Finite Group Databasebeta

← #16929949

Subgroups — #16929949

Order 4352.

530 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537094C211yesmaximal, characteristic
2#14528546C211yesmaximal, characteristic
3C2×#11762550C212yesmaximal, complemented
4#14526666C212yesmaximal, complemented
5C2×C17×#432C211yesmaximal, characteristic
6C2×#10587556C2211yescharacteristic
7C2×C22⋊#3622—21no—
8C2×#10587474C2212yes—
9#11762707C411yescharacteristic
10#11762707C411yescharacteristic
11#11762693—21no—
12#11762693—21no—
13#11762682—21no—
14#11762682—21no—
15#11762675C2211yescharacteristic
16#11762669C411yescharacteristic
17#11762669C411yescharacteristic
18#11762564—21no—
19#11762550—24no—
20C22×C42×C17C2211yescharacteristic
21C17×#432—24no—
22C2×C17×C4⋊C8—21no—
23C2×C17×C22⋊C8—21no—
24C2×C17×#97C2212yes—
25C23×C4×C17C2×C411yescharacteristic
26C23×C4×C17D411yescharacteristic
27C23×C4×C17D411yescharacteristic
28C22×C8×C17—22no—
29C2×C42×C17—22no—
30C2×C42×C17—22no—
31C2×C42×C17C2×C411yescharacteristic
32C2×C42×C17D411yescharacteristic
33C2×C42×C17D411yescharacteristic
34C2×C42×C17C2311yescharacteristic
35C2×C22⋊Dic17—21no—
36C2×C22⋊Dic17—21no—
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—
45C22×#3622—22no—
46#10587556—22no—
47#10587556—22no—
48C17×C4⋊C8—24no—
49C17×C22⋊C8—24no—
50C17×#97—22no—
51C17×#97D414yes—
52#10587502—21no—
53#10587502—21no—
54#10587502—21no—
55#10587502—21no—
56#10587502—21no—
57#10587502—21no—
58C22⋊#3622—24no—
59#10587474—22no—
60#10587474—22no—
61C24×C17C22⋊C411yescharacteristic
62C22×C4×C17—22no—
63C22×C4×C17—22no—
64C22×C4×C17—22no—
65C22×C4×C17—21no—
66C22×C4×C17—22no—
67C22×C4×C17—21no—
68C22×C4×C17—41no—
69C22×C4×C17—41no—
70C22×C4×C17—41no—
71C22×C4×C17—41no—
72C22×C4×C17C22⋊C411yescharacteristic
73C22×C4×C17C22⋊C411yescharacteristic
74C22×C4×C17C22⋊C411yescharacteristic
75C22×C4×C17C22×C411yescharacteristic
76C22×C4×C17C2×D411yescharacteristic
77C22×C4×C17C2×D411yescharacteristic
78C22×Dic17—21no—
79C22×Dic17—21no—
80C22×Dic17—21no—
81C22×Dic17—21no—
82C2×C8×C17—24no—
83C2×C8×C17—42no—
84C2×C8×C17—42no—
85C42×C17—22no—
86C42×C17—21no—
87C42×C17—22no—
88C42×C17—21no—
89C42×C17C2×D412yes—
90C42×C17#4112yes—
91C22⋊Dic17—42no—
92C22⋊Dic17—42no—
93C4⋊Dic17—22no—
94C4⋊Dic17—22no—
95C4⋊Dic17—41no—
96C4⋊Dic17—41no—
97#63225—42no—
98#63225—42no—
99#63225—41no—
100#63225—42no—
101#63225—41no—
102C2×#3622—24no—
103C2×#3622—42no—
104C2×#3622—42no—
105#9125—171nomaximal, Sylow
106C23×C17—21no—
107C23×C17—21no—
108C23×C17—21no—
109C23×C17—21no—
110C23×C17—21no—
111C23×C17—21no—
112C23×C17#10412yes—
113C23×C17C2×C22⋊C411yescharacteristic
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—21no—
128C2×C4×C17—44no—
129C2×C4×C17—44no—
130C2×C4×C17—42no—
131C2×C4×C17—42no—
132C2×C4×C17#10112yes—
133C2×C4×C17C4×D412yes—
134C2×C4×C17#12011yescharacteristic
135C2×C4×C17#12112yes—
136C2×C4×C17#12311yescharacteristic
137C2×Dic17—41no—
138C2×Dic17—41no—
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—44no—
150#3622—44no—
151C2×#432D1711yescharacteristic
152#2851—171no—
153#1749—171no—
154C2×#330—172no—
155#1295—172no—
156C22×C17—22no—
157C22×C17—22no—
158C22×C17—22no—
159C22×C17—41no—
160C22×C17—41no—
161C22×C17—41no—
162C22×C17—41no—
163C22×C17#38611yescharacteristic
164C22×C17C2×#10111yescharacteristic
165C22×C17#41311yescharacteristic
166C22×C17C2×#10411yescharacteristic
167C22×C17#42111yescharacteristic
168C22×C17#42111yescharacteristic
169C22×C17#42111yescharacteristic
170C4×C17—22no—
171C4×C17—21no—
172C4×C17—21no—
173C4×C17—22no—
174C4×C17—22no—
175C4×C17—41no—
176C4×C17—41no—
177Dic17—81no—
178Dic17—81no—
179Dic17—81no—
180Dic17—81no—
181C2×#125—171no—
