Finite Group Databasebeta

← #17949778

Subgroups — #17949778

Order 4352.

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

normal subgroups only

This group has 514 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#14544641C211yesmaximal, characteristic
2#14544641C211yesmaximal, characteristic
3#14543603C212yesmaximal, complemented
4#14543602C212yesmaximal, complemented
5#14531265C211yesmaximal, characteristic
6C2×#10587544—21no—
7C2×#10587544—21no—
8C2×#10587543—21no—
9C2×#10587543—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—42no—
46#10587578C814yescomplemented
47C42×D17—42no—
48#10587544—42no—
49#10587544—42no—
50#10587543—42no—
51#10587543—42no—
52C17×#95—21no—
53#10587502—21no—
54#10587502—21no—
55#10587502—21no—
56C23×D17C22⋊C411yescharacteristic
57C22×C4×C17—21no—
58C22×C4×C17—21no—
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22⋊C411yescharacteristic
61C22×C4×C17C22×C411yescharacteristic
62C22×Dic17—21no—
63C22×Dic17—21no—
64C22×Dic17C22⋊C411yescharacteristic
65C22×Dic17C2×D411yescharacteristic
66C22×Dic17C2×D411yescharacteristic
67C2×C4×D17—22no—
68C2×C4×D17—22no—
69C2×C4×D17—21no—
70C2×C4×D17—21no—
71C2×C4×D17—21no—
72C2×C4×D17—21no—
73C2×C4×D17—41no—
74C2×C4×D17—41no—
75C2×C4×D17—41no—
76C2×C4×D17—41no—
77C2×C4×D17C2×C812yes—
78C2×C4×D17M1612yes—
79C2×#3624—42no—
80C2×#3624—42no—
81C2×#3624—42no—
82C2×#3624—42no—
83C2×#3624—42no—
84C2×#3624—42no—
85C4⋊C4×C17—21no—
86C4⋊C4×C17—41no—
87C4⋊C4×C17—42no—
88C4⋊C4×C17C2×C812yes—
89C42×C17—41no—
90#63227—24no—
91#63227—42no—
92C4⋊Dic17—21no—
93C4⋊Dic17—41no—
94C4⋊Dic17—41no—
95C4⋊Dic17—41no—
96C4⋊Dic17C2×C812yes—
97#63225—42no—
98#63225—41no—
99#63225—41no—
100C4×Dic17—24no—
101C4×Dic17—22no—
102C4×Dic17—22no—
103C4×Dic17—41no—
104C4×Dic17—42no—
105#7598—171nomaximal, Sylow
106C23×C17C2×C22⋊C411yescharacteristic
107C22×D17—21no—
108C22×D17—21no—
109C22×D17—21no—
110C22×D17—21no—
111C22×D17—21no—
112C22×D17—21no—
113C22×D17C22⋊C812yes—
114C2×C4×C17—21no—
115C2×C4×C17—21no—
116C2×C4×C17—22no—
117C2×C4×C17—21no—
118C2×C4×C17—21no—
119C2×C4×C17—21no—
120C2×C4×C17—21no—
121C2×C4×C17—21no—
122C2×C4×C17—21no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17—41no—
126C2×C4×C17—41no—
127C2×C4×C17—41no—
128C2×C4×C17C22×C811yescharacteristic
129C2×C4×C17C2×M1611yescharacteristic
130C2×Dic17—21no—
131C2×Dic17—21no—
132C2×Dic17—21no—
133C2×Dic17—21no—
134C2×Dic17—22no—
135C2×Dic17—41no—
136C2×Dic17—41no—
137C2×Dic17—41no—
138C2×Dic17—41no—
139C2×Dic17—41no—
140C2×Dic17C22⋊C812yes—
141C2×Dic17#9912yes—
142C2×Dic17#10112yes—
143C2×Dic17AGL(1,ℤ/8)11yescharacteristic
144C2×Dic17AGL(1,ℤ/8)11yescharacteristic
145C2×Dic17#13711yescharacteristic
146C2×Dic17#13711yescharacteristic
147C4×D17—24no—
148C4×D17—24no—
149C4×D17—42no—
150C4×D17—42no—
151C4×D17—42no—
152C4×D17—42no—
153#3624—82no—
154#3624—82no—
155#2296—171no—
156#1797—171no—
157#1797—171no—
158#1271—172no—
159#1271—172no—
160C22×C17C2×C22⋊C811yescharacteristic
161C22×C17C2×#9911yescharacteristic
162C22×C17C2×#10111yescharacteristic
163C22×C17#41711yescharacteristic
164C22×C17#41711yescharacteristic
165C22×C17#42111yescharacteristic
166C22×C17#42111yescharacteristic
167C2×D17—22no—
168C2×D17—22no—
169C2×D17—22no—
170C2×D17—41no—
171C2×D17—41no—
172C2×D17—41no—
173C2×D17—41no—
174C4×C17—21no—
175C4×C17—21no—
176C4×C17—42no—
177C4×C17—41no—
178C4×C17—41no—
179C4×C17—81no—
180Dic17—21no—
181Dic17—21no—
182Dic17—21no—
183Dic17—21no—
184Dic17—42no—
185Dic17—81no—
186Dic17#32414yes—
187C2×#117—171no—
188C2×#117—171no—
189C22×C42—171no—
190C2×C4⋊C8—341no—
191C2×C4⋊C8—341no—
192C2×C22⋊C8—341no—
193C2×C22⋊C8—341no—
194#389—171no—
195#389—171no—
196#389—171no—
