Finite Group Databasebeta

← C2×#14543872 #17960586

Subgroups — C2×#14543872 #17960586

Order 4352.

782 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763788C212yesmaximal
2#14543872C214yesmaximal, direct product factor
3C2×#11762775C211yesmaximal, characteristic
4C2×#10587677—22no—
5#11763788—22no—
6#11763788—22no—
7#11763788C414yescomplemented
8#11763788C2214yes—
9C2×#10587539—22no—
10C2×#10587551C414yescomplemented
11C22×#63252C2211yescharacteristic
12C22×#63223C411yescharacteristic, complemented
13#11762775—22no—
14#11762775C412yescomplemented
15#11762775C2212yes—
16C2×#10587491—22no—
17C23×C8×C17C411yescharacteristic, complemented
18C23×C4×C17C2×C411yescharacteristic
19C22×C22⋊D17C2×C412yes—
20C2×#63252—41no—
21C2×#63252—41no—
22C2×#63252—41no—
23C2×#63252—41no—
24C2×#63252C2×C411yescharacteristic
25C2×#63252C2×C412yes—
26C2×#63252D411yescharacteristic
27C2×#63252D412yes—
28C2×#63252Q811yescharacteristic
29C2×#63252C2311yescharacteristic
30C22×D68D411yescharacteristic
31C22×C4×D17D412yes—
32C22×Dic34Q811yescharacteristic
33C2×C22⋊#595—24no—
34#10587677—24no—
35#10587677—24no—
36#10587677—42no—
37#10587677—42no—
38C2×C4⋊#595—42no—
39C2×C4×#595—42no—
40C22×C8×C17—21no—
41C22×C8×C17—21no—
42C22×C8×C17—41no—
43C22×C8×C17—41no—
44C22×C8×C17C2×C412yescomplemented
45C2×#63223—21no—
46C2×#63223—41no—
47C2×#63223—41no—
48C2×#63223C2×C412yescomplemented
49C22×#3622—21no—
50#10587551—24no—
51#10587551C2×C418yescomplemented
52#10587539—24no—
53#10587539—24no—
54#10587491—24no—
55#10587491—24no—
56C24×C17C4211yescharacteristic
57C23×D17C22⋊C412yes—
58C22×#595—44no—
59C22×C4×C17—21no—
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17—21no—
63C22×C4×C17C4211yescharacteristic
64C22×C4×C17C22⋊C411yescharacteristic
65C22×C4×C17C22⋊C411yescharacteristic
66C22×C4×C17C4⋊C411yescharacteristic
67C22×C4×C17C4⋊C411yescharacteristic
68C22×C4×C17C22×C411yescharacteristic
69C2×C22⋊D17—42no—
70C2×C22⋊D17—42no—
71C2×C22⋊D17C4212yes—
72C2×C22⋊D17C22⋊C412yes—
73C2×C22⋊D17C4⋊C412yes—
74C2×C22⋊D17C22×C412yes—
75C22×Dic17C4⋊C412yes—
76#63252—42no—
77#63252—42no—
78#63252—41no—
79#63252—41no—
80#63252—41no—
81#63252—41no—
82#63252—42no—
83#63252—42no—
84#63252—41no—
85#63252—41no—
86#63252—41no—
87#63252—41no—
88C2×D68—41no—
89C2×D68—41no—
90C2×D68C22⋊C412yes—
91C2×D68C4⋊C411yescharacteristic
92C2×D68C2×D411yescharacteristic
93C2×C4×D17—22no—
94C2×C4×D17—22no—
95C2×C4×D17—22no—
96C2×C4×D17—22no—
97C2×C4×D17C22⋊C412yes—
98C2×C4×D17C22⋊C412yes—
99C2×C4×D17C4⋊C412yes—
100C2×C4×D17C2×D412yes—
101C2×Dic34—41no—
102C2×Dic34—41no—
103C2×Dic34C4⋊C411yescharacteristic
104C2×Dic34C4⋊C412yes—
105C2×Dic34C2×Q811yescharacteristic
106C22⋊#595—28no—
107C22⋊#595—44no—
108C4⋊#595—44no—
109C4⋊#595—44no—
110C4×#595—44no—
111C4×#595—44no—
112C2×C8×C17—22no—
113C2×C8×C17—42no—
114C2×C8×C17—41no—
115C2×C8×C17—41no—
116C2×C8×C17—42no—
117#63223—42no—
118#63223—42no—
119C2×#3622—22no—
120C2×#3622—41no—
121C2×#3622—41no—
122C2×#1391—171nomaximal, Sylow
123C23×C17—21no—
124C23×C17—21no—
125C23×C17—42no—
126C23×C17#9511yescharacteristic
127C23×C17#9511yescharacteristic
128C23×C17C2×C4211yescharacteristic
