Finite Group Databasebeta

← #16952988

Subgroups — #16952988

Order 4352.

488 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 99 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#14534127C211yesmaximal, characteristic
2C4×#10587505C211yesmaximal, characteristic
3#14526903C212yesmaximal
4#14526903C212yesmaximal
5C17×#1800C211yesmaximal, characteristic
6C22×#63225C411yescharacteristic, complemented
7C2×#10587505C2212yes—
8#11762742—21no—
9#11762732—21no—
10#11762693—21no—
11#11762689C2211yescharacteristic
12#11762689C2211yescharacteristic
13#11762682—21no—
14#11762681C411yescharacteristic, complemented
15#11762681C411yescharacteristic, complemented
16#11762669C411yescharacteristic, complemented
17C4×C22⋊Dic17—21no—
18#11762576—21no—
19C2×C4×D4×C17C2211yescharacteristic
20C17×#423—21no—
21C2×C17×#100C2212yes—
22C17×#343—21no—
23C22×D4×C17C2311yescharacteristic
24C23×C4×C17C2×C411yescharacteristic
25C23×C4×C17D411yescharacteristic
26C23×Dic17C2×C411yescharacteristic
27C23×Dic17C2×C411yescharacteristic
28C2×M16×C17—22no—
29C4×D4×C17—41no—
30C4×D4×C17—41no—
31C2×C4⋊C4×C17D411yescharacteristic
32C2×C22⋊C4×C17C2×C411yescharacteristic
33C2×C22⋊C4×C17D411yescharacteristic
34C2×C42×C17D411yescharacteristic
35C2×C22⋊Dic17—22no—
36C2×C22⋊Dic17—21no—
37C2×C22⋊Dic17—21no—
38C2×C22⋊Dic17C2×C411yescharacteristic
39C2×C22⋊Dic17C2×C411yescharacteristic
40C2×C4⋊Dic17—21no—
41C2×#63225—21no—
42C2×#63225—21no—
43C2×#63225—21no—
44C2×#63225—21no—
45C2×#63225—41no—
46C2×#63225—41no—
47C2×C4×Dic17—41no—
48C17×C4⋊C8—41no—
49C17×C4⋊C8—41no—
50C17×#100—24no—
51#10587505—22no—
52#10587505Q814yes—
53#10587502—21no—
54#10587502—21no—
55#10587502—21no—
56#10587502—21no—
57#10587502—21no—
58#10587502—41no—
59C24×C17C22×C411yescharacteristic
60C24×C17C2×D411yescharacteristic
61C2×D4×C17—41no—
62C2×D4×C17—41no—
63C2×D4×C17C2×Q812yes—
64C2×D4×C17#4112yes—
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17—81no—
70C22×C4×C17—81no—
71C22×C4×C17C22⋊C411yescharacteristic
72C22×C4×C17C22⋊C411yescharacteristic
73C22×C4×C17C22⋊C411yescharacteristic
74C22×C4×C17C22⋊C411yescharacteristic
75C22×C4×C17C2×D411yescharacteristic
76C22×Dic17—21no—
77C22×Dic17—21no—
78C22×Dic17—21no—
79C22×Dic17—21no—
80C22×Dic17—42no—
81C22×Dic17—41no—
82C22×Dic17—42no—
83C22×Dic17—41no—
84C22×Dic17—81no—
85M16×C17—42no—
86M16×C17—42no—
87C2×C8×C17—42no—
88C4⋊C4×C17—41no—
89C22⋊C4×C17—41no—
90C22⋊C4×C17—41no—
91C42×C17—21no—
92C42×C17—21no—
93C22⋊Dic17—24no—
94C22⋊Dic17—42no—
95C22⋊Dic17—42no—
96C22⋊Dic17—41no—
97C22⋊Dic17—41no—
98C22⋊Dic17—81no—
99C4⋊Dic17—81no—
100#63225—42no—
101#63225—42no—
102#63225—41no—
103#63225—41no—
104#63225—81no—
105C4×Dic17—82no—
106#13297—171nomaximal, Sylow
