Finite Group Databasebeta

← #16929770

Subgroups — #16929770

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
1C2×#11762914C211yesmaximal, characteristic
2#14527180C211yesmaximal, characteristic
3#14527179C211yesmaximal, characteristic
4#14527107C211yesmaximal, characteristic
5#14526628C211yesmaximal, characteristic
6#14526614C211yesmaximal, characteristic
7C17×#2983C211yesmaximal, characteristic
8C22×#63231C411yescharacteristic
9C2×C4×Dic34C2211yescharacteristic
10#11762914—22no—
11#11762914—22no—
12#11762862C2211yescharacteristic
13#11762862C2211yescharacteristic
14C2×#10587479C411yescharacteristic
15C2×#10587506C411yescharacteristic
16C2×#10587481C411yescharacteristic
17C2×#10587474C2211yescharacteristic
18#11762541—22no—
19Q8⋊#3622—22no—
20#11762534—22no—
21C2×C4×Q8×C17C2211yescharacteristic
22C17×#446—22no—
23C17×#446—22no—
24C17×#432—22no—
25C17×#431C2211yescharacteristic
26C17×#431C2211yescharacteristic
27C22×Q8×C17C2×C411yescharacteristic
28C22×Dic34C2×C411yescharacteristic
29C4×Q8×C17—21no—
30C4×Q8×C17—21no—
31C4×Q8×C17D412yes—
32C4×Q8×C17D412yes—
33C2×C4⋊C4×C17—21no—
34C2×C4⋊C4×C17C2×C411yescharacteristic
35C2×C42×C17—21no—
36C2×C42×C17C2311yescharacteristic
37C2×#63231—22no—
38C2×#63231—22no—
39C2×#63231—22no—
40C2×C4⋊Dic17C2×C411yescharacteristic
41C2×#63225—21no—
42C2×C4×Dic17—21no—
43C22×#3622C2×C411yescharacteristic
44C22×#3622C2×C411yescharacteristic
45C4×Dic34—21no—
46C4×Dic34—21no—
47C4×Dic34—21no—
48C4×Dic34—21no—
49C17×C4⋊C8—24no—
50C17×C4⋊C8—21no—
51C17×C4⋊C8—21no—
52C17×C22⋊C8—21no—
53C17×C22⋊C8D412yes—
54C17×#97—24no—
55C4×C8×C17—21no—
56C4×C8×C17D412yes—
57#10587506—22no—
58C22⋊#3622—21no—
59C22⋊#3622—21no—
60#10587481—22no—
61#10587479—22no—
62C4⋊#3622—21no—
63C4⋊#3622—21no—
64#10587474—21no—
65#10587474—21no—
66C4×#3622—21no—
67C4×#3622—21no—
68C2×Q8×C17—21no—
69C2×Q8×C17—21no—
70C2×Q8×C17—21no—
71C2×Q8×C17—21no—
72C2×Q8×C17—21no—
73C2×Q8×C17C22⋊C412yes—
74C22×C4×C17—21no—
75C22×C4×C17—21no—
76C22×C4×C17C22×C411yescharacteristic
77C22×C4×C17C2×D411yescharacteristic
78C22×C4×C17#4111yescharacteristic
79C22×Dic17—21no—
80C22×Dic17—21no—
81C2×Dic34—21no—
82C2×Dic34—21no—
83C2×Dic34—21no—
84C2×Dic34—21no—
85C2×Dic34—21no—
86C2×Dic34M1612yes—
87C2×C8×C17—22no—
88C2×C8×C17—22no—
89C4⋊C4×C17—21no—
90C4⋊C4×C17—22no—
91C4⋊C4×C17—22no—
92C4⋊C4×C17C22⋊C412yes—
93C42×C17—22no—
94C42×C17—22no—
95C42×C17C2×D411yescharacteristic
96C42×C17C2×D411yescharacteristic
97C42×C17C2×D411yescharacteristic
98C42×C17#4111yescharacteristic
99#63231—28no—
100C4⋊Dic17—21no—
101C4⋊Dic17—21no—
102#63225—41no—
103#63225—41no—
104C4×Dic17—41no—
105C4×Dic17—41no—
106C2×#3622—21no—
107C2×#3622—21no—
108C2×#3622—21no—
109C2×#3622—21no—
110C2×#3622—21no—
111C2×#3622—41no—
112C2×#3622—41no—
113C2×#3622M1612yes—
114#9092—171nomaximal, Sylow
115C23×C17C4×D411yescharacteristic
116Q8×C17—22no—
117Q8×C17—22no—
118Q8×C17—41no—
119Q8×C17—41no—
120C2×C4×C17—22no—
121C2×C4×C17—22no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17—41no—
126C2×C4×C17—81no—
127C2×C4×C17C2×C22⋊C411yescharacteristic
128C2×C4×C17C4×D411yescharacteristic
129C2×C4×C17#12011yescharacteristic
130C2×C4×C17#12111yescharacteristic
131C2×C4×C17#12111yescharacteristic
132C2×C4×C17#12311yescharacteristic
133C2×C4×C17C2×M1611yescharacteristic
134C2×C4×C17C2×M1611yescharacteristic
135C2×C4×C17#13111yescharacteristic
136C2×C4×C17#13111yescharacteristic
137C2×Dic17—22no—
138C2×Dic17—41no—
139C2×Dic17—41no—
140C2×Dic17—41no—
141C2×Dic17—81no—
142Dic34—22no—
143Dic34—22no—
144Dic34—41no—
145Dic34—41no—
146C8×C17—42no—
147C8×C17—42no—
148#3622—22no—
149#3622—41no—
150#3622—81no—
151#3622—81no—
152#2983D1711yescharacteristic
153C2×#441—171no—
154#1479—171no—
155#1479—171no—
156#1461—171no—
157#1281—171no—
158#1275—171no—
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—42no—
169C4×C17—42no—
