Finite Group Databasebeta

← #17953601

Subgroups — #17953601

Order 4352.

514 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 114 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#14544640C211yesmaximal, characteristic
2#14544640C211yesmaximal, characteristic
3#14543662C212yesmaximal, complemented
4#14543662C212yesmaximal, complemented
5#14531186C211yesmaximal, characteristic
6C2×#10587544C2212yes—
7C2×#10587544C2212yes—
8C2×C22⋊#3624—21no—
9C2×C22⋊#3624—21no—
10#11763675—21no—
11#11763675—21no—
12C2×#10587563—21no—
13C22×C4×Dic17C2211yescharacteristic
14#11762678C2211yescharacteristic
15#11762678C2211yescharacteristic
16#11762673—21no—
17#11762669C411yescharacteristic
18#11762667—21no—
19C4⋊C4×Dic17C411yescharacteristic
20C4⋊C4×Dic17C411yescharacteristic
21#11762660—21no—
22C17×#380C411yescharacteristic
23C23×C4×C17C2×C411yescharacteristic
24C23×Dic17D411yescharacteristic
25C23×Dic17D411yescharacteristic
26C22×#3624—22no—
27C22×#3624—22no—
28C2×C4⋊C4×C17C2×C411yescharacteristic
29C2×C4⋊C4×C17C2×C411yescharacteristic
30C2×C22⋊C4×C17—21no—
31C2×C22⋊Dic17—21no—
32C2×C4⋊Dic17C2×C411yescharacteristic
33C2×C4⋊Dic17C2×C411yescharacteristic
34C2×#63225—21no—
35C2×#63225—21no—
36C2×#63225—21no—
37C2×#63225—21no—
38C2×C4×Dic17—24no—
39C2×C4×Dic17—21no—
40C2×C4×Dic17—21no—
41C2×C4×Dic17C2×C411yescharacteristic
42C2×C4×Dic17D411yescharacteristic
43C2×C4×Dic17D411yescharacteristic
44C2×C4×Dic17C2311yescharacteristic
45#10587563—44no—
46C22⋊#3624—42no—
47C22⋊#3624—42no—
48#10587544—24no—
49#10587544—24no—
50C17×#95—21no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54C24×C17C22⋊C411yescharacteristic
55C22×C4×C17—22no—
56C22×C4×C17—21no—
57C22×C4×C17—21no—
58C22×C4×C17—41no—
59C22×C4×C17—41no—
60C22×C4×C17C22⋊C411yescharacteristic
61C22×C4×C17C22×C411yescharacteristic
62C22×Dic17—22no—
63C22×Dic17—22no—
64C22×Dic17—22no—
65C22×Dic17—22no—
66C22×Dic17—21no—
67C22×Dic17—21no—
68C22×Dic17—21no—
69C22×Dic17—21no—
70C22×Dic17C22⋊C411yescharacteristic
71C22×Dic17C22⋊C411yescharacteristic
72C22×Dic17SD1612yes—
73C22×Dic17Q1612yes—
74C22×Dic17C2×D411yescharacteristic
75C22×Dic17C2×D411yescharacteristic
76C2×#3624—42no—
77C2×#3624—42no—
78C2×#3624—42no—
79C2×#3624—42no—
80C2×#3624—42no—
81C2×#3624—42no—
82C4⋊C4×C17—41no—
83C4⋊C4×C17—41no—
84C22⋊C4×C17—42no—
85C22⋊Dic17—42no—
86C4⋊Dic17—41no—
87C4⋊Dic17—41no—
88#63225—42no—
89#63225—42no—
90#63225—42no—
91#63225—41no—
92#63225—41no—
93C4×Dic17—22no—
94C4×Dic17—22no—
95C4×Dic17—22no—
96C4×Dic17—42no—
97C4×Dic17—42no—
98C4×Dic17#4114yes—
99#8727—171nomaximal, Sylow
100C23×C17—21no—
101C23×C17—21no—
102C23×C17—21no—
103C23×C17—21no—
104C23×C17—21no—
105C23×C17—21no—
106C23×C17#10312yes—
107C23×C17C2×C22⋊C411yescharacteristic
108C2×C4×C17—21no—
109C2×C4×C17—21no—
110C2×C4×C17—21no—
111C2×C4×C17—21no—
112C2×C4×C17—21no—
113C2×C4×C17—44no—
114C2×C4×C17—41no—
115C2×C4×C17—41no—
116C2×C4×C17—41no—
117C2×C4×C17—41no—
118C2×C4×C17—41no—
119C2×C4×C17—41no—
120C2×C4×C17#11712yes—
121C2×Dic17—21no—
122C2×Dic17—21no—
123C2×Dic17—24no—
124C2×Dic17—24no—
125C2×Dic17—21no—
126C2×Dic17—21no—
127C2×Dic17—21no—
128C2×Dic17—42no—
129C2×Dic17—42no—
130C2×Dic17—41no—
131C2×Dic17—41no—
132C2×Dic17—41no—
133C2×Dic17—41no—
134C2×Dic17—41no—
135C2×Dic17—41no—
136C2×Dic17#10312yes—
137C2×Dic17#12312yes—
138C2×Dic17#12312yes—
139C2×Dic17C2×SD1611yescharacteristic
140C2×Dic17C2×Q1611yescharacteristic
141C2×Dic17#13512yes—
142C2×Dic17AGL(1,ℤ/8)12yes—
143C2×Dic17AGL(1,ℤ/8)11yescharacteristic
144C2×Dic17#13711yescharacteristic
145#3624—82no—
146#3624—82no—
147#2285—171no—
148#1797—171no—
149#1797—171no—
150#1296—172no—
151#1296—172no—
152C22×C17—22no—
153C22×C17—22no—
154C22×C17—22no—
155C22×C17—41no—
156C22×C17—41no—
157C22×C17—41no—
158C22×C17—41no—
159C22×C17#38111yescharacteristic
160C22×C17#41311yescharacteristic
161C22×C17#41311yescharacteristic
162C22×C17C2×#10311yescharacteristic
163C22×C17#41611yescharacteristic
164C22×C17#41711yescharacteristic
165C22×C17#41811yescharacteristic
