Finite Group Databasebeta

← #17952433

Subgroups — #17952433

Order 4352.

1158 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 1158 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14544675C212yesmaximal, complemented
2C2×#11763655C212yesmaximal, complemented
3C2×#11763652C212yesmaximal
4C22×#10587563C211yesmaximal, characteristic
5C2×C22⋊#3624C2214yes—
6#11763675—24no—
7#11763655—24no—
8#11763652—24no—
9C24×Dic17C411yescharacteristic
10C2×#10587563—24no—
11C2×#10587563—24no—
12C2×#10587563—24no—
13C22×#63225C411yescharacteristic
14C22×#63225C2211yescharacteristic
15C22×C22⋊Dic17C2211yescharacteristic
16C22×C4×Dic17C411yescharacteristic
17C22×C4×Dic17C2211yescharacteristic
18C22×C22⋊C4×C17C411yescharacteristic
19C25×C17C2×C411yescharacteristic
20C23×C4×C17C2×C411yescharacteristic
21C23×C4×C17C2×C411yescharacteristic
22C23×Dic17—22no—
23C23×Dic17—22no—
24C23×Dic17—22no—
25C23×Dic17—22no—
26C23×Dic17—22no—
27C23×Dic17—22no—
28C23×Dic17C814yescomplemented
29C23×Dic17C2×C411yescharacteristic
30C23×Dic17C2×C411yescharacteristic
31C23×Dic17C2×C411yescharacteristic
32C23×Dic17C2311yescharacteristic
33C22×#3624—24no—
34C2×C22⋊C4×C17—22no—
35C2×C22⋊C4×C17—22no—
36C2×C22⋊C4×C17—22no—
37C2×C22⋊Dic17—22no—
38C2×C22⋊Dic17—22no—
39C2×C22⋊Dic17D414yes—
40C2×#63225—22no—
41C2×#63225—22no—
42C2×#63225—22no—
43C2×#63225—22no—
44C2×#63225—22no—
45C2×#63225D414yes—
46C2×C4×Dic17—22no—
47C2×C4×Dic17—22no—
48C2×C4×Dic17—22no—
49C2×C4×Dic17—22no—
50C2×C4×Dic17—22no—
51C2×C4×Dic17D414yes—
52#10587563—232no—
53C22⋊#3624—24no—
54C22⋊#3624—24no—
55C24×C17—21no—
56C24×C17—21no—
57C24×C17—21no—
58C24×C17—21no—
59C24×C17—42no—
60C24×C17—42no—
61C24×C17C22⋊C412yes—
62C24×C17C2×C812yes—
63C24×C17M1612yes—
64C24×C17C22×C411yescharacteristic
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17—42no—
70C22×C4×C17—42no—
71C22×C4×C17C22⋊C412yes—
72C22×C4×C17C22⋊C412yes—
73C22×Dic17—28no—
74C22×Dic17—28no—
75C22×Dic17—28no—
76C22×Dic17—28no—
77C22×Dic17—28no—
78C22×Dic17—21no—
79C22×Dic17—21no—
80C22×Dic17—21no—
81C22×Dic17—21no—
82C22×Dic17—21no—
83C22×Dic17—21no—
84C22×Dic17—21no—
85C22×Dic17—21no—
86C22×Dic17—28no—
87C22×Dic17—28no—
88C22×Dic17—21no—
89C22×Dic17—21no—
90C22×Dic17—42no—
91C22×Dic17—42no—
92C22×Dic17C22⋊C412yes—
93C22×Dic17C22⋊C412yes—
94C22×Dic17C22⋊C412yes—
95C22×Dic17C2×C812yes—
96C22×Dic17C2×C812yes—
97C22×Dic17M1612yes—
98C22×Dic17M1612yes—
99C22×Dic17C2×D412yes—
100C22×Dic17C2×D412yes—
101C22×Dic17C2×D412yes—
102C2×#3624—48no—
103C2×#3624—44no—
104C22⋊C4×C17—28no—
105C22⋊Dic17—28no—
106#63225—28no—
107#63225—28no—
108C4×Dic17—28no—
109C4×Dic17—28no—
110#8300—171nomaximal, Sylow
111C23×C17—22no—
112C23×C17—22no—
113C23×C17—22no—
114C23×C17—22no—
115C23×C17—22no—
116C23×C17—22no—
117C23×C17—22no—
118C23×C17—22no—
119C23×C17—42no—
120C23×C17—42no—
121C23×C17—44no—
122C23×C17—44no—
123C23×C17—44no—
124C23×C17—44no—
125C23×C17—42no—
126C23×C17—42no—
127C23×C17—42no—
128C23×C17—42no—
