Finite Group Databasebeta

← #16931081

Subgroups — #16931081

Order 4352.

488 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537808C211yesmaximal, characteristic
2#14528794C211yesmaximal, characteristic
3#14527348C211yesmaximal, characteristic, complemented
4#14527187C211yesmaximal, characteristic, complemented
5#14526679C211yesmaximal, characteristic, complemented
6#14526644C211yesmaximal, characteristic, complemented
7C17×#3077C211yesmaximal, characteristic
8D4×#3622—22no—
9D4×#3622—22no—
10#11762862C2211yescharacteristic
11#11762862C2211yescharacteristic
12C2×C4⋊#3622C2211yescharacteristic
13C2×#10587503—21no—
14C2×C22⋊#3622—22no—
15#11762675C2211yescharacteristic
16#11762571—21no—
17#11762546—22no—
18Q8⋊#3622—22no—
19C17×#533C2211yescharacteristic
20C2×C4×D4×C17C2211yescharacteristic
21C17×#478—22no—
22C17×#476C412yescomplemented
23C17×#474C412yescomplemented
24C17×#428—21no—
25C17×#423C2211yescharacteristic
26C17×#418—21no—
27C22×D4×C17D411yescharacteristic
28C23×C4×C17—21no—
29C2×M16×C17—21no—
30C17×C4⋊Q8C2×C411yescharacteristic
31C17×C4⋊Q8C2×C411yescharacteristic
32C17×#125—21no—
33C17×C22⋊Q8—21no—
34C17×C22⋊Q8—21no—
35C4×Q8×C17—21no—
36C4×Q8×C17—21no—
37C4×D4×C17—21no—
38C4×D4×C17—21no—
39C4×D4×C17C2×C412yes—
40C4×D4×C17D412yes—
41C17×#117—21no—
42C2×C4⋊C4×C17D411yescharacteristic
43C2×C22⋊C4×C17—21no—
44C2×C42×C17C2311yescharacteristic
45C2×C4⋊Dic17—21no—
46C22×#3622—24no—
47C22×#3622—21no—
48C17×#107—22no—
49C17×#106—22no—
50C17×C4⋊C8—21no—
51C17×C4⋊C8C2×C412yes—
52C17×#102—22no—
53C17×#102—22no—
54#10587503—42no—
55#10587502—21no—
56#10587502—21no—
57C22⋊#3622—24no—
58C22⋊#3622—21no—
59C22⋊#3622D412yes—
60C4⋊#3622—21no—
61C4⋊#3622—21no—
62C4⋊#3622—21no—
63C4⋊#3622—21no—
64C4×#3622—21no—
65C4×#3622D412yes—
66C24×C17—21no—
67C2×Q8×C17—21no—
68C2×Q8×C17—21no—
69C2×D4×C17—21no—
70C2×D4×C17—21no—
71C2×D4×C17—21no—
72C2×D4×C17C22⋊C412yes—
73C2×D4×C17SD1612yes—
74C2×D4×C17Q1612yes—
75C22×C4×C17—21no—
76C22×C4×C17—22no—
77C22×C4×C17—22no—
78C22×C4×C17—82no—
79C22×C4×C17C2×D411yescharacteristic
80C22×C4×C17C2×D411yescharacteristic
81C22×C4×C17#4111yescharacteristic
82C22×Dic17—41no—
83M16×C17—41no—
84M16×C17—41no—
85C2×C8×C17—22no—
86C4⋊C4×C17—21no—
87C4⋊C4×C17—21no—
88C4⋊C4×C17—21no—
89C4⋊C4×C17—21no—
90C4⋊C4×C17—21no—
91C4⋊C4×C17—41no—
92C4⋊C4×C17—41no—
93C4⋊C4×C17C22⋊C412yes—
94C22⋊C4×C17—22no—
95C22⋊C4×C17—22no—
96C22⋊C4×C17—41no—
97C42×C17—41no—
98C42×C17C22×C411yescharacteristic
99C42×C17C2×D411yescharacteristic
100C42×C17C2×D411yescharacteristic
101C42×C17#4111yescharacteristic
102C4⋊Dic17—41no—
103C4⋊Dic17—41no—
104C2×#3622—22no—
105C2×#3622—22no—
106C2×#3622—41no—
107C2×#3622—41no—
108C2×#3622—41no—
109C2×#3622—84no—
110#9303—171nomaximal, Sylow
111C23×C17—22no—
112C23×C17—22no—
113C23×C17—22no—
