Finite Group Databasebeta

← #17956923

Subgroups — #17956923

Order 4352.

918 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#63242C211yesmaximal, characteristic
2C2×#11763674C212yesmaximal
3C2×#11763674C212yesmaximal
4C4×(C2×#595)⋊C4C211yesmaximal, characteristic
5D17×#336C211yesmaximal, characteristic
6C22×#63242C2211yescharacteristic
7C22×#63242C2211yescharacteristic
8C22×C4×#595C2212yes—
9C4×#63242—24no—
10C2×C4×#3624C412yescomplemented
11C2×C4×#3624C412yescomplemented
12C2×(C2×#595)⋊C4C412yes—
13C2×(C2×#595)⋊C4C412yes—
14#11763674—24no—
15#11763674—24no—
16C22×C8×D17C2212yes—
17C2×C42×D17C2211yescharacteristic
18#11762564C411yescharacteristic, complemented
19#11762563C412yescomplemented
20C17×#336C411yescharacteristic, complemented
21C23×#595C2×C414yes—
22C22×C4×D17C2×C411yescharacteristic
23C22×C4×D17C2×C411yescharacteristic
24C22×C4×D17C2311yescharacteristic
25C22×#3624C2×C412yes—
26C22×#3624C2×C412yes—
27C2×C4×#595—22no—
28C2×C4×#595—22no—
29C2×C4×#595—22no—
30C2×C4×#595—22no—
31C2×C4×#595—22no—
32C2×C4×#595—22no—
33C2×#63242—22no—
34C2×#63242—22no—
35C2×#63242—22no—
36C2×#63242—21no—
37C2×#63242—21no—
38C2×#63242D414yes—
39C2×#63242D412yes—
40C2×#63242Q812yes—
41C22×C8×C17C2×C412yes—
42C2×C42×C17C2×C411yescharacteristic
43C2×C4×Dic17C2×C411yescharacteristic
44C2×C4×Dic17C2×C411yescharacteristic
45C2×C4×Dic17C2×C411yescharacteristic
46C22×#3622C2×C412yes—
47C2×C8×D17—22no—
48C2×C8×D17—22no—
49C2×C8×D17—22no—
50C2×C8×D17—22no—
51C2×C8×D17—22no—
52C2×C8×D17—22no—
53C42×D17—22no—
54C42×D17—22no—
55(C2×#595)⋊C4—24no—
56(C2×#595)⋊C4C818yescomplemented
57C4×#3624—24no—
58C4×#3624—24no—
59C23×D17C22×C411yescharacteristic
60C22×#595—24no—
61C22×#595—24no—
62C22×#595—24no—
63C22×#595—24no—
64C22×#595—24no—
65C22×#595—24no—
66C22×#595C2×C818yes—
67C22×C4×C17C4211yescharacteristic
68C22×C4×C17C4211yescharacteristic
69C22×C4×C17C22×C411yescharacteristic
70C22×Dic17C4211yescharacteristic
71C22×Dic17C4211yescharacteristic
72C22×Dic17C22×C411yescharacteristic
73C2×C4×D17—22no—
74C2×C4×D17—22no—
75C2×C4×D17—22no—
76C2×C4×D17—22no—
77C2×C4×D17C2×C814yes—
78C2×C4×D17M1614yes—
79C2×C4×D17C2×D411yescharacteristic
80C2×C4×D17C2×D412yes—
81C2×C4×D17C2×Q811yescharacteristic
82C2×C4×D17#4112yes—
83C2×C4×D17#4112yes—
84C2×C4×D17#4111yescharacteristic
85C2×C4×D17#4111yescharacteristic
86C2×C4×D17#4112yes—
87C2×#3624—22no—
88C2×#3624—22no—
89C2×#3624—22no—
90C2×#3624—22no—
91C2×#3624C22⋊C414yes—
92C2×#3624C4⋊C414yes—
93C4×#595—42no—
94C4×#595—42no—
95C4×#595—42no—
96C4×#595—42no—
97#63242—24no—
98#63242—24no—
99#63242—24no—
100#63242—24no—
101C2×C8×C17—22no—
102C2×C8×C17—22no—
103C2×C8×C17—22no—
104C42×C17—22no—
105C4×Dic17—22no—
106C4×Dic17—21no—
107C4×Dic17—21no—
108C4×Dic17—21no—
109C4×Dic17—21no—
110C2×#3622—22no—
111C2×#3622—22no—
112C2×#3622—22no—
113C8×D17—42no—
114C8×D17—42no—
115C8×D17—42no—
116C8×D17—42no—
117#10797—171nomaximal, Sylow
118C23×C17C2×C4211yescharacteristic
119C22×D17#11712yes—
120C22×D17C4×D412yes—
121C22×D17C4×D411yescharacteristic
122C22×D17C4×Q811yescharacteristic
123C22×D17C22×C812yes—
124C22×D17C2×M1612yes—
125C22×D17#13112yes—
126C22×D17#13112yes—
127C2×#595—28no—
128C2×#595—28no—
