Finite Group Databasebeta

← #16932318

Subgroups — #16932318

Order 4352.

478 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 99 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#14533067C211yesmaximal, characteristic
2#14528867C211yesmaximal, characteristic
3#14527113C212yesmaximal
4#14526693C212yesmaximal
5C17×#2921C211yesmaximal, characteristic
6C22×#63225C2211yescharacteristic
7#11762773C2212yes—
8#11762747—21no—
9#11762740—21no—
10#11762693—21no—
11#11762693—21no—
12#11762681C411yescharacteristic
13#11762681C411yescharacteristic
14#11762672C2211yescharacteristic
15#11762670C411yescharacteristic
16#11762670C411yescharacteristic
17#11762578—21no—
18#11762578—21no—
19#11762534—24no—
20C2×C17×#117C2211yescharacteristic
21C17×#433—24no—
22C17×#423—21no—
23C17×#407C2212yes—
24C4×M16×C17—21no—
25C23×C4×C17C2311yescharacteristic
26C23×Dic17C2×C411yescharacteristic
27C23×Dic17C2×C411yescharacteristic
28C2×M16×C17—22no—
29C17×#117—22no—
30C17×#117—22no—
31C2×C4⋊C4×C17D411yescharacteristic
32C2×C4⋊C4×C17D411yescharacteristic
33C2×C22⋊C4×C17C2×C411yescharacteristic
34C2×C22⋊C4×C17C2×C411yescharacteristic
35C2×C42×C17D411yescharacteristic
36C2×C42×C17D411yescharacteristic
37C2×C22⋊Dic17C2×C411yescharacteristic
38C2×C22⋊Dic17C2×C411yescharacteristic
39C2×#63225—21no—
40C2×#63225—21no—
41C2×#63225—21no—
42C2×#63225—21no—
43C2×#63225—22no—
44C2×#63225—22no—
45C2×#63223—22no—
46C17×C4⋊C8—24no—
47C17×C22⋊C8—22no—
48C17×C22⋊C8D414yes—
49C17×#97—22no—
50C4×C8×C17—22no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54#10587502—21no—
55#10587502—21no—
56#10587502—21no—
57#10587502—21no—
58#10587502—21no—
59C22⋊#3622—22no—
60C22⋊#3622—22no—
61C24×C17C22×C411yescharacteristic
62C22×C4×C17—41no—
63C22×C4×C17—41no—
64C22×C4×C17C22⋊C411yescharacteristic
65C22×C4×C17C22⋊C411yescharacteristic
66C22×C4×C17C22⋊C411yescharacteristic
67C22×C4×C17C22⋊C411yescharacteristic
68C22×C4×C17C2×D411yescharacteristic
69C22×C4×C17C2×D411yescharacteristic
70C22×C4×C17C2×D412yes—
71C22×C4×C17#4112yes—
72C22×Dic17—21no—
73C22×Dic17—22no—
74C22×Dic17—21no—
75C22×Dic17—21no—
76C22×Dic17—21no—
77C22×Dic17—22no—
78C22×Dic17—42no—
79C22×Dic17—41no—
80C22×Dic17—41no—
81M16×C17—42no—
82M16×C17—42no—
83C2×C8×C17—24no—
84C4⋊C4×C17—22no—
85C4⋊C4×C17—22no—
86C22⋊C4×C17—22no—
87C22⋊C4×C17—22no—
88C42×C17—21no—
89C42×C17—21no—
90C42×C17—21no—
91C42×C17—21no—
92C22⋊Dic17—41no—
93C22⋊Dic17—41no—
94#63225—42no—
95#63225—42no—
96#63225—41no—
97#63225—42no—
98#63225—41no—
99#63223—42no—
100#63223—42no—
101C2×#3622—42no—
102#9514—171nomaximal, Sylow
103C23×C17—21no—
104C23×C17—21no—
105C23×C17—41no—
106C23×C17—41no—
107C23×C17C2×C22⋊C411yescharacteristic
108C23×C17C4×D412yes—
109C2×C4×C17—21no—
110C2×C4×C17—21no—
111C2×C4×C17—21no—
112C2×C4×C17—21no—
113C2×C4×C17—21no—
114C2×C4×C17—21no—
115C2×C4×C17—21no—
116C2×C4×C17—21no—
117C2×C4×C17—42no—
118C2×C4×C17—42no—
119C2×C4×C17—41no—
120C2×C4×C17—41no—
121C2×C4×C17—41no—
122C2×C4×C17—41no—
123C2×C4×C17#12011yescharacteristic
124C2×C4×C17#12112yes—
125C2×C4×C17#12311yescharacteristic
126C2×Dic17—24no—
127C2×Dic17—22no—
128C2×Dic17—41no—
129C2×Dic17—42no—
130C2×Dic17—41no—
131C2×Dic17—41no—
132C2×Dic17—41no—
133C2×Dic17—41no—
134C2×Dic17—41no—
135C2×Dic17—41no—
136C2×Dic17—41no—
137C2×Dic17—41no—
138C2×Dic17—41no—
139C2×Dic17—41no—
140C2×Dic17—82no—
141C8×C17—44no—
142#3622—82no—
143#2921D1711yescharacteristic
144#2484—171no—
145#1822—171no—
146#1463—172no—
147#1306—172no—
148C22×C17—21no—
149C22×C17—21no—
150C22×C17—22no—
151C22×C17—22no—
152C22×C17—22no—
153C22×C17—42no—
154C22×C17—42no—
155C22×C17#38611yescharacteristic
156C22×C17#41011yescharacteristic
157C22×C17#41011yescharacteristic
158C4×C17—22no—
159C4×C17—21no—
