Finite Group Databasebeta

← #17949873

Subgroups — #17949873

Order 4352.

462 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 106 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#14544712C211yesmaximal, characteristic
2#14544570C211yesmaximal, characteristic
3#14543603C212yesmaximal
4#14543602C212yesmaximal
5C4×#10587574C211yesmaximal, characteristic
6C2×C4⋊#3624—21no—
7C2×#10587542—21no—
8#11763675—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587574C411yescharacteristic
13C2×C4×Dic34—21no—
14#11762713—21no—
15#11762708C2211yescharacteristic
16#11762706—21no—
17#11762705C2211yescharacteristic
18#11762678C411yescharacteristic
19C4×#63225—21no—
20C4×C4⋊Dic17C411yescharacteristic
21C42×Dic17C2211yescharacteristic
22C4×C4⋊C4×C17C411yescharacteristic
23C22×Dic34—21no—
24C22×#3624—22no—
25C22×#3624—22no—
26C2×C4⋊C4×C17C2×C411yescharacteristic
27C2×C4⋊C4×C17C2×C411yescharacteristic
28C2×C42×C17—21no—
29C2×C42×C17C2×C411yescharacteristic
30C2×C4⋊Dic17—21no—
31C2×C4⋊Dic17C2×C411yescharacteristic
32C2×C4⋊Dic17C2×C411yescharacteristic
33C2×#63225—21no—
34C2×#63225—21no—
35C2×#63225—21no—
36C2×#63225—21no—
37C2×C4×Dic17—21no—
38C2×C4×Dic17C2×C411yescharacteristic
39C2×C4×Dic17D411yescharacteristic
40C2×C4×Dic17D411yescharacteristic
41C2×C4×Dic17D411yescharacteristic
42C2×C4×Dic17D411yescharacteristic
43C2×C4×Dic17C2311yescharacteristic
44#10587574—22no—
45#10587574—22no—
46C4×Dic34—42no—
47C4×Dic34—42no—
48#10587542—42no—
49C4⋊#3624—24no—
50C17×#95—21no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54C22×C4×C17—21no—
55C22×C4×C17—21no—
56C22×C4×C17C22⋊C411yescharacteristic
57C22×C4×C17C22⋊C411yescharacteristic
58C22×C4×C17C22×C411yescharacteristic
59C22×Dic17—21no—
60C22×Dic17—21no—
61C22×Dic17C22⋊C411yescharacteristic
62C22×Dic17C22⋊C411yescharacteristic
63C22×Dic17C2×D411yescharacteristic
64C22×Dic17C2×D411yescharacteristic
65C2×Dic34—24no—
66C2×Dic34—42no—
67C2×Dic34—42no—
68C2×#3624—24no—
69C2×#3624—42no—
70C2×#3624—42no—
71C2×#3624—42no—
72C2×#3624—42no—
73C2×#3624—42no—
74C4⋊C4×C17—21no—
75C4⋊C4×C17—41no—
76C4⋊C4×C17M1612yes—
77C42×C17—22no—
78C42×C17—42no—
79C4⋊Dic17—21no—
80C4⋊Dic17—41no—
81C4⋊Dic17—41no—
82C4⋊Dic17—41no—
83C4⋊Dic17M1612yes—
84#63225—24no—
85#63225—42no—
86#63225—42no—
87#63225—41no—
88#63225—41no—
89C4×Dic17—21no—
90C4×Dic17—21no—
91C4×Dic17—22no—
92C4×Dic17—22no—
93C4×Dic17—41no—
94C4×Dic17—41no—
95C4×Dic17—42no—
96C4×Dic17D812yes—
97C4×Dic17SD1612yes—
98#7625—171nomaximal, Sylow
99C23×C17C2×C22⋊C411yescharacteristic
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—21no—
105C2×C4×C17—21no—
106C2×C4×C17—22no—
107C2×C4×C17—41no—
108C2×C4×C17—41no—
109C2×C4×C17—41no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17#10112yes—
113C2×C4×C17#10212yes—
114C2×C4×C17C2×M1611yescharacteristic
115C2×C4×C17C2×M1611yescharacteristic
116C2×Dic17—21no—
117C2×Dic17—21no—
118C2×Dic17—21no—
119C2×Dic17—21no—
120C2×Dic17—21no—
121C2×Dic17—21no—
122C2×Dic17—21no—
123C2×Dic17—21no—
124C2×Dic17—22no—
125C2×Dic17—41no—
126C2×Dic17—41no—
127C2×Dic17—41no—
128C2×Dic17—41no—
129C2×Dic17—41no—
130C2×Dic17#10212yes—
131C2×Dic17#10412yes—
132C2×Dic17C2×D811yescharacteristic
133C2×Dic17C2×SD1611yescharacteristic
134C2×Dic17#13712yes—
135Dic34—48no—
136#3624—44no—
137#3624—82no—
138C4×C4⋊Q8—171no—
139#1839—171no—
140#1767—171no—
141#1271—172no—
142#1271—172no—
143C22×C17#40711yescharacteristic
144C22×C17#41011yescharacteristic
145C22×C17C2×#10111yescharacteristic
146C22×C17C2×#10211yescharacteristic
147C22×C17#41911yescharacteristic
148C22×C17C2×#10411yescharacteristic
149C22×C17#42111yescharacteristic
150C4×C17—22no—
151C4×C17—21no—
152C4×C17—21no—
153C4×C17—22no—
