Finite Group Databasebeta

← #16950632

Subgroups — #16950632

Order 4352.

442 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#107×D17C211yesmaximal, characteristic
2#14530394C211yesmaximal, characteristic
3#14528819C211yesmaximal, characteristic
4#14526894C211yesmaximal, characteristic, complemented
5#14526893C211yesmaximal, characteristic, complemented
6#14526892C211yesmaximal, characteristic, complemented
7C17×#1387C211yesmaximal, characteristic, complemented
8C22×C8×D17C2211yescharacteristic
9C2×C4⋊C4×D17—21no—
10C2×#10587483C2211yescharacteristic
11C2×#10587490C2211yescharacteristic
12C2×#10587489C2211yescharacteristic
13C2×#10587478—21no—
14#107×D17—21no—
15#107×D17—21no—
16#107×D17C412yes—
17#107×D17C412yes—
18#11762772—21no—
19#11762588—21no—
20#11762588—21no—
21#11762573—21no—
22C2×C17×M32C2211yescharacteristic
23C2×C17×#108C2211yescharacteristic
24C2×C17×#107C2211yescharacteristic
25C22×C4×D17—41no—
26C22×C4×D17D411yescharacteristic
27C2×M16×C17—21no—
28C22×C8×C17C2311yescharacteristic
29C2×C4⋊C4×C17—21no—
30C2×C4⋊Dic17—21no—
31C2×#63225—41no—
32C2×#63223—21no—
33C22×#3622D411yescharacteristic
34C2×C8×D17—21no—
35C2×C8×D17—21no—
36C2×C8×D17—21no—
37C2×C8×D17—21no—
38C2×C8×D17C2×C411yescharacteristic
39C2×C8×D17C2×C411yescharacteristic
40C2×C8×D17D411yescharacteristic
41C2×C8×D17D411yescharacteristic
42C4⋊C4×D17—22no—
43C4⋊C4×D17—22no—
44C4⋊C4×D17—41no—
45C4⋊C4×D17—41no—
46C17×M32—21no—
47C17×M32—21no—
48C2×C16×C17—21no—
49C17×#108—21no—
50C17×#108—21no—
51C17×#107—21no—
52C17×#107C2×C412yes—
53#10587491—41no—
54#10587491—41no—
55#10587490—21no—
56#10587490—21no—
57#10587489—21no—
58#10587489C2×C412yes—
59#10587483—21no—
60#10587483—21no—
61C2×#63214—21no—
62#10587478—22no—
63#10587478—22no—
64C23×D17SD1611yescharacteristic
65C22×C4×C17—41no—
66C22×C4×C17C2×D411yescharacteristic
67C22×Dic17—41no—
68C22×Dic17SD1611yescharacteristic
69C2×C4×D17—21no—
70C2×C4×D17—21no—
71C2×C4×D17—21no—
72C2×C4×D17—21no—
73C2×C4×D17—42no—
74C2×C4×D17—42no—
75C2×C4×D17—84no—
76C2×C4×D17C22⋊C411yescharacteristic
77C2×C4×D17C22⋊C411yescharacteristic
78C2×C4×D17D811yescharacteristic
79C2×C4×D17D811yescharacteristic
80M16×C17—41no—
81M16×C17—41no—
82C2×C8×C17—41no—
83C2×C8×C17C22×C411yescharacteristic
84C2×C8×C17C2×D411yescharacteristic
85C2×C8×C17#4111yescharacteristic
86C2×C8×C17#4111yescharacteristic
87C2×C8×C17#4111yescharacteristic
88C2×C8×C17#4111yescharacteristic
89C4⋊C4×C17—22no—
90C4⋊C4×C17—41no—
91C4⋊Dic17—22no—
92C4⋊Dic17—41no—
93#63225—42no—
94#63225—42no—
95#63223—41no—
96#63223—41no—
97C2×#3622—21no—
98C2×#3622—21no—
99C2×#3622—41no—
100C2×#3622C22⋊C411yescharacteristic
101C2×#3622C22⋊C411yescharacteristic
102C8×D17—21no—
103C8×D17—21no—
104C8×D17—21no—
105C8×D17—21no—
106C8×D17—21no—
107C8×D17—21no—
108C8×D17—21no—
109C8×D17—21no—
110C16×C17—41no—
111#63214—41no—
