Finite Group Databasebeta

← #17950084

Subgroups — #17950084

Order 4352.

562 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 108 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
1C4×C22⋊#3624C211yesmaximal, characteristic
2#14544447C211yesmaximal, characteristic
3#14543603C212yesmaximal, complemented
4#14543602C212yesmaximal, complemented
5#14537134C211yesmaximal, characteristic
6C22×#63247—21no—
7C2×C22⋊#3624—21no—
8C2×C4×#3624—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587574C411yescharacteristic
13C2×#10587564—21no—
14C22×C4×Dic17C2211yescharacteristic
15#11762713—21no—
16#11762708C2211yescharacteristic
17#11762706—21no—
18#11762705C2211yescharacteristic
19#11762678C411yescharacteristic
20#11762669C411yescharacteristic
21#11762667—21no—
22C17×#380C411yescharacteristic
23C23×C4×C17C2×C411yescharacteristic
24C23×Dic17D411yescharacteristic
25C23×Dic17D411yescharacteristic
26C22×Dic34—21no—
27C2×#63247—24no—
28C2×#63247—42no—
29C2×#63247—42no—
30C22×#3624—22no—
31C22×#3624—22no—
32C2×C4⋊C4×C17C2×C411yescharacteristic
33C2×C4⋊C4×C17C2×C411yescharacteristic
34C2×C22⋊C4×C17—21no—
35C2×C22⋊Dic17—21no—
36C2×C4⋊Dic17—21no—
37C2×C4⋊Dic17C2×C411yescharacteristic
38C2×C4⋊Dic17C2×C411yescharacteristic
39C2×#63225—21no—
40C2×#63225—21no—
41C2×#63225—21no—
42C2×#63225—21no—
43C2×C4×Dic17—42no—
44C2×C4×Dic17C2×C411yescharacteristic
45C2×C4×Dic17D411yescharacteristic
46C2×C4×Dic17D411yescharacteristic
47C2×C4×Dic17C2311yescharacteristic
48#10587574—42no—
49#10587564—42no—
50#10587564—42no—
51C22⋊#3624—24no—
52C4×#3624—42no—
53C17×#95—21no—
54#10587502—21no—
55#10587502—21no—
56#10587502—21no—
57C24×C17C22⋊C411yescharacteristic
58C22×C4×C17—22no—
59C22×C4×C17—22no—
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17—41no—
63C22×C4×C17C22⋊C411yescharacteristic
64C22×C4×C17C22×C411yescharacteristic
65C22×Dic17—22no—
66C22×Dic17—22no—
67C22×Dic17—22no—
68C22×Dic17—22no—
69C22×Dic17—21no—
70C22×Dic17—21no—
71C22×Dic17—41no—
72C22×Dic17C22⋊C411yescharacteristic
73C22×Dic17C22⋊C411yescharacteristic
74C22×Dic17D812yes—
75C22×Dic17SD1612yes—
76C22×Dic17C2×D411yescharacteristic
77C22×Dic17C2×D411yescharacteristic
78C2×Dic34—42no—
79C2×Dic34—42no—
80C2×Dic34—42no—
81#63247—48no—
82C2×#3624—24no—
83C2×#3624—24no—
84C2×#3624—42no—
85C2×#3624—42no—
86C2×#3624—42no—
87C2×#3624—42no—
88C4⋊C4×C17—22no—
89C4⋊C4×C17—41no—
90C22⋊C4×C17—42no—
91C22⋊Dic17—42no—
92C4⋊Dic17—22no—
93C4⋊Dic17—41no—
94C4⋊Dic17—41no—
95C4⋊Dic17—41no—
96#63225—42no—
97#63225—42no—
98#63225—42no—
99#63225—41no—
100#63225—41no—
101C4×Dic17—22no—
102C4×Dic17—22no—
103C4×Dic17—41no—
104C4×Dic17—41no—
105#7685—171nomaximal, Sylow
106C23×C17—21no—
