Finite Group Databasebeta

← #17950030

Subgroups — #17950030

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#14543605C212yesmaximal, complemented
4#14543601C212yesmaximal, complemented
5#14537086C211yesmaximal, characteristic
6C2×#10587543—21no—
7C2×#10587543—21no—
8C2×C4×#3624—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587561C411yescharacteristic
13C2×#10587583C411yescharacteristic
14C2×#10587581C411yescharacteristic
15C2×C42×D17C2211yescharacteristic
16#11762714C2211yescharacteristic
17#11762710C2211yescharacteristic
18#11762701—21no—
19#11762701—21no—
20#11762687—21no—
21#11762687—21no—
22C17×#382C411yescharacteristic
23C22×D68—21no—
24C22×D68C2×C411yescharacteristic
25C22×C4×D17C2×C411yescharacteristic
26C22×C4×D17D411yescharacteristic
27C22×C4×D17D411yescharacteristic
28C22×Dic34C2×C411yescharacteristic
29C22×#3624—22no—
30C22×#3624—22no—
31C2×C4⋊C4×C17C2×C411yescharacteristic
32C2×C4⋊C4×C17C2×C411yescharacteristic
33C2×C42×C17C2×C411yescharacteristic
34C2×#63227—21no—
35C2×#63227—21no—
36C2×#63227—21no—
37C2×#63227—21no—
38C2×#63227—21no—
39C2×#63227—21no—
40C2×C4⋊Dic17—21no—
41C2×C4×Dic17D411yescharacteristic
42C2×C4×Dic17D411yescharacteristic
43C2×C4×Dic17C2311yescharacteristic
44#10587583—42no—
45#10587581—42no—
46#10587561—42no—
47C42×D17—42no—
48#10587543—24no—
49#10587543—42no—
50C4×#3624—42no—
51C17×#95—21no—
52C17×#95—21no—
53#10587502—21no—
54#10587502—21no—
55C23×D17—21no—
56C23×D17C22⋊C411yescharacteristic
57C22×C4×C17—21no—
58C22×C4×C17—21no—
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22⋊C411yescharacteristic
61C22×C4×C17C22×C411yescharacteristic
62C22×Dic17—21no—
63C22×Dic17C22⋊C411yescharacteristic
64C22×Dic17C2×D411yescharacteristic
65C22×Dic17C2×D411yescharacteristic
66C2×D68—22no—
67C2×D68—41no—
68C2×D68—41no—
69C2×D68—42no—
70C2×D68—42no—
71C2×D68—42no—
72C2×C4×D17—22no—
73C2×C4×D17—22no—
74C2×C4×D17—22no—
75C2×C4×D17—22no—
76C2×C4×D17—22no—
77C2×C4×D17—22no—
78C2×C4×D17—41no—
79C2×C4×D17—41no—
80C2×C4×D17—41no—
81C2×Dic34—22no—
82C2×Dic34—41no—
83C2×Dic34—41no—
84C2×#3624—24no—
85C2×#3624—42no—
86C2×#3624—42no—
87C2×#3624—42no—
88C2×#3624—42no—
89C2×#3624—42no—
90C4⋊C4×C17—41no—
91C4⋊C4×C17—41no—
92C42×C17—22no—
93#63227—42no—
94#63227—42no—
95#63227—42no—
96#63227—42no—
97#63227—42no—
98#63227—42no—
99C4⋊Dic17—42no—
100C4×Dic17—22no—
101C4×Dic17—41no—
102C4×Dic17—41no—
103#7670—171nomaximal, Sylow
104C23×C17C2×C22⋊C411yescharacteristic
105C22×D17—21no—
106C22×D17—21no—
107C22×D17—21no—
108C22×D17—21no—
109C22×D17—21no—
110C22×D17—21no—
111C22×D17—41no—
112C22×D17—41no—
113C22×D17—41no—
114C22×D17—41no—
115C22×D17—41no—
116C22×D17—41no—
117C22×D17—41no—
118C22×D17#10412yes—
119C2×C4×C17—21no—
120C2×C4×C17—21no—
121C2×C4×C17—21no—
122C2×C4×C17—21no—
123C2×C4×C17—21no—
124C2×C4×C17—21no—
125C2×C4×C17—21no—
126C2×C4×C17—41no—
127C2×C4×C17—41no—
128C2×C4×C17—41no—
129C2×C4×C17—41no—
130C2×C4×C17—41no—
131C2×C4×C17—41no—
132C2×C4×C17#9912yes—
133C2×C4×C17#13112yes—
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#10012yes—
144C2×Dic17#13512yes—
145C2×Dic17#13512yes—
146D68—82no—
147D68—84no—
148C4×D17—44no—
149C4×D17—44no—
150C4×D17—44no—
151Dic34—82no—
152#3624—44no—
153#3624—82no—
154#2850—171no—
155#1817—171no—
156C4×C22⋊C8—171no—
157#1272—172no—
158#1270—172no—
159C22×C17#40811yescharacteristic
160C22×C17C2×#9911yescharacteristic
161C22×C17C2×#10011yescharacteristic
162C22×C17#41611yescharacteristic
163C22×C17#41611yescharacteristic
164C22×C17C2×#10411yescharacteristic
165C22×C17#42111yescharacteristic
166C2×D17—22no—
167C2×D17—22no—
168C2×D17—22no—
169C2×D17—41no—
170C2×D17—41no—
171C2×D17—41no—
172C2×D17—41no—
