Finite Group Databasebeta

← C2×#14543855 #17960536

Subgroups — C2×#14543855 #17960536

Order 4352.

630 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587530C211yesmaximal, characteristic
2C22×#10587533C211yesmaximal, characteristic
3#14543855C214yesmaximal, direct product factor
4C2×#11762846C211yesmaximal, characteristic
5C22×C4⋊#595—21no—
6C2×#10587530—21no—
7C2×#10587530—22no—
8C2×#10587530C414yescomplemented
9C2×#10587530C2212yes—
10C22×#63216—21no—
11C2×#10587533—22no—
12C2×#10587533—21no—
13C2×#10587533C414yescomplemented
14C2×#10587533C2212yes—
15C22×C8×D17C2211yescharacteristic
16C2×#10587578—21no—
17#11762846—21no—
18#11762846—21no—
19#11762846C412yescomplemented
20#11762846C2212yes—
21C2×#10587489C411yescharacteristic, complemented
22C2×#10587479—21no—
23C2×C17×#107C411yescharacteristic, complemented
24C23×#595—41no—
25C22×C4×D17D411yescharacteristic
26C2×C4⋊#595—24no—
27C2×C4⋊#595—22no—
28C2×C4⋊#595—41no—
29C2×C4⋊#595—42no—
30C22×C8×C17C2×C411yescharacteristic
31C2×C4⋊C4×C17—21no—
32C2×#63227—41no—
33C2×C4⋊Dic17—21no—
34C2×C4×Dic17—41no—
35C22×#3622D411yescharacteristic
36C2×C8×D17C2×C412yes—
37C2×C8×D17C2×C412yes—
38C2×C8×D17C2×C411yescharacteristic
39C2×C8×D17D411yescharacteristic
40C2×C8×D17D411yescharacteristic
41C2×C8×D17D412yes—
42C2×C8×D17Q812yes—
43C2×C8×D17C2311yescharacteristic
44#10587578—22no—
45#10587578—22no—
46#10587578—41no—
47#10587578—41no—
48C2×#63216—24no—
49C2×#63216—22no—
50#10587533—24no—
51#10587533—22no—
52#10587533C2×C414yescomplemented
53#10587530—24no—
54#10587530—22no—
55#10587530C2×C414yescomplemented
56C17×#107—21no—
57C17×#107C2×C412yescomplemented
58#10587489—21no—
59#10587489C2×C412yescomplemented
60#10587479—22no—
61#10587479—22no—
62C23×D17D811yescharacteristic
63C22×#595—44no—
64C22×#595—42no—
65C22×#595—82no—
66C22×#595—82no—
67C22×C4×C17—41no—
68C22×C4×C17C22⋊C411yescharacteristic
69C22×Dic17—41no—
70C22×Dic17SD1611yescharacteristic
71C2×C4×D17C22⋊C411yescharacteristic
72C2×C4×D17C22⋊C412yes—
73C2×C4×D17C4⋊C412yes—
74C2×C4×D17D811yescharacteristic
75C2×C4×D17SD1612yes—
76C2×C4×D17SD1611yescharacteristic
77C2×C4×D17Q1612yes—
78C2×C4×D17C2×D411yescharacteristic
79C4⋊#595—24no—
80C4⋊#595—44no—
81C4⋊#595—42no—
82C2×C8×C17C4212yes—
83C2×C8×C17C22⋊C411yescharacteristic
84C2×C8×C17C4⋊C412yes—
85C2×C8×C17C22×C411yescharacteristic
86C4⋊C4×C17—22no—
87C4⋊C4×C17—41no—
88#63227—42no—
89#63227—42no—
90C4⋊Dic17—22no—
91C4⋊Dic17—41no—
92C4×Dic17—42no—
93C4×Dic17—42no—
94C2×#3622C22⋊C411yescharacteristic
95C2×#3622C22⋊C412yes—
96C2×#3622C4⋊C412yes—
97C2×#3622C2×D411yescharacteristic
98C8×D17C4212yes—
99C8×D17C22⋊C412yes—
100C8×D17C22⋊C412yes—
101C8×D17C4⋊C412yes—
102C8×D17C4⋊C412yes—
103C8×D17C4⋊C412yes—
104C8×D17C22×C411yescharacteristic
105C8×D17C22×C411yescharacteristic
106C8×D17C2×D411yescharacteristic
107C8×D17C2×Q811yescharacteristic
108#63216—24no—
109C2×#1386—171nomaximal, Sylow