129C2×#595—28no—
130C2×#595—44no—
131C2×#595—44no—
132C2×#595—44no—
133C2×#595—44no—
134C2×C4×C17—21no—
135C2×C4×C17—21no—
136C2×C4×C17—21no—
137C2×C4×C17—21no—
138C2×C4×C17C4×C812yes—
139C2×C4×C17#9712yes—
140C2×C4×C17#11712yes—
141C2×C4×C17C4×D412yes—
142C2×C4×C17C4×D411yescharacteristic
143C2×C4×C17C4×Q811yescharacteristic
144C2×Dic17—21no—
145C2×Dic17—21no—
146C2×Dic17—21no—
147C2×Dic17—21no—
148C2×Dic17C4×C812yes—
149C2×Dic17#9712yes—
150C2×Dic17C2×C22⋊C411yescharacteristic
151C2×Dic17C2×C4⋊C411yescharacteristic
152C2×Dic17#11711yescharacteristic
153C2×Dic17#11711yescharacteristic
154C2×Dic17#11711yescharacteristic
155C2×Dic17#11711yescharacteristic
156C4×D17—28no—
157C4×D17—28no—
158C4×D17#12112yes—
159C4×D17C22⋊Q812yes—
160C4×D17#12312yes—
161C4×D17#12312yes—
162C4×D17#12412yes—
163C4×D17#12512yes—
164C4×D17#12612yes—
165C4×D17#12612yes—
166#3624—24no—
167#3624—24no—
168C8×C17—42no—
169#3622—42no—
170C22×C4×C8—171no—
171C2×#336—171no—
172C2×#336—172no—
173C2×#336—172no—
174C4×#95—171no—
175C22×C17#37611yescharacteristic
176C22×C17C4×C22⋊C411yescharacteristic
177C22×C17C4×C4⋊C411yescharacteristic
178C22×C17C2×C4×C811yescharacteristic
179C22×C17C2×#9711yescharacteristic
180C22×C17#40511yescharacteristic
181C22×C17#40511yescharacteristic
182C2×D17#38712yes—
183C2×D17#38812yes—
184C2×D17#43114yes—
185C2×D17#43314yes—
186C2×D17C8×D414yes—
187C2×D17C8×D412yes—
188C2×D17#43514yes—
189C2×D17#43612yes—
190C2×D17C8×Q812yes—
191C2×D17#44612yes—
192#595—48no—
193C4×C17—22no—
194C4×C17—22no—
195C4×C17#38712yes—
196C4×C17#38812yes—
197Dic17—22no—
198Dic17—22no—
199Dic17#38011yescharacteristic
200Dic17#38111yescharacteristic
201Dic17#38211yescharacteristic
202Dic17#38311yescharacteristic
203C23×C8—171no—
204C23×C8—171no—
205C23×C8—172no—
206C22×C42—171no—
207C22×C42—172no—
208C2×C4×C8—172no—
209C2×C4×C8—172no—
210C2×C4×C8—344no—
211C2×#95—172no—
212C2×#95—172no—
213#336—172no—
214#336—171no—
215#336—344no—
216#336—344no—
217#336#59511yescharacteristic, complemented
218C2×C17#143411yescharacteristic
219C2×C17#174411yescharacteristic
220C2×C17#174611yescharacteristic
221C2×C17C8×C22⋊C411yescharacteristic
222C2×C17#175211yescharacteristic
223C2×C17C8×C4⋊C411yescharacteristic
224C2×C17#177011yescharacteristic
225D17#191614yes—
226D17#192314yes—
227C23×C4—171no—
228C23×C4—171no—
229C23×C4—171no—
230C23×C4—174no—
231C22×C8—172no—
232C22×C8—174no—
233C22×C8—172no—
234C22×C8—172no—
235C22×C8—172no—
236C22×C8—172no—
237C22×C8—342no—
238C22×C8—342no—
239C22×C8—342no—
240C22×C8—342no—
241C22×C8—342no—
242C22×C8—342no—
243C22×C8—342no—
244C22×C8—342no—
245C22×C8—341no—
246C22×C8—341no—
247C22×C8—342no—
248C22×C8C2×#59512yes—
249C2×C42—171no—
250C2×C42—171no—
251C2×C42—171no—
252C2×C42—342no—
253C2×C42—342no—
254C2×C42—342no—
255C2×C42—342no—
256C2×C42—342no—
257C2×C42—342no—
258C2×C42—342no—
259C2×C42—342no—
260C2×C42C2×#59511yescharacteristic
261C4×C8—344no—
262C4×C8—344no—
263#95—178no—
264#95—344no—
265C17#1079711yescharacteristic, complemented, Sylow
266C24—171no—
267C22×C4—171no—
268C22×C4—172no—
269C22×C4—172no—
270C22×C4—172no—
271C22×C4—171no—
272C22×C4—172no—
273C22×C4—171no—
274C22×C4—171no—
275C22×C4—171no—
