Finite Group Databasebeta

← C4×#11763160 #17042300

Subgroups — C4×#11763160 #17042300

Order 4352.

878 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763160C211yesmaximal, characteristic
2C4×#10587555C211yesmaximal, characteristic
3C4×#10587555C211yesmaximal, characteristic
4#14529745C211yesmaximal, characteristic
5#14529586C211yesmaximal, characteristic
6#14529460C214yesmaximal
7#14528912C211yesmaximal, characteristic
8C4×#10587487C214yesmaximal
9C42×C8×C17C211yesmaximal, characteristic
10C2×#10587555C2211yescharacteristic
11C2×#10587555C2211yescharacteristic
12C2×C4×Dic34—21no—
13C2×C4×Dic34C2212yes—
14#11763160C418yesdirect product factor
15C2×#10587487C2214yes—
16C2×#10587487C2214yes—
17#11762715—21no—
18#11762715C2212yes—
19#11762707—21no—
20#11762707—21no—
21#11762707—21no—
22#11762707C2212yes—
23#11762679C2211yescharacteristic
24#11762679C2211yescharacteristic
25C4×C4⋊Dic17—21no—
26C4×C4⋊Dic17—21no—
27C4×C4⋊Dic17—21no—
28C4×C4⋊Dic17C2212yes—
29#11762572C2214yes—
30#11762572C2214yes—
31C2×C4×C8×C17C2211yescharacteristic
32C2×C4×C8×C17C2212yes—
33C2×C4×C8×C17C2212yes—
34C2×C4×C8×C17C2211yescharacteristic
35C43×C17C2211yescharacteristic
36C22×Dic34—21no—
37C22×Dic34C2312yes—
38C22×C8×C17C2312yes—
39C22×C8×C17C2312yes—
40C2×C42×C17D411yescharacteristic
41C2×C42×C17D411yescharacteristic
42C2×C42×C17D411yescharacteristic
43C2×C42×C17D411yescharacteristic
44C2×C42×C17C2311yescharacteristic
45C2×C42×C17C2311yescharacteristic
46C2×C42×C17C2311yescharacteristic
47C2×C4⋊Dic17—21no—
48C2×C4⋊Dic17—21no—
49C2×C4⋊Dic17—21no—
50C2×C4⋊Dic17—21no—
51C2×C4⋊Dic17—21no—
52C2×C4⋊Dic17—21no—
53C2×C4⋊Dic17—21no—
54C2×C4⋊Dic17C2312yes—
55C2×C4⋊Dic17C2312yes—
56C2×C4⋊Dic17C2312yes—
57C2×#63225—22no—
58C2×#63225—22no—
59C2×C4×Dic17—22no—
60C2×C4×Dic17—22no—
61#10587555—22no—
62#10587555—22no—
63#10587555C2×C414yes—
64#10587555C2×C414yes—
65C4×Dic34—28no—
66C4×Dic34—44no—
67C4×C8×C17—24no—
68C4×C8×C17—22no—
69C4×C8×C17—24no—
70C4×C8×C17C2×C414yes—
71#10587502—22no—
72#10587502—22no—
73#10587502—22no—
74#10587502—22no—
75#10587487—28no—
76#10587487C2×C4116yes—
77C22×C4×C17C2×D411yescharacteristic
78C22×C4×C17C2×D411yescharacteristic
79C22×C4×C17C2×D411yescharacteristic
80C22×C4×C17C2×D411yescharacteristic
81C22×C4×C17C2×D411yescharacteristic
82C22×C4×C17C2×D411yescharacteristic
83C22×C4×C17C2411yescharacteristic
84C22×Dic17—22no—
85C22×Dic17—22no—
86C22×Dic17—22no—
87C22×Dic17—22no—
88C2×Dic34—24no—
89C2×Dic34—24no—
90C2×Dic34—24no—
91C2×Dic34—22no—
92C2×Dic34—42no—
93C2×Dic34—42no—
94C2×Dic34C22×C414yes—
95C2×C8×C17—22no—
96C2×C8×C17—22no—
97C2×C8×C17—22no—
98C2×C8×C17—22no—
99C2×C8×C17C22×C414yes—
100C2×C8×C17#4114yes—
101C42×C17—22no—
102C42×C17—22no—
103C42×C17—22no—
104C42×C17SD1614yes—
105C42×C17Q1614yes—
106C42×C17C22×C412yes—
107C42×C17#4112yes—
108C42×C17#4114yes—
109C4⋊Dic17—24no—
110C4⋊Dic17—24no—
111C4⋊Dic17—24no—
112C4⋊Dic17—22no—
113C4⋊Dic17—24no—
114C4⋊Dic17—24no—
115C4⋊Dic17—42no—
116C4⋊Dic17—42no—
117C4⋊Dic17—42no—
118C4⋊Dic17—42no—
119C4⋊Dic17C22×C414yes—
120#63225—44no—
121#63225—44no—
122C4×Dic17—44no—
