Finite Group Databasebeta

← #17968549

Subgroups — #17968549

Order 4352.

1110 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D17⋊#423C211yesmaximal, characteristic
2C2×#11763772C212yesmaximal
3#14545233C211yesmaximal, characteristic
4#14544582C218yesmaximal, complemented
5#14544449C212yesmaximal
6C2×#97×D17C211yesmaximal, characteristic
7C2×D17⋊M16C2212yes—
8C2×#10587677C2212yes—
9#11763814C412yescomplemented
10#11763813C412yescomplemented
11#11763812C414yescomplemented
12#11763810C2214yes—
13#11763772—28no—
14C2×#10587532C2214yes—
15C2×C8×#595C2214yes—
16#11763755C412yes—
17#11763753C412yes—
18#11763751C414yes—
19C4×C4⋊#595C2214yes—
20#11763674C2218yes—
21C22×C8×D17C2211yescharacteristic
22C22×C8×D17C2211yescharacteristic
23C2×C42×D17C2211yescharacteristic
24C2×#10587474C411yescharacteristic, complemented
25C2×#10587486C411yescharacteristic, complemented
26C2×#10587486C411yescharacteristic, complemented
27#97×D17C414yescomplemented
28#97×D17C2214yes—
29C2×C17×#97C411yescharacteristic, complemented
30C22×C4×D17C2×C412yes—
31C22×C4×D17C2311yescharacteristic
32C2×C22⋊#595C2×C414yes—
33C2×#63247C2×C414yes—
34#10587677—24no—
35#10587677—24no—
36C2×C4⋊#595C2×C414yes—
37C2×C4⋊#595C2×C418yes—
38C2×C4×#595C2314yes—
39D17⋊M16—24no—
40D17⋊M16—24no—
41C2×#63243C2×C414yes—
42C2×#63242C2314yes—
43C22×C8×C17C2×C411yescharacteristic
44C22×C8×C17C2×C411yescharacteristic
45C2×C42×C17C2×C411yescharacteristic
46C2×C4×Dic17C2×C411yescharacteristic
47C2×C4×Dic17C2×C412yes—
48C22×#3622C2×C411yescharacteristic
49C22×#3622C2×C411yescharacteristic
50C2×C8×D17—22no—
51C2×C8×D17—22no—
52C2×C8×D17C2×C412yes—
53C2×C8×D17C2×C412yes—
54C2×C8×D17D414yes—
55C2×C8×D17Q814yes—
56C2×C8×D17C2312yes—
57C2×C8×D17C2312yes—
58C42×D17C2×C411yescharacteristic
59C42×D17C2×C411yescharacteristic
60C42×D17C2×C411yescharacteristic
61C42×D17C2×C411yescharacteristic
62C42×D17C2×C412yes—
63C42×D17C2312yes—
64(C2×#595)⋊C4C2×C418yes—
65#10587544C2×C418yes—
66C4⋊#3624C2×C418yes—
67#10587532—28no—
68C8×#595—28no—
69C17×#97C2×C414yes—
70#10587486C2×C414yes—
71#10587486C2×C414yes—
72#10587474C2×C414yes—
73C23×D17C22×C411yescharacteristic
74C22×#595C22×C418yes—
75C22×C4×C17C4212yes—
76C22×C4×C17C22×C411yescharacteristic
77C22×Dic17C4212yes—
78C22×Dic17C22×C411yescharacteristic
79C2×C4×D17—44no—
80C2×C4×D17C4212yes—
81C2×C4×D17C4212yes—
82C2×C4×D17C22×C412yes—
83C2×C4×D17C22×C412yes—
84C2×C4×D17C22×C411yescharacteristic
85C2×C4×D17C22×C411yescharacteristic
86C2×C4×D17C22×C411yescharacteristic
87C2×C4×D17C2×D412yes—
88C2×C4×D17C2×Q812yes—
89C2×C4×D17#4112yes—
90C2×C4×D17#4112yes—
91C2×C4×D17C2411yescharacteristic
92C22⋊#595—28no—
93#63247—28no—
94C2×#3624C22×C418yes—
95C4⋊#595—28no—
96C4⋊#595—48no—
97C4×#595—24no—
98C4×#595—24no—
99#63243—28no—
100#63242—24no—
101#63242—24no—
102C2×C8×C17—22no—
103C2×C8×C17C4⋊C414yescomplemented
104C2×C8×C17C22×C412yes—
105C2×C8×C17C22×C412yes—
106C42×C17C4211yescharacteristic
107C42×C17C4211yescharacteristic
108C42×C17C22×C412yes—
109C4×Dic17C4211yescharacteristic
110C4×Dic17C4211yescharacteristic
111C4×Dic17C4212yes—
112C4×Dic17C4212yes—
113C4×Dic17C22×C412yes—
114C4×Dic17C22×C412yes—
