Finite Group Databasebeta

← #17019676

Subgroups — #17019676

Order 4352.

676 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14539907C211yesmaximal, characteristic
2#14538256C211yesmaximal, characteristic
3C2×#11763019C211yesmaximal, characteristic, complemented
4#14528228C214yesmaximal, complemented
5#14528178C214yesmaximal, complemented
6#14527559C211yesmaximal, characteristic, complemented
7#14527455C211yesmaximal, characteristic, complemented
8#14527431C211yesmaximal, characteristic
9C17×#2982C211yesmaximal, characteristic, complemented
10C2×#10587628—21no—
11C22×#63231—21no—
12#11763359C2211yescharacteristic
13C2×#10587555C2211yescharacteristic
14#11763214C2212yes—
15#11763156C2212yes—
16#11763123—22no—
17#11763090—22no—
18#11763031—22no—
19#11763019—22no—
20#11763019C2212yes—
21#11763019C2214yes—
22#11763009C2212yes—
23#11762833C2211yescharacteristic
24C2×C4⋊#3622C2211yescharacteristic
25#11762808—21no—
26C2×#10587481—21no—
27#11762562C2214yes—
28#11762554C2212yes—
29#11762554C2214yes—
30#11762552C2212yes—
31C2×C4×Q8×C17C2211yescharacteristic
32C8×Q8×C17—22no—
33C8×Q8×C17C2214yes—
34C17×#431—22no—
35C17×#431C2211yescharacteristic
36C17×#431C2211yescharacteristic
37C22×Q8×C17D411yescharacteristic
38C2×#63252—21no—
39C22×Dic34—21no—
40C4×Q8×C17—21no—
41C4×Q8×C17—21no—
42C4×Q8×C17D412yes—
43C4×Q8×C17C2312yes—
44C2×C4⋊C4×C17—21no—
45C2×C4⋊C4×C17D411yescharacteristic
46C2×C42×C17—21no—
47C2×C42×C17C2311yescharacteristic
48C2×#63231—24no—
49C2×#63231—22no—
50C2×#63231—44no—
51#10587628—44no—
52C2×#63230—22no—
53#10587616—21no—
54#10587616—21no—
55C2×C4⋊Dic17—21no—
56C2×C4⋊Dic17—21no—
57C2×#63223—21no—
58C22×#3622—21no—
59#10587561—21no—
60#10587560C2311yescharacteristic
61C4×D68—21no—
62C4×D68—21no—
63#10587555—21no—
64#10587555—21no—
65#10587555—21no—
66#10587555C2311yescharacteristic
67#10587555C2312yes—
68C17×C4⋊C8—24no—
69C17×C4⋊C8D412yes—
70C17×C4⋊C8C2312yes—
71C17×C22⋊C8—21no—
72C17×C22⋊C8D412yes—
73C4×C8×C17—24no—
74C4×C8×C17—21no—
75C4×C8×C17C2312yes—
76#10587492—24no—
77#10587489—24no—
78#10587481—24no—
79#10587481—22no—
80#10587480—22no—
81C4⋊#3622—21no—
82C4⋊#3622—21no—
83C4⋊#3622C2312yes—
84C4⋊#3622C2312yes—
85C2×Q8×C17—21no—
86C2×Q8×C17—22no—
87C2×Q8×C17D814yes—
88C2×Q8×C17C2×D412yes—
89C22×C4×C17—21no—
90C22×C4×C17—21no—
91C22×C4×C17C2×D411yescharacteristic
92C22×C4×C17C2×D411yescharacteristic
93C22×C4×C17#4111yescharacteristic
94C2×C22⋊D17—41no—
95C22×Dic17—41no—
96#63252—42no—
97#63252—42no—
98C2×D68—21no—
99C2×D68—21no—
100C2×D68—21no—
101C2×C4×D17—41no—
102C2×Dic34—22no—
103C2×Dic34—21no—
104C2×Dic34—42no—
105C2×Dic34—42no—
106C2×Dic34—41no—
107C2×C8×C17—22no—
108C2×C8×C17C2×D414yes—
109C4⋊C4×C17—22no—
110C4⋊C4×C17—21no—
111C4⋊C4×C17—22no—
112C4⋊C4×C17C2×D412yes—
113C42×C17—22no—
114C42×C17—22no—
115C42×C17C2×D411yescharacteristic
116C42×C17C2×D411yescharacteristic
117C42×C17#4111yescharacteristic
118C42×C17C2411yescharacteristic
119#63231—44no—
120#63231—48no—
121#63230—44no—