107C23×C17—21no—
108C23×C17—21no—
109C23×C17—21no—
110C23×C17—21no—
111C23×C17—21no—
112C23×C17#10212yes—
113C23×C17C2×C22⋊C411yescharacteristic
114C2×C4×C17—21no—
115C2×C4×C17—21no—
116C2×C4×C17—21no—
117C2×C4×C17—21no—
118C2×C4×C17—44no—
119C2×C4×C17—41no—
120C2×C4×C17—41no—
121C2×C4×C17—41no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17#10112yes—
126C2×C4×C17#13112yes—
127C2×Dic17—21no—
128C2×Dic17—21no—
129C2×Dic17—21no—
130C2×Dic17—21no—
131C2×Dic17—21no—
132C2×Dic17—21no—
133C2×Dic17—24no—
134C2×Dic17—24no—
135C2×Dic17—44no—
136C2×Dic17—41no—
137C2×Dic17—41no—
138C2×Dic17—41no—
139C2×Dic17—41no—
140C2×Dic17—41no—
141C2×Dic17—41no—
142C2×Dic17#9912yes—
143C2×Dic17#10212yes—
144C2×Dic17#10412yes—
145C2×Dic17#10412yes—
146C2×Dic17C2×D811yescharacteristic
147C2×Dic17C2×SD1611yescharacteristic
148C2×Dic17#13712yes—
149Dic34—84no—
150#3624—44no—
151#3624—44no—
152#2857—171no—
153C4×C22⋊C8—171no—
154#1728—171no—
155#1271—172no—
156#1271—172no—
157C22×C17—22no—
158C22×C17—22no—
159C22×C17—22no—
160C22×C17—41no—
161C22×C17—41no—
162C22×C17—41no—
163C22×C17—41no—
164C22×C17#40811yescharacteristic
165C22×C17C2×#9911yescharacteristic
166C22×C17C2×#10111yescharacteristic
167C22×C17C2×#10211yescharacteristic
168C22×C17#41911yescharacteristic
169C22×C17C2×#10411yescharacteristic
170C22×C17C2×#10411yescharacteristic
171C4×C17—22no—
172C4×C17—22no—
173C4×C17—81no—
174C4×C17—81no—
175Dic17—21no—
176Dic17—21no—
177Dic17—22no—
178Dic17—22no—
179Dic17—81no—
180Dic17—81no—
181Dic17#32714yes—
182C22×M16—341no—
183C2×C4⋊Q8—171no—
184C2×C22⋊Q8—341no—
185C22×C42—171no—
186C2×C22⋊C8—341no—
187C2×C4×C8—341no—
188#391—341no—
189#389—171no—
190#389—171no—
191#389—341no—
192#384—171no—
193#380—171no—
194#380—341no—
195#380#59511yescharacteristic
196#336—172no—
197#336—172no—
198#336—341no—
199C2×C17—42no—
200C2×C17#147211yescharacteristic
201C2×C17#148511yescharacteristic
202C2×C17#149211yescharacteristic
203C2×C17C2×#32711yescharacteristic
204C2×C17#150811yescharacteristic
205C2×C17#152611yescharacteristic
206C2×C17#154611yescharacteristic
207C22×Q8—341no—
208C23×C4—171no—
209C23×C4—171no—
210C23×C4C2×#59511yescharacteristic
211C2×M16—344no—
212C2×M16—682no—
213C2×M16—682no—
214C22×C8—342no—
215C22×C8—342no—
216C4⋊Q8—682no—
217C22⋊Q8—682no—
218C22⋊Q8—682no—
219C2×C4⋊C4—171no—
220C2×C4⋊C4—171no—
221C2×C4⋊C4—341no—
222C2×C4⋊C4—341no—
223C2×C4⋊C4—341no—
224C2×C4⋊C4—341no—
225C2×C4⋊C4—341no—
226C2×C4⋊C4C2×#59511yescharacteristic
227C2×C4⋊C4C2×#59511yescharacteristic
228C2×C22⋊C4—21no—
229C2×C22⋊C4—341no—
230C2×C42—171no—
231C2×C42—171no—
232C2×C42—171no—
233C2×C42—171no—
234C2×C42—682no—
235C22⋊C8—344no—
236C4×C8—682no—
237#95—21no—
