Finite Group Databasebeta

← #17950028

Subgroups — #17950028

Order 4352.

538 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 92 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#14544676C211yesmaximal, characteristic, complemented
2C4×#10587543C211yesmaximal, characteristic, complemented
3#14543604C212yesmaximal, complemented
4#14543600C212yesmaximal, complemented
5#14537080C211yesmaximal, characteristic
6C2×#10587543—21no—
7C2×#10587543—21no—
8C2×C4×#3624—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587632C411yescharacteristic
13C2×#10587624C411yescharacteristic
14C2×C42×D17C2211yescharacteristic
15#11762716C2211yescharacteristic
16#11762712C2211yescharacteristic
17#11762697—21no—
18#11762697—21no—
19#11762685—21no—
20#11762685—21no—
21#11762675C411yescharacteristic
22C2×C17×#124C411yescharacteristic
23C22×Q8×C17C2×C411yescharacteristic
24C22×D4×C17C2×C411yescharacteristic
25C22×C22⋊D17—21no—
26C22×C4×D17C2×C411yescharacteristic
27C22×C4×D17D411yescharacteristic
28C22×C4×D17D411yescharacteristic
29C22×#3624—22no—
30C22×#3624—22no—
31C17×#124—42no—
32C2×C22⋊C4×C17—21no—
33C2×C22⋊C4×C17—21no—
34C2×C42×C17C2×C411yescharacteristic
35C2×C22⋊Dic17—21no—
36C2×C22⋊Dic17—21no—
37C2×C22⋊Dic17—21no—
38#10587632—42no—
39#10587624—42no—
40C2×#63227—21no—
41C2×C4⋊Dic17C2×C411yescharacteristic
42C2×C4⋊Dic17C2×C411yescharacteristic
43C2×#63225—21no—
44C2×C4×Dic17D411yescharacteristic
45C2×C4×Dic17D411yescharacteristic
46C2×C4×Dic17C2311yescharacteristic
47C42×D17—42no—
48#10587543—24no—
49#10587543—42no—
50C4×#3624—42no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54#10587502—21no—
55C24×C17—21no—
56C23×D17C22⋊C411yescharacteristic
57C2×Q8×C17—22no—
58C2×Q8×C17—41no—
59C2×Q8×C17—41no—
60C2×D4×C17—22no—
61C2×D4×C17—41no—
62C2×D4×C17—41no—
63C22×C4×C17—21no—
64C22×C4×C17C22⋊C411yescharacteristic
65C22×C4×C17C22⋊C411yescharacteristic
66C22×C4×C17C22×C411yescharacteristic
67C2×C22⋊D17—42no—
68C2×C22⋊D17—42no—
69C2×C22⋊D17—42no—
70C22×Dic17—21no—
71C22×Dic17—21no—
72C22×Dic17C22⋊C411yescharacteristic
73C22×Dic17C2×D411yescharacteristic
74C22×Dic17C2×D411yescharacteristic
75C2×C4×D17—22no—
76C2×C4×D17—22no—
77C2×C4×D17—22no—
78C2×C4×D17—22no—
79C2×C4×D17—22no—
80C2×C4×D17—22no—
81C2×C4×D17—41no—
82C2×C4×D17—41no—
83C2×C4×D17—41no—
84C2×#3624—24no—
85C2×#3624—42no—
86C2×#3624—42no—
87C2×#3624—42no—
88C2×#3624—42no—
89C2×#3624—42no—
90C22⋊C4×C17—42no—
91C22⋊C4×C17—42no—
92C42×C17—22no—
93C22⋊Dic17—42no—
94C22⋊Dic17—42no—
95C22⋊Dic17—42no—
96#63227—42no—
97C4⋊Dic17—41no—
98C4⋊Dic17—41no—
99#63225—42no—
100C4×Dic17—22no—
101C4×Dic17—41no—
102C4×Dic17—41no—
103#7670—171nomaximal, Sylow
104C23×C17—41no—
105C23×C17—41no—
106C23×C17—41no—
107C23×C17—41no—
108C23×C17—41no—
109C23×C17—41no—
110C23×C17—41no—
