Finite Group Databasebeta

← #17952434

Subgroups — #17952434

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#14544674C212yesmaximal, complemented
2C2×#11763655C212yesmaximal, complemented
3C2×#11763653C212yesmaximal
4C22×#10587558C211yesmaximal, characteristic
5C2×C22⋊#3624C2214yes—
6#11763675—24no—
7#11763655—24no—
8#11763653—24no—
9C23×C4×D17C411yescharacteristic
10C2×#10587558—24no—
11C2×#10587558—24no—
12C2×#10587558—24no—
13C22×#63225C411yescharacteristic
14C22×#63225C2211yescharacteristic
15C22×#63227C411yescharacteristic
16C22×#63227C2211yescharacteristic
17C22×C4×Dic17C2211yescharacteristic
18C22×C42×C17C411yescharacteristic
19C24×D17C2×C411yescharacteristic
20C23×C4×C17C2×C411yescharacteristic
21C23×C4×C17C2×C411yescharacteristic
22C23×C4×C17C2×C411yescharacteristic
23C23×Dic17C2×C411yescharacteristic
24C23×Dic17C2×C411yescharacteristic
25C23×Dic17C2311yescharacteristic
26C22×C4×D17—22no—
27C22×C4×D17—22no—
28C22×C4×D17—22no—
29C22×C4×D17—22no—
30C22×C4×D17—22no—
31C22×C4×D17—22no—
32C22×C4×D17C814yescomplemented
33C22×#3624—24no—
34C2×C42×C17—22no—
35C2×C42×C17—22no—
36C2×C42×C17—22no—
37C2×#63227—22no—
38C2×#63227—22no—
39C2×#63227—22no—
40C2×#63227—22no—
41C2×#63227—22no—
42C2×#63227D414yes—
43C2×#63225—22no—
44C2×#63225—22no—
45C2×#63225—22no—
46C2×#63225—22no—
47C2×#63225—22no—
48C2×#63225D414yes—
49C2×C4×Dic17—22no—
50C2×C4×Dic17—22no—
51C2×C4×Dic17D414yes—
52#10587558—232no—
53C22⋊#3624—24no—
54C22⋊#3624—24no—
55C24×C17C22×C411yescharacteristic
56C23×D17—21no—
57C23×D17—21no—
58C23×D17—21no—
59C23×D17—21no—
60C23×D17—42no—
61C23×D17—42no—
62C23×D17C22⋊C412yes—
63C23×D17C2×C812yes—
64C23×D17M1612yes—
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17—21no—
70C22×C4×C17—21no—
71C22×C4×C17—21no—
72C22×C4×C17—21no—
73C22×C4×C17—42no—
74C22×C4×C17—42no—
75C22×C4×C17C22⋊C412yes—
76C22×C4×C17C22⋊C412yes—
77C22×C4×C17C22⋊C412yes—
78C22×C4×C17C2×C812yes—
79C22×C4×C17M1612yes—
80C22×Dic17—21no—
81C22×Dic17—21no—
82C22×Dic17—21no—
83C22×Dic17—21no—
84C22×Dic17—21no—
85C22×Dic17—21no—
86C22×Dic17—42no—
87C22×Dic17—42no—
88C22×Dic17C22⋊C412yes—
89C22×Dic17C22⋊C412yes—
90C22×Dic17C2×C812yes—
91C22×Dic17M1612yes—
92C22×Dic17C2×D412yes—
93C22×Dic17C2×D412yes—
94C22×Dic17C2×D412yes—
95C2×C4×D17—28no—
96C2×C4×D17—28no—
97C2×C4×D17—28no—
98C2×C4×D17—28no—
99C2×C4×D17—28no—
100C2×C4×D17—28no—
101C2×C4×D17—28no—
102C2×#3624—48no—
103C2×#3624—44no—
104C42×C17—28no—
105#63227—28no—
106#63227—28no—
107#63225—28no—
108#63225—28no—
109C4×Dic17—28no—
110#8300—171nomaximal, Sylow
111C23×C17—22no—
112C23×C17—22no—
113C23×C17C2×C22⋊C411yescharacteristic
114C23×C17C2×C22⋊C411yescharacteristic
115C23×C17C2×C22⋊C411yescharacteristic
116C23×C17C22×C811yescharacteristic
117C23×C17C2×M1611yescharacteristic
118C23×C17C2×M1611yescharacteristic
119C23×C17C2×M1611yescharacteristic
120C22×D17—22no—
121C22×D17—22no—
122C22×D17—22no—
123C22×D17—22no—
124C22×D17—22no—
125C22×D17—22no—
126C22×D17—44no—
127C22×D17—44no—
128C22×D17—42no—
129C22×D17—42no—
130C22×D17—42no—
131C22×D17—42no—
132C22×D17—42no—
133C22×D17—42no—
134C22×D17—44no—
135C22×D17—44no—
136C22×D17C22⋊C814yes—
137C2×C4×C17—22no—
138C2×C4×C17—22no—
139C2×C4×C17—22no—
140C2×C4×C17—22no—
141C2×C4×C17—22no—
142C2×C4×C17—22no—
143C2×C4×C17—22no—
144C2×C4×C17—22no—
145C2×C4×C17—42no—
146C2×C4×C17—42no—
147C2×C4×C17—42no—
148C2×C4×C17—42no—
149C2×C4×C17—42no—
150C2×C4×C17—42no—
151C2×C4×C17C22⋊C814yes—
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—24no—
161C2×Dic17—42no—
162C2×Dic17—42no—
163C2×Dic17—42no—
164C2×Dic17—42no—
165C2×Dic17C22⋊C814yes—
166C2×Dic17#12014yes—
167C4×D17—232no—
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#37911yescharacteristic
182C22×C17C2×C22⋊C811yescharacteristic
183C22×C17C2×C22⋊C811yescharacteristic
184C22×C17C2×C22⋊C811yescharacteristic
185C22×C17#40711yescharacteristic
186C22×C17#40711yescharacteristic
