Finite Group Databasebeta

← #16930606

Subgroups — #16930606

Order 4352.

550 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14538788C211yesmaximal, characteristic
2#14531248C211yesmaximal, characteristic
3#14527283C211yesmaximal, characteristic, complemented
4#14527208C211yesmaximal, characteristic
5#14526685C211yesmaximal, characteristic, complemented
6#14526617C211yesmaximal, characteristic, complemented
7C17×#1994C211yesmaximal, characteristic, complemented
8C2×C4×D68C2211yescharacteristic
9C2×#10587558—21no—
10#11763137—21no—
11#11763096C412yescomplemented
12#11763011C412yescomplemented
13#11762959—21no—
14C4×#63230—22no—
15#11762862C2211yescharacteristic
16#11762862C2211yescharacteristic
17#11762711—21no—
18#11762707—21no—
19#11762700—22no—
20C4×C4⋊Dic17C2211yescharacteristic
21C4×#63227—21no—
22#11762546—22no—
23#11762536—22no—
24C17×#533C2211yescharacteristic
25C17×#423C2211yescharacteristic
26C43×C17C2211yescharacteristic
27C17×#339—21no—
28C17×#339—21no—
29C22×D68D411yescharacteristic
30C22×C4×D17—21no—
31C2×M16×C17—21no—
32C17×C4⋊Q8C2×C411yescharacteristic
33C17×C4⋊Q8C2×C411yescharacteristic
34C17×#125—21no—
35C17×C22⋊Q8—21no—
36C17×C22⋊Q8—21no—
37C4×Q8×C17—21no—
38C4×Q8×C17—21no—
39C17×#117—21no—
40C2×C42×C17—21no—
41C2×C42×C17—21no—
42C2×C42×C17D411yescharacteristic
43C2×C42×C17D411yescharacteristic
44C2×C42×C17C2311yescharacteristic
45C2×#63230—22no—
46C2×#63227—22no—
47C2×#63227—22no—
48C2×#63227—21no—
49C2×C4⋊Dic17—21no—
50C2×C4⋊Dic17D411yescharacteristic
51C2×#63225—22no—
52C2×C4×Dic17—21no—
53C4×D68—21no—
54C4×D68—21no—
55C4×D68C2×C412yes—
56C4×D68D412yes—
57#10587558—42no—
58#10587558—42no—
59C17×C4⋊C8—21no—
60C17×C4⋊C8—21no—
61#10587506—22no—
62#10587502—22no—
63#10587502D412yes—
64C22⋊#3622—21no—
65C22⋊#3622—21no—
66#10587480—22no—
67#10587479—22no—
68C4⋊#3622—21no—
69C4⋊#3622C2×C412yes—
70C4×#3622—21no—
71C4×#3622—21no—
72C23×D17—21no—
73C2×Q8×C17—21no—
74C2×Q8×C17—21no—
75C22×C4×C17—21no—
76C22×C4×C17—21no—
77C22×C4×C17C2×D411yescharacteristic
78C22×C4×C17C2×D411yescharacteristic
79C22×C4×C17C2×D411yescharacteristic
80C22×Dic17—21no—
81C22×Dic17—22no—
82C2×D68—21no—
83C2×D68—42no—
84C2×D68C22⋊C412yes—
85C2×C4×D17—22no—
86C2×C4×D17—22no—
87C2×C4×D17—41no—
88C2×C4×D17—41no—
89C2×C4×D17—41no—
90C2×C4×D17—41no—
91M16×C17—41no—
92M16×C17—41no—
93C2×C8×C17—41no—
94C4⋊C4×C17—21no—
95C4⋊C4×C17—21no—
96C4⋊C4×C17—21no—
97C4⋊C4×C17—21no—
98C4⋊C4×C17—41no—
99C4⋊C4×C17—41no—
100C22⋊C4×C17—41no—
101C42×C17—21no—
102C42×C17—21no—
103C42×C17—21no—
104C42×C17—42no—
105C42×C17—42no—
106C42×C17—41no—
107C42×C17SD1612yescomplemented
108C42×C17C22×C411yescharacteristic
109C42×C17C2×D411yescharacteristic
110C42×C17#4111yescharacteristic
111C42×C17#4111yescharacteristic
112#63230—44no—
113#63227—22no—
114#63227—22no—
115#63227—44no—
116#63227—44no—
117C4⋊Dic17—21no—
118C4⋊Dic17—42no—
119C4⋊Dic17C22⋊C412yes—
120#63225—44no—
121C4×Dic17—41no—
122C4×Dic17—41no—
123C2×#3622—22no—
124C2×#3622—41no—
125#9235—171nomaximal, Sylow
126C23×C17#12011yescharacteristic
