Finite Group Databasebeta

← C2×#14545513 #17979682

Subgroups — C2×#14545513 #17979682

Order 4352.

2806 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
1C22×#10587678C212yesmaximal, complemented
2#14545513C2116yesmaximal, direct product factor
3C2×#11763840C218yesmaximal, complemented
4C2×#11763814C211yesmaximal, characteristic, complemented
5C2×#11763783C212yesmaximal, complemented
6C2×#11763768C211yesmaximal, characteristic, complemented
7C2×#11763357C211yesmaximal, characteristic
8C2×#10587678—216no—
9C2×#10587678C22116yescomplemented
10C22×#63243C2212yes—
11C22×#63247C2214yes—
12C22×#63242C2211yescharacteristic
13C22×#63242C2211yescharacteristic
14C23×#3624C2214yes—
15#11763840C22164yescomplemented
16#11763814C2218yescomplemented
17C2×#10587544C2214yes—
18#11763783C22116yescomplemented
19C2×C22⋊#3624C2218yes—
20#11763768C2218yescomplemented
21C2×#10587542C2214yes—
22C22×#63254C2212yes—
23#11763357C418yes—
24#11763357C2218yes—
25C2×#10587555C411yescharacteristic
26C2×#10587622C412yes—
27C2×#10587624C414yes—
28C2×D4×Dic17C2214yes—
29C2×C42×D17C2211yescharacteristic
30C2×C17×#127C411yescharacteristic
31C22×D4×C17C2×C412yes—
32C22×D4×C17C2×C414yes—
33C22×C22⋊D17C2×C414yes—
34C23×Dic17C2314yes—
35C2×#63254—28no—
36C2×#63254—28no—
37C2×#63254C2×C418yes—
38C2×#63254C2318yes—
39C22×C4×D17C2×C412yes—
40C22×C4×D17C2311yescharacteristic
41C22×Dic34C2×C412yes—
42C2×#63247—216no—
43C2×#63247C23116yes—
44C22×#3624—216no—
45C22×#3624C2312yes—
46C22×#3624C2314yes—
47C22×#3624C23116yes—
48C22×#3624C2312yes—
49#10587678—264no—
50C2×#63243—28no—
51C2×#63243C2318yes—
52C2×#63242—24no—
53C2×#63242D418yescomplemented
54C2×#63242C2314yes—
55C2×#63242C2314yes—
56C17×#127C2×C418yes—
57C2×C42×C17C2×C411yescharacteristic
58C2×C22⋊Dic17C2×C418yes—
59#10587624C2×C4132yes—
60#10587622C2×C4116yes—
61D4×Dic17C2×C4116yes—
62D4×Dic17C23116yes—
63C2×C4⋊Dic17C2×C414yes—
64C2×C4×Dic17C2×C411yescharacteristic
65C2×C4×Dic17C2312yes—
66C42×D17C2×C414yes—
67C42×D17C2314yes—
68#10587555C2×C418yes—
69C22⋊#3624C23132yes—
70#10587544C23116yes—
71#10587542C23116yes—
72C24×C17C22×C414yes—
73C23×D17C22×C411yescharacteristic
74C2×D4×C17—28no—
75C2×D4×C17—48no—
76C2×D4×C17C22×C418yes—
77C2×D4×C17C22×C4116yes—
78C22×C4×C17C22×C412yes—
79C22×C4×C17C22×C411yescharacteristic
80C2×C22⋊D17—216no—
81C2×C22⋊D17C22×C4116yes—
82C22×Dic17—28no—
83C22×Dic17—28no—
84C22×Dic17C22×C414yes—
85C22×Dic17C22×C412yes—
86C22×Dic17C22×C418yes—
87C22×Dic17C2418yes—
88C22×Dic17C2411yescharacteristic
89#63254—232no—
90#63254—216no—
91#63254—216no—
92C2×C4×D17—44no—
93C2×C4×D17C22×C418yes—
94C2×C4×D17C22×C412yes—
95C2×C4×D17C2×D414yes—
96C2×C4×D17#4114yes—
97C2×C4×D17C2412yes—
98C2×Dic34—28no—
99C2×Dic34C22×C418yes—
100#63247—232no—
