Finite Group Databasebeta

← #16935771

Subgroups — #16935771

Order 4352.

458 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 85 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
1#14539990C211yesmaximal, characteristic
2#14539326C211yesmaximal, characteristic
3#14527501C211yesmaximal, characteristic
4#14527386C211yesmaximal, characteristic
5#14527295C211yesmaximal, characteristic
6#14526677C211yesmaximal, characteristic
7C17×#2642C211yesmaximal, characteristic
8#11763366C2211yescharacteristic
9#11763219—21no—
10#11763215—22no—
11#11763212—21no—
12#11763205—21no—
13#11763179—21no—
14#11763144—21no—
15#11763139—21no—
16#11763113—22no—
17#11762866C2211yescharacteristic
18#11762866C2211yescharacteristic
19#11762849—22no—
20C4×#63223C2211yescharacteristic
21#11762555—22no—
22#11762551—22no—
23#11762545—22no—
24C2×C17×C4⋊Q8C2211yescharacteristic
25C2×C17×#125C2211yescharacteristic
26C17×#400—22no—
27C17×#400—22no—
28C17×#391—21no—
29C17×#391—21no—
30C17×#376C2211yescharacteristic
31C22×Q8×C17—21no—
32C17×C4⋊Q8—21no—
33C17×C4⋊Q8—21no—
34C17×C4⋊Q8—21no—
35C17×C4⋊Q8—21no—
36C17×#125—21no—
37C17×#125—21no—
38C17×#125—21no—
39C17×#125—21no—
40C2×C4⋊C4×C17—21no—
41C2×C4⋊C4×C17—21no—
42C2×C4⋊C4×C17—21no—
43C2×C4⋊C4×C17D411yescharacteristic
44C2×C4⋊C4×C17D411yescharacteristic
45C2×C4⋊C4×C17D412yes—
46C2×C42×C17—21no—
47C2×C42×C17C2311yescharacteristic
48#10587612—21no—
49#10587610—21no—
50#10587610—21no—
51C2×#63223—21no—
52#10587556—21no—
53#10587555D411yescharacteristic
54#10587555D411yescharacteristic
55C4×Dic34—21no—
56C4×Dic34—21no—
57C17×#95—24no—
58C17×#95—24no—
59C17×#95—21no—
60C17×#95D412yes—
61C22⋊#3622—21no—
62C22⋊#3622—21no—
63#10587481—22no—
64#10587481—22no—
65#10587479—24no—
66#10587479—22no—
67#10587478—24no—
68#10587478—22no—
69C4⋊#3622—21no—
70C4⋊#3622D412yes—
71#10587474—21no—
72#10587474—21no—
73#10587474D412yes—
74C4×#3622—21no—
75C2×Q8×C17—44no—
76C2×Q8×C17—41no—
77C2×Q8×C17—41no—
78C22×C4×C17—22no—
79C22×C4×C17—22no—
80C22×C4×C17—21no—
81C22×C4×C17—21no—
82C22×C4×C17C2×D411yescharacteristic
83C22×C4×C17C2×D411yescharacteristic
84C22×C4×C17C2×D411yescharacteristic
85C2×Dic34—21no—
86C2×Dic34—21no—
87C4⋊C4×C17—21no—
88C4⋊C4×C17—21no—
89C4⋊C4×C17—22no—
90C4⋊C4×C17—21no—
91C4⋊C4×C17—21no—
92C4⋊C4×C17—22no—
93C4⋊C4×C17—41no—
94C4⋊C4×C17—41no—
95C4⋊C4×C17—41no—
96C4⋊C4×C17—41no—
97C4⋊C4×C17—41no—
98C4⋊C4×C17—41no—
99C42×C17—42no—
100C42×C17C2×D411yescharacteristic
101C42×C17C2×D411yescharacteristic
102C42×C17C2×D411yescharacteristic
103C42×C17#4111yescharacteristic
104C22⋊Dic17—41no—
105C4⋊Dic17—21no—
106C4⋊Dic17—21no—
107C4⋊Dic17—21no—
108C4⋊Dic17—21no—
109#63225—41no—
110#63225—41no—
111C4×Dic17—41no—
112#63223—24no—
113C2×#3622—22no—
114C2×#3622—22no—
115C2×#3622—41no—
116#10103—171nomaximal, Sylow
117C23×C17#12011yescharacteristic
118Q8×C17—82no—
119Q8×C17—82no—
120C2×C4×C17—22no—
121C2×C4×C17—22no—
122C2×C4×C17—41no—
123C2×C4×C17—42no—
124C2×C4×C17—42no—
125C2×C4×C17—42no—
126C2×C4×C17—44no—
127C2×C4×C17—41no—
128C2×C4×C17—41no—
129C2×C4×C17—42no—
130C2×C4×C17—42no—
131C2×C4×C17—42no—
132C2×C4×C17#12011yescharacteristic
133C2×C4×C17#12011yescharacteristic
134C2×C4×C17#12111yescharacteristic
135C2×C4×C17#12111yescharacteristic
136C2×C4×C17#12111yescharacteristic
137C2×C4×C17#12711yescharacteristic
138C2×Dic17—41no—
139C2×Dic17—41no—
140Dic34—42no—
141Dic34—81no—
142#3622—24no—
143#3622—42no—
144#3622—81no—
145#3236—171no—
146#3165—171no—
147#2642D1711yescharacteristic
148#1556—171no—
149#1528—171no—
150#1506—171no—
151#1300—171no—
152C22×C17—21no—
153C22×C17—21no—
154C22×C17#39211yescharacteristic
155C22×C17#45612yes—