111C23×C17C2×C22⋊C411yescharacteristic
112C22×D17—21no—
113C22×D17—21no—
114C22×D17—21no—
115C22×D17—21no—
116C22×D17—21no—
117C22×D17—21no—
118C22×D17#10412yes—
119Q8×C17—82no—
120D4×C17—82no—
121C2×C4×C17—21no—
122C2×C4×C17—21no—
123C2×C4×C17—21no—
124C2×C4×C17—21no—
125C2×C4×C17—21no—
126C2×C4×C17—21no—
127C2×C4×C17—21no—
128C2×C4×C17—41no—
129C2×C4×C17—41no—
130C2×C4×C17—41no—
131C2×C4×C17#9912yes—
132C2×C4×C17#13112yes—
133C22⋊D17—84no—
134C2×Dic17—21no—
135C2×Dic17—21no—
136C2×Dic17—21no—
137C2×Dic17—21no—
138C2×Dic17—21no—
139C2×Dic17—21no—
140C2×Dic17—41no—
141C2×Dic17—41no—
142C2×Dic17—41no—
143C2×Dic17—41no—
144C2×Dic17—41no—
145C2×Dic17—41no—
146C2×Dic17#10012yes—
147C2×Dic17#13512yes—
148C2×Dic17#13512yes—
149C4×D17—44no—
150C4×D17—44no—
151C4×D17—44no—
152#3624—44no—
153#3624—82no—
154#2850—171no—
155#1817—171no—
156C4×C22⋊C8—171no—
157#1272—172no—
158#1270—172no—
159C22×C17—81no—
160C22×C17—81no—
161C22×C17—81no—
162C22×C17—81no—
163C22×C17—81no—
164C22×C17—81no—
165C22×C17—81no—
166C22×C17#40811yescharacteristic
167C22×C17C2×#9911yescharacteristic
168C22×C17C2×#10011yescharacteristic
169C22×C17#41611yescharacteristic
170C22×C17#41611yescharacteristic
171C22×C17C2×#10411yescharacteristic
172C22×C17#42111yescharacteristic
173C2×D17—22no—
174C2×D17—22no—
175C2×D17—22no—
176C2×D17—41no—
177C2×D17—41no—
178C2×D17—41no—
179C2×D17—41no—
180C4×C17—22no—
181C4×C17—22no—
182C4×C17—41no—
183C4×C17—81no—
184Dic17—22no—
185Dic17—22no—
186Dic17—22no—
187Dic17—81no—
188Dic17—81no—
189C2×#124#59511yescharacteristic
190C2×C22⋊Q8—171no—
191C2×#121—171no—
192C22×C42—171no—
193C2×C22⋊C8—341no—
194C2×C22⋊C8—341no—
195C2×C4×C8—341no—
196#391—171no—
197#390—171no—
198#388—341no—
199#388—341no—
200#386—341no—
201#386—341no—
202#382—171no—
203#336—172no—
204#336—172no—
205#336—341no—
206C2×C17—161no—
207C2×C17#147111yescharacteristic
208C2×C17#148211yescharacteristic
209C2×C17#149411yescharacteristic
210C2×C17#150111yescharacteristic
211C2×C17#151611yescharacteristic
212C2×C17#152711yescharacteristic
213C2×C17#154311yescharacteristic
214D17—42no—
215C22×Q8C2×#59511yescharacteristic
216C22×D4—341no—
217C22×D4C2×#59511yescharacteristic
218C23×C4—171no—
219C23×C4—171no—
220C23×C4—171no—
221C22×C8—342no—
222C22×C8—342no—
223#124—42no—
224C22⋊Q8—682no—
225#121—682no—
226C2×C4⋊C4—171no—
227C2×C4⋊C4—171no—
228C2×C4⋊C4—341no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—341no—
232C2×C22⋊C4—341no—
233C2×C22⋊C4—341no—
234C2×C22⋊C4—341no—
235C2×C42—171no—
236C2×C42—171no—
237C2×C42—171no—
238C2×C42—682no—
239C2×C42C2×#59511yescharacteristic
240C22⋊C8—344no—
241C22⋊C8—682no—
242C4×C8—682no—
243#95—341no—
244#95—341no—
245#95—341no—
246#95—341no—
247C17#767011yescharacteristic, complemented, Sylow
248C24—21no—
