Finite Group Databasebeta

← #17966547

Subgroups — #17966547

Order 4352.

616 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#14545714C212yesmaximal
2#14544362C212yesmaximal, complemented
3#14544358C214yesmaximal, complemented
4#14544347C212yesmaximal, complemented
5#14544343C211yesmaximal, characteristic, complemented
6#14544332C211yesmaximal, characteristic, complemented
7#14544329C212yesmaximal, complemented
8C8×#63256C211yesmaximal, characteristic
9#11763860—22no—
10#11763839—24no—
11#11763837—22no—
12#11763831C2214yes—
13#11763828C2212yes—
14#11763813C2212yes—
15#11763810C2214yes—
16#11763673C2211yescharacteristic
17#11763673C2212yes—
18#11763673C2211yescharacteristic
19#11763673C2212yes—
20#11763672C2214yes—
21#11763671C2214yes—
22#11763670C2212yes—
23C4×#63256C2211yescharacteristic
24Q8×#3622C411yescharacteristic
25C8×D68C412yes—
26C8×D68C411yescharacteristic
27#11762874C412yes—
28#11762874C411yescharacteristic
29#11762861C2212yes—
30#11762861C2211yescharacteristic
31C4×C8×D17C2212yes—
32C4×C8×D17C2211yescharacteristic
33C8×Q8×C17C411yescharacteristic
34C2×#63256Q811yescharacteristic
35C2×#63243—22no—
36C2×#63242—24no—
37C4×Q8×C17C2×C411yescharacteristic
38Q8×Dic17D411yescharacteristic
39C2×C8×D17C2×C412yes—
40C2×C8×D17C2×C411yescharacteristic
41C2×C8×D17C2×C412yes—
42C2×C8×D17C2×C411yescharacteristic
43#10587579D411yescharacteristic
44#10587579D412yes—
45#10587578Q812yes—
46#10587578Q811yescharacteristic
47C4×D68C2×C412yes—
48C4×D68C2×C411yescharacteristic
49C42×D17C2312yes—
50C42×D17C2311yescharacteristic
51#10587544—24no—
52#10587543—22no—
53#10587543—24no—
54#10587542—24no—
55C4⋊#3624—22no—
56C4⋊#3624C2312yes—
57C4⋊#3624C2314yes—
58C4⋊#3624C2312yes—
59C4×#3624—22no—
60C17×C4⋊C8C2×C412yes—
61C17×C4⋊C8C2×C411yescharacteristic
62C4×C8×C17C2×C412yes—
63C4×C8×C17C2×C411yescharacteristic
64#10587491C2×C412yes—
65#10587491C2×C412yes—
66#10587491C2×C412yes—
67C8×Dic17C2311yescharacteristic
68C8×Dic17C2311yescharacteristic
69C8×Dic17C2312yes—
70C4⋊#3622C2×C412yes—
71C4⋊#3622C2×C411yescharacteristic
72C4×#3622C2×C412yes—
73C4×#3622C2×C411yescharacteristic
74C2×Q8×C17C4⋊C411yescharacteristic
75#63256—24no—
76C2×D68C4⋊C412yes—
77C2×D68C4⋊C411yescharacteristic
78C2×C4×D17C22×C411yescharacteristic
79C2×C4×D17C22×C412yes—
80C2×C4×D17C2×D412yes—
81C2×C4×D17C2×D411yescharacteristic
82C2×C4×D17C2×Q812yes—
83C2×C4×D17C2×Q811yescharacteristic
84C2×#3624—22no—
85C2×#3624—24no—
86C2×#3624—22no—
87#63243—82no—
88#63242—84no—
89C2×C8×C17C22×C411yescharacteristic
90C2×C8×C17C22×C412yes—
91C2×C8×C17C22×C411yescharacteristic
92C4⋊C4×C17C4⋊C412yes—
93C4⋊C4×C17C4⋊C411yescharacteristic
94C42×C17C22×C412yes—
95C42×C17C22×C411yescharacteristic
96#63227C4⋊C412yes—
97#63227C4⋊C412yes—
