Finite Group Databasebeta

← #16922488

Subgroups — #16922488

Order 4352.

516 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14531267C211yesmaximal, characteristic
2#14528546C211yesmaximal, characteristic
3#14526608C212yesmaximal, complemented
4#14526606C212yesmaximal, complemented
5C17×#1797C211yesmaximal, characteristic
6C2×#10587612C411yescharacteristic
7C2×#10587612C411yescharacteristic
8C2×C22⋊#3622—21no—
9C2×#10587474—21no—
10#11762707C411yescharacteristic
11#11762707C411yescharacteristic
12#11762707C2211yescharacteristic
13#11762707C2211yescharacteristic
14#11762682—21no—
15#11762682—21no—
16C4×#63225—21no—
17C4×#63225—21no—
18#11762564C2212yes—
19C22×C42×C17C2211yescharacteristic
20C2×C17×C4⋊C8—21no—
21C2×C17×C22⋊C8—21no—
22C17×#336C2212yes—
23C23×C4×C17C2×C411yescharacteristic
24C23×C4×C17D411yescharacteristic
25C23×C4×C17D411yescharacteristic
26C22×C8×C17—22no—
27C2×C42×C17—42no—
28C2×C42×C17C2×C411yescharacteristic
29C2×C42×C17D411yescharacteristic
30C2×C42×C17D411yescharacteristic
31C2×C42×C17C2311yescharacteristic
32C2×C22⋊Dic17—21no—
33C2×C22⋊Dic17—21no—
34#10587612—22no—
35#10587612—22no—
36#10587612—42no—
37C2×C4⋊Dic17C2×C411yescharacteristic
38C2×C4⋊Dic17C2×C411yescharacteristic
39C2×C4⋊Dic17C2×C411yescharacteristic
40C2×C4⋊Dic17C2×C411yescharacteristic
41C2×#63225—21no—
42C2×#63225—21no—
43C2×#63225—21no—
44C2×#63225—21no—
45C2×C4×Dic17—21no—
46C2×C4×Dic17—21no—
47C22×#3622—22no—
48C17×C4⋊C8—42no—
49C17×C22⋊C8—42no—
50#10587502—21no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54C22⋊#3622—24no—
55#10587474—42no—
56C24×C17C22⋊C411yescharacteristic
57C22×C4×C17—22no—
58C22×C4×C17—22no—
59C22×C4×C17—21no—
60C22×C4×C17—21no—
61C22×C4×C17—22no—
62C22×C4×C17—22no—
63C22×C4×C17—21no—
64C22×C4×C17—21no—
65C22×C4×C17—41no—
66C22×C4×C17—41no—
67C22×C4×C17—41no—
68C22×C4×C17C22⋊C411yescharacteristic
69C22×C4×C17C22⋊C411yescharacteristic
70C22×C4×C17C22⋊C411yescharacteristic
71C22×C4×C17C22×C411yescharacteristic
72C22×C4×C17C2×D411yescharacteristic
73C22×C4×C17C2×D411yescharacteristic
74C22×Dic17—21no—
75C22×Dic17—21no—
76C22×Dic17—21no—
77C22×Dic17—21no—
78C2×C8×C17—42no—
79C2×C8×C17—42no—
80C2×C8×C17—42no—
81C42×C17—22no—
82C42×C17—22no—
83C42×C17—41no—
84C42×C17—41no—
85C22⋊Dic17—24no—
86C22⋊Dic17—42no—
87C4⋊Dic17—21no—
88C4⋊Dic17—21no—
89C4⋊Dic17—41no—
90C4⋊Dic17—41no—
91C4⋊Dic17M1612yes—
92C4⋊Dic17M1612yes—
93#63225—42no—
94#63225—42no—
95#63225—42no—
96#63225—41no—
97#63225—41no—
98C4×Dic17—24no—
99C4×Dic17—42no—
100C2×#3622—24no—
101C2×#3622—42no—
102C2×#3622—42no—
103#7613—171nomaximal, Sylow
104C23×C17—21no—
105C23×C17—21no—
106C23×C17—21no—
107C23×C17—21no—
108C23×C17—21no—
109C23×C17—21no—
110C23×C17#10112yes—
111C23×C17C2×C22⋊C411yescharacteristic
112C2×C4×C17—24no—
113C2×C4×C17—24no—
114C2×C4×C17—21no—
115C2×C4×C17—21no—
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—21no—
123C2×C4×C17—21no—
124C2×C4×C17—21no—
125C2×C4×C17—21no—
126C2×C4×C17—21no—
127C2×C4×C17—44no—
128C2×C4×C17—42no—
129C2×C4×C17—42no—
130C2×C4×C17#9912yes—
131C2×C4×C17#10412yes—
132C2×C4×C17C2×M1611yescharacteristic
133C2×C4×C17C2×M1611yescharacteristic
134C2×C4×C17#13512yes—
135C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C17#13711yescharacteristic
137C2×Dic17—22no—
138C2×Dic17—22no—
139C2×Dic17—41no—
140C2×Dic17—41no—
141C2×Dic17—41no—
142C2×Dic17—41no—
143C2×Dic17—41no—
144C2×Dic17—41no—
145C2×Dic17—41no—
146C2×Dic17—41no—
147C2×Dic17—41no—
148C2×Dic17—41no—
149C8×C17—82no—
150#3622—44no—
151#2296—171no—
152#1797D1711yescharacteristic
153#1749—171no—
154#1271—172no—
155#1271—172no—
156C22×C17—22no—
157C22×C17—22no—
158C22×C17—22no—
159C22×C17—41no—
160C22×C17—41no—
161C22×C17—41no—
162C22×C17—41no—
163C22×C17#40711yescharacteristic
164C22×C17C2×#9911yescharacteristic
165C22×C17C2×#10111yescharacteristic
166C22×C17#41611yescharacteristic
167C22×C17#41711yescharacteristic
168C22×C17C2×#10411yescharacteristic
169C22×C17#42111yescharacteristic
170C4×C17—22no—
171C4×C17—21no—
172C4×C17—21no—
173C4×C17—22no—
174C4×C17—22no—
