Finite Group Databasebeta

← #16930185

Subgroups — #16930185

Order 4352.

432 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#14538593C211yesmaximal, characteristic
2#14537449C211yesmaximal, characteristic
3#14527465C211yesmaximal, characteristic, complemented
4#14527169C211yesmaximal, characteristic
5#14526681C211yesmaximal, characteristic, complemented
6#14526659C211yesmaximal, characteristic, complemented
7C2×C17×#332C211yesmaximal, characteristic, complemented
8C4×#63252C2211yescharacteristic
9#11763101C412yes—
10#11763096C412yes—
11#11763091—21no—
12#11763086—21no—
13#11762869—22no—
14#11762865—21no—
15#11762862C2211yescharacteristic
16#11762861—21no—
17#11762849—21no—
18#11762833C2211yescharacteristic
19#11762833C2211yescharacteristic
20#11762808—21no—
21#11762775—21no—
22#11762764—21no—
23#11762558—22no—
24#11762539—21no—
25#11762536—21no—
26C2×C17×C4⋊Q8C2211yescharacteristic
27C2×C17×C4⋊C8C2211yescharacteristic
28C2×C17×C4⋊C8C2211yescharacteristic
29C17×#332—21no—
30C17×#332—21no—
31C22×Q8×C17—21no—
32C2×#63252D411yescharacteristic
33C22×C8×C17—21no—
34C22×C8×C17—21no—
35C17×C4⋊Q8—21no—
36C17×C4⋊Q8—21no—
37C17×C4⋊Q8—21no—
38C17×C4⋊Q8C2×C412yes—
39C2×C4⋊C4×C17—21no—
40C2×C4⋊C4×C17—21no—
41C2×C42×C17C2311yescharacteristic
42C4×C22⋊D17—21no—
43C4×C22⋊D17—21no—
44#10587612D411yescharacteristic
45C2×#63223—21no—
46C2×#63223—21no—
47C4×D68C2×C411yescharacteristic
48C4×D68D411yescharacteristic
49#10587558—21no—
50C42×D17—21no—
51C4×Dic34C2×C411yescharacteristic
52C4×Dic34D411yescharacteristic
53C17×C4⋊C8—21no—
54C17×C4⋊C8—21no—
55C17×C4⋊C8—21no—
56C17×C4⋊C8D411yescharacteristic
57C17×C4⋊C8D411yescharacteristic
58C22⋊#3622—21no—
59#10587491—22no—
60#10587491—22no—
61#10587486—22no—
62C8×Dic17—22no—
63#10587481—22no—
64#10587480—22no—
65#10587479—22no—
66#10587478—22no—
67C4⋊#3622—21no—
68C4⋊#3622—21no—
69C4⋊#3622—21no—
70C4⋊#3622C2×C412yes—
71C4⋊#3622D412yes—
72C4×#3622—21no—
73C2×Q8×C17—22no—
74C2×Q8×C17—41no—
75C2×Q8×C17—81no—
76C2×Q8×C17—81no—
77C22×C4×C17—41no—
78C22×C4×C17C2×D411yescharacteristic
79C22×C4×C17#4111yescharacteristic
80C22×C4×C17#4111yescharacteristic
81C2×C22⋊D17—21no—
82#63252—21no—
83#63252—21no—
84#63252—21no—
85#63252—21no—
86C2×D68C22⋊C411yescharacteristic
87C2×C4×D17—21no—
88C2×C4×D17—21no—
89C2×C4×D17—21no—
90C2×Dic34C22⋊C411yescharacteristic
91C2×C8×C17—21no—
92C2×C8×C17—21no—
93C2×C8×C17—41no—
94C2×C8×C17—41no—
95C2×C8×C17—41no—
96C2×C8×C17—81no—
97C4⋊C4×C17—22no—
98C4⋊C4×C17—22no—
99C4⋊C4×C17—41no—
100C4⋊C4×C17—41no—
101C42×C17C22×C411yescharacteristic
102C42×C17C2×D411yescharacteristic
103C42×C17C2×D411yescharacteristic
104C42×C17C2×D411yescharacteristic
105C22⋊Dic17—21no—
106#63227—21no—
107#63227—21no—
108C4⋊Dic17C22⋊C411yescharacteristic
109C4⋊Dic17C22⋊C411yescharacteristic
110#63225—21no—
111#63225—21no—
112C4×Dic17—21no—
113C4×Dic17—21no—
114C4×Dic17—21no—
115#63223—41no—
116#63223—41no—
