Finite Group Databasebeta

← #17950228

Subgroups — #17950228

Order 4352.

494 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 100 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#14544675C211yesmaximal, characteristic
2#14544638C211yesmaximal, characteristic
3#14543603C212yesmaximal, complemented
4#14543602C212yesmaximal, complemented
5#14537134C211yesmaximal, characteristic
6C2×C4⋊#3624—21no—
7C2×C22⋊#3624—21no—
8C2×C22⋊#3624—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587574C411yescharacteristic
13C2×#10587564—21no—
14C22×C4×Dic17C2211yescharacteristic
15#11762713—21no—
16#11762708C2211yescharacteristic
17#11762706—21no—
18#11762705C2211yescharacteristic
19#11762678C411yescharacteristic
20#11762669C411yescharacteristic
21#11762667—21no—
22C17×#380C411yescharacteristic
23C23×C4×C17C2×C411yescharacteristic
24C23×Dic17D411yescharacteristic
25C23×Dic17D411yescharacteristic
26C22×Dic34—21no—
27C22×#3624—22no—
28C22×#3624—22no—
29C2×C4⋊C4×C17C2×C411yescharacteristic
30C2×C4⋊C4×C17C2×C411yescharacteristic
31C2×C22⋊C4×C17—21no—
32C2×C22⋊Dic17—21no—
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17C2×C411yescharacteristic
35C2×C4⋊Dic17C2×C411yescharacteristic
36C2×#63225—21no—
37C2×#63225—21no—
38C2×#63225—21no—
39C2×#63225—21no—
40C2×C4×Dic17—42no—
41C2×C4×Dic17C2×C411yescharacteristic
42C2×C4×Dic17D411yescharacteristic
43C2×C4×Dic17D411yescharacteristic
44C2×C4×Dic17C2311yescharacteristic
45#10587574—42no—
46#10587564—44no—
47C22⋊#3624—42no—
48C22⋊#3624—42no—
49C4⋊#3624—42no—
50C17×#95—21no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54C24×C17C22⋊C411yescharacteristic
55C22×C4×C17—22no—
56C22×C4×C17—22no—
57C22×C4×C17—21no—
58C22×C4×C17—21no—
59C22×C4×C17—41no—
60C22×C4×C17C22⋊C411yescharacteristic
61C22×C4×C17C22×C411yescharacteristic
62C22×Dic17—22no—
63C22×Dic17—22no—
64C22×Dic17—21no—
65C22×Dic17—21no—
66C22×Dic17—41no—
67C22×Dic17—41no—
68C22×Dic17—41no—
69C22×Dic17C22⋊C411yescharacteristic
70C22×Dic17C22⋊C411yescharacteristic
71C22×Dic17SD1612yes—
72C22×Dic17Q1612yes—
73C22×Dic17C2×D411yescharacteristic
74C22×Dic17C2×D411yescharacteristic
75C2×Dic34—42no—
76C2×Dic34—42no—
77C2×Dic34—42no—
78C2×#3624—42no—
79C2×#3624—42no—
80C2×#3624—42no—
81C2×#3624—42no—
82C2×#3624—42no—
83C2×#3624—42no—
84C4⋊C4×C17—22no—
85C4⋊C4×C17—41no—
86C22⋊C4×C17—42no—
87C22⋊Dic17—42no—
88C4⋊Dic17—22no—
89C4⋊Dic17—42no—
90C4⋊Dic17—41no—
91#63225—42no—
92#63225—42no—
93#63225—42no—
94#63225—42no—
95C4×Dic17—22no—
96C4×Dic17—22no—
97C4×Dic17—41no—
98C4×Dic17—41no—
99#7725—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—44no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17—41no—
116C2×C4×C17—41no—
117C2×C4×C17—41no—
118C2×C4×C17—41no—
119C2×C4×C17#10112yes—
120C2×C4×C17#13112yes—
121C2×Dic17—21no—
122C2×Dic17—21no—
123C2×Dic17—21no—
124C2×Dic17—21no—
125C2×Dic17—21no—
126C2×Dic17—21no—
127C2×Dic17—21no—
128C2×Dic17—21no—
129C2×Dic17—42no—
130C2×Dic17—42no—
131C2×Dic17—44no—
132C2×Dic17—41no—
133C2×Dic17—41no—
134C2×Dic17—41no—
135C2×Dic17—41no—
136C2×Dic17—41no—
137C2×Dic17—41no—
138C2×Dic17#9912yes—
139C2×Dic17#10312yes—
140C2×Dic17C2×SD1611yescharacteristic
141C2×Dic17C2×Q1611yescharacteristic
142C2×Dic17AGL(1,ℤ/8)12yes—
143Dic34—84no—
144#3624—82no—
145#3624—82no—
146#2857—171no—
147#1817—171no—
148#1797—171no—
149#1271—172no—
150#1271—172no—
151C22×C17—22no—
152C22×C17—22no—
153C22×C17—22no—
154C22×C17—41no—
155C22×C17—41no—
156C22×C17—41no—
157C22×C17—41no—
158C22×C17#40811yescharacteristic
159C22×C17C2×#9911yescharacteristic
160C22×C17C2×#10111yescharacteristic
161C22×C17C2×#10311yescharacteristic
162C22×C17#41811yescharacteristic
163C22×C17#42111yescharacteristic