107C23×C17—21no—
108C23×C17—21no—
109C23×C17—21no—
110C23×C17—21no—
111C23×C17—41no—
112C23×C17—41no—
113C23×C17—41no—
114C23×C17—41no—
115C23×C17C2×C22⋊C411yescharacteristic
116C23×C17C4×Q812yes—
117C23×C17C22⋊Q812yes—
118D4×C17—42no—
119D4×C17—42no—
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—42no—
127C2×C4×C17—41no—
128C2×C4×C17—41no—
129C2×C4×C17—41no—
130C2×C4×C17—81no—
131C2×C4×C17—81no—
132C2×C4×C17—81no—
133C2×C4×C17#9911yescharacteristic
134C2×C4×C17#9911yescharacteristic
135C2×C4×C17#12411yescharacteristic
136C2×C4×C17C4⋊Q811yescharacteristic
137C2×Dic17—22no—
138C2×Dic17—41no—
139C2×Dic17—42no—
140C2×Dic17—41no—
141C2×Dic17—42no—
142C2×Dic17—44no—
143C2×Dic17—41no—
144C2×Dic17—41no—
145C2×Dic17—41no—
146C2×Dic17—41no—
147C2×Dic17—41no—
148C2×Dic17—41no—
149C2×Dic17—41no—
150C2×Dic17—41no—
151C2×Dic17—41no—
152C2×Dic17—82no—
153C2×Dic17—82no—
154C2×Dic17—82no—
155C8×C17—82no—
156#2579—171no—
157#1800D1711yescharacteristic
158C4×#99—171no—
159#1390—172no—
160#1390—172no—
161C22×C17—21no—
162C22×C17—21no—
163C22×C17—22no—
164C22×C17—22no—
165C22×C17—42no—
166C22×C17—42no—
167C22×C17—42no—
168C22×C17—41no—
169C22×C17—41no—
170C22×C17—41no—
171C22×C17—41no—
172C22×C17—81no—
173C22×C17#39111yescharacteristic
174C22×C17C2×#9911yescharacteristic
175C22×C17#41011yescharacteristic
176C4×C17—21no—
177C4×C17—21no—
178C4×C17—21no—
179C4×C17—21no—
180C4×C17—41no—
181C4×C17—41no—
182C4×C17—41no—
183Dic17—42no—
184Dic17—81no—
185Dic17—81no—
186Dic17—84no—
187Dic17—81no—
188C2×C4×D4C2×D1711yescharacteristic
189C22×C4⋊C4—171no—
190#423—21no—
191C2×#100C2×D1712yes—
192C2×#99—172no—
193#398—341no—
194#396—341no—
195#387—341no—
196#386—171no—
197#386—171no—
198#385—171no—
199#385—171no—
200#385—341no—
201#380—171no—
202C4×C22⋊C4—341no—
203#343—21no—
204#342—341no—
205C2×C17—21no—
206C2×C17—21no—
207C2×C17—42no—
208C2×C17—42no—
209C2×C17#199611yescharacteristic
210C2×C17#212011yescharacteristic
211C2×C17#212111yescharacteristic
212C22×D4C22×D1711yescharacteristic
213C23×C4—171no—
214C23×C4—171no—
215C23×C4C4×D1711yescharacteristic
216C23×C4D6811yescharacteristic
217C2×M16—22no—
218C4×D4—41no—
219C4×D4—41no—
220C2×C4⋊C4—341no—
221C2×C4⋊C4—341no—
222C2×C4⋊C4—341no—
223C2×C4⋊C4—341no—
224C2×C4⋊C4—341no—
225C2×C4⋊C4—681no—
226C2×C4⋊C4—681no—
227C2×C4⋊C4C22⋊D1711yescharacteristic
228C2×C22⋊C4—171no—
229C2×C22⋊C4—171no—
230C2×C22⋊C4—342no—
231C2×C22⋊C4—341no—
232C2×C22⋊C4—341no—
233C2×C22⋊C4C4×D1711yescharacteristic
234C2×C22⋊C4D6811yescharacteristic
235C2×C42—681no—
236C2×C42C22⋊D1711yescharacteristic
237C4⋊C8—41no—
238C4⋊C8—41no—
239#100—24no—
240#99—174no—
241#99—342no—
242#95—341no—
243#95—341no—
244#95—341no—
245#95—341no—
246#95—341no—
247#95—681no—