127C22×D17—22no—
128C22×D17—42no—
129C22×D17—42no—
130C22×D17—41no—
131C22×D17—41no—
132Q8×C17—42no—
133Q8×C17—81no—
134C2×C4×C17—22no—
135C2×C4×C17—22no—
136C2×C4×C17—22no—
137C2×C4×C17—41no—
138C2×C4×C17—41no—
139C2×C4×C17—41no—
140C2×C4×C17—41no—
141C2×C4×C17—41no—
142C2×C4×C17—41no—
143C2×C4×C17—41no—
144C2×C4×C17C2×C22⋊C411yescharacteristic
145C2×C4×C17C4×D411yescharacteristic
146C2×C4×C17C4×D411yescharacteristic
147C2×C4×C17#12111yescharacteristic
148C2×C4×C17#12111yescharacteristic
149C2×C4×C17#12311yescharacteristic
150C2×C4×C17C2×SD1611yescharacteristic
151C2×C4×C17#13511yescharacteristic
152C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C17#13711yescharacteristic
154C2×Dic17—22no—
155C2×Dic17—41no—
156C2×Dic17—41no—
157C2×Dic17—42no—
158C2×Dic17—42no—
159C2×Dic17—42no—
160D68—22no—
161D68—22no—
162D68—42no—
163C4×D17—42no—
164C4×D17—42no—
165C4×D17—42no—
166C4×D17—42no—
167C8×C17—81no—
168#3622—42no—
169#3622—81no—
170#3101—171no—
171#2293—171no—
172#1994D1711yescharacteristic, complemented
173#1503—171no—
174#1486—171no—
175#1303—171no—
176#1276—171no—
177C22×C17—21no—
178C22×C17—21no—
179C22×C17#38611yescharacteristic
180C22×C17#45011yescharacteristic
181C22×C17#45211yescharacteristic
182C2×D17—42no—
183C2×D17—42no—
184C2×D17—42no—
185C2×D17—82no—
186C2×D17—82no—
187C4×C17—21no—
188C4×C17—21no—
189C4×C17—21no—
190C4×C17—42no—
191C4×C17—42no—
192C4×C17—81no—
193C4×C17—81no—
194C4×C17#42112yes—
195C4×C17C4×SD1611yescharacteristic
196C4×C17#44011yescharacteristic
197C4×C17#46111yescharacteristic
198C4×C17#46311yescharacteristic
199Dic17—42no—
200Dic17—82no—
201#533C2×D1711yescharacteristic
202C2×C4×D4—171no—
203C2×#117—341no—
204#483—341no—
205#476—172no—
206#461—172no—
207#450—341no—
208C4×SD16—342no—
209#431—171no—
210#431—171no—
211#423C2×D1711yescharacteristic
212#390—341no—
213#389—341no—
214#388—342no—
215C4×C4⋊C4—171no—
216C4×C22⋊C4—341no—
217C43C2×D1711yescharacteristic
218#339—21no—
219#339—21no—
220#328—342no—
221D4⋊C8—342no—
222C2×C17—21no—
223C2×C17—21no—
224C2×C17#187711yescharacteristic
225C2×C17#189711yescharacteristic
226C2×C17#190611yescharacteristic
227D17—82no—
228C22×D4—171no—
229C23×C4—341no—
230C2×SD16—342no—
231C2×M16—21no—
232C4⋊Q8C4×D1711yescharacteristic
233C4⋊Q8C4×D1711yescharacteristic
234#125—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×D4—172no—
240C4×D4—172no—
241C4×D4—341no—
242C4×D4—341no—
243#117—21no—
244#117—682no—
245#117—682no—
246C2×C4⋊C4—171no—
247C2×C4⋊C4—342no—
248C2×C4⋊C4—341no—
249C2×C22⋊C4—341no—
250C2×C22⋊C4—342no—
251C2×C22⋊C4—342no—
252C2×C42—21no—
253C2×C42—21no—
254C2×C42—341no—
255C2×C42C22⋊D1711yescharacteristic
256C2×C42C22⋊D1711yescharacteristic
257C2×C42C22×D1711yescharacteristic
258#106—342no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8—172no—
262C4⋊C8—341no—
263#103—342no—
264#102—342no—
265C22⋊C8—341no—
266C22⋊C8—341no—
267C4×C8—341no—
268C4×C8—341no—
269#95—172no—
270#95—342no—
271C17#923511yescharacteristic, complemented, Sylow
272C24—341no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×D4—172no—