173C2×D17—81no—
174C2×D17—81no—
175C2×D17—81no—
176C2×D17—81no—
177C2×D17—81no—
178C2×D17—81no—
179C2×D17—81no—
180C4×C17—22no—
181C4×C17—22no—
182C4×C17—41no—
183C4×C17—81no—
184C4×C17—81no—
185Dic17—22no—
186Dic17—22no—
187Dic17—22no—
188Dic17—81no—
189C2×#124—171no—
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#59511yescharacteristic
203#336—172no—
204#336—172no—
205#336—341no—
206C2×C17#147111yescharacteristic
207C2×C17#148211yescharacteristic
208C2×C17#149411yescharacteristic
209C2×C17#150111yescharacteristic
210C2×C17#151611yescharacteristic
211C2×C17#152711yescharacteristic
212C2×C17#154311yescharacteristic
213D17—42no—
214D17—161no—
215C22×Q8—171no—
216C22×D4—171no—
217C22×D4—341no—
218C23×C4—171no—
219C23×C4—171no—
220C23×C4—171no—
221C22×C8—342no—
222C22×C8—342no—
223#124—682no—
224C22⋊Q8—682no—
225#121—682no—
226C2×C4⋊C4—341no—
227C2×C4⋊C4C2×#59511yescharacteristic
228C2×C4⋊C4C2×#59511yescharacteristic
229C2×C22⋊C4—341no—
230C2×C22⋊C4—341no—
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—21no—
244#95—21no—
245#95—341no—
246#95—341no—
247C17#767011yescharacteristic, complemented, Sylow
248C24—171no—
249C24—341no—
250C2×Q8—342no—
251C2×Q8—681no—
252C2×Q8—681no—
253C2×D4—342no—
254C2×D4—681no—
255C2×D4—681no—
256C2×D4—682no—
257C2×D4—682no—
258C2×D4—682no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—171no—
262C22×C4—171no—
263C22×C4—171no—
264C22×C4—342no—
265C22×C4—342no—
266C22×C4—342no—
267C22×C4—342no—
268C22×C4—342no—
269C22×C4—342no—
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—41no—
284C4⋊C4—41no—
285C4⋊C4—682no—
286C22⋊C4—682no—
287C22⋊C4—682no—
288C22⋊C4—682no—
289C22⋊C4—682no—
290C22⋊C4—682no—
291C22⋊C4—682no—
292C42—22no—
293C42—342no—
294C42—681no—
295C42—681no—
296C23—172no—
297C23—341no—
298C23—341no—
299C23—341no—
300C23—341no—
301C23—341no—
302C23—341no—
303C23—681no—
304C23—681no—
305C23—681no—
306C23—681no—
307C23—681no—
308C23—681no—
309C23—681no—
310C23C2×C22⋊#59511yescharacteristic
311Q8—1362no—
312D4—1362no—
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—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—172no—
328C2×C4—172no—
329C2×C4—172no—
330C2×C4—341no—
331C2×C4—341no—
332C2×C4—341no—
333C2×C4—341no—
334C2×C4—341no—
335C2×C4—341no—
336C2×C4—684no—
337C2×C4—684no—
338C2×C4—684no—
339C2×C4—681no—
340C2×C4—681no—
341C2×C4—681no—
342C2×C4#1058753912yes—
343C2×C4#1058768012yes—
344C8—684no—
345C8—1362no—
346C22—342no—
347C22—342no—
348C22—342no—
349C22—681no—
350C22—681no—
351C22—681no—
352C22—681no—
353C22—1361no—
354C22—1361no—
355C22—1361no—
356C22—1361no—
357C22—1361no—
358C22—1361no—
359C22—1361no—
360C22#1176378411yescharacteristic
361C22C2×#1058753911yescharacteristic
362C22D17⋊#10011yescharacteristic
363C22#1176379911yescharacteristic
364C22#1176379911yescharacteristic
365C22D17⋊#10411yescharacteristic
366C22#1176380611yescharacteristic
367C4—22no—
368C4—22no—
369C4—41no—
370C4—81no—
371C4—81no—
372C4—342no—
373C4—342no—
374C4—342no—
375C4—1361no—
376C2—2721no—
377C2—682no—
378C2#1454406111yescharacteristic
379C2#1454409811yescharacteristic
380C2#1454413811yescharacteristic
381C2#1454416111yescharacteristic
382C2#1454421211yescharacteristic
383C2#1454424411yescharacteristic
384C2#1454428811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#382C4
socleC23×C17C2×C22⋊C4
prime radicalC2×#10587581C4
cosocleC2×C4×Dic17C23
hypercenter#382#595
hypocenterC17#7670
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
1. #14544676C2semidirect
2. C4×#10587543C2semidirect
3. #14543605C2semidirect
4. #14543601C2semidirect
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
#145436052
#145436012
#145370862
#767017