248C17#1329711yescharacteristic, complemented, Sylow
249C24C2×C4×D1711yescharacteristic
250C24C2×D6811yescharacteristic
251C2×D4—41no—
252C2×D4—41no—
253C2×D4#6325412yes—
254C2×D4Q8×D1712yes—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—81no—
260C22×C4—81no—
261C22×C4—341no—
262C22×C4—341no—
263C22×C4—341no—
264C22×C4—341no—
265C22×C4—682no—
266C22×C4—681no—
267C22×C4—682no—
268C22×C4—681no—
269C22×C4—1361no—
270C22×C4#6322711yescharacteristic
271C22×C4#6322711yescharacteristic
272C22×C4#6322711yescharacteristic
273C22×C4#6322711yescharacteristic
274C22×C4C2×C22⋊D1711yescharacteristic
275M16—42no—
276M16—42no—
277C2×C8—42no—
278C4⋊C4—41no—
279C4⋊C4—682no—
280C4⋊C4—682no—
281C4⋊C4—681no—
282C4⋊C4—681no—
283C4⋊C4—1361no—
284C4⋊C4—1361no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—344no—
288C22⋊C4—682no—
289C22⋊C4—682no—
290C22⋊C4—681no—
291C22⋊C4—681no—
292C22⋊C4—1361no—
293C42—21no—
294C42—21no—
295C42—1362no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23#1058757312yes—
305C23#1058758312yes—
306C23C2×#6322711yescharacteristic
307D4—42no—
308D4—42no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—342no—
323C2×C4—681no—
324C2×C4—682no—
325C2×C4—681no—
326C2×C4—682no—
327C2×C4—684no—
328C2×C4—681no—
329C2×C4—681no—
330C2×C4—681no—
331C2×C4—681no—
332C2×C4—681no—
333C2×C4—681no—
334C2×C4—681no—
335C2×C4—681no—
336C2×C4—681no—
337C2×C4—1362no—
338C2×C4—1362no—
339C2×C4—1362no—
340C2×C4#1058747711yescharacteristic
341C2×C4#1058747711yescharacteristic
342C2×C4#1058762211yescharacteristic
343C2×C4#1058763011yescharacteristic
344C8—82no—
345C22—21no—
346C22—21no—
347C22—22no—
348C22—22no—
349C22—42no—
350C22—42no—
351C22—42no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—81no—
357C22#1176271411yescharacteristic
358C22C2×#1058747711yescharacteristic
359C22#1176278211yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—682no—
368C4—1361no—
369C4—1361no—
370C4—1364no—
371C4—1361no—
372C2—21no—
373C2—21no—
374C2—42no—
375C2—42no—
376C2#1452976811yescharacteristic
377C2#1453042611yescharacteristic
378C2#1453043111yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC24×C17C22×C4
FrattiniC22×D4C22×D17
FittingC17×#1800C2
socleC22×C17C2×#99
prime radical, cosocleC22×D4×C17C23
hypercenter#1800D17
hypocenterC17#13297
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1800

Complements

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

NH ≅ G/Ntype
6. C22×#63225C4semidirect
14. #11762681C4semidirect
15. #11762681C4semidirect
16. #11762669C4semidirect
248. C17#13297semidirect

Maximal subgroups

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

subgroupindex
#145341272
C4×#105875052
#145269032
C17×#18002
#1329717