Finite Group Databasebeta

← #16929552

Subgroups — #16929552

Order 4352.

470 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14539344C211yesmaximal, characteristic
2#14529703C211yesmaximal, characteristic
3#14527283C211yesmaximal, characteristic, complemented
4#14527182C211yesmaximal, characteristic
5#14526623C211yesmaximal, characteristic, complemented
6#14526622C211yesmaximal, characteristic, complemented
7C17×#2962C211yesmaximal, characteristic, complemented
8#11763359C2211yescharacteristic
9#11763205C411yescharacteristic, complemented
10#11763183C411yescharacteristic, complemented
11#11763159C411yescharacteristic, complemented
12#11763157C411yescharacteristic, complemented
13#11763040—22no—
14C4×#63230—22no—
15#11762862C2211yescharacteristic
16C2×#10587496—21no—
17C2×#10587496—21no—
18C2×C4×#3622C2211yescharacteristic
19C4×C4⋊Dic17C2211yescharacteristic
20#11762546—22no—
21#11762536—21no—
22#11762536—21no—
23C17×#533C2211yescharacteristic
24C17×#446—22no—
25C17×#446—21no—
26C8×Q8×C17—21no—
27C17×#424—21no—
28C2×C17×C4⋊C8C2211yescharacteristic
29C17×#405—21no—
30C4×M16×C17C2211yescharacteristic
31C2×#63252—21no—
32C2×M16×C17D411yescharacteristic
33C2×M16×C17D411yescharacteristic
34C22×C8×C17—21no—
35C17×C4⋊Q8C2×C411yescharacteristic
36C17×C4⋊Q8C2×C411yescharacteristic
37C17×#125—21no—
38C17×C22⋊Q8—21no—
39C17×C22⋊Q8D412yes—
40C4×Q8×C17—21no—
41C4×Q8×C17D412yes—
42C17×#117—21no—
43C2×C42×C17C2311yescharacteristic
44C2×#63230—22no—
45#10587616—21no—
46#10587616—21no—
47C2×C4⋊Dic17—21no—
48C2×C4×Dic17—21no—
49C22×#3622—21no—
50#10587561—21no—
51#10587560C2×C411yescharacteristic
52C4×D68—21no—
53C4×D68—21no—
54#10587555C2×C411yescharacteristic
55C17×C4⋊C8—22no—
56C17×C4⋊C8—22no—
57C17×C4⋊C8—21no—
58C17×C4⋊C8D411yescharacteristic
59C17×C4⋊C8D411yescharacteristic
60C17×#97—22no—
61C17×#97—21no—
62C4×C8×C17—22no—
63C4×C8×C17—21no—
64#10587506—22no—
65#10587502—21no—
66C22⋊#3622—21no—
67#10587496—42no—
68#10587496—42no—
69#10587480—22no—
70#10587479—22no—
71C4⋊#3622—21no—
72C4×#3622—21no—
73C4×#3622—21no—
74C4×#3622C2×C411yescharacteristic
75C4×#3622C2×C411yescharacteristic
76C2×Q8×C17—21no—
77C2×Q8×C17C22⋊C412yes—
78C22×C4×C17C2×D411yescharacteristic
79C22×C4×C17C2×D411yescharacteristic
80C22×C4×C17#4111yescharacteristic
81C2×C22⋊D17—41no—
82C22×Dic17—41no—
83#63252—41no—
84#63252—41no—
85#63252—41no—
86#63252—41no—
87C2×D68—21no—
88C2×D68—21no—
89C2×D68—21no—
90C2×C4×D17—41no—
91C2×Dic34—21no—
92M16×C17—21no—
93M16×C17—21no—
94M16×C17—21no—
95M16×C17SD1612yescomplemented
96C2×C8×C17—21no—
97C2×C8×C17—21no—
98C2×C8×C17—21no—
99C2×C8×C17—21no—
100C2×C8×C17—41no—
101C2×C8×C17—41no—
102C4⋊C4×C17—21no—
103C4⋊C4×C17—21no—
104C4⋊C4×C17—21no—
105C4⋊C4×C17—22no—
106C4⋊C4×C17—22no—
107C4⋊C4×C17C22⋊C412yes—
108C22⋊C4×C17—22no—
109C42×C17—22no—
110C42×C17C22×C411yescharacteristic
111C42×C17C2×D411yescharacteristic
112C42×C17C2×D411yescharacteristic
113C42×C17#4111yescharacteristic
114#63230—44no—
115#63227—41no—
116#63227—41no—
117C4⋊Dic17—22no—
118C4⋊Dic17—21no—
119C4⋊Dic17—21no—
120C4⋊Dic17—41no—
121C4×Dic17—41no—
122C4×Dic17—41no—
123C2×#3622—21no—