117#63223—41no—
118#63223—41no—
119C2×#3622—22no—
120C2×#3622—22no—
121C2×#3622—41no—
122#9168—171nomaximal, Sylow
123C23×C17#12311yescharacteristic
124C22×D17—21no—
125Q8×C17—82no—
126Q8×C17—81no—
127Q8×C17—81no—
128C2×C4×C17—21no—
129C2×C4×C17—21no—
130C2×C4×C17—41no—
131C2×C4×C17—42no—
132C2×C4×C17—82no—
133C2×C4×C17C2×C22⋊C411yescharacteristic
134C2×C4×C17C4×D411yescharacteristic
135C2×C4×C17C4×D411yescharacteristic
136C2×C4×C17#12011yescharacteristic
137C2×C4×C17#12111yescharacteristic
138C2×C4×C17#12111yescharacteristic
139C2×C4×C17#13511yescharacteristic
140C2×C4×C17#13511yescharacteristic
141C2×C4×C17#13711yescharacteristic
142C2×C4×C17#13711yescharacteristic
143C22⋊D17—41no—
144C22⋊D17—41no—
145C2×Dic17—21no—
146C2×Dic17—21no—
147C2×Dic17—21no—
148D68—21no—
149D68—21no—
150C4×D17—41no—
151C4×D17—41no—
152C4×D17—41no—
153C4×D17—41no—
154C4×D17—81no—
155Dic34—21no—
156Dic34—21no—
157C8×C17—41no—
158C8×C17—41no—
159C8×C17—81no—
160#3622—42no—
161#3622—42no—
162#3622—81no—
163#3079—171no—
164#2925—171no—
165#1548—171no—
166C2×#332D1711yescharacteristic, complemented
167#1477—171no—
168#1301—171no—
169#1292—171no—
170C22×C17—21no—
171C22×C17—21no—
172C22×C17#38611yescharacteristic
173C22×C17#48511yescharacteristic
174C22×C17#48511yescharacteristic
175C2×D17—41no—
176C2×D17—41no—
177C2×D17—41no—
178C4×C17—21no—
179C4×C17—21no—
180C4×C17—21no—
181C4×C17—82no—
182C4×C17#41611yescharacteristic
183C4×C17#41911yescharacteristic
184C4×C17#45211yescharacteristic
185C4×C17#45211yescharacteristic
186C4×C17#47111yescharacteristic
187C4×C17#47211yescharacteristic
188Dic17—41no—
189Dic17—41no—
190Dic17—41no—
191C2×C4⋊Q8C2×D1711yescharacteristic
192C4×#41—171no—
193#477—172no—
194#476—172no—
195#475—341no—
196#474—341no—
197#433—342no—
198#432—341no—
199#431—171no—
200#431—341no—
201#428—341no—
202#423—171no—
203#423—171no—
204C2×C4⋊C8C2×D1711yescharacteristic
205C2×C4⋊C8C2×D1711yescharacteristic
206#417—341no—
207#408—341no—
208#405—341no—
209#333—342no—
210#332—21no—
211#332—21no—
212Q8⋊C8—341no—
213D4⋊C8—341no—
214C2×C17—21no—
215C2×C17—21no—
216C2×C17#187311yescharacteristic
217C2×C17#190211yescharacteristic
218C2×C17#190711yescharacteristic
219D17—81no—
220C2×#41—171no—
221C22×Q8—21no—
222C2×M16—341no—
223C2×M16—341no—
224C22×C8—21no—
225C22×C8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8C4×D1712yes—
230C4×Q8—171no—
231C4×Q8—171no—
232C4×D4—171no—
233C4×D4—171no—
234C4×D4—341no—
235C4×D4—341no—
236#117—171no—
237#117—341no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C42—341no—
241C2×C42C22×D1711yescharacteristic
242#107—342no—
243#106—342no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—172no—
248C4⋊C8—172no—
249C4⋊C8—341no—
250C4⋊C8—341no—
251C4⋊C8—341no—
252C4⋊C8C22⋊D1711yescharacteristic
253C4⋊C8C22⋊D1711yescharacteristic
254#103—342no—
255#102—342no—
256C22⋊C8—342no—
257C22⋊C8—342no—
258C22⋊C8—341no—
259#97—342no—