129C23×C17C22⋊C814yes—
130C23×C17C2×C22⋊C411yescharacteristic
131C23×C17C2×C22⋊C411yescharacteristic
132C23×C17C2×C22⋊C411yescharacteristic
133C23×C17C22×C811yescharacteristic
134C23×C17C2×M1611yescharacteristic
135C23×C17C2×M1611yescharacteristic
136C23×C17C2×M1611yescharacteristic
137C2×C4×C17—22no—
138C2×C4×C17—22no—
139C2×C4×C17—24no—
140C2×C4×C17—42no—
141C2×C4×C17—42no—
142C2×C4×C17—42no—
143C2×C4×C17—42no—
144C2×C4×C17—42no—
145C2×Dic17—232no—
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—22no—
155C2×Dic17—22no—
156C2×Dic17—22no—
157C2×Dic17—22no—
158C2×Dic17—24no—
159C2×Dic17—22no—
160C2×Dic17—42no—
161C2×Dic17—42no—
162C2×Dic17—42no—
163C2×Dic17—42no—
164C2×Dic17—42no—
165C2×Dic17C22⋊C814yes—
166C2×Dic17C22⋊C814yes—
167C2×Dic17#12014yes—
168#3624—84no—
169C22×#117—171no—
170#1817—172no—
171C2×#324—172no—
172C2×#323—172no—
173C22×C17—22no—
174C22×C17—22no—
175C22×C17—22no—
176C22×C17—22no—
177C22×C17—21no—
178C22×C17—21no—
179C22×C17—21no—
180C22×C17—21no—
181C22×C17—24no—
182C22×C17—44no—
183C22×C17—44no—
184C22×C17—44no—
185C22×C17—44no—
186C22×C17—44no—
187C22×C17—44no—
188C22×C17—42no—
189C22×C17—42no—
190C22×C17#37911yescharacteristic
191C22×C17C2×C22⋊C811yescharacteristic
192C22×C17C2×C22⋊C811yescharacteristic
193C22×C17C2×C22⋊C811yescharacteristic
194C22×C17#40711yescharacteristic
195C22×C17#40711yescharacteristic
196C22×C17#40711yescharacteristic
197C22×C17#41012yes—
198C22×C17#41312yes—
199C4×C17—42no—
200C4×C17—42no—
201Dic17—24no—
202Dic17—24no—
203Dic17—24no—
204Dic17—42no—
205C24×C4—171no—
206C2×#117—344no—
207C2×#117—344no—
208C2×#117—344no—
209C22×C4⋊C4—171no—
210C22×C4⋊C4—171no—
211C22×C22⋊C4—171no—
212C22×C22⋊C4#59511yescharacteristic
213C22×C42—171no—
214C22×C42—171no—
215C2×C22⋊C8—174no—
216#336—344no—
217#324—344no—
218#323—344no—
219C2×C17—21no—
220C2×C17—21no—
221C2×C17—21no—
222C2×C17—21no—
223C2×C17—44no—
224C2×C17#145812yes—
225C2×C17#146412yes—
226C2×C17#177911yescharacteristic
227C2×C17#178211yescharacteristic
228C2×C17#178511yescharacteristic
229C25C2×#59511yescharacteristic
230C23×C4—171no—
231C23×C4—171no—
232C23×C4—171no—
233C23×C4—174no—
234C23×C4—171no—
235C23×C4—342no—
236C23×C4—342no—
237C23×C4—342no—
238C23×C4—342no—
239C23×C4—342no—
240C23×C4—342no—
241C23×C4C2×#59511yescharacteristic
242C23×C4C2×#59511yescharacteristic
243C22×C8—344no—
244#117—3432no—
245C2×C4⋊C4—174no—
246C2×C4⋊C4—342no—
247C2×C4⋊C4—342no—
248C2×C4⋊C4—342no—
249C2×C4⋊C4—342no—
250C2×C4⋊C4—342no—
251C2×C22⋊C4—22no—
252C2×C22⋊C4—22no—
253C2×C22⋊C4—22no—
254C2×C22⋊C4—174no—
255C2×C22⋊C4—342no—
256C2×C22⋊C4—342no—
257C2×C42—174no—
258C2×C42—342no—
259C2×C42—342no—
260C2×C42—342no—
261C2×C42—342no—
262C2×C42—342no—
263C22⋊C8—344no—
264C22⋊C8—344no—
265C17#830011yescharacteristic, complemented, Sylow
266C24—21no—
267C24—21no—
268C24—21no—
269C24—21no—
270C24—42no—
271C24—42no—
272C24#6324212yes—
273C24#6324312yes—
274C24C22⋊#59512yes—
275C24C22×#59511yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—172no—