98#63227C4⋊C412yes—
99C4⋊Dic17C4⋊C412yes—
100C4⋊Dic17C4⋊C411yescharacteristic
101C4×Dic17C2×D411yescharacteristic
102C4×Dic17C2×D412yes—
103C4×Dic17C2×Q812yes—
104C4×Dic17C2×Q811yescharacteristic
105C4×Dic17C2411yescharacteristic
106C2×#3622C22×C411yescharacteristic
107C2×#3622C22×C412yes—
108C2×#3622C22×C411yescharacteristic
109C8×D17—24no—
110C8×D17—22no—
111C8×D17—42no—
112C8×D17—41no—
113#17836—171nomaximal, Sylow
114C22×D17C2×C4⋊C411yescharacteristic
115C22×D17C2×C4⋊C412yes—
116Q8×C17—22no—
117C2×C4×C17C2×C4⋊C412yes—
118C2×C4×C17C2×C4⋊C411yescharacteristic
119C2×C4×C17C2×C4⋊C412yes—
120C2×C4×C17C2×C4⋊C411yescharacteristic
121C2×C4×C17C23×C411yescharacteristic
122C2×Dic17C2×C4⋊C411yescharacteristic
123C2×Dic17C2×C4⋊C412yes—
124C2×Dic17C22×D411yescharacteristic
125C2×Dic17C22×Q811yescharacteristic
126D68—24no—
127D68#10814yes—
128C4×D17—24no—
129C4×D17—22no—
130C4×D17—21no—
131C4×D17—22no—
132C4×D17—21no—
133C4×D17—22no—
134C4×D17—22no—
135C4×D17—21no—
136C4×D17—22no—
137C4×D17—21no—
138#3624—42no—
139#3624—44no—
140#3624—42no—
141C8×C17—21no—
142C8×C17—22no—
143C8×C17—21no—
144#3622—21no—
145#3622—22no—
146#3622#13112yes—
147#2990—172no—
148C8×#41—171no—
149#1574—172no—
150#1573—174no—
151#1568—172no—
152#1567—171no—
153#1564—171no—
154C2×#335—172no—
155C22×C17C22×C4⋊C411yescharacteristic
156C2×D17—22no—
157C2×D17—22no—
158C2×D17—21no—
159C2×D17—21no—
160C2×D17—21no—
161C2×D17C2×#10814yes—
162C4×C17—22no—
163C4×C17—21no—
164C4×C17—22no—
165C4×C17C2×#10812yes—
166C4×C17C2×#13111yescharacteristic
167C4×C17#56811yescharacteristic
168Dic17—22no—
169Dic17—21no—
170Dic17—21no—
171Dic17#57611yescharacteristic
172Dic17#57811yescharacteristic
173C4×#41—171no—
174#446—342no—
175C8×Q8—171no—
176C8×Q8#59511yescharacteristic
177#435—344no—
178C8×D4—172no—
179C8×D4—171no—
180C8×D4—172no—
181C8×D4—171no—
182C8×D4—342no—
183#432—174no—
184#431—172no—
185#431—171no—
186#431—172no—
187#423—172no—
188C2×C4⋊C8—174no—
189C2×C4×C8—172no—
190C2×C4×C8—171no—
191#335—171no—
192#335—172no—
193#335—174no—
194#335—171no—
195#335—172no—
196#334—172no—
197#334—174no—
198C2×C17#290611yescharacteristic
199C2×C17#291311yescharacteristic
200C2×C17C22×#10811yescharacteristic
201D17—24no—
202D17—41no—
203C2×#41—171no—
204C2×M16—342no—
205C22×C8—172no—
206C22×C8—171no—
207C22×C8—172no—
208C22×C8—171no—
209C22×C8—344no—
210C4×Q8—171no—
211C4×Q8C2×#59511yescharacteristic
212C4×D4—171no—
213C4×D4—172no—
214C4×D4—171no—
215C4×D4—172no—
216#117—171no—
217#117—172no—
218C2×C42—172no—
219C2×C42—171no—
220C4⋊C8—172no—
221C4⋊C8—172no—
222C4⋊C8—174no—
223C4⋊C8—172no—
224C4⋊C8—171no—
225C4⋊C8—342no—
226C4⋊C8—344no—
227C4⋊C8C2×#59512yes—
228C4⋊C8C2×#59511yescharacteristic
229C22⋊C8—172no—
230C22⋊C8—172no—
