Finite Group Databasebeta

← #17959802

Subgroups — #17959802

Order 4352.

372 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 76 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#14544650C211yesmaximal, characteristic
2#14544026C211yesmaximal, characteristic
3#14543785C212yesmaximal
4#14543783C212yesmaximal
5#14534150C211yesmaximal, characteristic
6#11763826—21no—
7#11763812—21no—
8C2×#10587545—21no—
9#11763689C2212yes—
10#11763655C2212yes—
11#11763654—21no—
12C2×C4×Dic34C2211yescharacteristic
13#11762747C411yescharacteristic
14#11762747C2211yescharacteristic
15#11762728C411yescharacteristic
16#11762728C2211yescharacteristic
17#11762715—21no—
18#11762707—21no—
19#11762690—21no—
20#11762690—21no—
21#11762675C411yescharacteristic
22C2×C4×Q8×C17C411yescharacteristic
23C22×Q8×C17C2×C411yescharacteristic
24C22×Dic34D411yescharacteristic
25C2×#63247—22no—
26C4×Q8×C17—41no—
27C4×Q8×C17—41no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17C2×C411yescharacteristic
30C2×C42×C17—21no—
31C2×C42×C17C2×C411yescharacteristic
32C2×C4⋊Dic17—21no—
33C2×C4⋊Dic17D411yescharacteristic
34C2×#63225—21no—
35C2×#63225—21no—
36C2×#63225C2×C411yescharacteristic
37C2×#63225C2311yescharacteristic
38C2×C4×Dic17D411yescharacteristic
39C2×C4×Dic17D411yescharacteristic
40C4×Dic34—41no—
41C4×Dic34—41no—
42C22⋊#3624—22no—
43#10587545—42no—
44#10587544—41no—
45#10587544—41no—
46C4⋊#3624—41no—
47C4×#3624—41no—
48#10587502—21no—
49#10587502—21no—
50#10587502—21no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54#10587502—21no—
55#10587502C2×C411yescharacteristic
56#10587502C2×C411yescharacteristic
57C2×Q8×C17—42no—
58C2×Q8×C17—41no—
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×Dic34SD1612yes—
73C2×Dic34Q1612yes—
74#63247—42no—
75#63247—42no—
76C2×#3624—42no—
77C2×#3624—42no—
78C4⋊C4×C17—41no—
79C4⋊C4×C17—41no—
80C4⋊C4×C17—41no—
81C42×C17—21no—
82C42×C17—21no—
83C42×C17—42no—
84C4⋊Dic17—41no—
85C4⋊Dic17—42no—
86#63225—41no—
87#63225—41no—
88#63225—42no—
89#63225—42no—
90C4×Dic17—21no—
91C4×Dic17—21no—
92C4×Dic17—21no—
93C4×Dic17—21no—
94#11905—171nomaximal, Sylow
95C23×C17C2×C22⋊C411yescharacteristic
96Q8×C17—42no—
97Q8×C17—42no—
98C2×C4×C17—21no—
99C2×C4×C17—21no—
100C2×C4×C17—22no—
101C2×C4×C17—21no—
102C2×C4×C17—41no—
103C2×C4×C17—41no—
104C2×C4×C17—41no—
105C2×C4×C17—41no—
106C2×C4×C17—42no—
107C2×C4×C17—41no—
108C2×C4×C17#9911yescharacteristic
109C2×C4×C17#9911yescharacteristic
110C2×C4×C17#10312yes—
111C2×Dic17—21no—
112C2×Dic17—21no—
113C2×Dic17—21no—
114C2×Dic17—21no—
115C2×Dic17—21no—
116C2×Dic17—21no—
117C2×Dic17—41no—
118C2×Dic17—41no—
119C2×Dic17—41no—
120C2×Dic17—41no—
121C2×Dic17—41no—
122C2×Dic17—41no—
123C2×Dic17—41no—
124C2×Dic17—41no—
125C2×Dic17#10312yes—
126C2×Dic17C2×SD1611yescharacteristic
127C2×Dic17C2×Q1611yescharacteristic
128Dic34—42no—
129Dic34—42no—
130#3624—82no—
131#3624—82no—
132#2581—171no—
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—22no—
145C4×C17—42no—
146C4×C17—41no—
147C4×C17—81no—
148Dic17—21no—
149Dic17—22no—