129C22×D17—22no—
130C22×D17—22no—
131C22×D17—44no—
132C22×D17#9512yes—
133C22×D17C2×C22⋊C412yes—
134C2×#595—48no—
135C2×#595—88no—
136C2×C4×C17—21no—
137C2×C4×C17—21no—
138C2×C4×C17—21no—
139C2×C4×C17—21no—
140C2×C4×C17—21no—
141C2×C4×C17—21no—
142C2×C4×C17—21no—
143C2×C4×C17—21no—
144C2×C4×C17—21no—
145C2×C4×C17—21no—
146C2×C4×C17#9511yescharacteristic
147C2×C4×C17#9511yescharacteristic
148C2×C4×C17#9911yescharacteristic
149C2×C4×C17#9911yescharacteristic
150C2×C4×C17#9911yescharacteristic
151C2×C4×C17#9911yescharacteristic
152C2×C4×C17C2×C22⋊C411yescharacteristic
153C2×C4×C17C2×C4⋊C411yescharacteristic
154C22⋊D17—42no—
155C22⋊D17—42no—
156C22⋊D17—42no—
157C22⋊D17—42no—
158C2×Dic17—22no—
159C2×Dic17—22no—
160C2×Dic17#9512yes—
161C2×Dic17C2×C4⋊C412yes—
162D68—42no—
163D68—41no—
164D68—41no—
165C4×D17—22no—
166C4×D17—22no—
167C4×D17—22no—
168C4×D17—22no—
169C4×D17—22no—
170C4×D17—22no—
171C4×D17—22no—
172C4×D17—22no—
173Dic34—41no—
174Dic34—42no—
175Dic34—41no—
176C8×C17—42no—
177#3622—42no—
178C2×#410—172no—
179C2×#408—171no—
180#1391—174no—
181C22×C17—22no—
182C22×C17—21no—
183C22×C17—21no—
184C22×C17—41no—
185C22×C17—41no—
186C22×C17—42no—
187C22×C17—42no—
188C22×C17#34211yescharacteristic
189C22×C17#34211yescharacteristic
190C22×C17C2×#9511yescharacteristic
191C2×D17—22no—
192C2×D17—22no—
193C2×D17—44no—
194C2×D17—42no—
195C2×D17—42no—
196C2×D17—82no—
197#595—88no—
198C4×C17—21no—
199C4×C17—21no—
200C4×C17#34211yescharacteristic
201C4×C17#34211yescharacteristic
202C4×C17C2×#9911yescharacteristic
203C4×C17C2×#9911yescharacteristic
204Dic17—22no—
205Dic17—22no—
206C22×#41—171no—
207C22×M16—171no—
208C23×C8#59511yescharacteristic, complemented
209C2×#117—342no—
210#410—174no—
211#410—174no—
212#410—342no—
213#410—342no—
214C2×#99—174no—
215C2×#99—342no—
216#408—172no—
217#408—172no—
218#408—342no—
219C2×C22⋊C8—342no—
220C2×C17—21no—
221C2×C17—21no—
222C2×C17—41no—
223C2×C17—41no—
224C2×C17#139112yescomplemented
225C2×C17C2×#34211yescharacteristic
226D17—42no—
227D17—42no—
228C2×#41—172no—
229C2×#41—171no—
230C2×#41—171no—
231C2×#41—172no—
232C2×#41—171no—
233C2×#41—171no—
234C2×#41—681no—
235C2×#41—681no—
236C2×#41—681no—
237C2×#41—681no—
238C22×Q8—171no—
239C22×D4—172no—
240C22×D4—171no—
241C23×C4—172no—
242C23×C4C2×#59511yescharacteristic
243C2×M16—172no—
244C2×M16—341no—
245C2×M16—681no—
246C2×M16—681no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—41no—
250C22×C8—41no—
251C22×C8—341no—
252C22×C8C2×#59512yescomplemented
253#117—344no—
254#117—344no—
255#117—682no—
256#117—682no—
257C2×C4⋊C4—682no—
258C2×C22⋊C4—344no—
259C2×C42—682no—
260#99—178no—
261#99—344no—
262#99—344no—
263#99—344no—
264C22⋊C8—344no—
265C22⋊C8—344no—
266C17C2×#139111yescharacteristic, complemented, Sylow
267C24—172no—
268C24C4×#59511yescharacteristic
269#41—682no—
270#41—681no—
271#41—681no—
272#41—682no—
273#41—681no—
274#41—681no—
275#41—682no—
276#41—682no—
277#41—681no—
278#41—681no—
279#41—681no—
280#41—681no—
281C2×Q8—171no—
282C2×Q8—171no—
283C2×Q8—172no—
284C2×Q8—681no—
285C2×Q8—681no—
286C2×D4—172no—
287C2×D4—172no—
288C2×D4—172no—
289C2×D4—172no—
290C2×D4—171no—