187C22×C17#40711yescharacteristic
188C22×C17#41012yes—
189C22×C17#41312yes—
190C2×D17—24no—
191C2×D17—44no—
192C2×D17—44no—
193C2×D17—44no—
194C2×D17—44no—
195C2×D17—44no—
196C2×D17—42no—
197C2×D17—42no—
198C2×D17—44no—
199C4×C17—24no—
200C4×C17—42no—
201C4×C17—42no—
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—171no—
213C22×C42—171no—
214C22×C42#59511yescharacteristic
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#145812yes—
224C2×C17#146412yes—
225C2×C17#177911yescharacteristic
226C2×C17#178211yescharacteristic
227C2×C17#178511yescharacteristic
228D17—44no—
229C25—171no—
230C23×C4—171no—
231C23×C4—171no—
232C23×C4—171no—
233C23×C4—174no—
234C23×C4—342no—
235C23×C4—342no—
236C23×C4—342no—
237C23×C4—342no—
238C23×C4—342no—
239C23×C4—342no—
240C23×C4C2×#59511yescharacteristic
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—174no—
252C2×C22⋊C4—342no—
253C2×C22⋊C4—342no—
254C2×C22⋊C4—342no—
255C2×C22⋊C4—342no—
256C2×C22⋊C4—342no—
257C2×C42—22no—
258C2×C42—22no—
259C2×C42—22no—
260C2×C42—174no—
261C2×C42—342no—
262C2×C42—342no—
263C22⋊C8—344no—
264C22⋊C8—344no—
265C17#830011yescharacteristic, complemented, Sylow
266C24—172no—
267C24—172no—
268C24—172no—
269C24—341no—
270C24—341no—
271C24—341no—
272C24—341no—
273C24—682no—
274C24—682no—
275C24C22×#59511yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—172no—
287C22×C4—172no—
288C22×C4—172no—
289C22×C4—172no—
290C22×C4—172no—
291C22×C4—172no—
292C22×C4—172no—
293C22×C4—348no—
294C22×C4—348no—
295C22×C4—348no—
296C22×C4—348no—
297C22×C4—348no—
298C22×C4—348no—
299C22×C4—341no—
300C22×C4—341no—
301C22×C4—341no—
302C22×C4—341no—
303C22×C4—348no—
304C22×C4—341no—
305C22×C4—341no—
306C22×C4—682no—
307C22×C4—682no—
308C22×C4#6324212yes—
309C22×C4#6324312yes—
310C22×C4C22⋊#59512yes—
311C22×C4C22⋊#59512yes—
312C22×C4C22⋊#59512yes—
313C2×C8—684no—
314C2×C8—688no—
315C4⋊C4—348no—
316C4⋊C4—348no—
317C22⋊C4—348no—
318C22⋊C4—348no—
319C42—28no—
320C42—348no—
321C23—22no—
322C23—22no—
323C23—174no—
324C23—342no—
325C23—342no—
326C23—342no—
327C23—342no—
328C23—342no—
329C23—342no—
330C23—684no—
331C23—684no—
332C23—682no—
333C23—682no—
334C23—684no—
335C23—684no—
336C23—682no—
337C23—682no—
338C23—682no—
339C23—682no—
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—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—174no—
362C2×C4—174no—
363C2×C4—3432no—
364C2×C4—342no—
365C2×C4—342no—
366C2×C4—342no—
367C2×C4—342no—
368C2×C4—342no—
369C2×C4—342no—
370C2×C4—344no—
371C2×C4—342no—
372C2×C4—344no—
373C2×C4—682no—
374C2×C4—682no—
375C2×C4—682no—
376C2×C4—682no—
377C2×C4#1058754314yes—
378C8—1364no—
379C22—22no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—344no—
388C22—684no—
389C22—684no—
390C22—684no—
391C22—684no—
392C22—684no—
393C22—684no—
394C22—682no—
395C22—682no—
396C22#1176375011yescharacteristic
397C22#1176377711yescharacteristic
398C22#1176377711yescharacteristic
399C22C2×#1058754311yescharacteristic
400C22#1176378011yescharacteristic
401C22#1176378011yescharacteristic
402C22#1176378111yescharacteristic
403C22#1176378812yes—
404C22#1176379512yes—
405C4—24no—
406C4—42no—
407C4—42no—
408C4—344no—
409C4—344no—
410C4—682no—
411C2—21no—
412C2—21no—
413C2—21no—
414C2—21no—
415C2—684no—
416C2#1454401712yes—
417C2#1454403712yes—
418C2#1454460711yescharacteristic
419C2#1454461311yescharacteristic
420C2#1454462011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC23×C17C22×C8
FrattiniC24C22×#595
FittingC22×C42×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC24×D17C2×C4
cosocleC23×Dic17C23
hypercenterC22×C42#595
hypocenterC17#8300
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
1. #14544674C2semidirect
2. C2×#11763655C2semidirect
32. C22×C4×D17C8semidirect
265. C17#8300semidirect

Maximal subgroups

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

subgroupindex
#145446742
C2×#117636552
C2×#117636532
C22×#105875582
#830017