Finite Group Databasebeta

← #16945478

Subgroups — #16945478

Order 4352.

372 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 103 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#14528780C211yesmaximal, characteristic
2#14527108C211yesmaximal, characteristic
3#14526814C212yesmaximal
4#14526811C212yesmaximal
5C17×#2581C211yesmaximal, characteristic
6#11762862—21no—
7#11762833—21no—
8C2×#10587507—21no—
9#11762578C2212yes—
10#11762535—21no—
11#11762535C2212yes—
12C2×C4×Q8×C17C411yescharacteristic
13C2×C4×Q8×C17C2211yescharacteristic
14C17×#400C411yescharacteristic
15C17×#400C2211yescharacteristic
16C17×#395C411yescharacteristic
17C17×#395C2211yescharacteristic
18C17×#391—21no—
19C17×#389—21no—
20C17×#387—21no—
21C17×#387—21no—
22C17×#382C411yescharacteristic
23C22×Q8×C17C2×C411yescharacteristic
24C22×Q8×C17D411yescharacteristic
25C4×Q8×C17—41no—
26C4×Q8×C17—41no—
27C4×Q8×C17—41no—
28C4×Q8×C17—41no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17C2×C411yescharacteristic
34C2×C4⋊C4×C17C2×C411yescharacteristic
35C2×C4⋊C4×C17D411yescharacteristic
36C2×C4⋊C4×C17C2311yescharacteristic
37C2×C42×C17—21no—
38C2×C42×C17C2×C411yescharacteristic
39C2×C42×C17D411yescharacteristic
40C2×C42×C17D411yescharacteristic
41C2×#63223—22no—
42C17×#95—21no—
43C17×#95—21no—
44C17×#95—21no—
45C17×#95—21no—
46C17×#95—21no—
47C17×#95—21no—
48C17×#95—21no—
49C17×#95C2×C411yescharacteristic
50C17×#95C2×C411yescharacteristic
51#10587507—42no—
52C22⋊#3622—22no—
53C4⋊#3622—41no—
54C4⋊#3622—41no—
55C4⋊#3622—41no—
56C4×#3622—41no—
57C2×Q8×C17—41no—
58C2×Q8×C17—41no—
59C2×Q8×C17—42no—
60C2×Q8×C17—41no—
61C2×Q8×C17SD1612yes—
62C2×Q8×C17Q1612yes—
63C22×C4×C17—21no—
64C22×C4×C17—21no—
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17C22⋊C411yescharacteristic
68C22×C4×C17C22⋊C411yescharacteristic
69C22×C4×C17C22⋊C411yescharacteristic
70C22×C4×C17C22⋊C411yescharacteristic
71C22×C4×C17C22×C411yescharacteristic
72C22×C4×C17C2×D411yescharacteristic
73C22×C4×C17C2×D411yescharacteristic
74C4⋊C4×C17—41no—
75C4⋊C4×C17—41no—
76C4⋊C4×C17—41no—
77C4⋊C4×C17—41no—
78C4⋊C4×C17—42no—
79C4⋊C4×C17—42no—
80C4⋊C4×C17—42no—
81C4⋊C4×C17—41no—
82C4⋊C4×C17—41no—
83C42×C17—21no—
84C42×C17—21no—
85C42×C17—21no—
86C42×C17—21no—
87C42×C17—21no—
88C42×C17—21no—
89C42×C17—42no—
90#63223—42no—
91#63223—42no—
92C2×#3622—42no—
93C2×#3622—42no—
94#11905—171nomaximal, Sylow
95C23×C17C2×C22⋊C411yescharacteristic
96Q8×C17—42no—
97Q8×C17—42no—
98Q8×C17—42no—
99Q8×C17—42no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—21no—
105C2×C4×C17—21no—
106C2×C4×C17—22no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—21no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17—41no—
116C2×C4×C17—41no—
117C2×C4×C17—41no—
118C2×C4×C17—41no—
119C2×C4×C17—41no—
120C2×C4×C17—42no—
121C2×C4×C17—41no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17#9911yescharacteristic
125C2×C4×C17#9911yescharacteristic
126C2×C4×C17#10312yes—
127C2×C4×C17#10312yes—
128C2×C4×C17C2×SD1611yescharacteristic
129C2×C4×C17C2×Q1611yescharacteristic
130#3622—82no—
131#3622—82no—
132#2581D1711yescharacteristic
133#1801—171no—
134#1461—171no—
135#1354—172no—
136#1353—172no—
137C22×C17—21no—
138C22×C17—21no—
139C22×C17C2×#9911yescharacteristic
140C22×C17C2×#10311yescharacteristic