110C23×C17#10211yescharacteristic
111C22×D17—22no—
112C22×D17—22no—
113C22×D17#10211yescharacteristic
114C22×D17#10212yes—
115C22×D17#10712yes—
116C22×D17C2×D811yescharacteristic
117C2×#595—44no—
118C2×#595—82no—
119C2×#595—82no—
120C2×#595—88no—
121C2×C4×C17—42no—
122C2×C4×C17—82no—
123C2×C4×C17#9512yes—
124C2×C4×C17#10211yescharacteristic
125C2×C4×C17#10312yes—
126C2×C4×C17C2×C22⋊C411yescharacteristic
127C2×Dic17—42no—
128C2×Dic17—82no—
129C2×Dic17#10211yescharacteristic
130C2×Dic17#10312yes—
131C2×Dic17#10612yes—
132C2×Dic17C2×SD1611yescharacteristic
133C4×D17#9512yes—
134C4×D17#10212yes—
135C4×D17#10312yes—
136C4×D17#10312yes—
137C4×D17#10612yes—
138C4×D17#10712yes—
139C4×D17C2×C22⋊C411yescharacteristic
140C4×D17C2×C4⋊C411yescharacteristic
141C4×D17C2×SD1611yescharacteristic
142C4×D17C2×Q1611yescharacteristic
143C8×C17#9512yes—
144C8×C17C2×C4211yescharacteristic
145C8×C17C2×C4⋊C411yescharacteristic
146#3622#9512yes—
147#3622C2×C22⋊C411yescharacteristic
148#3622C2×C4⋊C411yescharacteristic
149C22×M32—171no—
150C2×#427—171no—
151C22×#106—171no—
152#1386—174no—
153C22×C17#34012yes—
154C22×C17#36012yes—
155C22×C17#36012yes—
156C22×C17C2×#10211yescharacteristic
157C2×D17—21no—
158C2×D17—21no—
159C2×D17—21no—
160C2×D17—21no—
161C2×D17—24no—
162C2×D17—24no—
163C2×D17#34012yes—
164C2×D17C2×#10211yescharacteristic
165C2×D17C2×#10711yescharacteristic
166#595—84no—
167C4×C17—82no—
168C4×C17#34012yes—
169C4×C17C2×#9511yescharacteristic
170C4×C17C2×#10311yescharacteristic
171Dic17—82no—
172Dic17#34012yes—
173Dic17C2×#10311yescharacteristic
174Dic17C2×#10611yescharacteristic
175C23×C8—171no—
176C2×#117—341no—
177C22×C4⋊C4—341no—
178C2×M32—172no—
179C2×M32—174no—
180C2×M32—342no—
181C2×M32—341no—
182C22×C16—341no—
183#427—172no—
184#427—172no—
185#427—341no—
186#427—341no—
187C2×#107—171no—
188C2×#107#59511yescharacteristic, complemented
189C2×#106—174no—
190C2×#106—172no—
191C2×#106—341no—
192C2×#106—342no—
193C2×#106—341no—
194C2×C17#138614yescomplemented
195C2×C17C2×#34011yescharacteristic
196C2×C17C2×#36011yescharacteristic
197C2×C17C2×#36011yescharacteristic
198D17—21no—
199D17—22no—
200D17—21no—
201C23×C4—171no—
202C23×C4—681no—
203C22×C8—171no—
204C22×C8—172no—
205C22×C8—172no—
206C22×C8—172no—
207C22×C8—172no—
208C22×C8—171no—
209C22×C8—171no—
210C22×C8—171no—
211C22×C8—171no—
212C22×C8C2×#59511yescharacteristic
213#117—342no—
214#117—342no—
215#117—681no—
216#117—681no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—342no—
219C2×C4⋊C4—344no—
220C2×C4⋊C4—341no—
221C2×C4⋊C4—681no—
222C2×C4⋊C4—682no—
223C2×C22⋊C4—681no—
224C2×C42—681no—
225M32—174no—
226M32—342no—
227M32—344no—
228C2×C16—342no—
229C2×C16—344no—
230#107—21no—
231#107—172no—
232#107—341no—
233#107C2×#59512yescomplemented
234#106—174no—
235#106—342no—
236#106—342no—
237#106—342no—
238#106—344no—
239C17C2×#138611yescharacteristic, complemented, Sylow
240C24—171no—
241C22×C4—41no—
242C22×C4—171no—
