Finite Group Databasebeta

← #17964139

Subgroups — #17964139

Order 4352.

806 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545460C211yesmaximal, characteristic
2C2×C4×#63247C211yesmaximal, characteristic
3#14544007C214yesmaximal, complemented
4#14544001C214yesmaximal, complemented
5#14543999C212yesmaximal, complemented
6#14543989C212yesmaximal, complemented
7#14537413C211yesmaximal, characteristic
8C22×#63247C412yes—
9#11763830C412yes—
10#11763829C412yes—
11#11763826C2212yes—
12#11763825C2212yes—
13#11763812C412yes—
14#11763779C412yes—
15C4×#63247C412yes—
16C4×#63247C412yes—
17C4×#63247C2212yes—
18C4×#63247C2212yes—
19C4×#63247C2212yes—
20C2×#10587542C412yes—
21C2×C4×#3624C2211yescharacteristic
22C2×C4×#3624C2211yescharacteristic
23#11763651C2214yescomplemented
24#11763651C2214yescomplemented
25#11763650C2214yescomplemented
26C8×#3624C2214yescomplemented
27C22×C4×Dic17C2211yescharacteristic
28#11762863C412yes—
29#11762863C412yes—
30#11762859C2212yes—
31#11762859C2212yes—
32#11762832C412yes—
33#11762773C411yescharacteristic
34M16×Dic17C2212yes—
35C17×#407C411yescharacteristic
36C23×C4×C17C2×C411yescharacteristic
37C23×Dic17C2×C411yescharacteristic
38C23×Dic17C2×C411yescharacteristic
39C2×#63247—28no—
40C2×#63247C2×C414yes—
41C2×#63247C2×C414yes—
42C2×#63247C2×C414yes—
43C22×#3624C2×C412yes—
44C22×#3624C2×C412yes—
45C2×M16×C17C2×C412yes—
46C2×C4×Dic17C2×C411yescharacteristic
47C2×C4×Dic17C2×C411yescharacteristic
48C2×C4×Dic17C2×C411yescharacteristic
49C2×C4×Dic17C2×C411yescharacteristic
50C2×C4×Dic17C2×C411yescharacteristic
51C2×C4×Dic17C2×C411yescharacteristic
52C2×C4×Dic17C2×C411yescharacteristic
53C2×C4×Dic17C2×C411yescharacteristic
54C2×C4×Dic17C2×C411yescharacteristic
55C2×C4×Dic17C2311yescharacteristic
56C2×C4×Dic17C2311yescharacteristic
57C2×C4×Dic17C2311yescharacteristic
58C2×#63223C2×C412yes—
59C22⋊#3624C2×C414yes—
60C22⋊#3624C2×C414yes—
61#10587544C2×C414yes—
62#10587542C2×C414yes—
63#10587542C2×C414yes—
64#10587542C2×C414yes—
65C4⋊#3624C2×C414yes—
66C4×#3624C2×C412yes—
67C4×#3624C2×C412yes—
68C4×#3624C2312yes—
69C4×#3624C2312yes—
70C4×#3624C2314yes—
71C17×C22⋊C8C2×C412yes—
72C17×C22⋊C8C2×C412yes—
73C22⋊#3622C2×C412yes—
74C22⋊#3622C2×C412yes—
75#10587486C2×C414yes—
76#10587485C2×C414yes—
77#10587485C2×C414yes—
78C8×Dic17C2314yes—
79C24×C17C4211yescharacteristic
80C22×C4×C17—42no—
81C22×C4×C17C4211yescharacteristic
82C22×C4×C17C4211yescharacteristic
83C22×C4×C17C4211yescharacteristic
84C22×C4×C17C22×C411yescharacteristic
85C22×C4×C17C22×C411yescharacteristic
86C22×C4×C17C22×C411yescharacteristic
87C22×Dic17—24no—
88C22×Dic17—42no—
89C22×Dic17C4211yescharacteristic
90C22×Dic17C4211yescharacteristic
91C22×Dic17C4211yescharacteristic
92C22×Dic17C4211yescharacteristic
93C22×Dic17C4211yescharacteristic
94C22×Dic17C4211yescharacteristic
95C22×Dic17C22×C411yescharacteristic
96C22×Dic17C22×C411yescharacteristic
97C22×Dic17C22×C411yescharacteristic
98C22×Dic17C22×C411yescharacteristic
99C22×Dic17C22×C411yescharacteristic
100C22×Dic17C22×C411yescharacteristic
101#63247—28no—
102#63247—28no—
103#63247—44no—
104C2×#3624—24no—
105C2×#3624M1618yescomplemented
106C2×#3624C22×C414yes—
107C2×#3624C22×C418yes—
