Finite Group Databasebeta

← #17962534

Subgroups — #17962534

Order 4352.

396 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 78 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#14544651C211yesmaximal, characteristic
2#14544537C211yesmaximal, characteristic
3#14543882C212yesmaximal
4#14543881C212yesmaximal
5#14533972C211yesmaximal, characteristic
6#11763812—21no—
7C2×#10587545C2212yes—
8C2×#10587545C2212yes—
9C4×#63247—21no—
10#11763689—21no—
11#11763689—21no—
12C2×#10587576C411yescharacteristic
13C2×#10587573C2211yescharacteristic
14#11762740—21no—
15#11762740—21no—
16#11762715C2211yescharacteristic
17#11762714C2211yescharacteristic
18#11762695—21no—
19#11762695—21no—
20#11762674C411yescharacteristic
21C4×#63225C411yescharacteristic
22C17×#384C411yescharacteristic
23C22×Dic34C2311yescharacteristic
24C2×#63247—22no—
25C2×#63247—22no—
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17C2×C411yescharacteristic
29C2×C4⋊C4×C17C2×C411yescharacteristic
30C2×C42×C17C2×C411yescharacteristic
31C2×C4⋊Dic17—21no—
32C2×C4⋊Dic17C2×C411yescharacteristic
33C2×#63225—21no—
34C2×#63225—21no—
35C2×#63225D411yescharacteristic
36C2×#63225D411yescharacteristic
37C2×C4×Dic17C2×C411yescharacteristic
38C2×C4×Dic17C2×C411yescharacteristic
39C2×C4×Dic17D411yescharacteristic
40C2×C4×Dic17D411yescharacteristic
41#10587576—41no—
42#10587576—41no—
43#10587573—41no—
44#10587573—41no—
45#10587545—22no—
46#10587545—24no—
47#10587545Q814yes—
48#10587544—41no—
49#10587542—41no—
50C4⋊#3624—41no—
51C4×#3624—41no—
52#10587502—21no—
53#10587502—21no—
54#10587502—21no—
55#10587502—21no—
56#10587502—21no—
57#10587502—21no—
58#10587502—21no—
59C22×C4×C17—21no—
60C22×C4×C17—21no—
61C22×C4×C17C22⋊C411yescharacteristic
62C22×C4×C17C22⋊C411yescharacteristic
63C22×C4×C17C22×C411yescharacteristic
64C22×Dic17—21no—
65C22×Dic17—21no—
66C22×Dic17C22⋊C411yescharacteristic
67C22×Dic17C22⋊C411yescharacteristic
68C22×Dic17C2×D411yescharacteristic
69C22×Dic17C2×D411yescharacteristic
70C2×Dic34—41no—
71C2×Dic34—41no—
72C2×Dic34C2×Q812yes—
73C2×Dic34#4112yes—
74#63247—24no—
75#63247—42no—
76#63247—42no—
77#63247—42no—
78C2×#3624—42no—
79C2×#3624—42no—
80C4⋊C4×C17—41no—
81C4⋊C4×C17—41no—
82C4⋊C4×C17—42no—
83C4⋊C4×C17—42no—
84C42×C17—41no—
85C4⋊Dic17—41no—
86C4⋊Dic17—41no—
87C4⋊Dic17—41no—
88#63225—41no—
89#63225—41no—
90#63225—42no—
91#63225—42no—
92C4×Dic17—21no—
93C4×Dic17—21no—
94C4×Dic17—21no—
95C4×Dic17—21no—
96C4×Dic17—21no—
97C4×Dic17—21no—
98C4×Dic17—41no—
99#13303—171nomaximal, Sylow
100C23×C17C2×C22⋊C411yescharacteristic
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—22no—
104C2×C4×C17—21no—
105C2×C4×C17—21no—
106C2×C4×C17—41no—
107C2×C4×C17—41no—
108C2×C4×C17—41no—
109C2×C4×C17—41no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17C4×Q812yes—
114C2×Dic17—21no—
115C2×Dic17—21no—
116C2×Dic17—21no—
117C2×Dic17—21no—
118C2×Dic17—21no—
119C2×Dic17—41no—
120C2×Dic17—41no—
121C2×Dic17—41no—
122C2×Dic17—42no—
123C2×Dic17—41no—
124C2×Dic17—41no—
125C2×Dic17—41no—
126C2×Dic17#9911yescharacteristic
127C2×Dic17#9911yescharacteristic
128C2×Dic17C22⋊Q812yes—
129C2×Dic17#12411yescharacteristic
130C2×Dic17C4⋊Q811yescharacteristic
131Dic34—42no—
132Dic34—42no—
133#3624—44no—
134#3624—82no—
135#2565—171no—
136#1801—171no—
137C4×#101—171no—
138#1394—172no—
139#1394—172no—
140C22×C17—21no—
141C22×C17—21no—
142C22×C17#39111yescharacteristic
143C22×C17C2×#9911yescharacteristic