197#389#59511yescharacteristic
198#385—341no—
199#385—341no—
200C4×C4⋊C4—341no—
201C4×C4⋊C4—341no—
202#336—172no—
203#336—172no—
204C2×C17C2×#32411yescharacteristic
205C2×C17#147711yescharacteristic
206C2×C17#147711yescharacteristic
207C2×C17#151311yescharacteristic
208C2×C17#151311yescharacteristic
209C2×C17#153711yescharacteristic
210C2×C17#156111yescharacteristic
211D17—42no—
212C23×C4—171no—
213C23×C4—171no—
214C23×C4—171no—
215C22×C8—342no—
216C22×C8—342no—
217#117—174no—
218#117—342no—
219#117—682no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—171no—
222C2×C4⋊C4—171no—
223C2×C4⋊C4—341no—
224C2×C4⋊C4—341no—
225C2×C4⋊C4—341no—
226C2×C4⋊C4C2×#59511yescharacteristic
227C2×C4⋊C4C2×#59511yescharacteristic
228C2×C22⋊C4—341no—
229C2×C22⋊C4—341no—
230C2×C42—171no—
231C2×C42—171no—
232C2×C42—171no—
233C2×C42—341no—
234C2×C42—341no—
235C2×C42—682no—
236C2×C42C2×#59511yescharacteristic
237C4⋊C8—682no—
238C4⋊C8—682no—
239C22⋊C8—682no—
240C22⋊C8—682no—
241#95—21no—
242#95—341no—
243#95—341no—
244#95—341no—
245C17#759811yescharacteristic, complemented, Sylow
246C24—171no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—171no—
250C22×C4—171no—
251C22×C4—171no—
252C22×C4—172no—
253C22×C4—172no—
254C22×C4—342no—
255C22×C4—342no—
256C22×C4—341no—
257C22×C4—341no—
258C22×C4—341no—
259C22×C4—341no—
260C22×C4—341no—
261C22×C4—341no—
262C22×C4—681no—
263C22×C4—681no—
264C22×C4—681no—
265C22×C4—681no—
266C22×C4C22⋊#59511yescharacteristic
267C22×C4C22⋊#59511yescharacteristic
268C22×C4C22×#59511yescharacteristic
269C2×C8—682no—
270C2×C8—682no—
271C2×C8—682no—
272C2×C8—682no—
273C2×C8—682no—
274C2×C8—682no—
275C4⋊C4—21no—
276C4⋊C4—41no—
277C4⋊C4—42no—
278C4⋊C4—172no—
279C4⋊C4—341no—
280C4⋊C4—681no—
281C4⋊C4—682no—
282C4⋊C4—681no—
283C4⋊C4—681no—
284C4⋊C4—681no—
285C4⋊C4—681no—
286C4⋊C4#6324212yes—
287C22⋊C4—344no—
288C22⋊C4—682no—
289C42—41no—
290C42—342no—
291C42—342no—
292C42—344no—
293C42—681no—
294C42—682no—
295C23—172no—
296C23—341no—
297C23—341no—
298C23—341no—
299C23—341no—
300C23—341no—
301C23—341no—
302C23C2×C22⋊#59511yescharacteristic
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—172no—
318C2×C4—172no—
319C2×C4—172no—
320C2×C4—171no—
321C2×C4—171no—
322C2×C4—171no—
323C2×C4—171no—
324C2×C4—344no—
325C2×C4—344no—
326C2×C4—341no—
327C2×C4—341no—
328C2×C4—341no—
329C2×C4—341no—
330C2×C4—342no—
331C2×C4—682no—
332C2×C4—682no—
333C2×C4—682no—
334C2×C4—682no—
335C2×C4—681no—
336C2×C4—681no—
337C2×C4—681no—
338C2×C4—681no—
339C2×C4—681no—
340C2×C4C2×#6324211yescharacteristic
341C2×C4D17⋊M1611yescharacteristic
342C8—1362no—
343C8—1362no—
344C22—342no—
345C22—342no—
346C22—342no—
347C22—681no—
348C22—681no—
349C22—681no—
350C22—681no—
351C22#1176377711yescharacteristic
352C22D17⋊#9911yescharacteristic
353C22D17⋊#10111yescharacteristic
354C22#1176380011yescharacteristic
355C22#1176380011yescharacteristic
356C22#1176380711yescharacteristic
357C22#1176380811yescharacteristic
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—42no—
363C4—81no—
364C4—174no—
365C4—341no—
366C4—341no—
367C4—341no—
368C4—341no—
369C4—682no—
370C4—1361no—
371C2—682no—
372C2#1454401311yescharacteristic
373C2#1454408011yescharacteristic
374C2#1454408211yescharacteristic
375C2#1454420011yescharacteristic
376C2#1454420211yescharacteristic
377C2#1454427611yescharacteristic
378C2#1454432411yescharacteristic
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#7598
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
46. #10587578C8semidirect
245. C17#7598semidirect

Maximal subgroups

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

subgroupindex
#145446412
#145436032
#145436022
#145312652
#759817