283C22×C4—172no—
284C22×C4—172no—
285C22×C4—172no—
286C22×C4—172no—
287C22×C4—172no—
288C22×C4—172no—
289C22×C4—172no—
290C22×C4—172no—
291C22×C4—172no—
292C22×C4—348no—
293C22×C4—348no—
294C22×C4—348no—
295C22×C4—348no—
296C22×C4—348no—
297C22×C4—348no—
298C22×C4—341no—
299C22×C4—341no—
300C22×C4—341no—
301C22×C4—341no—
302C22×C4—341no—
303C22×C4—341no—
304C22×C4—341no—
305C22×C4—341no—
306C22×C4—348no—
307C22×C4—341no—
308C22×C4—341no—
309C22×C4—682no—
310C22×C4—682no—
311C22×C4C22⋊#59512yes—
312C22×C4C22⋊#59512yes—
313C2×C8—684no—
314C2×C8—688no—
315C4⋊C4—348no—
316C4⋊C4—348no—
317C22⋊C4—28no—
318C22⋊C4—348no—
319C42—348no—
320C42—348no—
321C23—22no—
322C23—22no—
323C23—22no—
324C23—22no—
325C23—22no—
326C23—22no—
327C23—22no—
328C23—22no—
329C23—44no—
330C23—44no—
331C23—42no—
332C23—42no—
333C23—44no—
334C23—44no—
335C23—42no—
336C23—42no—
337C23—42no—
338C23—42no—
339C23#1058754314yes—
340C23C2×#6324211yescharacteristic
341C23C2×#6324311yescharacteristic
342C23D17⋊M1611yescharacteristic
343C23D17⋊M1611yescharacteristic
344C23C2×C22⋊#59511yescharacteristic
345C23C2×C22⋊#59511yescharacteristic
346C23C2×C22⋊#59511yescharacteristic
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—24no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—174no—
356C2×C4—174no—
357C2×C4—174no—
358C2×C4—3432no—
359C2×C4—342no—
360C2×C4—342no—
361C2×C4—342no—
362C2×C4—342no—
363C2×C4—342no—
364C2×C4—342no—
365C2×C4—342no—
366C2×C4—342no—
367C2×C4—342no—
368C2×C4—342no—
369C2×C4—342no—
370C2×C4—342no—
371C2×C4—344no—
372C2×C4—342no—
373C2×C4—682no—
374C2×C4—682no—
375C2×C4—682no—
376C2×C4—682no—
377C2×C4—682no—
378C8—1364no—
379C22—22no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—24no—
388C22—44no—
389C22—44no—
390C22—44no—
391C22—44no—
392C22—44no—
393C22—44no—
394C22—42no—
395C22—42no—
396C22#1176375011yescharacteristic
397C22#1176377711yescharacteristic
398C22#1176377711yescharacteristic
399C22C2×#1058754311yescharacteristic
400C22#1176378011yescharacteristic
401C22#1176378011yescharacteristic
402C22#1176378111yescharacteristic
403C22#1176378912yes—
404C22#1176379612yes—
405C4—42no—
406C4—42no—
407C4—344no—
408C4—344no—
409C4—344no—
410C4—682no—
411C2—21no—
412C2—21no—
413C2—21no—
414C2—21no—
415C2—44no—
416C2#1454401612yes—
417C2#1454403612yes—
418C2#1454460711yescharacteristic
419C2#1454461411yescharacteristic
420C2#1454462111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC23×C17C22×C8
FrattiniC24C22×#595
FittingC22×C22⋊C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC25×C17C2×C4
cosocleC23×Dic17C23
hypercenterC22×C22⋊C4#595
hypocenterC17#8300
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #14544675C2semidirect
2. C2×#11763655C2semidirect
28. C23×Dic17C8semidirect
265. C17#8300semidirect

Maximal subgroups

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

subgroupindex
#145446752
C2×#117636552
C2×#117636522
C22×#105875632
#830017