122#63227—41no—
123#63227—41no—
124C4⋊Dic17—21no—
125C4⋊Dic17—22no—
126C4⋊Dic17—22no—
127C4⋊Dic17—21no—
128C4⋊Dic17—41no—
129C4⋊Dic17—41no—
130#63223—42no—
131C2×#3622—22no—
132C2×#3622—22no—
133C2×#3622—42no—
134#19404—171nomaximal, Sylow
135C23×C17#12111yescharacteristic
136C22×D17—41no—
137Q8×C17—22no—
138Q8×C17—24no—
139Q8×C17C2×D814yes—
140C2×C4×C17—22no—
141C2×C4×C17—24no—
142C2×C4×C17—22no—
143C2×C4×C17—22no—
144C2×C4×C17—41no—
145C2×C4×C17—81no—
146C2×C4×C17#12111yescharacteristic
147C2×C4×C17#12111yescharacteristic
148C2×C4×C17#12111yescharacteristic
149C2×C4×C17C2×D812yes—
150C2×C4×C17#13512yes—
151C2×C4×C17C22×D411yescharacteristic
152C2×C4×C17C22×D411yescharacteristic
153C2×C4×C17C2×#4111yescharacteristic
154C22⋊D17—82no—
155C2×Dic17—42no—
156C2×Dic17—41no—
157C2×Dic17—82no—
158D68—41no—
159D68—41no—
160D68—42no—
161D68—81no—
162C4×D17—82no—
163Dic34—42no—
164Dic34—41no—
165Dic34—42no—
166Dic34—41no—
167Dic34—82no—
168C8×C17—24no—
169C8×C17—42no—
170#3622—42no—
171#3622—42no—
172#3226—171no—
173#3037—171no—
174C2×#462—171no—
175#2982D1711yescharacteristic, complemented
176#1682—174no—
177#1674—174no—
178#1571—171no—
179#1546—171no—
180#1540—171no—
181C22×C17—21no—
182C22×C17—21no—
183C22×C17#46612yes—
184C22×C17C2×#12111yescharacteristic
185C2×D17—81no—
186C2×D17—81no—
187C2×D17—81no—
188C4×C17—21no—
189C4×C17—24no—
190C4×C17—21no—
191C4×C17—21no—
192C4×C17—42no—
193C4×C17#46612yes—
194C4×C17C22×D811yescharacteristic
195C4×C17C2×#13511yescharacteristic
196C4×C17#57812yes—
197Dic17—82no—
198Dic17—81no—
199C2×#137—341no—
200C22×Q16—341no—
201#532—171no—
202C2×C4⋊Q8—171no—
203C2×C4×Q8C2×D1711yescharacteristic
204#500—172no—
205#486—172no—
206#480—342no—
207#474—342no—
208#464—342no—
209#462—172no—
210#462—174no—
211#462—342no—
212#460—172no—
213C8×Q8—22no—
214C8×Q8C2×D1714yes—
215#431—22no—
216#431C2×D1711yescharacteristic
217#431C2×D1711yescharacteristic
218#423—171no—
219C2×C4⋊C8—171no—
220#417—341no—
221C2×#103—341no—
222#335—174no—
223#332—172no—
224#332—174no—
225#331—172no—
226C2×C17—22no—
227C2×C17#304411yescharacteristic
228C2×C17C2×#46611yescharacteristic
229C2×C17#306911yescharacteristic
230D17—161no—
231C2×#41—341no—
232C22×Q8—341no—
233C22×Q8D6811yescharacteristic
234#137—684no—
235C2×Q16—344no—
236C2×Q16—342no—
237C2×Q16—684no—
238C2×SD16—342no—
239C2×M16—341no—
240C22×C8—341no—
241C4⋊Q8—172no—
242C4⋊Q8—171no—
243C4⋊Q8—341no—
244C4⋊Q8—341no—
245C4⋊Q8—341no—
246#127—171no—
247#124—341no—
248#121—341no—
249#121—341no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8D6812yes—
253C4×Q8C22×D1712yes—
254C4×D4—341no—
255C4×D4—341no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—341no—
258C2×C4⋊C4—341no—
259C2×C4⋊C4D6811yescharacteristic
260C2×C42—21no—
261C2×C42C22×D1711yescharacteristic
262#107—344no—
263C4⋊C8—24no—
264C4⋊C8—172no—
265C4⋊C8—172no—
266C4⋊C8—341no—
267C4⋊C8—341no—
268C4⋊C8C22⋊D1712yes—
269C4⋊C8C22×D1712yes—
270#103—344no—
271#103—342no—
272#102—344no—
273#102—342no—
