Finite Group Databasebeta

← #17958409

Subgroups — #17958409

Order 4352.

586 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 80 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#14544035C212yesmaximal, complemented
2#14543714C212yesmaximal, complemented
3#14543712C212yesmaximal, complemented
4#14531275C211yesmaximal, characteristic
5#11763829—22no—
6#11763654C2214yes—
7#11763652—22no—
8C2×#10587612C2211yescharacteristic
9C22×C4×Dic17C411yescharacteristic
10#11762716C411yescharacteristic
11#11762716C2211yescharacteristic
12#11762712C411yescharacteristic
13#11762712C2211yescharacteristic
14#11762689—22no—
15C4×C22⋊Dic17—22no—
16C22×#41×C17C411yescharacteristic
17C2×#41×C17—22no—
18C2×#41×C17—22no—
19C2×#41×C17—42no—
20C2×#41×C17—41no—
21C2×#41×C17—41no—
22C22×Q8×C17C2×C411yescharacteristic
23C22×D4×C17—21no—
24C22×D4×C17C2×C411yescharacteristic
25C23×C4×C17—21no—
26C23×C4×C17C2×C411yescharacteristic
27C23×Dic17—21no—
28C2×C22⋊Dic17—22no—
29C2×C22⋊Dic17—22no—
30C2×C22⋊Dic17D412yes—
31#10587612—41no—
32#10587612—41no—
33C2×C4⋊Dic17C2×C411yescharacteristic
34C2×C4⋊Dic17C2311yescharacteristic
35C2×C4×Dic17—21no—
36C2×C4×Dic17—42no—
37C2×C4×Dic17C2×C411yescharacteristic
38C2×C4×Dic17C2×C411yescharacteristic
39C2×C4×Dic17D412yes—
40C22⋊#3624—24no—
41#10587544—42no—
42#10587542—42no—
43#10587502—22no—
44#10587502—22no—
45C24×C17—21no—
46C24×C17C22⋊C411yescharacteristic
47#41×C17—44no—
48#41×C17—44no—
49#41×C17—44no—
50#41×C17—44no—
51C2×Q8×C17—21no—
52C2×Q8×C17—41no—
53C2×Q8×C17—41no—
54C2×Q8×C17M1612yes—
55C2×D4×C17—24no—
56C2×D4×C17—21no—
57C2×D4×C17—41no—
58C2×D4×C17—41no—
59C2×D4×C17—42no—
60C2×D4×C17—42no—
61C2×D4×C17M1612yes—
62C22×C4×C17—22no—
63C22×C4×C17—21no—
64C22×C4×C17—21no—
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—24no—
68C22×C4×C17—21no—
69C22×C4×C17—42no—
70C22×C4×C17—41no—
71C22×C4×C17—41no—
72C22×C4×C17C22⋊C411yescharacteristic
73C22×C4×C17C22×C411yescharacteristic
74C22×Dic17—21no—
75C22×Dic17—21no—
76C22×Dic17—42no—
77C22×Dic17—42no—
78C22×Dic17—42no—
79C22×Dic17C22⋊C412yes—
80C22×Dic17C2×D412yes—
81C2×#3624—44no—
82C22⋊Dic17—42no—
83C22⋊Dic17—44no—
84C22⋊Dic17—44no—
85C4⋊Dic17—41no—
86C4⋊Dic17—41no—
87C4×Dic17—22no—
88C4×Dic17—22no—
89C4×Dic17—42no—
90C4×Dic17—41no—
91C4×Dic17—41no—
92#11507—171nomaximal, Sylow
93C23×C17—21no—
94C23×C17—21no—
95C23×C17—22no—
96C23×C17—41no—
97C23×C17—41no—
98C23×C17—42no—
99C23×C17—42no—
100C23×C17—41no—
101C23×C17—41no—
102C23×C17#10012yes—
103C23×C17C2×C22⋊C411yescharacteristic
104Q8×C17—42no—
105Q8×C17—42no—
106D4×C17—42no—
107D4×C17—42no—
108D4×C17—48no—
109C2×C4×C17—22no—
110C2×C4×C17—22no—
111C2×C4×C17—22no—
112C2×C4×C17—22no—
113C2×C4×C17—21no—
114C2×C4×C17—21no—
115C2×C4×C17—21no—
116C2×C4×C17—21no—
117C2×C4×C17—22no—
118C2×C4×C17—44no—
119C2×C4×C17—44no—
120C2×C4×C17—41no—
121C2×C4×C17—41no—
122C2×C4×C17#9911yescharacteristic
123C2×C4×C17#9911yescharacteristic
124C2×C4×C17C2×M1611yescharacteristic
125C2×C4×C17C2×M1611yescharacteristic
126C2×Dic17—22no—
127C2×Dic17—22no—
128C2×Dic17—22no—
129C2×Dic17—22no—
130C2×Dic17—41no—
131C2×Dic17—41no—
132C2×Dic17—48no—
133C2×Dic17—41no—
134C2×Dic17—41no—
135C2×Dic17—42no—
136C2×Dic17—42no—
137#3624—84no—
138#2297—171no—
139#1464—172no—
140#1319—172no—
141#1318—172no—
142C22×C17—21no—
143C22×C17—21no—
144C22×C17—22no—
145C22×C17—42no—
146C22×C17—42no—
147C22×C17—44no—
148C22×C17—41no—
149C22×C17—41no—
150C22×C17—42no—
151C22×C17—82no—
152C22×C17—81no—
153C22×C17—81no—
154C22×C17#40711yescharacteristic
155C22×C17C2×#9911yescharacteristic
156C22×C17C2×#10011yescharacteristic
