Finite Group Databasebeta

← #16933706

Subgroups — #16933706

Order 4352.

400 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14539106C211yesmaximal, characteristic
2#14528914C211yesmaximal, characteristic, complemented
3#14527349C211yesmaximal, characteristic, complemented
4#14527347C211yesmaximal, characteristic, complemented
5#14527344C211yesmaximal, characteristic
6#14527068C211yesmaximal, characteristic, complemented
7C17×#1517C211yesmaximal, characteristic
8#11763366C2211yescharacteristic
9#11763163—21no—
10#11763163—21no—
11#11763159C411yescharacteristic, complemented
12#11763159C411yescharacteristic, complemented
13#11763155C411yescharacteristic, complemented
14#11763155C411yescharacteristic, complemented
15#11762862C2211yescharacteristic
16#11762805—21no—
17#11762805—21no—
18C2×C4×#3622C2211yescharacteristic
19#11762675C2211yescharacteristic
20#11762571—21no—
21#11762571—21no—
22#11762547—22no—
23#11762545—22no—
24#11762543—22no—
25#11762531—21no—
26C8×#3622—21no—
27C17×#532C2211yescharacteristic
28C17×#431C2211yescharacteristic
29C17×#382C2211yescharacteristic
30C17×#327—22no—
31C2×#41×C17—21no—
32C17×C4⋊Q8C2×C411yescharacteristic
33C17×#127C2×C411yescharacteristic
34C17×#124—21no—
35C17×#121—21no—
36C17×#121—21no—
37C4×D4×C17—21no—
38C4×D4×C17—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#10587506—21no—
58#10587506—21no—
59#10587506—21no—
60#10587506—21no—
61#10587503—21no—
62#10587503—21no—
63#10587503—21no—
64#10587503—21no—
65#10587502—21no—
66#10587502—21no—
67C22⋊#3622D412yes—
68C4⋊#3622—21no—
69C4×#3622—21no—
70C4×#3622C2×C411yescharacteristic
71C4×#3622C2×C411yescharacteristic
72C4×#3622D411yescharacteristic
73C4×#3622D411yescharacteristic
74#41×C17—41no—
75#41×C17—41no—
76#41×C17—41no—
77#41×C17—41no—
78C2×Q8×C17—21no—
79C2×D4×C17—21no—
80C2×D4×C17—21no—
81C2×D4×C17—21no—
82C2×D4×C17—41no—
83C22×C4×C17—41no—
84C22×C4×C17—41no—
85C22×C4×C17C2×D411yescharacteristic
86C22×C4×C17C2×D411yescharacteristic
87C22×C4×C17C2×D411yescharacteristic
88C22×Dic17—41no—
89C2×Dic34—21no—
90C2×Dic34—21no—
91C2×C8×C17—22no—
92C4⋊C4×C17—21no—
93C4⋊C4×C17—21no—
94C4⋊C4×C17—41no—
95C4⋊C4×C17—41no—
96C22⋊C4×C17—41no—
97C22⋊C4×C17—41no—
98C42×C17C22×C411yescharacteristic
99C42×C17C2×D411yescharacteristic
100C42×C17#4111yescharacteristic
101C42×C17#4111yescharacteristic
102C22⋊Dic17—41no—
103C4⋊Dic17—21no—
104C4⋊Dic17—21no—
105C4⋊Dic17—21no—
106C4⋊Dic17—21no—
107C4⋊Dic17—41no—
108C4⋊Dic17—41no—
109#63225—41no—
110#63225—41no—
111C4×Dic17—41no—
112C2×#3622—21no—
113C2×#3622—21no—
114C2×#3622—21no—
115C2×#3622—21no—
116C2×#3622—22no—
117C2×#3622C22⋊C411yescharacteristic
118C2×#3622C22⋊C411yescharacteristic
119C2×#3622C22⋊C411yescharacteristic
120C2×#3622C22⋊C411yescharacteristic
121#9757—171nomaximal, Sylow
122C23×C17—41no—
123C23×C17#12711yescharacteristic
124Q8×C17—41no—
125Q8×C17—41no—
126D4×C17—41no—
127D4×C17—41no—
128D4×C17—81no—
129D4×C17—81no—
130D4×C17—81no—
131D4×C17—81no—
132C2×C4×C17—41no—
133C2×C4×C17—41no—
134C2×C4×C17—41no—
135C2×C4×C17—81no—
136C2×C4×C17—81no—
137C2×C4×C17—81no—
138C2×C4×C17—81no—
139C2×C4×C17—81no—
140C2×C4×C17C2×C22⋊C411yescharacteristic
141C2×C4×C17C4×D411yescharacteristic
142C2×C4×C17C4×D411yescharacteristic
143C2×C4×C17#12111yescharacteristic
144C2×C4×C17#12111yescharacteristic
145C2×C4×C17#12411yescharacteristic
146C2×C4×C17#13511yescharacteristic
147C2×C4×C17#13511yescharacteristic
148C2×C4×C17#13511yescharacteristic
149C2×C4×C17#13511yescharacteristic
150C2×Dic17—41no—
151C2×Dic17—41no—
152C2×Dic17—81no—
153C2×Dic17—81no—
154C2×Dic17—81no—
155Dic34—81no—
156Dic34—81no—
157C8×C17—42no—
158#3622—21no—
159#3622—21no—
160#3622—21no—
161#3622—21no—
162#3622—42no—
163#3131—171no—
164#1835—171no—
165#1518—171no—
166#1518—171no—
167#1517—171no—
168#1517D1711yescharacteristic
169#1450—171no—
170C22×C17—21no—
171C22×C17—21no—
172C22×C17—81no—
173C22×C17—81no—
174C22×C17—81no—
175C22×C17#39011yescharacteristic
176C22×C17#49511yescharacteristic
177C22×C17#49511yescharacteristic
178C4×C17—21no—
179C4×C17—21no—
180C4×C17—21no—
181C4×C17—21no—
182C4×C17—81no—
183C4×C17—161no—
184C4×C17#41611yescharacteristic
185C4×C17#41611yescharacteristic
186C4×C17#48811yescharacteristic
187C4×C17#48811yescharacteristic
188Dic17—81no—
