Finite Group Databasebeta

← #17959193

Subgroups — #17959193

Order 4352.

434 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 72 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×#10587545C211yesmaximal, characteristic, complemented
2#14544026C211yesmaximal, characteristic, complemented
3#14543783C212yesmaximal, complemented
4#14543766C212yesmaximal
5#14532068C211yesmaximal, characteristic
6#11763826—21no—
7C2×#10587545—21no—
8C4×#63247—21no—
9#11763689C2212yes—
10#11763655C2212yes—
11#11763654—21no—
12C2×C4×Dic34C2211yescharacteristic
13#11762747C411yescharacteristic
14#11762747C2211yescharacteristic
15#11762734—21no—
16#11762723C411yescharacteristic
17#11762723C2211yescharacteristic
18#11762721—21no—
19C4×C22⋊Dic17—21no—
20C4×C22⋊Dic17—21no—
21#11762655C411yescharacteristic
22C2×C4×D4×C17C411yescharacteristic
23C22×D4×C17C2×C411yescharacteristic
24C23×C4×C17—21no—
25C22×Dic34D411yescharacteristic
26C2×#63247—22no—
27C4×D4×C17—41no—
28C4×D4×C17—41no—
29C2×C4⋊C4×C17C2×C411yescharacteristic
30C2×C22⋊C4×C17—21no—
31C2×C42×C17C2×C411yescharacteristic
32C2×C22⋊Dic17—21no—
33C2×C22⋊Dic17—21no—
34C2×C22⋊Dic17—21no—
35C2×C22⋊Dic17—21no—
36C2×C4⋊Dic17D411yescharacteristic
37C2×#63225C2×C411yescharacteristic
38C2×#63225C2311yescharacteristic
39C2×C4×Dic17—21no—
40C2×C4×Dic17D411yescharacteristic
41C2×C4×Dic17D411yescharacteristic
42C4×Dic34—41no—
43C4×Dic34—41no—
44C22⋊#3624—22no—
45#10587545—24no—
46#10587544—41no—
47#10587542—41no—
48C4×#3624—41no—
49C4×#3624—41no—
50#10587502—21no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54#10587502—21no—
55#10587502C2×C411yescharacteristic
56#10587502C2×C411yescharacteristic
57C24×C17—21no—
58C2×D4×C17—41no—
59C2×D4×C17—42no—
60C22×C4×C17—21no—
61C22×C4×C17—42no—
62C22×C4×C17—42no—
63C22×C4×C17—41no—
64C22×C4×C17—41no—
65C22×C4×C17C22⋊C411yescharacteristic
66C22×C4×C17C22⋊C411yescharacteristic
67C22×C4×C17C22×C411yescharacteristic
68C22×Dic17—21no—
69C22×Dic17—21no—
70C22×Dic17C22⋊C411yescharacteristic
71C22×Dic17C22⋊C411yescharacteristic
72C22×Dic17C2×D411yescharacteristic
73C22×Dic17C2×D411yescharacteristic
74C2×Dic34—22no—
75C2×Dic34—22no—
76C2×Dic34—41no—
77#63247—24no—
78#63247—42no—
79C2×#3624—42no—
80C2×#3624—42no—
81C4⋊C4×C17—41no—
82C22⋊C4×C17—42no—
83C42×C17—21no—
84C42×C17—21no—
85C22⋊Dic17—42no—
86C22⋊Dic17—42no—
87C22⋊Dic17—42no—
88C22⋊Dic17—42no—
89C4⋊Dic17—41no—
90#63225—41no—
91#63225—41no—
92C4×Dic17—21no—
93C4×Dic17—21no—
94C4×Dic17—21no—
95C4×Dic17—21no—
96C4×Dic17—42no—
97#11734—171nomaximal, Sylow
98C23×C17—22no—
99C23×C17—41no—
100C23×C17—41no—
101C23×C17—41no—
102C23×C17—41no—
103C23×C17—41no—
104C23×C17—41no—
105C23×C17C2×C22⋊C411yescharacteristic
106D4×C17—42no—
107D4×C17—42no—
108C2×C4×C17—22no—
109C2×C4×C17—21no—
110C2×C4×C17—21no—
111C2×C4×C17—21no—
112C2×C4×C17—21no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17—41no—
116C2×C4×C17—41no—
117C2×C4×C17—82no—
118C2×C4×C17—82no—
119C2×C4×C17#9911yescharacteristic
120C2×C4×C17#9911yescharacteristic
121C2×Dic17—21no—
122C2×Dic17—21no—
123C2×Dic17—21no—
124C2×Dic17—21no—
125C2×Dic17—21no—
126C2×Dic17—21no—
127C2×Dic17—41no—
128C2×Dic17—41no—
129C2×Dic17—41no—
130C2×Dic17—41no—
131C2×Dic17—41no—
132C2×Dic17—41no—
133C2×Dic17—41no—
134C2×Dic17—41no—
135C2×Dic17#10412yes—
136C2×Dic17#13512yes—
137Dic34—44no—
138#3624—44no—
139#3624—82no—
140#2398—171no—
141C4×#101—171no—
142#1461—171no—
143#1353—172no—
144#1345—172no—
145C22×C17—21no—
146C22×C17—21no—
147C22×C17—42no—
148C22×C17—42no—
149C22×C17—42no—
150C22×C17—81no—
151C22×C17—81no—
152C22×C17—81no—
153C22×C17—81no—
154C22×C17C2×#9911yescharacteristic
155C22×C17#41611yescharacteristic