175C4×C17—21no—
176C4×C17—21no—
177C4×C17—41no—
178Dic17—42no—
179Dic17—42no—
180Dic17—81no—
181Dic17—81no—
182C2×#117—171no—
183C2×#117—171no—
184C22×C42C2×D1711yescharacteristic
185C2×C4⋊C8—21no—
186C2×C22⋊C8—21no—
187C2×C22⋊C8—341no—
188C2×#97—341no—
189#389—171no—
190#389—171no—
191#389—171no—
192#389—171no—
193#385—341no—
194#385—341no—
195C4×C4⋊C4—341no—
196C4×C4⋊C4—341no—
197#336—172no—
198#336C2×D1712yes—
199C2×C17—42no—
200C2×C17#146311yescharacteristic
201C2×C17#148811yescharacteristic
202C2×C17#148911yescharacteristic
203C2×C17#150111yescharacteristic
204C2×C17#151311yescharacteristic
205C2×C17#153111yescharacteristic
206C2×C17#155211yescharacteristic
207C23×C4C4×D1711yescharacteristic
208C23×C4D6811yescharacteristic
209C23×C4C22⋊D1711yescharacteristic
210C22×C8—22no—
211C22×C8—342no—
212#117—342no—
213#117—342no—
214#117—682no—
215C2×C4⋊C4—171no—
216C2×C4⋊C4—171no—
217C2×C4⋊C4—171no—
218C2×C4⋊C4—171no—
219C2×C4⋊C4—341no—
220C2×C4⋊C4—341no—
221C2×C4⋊C4—341no—
222C2×C4⋊C4—341no—
223C2×C22⋊C4—341no—
224C2×C22⋊C4—341no—
225C2×C42—42no—
226C2×C42—341no—
227C2×C42—341no—
228C2×C42C4×D1711yescharacteristic
229C2×C42D6811yescharacteristic
230C2×C42C22⋊D1711yescharacteristic
231C2×C42C22×D1711yescharacteristic
232C4⋊C8—42no—
233C22⋊C8—42no—
234C22⋊C8—344no—
235#97—682no—
236#95—341no—
237#95—341no—
238#95—341no—
239#95—341no—
240C17#761311yescharacteristic, complemented, Sylow
241C24#6322711yescharacteristic
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—341no—
254C22×C4—341no—
255C22×C4—341no—
256C22×C4—341no—
257C22×C4#6322711yescharacteristic
258C22×C4#6322711yescharacteristic
259C22×C4#6322711yescharacteristic
260C22×C4C2×C4×D1711yescharacteristic
261C22×C4C2×D6811yescharacteristic
262C22×C4C2×C22⋊D1711yescharacteristic
263C2×C8—42no—
264C2×C8—42no—
265C2×C8—42no—
266C2×C8—344no—
267C2×C8—682no—
268C2×C8—682no—
269C4⋊C4—172no—
270C4⋊C4—172no—
271C4⋊C4—341no—
272C4⋊C4—341no—
273C4⋊C4—681no—
274C4⋊C4—681no—
275C4⋊C4—682no—
276C4⋊C4—682no—
277C4⋊C4—682no—
278C4⋊C4—681no—
279C4⋊C4—681no—
280C22⋊C4—344no—
281C22⋊C4—682no—
282C42—22no—
283C42—22no—
284C42—41no—
285C42—41no—
286C42—344no—
287C42—682no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23#1058749512yes—
295C23C2×#6322711yescharacteristic
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—44no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—342no—
315C2×C4—342no—
316C2×C4—681no—
317C2×C4—681no—
318C2×C4—681no—
319C2×C4—681no—
320C2×C4—681no—
321C2×C4—681no—
322C2×C4—681no—
323C2×C4—681no—
324C2×C4—681no—
325C2×C4—681no—
326C2×C4#1058747712yes—
327C2×C4#1058749612yes—
328C2×C4#1058759012yes—
329C2×C4M16×D1711yescharacteristic
330C2×C4M16×D1711yescharacteristic
331C2×C4#1058761811yescharacteristic
332C2×C4#1058762811yescharacteristic
333C8—82no—
334C8—684no—
335C22—22no—
336C22—22no—
337C22—22no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22#1176277211yescharacteristic
343C22C2×#1058747711yescharacteristic
344C22C2×#1058749511yescharacteristic
345C22#1176280611yescharacteristic
346C22#1176280811yescharacteristic
347C22C2×#1058749611yescharacteristic
348C22#1176282711yescharacteristic
349C4—22no—
350C4—22no—
351C4—21no—
352C4—21no—
353C4—22no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—682no—
358C4—682no—
359C4—1361no—
360C4—1361no—
361C2—42no—
362C2#1452711311yescharacteristic
363C2#1452721911yescharacteristic
364C2#1452722111yescharacteristic
365C2#1452727611yescharacteristic
366C2#1452732511yescharacteristic
367C2#1452740011yescharacteristic
368C2#1452748211yescharacteristic
subgroupG/H
centerC23C2×#63227
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1797C2
socleC23×C17C2×C22⋊C4
prime radicalC24×C17C22⋊C4
cosocleC2×C42×C17C23
hypercenter#1797D17
hypocenterC17#7613
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
3. #14526608C2semidirect
4. #14526606C2semidirect
240. C17#7613semidirect

Maximal subgroups

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

subgroupindex
#145312672
#145285462
#145266082
#145266062
C17×#17972
#761317