yescharacteristic
191D17—21no—
192D17—21no—
193D17—22no—
194C23×C4—171no—
195C2×M16—342no—
196C2×M16—344no—
197C2×M16—682no—
198C2×M16—681no—
199C22×C8—171no—
200C22×C8—171no—
201C22×C8—172no—
202C22×C8—172no—
203C22×C8—171no—
204C22×C8—171no—
205C22×C8—172no—
206C22×C8—171no—
207C22×C8—172no—
208C22×C8—681no—
209C22×C8C2×#59511yescharacteristic
210#117—344no—
211#117—682no—
212C2×C4⋊C4—341no—
213C2×C4⋊C4—341no—
214C2×C22⋊C4—681no—
215C2×C42—681no—
216M32—174no—
217M32—174no—
218M32—174no—
219M32C2×#59514yescomplemented
220C2×C16—172no—
221C2×C16—178no—
222C2×C16C2×#59512yes—
223#108—174no—
224#108—342no—
225#108—344no—
226#107—344no—
227#106—172no—
228#106—172no—
229#106—341no—
230#106—341no—
231C17C2×#215511yescharacteristic, complemented, Sylow
232C24—171no—
233C22×C4—171no—
234C22×C4—172no—
235C22×C4—171no—
236C22×C4—171no—
237C22×C4—172no—
238C22×C4—171no—
239C22×C4—172no—
240C22×C4—172no—
241C22×C4—171no—
242C22×C4—681no—
243C22×C4—681no—
244C22×C4C4⋊#59511yescharacteristic
245M16—344no—
246M16—682no—
247M16—684no—
248C2×C8—172no—
249C2×C8—171no—
250C2×C8—172no—
251C2×C8—171no—
252C2×C8—171no—
253C2×C8—172no—
254C2×C8—172no—
255C2×C8—172no—
256C2×C8—172no—
257C2×C8—171no—
258C2×C8—172no—
259C2×C8—171no—
260C2×C8—172no—
261C2×C8—171no—
262C2×C8—684no—
263C2×C8—682no—
264C2×C8C4⋊#59512yes—
265C2×C8C4⋊#59511yescharacteristic
266C2×C8C22×#59511yescharacteristic
267C2×C8C22×#59512yes—
268C4⋊C4—342no—
269C4⋊C4—342no—
270C4⋊C4—681no—
271C4⋊C4—681no—
272C22⋊C4—684no—
273C42—684no—
274C16—174no—
275C16C22×#59514yes—
276C23—171no—
277C23—171no—
278C23—172no—
279C23—172no—
280C23—682no—
281C23#1058753311yescharacteristic
282C2×C4—172no—
283C2×C4—172no—
284C2×C4—171no—
285C2×C4—171no—
286C2×C4—172no—
287C2×C4—171no—
288C2×C4—171no—
289C2×C4—172no—
290C2×C4—172no—
291C2×C4—172no—
292C2×C4—172no—
293C2×C4—171no—
294C2×C4—172no—
295C2×C4—171no—
296C2×C4—682no—
297C2×C4—682no—
298C2×C4—1362no—
299C2×C4—1362no—
300C2×C4#1058753312yes—
301C2×C4#1058753311yescharacteristic
302C2×C4C2×C4⋊#59512yes—
303C2×C4C2×C4⋊#59511yescharacteristic
304C8—171no—
305C8—172no—
306C8—171no—
307C8—684no—
308C8C2×C4⋊#59511yescharacteristic
309C8C2×C4⋊#59512yes—
310C8C23×#59511yescharacteristic
311C22—22no—
312C22—171no—
313C22—171no—
314C22—172no—
315C22—342no—
316C22—342no—
317C22—682no—
318C22—682no—
319C22C2×#1058753312yes—
320C22C2×#1058753311yescharacteristic
321C4—171no—
322C4—172no—
323C4—171no—
324C4—1362no—
325C4—1362no—
326C4C2×#1058753312yes—
327C4C2×#1058753311yescharacteristic
328C4C22×C4⋊#59511yescharacteristic
329C2—22no—
330C2—341no—
331C2—341no—
332C2—342no—
333C2#1454513212yesdirect product factor
334C2C22×#1058753311yescharacteristic
subgroupG/H
centerC22C2×#10587533
commutatorC8×C17C23×C4
FrattiniC8C23×#595
FittingC2×C17×M32C4
socleC22×C17C2×#106
prime radicalC23×D17SD16
cosocleC8×D17C24
hypercenterC2×M32#595
hypocenterC17C2×#2155
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×M32

Complements

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

NH ≅ G/Ntype
3. #14545132C2direct (N × H)
4. C2×#11763734C2semidirect
5. C2×#11763733C2semidirect
18. #11763734C22semidirect
19. #11763733C22semidirect
21. C2×#10587483C4semidirect
23. M32×D17C4semidirect
25. C2×C16×D17C4semidirect
26. C2×C17×M32C4semidirect
57. C17×M32C2×C4semidirect
59. #10587483C2×C4semidirect
63. C16×D17C2×C4semidirect
175. C2×M32#595semidirect
189. C2×C17#2155semidirect
219. M32C2×#595semidirect
231. C17C2×#2155semidirect
333. C2#14545132direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875352
C2×#117638192
#145451322
C2×#117637342
C2×#117637332
C2×M32×D172
C2×#215517