Finite Group Databasebeta

← #17950205

Subgroups — #17950205

Order 4352.

506 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 86 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
2#14544676C211yesmaximal, characteristic, complemented
3#14543602C212yesmaximal, complemented
4#14543600C212yesmaximal, complemented
5#14537114C211yesmaximal, characteristic
6C2×#10587543—21no—
7C2×#10587543—21no—
8#11763675—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587569—21no—
13C2×#10587624C411yescharacteristic
14C2×C42×D17C2211yescharacteristic
15#11762712C2211yescharacteristic
16#11762708C2211yescharacteristic
17#11762707C411yescharacteristic
18#11762703—21no—
19#11762702—21no—
20#11762685—21no—
21#11762666C411yescharacteristic
22C17×#390C411yescharacteristic
23C22×D4×C17C2×C411yescharacteristic
24C22×C22⋊D17—21no—
25C22×C4×D17C2×C411yescharacteristic
26C22×C4×D17D411yescharacteristic
27C22×C4×D17D411yescharacteristic
28C22×#3624—22no—
29C22×#3624—22no—
30C2×C4⋊C4×C17C2×C411yescharacteristic
31C2×C22⋊C4×C17—21no—
32C2×C22⋊C4×C17—21no—
33C2×C42×C17C2×C411yescharacteristic
34C2×C22⋊Dic17—21no—
35C2×C22⋊Dic17—21no—
36C2×C22⋊Dic17—21no—
37#10587624—42no—
38C2×#63227—21no—
39C2×C4⋊Dic17—21no—
40C2×C4⋊Dic17C2×C411yescharacteristic
41C2×C4⋊Dic17C2×C411yescharacteristic
42C2×#63225—21no—
43C2×C4×Dic17D411yescharacteristic
44C2×C4×Dic17D411yescharacteristic
45C2×C4×Dic17C2311yescharacteristic
46#10587569—44no—
47C42×D17—42no—
48#10587543—42no—
49#10587543—42no—
50#10587502—21no—
51#10587502—21no—
52#10587502—21no—
53C24×C17—21no—
54C23×D17C22⋊C411yescharacteristic
55C2×D4×C17—22no—
56C2×D4×C17—41no—
57C2×D4×C17—41no—
58C22×C4×C17—21no—
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22⋊C411yescharacteristic
61C22×C4×C17C22×C411yescharacteristic
62C2×C22⋊D17—42no—
63C2×C22⋊D17—42no—
64C2×C22⋊D17—42no—
65C22×Dic17—21no—
66C22×Dic17—21no—
67C22×Dic17C22⋊C411yescharacteristic
68C22×Dic17C2×D411yescharacteristic
69C22×Dic17C2×D411yescharacteristic
70C2×C4×D17—22no—
71C2×C4×D17—22no—
72C2×C4×D17—22no—
73C2×C4×D17—22no—
74C2×C4×D17—22no—
75C2×C4×D17—22no—
76C2×C4×D17—41no—
77C2×C4×D17—41no—
78C2×C4×D17—41no—
79C2×#3624—42no—
80C2×#3624—42no—
81C2×#3624—42no—
82C2×#3624—42no—
83C2×#3624—42no—
84C2×#3624—42no—
85C4⋊C4×C17—22no—
86C22⋊C4×C17—42no—
87C22⋊C4×C17—42no—
88C42×C17—41no—
89C22⋊Dic17—42no—
90C22⋊Dic17—42no—
91C22⋊Dic17—42no—
92#63227—42no—
93C4⋊Dic17—42no—
94C4⋊Dic17—41no—
95C4⋊Dic17—41no—
96#63225—42no—
97C4×Dic17—41no—
98C4×Dic17—41no—
99C4×Dic17—41no—
100#7718—171nomaximal, Sylow
101C23×C17—41no—
102C23×C17—41no—
103C23×C17—41no—
104C23×C17—41no—
105C23×C17—41no—
106C23×C17—41no—
107C23×C17—41no—
108C23×C17C2×C22⋊C411yescharacteristic
109C22×D17—21no—
110C22×D17—21no—
111C22×D17—21no—
112C22×D17—21no—
113C22×D17—21no—
114C22×D17—21no—
115C22×D17#9912yes—
116D4×C17—82no—
117C2×C4×C17—21no—
118C2×C4×C17—21no—
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—41no—
126C2×C4×C17—41no—
127C2×C4×C17—41no—
128C2×C4×C17#13112yes—
129C22⋊D17—84no—
130C2×Dic17—21no—
131C2×Dic17—21no—
132C2×Dic17—21no—
133C2×Dic17—21no—
134C2×Dic17—21no—
135C2×Dic17—21no—
136C2×Dic17—21no—
137C2×Dic17—41no—
138C2×Dic17—41no—
139C2×Dic17—41no—
140C2×Dic17—41no—
141C2×Dic17—41no—
142C2×Dic17—41no—
143C2×Dic17#13512yes—
144C2×Dic17AGL(1,ℤ/8)12yes—
145C4×D17—44no—
146C4×D17—44no—
147C4×D17—44no—
148#3624—82no—
149#3624—82no—
150#2854—171no—
151#1817—171no—
152#1817—171no—
153#1271—172no—
154#1270—172no—
155C22×C17—81no—
156C22×C17—81no—
157C22×C17—81no—
158C22×C17—81no—
159C22×C17—81no—
160C22×C17—81no—
161C22×C17—81no—
162C22×C17#40811yescharacteristic
163C22×C17C2×#9911yescharacteristic
164C22×C17#41311yescharacteristic
165C22×C17#41611yescharacteristic
166C22×C17#41811yescharacteristic
167C22×C17#42111yescharacteristic
168C22×C17#42111yescharacteristic
169C2×D17—22no—
170C2×D17—22no—
171C2×D17—22no—
172C2×D17—41no—
173C2×D17—41no—
174C2×D17—41no—
175C2×D17—41no—
176C4×C17—22no—
177C4×C17—41no—
178C4×C17—41no—