115C4×Dic17C22×C412yes—
116C2×#3622—22no—
117C2×#3622C4⋊C414yescomplemented
118C2×#3622C22×C412yes—
119C2×#3622C22×C412yes—
120C8×D17—24no—
121C8×D17—22no—
122C8×D17—22no—
123C8×D17C4⋊C418yescomplemented
124C8×D17C2×D414yes—
125C8×D17C2×Q814yes—
126#20438—171nomaximal, Sylow
127C23×C17C2×C4211yescharacteristic
128C22×D17—24no—
129C22×D17C2×C4211yescharacteristic
130C22×D17C4×D412yes—
131C22×D17C4×Q812yes—
132C22×D17C23×C411yescharacteristic
133C2×#595—28no—
134C2×#595—216no—
135C2×C4×C17—42no—
136C2×C4×C17C2×C4212yes—
137C2×C4×C17C2×C4212yes—
138C2×C4×C17C2×C4211yescharacteristic
139C2×C4×C17C2×C4⋊C412yes—
140C2×C4×C17#11712yes—
141C2×C4×C17C23×C411yescharacteristic
142C2×Dic17—42no—
143C2×Dic17C2×C4212yes—
144C2×Dic17C2×C4212yes—
145C2×Dic17C2×C4211yescharacteristic
146C2×Dic17C4×D412yes—
147C2×Dic17C4×Q812yes—
148C2×Dic17C23×C411yescharacteristic
149C4×D17—24no—
150C4×D17—24no—
151C4×D17—42no—
152C4×D17—42no—
153C4×D17C2×C4⋊C412yes—
154C4×D17#11712yes—
155C4×D17C4×D412yes—
156C4×D17C4×D412yes—
157C4×D17C4×Q812yes—
158C4×D17C4×Q812yes—
159C4×D17C22×D411yescharacteristic
160C4×D17C22×Q811yescharacteristic
161C4×D17C2×#4111yescharacteristic
162C4×D17C2×#4111yescharacteristic
163#3624—28no—
164C8×C17—22no—
165C8×C17C2×C4⋊C414yes—
166#3622—22no—
167#3622C2×C4⋊C414yes—
168C2×#423—171no—
169C2×#405—172no—
170C22×#97—171no—
171#2285—171no—
172#1771—178no—
173#1729—172no—
174C22×C17—22no—
175C22×C17C4×C4⋊C412yes—
176C22×C17C22×C4211yescharacteristic
177C2×D17—22no—
178C2×D17—24no—
179C2×D17—24no—
180C2×D17C4×C4⋊C412yes—
181C2×D17C2×C4×D411yescharacteristic
182C2×D17C2×C4×Q811yescharacteristic
183C2×D17#56814yes—
184#595—48no—
185C4×C17—22no—
186C4×C17—22no—
187C4×C17C4×C4⋊C412yes—
188C4×C17C22×C4⋊C411yescharacteristic
189C4×C17C2×#11711yescharacteristic
190Dic17—22no—
191Dic17—22no—
192Dic17C4×C4⋊C412yes—
193Dic17C2×C4×D411yescharacteristic
194Dic17C2×C4×Q811yescharacteristic
195C22×M16—172no—
196C23×C8—171no—
197C23×C8—171no—
198C2×#117—172no—
199C22×C42—171no—
200#423—174no—
201#423—172no—
202#423—172no—
203C2×C4⋊C8—174no—
204#405—348no—
205C2×#97—171no—
206C2×#97—171no—
207C2×#97—171no—
208C2×#97—174no—
209C2×#97—174no—
210C2×#97—174no—
211C2×#97#59511yescharacteristic, complemented
212C2×C4×C8—174no—
213#384—172no—
214#382—172no—
215#380—174no—
216C4×C4⋊C4—174no—
217#336—178no—
218C2×C17—22no—
219C2×C17C2×C4×C4⋊C411yescharacteristic
220C2×C17#287312yes—
221D17—22no—
222D17#293212yes—
223D17#296112yes—
224C23×C4—171no—
225C23×C4—172no—
226C2×M16—174no—
227C2×M16—174no—
228C2×M16—344no—
229C2×M16—344no—
230C22×C8—171no—
231C22×C8—174no—
232C22×C8—174no—
233C22×C8—172no—
234C22×C8—172no—
235C22×C8—174no—
236C22×C8—171no—
237C22×C8—172no—
238C22×C8—172no—
239C22×C8—342no—
240C22×C8—342no—
241C22×C8C2×#59511yescharacteristic
242C22×C8C2×#59511yescharacteristic
243#117—344no—
244#117—344no—
245C2×C4⋊C4—174no—
246C2×C4⋊C4—178no—
247C2×C22⋊C4—174no—
248C2×C42—172no—
249C2×C42—171no—
250C2×C42—171no—
251C2×C42—171no—
252C2×C42—171no—
253C2×C42—171no—
254C2×C42—172no—
255C2×C42—172no—
256C2×C42—174no—
257C2×C42C2×#59511yescharacteristic
258C4⋊C8—178no—
259C4⋊C8—178no—