156C4×C17—21no—
157C4×C17—21no—
158C4×C17—21no—
159C4×C17—21no—
160C4×C17—21no—
161C4×C17—82no—
162C4×C17—82no—
163C4×C17—81no—
164C4×C17—81no—
165C4×C17#45412yes—
166Dic17—81no—
167Dic17—81no—
168#533—171no—
169C2×C4⋊Q8C2×D1711yescharacteristic
170C2×#125C2×D1711yescharacteristic
171#501—342no—
172#501—341no—
173#500—341no—
174#498—341no—
175#491—341no—
176#484—341no—
177#483—341no—
178#479—342no—
179#432—171no—
180#432—171no—
181#428—342no—
182C4×M16—171no—
183#400—22no—
184#400—22no—
185#391—21no—
186#391—21no—
187#376C2×D1711yescharacteristic
188#332—342no—
189#330—342no—
190#328—342no—
191C2×C17—22no—
192C2×C17#200311yescharacteristic
193C2×C17#200511yescharacteristic
194C2×C17#200911yescharacteristic
195C22×Q8—21no—
196C2×M16—341no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—171no—
202C4⋊Q8—171no—
203#125—21no—
204#125—21no—
205#125—21no—
206#125—21no—
207#125—341no—
208C22⋊Q8—341no—
209C22⋊Q8—341no—
210C4×Q8—341no—
211C4×Q8—341no—
212#117—341no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4C22⋊D1711yescharacteristic
217C2×C4⋊C4C22⋊D1711yescharacteristic
218C2×C4⋊C4C22⋊D1712yes—
219C2×C42—21no—
220C2×C42C22×D1711yescharacteristic
221#107—344no—
222#107—342no—
223#106—344no—
224#106—342no—
225C4⋊C8—172no—
226C4⋊C8—341no—
227#103—342no—
228#103—342no—
229C22⋊C8—341no—
230C22⋊C8—341no—
231#97—172no—
232#97—341no—
233#97—341no—
234C4×C8—341no—
235#95—24no—
236#95—24no—
237#95—21no—
238#95C22⋊D1712yes—
239C17#1010311yescharacteristic, complemented, Sylow
240C2×Q8—44no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—341no—
244C2×Q8—341no—
245C22×C4—22no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4C2×C22⋊D1711yescharacteristic
250C22×C4C2×C22⋊D1711yescharacteristic
251C22×C4C2×C22⋊D1711yescharacteristic
252M16—344no—
253C2×C8—342no—
254C2×C8—342no—
255C2×C8—681no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—22no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—22no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—341no—
269C4⋊C4—341no—
270C4⋊C4—341no—
271C4⋊C4—341no—
272C4⋊C4—681no—
273C4⋊C4—681no—
274C22⋊C4—681no—
275C42—42no—
276C42—681no—
277C42D4×D1711yescharacteristic
278C42D4×D1711yescharacteristic
279C42D4×D1711yescharacteristic
280C42#6325411yescharacteristic
281C23#1058763911yescharacteristic
282Q8—82no—
283Q8—82no—
284Q8—682no—
285Q8—1361no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—44no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—681no—
299C2×C4—681no—
300C2×C4#1058762311yescharacteristic
301C2×C4#1058762311yescharacteristic
302C2×C4#1058762411yescharacteristic
303C2×C4#1058762511yescharacteristic
304C2×C4#1058762511yescharacteristic
305C2×C4#1058762611yescharacteristic
306C8—344no—
307C8—682no—
308C8—1361no—
309C22—21no—
310C22—21no—
311C22#1176271711yescharacteristic
312C22#1176299212yes—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—82no—
319C4—82no—
320C4—81no—
321C4—81no—
322C4—1361no—
323C4—1361no—
324C4#1176298112yes—
325C2—22no—
326C2#1452980611yescharacteristic
327C2#1452981811yescharacteristic
328C2#1452984411yescharacteristic
subgroupG/H
centerC22#11762717
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#2642C2
socleC22×C17#392
prime radicalC23×C17#120
hypercenter#2642D17
hypocenterC17#10103
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2642

Complements

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

NH ≅ G/Ntype
239. C17#10103semidirect

Maximal subgroups

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

subgroupindex
#145399902
#145393262
#145275012
#145273862
#145272952
#145266772
C17×#26422
#1010317