150Dic17—21no—
151Dic17—41no—
152Dic17—41no—
153Dic17—81no—
154Dic17—81no—
155C2×C4×Q8—171no—
156C2×C4×Q8#59511yescharacteristic
157#431—341no—
158#423—341no—
159C2×#101—341no—
160#400—171no—
161#400—171no—
162#395—171no—
163#395—171no—
164#391—341no—
165#389—341no—
166#387—341no—
167#387—341no—
168#382—171no—
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×Q8—171no—
178C22×Q8C2×#59511yescharacteristic
179C2×M16—342no—
180C4×Q8—41no—
181C4×Q8—41no—
182C4×Q8—681no—
183C4×Q8—681no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—171no—
186C2×C4⋊C4—171no—
187C2×C4⋊C4—171no—
188C2×C4⋊C4—341no—
189C2×C4⋊C4—341no—
190C2×C4⋊C4—341no—
191C2×C4⋊C4C2×#59511yescharacteristic
192C2×C42—21no—
193C2×C42—171no—
194C2×C42—171no—
195C2×C42C2×#59511yescharacteristic
196C4⋊C8—681no—
197C4⋊C8—681no—
198C4⋊C8—681no—
199#101—682no—
200C22⋊C8—342no—
201C4×C8—681no—
202#95—171no—
203#95—171no—
204#95—341no—
205#95—341no—
206#95—341no—
207#95—341no—
208#95—341no—
209#95—341no—
210#95—341no—
211C17#1190511yescharacteristic, complemented, Sylow
212C2×Q8—42no—
213C2×Q8—41no—
214C2×Q8—172no—
215C2×Q8—172no—
216C2×Q8—681no—
217C2×Q8—681no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—171no—
221C22×C4—171no—
222C22×C4—171no—
223C22×C4—171no—
224C22×C4—341no—
225C22×C4—341no—
226C22×C4C22⋊#59511yescharacteristic
227C22×C4C22⋊#59511yescharacteristic
228C22×C4C22×#59511yescharacteristic
229M16—682no—
230M16—682no—
231C2×C8—682no—
232C2×C8—682no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—681no—
237C4⋊C4—681no—
238C4⋊C4—681no—
239C4⋊C4—682no—
240C4⋊C4—682no—
241C4⋊C4—682no—
242C42—21no—
243C42—21no—
244C42—42no—
245C42—341no—
246C42—341no—
247C42—341no—
248C42—341no—
249C23C2×C22⋊#59511yescharacteristic
250Q8—42no—
251Q8—42no—
252Q8—682no—
253Q8—682no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—42no—
263C2×C4—41no—
264C2×C4—171no—
265C2×C4—172no—
266C2×C4—171no—
267C2×C4—341no—
268C2×C4—341no—
269C2×C4—341no—
270C2×C4—341no—
271C2×C4—341no—
272C2×C4—341no—
273C2×C4—681no—
274C2×C4—681no—
275C2×C4—681no—
276C2×C4—681no—
277C2×C4—681no—
278C2×C4—681no—
279C2×C4—681no—
280C2×C4—681no—
281C2×C4#1058754912yes—
282C2×C4#1058755111yescharacteristic
283C2×C4#1058755111yescharacteristic
284C8—1362no—
285C8—1362no—
286C22—21no—
287C22—21no—
288C22C2×#1058755111yescharacteristic
289C22C2×#1058754911yescharacteristic
290C22#1176380811yescharacteristic
291C4—22no—
292C4—21no—
293C4—21no—
294C4—42no—
295C4—41no—
296C4—81no—
297C4—341no—
298C4—342no—
299C4—341no—
300C4—681no—
301C4—681no—
302C4—1361no—
303C4—1361no—
304C2—21no—
305C2—21no—
306C2#1454422411yescharacteristic
307C2#1454503511yescharacteristic
308C2#1454507911yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C4×Q8×C17C4
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×#63225C23
hypercenterC2×C4×Q8#595
hypocenterC17#11905
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

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
#145446502
#145440262
#145437852
#145437832
#145341502
#1190517