157C4×C17—21no—
158C4×C17—21no—
159C4×C17—21no—
160C4×C17—21no—
161C4×C17—42no—
162Dic17—42no—
163Dic17—42no—
164Dic17—42no—
165Dic17—42no—
166C22×#41#59511yescharacteristic
167C2×#117—171no—
168C22×C42—171no—
169#432—342no—
170#391—171no—
171#391—171no—
172#390—171no—
173#390—171no—
174#386—342no—
175C4×C22⋊C4—342no—
176#324—174no—
177#323—342no—
178C2×C17—21no—
179C2×C17—21no—
180C2×C17—42no—
181C2×C17—82no—
182C2×C17#146211yescharacteristic
183C2×C17#212611yescharacteristic
184C2×C17#213211yescharacteristic
185C2×#41—22no—
186C2×#41—22no—
187C2×#41—42no—
188C2×#41—41no—
189C2×#41—41no—
190C22×Q8C2×#59511yescharacteristic
191C22×D4—21no—
192C22×D4C2×#59511yescharacteristic
193C23×C4—21no—
194C23×C4—341no—
195C23×C4C2×#59511yescharacteristic
196#117—681no—
197#117—681no—
198C2×C4⋊C4—171no—
199C2×C4⋊C4—171no—
200C2×C22⋊C4—172no—
201C2×C22⋊C4—342no—
202C2×C22⋊C4—342no—
203C2×C42—172no—
204C2×C42—171no—
205C2×C42—171no—
206C2×C42—341no—
207C2×C42—682no—
208C4⋊C8—682no—
209C22⋊C8—344no—
210#97—682no—
211#95—342no—
212#95—342no—
213C17#1150711yescharacteristic, complemented, Sylow
214C24—21no—
215C24C22⋊#59511yescharacteristic
216#41—44no—
217#41—44no—
218#41—44no—
219#41—44no—
220C2×Q8—21no—
221C2×Q8—41no—
222C2×Q8—41no—
223C2×Q8#6324712yes—
224C2×D4—24no—
225C2×D4—21no—
226C2×D4—41no—
227C2×D4—41no—
228C2×D4—42no—
229C2×D4—42no—
230C2×D4#6324712yes—
231C22×C4—22no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—24no—
237C22×C4—21no—
238C22×C4—42no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—172no—
242C22×C4—172no—
243C22×C4—341no—
244C22×C4—341no—
245C22×C4—682no—
246C22×C4—682no—
247C22×C4—682no—
248C22×C4C22⋊#59511yescharacteristic
249C22×C4C22×#59511yescharacteristic
250C2×C8—684no—
251C4⋊C4—681no—
252C4⋊C4—681no—
253C22⋊C4—682no—
254C22⋊C4—684no—
255C22⋊C4—684no—
256C42—342no—
257C42—342no—
258C42—681no—
259C42—681no—
260C42—682no—
261C23—21no—
262C23—21no—
263C23—22no—
264C23—41no—
265C23—41no—
266C23—42no—
267C23—42no—
268C23—41no—
269C23—41no—
270C23#1058755312yes—
271C23C2×C22⋊#59511yescharacteristic
272Q8—42no—
273Q8—42no—
274D4—42no—
275D4—42no—
276D4—48no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—44no—
287C2×C4—44no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—342no—
291C2×C4—342no—
292C2×C4—342no—
293C2×C4—342no—
294C2×C4—681no—
295C2×C4—681no—
296C2×C4—688no—
297C2×C4—681no—
298C2×C4—681no—
299C2×C4—682no—
300C2×C4—682no—
301C2×C4#1058755111yescharacteristic
302C2×C4#1058755111yescharacteristic
303C2×C4C2×#6324711yescharacteristic
304C2×C4C2×#6324711yescharacteristic
305C8—1364no—
306C22—21no—
307C22—21no—
308C22—22no—
309C22—42no—
310C22—42no—
311C22—44no—
312C22—41no—
313C22—41no—
314C22—42no—
315C22—82no—
316C22—81no—
317C22—81no—
318C22#1176377911yescharacteristic
319C22C2×#1058755111yescharacteristic
320C22C2×#1058755311yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—42no—
326C4—682no—
327C4—682no—
328C4—682no—
329C4—682no—
330C2—21no—
331C2—21no—
332C2—42no—
333C2—82no—
334C2#1454402911yescharacteristic
335C2#1454505511yescharacteristic
336C2#1454507511yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
Fitting, prime radicalC22×#41×C17C4
socleC22×C17C2×#99
cosocleC2×C4⋊Dic17C23
hypercenterC22×#41#595
hypocenterC17#11507
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. #14544035C2semidirect
2. #14543714C2semidirect
3. #14543712C2semidirect
213. C17#11507semidirect

Maximal subgroups

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

subgroupindex
#145440352
#145437142
#145437122
#145312752
#1150717