231C22⋊C8—172no—
232C22⋊C8—342no—
233C22⋊C8—344no—
234#97—344no—
235C4×C8—171no—
236C4×C8—172no—
237C4×C8—171no—
238C4×C8—172no—
239C4×C8—171no—
240C4×C8—342no—
241C4×C8C2×#59512yes—
242C4×C8C2×#59511yescharacteristic
243C17#1783611yescharacteristic, complemented, Sylow
244#41—344no—
245C2×Q8C4⋊#59511yescharacteristic
246C2×D4—171no—
247C2×D4—172no—
248C22×C4—172no—
249C22×C4—171no—
250C22×C4—172no—
251C22×C4—171no—
252C22×C4—172no—
253C22×C4—171no—
254M16—1362no—
255C2×C8—171no—
256C2×C8—171no—
257C2×C8—172no—
258C2×C8—344no—
259C2×C8—342no—
260C2×C8—342no—
261C2×C8—342no—
262C2×C8—344no—
263C2×C8—682no—
264C2×C8—681no—
265C2×C8—1364no—
266C2×C8C22×#59511yescharacteristic
267C2×C8C22×#59511yescharacteristic
268C2×C8C22×#59512yes—
269C4⋊C4—172no—
270C4⋊C4—171no—
271C4⋊C4C4⋊#59512yes—
272C4⋊C4C4⋊#59511yescharacteristic
273C22⋊C4—172no—
274C22⋊C4—172no—
275C22⋊C4—172no—
276C42—171no—
277C42—172no—
278C42—172no—
279C42—171no—
280C42—171no—
281C42C22×#59512yes—
282C42C22×#59511yescharacteristic
283C23—172no—
284C23—171no—
285Q8—22no—
286D4—174no—
287D4—344no—
288C2×C4—171no—
289C2×C4—171no—
290C2×C4—171no—
291C2×C4—172no—
292C2×C4—342no—
293C2×C4—341no—
294C2×C4—342no—
295C2×C4—341no—
296C2×C4—344no—
297C2×C4—342no—
298C2×C4—342no—
299C2×C4—341no—
300C2×C4—342no—
301C2×C4—341no—
302C2×C4C2×C4⋊#59512yes—
303C2×C4C2×C4⋊#59511yescharacteristic
304C2×C4C2×C4⋊#59512yes—
305C2×C4C2×C4⋊#59511yescharacteristic
306C2×C4C23×#59511yescharacteristic
307C8—22no—
308C8—21no—
309C8—21no—
310C8—172no—
311C8—341no—
312C8—342no—
313C8—682no—
314C8—684no—
315C8—682no—
316C22—174no—
317C22—342no—
318C22—342no—
319C22—341no—
320C22—341no—
321C22—341no—
322C22C22×C4⋊#59511yescharacteristic
323C4—22no—
324C4—21no—
325C4—22no—
326C4—171no—
327C4—171no—
328C4—341no—
329C4—342no—
330C4—341no—
331C4D17⋊#10812yes—
332C4D17⋊#13111yescharacteristic
333C4#1176388911yescharacteristic
334C2—344no—
335C2—681no—
336C2#1454543211yescharacteristic
337C2#1454543911yescharacteristic
338C2C2×D17⋊#10811yescharacteristic
subgroupG/H
centerC22C22×C4⋊#595
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC8×Q8×C17C4
socleC22×C17C22×C4⋊C4
prime radicalC2×#63256Q8
cosocleC4×Dic17C24
hypercenterC8×Q8#595
hypocenterC17#17836
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8

Complements

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

NH ≅ G/Ntype
2. #14544362C2semidirect
3. #14544358C2semidirect
4. #14544347C2semidirect
5. #14544343C2semidirect
6. #14544332C2semidirect
7. #14544329C2semidirect
243. C17#17836semidirect

Maximal subgroups

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

subgroupindex
#145457142
#145443622
#145443582
#145443472
#145443432
#145443322
#145443292
C8×#632562
#1783617