101C2×#3624—28no—
102C2×#3624—24no—
103C2×#3624—232no—
104C2×#3624C2×D418yes—
105C2×#3624C2414yes—
106C2×#3624C2418yes—
107C2×#3624C2414yes—
108#63243—216no—
109#63242—28no—
110#63242C2×D4116yescomplemented
111C42×C17C22×C414yes—
112C22⋊Dic17C22×C4132yes—
113C4⋊Dic17C22×C4116yes—
114C4×Dic17C22×C414yes—
115C4×Dic17C22×C414yes—
116C4×Dic17C2414yes—
117C2×#2932—171nomaximal, Sylow
118C23×C17—28no—
119C23×C17—216no—
120C23×C17C23×C418yes—
121C23×C17C23×C411yescharacteristic
122C22×D17—24no—
123C22×D17C4×D414yes—
124C22×D17C23×C412yes—
125D4×C17—216no—
126D4×C17—416no—
127C2×C4×C17—24no—
128C2×C4×C17C4×D414yes—
129C2×C4×C17C23×C414yes—
130C2×C4×C17C23×C412yes—
131C22⋊D17—232no—
132C2×Dic17—28no—
133C2×Dic17—24no—
134C2×Dic17—216no—
135C2×Dic17—28no—
136C2×Dic17—28no—
137C2×Dic17C23×C414yes—
138C2×Dic17C23×C418yes—
139C2×Dic17C23×C411yescharacteristic
140C2×Dic17C22×D412yes—
141C2×Dic17C2×#4112yes—
142C2×Dic17C2511yescharacteristic
143C4×D17—48no—
144C4×D17C4×D418yes—
145C4×D17C22×D414yes—
146C4×D17C2×#4114yes—
147Dic34—216no—
148#3624—28no—
149#3624—24no—
150#3624C22×D418yes—
151C22×#131—172no—
152C2×#532—171no—
153#2932—1716no—
154C2×#435—178no—
155C2×#423—171no—
156C2×#408—172no—
157C22×#97—171no—
158C22×C17—28no—
159C22×C17—216no—
160C22×C17—416no—
161C22×C17C2×C4×D412yes—
162C22×C17#56814yes—
163C22×C17C24×C411yescharacteristic
164C2×D17—28no—
165C2×D17—24no—
166C2×D17C2×C4×D414yes—
167C4×C17—24no—
168C4×C17C2×C4×D414yes—
169Dic17—28no—
170Dic17—24no—
171Dic17C2×C4×D412yes—
172Dic17C23×D411yescharacteristic
173Dic17C22×#4111yescharacteristic
174C22×#41—172no—
175C2×#131—1716no—
176C2×#131—3416no—
177C22×M16—172no—
178C22×M16—174no—
179C23×C8—171no—
180C23×C8—171no—
181C23×C8—174no—
182#532—178no—
183#532—178no—
184C2×C4⋊Q8—171no—
185C2×#127#59511yescharacteristic
186C2×#124—172no—
187C2×#121—174no—
188C2×C4×D4—174no—
189C22×C42—171no—
190#435—1764no—
191#423—178no—
192C2×C4⋊C8—174no—
193#408—1716no—
194C2×C22⋊C8—178no—
195C2×#97—174no—
196C2×#97—178no—
197C2×C17—48no—
198C2×C17#293214yescomplemented
199C2×C17C22×C4×D411yescharacteristic
200C2×C17C2×#56812yes—
201D17—24no—
202C2×#41—178no—
203C2×#41—178no—
204C2×#41—348no—
205C2×#41—348no—
206C22×Q8—172no—
207C22×D4—174no—
208C22×D4C2×#59512yes—
209C22×D4C2×#59514yes—
210C23×C4—171no—
211C23×C4—174no—
212C23×C4—172no—
213#131—3464no—
214C2×M16—178no—
215C2×M16—1716no—
216C2×M16—3416no—
217C2×M16—348no—
218C22×C8—178no—
219C22×C8—174no—
220C22×C8—172no—
221C22×C8—174no—
222C22×C8—174no—
223C22×C8—1716no—
224C22×C8—172no—
225C22×C8—3416no—
226C22×C8—344no—
227C4⋊Q8—178no—
228#127C2×#59518yes—
229#124—1716no—
230#121—1732no—
231C4×D4—1716no—
232C4×D4—1716no—
233C2×C4⋊C4—174no—
234C2×C22⋊C4—178no—
235C2×C42—172no—
236C2×C42—171no—
