Finite Group Databasebeta

← C2×#14527791 #17006552

Subgroups — C2×#14527791 #17006552

Order 4352.

1028 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1028 conjugacy classes of subgroups — too many to draw. Only its 203 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763440C211yesmaximal, characteristic
2C2×#11763139C212yesmaximal
3#14527791C218yesmaximal, direct product factor
4C2×#11762545C212yesmaximal
5C2×#11762535C211yesmaximal, characteristic
6C2×C17×#398C211yesmaximal, characteristic
7#11763440—22no—
8#11763440—24no—
9#11763440C2214yes—
10C2×#10587574—22no—
11C2×#10587576—22no—
12C2×#10587610—21no—
13C2×#10587610C2212yes—
14C2×#10587612—21no—
15#11763139—24no—
16#11763139C2218yes—
17C2×#10587479—22no—
18C2×#10587481—22no—
19C2×C22⋊#3622C2212yes—
20#11762545C2218yes—
21#11762535C2214yes—
22C22×C4⋊C4×C17—21no—
23C22×C4⋊C4×C17C2211yescharacteristic
24C22×C4⋊C4×C17C2211yescharacteristic
25C17×#398—22no—
26C17×#398C2214yes—
27C2×C17×#95—21no—
28C2×C17×#95C2211yescharacteristic
29C23×C4×C17—21no—
30C23×C4×C17—21no—
31C23×C4×C17D411yescharacteristic
32C23×C4×C17D411yescharacteristic
33C23×C4×C17C2311yescharacteristic
34C22×Dic34—21no—
35C22×Dic34D412yes—
36C2×C4⋊C4×C17—22no—
37C2×C4⋊C4×C17—22no—
38C2×C4⋊C4×C17—22no—
39C2×C4⋊C4×C17—22no—
40C2×C4⋊C4×C17—24no—
41C2×C4⋊C4×C17—21no—
42C2×C4⋊C4×C17—44no—
43C2×C4⋊C4×C17D412yes—
44C2×C4⋊C4×C17C2312yes—
45C2×C4⋊C4×C17C2312yes—
46C2×C22⋊Dic17—22no—
47#10587612—24no—
48#10587612—24no—
49C2×C4⋊Dic17—21no—
50C2×C4⋊Dic17—21no—
51C2×C4⋊Dic17—21no—
52C2×C4⋊Dic17D412yes—
53#10587610—24no—
54#10587610—24no—
55#10587610—22no—
56#10587610—22no—
57#10587610D414yes—
58#10587610C2314yes—
59C2×#63225—22no—
60C2×#63225—22no—
61C2×C4×Dic17—22no—
62C22×#3622—22no—
63#10587576—28no—
64#10587576—28no—
65#10587574—28no—
66#10587574—28no—
67C17×#95—24no—
68C17×#95—21no—
69C17×#95C2312yes—
70C22⋊#3622—22no—
71C22⋊#3622C2314yes—
72#10587481—28no—
73#10587479—28no—
74C24×C17C2×D411yescharacteristic
75C22×C4×C17—21no—
76C22×C4×C17—21no—
77C22×C4×C17—22no—
78C22×C4×C17—24no—
79C22×C4×C17—21no—
80C22×C4×C17—22no—
81C22×C4×C17—21no—
82C22×C4×C17—22no—
83C22×C4×C17—42no—
84C22×C4×C17—42no—
85C22×C4×C17—42no—
86C22×C4×C17—42no—
87C22×C4×C17—41no—
88C22×C4×C17—41no—
89C22×C4×C17—42no—
90C22×C4×C17—42no—
91C22×C4×C17SD1614yes—
92C22×C4×C17C2×D412yes—
93C22×C4×C17C2×D412yes—
94C22×C4×C17C2×D412yes—
95C22×C4×C17C2×D412yes—
96C22×C4×C17C2×D411yescharacteristic
97C22×C4×C17C2411yescharacteristic
98C22×Dic17—22no—
99C22×Dic17—22no—
100C2×Dic34—24no—
101C2×Dic34—22no—
102C2×Dic34—44no—
103C2×Dic34—82no—
104C2×Dic34C2×D414yes—
105C4⋊C4×C17—24no—
106C4⋊C4×C17—24no—
107C4⋊C4×C17—24no—
108C4⋊C4×C17—42no—
109C4⋊C4×C17—48no—
110C22⋊Dic17—24no—
111C22⋊Dic17—24no—
112C4⋊Dic17—24no—