238#95—341no—
239#95—341no—
240#95—341no—
241C17#768511yescharacteristic, complemented, Sylow
242C24C22⋊#59511yescharacteristic
243C2×Q8—682no—
244C2×Q8—682no—
245C2×Q8—682no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—41no—
251C22×C4—171no—
252C22×C4—171no—
253C22×C4—171no—
254C22×C4—171no—
255C22×C4—172no—
256C22×C4—172no—
257C22×C4—342no—
258C22×C4—342no—
259C22×C4—342no—
260C22×C4—342no—
261C22×C4—341no—
262C22×C4—341no—
263C22×C4—681no—
264C22×C4C22⋊#59511yescharacteristic
265C22×C4C22×#59511yescharacteristic
266M16—688no—
267C2×C8—344no—
268C2×C8—344no—
269C2×C8—682no—
270C2×C8—682no—
271C2×C8—682no—
272C2×C8—682no—
273C4⋊C4—22no—
274C4⋊C4—41no—
275C4⋊C4—342no—
276C4⋊C4—681no—
277C4⋊C4—682no—
278C4⋊C4—681no—
279C4⋊C4—681no—
280C4⋊C4—681no—
281C4⋊C4—681no—
282C4⋊C4—682no—
283C4⋊C4—682no—
284C22⋊C4—42no—
285C22⋊C4—682no—
286C42—342no—
287C42—342no—
288C42—681no—
289C42—681no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23#1058754712yes—
297C23C2×C22⋊#59511yescharacteristic
298Q8—1364no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—44no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—172no—
311C2×C4—172no—
312C2×C4—172no—
313C2×C4—171no—
314C2×C4—171no—
315C2×C4—172no—
316C2×C4—172no—
317C2×C4—344no—
318C2×C4—344no—
319C2×C4—341no—
320C2×C4—341no—
321C2×C4—341no—
322C2×C4—341no—
323C2×C4—341no—
324C2×C4—341no—
325C2×C4—684no—
326C2×C4—681no—
327C2×C4—681no—
328C2×C4—681no—
329C2×C4—681no—
330C2×C4—681no—
331C2×C4—681no—
332C2×C4#1058754512yes—
333C2×C4#1058767812yes—
334C8—684no—
335C8—684no—
336C22—22no—
337C22—22no—
338C22—22no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22#1176378211yescharacteristic
344C22D17⋊#9911yescharacteristic
345C22C2×#1058754511yescharacteristic
346C22C2×#1058754711yescharacteristic
347C22#1176380211yescharacteristic
348C22D17⋊#10411yescharacteristic
349C22D17⋊#10411yescharacteristic
350C4—22no—
351C4—22no—
352C4—81no—
353C4—81no—
354C4—174no—
355C4—341no—
356C4—341no—
357C4—342no—
358C4—342no—
359C4—1361no—
360C4—1361no—
361C2—42no—
362C2#1454406311yescharacteristic
363C2#1454410611yescharacteristic
364C2#1454412911yescharacteristic
365C2D17⋊#32711yescharacteristic
366C2#1454418211yescharacteristic
367C2#1454424111yescharacteristic
368C2#1454429311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#380C4
socleC23×C17C2×C22⋊C4
prime radicalC24×C17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenter#380#595
hypocenterC17#7685
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #14543603C2semidirect
4. #14543602C2semidirect
241. C17#7685semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊#36242
#145444472
#145436032
#145436022
#145371342
#768517