237C2×C42—174no—
238C2×C42—174no—
239C2×C42C2×#59511yescharacteristic
240C4⋊C8—1716no—
241C22⋊C8—1732no—
242#97—1716no—
243C17C2×#293211yescharacteristic, complemented, Sylow
244C24—171no—
245C24C22×#59514yes—
246#41—3416no—
247#41—3416no—
248#41—3432no—
249C2×Q8—178no—
250C2×Q8—348no—
251C2×D4—28no—
252C2×D4—48no—
253C2×D4—1716no—
254C2×D4—3416no—
255C2×D4C22×#59518yes—
256C2×D4C22×#595116yes—
257C22×C4—171no—
258C22×C4—174no—
259C22×C4—174no—
260C22×C4—172no—
261C22×C4—172no—
262C22×C4—178no—
263C22×C4—178no—
264C22×C4—172no—
265C22×C4—174no—
266C22×C4—178no—
267C22×C4—348no—
268C22×C4—348no—
269C22×C4—684no—
270C22×C4C22×#59512yes—
271C22×C4C22×#59511yescharacteristic
272M16—3432no—
273M16—3416no—
274C2×C8—1716no—
275C2×C8—178no—
276C2×C8—174no—
277C2×C8—174no—
278C2×C8—178no—
279C2×C8—3432no—
280C2×C8—348no—
281C2×C8—344no—
282C2×C8—348no—
283C4⋊C4—1716no—
284C22⋊C4—1732no—
285C42—174no—
286C42—174no—
287C42—174no—
288C42C22×#59514yes—
289C23—28no—
290C23—216no—
291C23—174no—
292C23—172no—
293C23—344no—
294C23C23×#59518yes—
295C23C23×#59511yescharacteristic
296Q8—3416no—
297D4—216no—
298D4—416no—
299D4—3432no—
300C2×C4—24no—
301C2×C4—172no—
302C2×C4—172no—
303C2×C4—171no—
304C2×C4—171no—
305C2×C4—174no—
306C2×C4—174no—
307C2×C4—178no—
308C2×C4—174no—
309C2×C4—178no—
310C2×C4—348no—
311C2×C4—348no—
312C2×C4—3416no—
313C2×C4—348no—
314C2×C4—344no—
315C2×C4—688no—
316C2×C4D4×#59514yes—
317C2×C4C23×#59514yes—
318C2×C4C23×#59512yes—
319C8—178no—
320C8—348no—
321C8—344no—
322C22—28no—
323C22—216no—
324C22—416no—
325C22—174no—
326C22—348no—
327C22—344no—
328C22C2×D4×#59512yes—
329C22#1176388714yes—
330C22C24×#59511yescharacteristic
331C4—24no—
332C4—171no—
333C4—171no—
334C4—172no—
335C4—348no—
336C4—344no—
337C4C2×D4×#59514yes—
338C2—48no—
339C2—344no—
340C2#1454551314yesdirect product factor
341C2C22×D4×#59511yescharacteristic
342C2C2×#1176388712yes—
subgroupG/H
centerC23C23×#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC2×C17×#127C4
socleC23×C17C23×C4
prime radicalC2×#11763357C2
cosocleC2×Dic17C25
hypercenterC2×#127#595
hypocenterC17C2×#2932
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C22×#10587678C2semidirect
2. #14545513C2direct (N × H)
3. C2×#11763840C2semidirect
4. C2×#11763814C2semidirect
5. C2×#11763783C2semidirect
6. C2×#11763768C2semidirect
9. C2×#10587678C22semidirect
15. #11763840C22semidirect
16. #11763814C22semidirect
18. #11763783C22semidirect
20. #11763768C22semidirect
53. C2×#63242D4semidirect
110. #63242C2×D4semidirect
198. C2×C17#2932semidirect
243. C17C2×#2932semidirect
340. C2#14545513direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105876782
#145455132
C2×#117638402
C2×#117638142
C2×#117637832
C2×#117637682
C2×#117633572
C2×#293217