164C22×C17#42111yescharacteristic
165C4×C17—22no—
166C4×C17—22no—
167C4×C17—81no—
168C4×C17—81no—
169Dic17—22no—
170Dic17—22no—
171Dic17—21no—
172Dic17—22no—
173Dic17—21no—
174Dic17—81no—
175Dic17—81no—
176C2×C4⋊Q8—171no—
177C2×C22⋊Q8—341no—
178C22×C42—171no—
179C2×C4⋊C8—341no—
180C2×C22⋊C8—341no—
181C2×C22⋊C8—341no—
182#391—341no—
183#389—171no—
184#389—171no—
185#389—341no—
186#384—171no—
187#380—171no—
188#380—341no—
189#380#59511yescharacteristic
190#336—172no—
191#336—172no—
192#336—341no—
193C2×C17—42no—
194C2×C17#147211yescharacteristic
195C2×C17#148111yescharacteristic
196C2×C17#149611yescharacteristic
197C2×C17#151011yescharacteristic
198C2×C17#152011yescharacteristic
199C2×C17#153711yescharacteristic
200C2×C17#154911yescharacteristic
201C22×Q8—341no—
202C23×C4—171no—
203C23×C4—171no—
204C23×C4C2×#59511yescharacteristic
205C22×C8—342no—
206C22×C8—342no—
207C4⋊Q8—682no—
208C22⋊Q8—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⋊C4—341no—
216C2×C4⋊C4C2×#59511yescharacteristic
217C2×C4⋊C4C2×#59511yescharacteristic
218C2×C22⋊C4—21no—
219C2×C22⋊C4—341no—
220C2×C42—171no—
221C2×C42—171no—
222C2×C42—171no—
223C2×C42—171no—
224C2×C42—682no—
225C4⋊C8—682no—
226C22⋊C8—682no—
227C22⋊C8—682no—
228#95—21no—
229#95—341no—
230#95—341no—
231#95—341no—
232C17#772511yescharacteristic, complemented, Sylow
233C24C22⋊#59511yescharacteristic
234C2×Q8—682no—
235C2×Q8—682no—
236C2×Q8—682no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—41no—
242C22×C4—171no—
243C22×C4—171no—
244C22×C4—171no—
245C22×C4—171no—
246C22×C4—172no—
247C22×C4—172no—
248C22×C4—342no—
249C22×C4—342no—
250C22×C4—341no—
251C22×C4—341no—
252C22×C4—681no—
253C22×C4—681no—
254C22×C4—681no—
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—22no—
264C4⋊C4—41no—
265C4⋊C4—342no—
266C4⋊C4—681no—
267C4⋊C4—682no—
268C4⋊C4—682no—
269C4⋊C4—682no—
270C4⋊C4—682no—
271C4⋊C4—682no—
272C22⋊C4—42no—
273C22⋊C4—682no—
274C42—342no—
275C42—342no—
276C42—681no—
277C42—681no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23#1058754912yes—
285C23C2×C22⋊#59511yescharacteristic
286Q8—1364no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—44no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—172no—
299C2×C4—171no—
300C2×C4—172no—
301C2×C4—171no—
302C2×C4—172no—
303C2×C4—341no—
304C2×C4—341no—
305C2×C4—341no—
306C2×C4—341no—
307C2×C4—341no—
308C2×C4—341no—
309C2×C4—341no—
310C2×C4—341no—
311C2×C4—682no—
312C2×C4—682no—
313C2×C4—684no—
314C2×C4—681no—
315C2×C4—681no—
316C2×C4—681no—
317C2×C4—681no—
318C2×C4—681no—
319C2×C4—681no—
320C2×C4#1058754512yes—
321C2×C4#1058767812yes—
322C8—1362no—
323C8—1362no—
324C22—22no—
325C22—22no—
326C22—22no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22#1176378211yescharacteristic
332C22D17⋊#9911yescharacteristic
333C22C2×#1058754511yescharacteristic
334C22C2×#1058754911yescharacteristic
335C22#1176380111yescharacteristic
336C22#1176380611yescharacteristic
337C22#1176380611yescharacteristic
338C4—22no—
339C4—22no—
340C4—81no—
341C4—81no—
342C4—342no—
343C4—342no—
344C4—341no—
345C4—342no—
346C4—341no—
347C4—1361no—
348C4—1361no—
349C2—42no—
350C2#1454406311yescharacteristic
351C2#1454409211yescharacteristic
352C2#1454414311yescharacteristic
353C2#1454419011yescharacteristic
354C2#1454422211yescharacteristic
355C2#1454427511yescharacteristic
356C2#1454429911yescharacteristic
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#7725
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. #14543603C2semidirect
4. #14543602C2semidirect
232. C17#7725semidirect

Maximal subgroups

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

subgroupindex
#145446752
#145446382
#145436032
#145436022
#145371342
#772517