166C4×C17—22no—
167C4×C17—41no—
168C4×C17—81no—
169C4×C17—81no—
170Dic17—22no—
171Dic17—41no—
172Dic17—81no—
173Dic17—81no—
174Dic17#48112yes—
175Dic17#48212yes—
176Dic17#48412yes—
177Dic17#48512yes—
178C2×#117—341no—
179C22×C42—171no—
180C2×C4⋊C8—172no—
181C2×C4⋊C8—172no—
182C2×C22⋊C8—341no—
183C2×C22⋊C8—341no—
184#384—171no—
185#384—171no—
186#382—341no—
187#380—171no—
188#380—341no—
189#380#59511yescharacteristic
190C4×C4⋊C4—171no—
191C4×C4⋊C4—171no—
192C4×C4⋊C4—341no—
193#336—341no—
194#336—341no—
195C2×C17—42no—
196C2×C17#154211yescharacteristic
197C2×C17#155011yescharacteristic
198C2×C17#155311yescharacteristic
199C2×C17#155711yescharacteristic
200C2×C17#182211yescharacteristic
201C2×C17#182411yescharacteristic
202C2×C17#182511yescharacteristic
203C23×C4—171no—
204C23×C4—171no—
205C23×C4C2×#59511yescharacteristic
206C22×C8—342no—
207C22×C8—342no—
208#117—684no—
209C2×C4⋊C4—171no—
210C2×C4⋊C4—171no—
211C2×C4⋊C4—341no—
212C2×C4⋊C4—341no—
213C2×C4⋊C4—341no—
214C2×C4⋊C4—341no—
215C2×C4⋊C4C2×#59511yescharacteristic
216C2×C4⋊C4C2×#59511yescharacteristic
217C2×C22⋊C4—21no—
218C2×C22⋊C4—341no—
219C2×C42—171no—
220C2×C42—171no—
221C2×C42—171no—
222C2×C42—171no—
223C2×C42—344no—
224C2×C42—341no—
225C2×C42—341no—
226C4⋊C8—344no—
227C4⋊C8—344no—
228C22⋊C8—682no—
229C22⋊C8—682no—
230#95—21no—
231#95—341no—
232#95—341no—
233#95—341no—
234C17#872711yescharacteristic, complemented, Sylow
235C24C22⋊#59511yescharacteristic
236C22×C4—22no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—171no—
242C22×C4—171no—
243C22×C4—171no—
244C22×C4—172no—
245C22×C4—172no—
246C22×C4—171no—
247C22×C4—342no—
248C22×C4—342no—
249C22×C4—341no—
250C22×C4—342no—
251C22×C4—342no—
252C22×C4—341no—
253C22×C4—341no—
254C22×C4—341no—
255C22×C4C22⋊#59511yescharacteristic
256C22×C4C22×#59511yescharacteristic
257C2×C8—682no—
258C2×C8—682no—
259C2×C8—682no—
260C2×C8—682no—
261C2×C8—682no—
262C2×C8—682no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—681no—
266C4⋊C4—681no—
267C4⋊C4—682no—
268C4⋊C4—682no—
269C4⋊C4—682no—
270C4⋊C4—681no—
271C4⋊C4—681no—
272C22⋊C4—42no—
273C22⋊C4—682no—
274C42—174no—
275C42—342no—
276C42—342no—
277C42—342no—
278C42—682no—
279C42—682no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23#1058754912yes—
287C23C2×C22⋊#59511yescharacteristic
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—44no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—172no—
301C2×C4—172no—
302C2×C4—171no—
303C2×C4—171no—
304C2×C4—172no—
305C2×C4—171no—
306C2×C4—171no—
307C2×C4—172no—
308C2×C4—172no—
309C2×C4—344no—
310C2×C4—344no—
311C2×C4—341no—
312C2×C4—341no—
313C2×C4—341no—
314C2×C4—341no—
315C2×C4—341no—
316C2×C4—682no—
317C2×C4—682no—
318C2×C4—681no—
319C2×C4—681no—
320C2×C4—681no—
321C2×C4—681no—
322C2×C4—681no—
323C2×C4—681no—
324C2×C4#1058767712yes—
325C8—1362no—
326C8—1362no—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22#1176375211yescharacteristic
335C22#1176379611yescharacteristic
336C22#1176379611yescharacteristic
337C22C2×#1058754911yescharacteristic
338C22#1176379911yescharacteristic
339C22#1176380011yescharacteristic
340C22#1176380111yescharacteristic
341C4—22no—
342C4—41no—
343C4—81no—
344C4—81no—
345C4—172no—
346C4—172no—
347C4—172no—
348C4—172no—
349C4—342no—
350C4—681no—
351C4—1361no—
352C4—1361no—
353C2—42no—
354C2#1454428611yescharacteristic
355C2#1454430211yescharacteristic
356C2#1454430811yescharacteristic
357C2#1454431611yescharacteristic
358C2#1454468611yescharacteristic
359C2#1454468811yescharacteristic
360C2#1454468911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#380C4
socleC23×C17C2×C22⋊C4
prime radicalC24×C17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenter#380#595
hypocenterC17#8727
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #14543662C2semidirect
4. #14543662C2semidirect
234. C17#8727semidirect

Maximal subgroups

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

subgroupindex
#145446402
#145436622
#145311862
#872717