276C22×C4—171no—
277C22×C4—171no—
278C22×C4—174no—
279C22×C4—174no—
280C22×C4—178no—
281C22×C4—342no—
282C22×C4—342no—
283C22×C4—342no—
284C22×C4—342no—
285C22×C4—344no—
286C22×C4—344no—
287C22×C4—344no—
288C22×C4—344no—
289C22×C4—344no—
290C22×C4—344no—
291C22×C4C4×#59511yescharacteristic
292C22×C4C4×#59511yescharacteristic
293C22×C4C22×#59511yescharacteristic
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—174no—
298C2×C8—174no—
299C2×C8—344no—
300C2×C8—344no—
301C2×C8—344no—
302C2×C8—344no—
303C2×C8—342no—
304C2×C8—342no—
305C2×C8—342no—
306C2×C8—342no—
307C2×C8—342no—
308C2×C8—342no—
309C2×C8—342no—
310C2×C8—682no—
311C2×C8—682no—
312C2×C8—682no—
313C2×C8—682no—
314C42—22no—
315C42—341no—
316C42—341no—
317C42—341no—
318C42—341no—
319C42—342no—
320C42—682no—
321C42—682no—
322C42—682no—
323C42—682no—
324C23—172no—
325C23—172no—
326C23—171no—
327C23—171no—
328C23—172no—
329C23—172no—
330C23—172no—
331C23—172no—
332C23C2×C4×#59511yescharacteristic
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—171no—
338C2×C4—171no—
339C2×C4—171no—
340C2×C4—171no—
341C2×C4—171no—
342C2×C4—171no—
343C2×C4—172no—
344C2×C4—172no—
345C2×C4—172no—
346C2×C4—172no—
347C2×C4—172no—
348C2×C4—172no—
349C2×C4—172no—
350C2×C4—172no—
351C2×C4—172no—
352C2×C4—172no—
353C2×C4—348no—
354C2×C4—348no—
355C2×C4—341no—
356C2×C4—341no—
357C2×C4—341no—
358C2×C4—341no—
359C2×C4—348no—
360C2×C4—348no—
361C2×C4—348no—
362C2×C4—684no—
363C2×C4—684no—
364C2×C4—684no—
365C2×C4—684no—
366C2×C4C8×#59512yes—
367C2×C4#1058753212yes—
368C2×C4#1058767712yes—
369C2×C4D4×#59512yes—
370C2×C4D4×#59511yescharacteristic
371C2×C4Q8×#59511yescharacteristic
372C8—42no—
373C8—344no—
374C8—344no—
375C8—682no—
376C22—172no—
377C22—172no—
378C22—174no—
379C22—174no—
380C22—174no—
381C22—174no—
382C22—172no—
383C22—172no—
384C22—172no—
385C22—172no—
386C22#1176374511yescharacteristic
387C22C22⋊C4×#59511yescharacteristic
388C22C4⋊C4×#59511yescharacteristic
389C22C2×C8×#59511yescharacteristic
390C22C2×#1058753211yescharacteristic
391C22#1176377511yescharacteristic
392C22#1176377511yescharacteristic
393C4—22no—
394C4—22no—
395C4—171no—
396C4—171no—
397C4—171no—
398C4—171no—
399C4—342no—
400C4—342no—
401C4—688no—
402C4#1176375812yes—
403C4#1176375912yes—
404C2—174no—
405C2—174no—
406C2#1454395911yescharacteristic
407C2#1454449711yescharacteristic
408C2#1454450411yescharacteristic
409C2#1454451911yescharacteristic
410C2#1454452311yescharacteristic
411C2#1454457711yescharacteristic
412C2#1454458111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C22×#595
commutatorC22×C17C2×C4×C8
FittingC17×#336C4
socleC23×C17C2×C42
prime radicalC23×D17C22×C4
cosocleC22×C4×D17C23
hypercenter#336#595
hypocenterC17#10797
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ #336

Complements

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

NH ≅ G/Ntype
10. C2×C4×#3624C4semidirect
11. C2×C4×#3624C4semidirect
18. #11762564C4semidirect
19. #11762563C4semidirect
20. C17×#336C4semidirect
56. (C2×#595)⋊C4C8semidirect
217. #336#595semidirect
265. C17#10797semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#632422
C2×#117636742
C4×(C2×#595)⋊C42
D17×#3362
#1079717