Finite Group Databasebeta

← #17966550

Subgroups — #17966550

Order 4352.

612 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545715C212yesmaximal
2#14544362C212yesmaximal, complemented
3#14544360C214yesmaximal, complemented
4#14544343C211yesmaximal, characteristic, complemented
5#14544341C212yesmaximal, complemented
6#14544333C212yesmaximal, complemented
7#14544332C211yesmaximal, characteristic, complemented
8C8×#63254C211yesmaximal, characteristic
9#11763858—22no—
10#11763844—22no—
11#11763842—24no—
12#11763828C2212yes—
13#11763825C2214yes—
14#11763813C2212yes—
15#11763812C2214yes—
16#11763673C2211yescharacteristic
17#11763673C2211yescharacteristic
18#11763673C2212yes—
19#11763673C2212yes—
20#11763672C2214yes—
21#11763671C2214yes—
22#11763670C2212yes—
23C4×#63254C2211yescharacteristic
24C8×Dic34C411yescharacteristic
25#11762933C411yescharacteristic
26D4×#3622C411yescharacteristic
27C8×C22⋊D17C412yes—
28#11762872C412yes—
29#11762861C2211yescharacteristic
30#11762859C2212yes—
31C2×C8×Dic17C2212yes—
32C4×C8×D17C2211yescharacteristic
33C8×D4×C17C411yescharacteristic
34C2×#63254Q811yescharacteristic
35C2×#63247—24no—
36C2×#63243—22no—
37C22×C8×C17C2×C412yes—
38C4×D4×C17C2×C411yescharacteristic
39D4×Dic17D411yescharacteristic
40C4×C22⋊D17C2×C412yes—
41C2×C4×Dic17C2312yes—
42C22×#3622C2×C412yes—
43C2×C8×D17C2×C411yescharacteristic
44C2×C8×D17C2×C411yescharacteristic
45#10587578Q811yescharacteristic
46#10587573D411yescharacteristic
47#10587567D412yes—
48#10587563Q812yes—
49C42×D17C2311yescharacteristic
50C4×Dic34C2×C411yescharacteristic
51C22⋊#3624—24no—
52#10587544—24no—
53#10587543—22no—
54C4⋊#3624—22no—
55C4⋊#3624C2312yes—
56C4⋊#3624C2314yes—
57C4⋊#3624C2312yes—
58C4×#3624—24no—
59C4×#3624—22no—
60C17×C4⋊C8C2×C411yescharacteristic
61C17×C22⋊C8C2×C412yes—
62C4×C8×C17C2×C411yescharacteristic
63C22⋊#3622C2×C412yes—
64#10587491C2×C412yes—
65#10587485C2×C412yes—
66#10587485C2×C412yes—
67C8×Dic17C2×C412yes—
68C8×Dic17C2×C412yes—
69C8×Dic17C2311yescharacteristic
70C8×Dic17C2311yescharacteristic
71C8×Dic17C2312yes—
72C4⋊#3622C2×C411yescharacteristic
73C4×#3622C2×C411yescharacteristic
74C2×D4×C17C4⋊C411yescharacteristic
75C22×C4×C17C22×C412yes—
76C2×C22⋊D17C4⋊C412yes—
77C22×Dic17C2×D412yes—
78C22×Dic17C2×Q812yes—
79#63254—24no—
80C2×C4×D17C22×C411yescharacteristic
81C2×C4×D17C2×D411yescharacteristic
82C2×C4×D17C2×Q811yescharacteristic
83C2×Dic34C4⋊C411yescharacteristic
84#63247—84no—
85C2×#3624—24no—
86C2×#3624—22no—
87C2×#3624—22no—
88#63243—82no—
89C2×C8×C17—42no—
90C2×C8×C17C22×C411yescharacteristic
91C2×C8×C17C22×C412yes—
92C2×C8×C17C22×C411yescharacteristic
93C4⋊C4×C17C4⋊C411yescharacteristic
94C22⋊C4×C17C4⋊C412yes—
95C42×C17C22×C411yescharacteristic