189Dic17—81no—
190Dic17—161no—
191#533—171no—
192#532C2×D1711yescharacteristic
193#488—341no—
194#488—341no—
195#487—171no—
196#487—171no—
197#486—171no—
198#486—171no—
199#431—171no—
200#431C2×D1711yescharacteristic
201#416—341no—
202#416—341no—
203C2×C4×C8—171no—
204#382—171no—
205#382C2×D1711yescharacteristic
206#340—341no—
207#340—341no—
208#328—342no—
209#328—342no—
210#327—22no—
211#327—342no—
212#322—341no—
213C82—341no—
214C2×C17—21no—
215C2×C17—21no—
216C2×C17—161no—
217C2×C17#195811yescharacteristic
218C2×C17#197611yescharacteristic
219C2×C17#197611yescharacteristic
220C2×#41—21no—
221C22×C8—171no—
222C22×C8—171no—
223C4⋊Q8—171no—
224C4⋊Q8—171no—
225C4⋊Q8C4×D1711yescharacteristic
226#127C4×D1711yescharacteristic
227#125—341no—
228#124—21no—
229C22⋊Q8—341no—
230C22⋊Q8—341no—
231#121—21no—
232#121—21no—
233C4×Q8—341no—
234C4×Q8—341no—
235C4×D4—21no—
236C4×D4—21no—
237#117—341no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—341no—
240C2×C42C22×D1711yescharacteristic
241C4⋊C8—21no—
242C4⋊C8—341no—
243#103—341no—
244#103—341no—
245#103—341no—
246#103—341no—
247#102—341no—
248#102—341no—
249#102—341no—
250#102—341no—
251C22⋊C8—172no—
252C22⋊C8C22⋊D1712yes—
253C4×C8—21no—
254C4×C8—171no—
255C4×C8—171no—
256C4×C8—171no—
257C4×C8—171no—
258C4×C8—341no—
259#95—21no—
260#95—21no—
261#95—341no—
262#95—341no—
263C17#975711yescharacteristic, complemented, Sylow
264#41—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268C2×Q8—21no—
269C2×Q8—341no—
270C2×Q8—341no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—681no—
278C22×C4D4×D1711yescharacteristic
279C22×C4D4×D1711yescharacteristic
280C22×C4C2×C22⋊D1711yescharacteristic
281C2×C8—22no—
282C2×C8—171no—
283C2×C8—171no—
284C2×C8—171no—
285C2×C8—171no—
286C2×C8—341no—
287C2×C8—341no—
288C2×C8—341no—
289C2×C8—341no—
290C2×C8—342no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—341no—
296C4⋊C4—341no—
297C4⋊C4—341no—
298C4⋊C4—341no—
299C4⋊C4—681no—
300C4⋊C4—681no—
301C4⋊C4—681no—
302C4⋊C4—681no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—681no—
306C42—681no—
307C42C2×C4×D1711yescharacteristic
308C42#6325211yescharacteristic
309C42D4×D1711yescharacteristic
310C42#6325411yescharacteristic
311C23—41no—
312C23#1058762611yescharacteristic
313Q8—41no—
314Q8—41no—
315Q8—1361no—
316Q8—1361no—
317D4—41no—
318D4—41no—
319D4—81no—
320D4—81no—
321D4—81no—
322D4—81no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—681no—
332C2×C4—681no—
333C2×C4—1361no—
334C2×C4—1361no—
335C2×C4—1361no—
336C2×C4C22⋊C4×D1711yescharacteristic
337C2×C4#1058756711yescharacteristic
338C2×C4#1058757011yescharacteristic
339C2×C4#1058757111yescharacteristic
340C2×C4#1058759811yescharacteristic
341C2×C4#1058759811yescharacteristic
342C2×C4#1058760211yescharacteristic
343C2×C4#1058760211yescharacteristic
344C2×C4C4×C22⋊D1711yescharacteristic
345C2×C4#1058762511yescharacteristic
346C8—42no—
347C8—341no—
348C8—341no—
349C8—341no—
350C8—341no—
351C8—682no—
352C22—21no—
353C22—21no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22#1176270911yescharacteristic
358C22#1176319011yescharacteristic
359C22#1176319211yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—81no—
365C4—161no—
366C4—2721no—
367C4—1361no—
368C4—1361no—
369C4#1176280211yescharacteristic
370C4#1176280211yescharacteristic
371C4#1176316211yescharacteristic
372C4#1176316211yescharacteristic
373C2—21no—
374C2—21no—
375C2—161no—
376C2#1452959411yescharacteristic
377C2#1452967911yescharacteristic
378C2#1452968111yescharacteristic
subgroupG/H
centerC22#11762709
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1517C2
socleC22×C17#390
prime radicalC17×#532C22
cosocleC2×C42×C17C23
hypercenter#1517D17
hypocenterC17#9757
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1517

Complements

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

NH ≅ G/Ntype
2. #14528914C2semidirect
3. #14527349C2semidirect
4. #14527347C2semidirect
6. #14527068C2semidirect
11. #11763159C4semidirect
12. #11763159C4semidirect
13. #11763155C4semidirect
14. #11763155C4semidirect
263. C17#9757semidirect

Maximal subgroups

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

subgroupindex
#145391062
#145289142
#145273492
#145273472
#145273442
#145270682
C17×#15172
#975717