114C23×C17—81no—
115C23×C17—81no—
116C23×C17#12111yescharacteristic
117Q8×C17—42no—
118Q8×C17—81no—
119D4×C17—22no—
120D4×C17—22no—
121D4×C17—22no—
122D4×C17#10314yes—
123C2×C4×C17—22no—
124C2×C4×C17—41no—
125C2×C4×C17—41no—
126C2×C4×C17—44no—
127C2×C4×C17—41no—
128C2×C4×C17—41no—
129C2×C4×C17—82no—
130C2×C4×C17—81no—
131C2×C4×C17C2×C22⋊C411yescharacteristic
132C2×C4×C17C4×D411yescharacteristic
133C2×C4×C17C4×D411yescharacteristic
134C2×C4×C17#12011yescharacteristic
135C2×C4×C17#12111yescharacteristic
136C2×C4×C17#12311yescharacteristic
137C2×C4×C17C2×SD1611yescharacteristic
138C2×C4×C17C2×Q1611yescharacteristic
139C2×C4×C17#13511yescharacteristic
140C2×C4×C17#13511yescharacteristic
141C2×Dic17—81no—
142C2×Dic17—81no—
143C2×Dic17—81no—
144C8×C17—42no—
145#3622—42no—
146#3622—42no—
147#3622—81no—
148#3077D1711yescharacteristic
149#2972—171no—
150#1804—171no—
151#1518—171no—
152#1481—171no—
153#1301—171no—
154#1286—171no—
155C22×C17—21no—
156C22×C17—21no—
157C22×C17—24no—
158C22×C17—42no—
159C22×C17—42no—
160C22×C17—82no—
161C22×C17—82no—
162C22×C17#38611yescharacteristic
163C22×C17#46511yescharacteristic
164C22×C17#46711yescharacteristic
165C4×C17—21no—
166C4×C17—21no—
167C4×C17—21no—
168C4×C17—21no—
169C4×C17—42no—
170C4×C17—81no—
171C4×C17—81no—
172C4×C17C2×#10311yescharacteristic
173C4×C17#41611yescharacteristic
174C4×C17#46511yescharacteristic
175C4×C17#46711yescharacteristic
176Dic17—161no—
177#533C2×D1711yescharacteristic
178C2×C4×D4C2×D1711yescharacteristic
179#478—22no—
180#476Dic1712yescomplemented
181#474Dic1712yescomplemented
182C8×D4—342no—
183C8×D4—342no—
184#431—171no—
185#431—171no—
186#428—21no—
187#423C2×D1711yescharacteristic
188C2×C4⋊C8—171no—
189#418—21no—
190C2×#102—341no—
191C2×C22⋊C8—342no—
192#382—171no—
193#340—341no—
194#328—342no—
195Q8⋊C8—342no—
196C2×C17—21no—
197C2×C17—21no—
198C2×C17—44no—
199C2×C17#188111yescharacteristic
200C2×C17#189211yescharacteristic
201C2×C17#190411yescharacteristic
202C22×D4C22⋊D1711yescharacteristic
203C23×C4—21no—
204C2×M16—21no—
205C22×C8—344no—
206C22×C8—341no—
207C4⋊Q8C2×Dic1711yescharacteristic
208C4⋊Q8C2×Dic1711yescharacteristic
209#125—21no—
210C22⋊Q8—21no—
211C22⋊Q8—21no—
212C4×Q8—21no—
213C4×Q8—21no—
214C4×D4—21no—
215C4×D4—21no—
216C4×D4C2×Dic1712yes—
217C4×D4C22⋊D1712yes—
218#117—21no—
219C2×C4⋊C4—341no—
220C2×C4⋊C4C22⋊D1711yescharacteristic
221C2×C22⋊C4—21no—
222C2×C42C22×D1711yescharacteristic
223#107—22no—
224#106—22no—
225C4⋊C8—21no—
226C4⋊C8—341no—
227C4⋊C8—341no—
228C4⋊C8—341no—
229C4⋊C8—341no—
230C4⋊C8C2×Dic1712yes—
231#102—22no—
232#102—22no—
233#102—682no—
234C22⋊C8—172no—
235C22⋊C8—344no—
236C22⋊C8—341no—
237C4×C8—172no—
238C4×C8—341no—
239#95—341no—
240#95—341no—
241C17#930311yescharacteristic, complemented, Sylow
242C24—21no—
243C2×Q8—21no—