170C4×C17#40711yescharacteristic
171C4×C17#40811yescharacteristic
172C4×C17#43511yescharacteristic
173C4×C17#43611yescharacteristic
174Dic17—42no—
175Dic17—81no—
176C22×Q16—171no—
177C2×C4×Q8—171no—
178C2×C4×Q8C2×D1711yescharacteristic
179#446—22no—
180#446—22no—
181#441—342no—
182#441—342no—
183#432—22no—
184#431—171no—
185#431—171no—
186#431C2×D1711yescharacteristic
187#431C2×D1711yescharacteristic
188C2×#106—171no—
189C2×#103—171no—
190C2×#103—171no—
191C2×#97—171no—
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×Q8C4×D1711yescharacteristic
202C2×Q16—342no—
203C2×Q16—342no—
204C2×Q16—342no—
205C22×C8—171no—
206C22×C8—171no—
207C4×Q8—21no—
208C4×Q8—21no—
209C4×Q8—341no—
210C4×Q8—341no—
211C4×Q8—341no—
212C4×Q8—341no—
213C4×Q8D6812yes—
214C4×Q8C22⋊D1712yes—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—171no—
217C2×C4⋊C4—341no—
218C2×C4⋊C4C4×D1711yescharacteristic
219C2×C42—21no—
220C2×C42—341no—
221C2×C42C22×D1711yescharacteristic
222#106—342no—
223C4⋊C8—24no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—341no—
227C4⋊C8—341no—
228#103—342no—
229#103—342no—
230C22⋊C8—21no—
231C22⋊C8—341no—
232C22⋊C8—341no—
233C22⋊C8C22⋊D1712yes—
234#97—24no—
235#97—341no—
236#97—341no—
237C4×C8—21no—
238C4×C8—341no—
239C4×C8—341no—
240C4×C8C22⋊D1712yes—
241C17#909211yescharacteristic, complemented, Sylow
242C2×Q8—21no—
243C2×Q8—21no—
244C2×Q8—21no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—172no—
248C2×Q8—341no—
249C2×Q8—341no—
250C2×Q8—341no—
251C2×Q8—341no—
252C2×Q8—341no—
253C2×Q8#6322712yes—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—341no—
257C22×C4—341no—
258C22×C4C2×C4×D1711yescharacteristic
259C22×C4#6325211yescharacteristic
260C22×C4C2×C22⋊D1711yescharacteristic
261Q16—348no—
262C2×C8—22no—
263C2×C8—22no—
264C2×C8—172no—
265C2×C8—341no—
266C2×C8—341no—
267C2×C8—341no—
268C2×C8—341no—
269C2×C8—341no—
270C2×C8—681no—
271C2×C8—681no—
272C4⋊C4—21no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—341no—
276C4⋊C4—341no—
277C4⋊C4—681no—
278C4⋊C4—681no—
279C4⋊C4#6322712yes—
280C42—22no—
281C42—22no—
282C42—681no—
283C42—681no—
284C42C2×D6811yescharacteristic
285C42#6325211yescharacteristic
286C42C2×C22⋊D1711yescharacteristic
287C42C2×C22⋊D1711yescharacteristic
288C23C4×C22⋊D1711yescharacteristic
289Q8—22no—
290Q8—22no—
291Q8—41no—
292Q8—41no—
293Q8—342no—
294Q8—342no—
295Q8—681no—
296Q8—681no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—81no—
304C2×C4—342no—
305C2×C4—681no—
306C2×C4—681no—
307C2×C4—681no—
308C2×C4—1361no—
309C2×C4M16×D1711yescharacteristic
310C2×C4M16×D1711yescharacteristic
311C2×C4#1058759311yescharacteristic
312C2×C4#1058759311yescharacteristic
313C2×C4C2×#6322711yescharacteristic
314C2×C4C4×C22⋊D1711yescharacteristic
315C2×C4#1058761511yescharacteristic
316C2×C4#1058761611yescharacteristic
317C2×C4#1058761611yescharacteristic
318C2×C4#1058763911yescharacteristic
319C8—42no—
320C8—42no—
321C8—342no—
322C8—681no—
323C8—1361no—
324C8—1361no—
325C22—21no—
326C22—21no—
327C22#1176268811yescharacteristic
328C22#1176287811yescharacteristic
329C22#1176288511yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—42no—
335C4—42no—
336C4—682no—
337C4—1361no—
338C4#1176277211yescharacteristic
339C4#1176277711yescharacteristic
340C4#1176287811yescharacteristic
341C4#1176288511yescharacteristic
342C2—21no—
343C2—21no—
344C2#1452908111yescharacteristic
345C2#1452925711yescharacteristic
346C2#1452927811yescharacteristic
subgroupG/H
centerC22#11762688
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#2983C2
socleC22×C17#386
prime radicalC23×C17C4×D4
cosocleC2×C42×C17C23
hypercenter#2983D17
hypocenterC17#9092
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

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
C2×#117629142
#145271802
#145271792
#145271072
#145266282
#145266142
C17×#29832
#909217