123C4×Dic17—44no—
124C4×#487—171nomaximal, Sylow
125C23×C17C22×D411yescharacteristic
126C2×C4×C17—21no—
127C2×C4×C17—21no—
128C2×C4×C17—21no—
129C2×C4×C17—21no—
130C2×C4×C17—21no—
131C2×C4×C17—21no—
132C2×C4×C17C4×D412yes—
133C2×C4×C17C4×D412yes—
134C2×C4×C17#12412yes—
135C2×C4×C17#12412yes—
136C2×C4×C17C2×SD1612yes—
137C2×C4×C17C2×SD1612yes—
138C2×C4×C17C2×SD1612yes—
139C2×C4×C17C2×Q1612yes—
140C2×C4×C17C2×Q1612yes—
141C2×C4×C17C2×Q1612yes—
142C2×C4×C17#13512yes—
143C2×C4×C17#13512yes—
144C2×C4×C17C23×C411yescharacteristic
145C2×C4×C17C2×#4112yes—
146C2×C4×C17C2×#4112yes—
147C2×C4×C17C2×#4111yescharacteristic
148C2×Dic17—24no—
149C2×Dic17—24no—
150C2×Dic17—42no—
151C2×Dic17—42no—
152C2×Dic17—42no—
153C2×Dic17—42no—
154C2×Dic17—42no—
155C2×Dic17—42no—
156C2×Dic17—42no—
157C2×Dic17—42no—
158C2×Dic17—42no—
159C2×Dic17—42no—
160Dic34—28no—
161Dic34—44no—
162Dic34—48no—
163C8×C17—24no—
164C8×C17—24no—
165C2×#487—171no—
166C4×C4⋊Q8—171no—
167C4×C4⋊Q8—171no—
168#1990—171no—
169#1956—171no—
170#1933—174no—
171#1834—171no—
172C4×#103—174no—
173C42×C8D1711yescharacteristic
174C22×C17C2×C4×D411yescharacteristic
175C22×C17C2×#12411yescharacteristic
176C22×C17#53211yescharacteristic
177C22×C17C22×SD1611yescharacteristic
178C22×C17C22×Q1611yescharacteristic
179C22×C17C2×#13511yescharacteristic
180C22×C17C2×#13511yescharacteristic
181C4×C17—22no—
182C4×C17—22no—
183C4×C17—22no—
184C4×C17C4×SD1614yes—
185C4×C17C4×Q1614yes—
186C4×C17#48714yescomplemented
187C4×C17C4×#4112yes—
188C4×C17#52912yes—
189Dic17—44no—
190Dic17—44no—
191Dic17—82no—
192Dic17—82no—
193C2×C4⋊Q8—171no—
194C2×C4⋊Q8—171no—
195C2×C4×Q8—172no—
196C2×C4×Q8—341no—
197#487—178no—
198C2×#103—174no—
199C2×#103—174no—
200C2×C4×C8C2×D1712yes—
201C2×C4×C8C2×D1711yescharacteristic
202C2×C4×C8C2×D1712yes—
203C2×C4×C8C2×D1711yescharacteristic
204#391—172no—
205#391—341no—
206#389—172no—
207#389—341no—
208#389—341no—
209#389—341no—
210#384—171no—
211#384—171no—
212C4×C4⋊C4—172no—
213C4×C4⋊C4—341no—
214C4×C4⋊C4—341no—
215C4×C4⋊C4—341no—
216C43C2×D1711yescharacteristic
217#340—174no—
218#340—174no—
219C2×C17C4×#12411yescharacteristic
220C2×C17C2×C4×SD1611yescharacteristic
221C2×C17C2×C4×Q1611yescharacteristic
222C2×C17C2×#48711yescharacteristic
223C2×C17#313111yescharacteristic
224C2×C17#316711yescharacteristic
225C2×C17#317011yescharacteristic
226C22×Q8—172no—
227C22×Q8—341no—
228C22×C8C22×D1712yes—
229C22×C8C22×D1712yes—
230C4⋊Q8—174no—
231C4⋊Q8—174no—
232C4⋊Q8—342no—
233C4⋊Q8—342no—
234C4×Q8—348no—
235C4×Q8—684no—
236C2×C4⋊C4—172no—
237C2×C4⋊C4—172no—
238C2×C4⋊C4—172no—
239C2×C4⋊C4—341no—
240C2×C4⋊C4—341no—
241C2×C4⋊C4—341no—
242C2×C4⋊C4—342no—
243C2×C4⋊C4—341no—
244C2×C4⋊C4—342no—
245C2×C4⋊C4—341no—
246C2×C4⋊C4—341no—
247C2×C4⋊C4—341no—
248C2×C42—342no—
249C2×C42—342no—
250C2×C42D6811yescharacteristic
251C2×C42D6811yescharacteristic
252C2×C42D6811yescharacteristic
253C2×C42D6811yescharacteristic
254C2×C42C22×D1711yescharacteristic
255C2×C42C22×D1711yescharacteristic
256C2×C42C22×D1711yescharacteristic
257#103—1716no—
258#103—348no—
259C4×C8—24no—
260C4×C8—22no—
261C4×C8—24no—