179C4×C17—81no—
180Dic17—22no—
181Dic17—22no—
182Dic17—41no—
183Dic17—81no—
184Dic17—81no—
185C2×#123—341no—
186C2×#121—171no—
187C22×C42—171no—
188C2×C22⋊C8—341no—
189C2×C22⋊C8—341no—
190#390—171no—
191#390#59511yescharacteristic
192#389—171no—
193#389—171no—
194#388—341no—
195#388—341no—
196#386—341no—
197#380—171no—
198#336—172no—
199#336—172no—
200#336—341no—
201#336—341no—
202C2×C17—161no—
203C2×C17#146811yescharacteristic
204C2×C17#148211yescharacteristic
205C2×C17#149611yescharacteristic
206C2×C17#151011yescharacteristic
207C2×C17#151611yescharacteristic
208C2×C17#153511yescharacteristic
209C2×C17#155311yescharacteristic
210D17—42no—
211C22×D4—341no—
212C22×D4C2×#59511yescharacteristic
213C23×C4—171no—
214C23×C4—171no—
215C23×C4—171no—
216C22×C8—342no—
217C22×C8—342no—
218#123—684no—
219#121—682no—
220C2×C4⋊C4—171no—
221C2×C4⋊C4—171no—
222C2×C4⋊C4—341no—
223C2×C4⋊C4—341no—
224C2×C4⋊C4C2×#59511yescharacteristic
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—341no—
228C2×C22⋊C4—341no—
229C2×C22⋊C4—341no—
230C2×C22⋊C4—341no—
231C2×C42—171no—
232C2×C42—171no—
233C2×C42—171no—
234C2×C42—682no—
235C2×C42C2×#59511yescharacteristic
236C22⋊C8—682no—
237C22⋊C8—682no—
238#95—341no—
239#95—341no—
240#95—341no—
241C17#771811yescharacteristic, complemented, Sylow
242C24—21no—
243C24—171no—
244C2×D4—22no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—682no—
248C2×D4—682no—
249C2×D4—682no—
250C22×C4—21no—
251C22×C4—171no—
252C22×C4—171no—
253C22×C4—171no—
254C22×C4—342no—
255C22×C4—342no—
256C22×C4—342no—
257C22×C4—342no—
258C22×C4—342no—
259C22×C4—342no—
260C22×C4—341no—
261C22×C4—341no—
262C22×C4—681no—
263C22×C4—681no—
264C22×C4—681no—
265C22×C4C22⋊#59511yescharacteristic
266C22×C4C22⋊#59511yescharacteristic
267C22×C4C22×#59511yescharacteristic
268C2×C8—682no—
269C2×C8—682no—
270C2×C8—682no—
271C2×C8—682no—
272C2×C8—682no—
273C2×C8—682no—
274C4⋊C4—22no—
275C4⋊C4—681no—
276C4⋊C4—681no—
277C4⋊C4—682no—
278C4⋊C4—682no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—682no—
282C22⋊C4—682no—
283C22⋊C4—682no—
284C22⋊C4—682no—
285C42—41no—
286C42—681no—
287C42—681no—
288C42—681no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—172no—
297C23—341no—
298C23—341no—
299C23—341no—
300C23—341no—
301C23—341no—
302C23—341no—
303C23C2×C22⋊#59511yescharacteristic
304D4—82no—
305D4—1364no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—172no—
318C2×C4—172no—
319C2×C4—341no—
320C2×C4—341no—
321C2×C4—341no—
322C2×C4—341no—
323C2×C4—341no—
324C2×C4—341no—
325C2×C4—341no—
326C2×C4—684no—
327C2×C4—684no—
328C2×C4—684no—
329C2×C4—681no—
330C2×C4—681no—
331C2×C4—681no—
332C2×C4—681no—
333C2×C4—681no—
334C2×C4—681no—
335C2×C4#1058767812yes—
336C8—1362no—
337C8—1362no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22—81no—
344C22—81no—
345C22—342no—
346C22—342no—
347C22—342no—
348C22—681no—
349C22—681no—
350C22—681no—
351C22—681no—
352C22#1176378311yescharacteristic
353C22D17⋊#9911yescharacteristic
354C22#1176379511yescharacteristic
355C22#1176379911yescharacteristic
356C22#1176380111yescharacteristic
357C22#1176380611yescharacteristic
358C22#1176380711yescharacteristic
359C4—22no—
360C4—41no—
361C4—41no—
362C4—81no—
363C4—342no—
364C4—342no—
365C4—681no—
366C4—1361no—
367C4—1361no—
368C2—161no—
369C2—682no—
370C2#1454405011yescharacteristic
371C2#1454409611yescharacteristic
372C2#1454414411yescharacteristic
373C2#1454419011yescharacteristic
374C2#1454420911yescharacteristic
375C2#1454426811yescharacteristic
376C2#1454430711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#390C4
socleC23×C17C2×C22⋊C4
prime radicalC2×#10587624C4
cosocleC2×C4×Dic17C23
hypercenter#390#595
hypocenterC17#7718
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #14544676C2semidirect
2. #14544676C2semidirect
3. #14543602C2semidirect
4. #14543600C2semidirect
241. C17#7718semidirect

Maximal subgroups

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

subgroupindex
#145446762
#145436022
#145436002
#145371142
#771817