182C22×C42C2×D1711yescharacteristic
183#432—24no—
184C2×C4⋊C8—21no—
185C2×C22⋊C8—21no—
186C2×C22⋊C8—341no—
187C2×#97—172no—
188C2×#97C2×D1712yes—
189#389—171no—
190#389—171no—
191#387—341no—
192#387—341no—
193#385—341no—
194#385—341no—
195#382—171no—
196#380—171no—
197#380—171no—
198#336—341no—
199#330—344no—
200C2×C17—42no—
201C2×C17#152811yescharacteristic
202C2×C17#153211yescharacteristic
203C2×C17#153511yescharacteristic
204C2×C17#153711yescharacteristic
205C2×C17#187111yescharacteristic
206C2×C17#189711yescharacteristic
207C2×C17#190111yescharacteristic
208C23×C4C4×D1711yescharacteristic
209C23×C4D6811yescharacteristic
210C23×C4C22⋊D1711yescharacteristic
211C22×C8—22no—
212C22×C8—342no—
213#125—342no—
214#125—342no—
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—22no—
226C2×C42—22no—
227C2×C42C4×D1711yescharacteristic
228C2×C42D6811yescharacteristic
229C2×C42C22⋊D1711yescharacteristic
230C2×C42C22×D1711yescharacteristic
231C4⋊C8—24no—
232C22⋊C8—24no—
233C22⋊C8—344no—
234#97—22no—
235#97—342no—
236#97—342no—
237#97C22⋊D1714yes—
238#95—341no—
239#95—341no—
240#95—341no—
241#95—341no—
242#95—341no—
243#95—341no—
244C17#912511yescharacteristic, complemented, Sylow
245C24#6322711yescharacteristic
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—21no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—341no—
257C22×C4—341no—
258C22×C4—341no—
259C22×C4—341no—
260C22×C4#6322711yescharacteristic
261C22×C4#6322711yescharacteristic
262C22×C4#6322711yescharacteristic
263C22×C4C2×C4×D1711yescharacteristic
264C22×C4C2×D6811yescharacteristic
265C22×C4C2×C22⋊D1711yescharacteristic
266C2×C8—24no—
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—344no—
270C2×C8—682no—
271C2×C8—682no—
272C4⋊C4—342no—
273C4⋊C4—342no—
274C4⋊C4—681no—
275C4⋊C4—681no—
276C4⋊C4—682no—
277C4⋊C4—682no—
278C4⋊C4—681no—
279C4⋊C4—682no—
280C4⋊C4—681no—
281C22⋊C4—682no—
282C22⋊C4—682no—
283C42—22no—
284C42—21no—
285C42—22no—
286C42—21no—
287C42#6325212yes—
288C42C2×C22⋊D1712yes—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23#1058749612yes—
296C23C2×#6322711yescharacteristic
297C2×C4—21no—
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—44no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—681no—
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—681no—
327C2×C4#1058749512yes—
328C2×C4C4×C22⋊D1712yes—
329C2×C4#1058761511yescharacteristic
330C2×C4#1058761612yes—
331C2×C4#1058763911yescharacteristic
332C8—44no—
333C8—684no—
334C22—22no—
335C22—22no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22#1176268811yescharacteristic
342C22C2×#1058749511yescharacteristic
343C22#1176279111yescharacteristic
344C22C2×#1058749611yescharacteristic
345C22#1176282511yescharacteristic
346C22#1176282711yescharacteristic
347C22#1176282711yescharacteristic
348C4—22no—
349C4—21no—
350C4—21no—
351C4—22no—
352C4—22no—
353C4—41no—
354C4—41no—
355C4—1361no—
356C4—1361no—
357C4—1361no—
358C4—1361no—
359C2—42no—
360C2#1452738711yescharacteristic
361C2#1452740511yescharacteristic
362C2#1452741611yescharacteristic
363C2#1452742111yescharacteristic
364C2#1452908611yescharacteristic
365C2#1452923211yescharacteristic
366C2#1452925211yescharacteristic
subgroupG/H
centerC23C2×#63227
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC2×C17×#432C2
socleC23×C17C2×C22⋊C4
prime radicalC24×C17C22⋊C4
cosocleC2×C42×C17C23
hypercenterC2×#432D17
hypocenterC17#9125
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
3. C2×#11762550C2semidirect
4. #14526666C2semidirect
244. C17#9125semidirect

Maximal subgroups

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

subgroupindex
#145370942
#145285462
C2×#117625502
#145266662
C2×C17×#4322
#912517