124C2×#3622—21no—
125C2×#3622—42no—
126C2×#3622—41no—
127#9054—171nomaximal, Sylow
128C23×C17#12111yescharacteristic
129C22×D17—41no—
130Q8×C17—42no—
131Q8×C17—41no—
132Q8×C17—41no—
133C2×C4×C17—21no—
134C2×C4×C17—21no—
135C2×C4×C17—22no—
136C2×C4×C17—22no—
137C2×C4×C17—41no—
138C2×C4×C17C2×C22⋊C411yescharacteristic
139C2×C4×C17C4×D411yescharacteristic
140C2×C4×C17C4×D411yescharacteristic
141C2×C4×C17#12011yescharacteristic
142C2×C4×C17#12111yescharacteristic
143C2×C4×C17#12311yescharacteristic
144C2×C4×C17C2×SD1611yescharacteristic
145C2×C4×C17#13511yescharacteristic
146C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C17#13711yescharacteristic
148C22⋊D17—81no—
149C22⋊D17—81no—
150C2×Dic17—42no—
151C2×Dic17—41no—
152C2×Dic17—81no—
153C2×Dic17—81no—
154D68—42no—
155D68—41no—
156D68—41no—
157D68—41no—
158D68—41no—
159C4×D17—81no—
160C4×D17—81no—
161Dic34—41no—
162Dic34—41no—
163C8×C17—22no—
164C8×C17—41no—
165C8×C17—41no—
166C8×C17—41no—
167#3622—22no—
168#3622—41no—
169#3622—81no—
170#3167—171no—
171#2962D1711yescharacteristic, complemented
172#1980—171no—
173#1503—171no—
174#1480—171no—
175#1279—171no—
176#1278—171no—
177C22×C17—21no—
178C22×C17—21no—
179C22×C17#38611yescharacteristic
180C22×C17#46011yescharacteristic
181C22×C17#46411yescharacteristic
182C2×D17—81no—
183C2×D17—81no—
184C2×D17—81no—
185C4×C17—21no—
186C4×C17—21no—
187C4×C17—21no—
188C4×C17—42no—
189C4×C17—42no—
190C4×C17C4×SD1611yescharacteristic
191C4×C17#44011yescharacteristic
192C4×C17#44311yescharacteristic
193C4×C17#44411yescharacteristic
194C4×C17#44811yescharacteristic
195C4×C17#44911yescharacteristic
196Dic17—82no—
197Dic17—81no—
198#533C2×D1711yescharacteristic
199#532—171no—
200#498—171no—
201#492—171no—
202#487—171no—
203#486—171no—
204#465—342no—
205#446—22no—
206#446—21no—
207C8×Q8—21no—
208C4×SD16—342no—
209#431—171no—
210#424—21no—
211C2×C4⋊C8C2×D1711yescharacteristic
212C2×#104—341no—
213C2×#104—341no—
214#405—21no—
215C4×M16C2×D1711yescharacteristic
216C2×C4×C8—171no—
217C4×C4⋊C4—171no—
218#328—342no—
219D4⋊C8—341no—
220D4⋊C8—341no—
221C2×C17—21no—
222C2×C17—21no—
223C2×C17#187611yescharacteristic
224C2×C17#188011yescharacteristic
225C2×C17#188411yescharacteristic
226D17—161no—
227C2×#41—341no—
228C2×SD16—342no—
229C2×M16C22⋊D1711yescharacteristic
230C2×M16C22⋊D1711yescharacteristic
231C22×C8—21no—
232C22×C8—341no—
233C4⋊Q8—171no—
234C4⋊Q8C4×D1711yescharacteristic
235C4⋊Q8C4×D1711yescharacteristic
236#127—171no—
237#125—21no—
238#124—341no—
239C22⋊Q8—21no—
240C22⋊Q8D6812yes—
241#121—341no—
242#121—341no—
243C4×Q8—21no—
244C4×Q8C22⋊D1712yes—
245C4×D4—341no—
246C4×D4—341no—
247#117—21no—
248C2×C4⋊C4—341no—
249C2×C42—341no—
250C2×C42C22×D1711yescharacteristic
251#106—342no—
252C4⋊C8—22no—
253C4⋊C8—22no—
254C4⋊C8—21no—
255C4⋊C8—341no—
256C4⋊C8C22⋊D1711yescharacteristic
257C4⋊C8C22⋊D1711yescharacteristic
258#104—682no—
259#104—682no—
260#103—342no—
261#102—342no—
262C22⋊C8—341no—
263#97—22no—
264#97—21no—
265C4×C8—22no—
266C4×C8—21no—
267C4×C8—171no—
268C4×C8—171no—
269C4×C8—341no—
270C4×C8—341no—
271#95—341no—
272C17#905411yescharacteristic, complemented, Sylow
