Finite Group Databasebeta

← #17950510

Subgroups — #17950510

Order 4352.

722 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545448C211yesmaximal, characteristic
2#14545233C211yesmaximal, characteristic
3#14543619C214yesmaximal, complemented
4C4×M16×D17C211yesmaximal, characteristic
5C2×#10587677—21no—
6#11763828C412yescomplemented
7#11763827—21no—
8#11763826—21no—
9#11763825C412yescomplemented
10#11763810C2212yes—
11#11763777—21no—
12C4×#63242—21no—
13#11763755C412yes—
14#11763753—21no—
15#11763751—21no—
16#11763751C412yes—
17C4×C4⋊#595—21no—
18C4×C4⋊#595C2212yes—
19C2×M16×D17—21no—
20C2×C42×D17C2211yescharacteristic
21C4×#63223C411yescharacteristic, complemented
22#11762761—21no—
23M16×Dic17—21no—
24C4×#63218C412yescomplemented
25#97×D17—21no—
26C4×C8×D17C2212yes—
27C4×M16×C17C411yescharacteristic, complemented
28C22×C4×D17C2×C411yescharacteristic
29C22×C4×D17D411yescharacteristic
30C22×C4×D17D411yescharacteristic
31C2×C22⋊#595—22no—
32#10587677—44no—
33C2×C4⋊#595—22no—
34C2×C4⋊#595—22no—
35C2×C4⋊#595C2×C414yes—
36C2×C4×#595—22no—
37C2×#63242—22no—
38C2×M16×C17—21no—
39C2×C42×C17C2×C411yescharacteristic
40C2×C4×Dic17C2×C411yescharacteristic
41C2×C4×Dic17D411yescharacteristic
42C2×C4×Dic17Q811yescharacteristic
43C2×#63223—21no—
44M16×D17—28no—
45C2×#63218—22no—
46C2×C8×D17—22no—
47C42×D17C2×C411yescharacteristic
48C42×D17C2×C411yescharacteristic
49C42×D17C2×C411yescharacteristic
50C42×D17D411yescharacteristic
51C42×D17D411yescharacteristic
52C42×D17D411yescharacteristic
53C42×D17Q811yescharacteristic
54C42×D17C2311yescharacteristic
55C22⋊#3624—22no—
56(C2×#595)⋊C4—22no—
57(C2×#595)⋊C4—22no—
58#10587544—22no—
59#10587543—22no—
60C4⋊#3624C2×C414yes—
61C4×#3624—22no—
62C4×#3624—22no—
63C17×#97—21no—
64C4×C8×C17C2×C412yes—
65#10587486—22no—
66C8×Dic17—22no—
67#10587474—21no—
68C4×#3622C2×C412yes—
69C23×D17C22⋊C411yescharacteristic
70C22×#595—24no—
71C22×C4×C17C4211yescharacteristic
72C22×C4×C17C22⋊C411yescharacteristic
73C22×C4×C17C4⋊C411yescharacteristic
74C22×Dic17C22⋊C411yescharacteristic
75C22×Dic17C4⋊C411yescharacteristic
76C22×Dic17C4⋊C411yescharacteristic
77C2×C4×D17—24no—
78C2×C4×D17—24no—
79C2×C4×D17—22no—
80C2×C4×D17—22no—
81C2×C4×D17C4211yescharacteristic
82C2×C4×D17C22⋊C411yescharacteristic
83C2×C4×D17C22⋊C411yescharacteristic
84C2×C4×D17C22⋊C411yescharacteristic
85C2×C4×D17C22⋊C411yescharacteristic
86C2×C4×D17C22⋊C411yescharacteristic
87C2×C4×D17C4⋊C411yescharacteristic
88C2×C4×D17C4⋊C411yescharacteristic
89C2×C4×D17C4⋊C411yescharacteristic
90C2×C4×D17C22×C411yescharacteristic
91C2×C4×D17C2×D411yescharacteristic
92C2×C4×D17C2×D411yescharacteristic
93C22⋊#595—44no—
94C2×#3624—24no—
95C4⋊#595—28no—
96C4⋊#595—44no—
97C4⋊#595—44no—
98C4×#595—44no—
99#63242—42no—
100#63242—42no—
101M16×C17—24no—
102C2×C8×C17—22no—
103C42×C17C4211yescharacteristic
104C42×C17C22⋊C411yescharacteristic
105C42×C17C4⋊C411yescharacteristic
106C42×C17C22×C411yescharacteristic
107C4×Dic17C4211yescharacteristic
108C4×Dic17C22⋊C411yescharacteristic
109C4×Dic17C22⋊C411yescharacteristic
