Finite Group Databasebeta

← #16933714

Subgroups — #16933714

Order 4352.

370 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14539294C211yesmaximal, characteristic
2#14528914C211yesmaximal, characteristic
3#14527349C211yesmaximal, characteristic
4#14527348C211yesmaximal, characteristic
5#14527347C211yesmaximal, characteristic
6#14527077C211yesmaximal, characteristic
7C17×#1518C211yesmaximal, characteristic
8#11763366C2211yescharacteristic
9#11763212C411yescharacteristic, complemented
10#11763212C411yescharacteristic, complemented
11#11763208—21no—
12#11763208—21no—
13#11763205C411yescharacteristic, complemented
14#11763205C411yescharacteristic, complemented
15#11762862C2211yescharacteristic
16#11762845—21no—
17#11762845—21no—
18C2×C4×#3622C2211yescharacteristic
19#11762675C2211yescharacteristic
20#11762571—21no—
21#11762571—21no—
22#11762547—22no—
23#11762546—22no—
24#11762545—22no—
25#11762531—21no—
26#11762530—21no—
27C17×#533C2211yescharacteristic
28C17×#431C2211yescharacteristic
29C17×#382C2211yescharacteristic
30C17×#328—22no—
31C17×C4⋊Q8C2×C411yescharacteristic
32C17×C4⋊Q8C2×C411yescharacteristic
33C17×#125—21no—
34C17×C22⋊Q8—21no—
35C17×C22⋊Q8—21no—
36C4×Q8×C17—21no—
37C4×Q8×C17—21no—
38C17×#117—21no—
39C2×C4⋊C4×C17—21no—
40C2×C42×C17C2311yescharacteristic
41#10587612—21no—
42C2×C4⋊Dic17—21no—
43#10587610—21no—
44#10587610—21no—
45C22×#3622D411yescharacteristic
46C22×#3622D411yescharacteristic
47#10587556—21no—
48#10587555C2×C411yescharacteristic
49#10587555C2×C411yescharacteristic
50C4×Dic34—21no—
51C4×Dic34—21no—
52C17×C4⋊C8—21no—
53C17×C22⋊C8D412yes—
54C4×C8×C17—21no—
55C17×#95—21no—
56C17×#95—21no—
57#10587502—21no—
58#10587502—21no—
59C22⋊#3622D412yes—
60#10587479—21no—
61#10587479—21no—
62#10587479—21no—
63#10587479—21no—
64#10587478—21no—
65#10587478—21no—
66#10587478—21no—
67#10587478—21no—
68C4⋊#3622—21no—
69C4×#3622—21no—
70C4×#3622C2×C411yescharacteristic
71C4×#3622C2×C411yescharacteristic
72C4×#3622D411yescharacteristic
73C4×#3622D411yescharacteristic
74C2×Q8×C17—21no—
75C2×Q8×C17—21no—
76C22×C4×C17—41no—
77C22×C4×C17C2×D411yescharacteristic
78C22×C4×C17C2×D411yescharacteristic
79C22×C4×C17C2×D411yescharacteristic
80C22×Dic17—41no—
81C2×Dic34—21no—
82C2×Dic34—21no—
83C2×C8×C17—22no—
84C4⋊C4×C17—21no—
85C4⋊C4×C17—21no—
86C4⋊C4×C17—21no—
87C4⋊C4×C17—21no—
88C4⋊C4×C17—41no—
89C4⋊C4×C17—41no—
90C4⋊C4×C17—41no—
91C4⋊C4×C17—41no—
92C22⋊C4×C17—41no—
93C42×C17—41no—
94C42×C17C22×C411yescharacteristic
95C42×C17C2×D411yescharacteristic
96C42×C17#4111yescharacteristic
97C42×C17#4111yescharacteristic
98C22⋊Dic17—41no—
99C4⋊Dic17—21no—
100C4⋊Dic17—21no—
101C4⋊Dic17—21no—
102C4⋊Dic17—21no—
103C4⋊Dic17—41no—
104C4⋊Dic17—41no—
105#63225—41no—
106#63225—41no—
107C4×Dic17—41no—
108C2×#3622—21no—
109C2×#3622—21no—
110C2×#3622—21no—
111C2×#3622—21no—
112C2×#3622—22no—
113C2×#3622C22⋊C411yescharacteristic
114C2×#3622C22⋊C411yescharacteristic
115C2×#3622C22⋊C411yescharacteristic
116C2×#3622C22⋊C411yescharacteristic
117#9759—171nomaximal, Sylow
118C23×C17#12711yescharacteristic
119Q8×C17—81no—
120Q8×C17—81no—
121C2×C4×C17—41no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17—81no—
126C2×C4×C17—81no—
127C2×C4×C17—81no—
128C2×C4×C17C2×C22⋊C411yescharacteristic
129C2×C4×C17C4×D411yescharacteristic
130C2×C4×C17C4×D411yescharacteristic
131C2×C4×C17#12111yescharacteristic
132C2×C4×C17#12111yescharacteristic
133C2×C4×C17#12411yescharacteristic
134C2×C4×C17#13711yescharacteristic
135C2×C4×C17#13711yescharacteristic
136C2×C4×C17#13711yescharacteristic
137C2×C4×C17#13711yescharacteristic
138C2×Dic17—41no—
139C2×Dic17—41no—
140C2×Dic17—81no—
141C2×Dic17—81no—
142C2×Dic17—81no—
143Dic34—81no—
144Dic34—81no—
145C8×C17—42no—
146#3622—21no—
147#3622—21no—
148#3622—21no—
149#3622—21no—
150#3622—42no—
151#3160—171no—
152#1835—171no—
153#1518—171no—
154#1518—171no—
155#1518—171no—
156#1518D1711yescharacteristic
157#1452—171no—
158C22×C17—21no—
159C22×C17—21no—
160C22×C17#39011yescharacteristic
161C22×C17#49711yescharacteristic
162C22×C17#49711yescharacteristic
163C4×C17—21no—
164C4×C17—21no—
