Finite Group Databasebeta

← #17949760

Subgroups — #17949760

Order 4352.

566 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 110 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
5D17×#389C211yesmaximal, characteristic
6C2×#10587543—21no—
7C2×#10587543—21no—
8#11763675—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×C4⋊C4×D17—21no—
13C2×C4⋊C4×D17C411yescharacteristic
14C2×C4⋊C4×D17C411yescharacteristic
15C2×C42×D17C2211yescharacteristic
16#11762708C2211yescharacteristic
17#11762707C411yescharacteristic
18#11762706—21no—
19#11762705C2211yescharacteristic
20#11762704—21no—
21#95×D17—21no—
22C17×#389C411yescharacteristic
23C22×C4×D17—21no—
24C22×C4×D17—21no—
25C22×C4×D17C2×C411yescharacteristic
26C22×C4×D17D411yescharacteristic
27C22×C4×D17D411yescharacteristic
28C22×#3624—22no—
29C22×#3624—22no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17C2×C411yescharacteristic
32C2×C4⋊C4×C17C2×C411yescharacteristic
33C2×C42×C17C2×C411yescharacteristic
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17C2×C411yescharacteristic
36C2×C4⋊Dic17C2×C411yescharacteristic
37C2×#63225—21no—
38C2×#63225—21no—
39C2×#63225—21no—
40C2×#63225—21no—
41C2×C4×Dic17D411yescharacteristic
42C2×C4×Dic17D411yescharacteristic
43C2×C4×Dic17C2311yescharacteristic
44C4⋊C4×D17—22no—
45C4⋊C4×D17—44no—
46C4⋊C4×D17—42no—
47C4⋊C4×D17C814yescomplemented
48C42×D17—42no—
49#10587543—42no—
50#10587543—42no—
51C17×#95—21no—
52#10587502—21no—
53#10587502—21no—
54#10587502—21no—
55C23×D17C22⋊C411yescharacteristic
56C22×C4×C17—21no—
57C22×C4×C17—21no—
58C22×C4×C17C22⋊C411yescharacteristic
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22×C411yescharacteristic
61C22×Dic17—21no—
62C22×Dic17—21no—
63C22×Dic17C22⋊C411yescharacteristic
64C22×Dic17C2×D411yescharacteristic
65C22×Dic17C2×D411yescharacteristic
66C2×C4×D17—22no—
67C2×C4×D17—22no—
68C2×C4×D17—24no—
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×C4×D17—42no—
76C2×C4×D17—42no—
77C2×C4×D17—42no—
78C2×C4×D17—42no—
79C2×C4×D17—42no—
80C2×C4×D17C2×C812yes—
81C2×C4×D17M1612yes—
82C2×#3624—42no—
83C2×#3624—42no—
84C2×#3624—42no—
85C2×#3624—42no—
86C2×#3624—42no—
87C2×#3624—42no—
88C4⋊C4×C17—21no—
89C4⋊C4×C17—41no—
90C4⋊C4×C17—42no—
91C4⋊C4×C17C2×C812yes—
92C42×C17—41no—
93C4⋊Dic17—21no—
94C4⋊Dic17—42no—
95C4⋊Dic17—41no—
96C4⋊Dic17C2×C812yes—
97#63225—24no—
98#63225—42no—
99#63225—42no—
100#63225—42no—
101C4×Dic17—41no—
102C4×Dic17—41no—
103C4×Dic17—41no—
104#7593—171nomaximal, Sylow
105C23×C17C2×C22⋊C411yescharacteristic
106C22×D17—21no—
107C22×D17—21no—
108C22×D17—21no—
109C22×D17—21no—
110C22×D17C22⋊C812yes—
111C22×D17#9912yes—
112C22×D17#10112yes—
113C2×C4×C17—21no—
114C2×C4×C17—21no—
115C2×C4×C17—22no—
116C2×C4×C17—21no—
117C2×C4×C17—21no—
118C2×C4×C17—21no—
119C2×C4×C17—21no—
120C2×C4×C17—21no—
121C2×C4×C17—21no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17—41no—
126C2×C4×C17—41no—
127C2×C4×C17C22×C811yescharacteristic
128C2×C4×C17C2×M1611yescharacteristic
129C2×Dic17—21no—
130C2×Dic17—21no—
131C2×Dic17—21no—
132C2×Dic17—21no—
133C2×Dic17—21no—
134C2×Dic17—21no—
135C2×Dic17—22no—
136C2×Dic17—41no—
137C2×Dic17—41no—
138C2×Dic17—41no—
139C2×Dic17—41no—
140C2×Dic17—41no—
141C2×Dic17C22⋊C812yes—
142C2×Dic17AGL(1,ℤ/8)12yes—
143C2×Dic17#13712yes—
144C4×D17—24no—
145C4×D17—24no—
146C4×D17—44no—
147C4×D17—44no—
148C4×D17—48no—
149C4×D17—84no—
150#3624—82no—
151#3624—82no—
152C2×#389—171no—
153#1817—171no—
154#1817—171no—
155#1271—172no—
156#1271—172no—
157C22×C17C2×C22⋊C811yescharacteristic
158C22×C17C2×#9911yescharacteristic
159C22×C17C2×#10111yescharacteristic
160C22×C17#41811yescharacteristic
161C22×C17#41911yescharacteristic
162C22×C17#42111yescharacteristic
163C22×C17#42111yescharacteristic
164C2×D17—22no—
165C2×D17—22no—
166C2×D17—22no—
167C2×D17—22no—
168C2×D17—22no—
169C2×D17—22no—
170C2×D17#32414yes—
171C4×C17—21no—
172C4×C17—21no—
173C4×C17—42no—
174C4×C17—41no—
175C4×C17—41no—
