Finite Group Databasebeta

← #16939046

Subgroups — #16939046

Order 4352.

418 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14529578C211yesmaximal, characteristic
2#14528941C211yesmaximal, characteristic, complemented
3#14528785C211yesmaximal, characteristic
4#14528785C211yesmaximal, characteristic
5#14526668C211yesmaximal, characteristic, complemented
6#14526668C211yesmaximal, characteristic, complemented
7C17×#1277C211yesmaximal, characteristic, complemented
8C2×C4×D68C2211yescharacteristic
9C2×#10587488—21no—
10C2×#10587488—21no—
11C2×C4⋊#3622C2211yescharacteristic
12C2×#10587492—21no—
13C2×#10587492—21no—
14C2×#10587491—21no—
15C2×#10587491—21no—
16#11762679C2211yescharacteristic
17#11762679C2211yescharacteristic
18#11762572—21no—
19#11762572—21no—
20C2×C17×C4⋊C8C2211yescharacteristic
21C2×C17×C4⋊C8C2211yescharacteristic
22C2×C4×C8×C17C2211yescharacteristic
23C22×D68D411yescharacteristic
24C22×C4×D17—21no—
25C22×C8×C17—21no—
26C22×C8×C17—21no—
27C22×C8×C17D411yescharacteristic
28C22×C8×C17D411yescharacteristic
29C2×C42×C17C2311yescharacteristic
30C2×#63227—21no—
31C2×C4⋊Dic17—21no—
32C2×C4⋊Dic17—21no—
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17—21no—
36C2×C4⋊Dic17—21no—
37C2×C4⋊Dic17D411yescharacteristic
38C22×#3622—21no—
39C4×D68—21no—
40C4×D68—21no—
41C4×D68—21no—
42C4×D68—21no—
43C17×C4⋊C8—21no—
44C17×C4⋊C8—21no—
45C17×C4⋊C8—21no—
46C17×C4⋊C8—21no—
47C4×C8×C17—21no—
48C4×C8×C17—21no—
49#10587492—42no—
50#10587492—42no—
51#10587491—42no—
52#10587491—42no—
53#10587488—42no—
54#10587488—42no—
55C4⋊#3622—21no—
56C4⋊#3622—21no—
57C23×D17—21no—
58C22×C4×C17C2×D411yescharacteristic
59C22×C4×C17C2×D411yescharacteristic
60C22×C4×C17#4111yescharacteristic
61C22×Dic17—21no—
62C22×Dic17—41no—
63C22×Dic17—41no—
64C2×D68—21no—
65C2×D68—21no—
66C2×D68—21no—
67C2×D68—21no—
68C2×D68—21no—
69C2×D68SD1612yes—
70C2×C4×D17—41no—
71C2×C4×D17—41no—
72C2×C4×D17—41no—
73C2×C4×D17—41no—
74C2×C4×D17—41no—
75C2×C4×D17—41no—
76C2×C8×C17—21no—
77C2×C8×C17—21no—
78C2×C8×C17—21no—
79C2×C8×C17—21no—
80C2×C8×C17—41no—
81C2×C8×C17—41no—
82C2×C8×C17—41no—
83C2×C8×C17—41no—
84C2×C8×C17—41no—
85C2×C8×C17—41no—
86C2×C8×C17D812yes—
87C2×C8×C17SD1612yes—
88C42×C17#4111yescharacteristic
89C42×C17#4111yescharacteristic
90C42×C17#4111yescharacteristic
91C42×C17#4111yescharacteristic
92#63227—41no—
93#63227—41no—
94C4⋊Dic17—21no—
95C4⋊Dic17—21no—
96C4⋊Dic17—41no—
97C4⋊Dic17—41no—
98C4⋊Dic17—41no—
99C4⋊Dic17—41no—
100C4⋊Dic17—41no—
101C4⋊Dic17—41no—
102C4⋊Dic17—41no—
103C4⋊Dic17—41no—
104C4⋊Dic17—81no—
105C4⋊Dic17—81no—
106C2×#3622—41no—
107C2×#3622—41no—
108C2×#3622—41no—
109#10619—171nomaximal, Sylow
110C23×C17#12111yescharacteristic
111C22×D17—22no—
112C22×D17—41no—
113C22×D17—41no—
114C22×D17—41no—
115C22×D17—41no—
116C22×D17—41no—
117C22×D17—41no—
118C2×C4×C17—21no—
119C2×C4×C17—21no—
120C2×C4×C17#12311yescharacteristic
121C2×C4×C17#12311yescharacteristic