274C22⋊C8—21no—
275C22⋊C8C22⋊D1712yes—
276C4×C8—24no—
277C4×C8—21no—
278C4×C8C22×D1712yes—
279C17#1940411yescharacteristic, complemented, Sylow
280#41—682no—
281#41—682no—
282C2×Q8—22no—
283C2×Q8—21no—
284C2×Q8—341no—
285C2×Q8—342no—
286C2×Q8—681no—
287C2×Q8—682no—
288C2×Q8—682no—
289C2×Q8D13614yes—
290C2×Q8C2×D6812yes—
291C2×D4—341no—
292C2×D4—341no—
293C2×D4—341no—
294C2×D4—681no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—681no—
298C22×C4—681no—
299C22×C4C2×D6811yescharacteristic
300C22×C4#6325211yescharacteristic
301C22×C4C2×C22⋊D1711yescharacteristic
302Q16—688no—
303Q16—684no—
304SD16—684no—
305M16—682no—
306C2×C8—22no—
307C2×C8—342no—
308C2×C8—342no—
309C2×C8—682no—
310C2×C8C2×C22⋊D1714yes—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—21no—
314C4⋊C4—342no—
315C4⋊C4—341no—
316C4⋊C4—342no—
317C4⋊C4—341no—
318C4⋊C4—681no—
319C4⋊C4—681no—
320C4⋊C4C2×D6812yes—
321C22⋊C4—681no—
322C22⋊C4—681no—
323C42—22no—
324C42—22no—
325C42C2×D6811yescharacteristic
326C42#6325211yescharacteristic
327C42C2×C22⋊D1711yescharacteristic
328C42C23×D1711yescharacteristic
329C23—681no—
330C23#1058761611yescharacteristic
331Q8—24no—
332Q8—22no—
333Q8—682no—
334Q8—681no—
335Q8—682no—
336Q8—681no—
337Q8—1362no—
338Q8C2×D13614yes—
339D4—681no—
340D4—681no—
341D4—682no—
342D4—1361no—
343D4—1362no—
344C2×C4—24no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—81no—
350C2×C4—681no—
351C2×C4—682no—
352C2×C4—1362no—
353C2×C4—1362no—
354C2×C4C2×D13612yes—
355C2×C4#1058759012yes—
356C2×C4#1058761611yescharacteristic
357C2×C4#1058761611yescharacteristic
358C2×C4#1058761611yescharacteristic
359C2×C4C22×D6811yescharacteristic
360C2×C4C2×#6325211yescharacteristic
361C2×C4C22×C22⋊D1711yescharacteristic
362C8—24no—
363C8—42no—
364C8—682no—
365C8—682no—
366C22—21no—
367C22—21no—
368C22—1361no—
369C22—1361no—
370C22—1361no—
371C22#1176304512yes—
372C22C2×#1058761611yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—24no—
377C4—42no—
378C4—1361no—
379C4—1362no—
380C4#1176304512yes—
381C4C22×D13611yescharacteristic
382C4C2×#1058759011yescharacteristic
383C4#1176362412yes—
384C2—22no—
385C2—2721no—
386C2#1453831411yescharacteristic
387C2C2×#1176304511yescharacteristic
388C2#1453852111yescharacteristic
subgroupG/H
centerC22C2×#10587616
commutator, cosocleC42×C17C24
FrattiniC42C23×D17
FittingC17×#2982C2
socleC22×C17C2×#121
prime radical#11763359C22
hypercenter#2982D17
hypocenterC17#19404
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

Complements

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

NH ≅ G/Ntype
3. C2×#11763019C2semidirect
4. #14528228C2semidirect
5. #14528178C2semidirect
6. #14527559C2semidirect
7. #14527455C2semidirect
9. C17×#2982C2semidirect
175. #2982D17semidirect
279. C17#19404semidirect

Maximal subgroups

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

subgroupindex
#145399072
#145382562
C2×#117630192
#145282282
#145281782
#145275592
#145274552
#145274312
C17×#29822
#1940417