113C4⋊Dic17—24no—
114C4⋊Dic17—24no—
115C4⋊Dic17—22no—
116C4⋊Dic17C2×D414yes—
117#63225—28no—
118#63225—24no—
119#63225—24no—
120C4×Dic17—28no—
121C2×#3622—24no—
122C2×#3622—44no—
123C2×#1611—171nomaximal, Sylow
124C23×C17—22no—
125C23×C17—22no—
126C23×C17#12011yescharacteristic
127C23×C17#12011yescharacteristic
128C23×C17C2×SD1612yes—
129C23×C17#13712yes—
130C23×C17C22×D411yescharacteristic
131C2×C4×C17—22no—
132C2×C4×C17—22no—
133C2×C4×C17—24no—
134C2×C4×C17—24no—
135C2×C4×C17—24no—
136C2×C4×C17—24no—
137C2×C4×C17—22no—
138C2×C4×C17—42no—
139C2×C4×C17—41no—
140C2×C4×C17—41no—
141C2×C4×C17—48no—
142C2×C4×C17—42no—
143C2×C4×C17—42no—
144C2×C4×C17—42no—
145C2×C4×C17—42no—
146C2×C4×C17—42no—
147C2×C4×C17—42no—
148C2×C4×C17—42no—
149C2×C4×C17—81no—
150C2×C4×C17—82no—
151C2×C4×C17—82no—
152C2×C4×C17#12012yes—
153C2×C4×C17C2×SD1614yes—
154C2×C4×C17C22×D412yes—
155C2×Dic17—24no—
156C2×Dic17—24no—
157C2×Dic17—44no—
158C2×Dic17—44no—
159Dic34—44no—
160Dic34—82no—
161Dic34—84no—
162#3622—44no—
163C2×#544—171no—
164C2×#483—172no—
165C2×#398D1711yescharacteristic
166#1611—178no—
167C2×#328—172no—
168C2×#324—171no—
169C22×C17—24no—
170C22×C17—24no—
171C22×C17—21no—
172C22×C17—21no—
173C22×C17—21no—
174C22×C17—21no—
175C22×C17#44812yes—
176C22×C17#44812yes—
177C22×C17#45612yes—
178C22×C17#45812yes—
179C22×C17C2×#12011yescharacteristic
180C22×C17C22×SD1611yescharacteristic
181C22×C17C2×#13711yescharacteristic
182C4×C17—24no—
183C4×C17—22no—
184C4×C17—22no—
185C4×C17—44no—
186C4×C17—42no—
187C4×C17—82no—
188Dic17—44no—
189Dic17—44no—
190#544—174no—
191#544—344no—
192#544—342no—
193C2×C4⋊Q8—342no—
194C2×#125—342no—
195C2×C22⋊Q8—172no—
196C2×C22⋊Q8—341no—
197C2×#117—341no—
198C22×C4⋊C4—21no—
199C22×C4⋊C4C2×D1711yescharacteristic
200C22×C4⋊C4C2×D1711yescharacteristic
201#483—178no—
202#483—344no—
203C2×#106—342no—
204C2×#103—342no—
205C2×C22⋊C8—172no—
206#398—22no—
207#398C2×D1714yes—
208C2×#95—21no—
209C2×#95C2×D1711yescharacteristic
210#328—178no—
211#324—174no—
212C2×C17—21no—
213C2×C17—21no—
214C2×C17—22no—
215C2×C17#161114yescomplemented
216C2×C17C2×#44811yescharacteristic
217C2×C17C2×#45611yescharacteristic
218C2×C17C2×#45811yescharacteristic
219C22×Q8—172no—
220C22×Q8—341no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4C22⋊D1711yescharacteristic
224C23×C4C22⋊D1711yescharacteristic
225C23×C4C22×D1711yescharacteristic
226C22×C8—342no—
227C4⋊Q8—348no—
228C4⋊Q8—348no—
229#125—348no—
230#125—348no—
231C22⋊Q8—174no—
232C22⋊Q8—174no—
233C22⋊Q8—344no—
234C22⋊Q8—342no—
235C22⋊Q8—342no—
236C22⋊Q8—344no—
237#117—344no—
238#117—344no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—24no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—44no—
246C2×C4⋊C4—172no—
247C2×C4⋊C4—341no—