141C22×C17#42111yescharacteristic
142C4×C17—21no—
143C4×C17—21no—
144C4×C17—21no—
145C4×C17—22no—
146C4×C17—22no—
147C4×C17—21no—
148C4×C17—41no—
149C4×C17—41no—
150C4×C17—42no—
151C4×C17—41no—
152C4×C17—81no—
153C4×C17—81no—
154C4×C17—81no—
155C2×C4×Q8Dic1711yescharacteristic
156C2×C4×Q8C2×D1711yescharacteristic
157#431—341no—
158#423—341no—
159C2×#101—341no—
160#400Dic1711yescharacteristic
161#400C2×D1711yescharacteristic
162#395Dic1711yescharacteristic
163#395C2×D1711yescharacteristic
164#391—21no—
165#389—21no—
166#387—21no—
167#387—21no—
168#382Dic1711yescharacteristic
169#343—172no—
170#324—172no—
171#324—341no—
172C2×C17—21no—
173C2×C17—21no—
174C2×C17#152011yescharacteristic
175C2×C17#212011yescharacteristic
176C2×C17#213311yescharacteristic
177C22×Q8C2×Dic1711yescharacteristic
178C22×Q8C22⋊D1711yescharacteristic
179C2×M16—342no—
180C4×Q8—41no—
181C4×Q8—41no—
182C4×Q8—41no—
183C4×Q8—41no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4C2×Dic1711yescharacteristic
189C2×C4⋊C4C2×Dic1711yescharacteristic
190C2×C4⋊C4C22⋊D1711yescharacteristic
191C2×C4⋊C4C22×D1711yescharacteristic
192C2×C42—21no—
193C2×C42C2×Dic1711yescharacteristic
194C2×C42C22⋊D1711yescharacteristic
195C2×C42C22⋊D1711yescharacteristic
196C4⋊C8—681no—
197C4⋊C8—681no—
198C4⋊C8—681no—
199#101—682no—
200C22⋊C8—342no—
201C4×C8—681no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95C2×Dic1711yescharacteristic
210#95C2×Dic1711yescharacteristic
211C17#1190511yescharacteristic, complemented, Sylow
212C2×Q8—41no—
213C2×Q8—41no—
214C2×Q8—42no—
215C2×Q8—41no—
216C2×Q8#6323012yes—
217C2×Q8#6323112yes—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4C22⋊Dic1711yescharacteristic
223C22×C4C22⋊Dic1711yescharacteristic
224C22×C4C22⋊Dic1711yescharacteristic
225C22×C4C22⋊Dic1711yescharacteristic
226C22×C4C22×Dic1711yescharacteristic
227C22×C4C2×C22⋊D1711yescharacteristic
228C22×C4C2×C22⋊D1711yescharacteristic
229M16—682no—
230M16—682no—
231C2×C8—682no—
232C2×C8—682no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—42no—
249C23C2×C22⋊Dic1711yescharacteristic
250Q8—42no—
251Q8—42no—
252Q8—42no—
253Q8—42no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4#1058750511yescharacteristic
279C2×C4#1058750511yescharacteristic
280C2×C4#1058750612yes—
281C2×C4#1058750612yes—
282C2×C4C2×#6323011yescharacteristic
283C2×C4C2×#6323111yescharacteristic
284C8—1362no—
285C8—1362no—
286C22—21no—
287C22—21no—
288C22C2×#1058750511yescharacteristic
289C22C2×#1058750611yescharacteristic
290C22#1176282611yescharacteristic
291C4—21no—
292C4—22no—
293C4—22no—
294C4—21no—
295C4—21no—
296C4—21no—
297C4—41no—
298C4—42no—
299C4—41no—
300C4—41no—
301C4—81no—
302C4—81no—
303C4—81no—
304C2—21no—
305C2—21no—
306C2#1452735611yescharacteristic
307C2#1453042511yescharacteristic
308C2#1453047311yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2581C2
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenter#2581D17
hypocenterC17#11905
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2581

Complements

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

NH ≅ G/Ntype
211. C17#11905semidirect

Maximal subgroups

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

subgroupindex
#145287802
#145271082
#145268142
#145268112
C17×#25812
#1190517