144C22×C17#41011yescharacteristic
145C4×C17—22no—
146C4×C17—42no—
147C4×C17—41no—
148C4×C17—41no—
149C4×C17—81no—
150Dic17—21no—
151Dic17—21no—
152Dic17—22no—
153Dic17—21no—
154Dic17—21no—
155Dic17—41no—
156Dic17—81no—
157Dic17—81no—
158C2×#125—171no—
159C2×C4×Q8—171no—
160#423—341no—
161C2×#101—172no—
162C2×#101—172no—
163C4×M16—341no—
164#398—341no—
165#398—341no—
166#391—171no—
167#391—171no—
168#387—341no—
169#387—341no—
170#384#59511yescharacteristic
171#382—171no—
172C4×C4⋊C4—171no—
173#343—341no—
174#343—341no—
175C2×C17—21no—
176C2×C17—21no—
177C2×C17#199611yescharacteristic
178C2×C17#213211yescharacteristic
179C2×C17#213311yescharacteristic
180C22×Q8—171no—
181C2×M16—342no—
182C2×M16—342no—
183#125—681no—
184#125—681no—
185C4×Q8—681no—
186C4×Q8—681no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—171no—
190C2×C4⋊C4—171no—
191C2×C4⋊C4—171no—
192C2×C4⋊C4—341no—
193C2×C4⋊C4—341no—
194C2×C4⋊C4—341no—
195C2×C4⋊C4C2×#59511yescharacteristic
196C2×C4⋊C4C2×#59511yescharacteristic
197C2×C42—171no—
198C2×C42—171no—
199C2×C42—171no—
200C2×C42—171no—
201C2×C42C2×#59511yescharacteristic
202C4⋊C8—681no—
203C4⋊C8—681no—
204#101—174no—
205#101—342no—
206#101—344no—
207#97—681no—
208C4×C8—681no—
209#95—341no—
210#95—341no—
211#95—341no—
212#95—341no—
213#95—341no—
214#95—341no—
215#95—341no—
216C17#1330311yescharacteristic, complemented, Sylow
217C2×Q8—172no—
218C2×Q8—172no—
219C2×Q8—681no—
220C2×Q8—681no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—171no—
224C22×C4—171no—
225C22×C4—171no—
226C22×C4—171no—
227C22×C4—341no—
228C22×C4—341no—
229C22×C4C22⋊#59511yescharacteristic
230C22×C4C22⋊#59511yescharacteristic
231C22×C4C22×#59511yescharacteristic
232M16—344no—
233M16—682no—
234M16—682no—
235M16—682no—
236C2×C8—682no—
237C2×C8—682no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—42no—
241C4⋊C4—42no—
242C4⋊C4—681no—
243C4⋊C4—681no—
244C4⋊C4—681no—
245C4⋊C4—682no—
246C4⋊C4—681no—
247C4⋊C4—681no—
248C4⋊C4—682no—
249C42—41no—
250C42—341no—
251C42—341no—
252C42—341no—
253C42—341no—
254C42—341no—
255C42—341no—
256C42—681no—
257C23C2×C22⋊#59511yescharacteristic
258Q8—682no—
259Q8—682no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—172no—
273C2×C4—171no—
274C2×C4—171no—
275C2×C4—171no—
276C2×C4—171no—
277C2×C4—341no—
278C2×C4—341no—
279C2×C4—341no—
280C2×C4—341no—
281C2×C4—341no—
282C2×C4—681no—
283C2×C4—681no—
284C2×C4—681no—
285C2×C4—681no—
286C2×C4—682no—
287C2×C4—681no—
288C2×C4—681no—
289C2×C4Q8×#59512yes—
290C8—684no—
291C8—1362no—
292C22—21no—
293C22—21no—
294C22(C2×#595)⋊Q811yescharacteristic
295C22D17⋊#9911yescharacteristic
296C22#1176378811yescharacteristic
297C4—22no—
298C4—42no—
299C4—41no—
300C4—41no—
301C4—81no—
302C4—342no—
303C4—341no—
304C4—341no—
305C4—341no—
306C4—341no—
307C4—681no—
308C4—1361no—
309C4—1361no—
310C2—21no—
311C2—21no—
312C2#1454497511yescharacteristic
313C2#1454507611yescharacteristic
314C2#1454508211yescharacteristic
subgroupG/H
centerC22D17⋊#99
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#384C4
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC22×Dic34C23
hypercenter#384#595
hypocenterC17#13303
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #384

Complements

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

NH ≅ G/Ntype
216. C17#13303semidirect

Maximal subgroups

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

subgroupindex
#145446512
#145445372
#145438822
#145438812
#145339722
#1330317