262C4×C8C4×D1714yes—
263#95—342no—
264#95—342no—
265#95—342no—
266#95—342no—
267C17C4×#48711yescharacteristic, complemented, Sylow
268C2×Q8—174no—
269C2×Q8—342no—
270C2×Q8—344no—
271C2×Q8—344no—
272C2×Q8—344no—
273C2×Q8—682no—
274C2×Q8—682no—
275C22×C4—342no—
276C22×C4—342no—
277C22×C4—342no—
278C22×C4—342no—
279C22×C4C2×D6811yescharacteristic
280C22×C4C2×D6811yescharacteristic
281C22×C4C2×D6811yescharacteristic
282C22×C4C2×D6811yescharacteristic
283C22×C4C2×D6811yescharacteristic
284C22×C4C2×D6811yescharacteristic
285C22×C4C23×D1711yescharacteristic
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8C2×C4×D1714yes—
291C2×C8#6325214yes—
292C4⋊C4—174no—
293C4⋊C4—342no—
294C4⋊C4—344no—
295C4⋊C4—344no—
296C4⋊C4—344no—
297C4⋊C4—344no—
298C4⋊C4—344no—
299C4⋊C4—684no—
300C4⋊C4—684no—
301C4⋊C4—682no—
302C4⋊C4—682no—
303C4⋊C4—682no—
304C4⋊C4—682no—
305C42—22no—
306C42—22no—
307C42—22no—
308C42—684no—
309C42—684no—
310C42#6321914yes—
311C42Dic6814yes—
312C42C2×C4×D1712yes—
313C42#6325212yes—
314C42#6325214yes—
315C23C22×D6811yescharacteristic
316Q8—348no—
317Q8—684no—
318Q8—688no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—344no—
326C2×C4—344no—
327C2×C4—682no—
328C2×C4—682no—
329C2×C4—682no—
330C2×C4—682no—
331C2×C4—682no—
332C2×C4—682no—
333C2×C4—682no—
334C2×C4—682no—
335C2×C4—682no—
336C2×C4—682no—
337C2×C4C4×D6812yes—
338C2×C4C4×D6812yes—
339C2×C4#1058756112yes—
340C2×C4#1058756112yes—
341C2×C4C2×#6321912yes—
342C2×C4C2×#6321912yes—
343C2×C4C2×#6321912yes—
344C2×C4#1058759012yes—
345C2×C4#1058759012yes—
346C2×C4C2×Dic6812yes—
347C2×C4C2×Dic6812yes—
348C2×C4C2×Dic6812yes—
349C2×C4C22×C4×D1711yescharacteristic
350C2×C4C2×#6325212yes—
351C2×C4C2×#6325212yes—
352C2×C4C2×#6325211yescharacteristic
353C8—24no—
354C8—24no—
355C22C2×C4×D6811yescharacteristic
356C22C2×#1058756111yescharacteristic
357C22#1176335911yescharacteristic
358C22C22×#6321911yescharacteristic
359C22C22×Dic6811yescharacteristic
360C22C2×#1058759011yescharacteristic
361C22C2×#1058759011yescharacteristic
362C4—22no—
363C4—22no—
364C4—22no—
365C4—684no—
366C4—684no—
367C4—1362no—
368C4—1362no—
369C4C4×#6321914yes—
370C4C4×Dic6814yes—
371C4#1176316014yesdirect product factor
372C4C4×#6325212yes—
373C4#1176334312yes—
374C2C4×#1058756111yescharacteristic
375C2C2×C4×#6321911yescharacteristic
376C2C2×C4×Dic6811yescharacteristic
377C2C2×#1176316011yescharacteristic
378C2#1453910711yescharacteristic
379C2#1453934311yescharacteristic
380C2#1453937011yescharacteristic
subgroupG/H
centerC22×C4C2×D68
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC42×C8×C17C2
socle, prime radicalC23×C17C22×D4
cosocleC22×C4×C17C24
hypercenterC42×C8D17
hypocenterC17C4×#487
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C43 ◁ C42×C8

Complements

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

NH ≅ G/Ntype
14. #11763160C4direct (N × H)
186. C4×C17#487semidirect
267. C17C4×#487semidirect
371. C4#11763160direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117631602
C4×#105875552
#145297452
#145295862
#145294602
#145289122
C4×#105874872
C42×C8×C172
C4×#48717