Finite Group Databasebeta

← #17951268

Subgroups — #17951268

Order 4352.

696 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545231C211yesmaximal, characteristic
2C4×#10587677C211yesmaximal, characteristic
3#14543664C214yesmaximal
4#14537416C211yesmaximal, characteristic
5C2×#10587677—21no—
6#11763754C412yescomplemented
7#11763753C412yescomplemented
8#11763752—21no—
9#11763751—21no—
10C4×C4⋊#595—21no—
11C4×C4⋊#595—21no—
12C4×C4⋊#595C412yescomplemented
13C4×C22⋊#595—21no—
14C4×C22⋊#595C2212yes—
15C4×C22⋊#595C2212yes—
16#11763745—21no—
17#11763745C412yescomplemented
18C42×#595—21no—
19C2×C42×D17C2211yescharacteristic
20#11762865—21no—
21#11762865—21no—
22#11762861—21no—
23#11762861—21no—
24#11762833C411yescharacteristic, complemented
25#11762772C2212yes—
26M16×Dic17C412yescomplemented
27C17×#423C411yescharacteristic, complemented
28C22×C4×D17D411yescharacteristic
29C22×C4×D17D411yescharacteristic
30C22×C4×D17C2311yescharacteristic
31C2×C22⋊#595—22no—
32C2×C22⋊#595—22no—
33#10587677—28no—
34C2×C4⋊#595—22no—
35C2×C4⋊#595—22no—
36C2×C4×#595—22no—
37C2×C4×#595—22no—
38C2×C4×#595—22no—
39C2×C4×#595—22no—
40C2×M16×C17C2×C412yes—
41C2×C42×C17C2×C411yescharacteristic
42C2×C4×Dic17C2×C411yescharacteristic
43C2×C4×Dic17Q811yescharacteristic
44C2×C4×Dic17Q811yescharacteristic
45C2×#63223C2×C412yes—
46C42×D17C2×C411yescharacteristic
47C42×D17C2×C411yescharacteristic
48C42×D17C2×C411yescharacteristic
49C42×D17C2×C411yescharacteristic
50C42×D17D411yescharacteristic
51C42×D17D411yescharacteristic
52C42×D17D411yescharacteristic
53C42×D17D411yescharacteristic
54(C2×#595)⋊C4—22no—
55(C2×#595)⋊C4—22no—
56(C2×#595)⋊C4—22no—
57(C2×#595)⋊C4—22no—
58(C2×#595)⋊C4C2×C414yes—
59(C2×#595)⋊C4C2×C414yes—
60C17×C4⋊C8—21no—
61C17×C4⋊C8—21no—
62#10587491—22no—
63#10587491—22no—
64#10587486—22no—
65C8×Dic17—22no—
66C4⋊#3622—21no—
67C4⋊#3622—21no—
68C23×D17C2×D411yescharacteristic
69C22×#595—24no—
70C22×#595—24no—
71C22×C4×C17C4⋊C411yescharacteristic
72C22×C4×C17C4⋊C411yescharacteristic
73C22×C4×C17C22×C411yescharacteristic
74C22×Dic17C4⋊C411yescharacteristic
75C22×Dic17C4⋊C411yescharacteristic
76C22×Dic17C2×Q811yescharacteristic
77C2×C4×D17—24no—
78C2×C4×D17—41no—
79C2×C4×D17—41no—
80C2×C4×D17—42no—
81C2×C4×D17C22⋊C411yescharacteristic
82C2×C4×D17C22⋊C411yescharacteristic
83C2×C4×D17C22⋊C411yescharacteristic
84C2×C4×D17C22⋊C411yescharacteristic
85C2×C4×D17C22⋊C411yescharacteristic
86C2×C4×D17C22⋊C411yescharacteristic
87C2×C4×D17C22⋊C411yescharacteristic
88C2×C4×D17C22⋊C411yescharacteristic
89C2×C4×D17C22×C411yescharacteristic
90C2×C4×D17C22×C411yescharacteristic
91C2×C4×D17C2×D411yescharacteristic
92C2×C4×D17C2×D411yescharacteristic
93C22⋊#595—28no—
94C22⋊#595—44no—
95C4⋊#595—28no—
96C4⋊#595—44no—
97C4×#595—28no—
98C4×#595—44no—
99C4×#595—42no—
100C4×#595—42no—
101C4×#595—42no—
102C4×#595—42no—
103M16×C17—42no—
104C2×C8×C17—22no—
105C42×C17C4211yescharacteristic
106C42×C17C4211yescharacteristic
107C42×C17C22⋊C411yescharacteristic
108C42×C17C22⋊C411yescharacteristic
109C4×Dic17C4211yescharacteristic
110C4×Dic17C4211yescharacteristic
111C4×Dic17C22⋊C411yescharacteristic
112C4×Dic17C22⋊C411yescharacteristic
