Finite Group Databasebeta

← #16929771

Subgroups — #16929771

Order 4352.

456 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537867C211yesmaximal, characteristic
2C2×#11762917C211yesmaximal, characteristic
3#14527180C211yesmaximal, characteristic
4#14527178C211yesmaximal, characteristic
5#14527107C211yesmaximal, characteristic
6#14526629C211yesmaximal, characteristic
7C17×#1275C211yesmaximal, characteristic
8C22×Dic68C411yescharacteristic
9C2×C4×Dic34C2211yescharacteristic
10C2×C4×Dic34C2211yescharacteristic
11#11762939—22no—
12#11762936—22no—
13#11762917—22no—
14#11762917—22no—
15#11762863—22no—
16#11762862C2211yescharacteristic
17#11762862C2211yescharacteristic
18C2×#10587488C411yescharacteristic
19C2×#10587487C411yescharacteristic
20C2×#10587487C411yescharacteristic
21#11762541—22no—
22#11762539—22no—
23#11762534—22no—
24C17×#431C2211yescharacteristic
25C17×#431C2211yescharacteristic
26C2×C17×#97C2211yescharacteristic
27C22×Dic34C2×C411yescharacteristic
28C22×Dic34C2×C411yescharacteristic
29C22×C8×C17C2×C411yescharacteristic
30C22×C8×C17C2×C411yescharacteristic
31C2×C42×C17C2311yescharacteristic
32C2×C4⋊Dic17C2×C411yescharacteristic
33C2×C4⋊Dic17C2×C411yescharacteristic
34C2×#63225—21no—
35C2×#63225—21no—
36C2×C4×Dic17—21no—
37C2×C4×Dic17—21no—
38C2×Dic68—22no—
39C2×Dic68—22no—
40C2×Dic68—22no—
41C4×Dic34—21no—
42C4×Dic34—21no—
43C4×Dic34—21no—
44C4×Dic34—21no—
45C4×Dic34—21no—
46C4×Dic34—21no—
47C4×Dic34D412yes—
48C4×Dic34D412yes—
49C17×C4⋊C8—21no—
50C17×C4⋊C8—21no—
51C17×C22⋊C8—21no—
52C17×C22⋊C8—21no—
53C17×#97—21no—
54C17×#97—21no—
55C4×C8×C17—21no—
56C4×C8×C17D412yes—
57C22⋊#3622—21no—
58C22⋊#3622D412yes—
59#10587488—22no—
60#10587487—22no—
61#10587487—22no—
62#10587486—24no—
63#10587485—24no—
64C4⋊#3622—21no—
65C4⋊#3622—21no—
66C4×#3622—21no—
67C4×#3622—21no—
68C22×C4×C17C22×C411yescharacteristic
69C22×C4×C17C2×D411yescharacteristic
70C22×C4×C17#4111yescharacteristic
71C22×Dic17—21no—
72C22×Dic17—21no—
73C22×Dic17—21no—
74C22×Dic17—21no—
75C2×Dic34—21no—
76C2×Dic34—21no—
77C2×Dic34—21no—
78C2×Dic34—21no—
79C2×Dic34—21no—
80C2×Dic34—21no—
81C2×Dic34—21no—
82C2×Dic34—21no—
83C2×Dic34—21no—
84C2×Dic34—21no—
85C2×Dic34C22⋊C412yes—
86C2×Dic34M1612yes—
87C2×C8×C17—21no—
88C2×C8×C17—21no—
89C2×C8×C17—21no—
90C2×C8×C17—22no—
91C2×C8×C17—21no—
92C2×C8×C17—21no—
93C2×C8×C17—41no—
94C2×C8×C17M1612yes—
95C42×C17C2×D411yescharacteristic
96C42×C17C2×D411yescharacteristic
97C42×C17C2×D411yescharacteristic
98C42×C17#4111yescharacteristic
99C4⋊Dic17—21no—
100C4⋊Dic17—21no—
101C4⋊Dic17—21no—
102C4⋊Dic17C22⋊C412yes—
103#63225—22no—
104#63225—22no—
105#63225—41no—
106#63225—41no—
107C4×Dic17—22no—
108C4×Dic17—22no—
109C4×Dic17—41no—
110C4×Dic17—41no—