154C4×C17—42no—
155C4×C17—81no—
156Dic17—22no—
157Dic17—22no—
158Dic17—21no—
159Dic17—21no—
160Dic17—22no—
161Dic17—42no—
162Dic17—81no—
163C2×C4⋊Q8—171no—
164C2×C4×Q8—341no—
165C2×C4⋊C8—341no—
166C2×#97—341no—
167#391—341no—
168#389—171no—
169#389—171no—
170#389—341no—
171#384—171no—
172C4×C4⋊C4—171no—
173C4×C4⋊C4—341no—
174C4×C4⋊C4#59511yescharacteristic
175C43—171no—
176#336—172no—
177#336—172no—
178#336—341no—
179#336—341no—
180C2×C17#146711yescharacteristic
181C2×C17#148611yescharacteristic
182C2×C17#149111yescharacteristic
183C2×C17#150211yescharacteristic
184C2×C17#151511yescharacteristic
185C2×C17#153111yescharacteristic
186C2×C17#154611yescharacteristic
187C22×Q8—341no—
188C22×C8—342no—
189C22×C8—342no—
190C4⋊Q8—342no—
191C4⋊Q8—342no—
192C4×Q8—682no—
193C4×Q8—682no—
194C2×C4⋊C4—171no—
195C2×C4⋊C4—171no—
196C2×C4⋊C4—341no—
197C2×C4⋊C4—341no—
198C2×C4⋊C4—341no—
199C2×C4⋊C4—341no—
200C2×C4⋊C4—341no—
201C2×C4⋊C4C2×#59511yescharacteristic
202C2×C4⋊C4C2×#59511yescharacteristic
203C2×C42—21no—
204C2×C42—171no—
205C2×C42—171no—
206C2×C42—171no—
207C2×C42—171no—
208C2×C42—171no—
209C2×C42—171no—
210C2×C42—341no—
211C2×C42C2×#59511yescharacteristic
212C4⋊C8—344no—
213#97—682no—
214#95—21no—
215#95—341no—
216#95—341no—
217#95—341no—
218C17#762511yescharacteristic, complemented, Sylow
219C2×Q8—344no—
220C2×Q8—682no—
221C2×Q8—682no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—171no—
225C22×C4—171no—
226C22×C4—171no—
227C22×C4—171no—
228C22×C4—341no—
229C22×C4—341no—
230C22×C4C22⋊#59511yescharacteristic
231C22×C4C22⋊#59511yescharacteristic
232C22×C4C22×#59511yescharacteristic
233C2×C8—344no—
234C2×C8—682no—
235C2×C8—682no—
236C2×C8—682no—
237C2×C8—682no—
238C2×C8—682no—
239C4⋊C4—21no—
240C4⋊C4—41no—
241C4⋊C4—172no—
242C4⋊C4—344no—
243C4⋊C4—341no—
244C4⋊C4—681no—
245C4⋊C4—681no—
246C4⋊C4—681no—
247C4⋊C4—682no—
248C4⋊C4—681no—
249C4⋊C4—681no—
250C4⋊C4—682no—
251C4⋊C4#6324312yes—
252C42—22no—
253C42—42no—
254C42—172no—
255C42—172no—
256C42—342no—
257C42—342no—
258C42—341no—
259C42—341no—
260C42—681no—
261C42—681no—
262C42—682no—
263C23C2×C22⋊#59511yescharacteristic
264Q8—688no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—171no—
278C2×C4—171no—
279C2×C4—172no—
280C2×C4—172no—
281C2×C4—172no—
282C2×C4—341no—
283C2×C4—341no—
284C2×C4—341no—
285C2×C4—341no—
286C2×C4—341no—
287C2×C4—341no—
288C2×C4—341no—
289C2×C4—341no—
290C2×C4—342no—
291C2×C4—681no—
292C2×C4—681no—
293C2×C4—681no—
294C2×C4—681no—
295C2×C4—681no—
296C2×C4#1058754512yes—
297C2×C4#1058754712yes—
298C2×C4C2×#6324311yescharacteristic
299C2×C4D17⋊M1611yescharacteristic
300C8—684no—
301C8—1362no—
302C22#1176378011yescharacteristic
303C22#1176378811yescharacteristic
304C22C2×#1058754511yescharacteristic
305C22C2×#1058754711yescharacteristic
306C22#1176380211yescharacteristic
307C22D17⋊#10411yescharacteristic
308C22#1176380611yescharacteristic
309C4—22no—
310C4—22no—
311C4—21no—
312C4—21no—
313C4—42no—
314C4—81no—
315C4—341no—
316C4—341no—
317C4—342no—
318C4—342no—
319C4—342no—
320C4—682no—
321C4—1361no—
322C2#1454404611yescharacteristic
323C2#1454411011yescharacteristic
324C2#1454412711yescharacteristic
325C2#1454416311yescharacteristic
326C2#1454420611yescharacteristic
327C2#1454425611yescharacteristic
328C2#1454429311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC4×C4⋊C4×C17C4
socle, prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC4×C4⋊C4#595
hypocenterC17#7625
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
218. C17#7625semidirect

Maximal subgroups

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

subgroupindex
#145447122
#145445702
#145436032
#145436022
C4×#105875742
#762517