112#12871—171nomaximal, Sylow
113C23×C17C2×SD1611yescharacteristic
114C22×D17—21no—
115C22×D17—21no—
116C22×D17—22no—
117C22×D17—22no—
118C22×D17#10211yescharacteristic
119C22×D17#10211yescharacteristic
120C2×C4×C17—42no—
121C2×C4×C17—82no—
122C2×C4×C17C2×C22⋊C411yescharacteristic
123C2×C4×C17#12311yescharacteristic
124C2×C4×C17#12311yescharacteristic
125C2×C4×C17C2×D811yescharacteristic
126C2×C4×C17#13711yescharacteristic
127C2×C4×C17#13711yescharacteristic
128C2×Dic17—21no—
129C2×Dic17—21no—
130C2×Dic17—42no—
131C2×Dic17—82no—
132C2×Dic17#10211yescharacteristic
133C2×Dic17#10211yescharacteristic
134C4×D17—21no—
135C4×D17—21no—
136C4×D17—21no—
137C4×D17—21no—
138C4×D17—21no—
139C4×D17—21no—
140C4×D17—21no—
141C4×D17—21no—
142C4×D17—84no—
143C4×D17—84no—
144C8×C17—81no—
145C8×C17#11711yescharacteristic
146C8×C17#11711yescharacteristic
147C8×C17#12311yescharacteristic
148C8×C17#12311yescharacteristic
149#3622—21no—
150#3622—21no—
151#3622—81no—
152C22×#107—171no—
153#2112—171no—
154#1810—171no—
155#1387—171no—
156#1387—171no—
157#1387—171no—
158#1387D1711yescharacteristic, complemented
159C22×C17—21no—
160C22×C17—21no—
161C22×C17C2×#10211yescharacteristic
162C22×C17#48311yescharacteristic
163C22×C17#48311yescharacteristic
164C2×D17—24no—
165C2×D17—24no—
166C2×D17—21no—
167C2×D17—21no—
168C2×D17—21no—
169C2×D17—21no—
170C2×D17#36112yes—
171C2×D17#36212yes—
172C4×C17—82no—
173C4×C17#38111yescharacteristic
174C4×C17#41911yescharacteristic
175C4×C17#48011yescharacteristic
176C4×C17#48011yescharacteristic
177Dic17—21no—
178Dic17—21no—
179Dic17—82no—
180C23×C8—171no—
181C22×C4⋊C4—341no—
182C2×M32—171no—
183C2×M32C2×D1711yescharacteristic
184C2×#108—171no—
185C2×#108C2×D1711yescharacteristic
186C2×#107—171no—
187C2×#107—172no—
188C2×#107—172no—
189C2×#107—341no—
190C2×#107—341no—
191C2×#107—341no—
192C2×#107C2×D1711yescharacteristic
193#407—341no—
194C22⋊C16—341no—
195C22⋊C16—341no—
196#341—341no—
197C2×C17—21no—
198C2×C17—21no—
199C2×C17#182311yescharacteristic
200C2×C17C2×#36111yescharacteristic
201C2×C17C2×#36211yescharacteristic
202D17—22no—
203D17—22no—
204C23×C4—171no—
205C23×C4—681no—
206C2×M16—21no—
207C2×M16—341no—
208C22×C8—171no—
209C22×C8—171no—
210C22×C8—171no—
211C22×C8—171no—
212C22×C8—171no—
213C22×C8—341no—
214C22×C8—341no—
215C22×C8—341no—
216C22×C8—341no—
217C22×C8C22×D1711yescharacteristic
218C2×C4⋊C4—21no—
219C2×C4⋊C4—342no—
220C2×C4⋊C4—342no—
221C2×C4⋊C4—341no—
222C2×C4⋊C4—681no—
223C2×C4⋊C4—681no—
224C2×C4⋊C4—681no—
225M32—21no—
226M32—21no—
227M32—341no—
228M32—341no—
229C2×C16—21no—
230C2×C16—341no—
231#108—21no—
232#108—21no—
233#108—341no—
234#108—341no—
235#107—21no—
236#107—172no—
237#107—342no—
238#107—342no—
239#107—341no—
240#107C4×D1712yes—
241C22⋊C8—681no—
242C22⋊C8—681no—
243C17#1287111yescharacteristic, complemented, Sylow