249C24—171no—
250C2×Q8—22no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×D4—22no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—682no—
257C2×D4—682no—
258C2×D4—682no—
259C22×C4—21no—
260C22×C4—171no—
261C22×C4—171no—
262C22×C4—171no—
263C22×C4—342no—
264C22×C4—342no—
265C22×C4—342no—
266C22×C4—342no—
267C22×C4—342no—
268C22×C4—342no—
269C22×C4—341no—
270C22×C4—341no—
271C22×C4—681no—
272C22×C4—681no—
273C22×C4—681no—
274C22×C4C22⋊#59511yescharacteristic
275C22×C4C22⋊#59511yescharacteristic
276C22×C4C22×#59511yescharacteristic
277C2×C8—344no—
278C2×C8—682no—
279C2×C8—682no—
280C2×C8—682no—
281C2×C8—682no—
282C2×C8—682no—
283C4⋊C4—681no—
284C4⋊C4—681no—
285C4⋊C4—682no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C22⋊C4—682no—
289C22⋊C4—682no—
290C22⋊C4—682no—
291C22⋊C4—682no—
292C42—22no—
293C42—342no—
294C42—681no—
295C42—681no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—172no—
304C23—341no—
305C23—341no—
306C23—341no—
307C23—341no—
308C23—341no—
309C23—341no—
310C23C2×C22⋊#59511yescharacteristic
311Q8—82no—
312D4—82no—
313D4—1364no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—172no—
325C2×C4—172no—
326C2×C4—172no—
327C2×C4—341no—
328C2×C4—341no—
329C2×C4—341no—
330C2×C4—341no—
331C2×C4—341no—
332C2×C4—341no—
333C2×C4—684no—
334C2×C4—684no—
335C2×C4—684no—
336C2×C4—681no—
337C2×C4—681no—
338C2×C4—681no—
339C2×C4—681no—
340C2×C4—681no—
341C2×C4—681no—
342C2×C4#1058755112yes—
343C2×C4#1058767812yes—
344C8—684no—
345C8—1362no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—342no—
354C22—342no—
355C22—342no—
356C22—681no—
357C22—681no—
358C22—681no—
359C22—681no—
360C22#1176378311yescharacteristic
361C22C2×#1058755111yescharacteristic
362C22D17⋊#10011yescharacteristic
363C22#1176379911yescharacteristic
364C22#1176379911yescharacteristic
365C22D17⋊#10411yescharacteristic
366C22#1176380611yescharacteristic
367C4—22no—
368C4—22no—
369C4—41no—
370C4—81no—
371C4—342no—
372C4—342no—
373C4—342no—
374C4—1361no—
375C4—1361no—
376C2—161no—
377C2—682no—
378C2#1454405911yescharacteristic
379C2#1454409611yescharacteristic
380C2#1454413611yescharacteristic
381C2#1454415911yescharacteristic
382C2#1454421011yescharacteristic
383C2#1454424411yescharacteristic
384C2#1454428811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×#124C4
socleC23×C17C2×C22⋊C4
prime radicalC2×#10587624C4
cosocleC2×C4×Dic17C23
hypercenterC2×#124#595
hypocenterC17#7670
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #14544676C2semidirect
2. C4×#10587543C2semidirect
3. #14543604C2semidirect
4. #14543600C2semidirect
247. C17#7670semidirect

Maximal subgroups

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

subgroupindex
#145446762
C4×#105875432
#145436042
#145436002
#145370802
#767017