156C22×C17C2×#10411yescharacteristic
157C4×C17—21no—
158C4×C17—41no—
159C4×C17—41no—
160C4×C17—81no—
161C4×C17#35512yes—
162Dic17—22no—
163Dic17—22no—
164Dic17—41no—
165Dic17—41no—
166Dic17—81no—
167Dic17—81no—
168C2×C4×Q8—171no—
169C2×C4×D4#59511yescharacteristic
170#431—341no—
171C2×#101—341no—
172C4×M16—341no—
173#400—171no—
174#400—171no—
175#397—341no—
176#394—171no—
177#394—171no—
178#393—341no—
179C4×C22⋊C4—341no—
180C4×C22⋊C4—341no—
181#376—171no—
182#343—172no—
183#324—172no—
184#324—341no—
185C2×C17—21no—
186C2×C17—21no—
187C2×C17—82no—
188C2×C17#150111yescharacteristic
189C2×C17#212011yescharacteristic
190C2×C17C2×#35511yescharacteristic
191C22×Q8—171no—
192C22×D4C2×#59511yescharacteristic
193C23×C4—21no—
194C2×M16—342no—
195C4×Q8—681no—
196C4×Q8—681no—
197C4×D4—41no—
198C4×D4—41no—
199C2×C4⋊C4—171no—
200C2×C4⋊C4—171no—
201C2×C4⋊C4—171no—
202C2×C4⋊C4C2×#59511yescharacteristic
203C2×C22⋊C4—21no—
204C2×C22⋊C4—341no—
205C2×C22⋊C4—341no—
206C2×C22⋊C4—341no—
207C2×C22⋊C4—341no—
208C2×C42—171no—
209C2×C42—171no—
210C2×C42—341no—
211C2×C42C2×#59511yescharacteristic
212C4⋊C8—681no—
213#101—344no—
214C22⋊C8—342no—
215#97—681no—
216C4×C8—681no—
217C4×C8—681no—
218#95—171no—
219#95—171no—
220#95—341no—
221#95—341no—
222#95—341no—
223#95—341no—
224#95—341no—
225C17#1173411yescharacteristic, complemented, Sylow
226C24—21no—
227C2×Q8—342no—
228C2×Q8—342no—
229C2×Q8—681no—
230C2×D4—41no—
231C2×D4—42no—
232C22×C4—21no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—171no—
238C22×C4—171no—
239C22×C4—171no—
240C22×C4—171no—
241C22×C4—341no—
242C22×C4—341no—
243C22×C4C22⋊#59511yescharacteristic
244C22×C4C22⋊#59511yescharacteristic
245C22×C4C22×#59511yescharacteristic
246M16—344no—
247M16—682no—
248C2×C8—682no—
249C2×C8—682no—
250C4⋊C4—41no—
251C4⋊C4—681no—
252C4⋊C4—681no—
253C4⋊C4—681no—
254C22⋊C4—42no—
255C22⋊C4—682no—
256C22⋊C4—682no—
257C22⋊C4—682no—
258C22⋊C4—682no—
259C42—21no—
260C42—21no—
261C42—341no—
262C42—341no—
263C42—341no—
264C42—341no—
265C42—682no—
266C23—22no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23—41no—
272C23—41no—
273C23C2×C22⋊#59511yescharacteristic
274Q8—684no—
275D4—42no—
276D4—42no—
277C2×C4—22no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—82no—
287C2×C4—82no—
288C2×C4—172no—
289C2×C4—172no—
290C2×C4—341no—
291C2×C4—341no—
292C2×C4—341no—
293C2×C4—341no—
294C2×C4—341no—
295C2×C4—341no—
296C2×C4—681no—
297C2×C4—681no—
298C2×C4—681no—
299C2×C4—681no—
300C2×C4—681no—
301C2×C4—681no—
302C2×C4—681no—
303C2×C4—681no—
304C2×C4#1058755111yescharacteristic
305C2×C4#1058755111yescharacteristic
306C8—684no—
307C8—1362no—
308C22—21no—
309C22—21no—
310C22—42no—
311C22—42no—
312C22—42no—
313C22—81no—
314C22—81no—
315C22—81no—
316C22—81no—
317C22C2×#1058755111yescharacteristic
318C22#1176379911yescharacteristic
319C22D17⋊#10411yescharacteristic
320C4—21no—
321C4—41no—
322C4—41no—
323C4—81no—
324C4—342no—
325C4—342no—
326C4—681no—
327C4—681no—
328C4—1361no—
329C4—1361no—
330C4#1176371712yes—
331C2—21no—
332C2—21no—
333C2—82no—
334C2#1454415911yescharacteristic
335C2#1454503511yescharacteristic
336C2C2×#1176371711yescharacteristic
subgroupG/H
centerC2×C4#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C4×D4×C17C4
socleC22×C17C2×#99
prime radicalC22×D4×C17C2×C4
cosocleC2×#63225C23
hypercenterC2×C4×D4#595
hypocenterC17#11734
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C4×#10587545C2semidirect
2. #14544026C2semidirect
3. #14543783C2semidirect
225. C17#11734semidirect

Maximal subgroups

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

subgroupindex
C4×#105875452
#145440262
#145437832
#145437662
#145320682
#1173417