108C2×#3624C22×C414yes—
109M16×C17—42no—
110C2×C8×C17C22×C414yes—
111C4×Dic17C4211yescharacteristic
112C4×Dic17C4211yescharacteristic
113C4×Dic17C4211yescharacteristic
114C4×Dic17C4211yescharacteristic
115C4×Dic17C4211yescharacteristic
116C4×Dic17C4211yescharacteristic
117C4×Dic17C22×C411yescharacteristic
118C4×Dic17C22×C411yescharacteristic
119C4×Dic17C22×C411yescharacteristic
120C4×Dic17C22×C411yescharacteristic
121C4×Dic17C22×C411yescharacteristic
122C4×Dic17C22×C411yescharacteristic
123C4×Dic17C22×C411yescharacteristic
124C4×Dic17C22×C411yescharacteristic
125C4×Dic17C22×C411yescharacteristic
126C4×Dic17C2411yescharacteristic
127#63223—42no—
128C2×#3622C22×C414yes—
129#17334—171nomaximal, Sylow
130C23×C17—22no—
131C23×C17—41no—
132C23×C17—41no—
133C23×C17C2×C4211yescharacteristic
134C23×C17C2×C4211yescharacteristic
135C23×C17C2×C4211yescharacteristic
136C2×C4×C17—22no—
137C2×C4×C17—22no—
138C2×C4×C17—22no—
139C2×C4×C17—41no—
140C2×C4×C17—41no—
141C2×C4×C17—41no—
142C2×C4×C17C2×C4211yescharacteristic
143C2×C4×C17C2×C4211yescharacteristic
144C2×C4×C17C2×C4211yescharacteristic
145C2×C4×C17C23×C411yescharacteristic
146C2×Dic17—22no—
147C2×Dic17—22no—
148C2×Dic17—22no—
149C2×Dic17—22no—
150C2×Dic17—22no—
151C2×Dic17—22no—
152C2×Dic17—22no—
153C2×Dic17—22no—
154C2×Dic17—41no—
155C2×Dic17—41no—
156C2×Dic17—41no—
157C2×Dic17C2×C4211yescharacteristic
158C2×Dic17C2×C4211yescharacteristic
159C2×Dic17C2×C4211yescharacteristic
160C2×Dic17C2×C4211yescharacteristic
161C2×Dic17C2×C4211yescharacteristic
162C2×Dic17C2×C4211yescharacteristic
163C2×Dic17C2×M1614yes—
164C2×Dic17C23×C411yescharacteristic
165C2×Dic17C23×C411yescharacteristic
166#3624—24no—
167#3624—28no—
168#3624C2×M1618yes—
169C8×C17—24no—
170#3622—24no—
171#2920—171no—
172#2920—171no—
173C2×C4×M16—171no—
174#1455—174no—
175#1453—174no—
176#1452—172no—
177#1450—172no—
178C22×C17—21no—
179C22×C17—21no—
180C22×C17—21no—
181C22×C17—21no—
182C22×C17—21no—
183C22×C17—21no—
184C22×C17—21no—
185C22×C17—21no—
186C22×C17—44no—
187C22×C17C4×M1612yes—
188C22×C17C22×C4211yescharacteristic
189C4×C17—21no—
190C4×C17—21no—
191C4×C17—21no—
192C4×C17#56812yes—
193Dic17—21no—
194Dic17—21no—
195Dic17—21no—
196Dic17—21no—
197Dic17—21no—
198Dic17C4×M1612yes—
199Dic17C22×M1612yes—
200Dic17#56812yes—
201C22×M16—172no—
202C22×C42—171no—
203#432—172no—
204#432—172no—
205#432—172no—
206#432—172no—
207#431—172no—
208#431—172no—
209#431—172no—
210#431—172no—
211#423—172no—
212#423—172no—
213#407—172no—
214#407—171no—
215#407#59511yescharacteristic
216C4×M16—172no—
217C4×M16—172no—
218C4×M16—172no—
219C4×M16—172no—
220C4×M16—172no—
221C4×M16—172no—
222C2×#97—172no—
223C2×C4×C8—171no—
224C2×C4×C8—171no—
225#322—174no—
226#322—174no—
227#322—174no—
228C82—174no—
229C2×C17—22no—
230C2×C17—41no—
231C2×C17—41no—
232C2×C17C2×C4×M1611yescharacteristic
233C2×C17#287311yescharacteristic
234C2×C17#287311yescharacteristic
235C23×C4—171no—
236C23×C4—171no—
237C23×C4C2×#59511yescharacteristic
238C2×M16—174no—
239C2×M16—174no—
240C2×M16—174no—
241C2×M16—172no—
242C2×M16—348no—
243C2×M16C2×#59512yes—
244C22×C8—172no—
245C22×C8—172no—
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—171no—