160C4×C17—21no—
161C4×C17—41no—
162C4×C17—41no—
163C4×C17—41no—
164C4×C17—41no—
165Dic17—42no—
166Dic17—81no—
167Dic17—81no—
168Dic17—81no—
169C2×#117C2×D1711yescharacteristic
170C22×C4⋊C4—171no—
171#433—24no—
172#423—21no—
173#407—172no—
174#407C2×D1712yes—
175C4×M16—21no—
176#400—341no—
177#398—341no—
178#387—341no—
179#387—341no—
180#385—171no—
181#385—171no—
182#381—171no—
183#381—171no—
184#381—171no—
185#343—341no—
186#343—341no—
187#324—344no—
188C2×C17—21no—
189C2×C17—21no—
190C2×C17—42no—
191C2×C17#189111yescharacteristic
192C2×C17#189911yescharacteristic
193C2×C17#191511yescharacteristic
194C23×C4—171no—
195C23×C4—171no—
196C23×C4C22×D1711yescharacteristic
197C2×M16—22no—
198C2×M16—342no—
199#117—22no—
200#117—22no—
201C2×C4⋊C4—341no—
202C2×C4⋊C4—342no—
203C2×C4⋊C4—342no—
204C2×C4⋊C4—341no—
205C2×C4⋊C4—341no—
206C2×C4⋊C4—341no—
207C2×C4⋊C4D6811yescharacteristic
208C2×C4⋊C4D6811yescharacteristic
209C2×C22⋊C4—171no—
210C2×C22⋊C4—171no—
211C2×C22⋊C4C4×D1711yescharacteristic
212C2×C22⋊C4C4×D1711yescharacteristic
213C2×C42C22⋊D1711yescharacteristic
214C2×C42C22⋊D1711yescharacteristic
215C4⋊C8—24no—
216C22⋊C8—22no—
217C22⋊C8—342no—
218C22⋊C8—342no—
219C22⋊C8C22⋊D1714yes—
220#97—22no—
221C4×C8—22no—
222#95—341no—
223#95—341no—
224#95—341no—
225#95—341no—
226#95—341no—
227#95—341no—
228#95—341no—
229#95—341no—
230C17#951411yescharacteristic, complemented, Sylow
231C24C2×C4×D1711yescharacteristic
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—341no—
235C22×C4—342no—
236C22×C4—341no—
237C22×C4—341no—
238C22×C4—341no—
239C22×C4—342no—
240C22×C4—682no—
241C22×C4—681no—
242C22×C4—681no—
243C22×C4#6322711yescharacteristic
244C22×C4#6322711yescharacteristic
245C22×C4#6322711yescharacteristic
246C22×C4#6322711yescharacteristic
247C22×C4C2×D6811yescharacteristic
248C22×C4#6325212yes—
249C22×C4C2×C22⋊D1711yescharacteristic
250C22×C4C2×C22⋊D1712yes—
251M16—42no—
252M16—42no—
253M16—682no—
254M16—682no—
255C2×C8—24no—
256C2×C8—682no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—682no—
260C4⋊C4—682no—
261C4⋊C4—681no—
262C4⋊C4—682no—
263C4⋊C4—681no—
264C22⋊C4—22no—
265C22⋊C4—22no—
266C22⋊C4—681no—
267C22⋊C4—681no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42—21no—
272C23—21no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23C2×#6322711yescharacteristic
277C23C4×C22⋊D1712yes—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—342no—
293C2×C4—344no—
294C2×C4—681no—
295C2×C4—682no—
296C2×C4—681no—
297C2×C4—681no—
298C2×C4—681no—
299C2×C4—681no—
300C2×C4—681no—
301C2×C4—681no—
302C2×C4—681no—
303C2×C4—681no—
304C2×C4—681no—
305C2×C4—681no—
306C2×C4—1362no—
307C2×C4#1058761511yescharacteristic
308C2×C4#1058761612yes—
309C2×C4#1058763911yescharacteristic
310C8—44no—
311C8—1362no—
312C22—21no—
313C22—21no—
314C22—22no—
315C22—22no—
316C22—22no—
317C22—42no—
318C22—42no—
319C22#1176268811yescharacteristic
320C22#1176278211yescharacteristic
321C22#1176278211yescharacteristic
322C4—21no—
323C4—22no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—682no—
330C4—1361no—
331C4—1361no—
332C4—1361no—
333C2—21no—
334C2—21no—
335C2—42no—
336C2#1452920211yescharacteristic
337C2#1452924211yescharacteristic
338C2#1452933611yescharacteristic
subgroupG/H
centerC22#11762688
commutator, prime radicalC24×C17C22×C4
FrattiniC23×C4C22×D17
FittingC17×#2921C2
socleC22×C17#386
cosocleC23×C4×C17C23
hypercenter#2921D17
hypocenterC17#9514
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2921

Complements

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

NH ≅ G/Ntype
230. C17#9514semidirect

Maximal subgroups

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

subgroupindex
#145330672
#145288672
#145271132
#145266932
C17×#29212
#951417