248C2×C4⋊C4—341no—
249C2×C4⋊C4—341no—
250C2×C4⋊C4—342no—
251C2×C4⋊C4—342no—
252C2×C4⋊C4C22⋊D1712yes—
253C2×C4⋊C4C22×D1712yes—
254C2×C4⋊C4C22×D1712yes—
255C2×C22⋊C4—342no—
256C2×C42—342no—
257#106—348no—
258#103—348no—
259C22⋊C8—174no—
260C22⋊C8—342no—
261#95—24no—
262#95—21no—
263#95C22×D1712yes—
264C17C2×#161111yescharacteristic, complemented, Sylow
265C24C2×C22⋊D1711yescharacteristic
266C2×Q8—174no—
267C2×Q8—344no—
268C2×Q8—342no—
269C2×Q8—684no—
270C2×Q8—1362no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—24no—
275C22×C4—22no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—42no—
287C22×C4—342no—
288C22×C4—342no—
289C22×C4#6322914yes—
290C22×C4D4×D1712yes—
291C22×C4D4×D1712yes—
292C22×C4C2×C22⋊D1712yes—
293C22×C4C2×C22⋊D1712yes—
294C22×C4C2×C22⋊D1711yescharacteristic
295C22×C4C23×D1711yescharacteristic
296C2×C8—344no—
297C2×C8—684no—
298C4⋊C4—24no—
299C4⋊C4—24no—
300C4⋊C4—24no—
301C4⋊C4—48no—
302C4⋊C4—42no—
303C4⋊C4—174no—
304C4⋊C4—344no—
305C4⋊C4—344no—
306C4⋊C4—344no—
307C4⋊C4—348no—
308C4⋊C4—344no—
309C4⋊C4—342no—
310C4⋊C4—344no—
311C22⋊C4—344no—
312C22⋊C4—344no—
313C42—348no—
314C23—22no—
315C23—22no—
316C23C2×#6322912yes—
317C23#1058762311yescharacteristic
318C23#1058762311yescharacteristic
319C23#1058763712yes—
320C23C22×C22⋊D1711yescharacteristic
321Q8—684no—
322Q8—1362no—
323Q8—1364no—
324C2×C4—24no—
325C2×C4—24no—
326C2×C4—24no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—24no—
330C2×C4—22no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—48no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4—344no—
346C2×C4—344no—
347C2×C4—684no—
348C2×C4—684no—
349C2×C4C2×#6322914yes—
350C2×C4#1058762312yes—
351C2×C4C2×D4×D1712yes—
352C8—684no—
353C22—24no—
354C22—24no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22#1176294712yes—
360C22#1176294712yes—
361C22#1176299112yes—
362C22#1176299812yes—
363C22C2×#1058762311yescharacteristic
364C22C22×#6322911yescharacteristic
365C22C2×#1058763711yescharacteristic
366C4—22no—
367C4—22no—
368C4—24no—
369C4—44no—
370C4—42no—
371C4—82no—
372C4—684no—
373C4—684no—
374C2—21no—
375C2—22no—
376C2—21no—
377C2#1452779114yesdirect product factor
378C2C2×#1176294711yescharacteristic
379C2C2×#1176299111yescharacteristic
380C2C2×#1176299811yescharacteristic
subgroupG/H
centerC23#10587623
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC2×C17×#398C2
socleC23×C17#120
prime radicalC24×C17C2×D4
hypercenterC2×#398D17
hypocenterC17C2×#1611
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
3. #14527791C2direct (N × H)
215. C2×C17#1611semidirect
264. C17C2×#1611semidirect
377. C2#14527791direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634402
C2×#117631392
#145277912
C2×#117625452
C2×#117625352
C2×C17×#3982
C2×#161117