255C2×C42—171no—
256C2×C42—171no—
257C2×C42—171no—
258C4⋊C8—174no—
259C4⋊C8—174no—
260C4⋊C8—174no—
261C4⋊C8—174no—
262C22⋊C8—174no—
263C22⋊C8—174no—
264C22⋊C8—172no—
265C22⋊C8—172no—
266C22⋊C8C2×#59512yes—
267C22⋊C8C2×#59512yes—
268#97—174no—
269#97—174no—
270#97—174no—
271#97—174no—
272C4×C8—172no—
273C4×C8—174no—
274C4×C8—172no—
275C4×C8—172no—
276C4×C8—172no—
277C4×C8—174no—
278C17#1733411yescharacteristic, complemented, Sylow
279C24C4×#59511yescharacteristic
280C22×C4—42no—
281C22×C4—171no—
282C22×C4—171no—
283C22×C4—171no—
284C22×C4—171no—
285C22×C4—171no—
286C22×C4—171no—
287C22×C4—171no—
288C22×C4—171no—
289C22×C4—171no—
290C22×C4—171no—
291C22×C4—171no—
292C22×C4—171no—
293C22×C4—344no—
294C22×C4—682no—
295C22×C4C4×#59511yescharacteristic
296C22×C4C4×#59511yescharacteristic
297C22×C4C4×#59511yescharacteristic
298C22×C4C22×#59511yescharacteristic
299C22×C4C22×#59511yescharacteristic
300C22×C4C22×#59511yescharacteristic
301M16—42no—
302M16—348no—
303M16—348no—
304M16—682no—
305M16—684no—
306C2×C8—178no—
307C2×C8—174no—
308C2×C8—174no—
309C2×C8—178no—
310C2×C8—174no—
311C2×C8—344no—
312C2×C8C22×#59514yes—
313C42—171no—
314C42—171no—
315C42—171no—
316C42—171no—
317C42—171no—
318C42—171no—
319C42—171no—
320C42—171no—
321C42—171no—
322C42—171no—
323C42—171no—
324C42—171no—
325C42—171no—
326C42—171no—
327C42—171no—
328C42—171no—
329C23—22no—
330C23—41no—
331C23—41no—
332C23C2×C4×#59511yescharacteristic
333C23C2×C4×#59511yescharacteristic
334C23C2×C4×#59511yescharacteristic
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—174no—
342C2×C4—171no—
343C2×C4—171no—
344C2×C4—171no—
345C2×C4—171no—
346C2×C4—171no—
347C2×C4—171no—
348C2×C4—171no—
349C2×C4—171no—
350C2×C4—342no—
351C2×C4—342no—
352C2×C4—342no—
353C2×C4—342no—
354C2×C4—342no—
355C2×C4—342no—
356C2×C4—342no—
357C2×C4—342no—
358C2×C4—681no—
359C2×C4—681no—
360C2×C4—681no—
361C2×C4C2×C4×#59511yescharacteristic
362C2×C4C2×C4×#59511yescharacteristic
363C2×C4C2×C4×#59511yescharacteristic
364C2×C4C23×#59511yescharacteristic
365C8—24no—
366C8—178no—
367C8—344no—
368C8—348no—
369C8—344no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—44no—
379C22M16×#59512yes—
380C22C22×C4×#59511yescharacteristic
381C4—21no—
382C4—21no—
383C4—21no—
384C4—172no—
385C4—172no—
386C4—172no—
387C4—341no—
388C4—341no—
389C4—341no—
390C4—341no—
391C4—341no—
392C4#1176388712yes—
393C2—22no—
394C2—41no—
395C2—41no—
396C2C2×M16×#59511yescharacteristic
397C2#1454534711yescharacteristic
398C2#1454534811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×#595
commutator, socleC22×C17C22×C42
FittingC17×#407C4
prime radicalC24×C17C42
cosocleC4×Dic17C24
hypercenter#407#595
hypocenterC17#17334
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
3. #14544007C2semidirect
4. #14544001C2semidirect
5. #14543999C2semidirect
6. #14543989C2semidirect
23. #11763651C22semidirect
24. #11763651C22semidirect
25. #11763650C22semidirect
26. C8×#3624C22semidirect
105. C2×#3624M16semidirect
278. C17#17334semidirect

Maximal subgroups

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

subgroupindex
#145454602
C2×C4×#632472
#145440072
#145440012
#145439992
#145439892
#145374132
#1733417