291C2×D4—171no—
292C2×D4—172no—
293C2×D4—681no—
294C2×D4—681no—
295C2×D4—682no—
296C2×D4—682no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—172no—
302C22×C4—172no—
303C22×C4—172no—
304C22×C4—172no—
305C22×C4—172no—
306C22×C4—342no—
307C22×C4—342no—
308C22×C4—342no—
309C22×C4—342no—
310C22×C4—684no—
311C22×C4C4×#59511yescharacteristic
312C22×C4C4⋊#59511yescharacteristic
313C22×C4C4⋊#59511yescharacteristic
314C22×C4C22⋊#59511yescharacteristic
315C22×C4C22⋊#59511yescharacteristic
316C22×C4C22×#59511yescharacteristic
317M16—682no—
318M16—682no—
319C2×C8—22no—
320C2×C8—42no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—42no—
324C2×C8—342no—
325C2×C8—681no—
326C2×C8—681no—
327C4⋊C4—684no—
328C4⋊C4—684no—
329C22⋊C4—348no—
330C22⋊C4—684no—
331C42—684no—
332C42—684no—
333C23—21no—
334C23—21no—
335C23—42no—
336C23—172no—
337C23—172no—
338C23—342no—
339C23—342no—
340C23—684no—
341C23(C2×#595)⋊C411yescharacteristic
342C23(C2×#595)⋊C411yescharacteristic
343C23C2×C4×#59511yescharacteristic
344Q8—681no—
345Q8—681no—
346Q8—682no—
347D4—681no—
348D4—681no—
349D4—682no—
350D4—682no—
351D4—682no—
352D4—682no—
353D4—682no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—172no—
365C2×C4—172no—
366C2×C4—342no—
367C2×C4—342no—
368C2×C4—342no—
369C2×C4—342no—
370C2×C4—342no—
371C2×C4—342no—
372C2×C4—342no—
373C2×C4—342no—
374C2×C4—342no—
375C2×C4—342no—
376C2×C4—688no—
377C2×C4—1368no—
378C2×C4#1058753911yescharacteristic
379C2×C4#1058753911yescharacteristic
380C2×C4(C2×#595)⋊C411yescharacteristic
381C2×C4(C2×#595)⋊C411yescharacteristic
382C2×C4#1058755111yescharacteristic
383C2×C4#1058755111yescharacteristic
384C2×C4C2×C4⋊#59511yescharacteristic
385C2×C4C2×C22⋊#59511yescharacteristic
386C8—42no—
387C8—682no—
388C22—22no—
389C22—21no—
390C22—21no—
391C22—41no—
392C22—41no—
393C22—42no—
394C22—42no—
395C22—342no—
396C22—342no—
397C22—682no—
398C22—682no—
399C22—684no—
400C22—1362no—
401C22#1176368711yescharacteristic
402C22#1176368711yescharacteristic
403C22C2×(C2×#595)⋊C411yescharacteristic
404C4—21no—
405C4—21no—
406C4—342no—
407C4—342no—
408C4—1368no—
409C4#1176368711yescharacteristic
410C4#1176368711yescharacteristic
411C4C2×#1058755111yescharacteristic
412C4C2×#1058753911yescharacteristic
413C2—21no—
414C2—21no—
415C2—41no—
416C2—41no—
417C2—682no—
418C2—682no—
419C2#1454387212yesdirect product factor
420C2C2×#1176368711yescharacteristic
subgroupG/H
centerC2×C4#10587551
commutatorC23×C17C2×C42
FrattiniC22×C4C22×#595
FittingC23×C8×C17C4
socleC22×C17#342
prime radicalC22×#63252C22
cosocleC2×#63252C23
hypercenterC23×C8#595
hypocenterC17C2×#1391
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
2. #14543872C2direct (N × H)
7. #11763788C4semidirect
10. C2×#10587551C4semidirect
12. C22×#63223C4semidirect
14. #11762775C4semidirect
17. C23×C8×C17C4semidirect
44. C22×C8×C17C2×C4semidirect
48. C2×#63223C2×C4semidirect
51. #10587551C2×C4semidirect
208. C23×C8#595semidirect
224. C2×C17#1391semidirect
252. C22×C8C2×#595semidirect
266. C17C2×#1391semidirect
419. C2#14543872direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117637882
#145438722
C2×#117627752
C2×#139117