113C4×Dic17C4⋊C411yescharacteristic
114C4×Dic17C4⋊C411yescharacteristic
115C4×Dic17C4⋊C411yescharacteristic
116C4×Dic17C4⋊C411yescharacteristic
117C4×Dic17C4⋊C411yescharacteristic
118C4×Dic17C4⋊C411yescharacteristic
119C4×Dic17C4⋊C411yescharacteristic
120C4×Dic17C4⋊C411yescharacteristic
121#63223—42no—
122C2×#3622—22no—
123#8052—171nomaximal, Sylow
124C23×C17C2×C4⋊C411yescharacteristic
125C22×D17—22no—
126C22×D17—22no—
127C22×D17—41no—
128C22×D17C2×C22⋊C411yescharacteristic
129C22×D17C2×C22⋊C411yescharacteristic
130C2×#595—28no—
131C2×#595—44no—
132C2×#595—44no—
133C2×#595—44no—
134C2×#595—44no—
135C2×#595—44no—
136C2×C4×C17—22no—
137C2×C4×C17—21no—
138C2×C4×C17—21no—
139C2×C4×C17—41no—
140C2×C4×C17#9511yescharacteristic
141C2×C4×C17#9511yescharacteristic
142C2×C4×C17#9511yescharacteristic
143C2×C4×C17#9511yescharacteristic
144C2×C4×C17C2×C4211yescharacteristic
145C2×C4×C17C2×C22⋊C411yescharacteristic
146C2×Dic17—22no—
147C2×Dic17—41no—
148C2×Dic17—41no—
149C2×Dic17#9511yescharacteristic
150C2×Dic17#9511yescharacteristic
151C2×Dic17#9511yescharacteristic
152C2×Dic17#9511yescharacteristic
153C2×Dic17C2×C4⋊C411yescharacteristic
154C2×Dic17C2×C4⋊C411yescharacteristic
155C4×D17—22no—
156C4×D17—22no—
157C4×D17—22no—
158C4×D17—22no—
159C4×D17—21no—
160C4×D17—21no—
161C4×D17—21no—
162C4×D17—21no—
163C4×D17—22no—
164C4×D17—41no—
165C4×D17—41no—
166C4×D17—41no—
167C4×D17—41no—
168C4×D17#10414yes—
169C8×C17—42no—
170#3622—42no—
171#2920—171no—
172#2283—171no—
173C4×#117—171no—
174#1297—174no—
175C22×C17—21no—
176C22×C17—21no—
177C22×C17—21no—
178C22×C17C2×#9511yescharacteristic
179C2×D17—21no—
180C2×D17—21no—
181C2×D17—21no—
182C2×D17—21no—
183C2×D17—44no—
184C2×D17C2×#10412yes—
185C2×D17#42112yes—
186#595—48no—
187#595—84no—
188C4×C17—21no—
189C4×C17—21no—
190C4×C17—21no—
191C4×C17—21no—
192C4×C17#33912yes—
193C4×C17#41011yescharacteristic
194C4×C17#41011yescharacteristic
195Dic17—21no—
196Dic17—21no—
197Dic17—21no—
198Dic17—21no—
199Dic17—21no—
200Dic17#33912yes—
201C2×#117—341no—
202C22×C42—171no—
203#432—341no—
204#432—341no—
205#431—341no—
206#431—341no—
207#423—171no—
208#423#59511yescharacteristic, complemented
209#407—172no—
210C4×M16—172no—
211#383—172no—
212#382—172no—
213#381—341no—
214#380—341no—
215C4×C4⋊C4—172no—
216C4×C4⋊C4—341no—
217C4×C4⋊C4—341no—
218C4×C22⋊C4—172no—
219C4×C22⋊C4—172no—
220C4×C22⋊C4—341no—
221#376—172no—
222#376—341no—
223C43—341no—
224C2×C17—41no—
225C2×C17C2×#33911yescharacteristic
226C2×C17#173311yescharacteristic
227C2×C17#174011yescharacteristic
228D17—22no—
229D17—22no—
230C23×C4—171no—
231C23×C4—171no—
232C23×C4—171no—
233C2×M16—172no—
234C2×M16C2×#59512yes—
235#117—348no—
236C2×C4⋊C4—342no—
237C2×C4⋊C4—342no—
238C2×C22⋊C4—342no—
239C2×C22⋊C4—342no—
240C2×C42—171no—
241C2×C42—171no—
242C2×C42—171no—
243C2×C42—171no—
244C2×C42—171no—
245C2×C42—171no—
246C2×C42—171no—
247C2×C42—171no—
248C2×C42—171no—
249C2×C42—171no—
250C2×C42—171no—
251C2×C42—342no—
252C2×C42—342no—
253C2×C42—342no—
254C2×C42—342no—
255C2×C42C2×#59511yescharacteristic
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—341no—
259C4⋊C8—341no—
260C22⋊C8—342no—
261C22⋊C8—342no—
262#97—342no—
263C4×C8—342no—