260#97—174no—
261#97—174no—
262#97—174no—
263#97—348no—
264#97C2×#59514yes—
265C4×C8—348no—
266#95—178no—
267C17#2043811yescharacteristic, complemented, Sylow
268C24—171no—
269C22×C4—171no—
270C22×C4—171no—
271C22×C4—171no—
272C22×C4—172no—
273C22×C4—172no—
274C22×C4—172no—
275C22×C4—172no—
276C22×C4—171no—
277C22×C4—171no—
278C22×C4—172no—
279C22×C4—172no—
280C22×C4—172no—
281C22×C4—172no—
282C22×C4—172no—
283C22×C4—178no—
284C22×C4—684no—
285C22×C4C4×#59512yes—
286C22×C4C22×#59511yescharacteristic
287M16—348no—
288M16—348no—
289C2×C8—22no—
290C2×C8—174no—
291C2×C8—172no—
292C2×C8—174no—
293C2×C8—178no—
294C2×C8—174no—
295C2×C8—178no—
296C2×C8—172no—
297C2×C8—342no—
298C2×C8—342no—
299C2×C8—344no—
300C2×C8—344no—
301C2×C8—344no—
302C2×C8—342no—
303C2×C8C4⋊#59514yescomplemented
304C2×C8C22×#59512yes—
305C2×C8C22×#59512yes—
306C4⋊C4—348no—
307C4⋊C4—688no—
308C22⋊C4—348no—
309C42—172no—
310C42—172no—
311C42—172no—
312C42—172no—
313C42—171no—
314C42—171no—
315C42—172no—
316C42—344no—
317C42—344no—
318C42C4×#59511yescharacteristic
319C42C4×#59511yescharacteristic
320C42C22×#59512yes—
321C23—171no—
322C23—172no—
323C23—172no—
324C23—171no—
325C23—344no—
326C23C2×C4×#59511yescharacteristic
327C2×C4—42no—
328C2×C4—172no—
329C2×C4—172no—
330C2×C4—171no—
331C2×C4—171no—
332C2×C4—172no—
333C2×C4—172no—
334C2×C4—172no—
335C2×C4—172no—
336C2×C4—171no—
337C2×C4—172no—
338C2×C4—171no—
339C2×C4—171no—
340C2×C4—171no—
341C2×C4—172no—
342C2×C4—172no—
343C2×C4—172no—
344C2×C4—344no—
345C2×C4—344no—
346C2×C4—348no—
347C2×C4—3416no—
348C2×C4—682no—
349C2×C4—682no—
350C2×C4—682no—
351C2×C4C2×C4×#59512yes—
352C2×C4C2×C4×#59512yes—
353C2×C4C2×C4×#59511yescharacteristic
354C2×C4C2×C4⋊#59512yes—
355C2×C4#1058767712yes—
356C2×C4C23×#59511yescharacteristic
357C8—22no—
358C8—174no—
359C8—348no—
360C8—342no—
361C8C2×C4⋊#59514yes—
362C22—22no—
363C22—171no—
364C22—171no—
365C22—174no—
366C22—172no—
367C22—344no—
368C22—344no—
369C22—342no—
370C22C4×C4⋊#59512yes—
371C22C22×C4×#59511yescharacteristic
372C4—22no—
373C4—22no—
374C4—171no—
375C4—171no—
376C4—172no—
377C4—342no—
378C4—342no—
379C4—688no—
380C4C4×C4⋊#59512yes—
381C4C22×C4⋊#59511yescharacteristic
382C4C2×#1058767711yescharacteristic
383C2—22no—
384C2—172no—
385C2—172no—
386C2—342no—
387C2C2×C4×C4⋊#59511yescharacteristic
388C2#1454534712yes—
subgroupG/H
center, FrattiniC2×C4C23×#595
commutator, socleC22×C17C22×C42
FittingC2×C17×#97C4
prime radicalC23×D17C22×C4
cosocleC2×C4×D17C24
hypercenterC2×#97#595
hypocenterC17#20438
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
4. #14544582C2semidirect
9. #11763814C4semidirect
10. #11763813C4semidirect
11. #11763812C4semidirect
24. C2×#10587474C4semidirect
25. C2×#10587486C4semidirect
26. C2×#10587486C4semidirect
27. #97×D17C4semidirect
29. C2×C17×#97C4semidirect
103. C2×C8×C17C4⋊C4semidirect
117. C2×#3622C4⋊C4semidirect
123. C8×D17C4⋊C4semidirect
211. C2×#97#595semidirect
267. C17#20438semidirect
303. C2×C8C4⋊#595semidirect

Maximal subgroups

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

subgroupindex
D17⋊#4232
C2×#117637722
#145452332
#145445822
#145444492
C2×#97×D172
#2043817