244C24—171no—
245C22×C4—41no—
246C22×C4—171no—
247C22×C4—171no—
248C22×C4—171no—
249C22×C4—171no—
250C22×C4—171no—
251C22×C4—341no—
252C22×C4—341no—
253C22×C4—341no—
254C22×C4—341no—
255C22×C4—682no—
256C22×C4—682no—
257C22×C4—681no—
258C22×C4—1364no—
259C22×C4D4×D1711yescharacteristic
260M16—41no—
261M16—41no—
262M16—681no—
263M16—681no—
264C2×C8—41no—
265C2×C8—171no—
266C2×C8—171no—
267C2×C8—341no—
268C2×C8—341no—
269C2×C8—341no—
270C2×C8—341no—
271C2×C8—341no—
272C2×C8—341no—
273C2×C8—341no—
274C2×C8—341no—
275C2×C8—341no—
276C2×C8—341no—
277C2×C8—681no—
278C2×C8C2×C4×D1711yescharacteristic
279C2×C8#6325211yescharacteristic
280C2×C8#6325211yescharacteristic
281C2×C8D4×D1711yescharacteristic
282C2×C8#6325411yescharacteristic
283C2×C8#6325611yescharacteristic
284C4⋊C4—22no—
285C4⋊C4—41no—
286C4⋊C4—342no—
287C4⋊C4—682no—
288C4⋊C4—682no—
289C4⋊C4—681no—
290C16—41no—
291C16—681no—
292C23—171no—
293C23—171no—
294C23—342no—
295C23—342no—
296C23—341no—
297C23—341no—
298C23SD16×D1711yescharacteristic
299C2×C4—42no—
300C2×C4—82no—
301C2×C4—171no—
302C2×C4—171no—
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—341no—
312C2×C4—341no—
313C2×C4—682no—
314C2×C4—1364no—
315C2×C4—1364no—
316C2×C4—1362no—
317C2×C4C22⋊C4×D1711yescharacteristic
318C2×C4#1058756911yescharacteristic
319C2×C4#1058758011yescharacteristic
320C2×C4D8×D1711yescharacteristic
321C2×C4#1058760111yescharacteristic
322C2×C4#1058760411yescharacteristic
323C8—81no—
324C8—341no—
325C8—341no—
326C8—1361no—
327C8#1058755811yescharacteristic
328C8#1058756911yescharacteristic
329C8#1058757811yescharacteristic
330C8#1058758011yescharacteristic
331C22—21no—
332C22—21no—
333C22—172no—
334C22—172no—
335C22—344no—
336C22—344no—
337C22—341no—
338C22—341no—
339C22—341no—
340C22—341no—
341C22#102×D1711yescharacteristic
342C22#1176313811yescharacteristic
343C22#1176314111yescharacteristic
344C4—82no—
345C4—341no—
346C4—341no—
347C4—1362no—
348C4#1176267111yescharacteristic
349C4#1176281611yescharacteristic
350C4#1176312111yescharacteristic
351C4#1176312411yescharacteristic
352C2—21no—
353C2—21no—
354C2—342no—
355C2—342no—
356C2#1452886911yescharacteristic
357C2D17×#36111yescharacteristic
358C2D17×#36211yescharacteristic
subgroupG/H
centerC22#102×D17
commutatorC2×C8×C17C22×C4
FrattiniC22×C8C22×D17
FittingC17×#1387C2
socleC22×C17C2×#102
prime radicalC23×D17SD16
cosocleC22×C8×C17C23
hypercenter#1387D17
hypocenterC17#12871
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1387

Complements

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

NH ≅ G/Ntype
4. #14526894C2semidirect
5. #14526893C2semidirect
6. #14526892C2semidirect
7. C17×#1387C2semidirect
158. #1387D17semidirect
243. C17#12871semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D172
#145303942
#145288192
#145268942
#145268932
#145268922
C17×#13872
#1287117