276C2×D4—341no—
277C2×D4—682no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—341no—
281C22×C4—342no—
282C22×C4—342no—
283C22×C4—342no—
284C22×C4—681no—
285C22×C4—681no—
286C22×C4—681no—
287C22×C4—681no—
288C22×C4D4×D1711yescharacteristic
289C22×C4D4×D1711yescharacteristic
290C22×C4C2×C22⋊D1711yescharacteristic
291SD16—684no—
292M16—41no—
293M16—41no—
294C2×C8—41no—
295C2×C8—342no—
296C2×C8—681no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—172no—
304C4⋊C4—341no—
305C4⋊C4—684no—
306C4⋊C4—682no—
307C22⋊C4—41no—
308C22⋊C4—342no—
309C22⋊C4—342no—
310C22⋊C4—684no—
311C22⋊C4—684no—
312C42—21no—
313C42—21no—
314C42—21no—
315C42—42no—
316C42—42no—
317C42—41no—
318C42—681no—
319C42—681no—
320C42#6323012yescomplemented
321C42C2×C4×D1711yescharacteristic
322C42#6325211yescharacteristic
323C42D4×D1711yescharacteristic
324C42#6325411yescharacteristic
325C23—342no—
326C23—682no—
327C23—682no—
328C23—681no—
329C23—681no—
330C23#1058762311yescharacteristic
331Q8—42no—
332Q8—81no—
333D4—342no—
334D4—342no—
335D4—682no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—342no—
347C2×C4—681no—
348C2×C4—681no—
349C2×C4—682no—
350C2×C4—682no—
351C2×C4—682no—
352C2×C4—682no—
353C2×C4—682no—
354C2×C4—682no—
355C2×C4—682no—
356C2×C4C22⋊C4×D1711yescharacteristic
357C2×C4#1058756711yescharacteristic
358C2×C4#1058756911yescharacteristic
359C2×C4#1058757011yescharacteristic
360C2×C4C4×C22⋊D1711yescharacteristic
361C2×C4#1058762411yescharacteristic
362C2×C4C2×#6323011yescharacteristic
363C2×C4#1058762811yescharacteristic
364C2×C4#1058763511yescharacteristic
365C2×C4#1058763611yescharacteristic
366C8—81no—
367C8—682no—
368C8—1361no—
369C22—21no—
370C22—21no—
371C22—682no—
372C22—682no—
373C22—682no—
374C22—1362no—
375C22—1362no—
376C22#1176268511yescharacteristic
377C22#1176295911yescharacteristic
378C22#1176296911yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—42no—
383C4—42no—
384C4—81no—
385C4—81no—
386C4—682no—
387C4—1362no—
388C4#1176282412yes—
389C4C4×#6323011yescharacteristic
390C4#1176290711yescharacteristic
391C4#1176301111yescharacteristic
392C4#1176302111yescharacteristic
393C2—21no—
394C2—21no—
395C2—1362no—
396C2#1452912111yescharacteristic
397C2#1452922911yescharacteristic
398C2#1452928811yescharacteristic
subgroupG/H
centerC2×C4#10587624
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1994C2
socleC22×C17#386
prime radicalC22×D68D4
cosocleC2×C42×C17C23
hypercenter#1994D17
hypocenterC17#9235
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1994

Complements

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

NH ≅ G/Ntype
3. #14527283C2semidirect
5. #14526685C2semidirect
6. #14526617C2semidirect
7. C17×#1994C2semidirect
11. #11763096C4semidirect
12. #11763011C4semidirect
107. C42×C17SD16semidirect
172. #1994D17semidirect
271. C17#9235semidirect
320. C42#63230semidirect

Maximal subgroups

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

subgroupindex
#145387882
#145312482
#145272832
#145272082
#145266852
#145266172
C17×#19942
#923517