96C22⋊Dic17C4⋊C412yes—
97#63227C4⋊C412yes—
98C4⋊Dic17C4⋊C411yescharacteristic
99#63225C4⋊C412yes—
100#63225C4⋊C412yes—
101C4×Dic17C22×C412yes—
102C4×Dic17C2×D411yescharacteristic
103C4×Dic17C2×D412yes—
104C4×Dic17C2×Q811yescharacteristic
105C4×Dic17C2×Q812yes—
106C4×Dic17C2411yescharacteristic
107C2×#3622—24no—
108C2×#3622C22×C411yescharacteristic
109C2×#3622C22×C412yes—
110C2×#3622C22×C411yescharacteristic
111C8×D17—22no—
112C8×D17—41no—
113#17837—171nomaximal, Sylow
114C23×C17C2×C4⋊C412yes—
115C22×D17C2×C4⋊C411yescharacteristic
116D4×C17—22no—
117C2×C4×C17—22no—
118C2×C4×C17—22no—
119C2×C4×C17C2×C4⋊C411yescharacteristic
120C2×C4×C17C2×C4⋊C412yes—
121C2×C4×C17C2×C4⋊C411yescharacteristic
122C2×C4×C17C23×C411yescharacteristic
123C22⋊D17—24no—
124C2×Dic17—22no—
125C2×Dic17—22no—
126C2×Dic17—24no—
127C2×Dic17C2×C4⋊C411yescharacteristic
128C2×Dic17C2×C4⋊C412yes—
129C2×Dic17C2×C4⋊C412yes—
130C2×Dic17C22×D411yescharacteristic
131C2×Dic17C22×Q811yescharacteristic
132C4×D17—21no—
133C4×D17—21no—
134C4×D17—22no—
135C4×D17—21no—
136C4×D17—21no—
137Dic34#10814yes—
138#3624—44no—
139#3624—42no—
140#3624—42no—
141C8×C17—21no—
142C8×C17—21no—
143C8×C17—22no—
144#3622—22no—
145#3622—21no—
146#3622#13112yes—
147#2991—172no—
148C8×#41—171no—
149#1574—174no—
150#1574—172no—
151#1567—172no—
152#1567—171no—
153#1564—171no—
154#1564—172no—
155C22×C17—22no—
156C22×C17—22no—
157C22×C17—22no—
158C22×C17C22×C4⋊C411yescharacteristic
159C2×D17—21no—
160C2×D17—21no—
161C2×D17—21no—
162C4×C17—22no—
163C4×C17—21no—
164C4×C17C2×#10812yes—
165C4×C17C2×#13111yescharacteristic
166C4×C17#56811yescharacteristic
167Dic17—21no—
168Dic17—22no—
169Dic17—21no—
170Dic17C2×#10814yes—
171Dic17#57611yescharacteristic
172Dic17#57811yescharacteristic
173C4×#41—171no—
174C8×Q8—171no—
175C8×Q8—171no—
176C8×Q8—342no—
177#436—344no—
178#436—342no—
179C8×D4—172no—
180C8×D4—171no—
181C8×D4—172no—
182C8×D4#59511yescharacteristic
183#431—171no—
184#431—172no—
185#431—174no—
186#431—172no—
187#423—174no—
188#423—172no—
189C2×C4×C8—172no—
190C2×C4×C8—171no—
191#335—171no—
192#335—171no—
193#335—172no—
194#335—174no—
195#335—172no—
196#334—172no—
197#334—174no—
198C2×C17—42no—
199C2×C17#290611yescharacteristic
200C2×C17#291311yescharacteristic
201C2×C17C22×#10811yescharacteristic
202D17—41no—
203C2×#41—171no—
204C2×M16—342no—
205C2×M16—344no—
206C22×C8—172no—
207C22×C8—171no—
208C22×C8—171no—
209C22×C8C2×#59512yes—
210C4×Q8—171no—
211C4×Q8—171no—
212C4×D4—171no—
213C4×D4—172no—
214C4×D4—172no—
215C4×D4C2×#59511yescharacteristic
216#117—171no—
217#117—172no—
218C2×C42—172no—
219C2×C42—171no—
220C4⋊C8—172no—
221C4⋊C8—172no—
222C4⋊C8—172no—
223C4⋊C8—172no—
224C4⋊C8—174no—
225C4⋊C8—171no—
226C4⋊C8—342no—
227C4⋊C8—344no—
