Finite Group Databasebeta

← #17949946

Subgroups — #17949946

Order 4352.

490 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 94 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#14544676C211yesmaximal, characteristic
2#14544676C211yesmaximal, characteristic
3#14543603C212yesmaximal, complemented
4#14543602C212yesmaximal, complemented
5#14531265C211yesmaximal, characteristic
6C2×#10587543—21no—
7C2×#10587543—21no—
8#11763675—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587578C411yescharacteristic
13C2×#10587578C411yescharacteristic
14C2×C42×D17C2211yescharacteristic
15#11762708C2211yescharacteristic
16#11762707C411yescharacteristic
17#11762705C2211yescharacteristic
18#11762683—21no—
19#11762680—21no—
20C4⋊C4×Dic17—21no—
21#11762660—21no—
22C17×#389C411yescharacteristic
23C22×C4×D17C2×C411yescharacteristic
24C22×C4×D17D411yescharacteristic
25C22×C4×D17D411yescharacteristic
26C22×#3624—22no—
27C22×#3624—22no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17C2×C411yescharacteristic
30C2×C4⋊C4×C17C2×C411yescharacteristic
31C2×C42×C17C2×C411yescharacteristic
32C2×#63227—21no—
33C2×#63227—21no—
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17C2×C411yescharacteristic
36C2×C4⋊Dic17C2×C411yescharacteristic
37C2×#63225—21no—
38C2×#63225—21no—
39C2×C4×Dic17—21no—
40C2×C4×Dic17—21no—
41C2×C4×Dic17D411yescharacteristic
42C2×C4×Dic17D411yescharacteristic
43C2×C4×Dic17C2311yescharacteristic
44#10587578—22no—
45#10587578—22no—
46#10587578—42no—
47C42×D17—42no—
48#10587543—42no—
49#10587543—42no—
50C17×#95—21no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54C23×D17C22⋊C411yescharacteristic
55C22×C4×C17—21no—
56C22×C4×C17—21no—
57C22×C4×C17C22⋊C411yescharacteristic
58C22×C4×C17C22⋊C411yescharacteristic
59C22×C4×C17C22×C411yescharacteristic
60C22×Dic17—21no—
61C22×Dic17—21no—
62C22×Dic17C22⋊C411yescharacteristic
63C22×Dic17C2×D411yescharacteristic
64C22×Dic17C2×D411yescharacteristic
65C2×C4×D17—22no—
66C2×C4×D17—21no—
67C2×C4×D17—21no—
68C2×C4×D17—22no—
69C2×C4×D17—22no—
70C2×C4×D17—22no—
71C2×C4×D17—22no—
72C2×C4×D17—22no—
73C2×C4×D17—41no—
74C2×C4×D17—41no—
75C2×#3624—42no—
76C2×#3624—42no—
77C2×#3624—42no—
78C2×#3624—42no—
79C2×#3624—42no—
80C2×#3624—42no—
81C4⋊C4×C17—21no—
82C4⋊C4×C17—41no—
83C4⋊C4×C17—42no—
84C4⋊C4×C17M1612yes—
85C42×C17—41no—
86#63227—24no—
87#63227—42no—
88C4⋊Dic17—21no—
89C4⋊Dic17—42no—
90C4⋊Dic17—41no—
91C4⋊Dic17M1612yes—
92#63225—42no—
93#63225—42no—
94C4×Dic17—24no—
95C4×Dic17—41no—
96C4×Dic17—41no—
97C4×Dic17—41no—
98C4×Dic17—42no—
99#7646—171nomaximal, Sylow
100C23×C17C2×C22⋊C411yescharacteristic
101C22×D17—21no—
102C22×D17—21no—
103C22×D17—21no—
104C22×D17—21no—
105C22×D17—21no—
106C22×D17—21no—
107C22×D17#9912yes—
108C2×C4×C17—21no—
109C2×C4×C17—21no—
110C2×C4×C17—22no—
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—41no—
118C2×C4×C17—41no—
119C2×C4×C17—41no—
120C2×C4×C17—41no—
121C2×C4×C17—41no—
122C2×C4×C17C2×M1611yescharacteristic
123C2×C4×C17C2×M1611yescharacteristic
124C2×Dic17—21no—
125C2×Dic17—21no—
126C2×Dic17—21no—
127C2×Dic17—21no—
128C2×Dic17—21no—
129C2×Dic17—21no—
130C2×Dic17—22no—
131C2×Dic17—41no—
132C2×Dic17—41no—
133C2×Dic17—41no—
134C2×Dic17—41no—
135C2×Dic17—41no—
136C2×Dic17#10112yes—
137C2×Dic17#13512yes—
138C2×Dic17#13512yes—
139C4×D17—24no—
140C4×D17—24no—
141C4×D17—44no—
142C4×D17—44no—
143#3624—82no—
144#3624—82no—
145#2296—171no—
146#1817—171no—
147#1817—171no—
148#1271—172no—
149#1271—172no—
150C22×C17#40711yescharacteristic
151C22×C17C2×#9911yescharacteristic
152C22×C17C2×#10111yescharacteristic
153C22×C17#41611yescharacteristic
154C22×C17#41611yescharacteristic
155C22×C17#42111yescharacteristic
156C22×C17#42111yescharacteristic
157C2×D17—22no—
158C2×D17—22no—
159C2×D17—22no—
160C2×D17—41no—
161C2×D17—41no—
162C2×D17—41no—
163C2×D17—41no—
164C4×C17—21no—
165C4×C17—21no—