273#41—681no—
274#41—681no—
275#41—681no—
276#41—681no—
277C2×Q8—21no—
278C2×Q8—341no—
279C2×Q8#6322712yes—
280C2×D4—341no—
281C2×D4—341no—
282C2×D4—341no—
283C2×D4—681no—
284C22×C4—681no—
285C22×C4—681no—
286C22×C4C2×D6811yescharacteristic
287C22×C4#6325211yescharacteristic
288C22×C4C2×C22⋊D1711yescharacteristic
289SD16—684no—
290M16—21no—
291M16—21no—
292M16—21no—
293M16#6323012yescomplemented
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—341no—
301C2×C8—341no—
302C2×C8—682no—
303C2×C8—681no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—342no—
310C4⋊C4—341no—
311C4⋊C4—341no—
312C4⋊C4—681no—
313C4⋊C4#6322712yes—
314C22⋊C4—22no—
315C22⋊C4—681no—
316C22⋊C4—681no—
317C42—22no—
318C42—681no—
319C42—681no—
320C42C2×C4×D1711yescharacteristic
321C42#6325211yescharacteristic
322C42C2×C22⋊D1711yescharacteristic
323C42C2×C22⋊D1711yescharacteristic
324C23—681no—
325C23#1058761611yescharacteristic
326Q8—42no—
327Q8—41no—
328Q8—41no—
329Q8—681no—
330Q8—681no—
331D4—682no—
332D4—681no—
333D4—681no—
334D4—681no—
335D4—681no—
336D4—1361no—
337D4—1361no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—682no—
344C2×C4—681no—
345C2×C4—1361no—
346C2×C4—1361no—
347C2×C4—1361no—
348C2×C4—1361no—
349C2×C4C2×#6322711yescharacteristic
350C2×C4C4×C22⋊D1711yescharacteristic
351C2×C4C4×C22⋊D1711yescharacteristic
352C2×C4#1058761511yescharacteristic
353C2×C4#1058761611yescharacteristic
354C2×C4C2×#6323011yescharacteristic
355C2×C4#1058762811yescharacteristic
356C2×C4#1058763511yescharacteristic
357C2×C4#1058763611yescharacteristic
358C2×C4#1058763911yescharacteristic
359C8—22no—
360C8—41no—
361C8—41no—
362C8—41no—
363C8—342no—
364C8—681no—
365C8—1361no—
366C22—21no—
367C22—21no—
368C22—1361no—
369C22—1361no—
370C22—1361no—
371C22#1176268811yescharacteristic
372C22#1176300911yescharacteristic
373C22#1176303111yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—42no—
378C4—42no—
379C4—1362no—
380C4—1361no—
381C4C4×#6323011yescharacteristic
382C4#1176290711yescharacteristic
383C4#1176292411yescharacteristic
384C4#1176292911yescharacteristic
385C4#1176294811yescharacteristic
386C4#1176295411yescharacteristic
387C2—21no—
388C2—21no—
389C2—2721no—
390C2#1452911111yescharacteristic
391C2#1452913911yescharacteristic
392C2#1452916711yescharacteristic
subgroupG/H
centerC2×C4#10587639
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#2962C2
socleC22×C17#386
prime radical#11763359C22
cosocleC2×C42×C17C23
hypercenter#2962D17
hypocenterC17#9054
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2962

Complements

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

NH ≅ G/Ntype
3. #14527283C2semidirect
5. #14526623C2semidirect
6. #14526622C2semidirect
7. C17×#2962C2semidirect
9. #11763205C4semidirect
10. #11763183C4semidirect
11. #11763159C4semidirect
12. #11763157C4semidirect
95. M16×C17SD16semidirect
171. #2962D17semidirect
272. C17#9054semidirect
293. M16#63230semidirect

Maximal subgroups

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

subgroupindex
#145393442
#145297032
#145272832
#145271822
#145266232
#145266222
C17×#29622
#905417