244C2×Q8—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4#6323012yes—
249C2×D4#6323112yes—
250C2×D4C22⋊Dic1712yes—
251C22×C4—21no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—82no—
255C22×C4—681no—
256C22×C4D4×D1711yescharacteristic
257C22×C4#6325411yescharacteristic
258C22×C4C2×C22⋊D1711yescharacteristic
259M16—41no—
260M16—41no—
261C2×C8—22no—
262C2×C8—342no—
263C2×C8—342no—
264C2×C8—681no—
265C2×C8—681no—
266C2×C8—681no—
267C2×C8—1364no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—681no—
276C4⋊C4—681no—
277C4⋊C4C22⋊Dic1712yes—
278C22⋊C4—22no—
279C22⋊C4—22no—
280C22⋊C4—41no—
281C42—41no—
282C42D4×D1711yescharacteristic
283C42#6325411yescharacteristic
284C42C22×Dic1711yescharacteristic
285C42C2×C22⋊D1711yescharacteristic
286C23—22no—
287C23—22no—
288C23—22no—
289C23—81no—
290C23—81no—
291C23#1058762511yescharacteristic
292Q8—42no—
293Q8—81no—
294D4—22no—
295D4—22no—
296D4—22no—
297D4#1058750614yes—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—44no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—82no—
305C2×C4—81no—
306C2×C4—1361no—
307C2×C4—1361no—
308C2×C4—1361no—
309C2×C4D4×Dic1711yescharacteristic
310C2×C4D4×Dic1711yescharacteristic
311C2×C4#1058762111yescharacteristic
312C2×C4#1058762311yescharacteristic
313C2×C4#1058762511yescharacteristic
314C2×C4C2×#6323011yescharacteristic
315C2×C4C2×#6323111yescharacteristic
316C2×C4#1058763611yescharacteristic
317C2×C4#1058763611yescharacteristic
318C2×C4C2×C22⋊Dic1711yescharacteristic
319C8—42no—
320C8—682no—
321C8—682no—
322C8—1361no—
323C22—21no—
324C22—21no—
325C22—24no—
326C22—42no—
327C22—42no—
328C22—82no—
329C22—82no—
330C22#1176268911yescharacteristic
331C22#1176304011yescharacteristic
332C22#1176304811yescharacteristic
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—42no—
338C4—81no—
339C4—81no—
340C4—2721no—
341C4C2×#1058750611yescharacteristic
342C4#1176280511yescharacteristic
343C4#1176304011yescharacteristic
344C4#1176304811yescharacteristic
345C2—21no—
346C2—21no—
347C2—44no—
348C2#1452914811yescharacteristic
349C2#1452920811yescharacteristic
350C2#1452927311yescharacteristic
subgroupG/H
centerC22#11762689
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#3077C2
socleC22×C17#386
prime radicalC22×D4×C17D4
cosocleC2×C42×C17C23
hypercenter#3077D17
hypocenterC17#9303
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
3. #14527348C2semidirect
4. #14527187C2semidirect
5. #14526679C2semidirect
6. #14526644C2semidirect
22. C17×#476C4semidirect
23. C17×#474C4semidirect
180. #476Dic17semidirect
181. #474Dic17semidirect
241. C17#9303semidirect

Maximal subgroups

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

subgroupindex
#145378082
#145287942
#145273482
#145271872
#145266792
#145266442
C17×#30772
#930317