110C4×Dic17C22⋊C411yescharacteristic
111C4×Dic17C4⋊C411yescharacteristic
112C4×Dic17C4⋊C411yescharacteristic
113C4×Dic17C4⋊C411yescharacteristic
114C4×Dic17C4⋊C411yescharacteristic
115C4×Dic17C4⋊C411yescharacteristic
116C4×Dic17C22×C411yescharacteristic
117C4×Dic17C2×D411yescharacteristic
118C4×Dic17C2×Q811yescharacteristic
119#63223—24no—
120C2×#3622—22no—
121#63218—28no—
122C8×D17—28no—
123#7896—171nomaximal, Sylow
124C23×C17#9511yescharacteristic
125C22×D17—22no—
126C22×D17—21no—
127C22×D17—21no—
128C22×D17—22no—
129C22×D17#9511yescharacteristic
130C22×D17C2×C22⋊C411yescharacteristic
131C2×#595—44no—
132C2×#595—44no—
133C2×#595—44no—
134C2×C4×C17—22no—
135C2×C4×C17—22no—
136C2×C4×C17—22no—
137C2×C4×C17#9511yescharacteristic
138C2×C4×C17#9511yescharacteristic
139C2×C4×C17#9511yescharacteristic
140C2×C4×C17C2×C4211yescharacteristic
141C2×C4×C17C2×C22⋊C411yescharacteristic
142C2×C4×C17C2×C4⋊C411yescharacteristic
143C2×Dic17—22no—
144C2×Dic17—22no—
145C2×Dic17—22no—
146C2×Dic17#9511yescharacteristic
147C2×Dic17#9511yescharacteristic
148C2×Dic17#9511yescharacteristic
149C2×Dic17C2×C22⋊C411yescharacteristic
150C2×Dic17C2×C4⋊C411yescharacteristic
151C2×Dic17C2×C4⋊C411yescharacteristic
152C4×D17—22no—
153C4×D17—21no—
154C4×D17—21no—
155C4×D17—22no—
156C4×D17—22no—
157C4×D17—22no—
158C4×D17—22no—
159C4×D17—22no—
160C4×D17—22no—
161C4×D17—22no—
162C4×D17#10414yes—
163C4×D17#13114yes—
164C4×D17AGL(1,ℤ/8)12yes—
165C4×D17#13712yes—
166#3624—44no—
167C8×C17—24no—
168#3622—24no—
169C2×#431—171no—
170C2×C4×M16—171no—
171#2285—171no—
172#1279—174no—
173C22×C17—21no—
174C22×C17—21no—
175C22×C17—21no—
176C22×C17C2×#9511yescharacteristic
177C2×D17—21no—
178C2×D17—21no—
179C2×D17—21no—
180C2×D17—42no—
181C2×D17—42no—
182C2×D17#40812yes—
183C2×D17#41811yescharacteristic
184C2×D17#41911yescharacteristic
185C2×D17C2×#10412yes—
186#595—84no—
187C4×C17—21no—
188C4×C17—21no—
189C4×C17—21no—
190C4×C17#33912yes—
191C4×C17#40512yes—
192C4×C17#42812yes—
193Dic17—21no—
194Dic17—21no—
195Dic17—21no—
196Dic17#33912yes—
197Dic17#41712yes—
198Dic17#42412yes—
199C22×M16—341no—
200C2×#117—341no—
201C22×C42—171no—
202#431—172no—
203#431—172no—
204#431—341no—
205#431—341no—
206C2×C4⋊C8—172no—
207C2×C22⋊C8—341no—
208C4×M16—171no—
209C4×M16—172no—
210C4×M16—341no—
211C4×M16—341no—
212C4×M16#59511yescharacteristic, complemented
213C2×#97—341no—
214C2×C4×C8—172no—
215C2×C4×C8—341no—
216#384—172no—
217#382—341no—
218#380—172no—
219#380—341no—
220C4×C4⋊C4—172no—
221C4×C4⋊C4—341no—
222C2×C17—41no—
223C2×C17#172911yescharacteristic
224C2×C17C2×#33911yescharacteristic
225C2×C17#173611yescharacteristic
226D17—41no—
227D17#148412yes—
228D17#148512yes—
229C23×C4—171no—
230C23×C4—171no—
231C23×C4—171no—
232C2×M16—21no—
233C2×M16—342no—
234C2×M16—348no—
235C2×M16—341no—
236C22×C8—342no—
237C22×C8—342no—
238#117—684no—
239C2×C4⋊C4—174no—
240C2×C4⋊C4—342no—
241C2×C4⋊C4—342no—
242C2×C22⋊C4—342no—
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—171no—
252C2×C42—171no—
253C2×C42—171no—
254C2×C42—342no—
255C2×C42C2×#59511yescharacteristic