166C4×C17—42no—
167C4×C17—41no—
168C4×C17—41no—
169C4×C17—81no—
170Dic17—22no—
171Dic17—22no—
172Dic17—22no—
173Dic17—42no—
174Dic17—81no—
175C2×#117—171no—
176C2×#117—171no—
177C22×C42—171no—
178C2×C22⋊C8—341no—
179C2×C22⋊C8—341no—
180#389—171no—
181#389—171no—
182#389—171no—
183#389#59511yescharacteristic
184#385—341no—
185#385—341no—
186C4×C4⋊C4—341no—
187C4×C4⋊C4—341no—
188#336—172no—
189#336—172no—
190#336—341no—
191#336—341no—
192C2×C17#146311yescharacteristic
193C2×C17#148811yescharacteristic
194C2×C17#148811yescharacteristic
195C2×C17#151611yescharacteristic
196C2×C17#151611yescharacteristic
197C2×C17#153711yescharacteristic
198C2×C17#154411yescharacteristic
199D17—42no—
200C23×C4—171no—
201C23×C4—171no—
202C23×C4—171no—
203C22×C8—342no—
204C22×C8—342no—
205#117—342no—
206#117—342no—
207#117—682no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—171no—
210C2×C4⋊C4—171no—
211C2×C4⋊C4—341no—
212C2×C4⋊C4—341no—
213C2×C4⋊C4—341no—
214C2×C4⋊C4C2×#59511yescharacteristic
215C2×C4⋊C4C2×#59511yescharacteristic
216C2×C22⋊C4—341no—
217C2×C22⋊C4—341no—
218C2×C42—171no—
219C2×C42—171no—
220C2×C42—171no—
221C2×C42—341no—
222C2×C42—341no—
223C2×C42—682no—
224C2×C42C2×#59511yescharacteristic
225C22⋊C8—682no—
226C22⋊C8—682no—
227#95—21no—
228#95—341no—
229#95—341no—
230#95—341no—
231C17#764611yescharacteristic, complemented, Sylow
232C24—171no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—171no—
236C22×C4—171no—
237C22×C4—171no—
238C22×C4—342no—
239C22×C4—342no—
240C22×C4—342no—
241C22×C4—342no—
242C22×C4—342no—
243C22×C4—342no—
244C22×C4—341no—
245C22×C4—341no—
246C22×C4—341no—
247C22×C4—341no—
248C22×C4—681no—
249C22×C4—681no—
250C22×C4C22⋊#59511yescharacteristic
251C22×C4C22⋊#59511yescharacteristic
252C22×C4C22×#59511yescharacteristic
253C2×C8—682no—
254C2×C8—682no—
255C2×C8—682no—
256C2×C8—682no—
257C2×C8—682no—
258C2×C8—682no—
259C4⋊C4—21no—
260C4⋊C4—41no—
261C4⋊C4—42no—
262C4⋊C4—172no—
263C4⋊C4—341no—
264C4⋊C4—681no—
265C4⋊C4—682no—
266C4⋊C4—682no—
267C4⋊C4—682no—
268C4⋊C4#6324312yes—
269C22⋊C4—344no—
270C22⋊C4—682no—
271C42—41no—
272C42—344no—
273C42—681no—
274C42—681no—
275C42—681no—
276C42—682no—
277C23—172no—
278C23—341no—
279C23—341no—
280C23—341no—
281C23—341no—
282C23—341no—
283C23—341no—
284C23C2×C22⋊#59511yescharacteristic
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—172no—
300C2×C4—172no—
301C2×C4—172no—
302C2×C4—344no—
303C2×C4—344no—
304C2×C4—341no—
305C2×C4—341no—
306C2×C4—341no—
307C2×C4—341no—
308C2×C4—341no—
309C2×C4—341no—
310C2×C4—342no—
311C2×C4—684no—
312C2×C4—684no—
313C2×C4—681no—
314C2×C4—681no—
315C2×C4—681no—
316C2×C4—681no—
317C2×C4—681no—
318C2×C4C2×#6324311yescharacteristic
319C2×C4D17⋊M1611yescharacteristic
320C8—1362no—
321C8—1362no—
322C22—342no—
323C22—342no—
324C22—342no—
325C22—681no—
326C22—681no—
327C22—681no—
328C22—681no—
329C22#1176378011yescharacteristic
330C22D17⋊#9911yescharacteristic
331C22D17⋊#10111yescharacteristic
332C22#1176379911yescharacteristic
333C22#1176379911yescharacteristic
334C22#1176380711yescharacteristic
335C22#1176380811yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—42no—
341C4—81no—
342C4—342no—
343C4—342no—
344C4—342no—
345C4—682no—
346C4—1361no—
347C2—682no—
348C2#1454403311yescharacteristic
349C2#1454411611yescharacteristic
350C2#1454411811yescharacteristic
351C2#1454420911yescharacteristic
352C2#1454421111yescharacteristic
353C2#1454427611yescharacteristic
354C2#1454429011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#389C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenter#389#595
hypocenterC17#7646
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
3. #14543603C2semidirect
4. #14543602C2semidirect
231. C17#7646semidirect

Maximal subgroups

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

subgroupindex
#145446762
#145436032
#145436022
#145312652
#764617