228C4⋊C8C2×#59511yescharacteristic
229C22⋊C8—172no—
230C22⋊C8—172no—
231C22⋊C8—342no—
232C22⋊C8—344no—
233C22⋊C8C2×#59512yes—
234C4×C8—172no—
235C4×C8—171no—
236C4×C8—171no—
237C4×C8—172no—
238C4×C8—172no—
239C4×C8—171no—
240C4×C8—344no—
241C4×C8—342no—
242C4×C8C2×#59511yescharacteristic
243C17#1783711yescharacteristic, complemented, Sylow
244#41—344no—
245C2×Q8—171no—
246C2×D4—172no—
247C2×D4C4⋊#59511yescharacteristic
248C22×C4—172no—
249C22×C4—172no—
250C22×C4—171no—
251C22×C4—171no—
252C22×C4—171no—
253C22×C4C22×#59512yes—
254M16—1362no—
255M16—1364no—
256C2×C8—42no—
257C2×C8—171no—
258C2×C8—172no—
259C2×C8—171no—
260C2×C8—342no—
261C2×C8—344no—
262C2×C8—342no—
263C2×C8—344no—
264C2×C8—342no—
265C2×C8—681no—
266C2×C8C22×#59511yescharacteristic
267C2×C8C22×#59512yes—
268C2×C8C22×#59511yescharacteristic
269C4⋊C4—172no—
270C4⋊C4—172no—
271C4⋊C4—171no—
272C4⋊C4C4⋊#59511yescharacteristic
273C22⋊C4—172no—
274C22⋊C4—172no—
275C22⋊C4C4⋊#59512yes—
276C42—172no—
277C42—171no—
278C42—172no—
279C42—171no—
280C42—171no—
281C42—172no—
282C42C22×#59511yescharacteristic
283C23—171no—
284C23C2×C4⋊#59512yes—
285Q8—174no—
286D4—22no—
287D4—344no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—171no—
291C2×C4—172no—
292C2×C4—171no—
293C2×C4—171no—
294C2×C4—172no—
295C2×C4—341no—
296C2×C4—341no—
297C2×C4—342no—
298C2×C4—344no—
299C2×C4—342no—
300C2×C4—342no—
301C2×C4—341no—
302C2×C4—341no—
303C2×C4C2×C4⋊#59512yes—
304C2×C4C2×C4⋊#59511yescharacteristic
305C2×C4C2×C4⋊#59511yescharacteristic
306C2×C4C23×#59511yescharacteristic
307C8—21no—
308C8—21no—
309C8—22no—
310C8—172no—
311C8—342no—
312C8—341no—
313C8—684no—
314C8—682no—
315C8—682no—
316C22—22no—
317C22—22no—
318C22—22no—
319C22—341no—
320C22—341no—
321C22—341no—
322C22C22×C4⋊#59511yescharacteristic
323C4—22no—
324C4—21no—
325C4—171no—
326C4—171no—
327C4—174no—
328C4—341no—
329C4—342no—
330C4—341no—
331C4D17⋊#10812yes—
332C4D17⋊#13111yescharacteristic
333C4#1176388711yescharacteristic
334C2—42no—
335C2—681no—
336C2#1454543111yescharacteristic
337C2#1454543911yescharacteristic
338C2C2×D17⋊#10811yescharacteristic
subgroupG/H
centerC22C22×C4⋊#595
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC8×D4×C17C4
socleC22×C17C22×C4⋊C4
prime radicalC2×#63254Q8
cosocleC4×Dic17C24
hypercenterC8×D4#595
hypocenterC17#17837
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
2. #14544362C2semidirect
3. #14544360C2semidirect
4. #14544343C2semidirect
5. #14544341C2semidirect
6. #14544333C2semidirect
7. #14544332C2semidirect
243. C17#17837semidirect

Maximal subgroups

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

subgroupindex
#145457152
#145443622
#145443602
#145443432
#145443412
#145443332
#145443322
C8×#632542
#1783717