111C2×#3622—22no—
112C2×#3622—41no—
113Dic68—28no—
114#9092—171nomaximal, Sylow
115C23×C17C4×D411yescharacteristic
116C2×C4×C17—41no—
117C2×C4×C17—41no—
118C2×C4×C17C2×C22⋊C411yescharacteristic
119C2×C4×C17C4×D411yescharacteristic
120C2×C4×C17#12011yescharacteristic
121C2×C4×C17#12111yescharacteristic
122C2×C4×C17#12111yescharacteristic
123C2×C4×C17#12311yescharacteristic
124C2×C4×C17C2×M1611yescharacteristic
125C2×C4×C17C2×M1611yescharacteristic
126C2×C4×C17#13111yescharacteristic
127C2×C4×C17#13111yescharacteristic
128C2×Dic17—22no—
129C2×Dic17—22no—
130C2×Dic17—22no—
131C2×Dic17—41no—
132C2×Dic17—41no—
133C2×Dic17—41no—
134C2×Dic17—41no—
135C2×Dic17—41no—
136C2×Dic17—81no—
137C2×Dic17—81no—
138Dic34—22no—
139Dic34—22no—
140Dic34—22no—
141Dic34—22no—
142Dic34—41no—
143Dic34—41no—
144Dic34—41no—
145Dic34—41no—
146C8×C17—22no—
147C8×C17—42no—
148C8×C17—41no—
149C8×C17—81no—
150#3622—42no—
151#3622—81no—
152#2983—171no—
153C2×#441—171no—
154#1479—171no—
155#1479—171no—
156#1461—171no—
157#1281—171no—
158#1275D1711yescharacteristic
159C22×C17—21no—
160C22×C17—21no—
161C22×C17#38611yescharacteristic
162C22×C17#43511yescharacteristic
163C22×C17#43611yescharacteristic
164C4×C17—21no—
165C4×C17—21no—
166C4×C17—21no—
167C4×C17—21no—
168C4×C17#40711yescharacteristic
169C4×C17#40811yescharacteristic
170C4×C17#43511yescharacteristic
171C4×C17#43611yescharacteristic
172Dic17—42no—
173Dic17—42no—
174Dic17—42no—
175Dic17—81no—
176C22×Q16—171no—
177C2×C4×Q8—171no—
178C2×C4×Q8—171no—
179#446—342no—
180#446—342no—
181#441—342no—
182#441—342no—
183#432—342no—
184#431—171no—
185#431—171no—
186#431C2×D1711yescharacteristic
187#431C2×D1711yescharacteristic
188C2×#106—171no—
189C2×#103—171no—
190C2×#103—171no—
191C2×#97C2×D1711yescharacteristic
192Q8⋊C8—342no—
193Q8⋊C8—342no—
194#324—342no—
195C2×C17—21no—
196C2×C17—21no—
197C2×C17#187011yescharacteristic
198C2×C17#190211yescharacteristic
199C2×C17#190511yescharacteristic
200C22×Q8—171no—
201C22×Q8—171no—
202C2×Q16—342no—
203C2×Q16—342no—
204C2×Q16—342no—
205C22×C8C4×D1711yescharacteristic
206C22×C8C4×D1711yescharacteristic
207C4×Q8—172no—
208C4×Q8—172no—
209C4×Q8—341no—
210C4×Q8—341no—
211C4×Q8—341no—
212C4×Q8—341no—
213C4×Q8—341no—
214C4×Q8—341no—
215C2×C4⋊C4—171no—
216C2×C4⋊C4—171no—
217C2×C4⋊C4—341no—
218C2×C4⋊C4—341no—
219C2×C42—341no—
220C2×C42—341no—
221C2×C42C22×D1711yescharacteristic
222#106—342no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—344no—
226C4⋊C8—341no—
227C4⋊C8—341no—
228#103—342no—
229#103—342no—
230C22⋊C8—21no—
231C22⋊C8—21no—
232C22⋊C8—172no—
233C22⋊C8—341no—
234#97—21no—
235#97—21no—
236#97—344no—
237C4×C8—21no—
238C4×C8—341no—
239C4×C8—341no—
240C4×C8D6812yes—