176C4×C17—81no—
177Dic17—22no—
178Dic17—22no—
179Dic17—22no—
180Dic17—42no—
181Dic17—81no—
182C22×C4⋊C4—171no—
183C22×C4⋊C4—171no—
184C22×C4⋊C4—341no—
185C22×C42—171no—
186C2×C22⋊C8—341no—
187C2×C22⋊C8—341no—
188#389—171no—
189#389—171no—
190#389—171no—
191#389—341no—
192#389—341no—
193#389#59511yescharacteristic
194C2×#95—341no—
195#336—172no—
196#336—172no—
197#336—341no—
198#336—341no—
199C2×C17C2×#32411yescharacteristic
200C2×C17#147811yescharacteristic
201C2×C17#147911yescharacteristic
202C2×C17#151011yescharacteristic
203C2×C17#151111yescharacteristic
204C2×C17#153411yescharacteristic
205C2×C17#155611yescharacteristic
206D17—24no—
207C23×C4—171no—
208C23×C4—171no—
209C23×C4—171no—
210C23×C4—341no—
211C23×C4—341no—
212C22×C8—342no—
213C22×C8—342no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—171no—
216C2×C4⋊C4—174no—
217C2×C4⋊C4—171no—
218C2×C4⋊C4—342no—
219C2×C4⋊C4—341no—
220C2×C4⋊C4—341no—
221C2×C4⋊C4—341no—
222C2×C4⋊C4—341no—
223C2×C4⋊C4—341no—
224C2×C4⋊C4—682no—
225C2×C4⋊C4—684no—
226C2×C4⋊C4C2×#59511yescharacteristic
227C2×C4⋊C4C2×#59511yescharacteristic
228C2×C42—171no—
229C2×C42—171no—
230C2×C42—171no—
231C2×C42—682no—
232C2×C42C2×#59511yescharacteristic
233C22⋊C8—682no—
234C22⋊C8—682no—
235#95—21no—
236#95—341no—
237#95—341no—
238#95—341no—
239C17#759311yescharacteristic, complemented, Sylow
240C24—171no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—171no—
244C22×C4—171no—
245C22×C4—171no—
246C22×C4—172no—
247C22×C4—172no—
248C22×C4—342no—
249C22×C4—342no—
250C22×C4—342no—
251C22×C4—342no—
252C22×C4—342no—
253C22×C4—342no—
254C22×C4—344no—
255C22×C4—341no—
256C22×C4—341no—
257C22×C4—681no—
258C22×C4—681no—
259C22×C4—682no—
260C22×C4—682no—
261C22×C4—682no—
262C22×C4—682no—
263C22×C4—682no—
264C22×C4C22⋊#59511yescharacteristic
265C22×C4C22⋊#59511yescharacteristic
266C22×C4C22×#59511yescharacteristic
267C2×C8—682no—
268C2×C8—682no—
269C2×C8—682no—
270C2×C8—682no—
271C2×C8—682no—
272C2×C8—682no—
273C4⋊C4—21no—
274C4⋊C4—41no—
275C4⋊C4—42no—
276C4⋊C4—172no—
277C4⋊C4—344no—
278C4⋊C4—341no—
279C4⋊C4—681no—
280C4⋊C4—682no—
281C4⋊C4—682no—
282C4⋊C4—682no—
283C4⋊C4—682no—
284C4⋊C4#6324212yes—
285C42—41no—
286C42—681no—
287C42—681no—
288C42—681no—
289C23—172no—
290C23—172no—
291C23—172no—
292C23—341no—
293C23—341no—
294C23—341no—
295C23—341no—
296C23C2×C22⋊#59511yescharacteristic
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—172no—
312C2×C4—172no—
313C2×C4—172no—
314C2×C4—344no—
315C2×C4—344no—
316C2×C4—341no—
317C2×C4—341no—
318C2×C4—341no—
319C2×C4—341no—
320C2×C4—341no—
321C2×C4—341no—
322C2×C4—342no—
323C2×C4—684no—
324C2×C4—684no—
325C2×C4—688no—
326C2×C4—681no—
327C2×C4—681no—
328C2×C4—681no—
329C2×C4—681no—
330C2×C4—681no—
331C2×C4—1364no—
332C2×C4C2×#6324211yescharacteristic
333C2×C4D17⋊M1611yescharacteristic
334C8—1362no—
335C8—1362no—
336C22—174no—
337C22—342no—
338C22—342no—
339C22—342no—
340C22—342no—
341C22—342no—
342C22—342no—
343C22#1176377711yescharacteristic
344C22D17⋊#9911yescharacteristic
345C22D17⋊#10111yescharacteristic
346C22#1176380111yescharacteristic
347C22#1176380211yescharacteristic
348C22#1176380611yescharacteristic
349C22#1176380611yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—42no—
355C4—81no—
356C4—342no—
357C4—342no—
358C4—342no—
359C4—682no—
360C4—1361no—
361C2—344no—
362C2#1454401311yescharacteristic
363C2#1454408411yescharacteristic
364C2#1454408711yescharacteristic
365C2#1454419011yescharacteristic
366C2#1454419311yescharacteristic
367C2#1454426711yescharacteristic
368C2#1454431411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#389C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenter#389#595
hypocenterC17#7593
LCSG ▷ C2×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
47. C4⋊C4×D17C8semidirect
239. C17#7593semidirect

Maximal subgroups

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

subgroupindex
#145446762
#145436032
#145436022
D17×#3892
#759317