165C4×C17—21no—
166C4×C17—21no—
167C4×C17—81no—
168C4×C17—81no—
169C4×C17—161no—
170C4×C17#41911yescharacteristic
171C4×C17#41911yescharacteristic
172C4×C17#49111yescharacteristic
173C4×C17#49111yescharacteristic
174Dic17—81no—
175Dic17—81no—
176Dic17—161no—
177#533—171no—
178#533C2×D1711yescharacteristic
179#500—171no—
180#500—171no—
181#499—341no—
182#499—341no—
183#498—171no—
184#498—171no—
185#431—171no—
186#431C2×D1711yescharacteristic
187#427—341no—
188#427—341no—
189C2×C4×C8—171no—
190#382—171no—
191#382C2×D1711yescharacteristic
192#340—341no—
193#340—341no—
194#328—22no—
195#328—342no—
196#328—342no—
197#328—342no—
198#322—341no—
199#322—341no—
200C2×C17—21no—
201C2×C17—21no—
202C2×C17#196011yescharacteristic
203C2×C17#197611yescharacteristic
204C2×C17#197611yescharacteristic
205C22×C8—171no—
206C22×C8—171no—
207C4⋊Q8—171no—
208C4⋊Q8—171no—
209C4⋊Q8C4×D1711yescharacteristic
210C4⋊Q8C4×D1711yescharacteristic
211#125—21no—
212#125—341no—
213C22⋊Q8—21no—
214C22⋊Q8—21no—
215C22⋊Q8—341no—
216C22⋊Q8—341no—
217C4×Q8—21no—
218C4×Q8—21no—
219C4×Q8—341no—
220C4×Q8—341no—
221#117—21no—
222#117—341no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—341no—
225C2×C42C22×D1711yescharacteristic
226#107—341no—
227#107—341no—
228#107—341no—
229#107—341no—
230#106—341no—
231#106—341no—
232#106—341no—
233#106—341no—
234C4⋊C8—21no—
235C4⋊C8—341no—
236C22⋊C8—172no—
237C22⋊C8C22⋊D1712yes—
238C4×C8—21no—
239C4×C8—171no—
240C4×C8—171no—
241C4×C8—171no—
242C4×C8—171no—
243C4×C8—341no—
244#95—21no—
245#95—21no—
246#95—341no—
247#95—341no—
248C17#975911yescharacteristic, complemented, Sylow
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—341no—
252C2×Q8—341no—
253C22×C4—41no—
254C22×C4—681no—
255C22×C4D4×D1711yescharacteristic
256C22×C4D4×D1711yescharacteristic
257C22×C4C2×C22⋊D1711yescharacteristic
258C2×C8—22no—
259C2×C8—171no—
260C2×C8—171no—
261C2×C8—171no—
262C2×C8—171no—
263C2×C8—341no—
264C2×C8—341no—
265C2×C8—341no—
266C2×C8—341no—
267C2×C8—342no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—341no—
277C4⋊C4—341no—
278C4⋊C4—341no—
279C4⋊C4—341no—
280C4⋊C4—681no—
281C4⋊C4—681no—
282C4⋊C4—681no—
283C4⋊C4—681no—
284C22⋊C4—41no—
285C22⋊C4—681no—
286C42—41no—
287C42—681no—
288C42C2×C4×D1711yescharacteristic
289C42#6325211yescharacteristic
290C42D4×D1711yescharacteristic
291C42#6325411yescharacteristic
292C23#1058762611yescharacteristic
293Q8—81no—
294Q8—81no—
295Q8—1361no—
296Q8—1361no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—681no—
305C2×C4—681no—
306C2×C4—1361no—
307C2×C4—1361no—
308C2×C4—1361no—
309C2×C4C22⋊C4×D1711yescharacteristic
310C2×C4#1058756711yescharacteristic
311C2×C4#1058757011yescharacteristic
312C2×C4#1058757111yescharacteristic
313C2×C4#1058760111yescharacteristic
314C2×C4#1058760111yescharacteristic
315C2×C4#1058760411yescharacteristic
316C2×C4#1058760411yescharacteristic
317C2×C4C4×C22⋊D1711yescharacteristic
318C2×C4#1058762511yescharacteristic
319C8—42no—
320C8—341no—
321C8—341no—
322C8—341no—
323C8—341no—
324C8—682no—
325C22—21no—
326C22—21no—
327C22#1176270911yescharacteristic
328C22#1176320011yescharacteristic
329C22#1176320211yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—81no—
335C4—81no—
336C4—161no—
337C4—2721no—
338C4—1361no—
339C4—1361no—
340C4#1176281611yescharacteristic
341C4#1176281611yescharacteristic
342C4#1176317611yescharacteristic
343C4#1176317611yescharacteristic
344C2—21no—
345C2—21no—
346C2#1452960211yescharacteristic
347C2#1452967911yescharacteristic
348C2#1452968111yescharacteristic
subgroupG/H
centerC22#11762709
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1518C2
socleC22×C17#390
prime radicalC23×C17#127
cosocleC2×C42×C17C23
hypercenter#1518D17
hypocenterC17#9759
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
9. #11763212C4semidirect
10. #11763212C4semidirect
13. #11763205C4semidirect
14. #11763205C4semidirect
248. C17#9759semidirect

Maximal subgroups

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

subgroupindex
#145392942
#145289142
#145273492
#145273482
#145273472
#145270772
C17×#15182
#975917