241C17#909211yescharacteristic, complemented, Sylow
242C2×Q8—172no—
243C2×Q8—172no—
244C2×Q8—341no—
245C2×Q8—341no—
246C2×Q8—341no—
247C2×Q8—341no—
248C2×Q8—341no—
249C2×Q8—341no—
250C2×Q8—341no—
251C2×Q8—341no—
252C2×Q8—341no—
253C2×Q8—341no—
254C22×C4—341no—
255C22×C4—341no—
256C22×C4—341no—
257C22×C4—341no—
258C22×C4C2×C4×D1711yescharacteristic
259C22×C4D4×D1711yescharacteristic
260C22×C4#6325611yescharacteristic
261Q16—348no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—22no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—41no—
269C2×C8—342no—
270C2×C8—681no—
271C2×C8#6321812yes—
272C4⋊C4—172no—
273C4⋊C4—341no—
274C4⋊C4—342no—
275C4⋊C4—342no—
276C4⋊C4—341no—
277C4⋊C4—341no—
278C4⋊C4—681no—
279C4⋊C4—681no—
280C42—342no—
281C42—342no—
282C42—681no—
283C42—681no—
284C42C2×D6811yescharacteristic
285C42#6325211yescharacteristic
286C42D4×D1711yescharacteristic
287C42D4×D1711yescharacteristic
288C23#1058757911yescharacteristic
289Q8—342no—
290Q8—342no—
291Q8—342no—
292Q8—342no—
293Q8—681no—
294Q8—681no—
295Q8—681no—
296Q8—681no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—342no—
300C2×C4—342no—
301C2×C4—342no—
302C2×C4—681no—
303C2×C4—681no—
304C2×C4—681no—
305C2×C4—681no—
306C2×C4—681no—
307C2×C4—1361no—
308C2×C4—1361no—
309C2×C4C4×D6811yescharacteristic
310C2×C4C22⋊C4×D1711yescharacteristic
311C2×C4#1058756811yescharacteristic
312C2×C4#1058757011yescharacteristic
313C2×C4#1058758011yescharacteristic
314C2×C4#1058758111yescharacteristic
315C2×C4C2×#6321811yescharacteristic
316C2×C4#1058758711yescharacteristic
317C2×C4M16×D1711yescharacteristic
318C2×C4#1058759311yescharacteristic
319C8—22no—
320C8—42no—
321C8—41no—
322C8—81no—
323C8—682no—
324C8—1361no—
325C22—21no—
326C22—21no—
327C22#1176268711yescharacteristic
328C22#1176287911yescharacteristic
329C22#1176288611yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—682no—
335C4—682no—
336C4—682no—
337C4—1361no—
338C4#1176277111yescharacteristic
339C4#1176277411yescharacteristic
340C4#1176288211yescharacteristic
341C4#1176288811yescharacteristic
342C2—21no—
343C2—21no—
344C2#1452908011yescharacteristic
345C2#1452925811yescharacteristic
346C2#1452927911yescharacteristic
subgroupG/H
centerC22#11762687
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1275C2
socleC22×C17#386
prime radicalC23×C17C4×D4
cosocleC2×C42×C17C23
hypercenter#1275D17
hypocenterC17#9092
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1275

Complements

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

NH ≅ G/Ntype
241. C17#9092semidirect

Maximal subgroups

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

subgroupindex
#145378672
C2×#117629172
#145271802
#145271782
#145271072
#145266292
C17×#12752
#909217