243C22×C4—171no—
244C22×C4—171no—
245C22×C4—172no—
246C22×C4—172no—
247C22×C4—171no—
248C22×C4—171no—
249C22×C4—172no—
250C22×C4—172no—
251C22×C4—682no—
252C22×C4—684no—
253C22×C4—681no—
254C22×C4—1362no—
255C22×C4—1362no—
256C22×C4C22⋊#59511yescharacteristic
257C2×C8—171no—
258C2×C8—171no—
259C2×C8—172no—
260C2×C8—172no—
261C2×C8—171no—
262C2×C8—171no—
263C2×C8—172no—
264C2×C8—171no—
265C2×C8—172no—
266C2×C8—171no—
267C2×C8—172no—
268C2×C8—172no—
269C2×C8—172no—
270C2×C8—172no—
271C2×C8C4×#59512yes—
272C2×C8C4⋊#59512yes—
273C2×C8C22⋊#59511yescharacteristic
274C2×C8C22×#59511yescharacteristic
275C4⋊C4—22no—
276C4⋊C4—41no—
277C4⋊C4—344no—
278C4⋊C4—342no—
279C4⋊C4—682no—
280C4⋊C4—684no—
281C4⋊C4—681no—
282C22⋊C4—682no—
283C22⋊C4—682no—
284C42—682no—
285C42—682no—
286C16—344no—
287C23—171no—
288C23—171no—
289C23—172no—
290C23—172no—
291C23—342no—
292C23—342no—
293C23#1058754711yescharacteristic
294C2×C4—42no—
295C2×C4—82no—
296C2×C4—171no—
297C2×C4—171no—
298C2×C4—172no—
299C2×C4—172no—
300C2×C4—171no—
301C2×C4—172no—
302C2×C4—171no—
303C2×C4—171no—
304C2×C4—172no—
305C2×C4—171no—
306C2×C4—172no—
307C2×C4—172no—
308C2×C4—172no—
309C2×C4—172no—
310C2×C4—684no—
311C2×C4—682no—
312C2×C4—1362no—
313C2×C4—1362no—
314C2×C4—1368no—
315C2×C4—1362no—
316C2×C4(C2×#595)⋊C412yes—
317C2×C4#1058754711yescharacteristic
318C2×C4#1058754912yes—
319C2×C4C2×C22⋊#59511yescharacteristic
320C8—171no—
321C8—172no—
322C8—171no—
323C8(C2×#595)⋊C412yes—
324C8C2×C4×#59511yescharacteristic
325C8C2×C4⋊#59511yescharacteristic
326C22—171no—
327C22—172no—
328C22—171no—
329C22—341no—
330C22—341no—
331C22—341no—
332C22—341no—
333C22—344no—
334C22—344no—
335C22#1176368212yes—
336C22#1176372512yes—
337C22#1176372612yes—
338C22C2×#1058754711yescharacteristic
339C4—82no—
340C4—172no—
341C4—171no—
342C4—171no—
343C4—1364no—
344C4—1362no—
345C4#1176368212yes—
346C4C2×(C2×#595)⋊C411yescharacteristic
347C4C2×#1058754911yescharacteristic
348C2—341no—
349C2—342no—
350C2—341no—
351C2#1454385514yesdirect product factor
352C2C2×#1176368211yescharacteristic
353C2C2×#1176372511yescharacteristic
354C2C2×#1176372611yescharacteristic
subgroupG/H
centerC23#10587547
commutatorC8×C17C2×C42
FrattiniC2×C8C22×#595
FittingC2×C17×#107C4
socleC23×C17#102
prime radicalC23×D17D8
cosocleC2×C8×D17C23
hypercenterC2×#107#595
hypocenterC17C2×#1386
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
3. #14543855C2direct (N × H)
8. C2×#10587530C4semidirect
13. C2×#10587533C4semidirect
19. #11762846C4semidirect
21. C2×#10587489C4semidirect
23. C2×C17×#107C4semidirect
52. #10587533C2×C4semidirect
55. #10587530C2×C4semidirect
57. C17×#107C2×C4semidirect
59. #10587489C2×C4semidirect
188. C2×#107#595semidirect
194. C2×C17#1386semidirect
233. #107C2×#595semidirect
239. C17C2×#1386semidirect
351. C2#14543855direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875302
C22×#105875332
#145438552
C2×#117628462
C2×#138617