264#95—174no—
265#95—174no—
266#95—342no—
267#95—342no—
268#95—342no—
269#95—342no—
270C17#805211yescharacteristic, complemented, Sylow
271C24—171no—
272C22×C4—171no—
273C22×C4—171no—
274C22×C4—171no—
275C22×C4—171no—
276C22×C4—171no—
277C22×C4—171no—
278C22×C4—171no—
279C22×C4—171no—
280C22×C4—171no—
281C22×C4—171no—
282C22×C4—171no—
283C22×C4—171no—
284C22×C4—171no—
285C22×C4—171no—
286C22×C4—171no—
287C22×C4—344no—
288C22×C4—344no—
289C22×C4—344no—
290C22×C4—681no—
291C22×C4—681no—
292C22×C4—682no—
293C22×C4C4⋊#59511yescharacteristic
294C22×C4C4⋊#59511yescharacteristic
295C22×C4C22×#59511yescharacteristic
296M16—42no—
297M16—682no—
298C2×C8—22no—
299C2×C8—342no—
300C4⋊C4—348no—
301C4⋊C4—684no—
302C22⋊C4—348no—
303C22⋊C4—684no—
304C42—171no—
305C42—171no—
306C42—171no—
307C42—171no—
308C42—171no—
309C42—171no—
310C42—171no—
311C42—171no—
312C42—171no—
313C42—171no—
314C42—171no—
315C42—171no—
316C42—348no—
317C42—684no—
318C42—682no—
319C42—682no—
320C42—682no—
321C42—682no—
322C42C4×#59511yescharacteristic
323C42C4×#59511yescharacteristic
324C42C22⋊#59511yescharacteristic
325C42C22⋊#59511yescharacteristic
326C23—171no—
327C23—171no—
328C23—342no—
329C23—342no—
330C23—681no—
331C23C2×C4⋊#59511yescharacteristic
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—41no—
336C2×C4—171no—
337C2×C4—174no—
338C2×C4—171no—
339C2×C4—171no—
340C2×C4—171no—
341C2×C4—171no—
342C2×C4—171no—
343C2×C4—342no—
344C2×C4—342no—
345C2×C4—342no—
346C2×C4—342no—
347C2×C4—342no—
348C2×C4—341no—
349C2×C4—341no—
350C2×C4—341no—
351C2×C4—341no—
352C2×C4—342no—
353C2×C4—348no—
354C2×C4—681no—
355C2×C4—681no—
356C2×C4—681no—
357C2×C4—681no—
358C2×C4—681no—
359C2×C4—681no—
360C2×C4—684no—
361C2×C4—684no—
362C2×C4—684no—
363C2×C4—684no—
364C2×C4—684no—
365C2×C4(C2×#595)⋊C411yescharacteristic
366C2×C4(C2×#595)⋊C411yescharacteristic
367C2×C4(C2×#595)⋊C411yescharacteristic
368C2×C4(C2×#595)⋊C411yescharacteristic
369C2×C4C2×C4×#59511yescharacteristic
370C2×C4C2×C22⋊#59511yescharacteristic
371C8—42no—
372C8—682no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—172no—
377C22—172no—
378C22—341no—
379C22—341no—
380C22—341no—
381C22—341no—
382C22—684no—
383C22C2×(C2×#595)⋊C411yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—172no—
389C4—341no—
390C4—341no—
391C4—341no—
392C4—341no—
393C4—341no—
394C4—688no—
395C4—1364no—
396C4#1176368112yes—
397C4#1176378911yescharacteristic
398C4#1176379011yescharacteristic
399C2—41no—
400C2—342no—
401C2—342no—
402C2C2×#1176368111yescharacteristic
403C2#1454446611yescharacteristic
404C2#1454448411yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC17×#423C4
socleC22×C17C2×#95
prime radicalC23×D17C2×D4
cosocleC22×C4×D17C23
hypercenter#423#595
hypocenterC17#8052
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
6. #11763754C4semidirect
7. #11763753C4semidirect
12. C4×C4⋊#595C4semidirect
17. #11763745C4semidirect
24. #11762833C4semidirect
26. M16×Dic17C4semidirect
27. C17×#423C4semidirect
208. #423#595semidirect
270. C17#8052semidirect

Maximal subgroups

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

subgroupindex
#145452312
C4×#105876772
#145436642
#145374162
#805217