260C4×C8—342no—
261C4×C8—341no—
262C17#916811yescharacteristic, complemented, Sylow
263#41—341no—
264#41—341no—
265#41—341no—
266#41—341no—
267C2×Q8—22no—
268C2×Q8—41no—
269C2×Q8—81no—
270C2×Q8—81no—
271C2×Q8—171no—
272C2×D4—171no—
273C2×D4—341no—
274C22×C4—41no—
275C22×C4—341no—
276C22×C4—341no—
277C22×C4—341no—
278C22×C4#6325211yescharacteristic
279C22×C4D4×D1711yescharacteristic
280C22×C4#6325411yescharacteristic
281M16—681no—
282M16—681no—
283M16—681no—
284M16—681no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—81no—
291C2×C8—342no—
292C2×C8—342no—
293C2×C8—681no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—171no—
299C4⋊C4—171no—
300C4⋊C4—341no—
301C4⋊C4—341no—
302C22⋊C4—341no—
303C22⋊C4—341no—
304C22⋊C4—341no—
305C42—341no—
306C42—341no—
307C42—341no—
308C42C2×C4×D1711yescharacteristic
309C42D4×D1711yescharacteristic
310C42D4×D1711yescharacteristic
311C42C2×C22⋊D1711yescharacteristic
312C23—341no—
313C23#1058756911yescharacteristic
314Q8—82no—
315Q8—81no—
316Q8—81no—
317Q8—341no—
318Q8—341no—
319D4—341no—
320D4—341no—
321D4—681no—
322D4—681no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—82no—
328C2×C4—341no—
329C2×C4—341no—
330C2×C4—341no—
331C2×C4—681no—
332C2×C4—681no—
333C2×C4—681no—
334C2×C4—681no—
335C2×C4—1361no—
336C2×C4C22⋊C4×D1711yescharacteristic
337C2×C4#1058756711yescharacteristic
338C2×C4#1058757011yescharacteristic
339C2×C4#1058760111yescharacteristic
340C2×C4#1058760211yescharacteristic
341C2×C4#1058760411yescharacteristic
342C2×C4#1058760511yescharacteristic
343C2×C4C4×C22⋊D1711yescharacteristic
344C2×C4#1058762311yescharacteristic
345C2×C4#1058762411yescharacteristic
346C8—41no—
347C8—41no—
348C8—81no—
349C8—682no—
350C8—682no—
351C8—1361no—
352C22—21no—
353C22—21no—
354C22—681no—
355C22—681no—
356C22—681no—
357C22#1176268511yescharacteristic
358C22#1176314811yescharacteristic
359C22#1176314911yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—82no—
364C4—681no—
365C4—681no—
366C4—681no—
367C4#1176280411yescharacteristic
368C4#1176281611yescharacteristic
369C4#1176296811yescharacteristic
370C4#1176297011yescharacteristic
371C4#1176306911yescharacteristic
372C4#1176307611yescharacteristic
373C2—21no—
374C2—21no—
375C2—1361no—
376C2#1452909311yescharacteristic
377C2#1452926011yescharacteristic
378C2#1452929511yescharacteristic
subgroupG/H
centerC22#11762685
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC2×C17×#332C2
socleC22×C17#386
prime radicalC2×#63252D4
cosocleC2×C42×C17C23
hypercenterC2×#332D17
hypocenterC17#9168
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
3. #14527465C2semidirect
5. #14526681C2semidirect
6. #14526659C2semidirect
7. C2×C17×#332C2semidirect
166. C2×#332D17semidirect
262. C17#9168semidirect

Maximal subgroups

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

subgroupindex
#145385932
#145374492
#145274652
#145271692
#145266812
#145266592
C2×C17×#3322
#916817