256C4⋊C8—174no—
257C4⋊C8—342no—
258C22⋊C8—342no—
259C22⋊C8—342no—
260#97—21no—
261#97—342no—
262#97—341no—
263C4×C8—172no—
264C4×C8—342no—
265C4×C8—342no—
266C4×C8—342no—
267C4×C8C2×#59512yes—
268#95—342no—
269#95—342no—
270C17#789611yescharacteristic, 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—342no—
288C22×C4—344no—
289C22×C4—344no—
290C22×C4—342no—
291C22×C4—344no—
292C22×C4C4×#59511yescharacteristic
293C22×C4C4⋊#59511yescharacteristic
294C22×C4C22⋊#59511yescharacteristic
295M16—24no—
296M16—348no—
297M16—344no—
298C2×C8—22no—
299C2×C8—348no—
300C2×C8—342no—
301C2×C8—344no—
302C2×C8—682no—
303C2×C8—682no—
304C4⋊C4—348no—
305C4⋊C4—684no—
306C4⋊C4—684no—
307C22⋊C4—684no—
308C42—171no—
309C42—171no—
310C42—171no—
311C42—171no—
312C42—171no—
313C42—171no—
314C42—171no—
315C42—171no—
316C42—171no—
317C42—171no—
318C42—171no—
319C42—171no—
320C42—684no—
321C42C4×#59511yescharacteristic
322C42C4⋊#59511yescharacteristic
323C42C22⋊#59511yescharacteristic
324C42C22×#59511yescharacteristic
325C23—171no—
326C23—171no—
327C23—341no—
328C23—342no—
329C23—342no—
330C23—341no—
331C23(C2×#595)⋊C411yescharacteristic
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—171no—
336C2×C4—171no—
337C2×C4—171no—
338C2×C4—174no—
339C2×C4—172no—
340C2×C4—172no—
341C2×C4—174no—
342C2×C4—171no—
343C2×C4—171no—
344C2×C4—171no—
345C2×C4—342no—
346C2×C4—342no—
347C2×C4—342no—
348C2×C4—341no—
349C2×C4—342no—
350C2×C4—342no—
351C2×C4—341no—
352C2×C4—342no—
353C2×C4—342no—
354C2×C4—342no—
355C2×C4—342no—
356C2×C4—342no—
357C2×C4—342no—
358C2×C4—684no—
359C2×C4—684no—
360C2×C4—684no—
361C2×C4(C2×#595)⋊C411yescharacteristic
362C2×C4(C2×#595)⋊C411yescharacteristic
363C2×C4(C2×#595)⋊C411yescharacteristic
364C2×C4C2×C4×#59511yescharacteristic
365C2×C4C2×C4⋊#59511yescharacteristic
366C2×C4C2×C22⋊#59511yescharacteristic
367C8—24no—
368C8—344no—
369C8—684no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—172no—
374C22—172no—
375C22—171no—
376C22—171no—
377C22—341no—
378C22—341no—
379C22—341no—
380C22—682no—
381C22—682no—
382C22C2×(C2×#595)⋊C411yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—172no—
387C4—172no—
388C4—172no—
389C4—341no—
390C4—341no—
391C4—341no—
392C4—1364no—
393C4#1176368012yes—
394C4#1176377512yes—
395C4#1176382012yes—
396C2—41no—
397C2—172no—
398C2—172no—
399C2—681no—
400C2#1454445211yescharacteristic
401C2C2×#1176368011yescharacteristic
402C2#1454447211yescharacteristic
subgroupG/H
centerC2×C4C2×C4⋊#595
commutatorC2×C4×C17C2×C42
FrattiniC42C22×#595
FittingC4×M16×C17C4
socleC22×C17C2×#95
prime radicalC23×D17C22⋊C4
cosocleC42×D17C23
hypercenterC4×M16#595
hypocenterC17#7896
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
3. #14543619C2semidirect
6. #11763828C4semidirect
9. #11763825C4semidirect
21. C4×#63223C4semidirect
24. C4×#63218C4semidirect
27. C4×M16×C17C4semidirect
212. C4×M16#595semidirect
270. C17#7896semidirect

Maximal subgroups

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

subgroupindex
#145454482
#145452332
#145436192
C4×M16×D172
#789617