122C2×C4×C17#12311yescharacteristic
123C2×C4×C17#12411yescharacteristic
124C2×C4×C17#12611yescharacteristic
125C2×C4×C17#12611yescharacteristic
126C2×C4×C17C2×D811yescharacteristic
127C2×C4×C17C2×SD1611yescharacteristic
128C2×C4×C17C2×SD1611yescharacteristic
129C2×C4×C17#13511yescharacteristic
130C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C17#13711yescharacteristic
133C2×C4×C17#13711yescharacteristic
134C2×Dic17—41no—
135C2×Dic17—41no—
136C2×Dic17—41no—
137C2×Dic17—81no—
138C2×Dic17—81no—
139C2×Dic17—81no—
140C2×Dic17—81no—
141C2×Dic17—81no—
142C2×Dic17—81no—
143D68—22no—
144D68—22no—
145D68—41no—
146D68—41no—
147C4×D17—81no—
148C4×D17—81no—
149C4×D17—81no—
150C4×D17—81no—
151C8×C17—22no—
152C8×C17—22no—
153C8×C17—81no—
154C8×C17—81no—
155#3622—81no—
156#1954—171no—
157#1844—171no—
158#1802—171no—
159#1802—171no—
160#1296—171no—
161#1296—171no—
162#1277D1711yescharacteristic, complemented
163C22×C17#39711yescharacteristic
164C22×C17#45911yescharacteristic
165C22×C17#46111yescharacteristic
166C22×C17#46511yescharacteristic
167C22×C17#46811yescharacteristic
168C22×C17#47111yescharacteristic
169C22×C17#47111yescharacteristic
170C2×D17—42no—
171C2×D17—42no—
172C2×D17—42no—
173C2×D17—81no—
174C2×D17—81no—
175C2×D17—81no—
176C2×D17—81no—
177C4×C17—21no—
178C4×C17—21no—
179C4×C17#48011yescharacteristic
180C4×C17#48111yescharacteristic
181C4×C17#48111yescharacteristic
182C4×C17#48211yescharacteristic
183C4×C17#48311yescharacteristic
184C4×C17#48511yescharacteristic
185C4×C17#48611yescharacteristic
186C4×C17#48911yescharacteristic
187Dic17—81no—
188Dic17—161no—
189Dic17—161no—
190C2×C4×D4—171no—
191C2×#106—341no—
192C2×#106—341no—
193C2×C4⋊C8—171no—
194C2×C4⋊C8C2×D1711yescharacteristic
195C2×C4⋊C8C2×D1711yescharacteristic
196C2×#102—341no—
197C2×#102—341no—
198C2×C22⋊C8—341no—
199C2×C22⋊C8—341no—
200C2×C4×C8C2×D1711yescharacteristic
201#384—171no—
202#384—171no—
203#340—341no—
204#340—341no—
205C2×C17#166511yescharacteristic
206C2×C17#167111yescharacteristic
207C2×C17#168511yescharacteristic
208C2×C17#169111yescharacteristic
209C2×C17#207111yescharacteristic
210C2×C17#207711yescharacteristic
211C2×C17#207911yescharacteristic
212D17—82no—
213C22×D4—171no—
214C23×C4—341no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—341no—
218C22×C8D6811yescharacteristic
219C22×C8D6811yescharacteristic
220C4×D4—341no—
221C4×D4—341no—
222C4×D4—341no—
223C4×D4—341no—
224C2×C4⋊C4—171no—
225C2×C4⋊C4—341no—
226C2×C4⋊C4—341no—
227C2×C4⋊C4—341no—
228C2×C4⋊C4—341no—
229C2×C4⋊C4—341no—
230C2×C4⋊C4—341no—
231C2×C22⋊C4—341no—
232C2×C42C22×D1711yescharacteristic
233#106—682no—
234#106—682no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—341no—
240C4⋊C8—341no—
241#102—682no—
242#102—682no—
243C22⋊C8—682no—
244C22⋊C8—682no—
245C4×C8—21no—
246C4×C8—21no—
247C17#1061911yescharacteristic, complemented, Sylow
248C24—341no—
249C2×D4—172no—
250C2×D4—341no—
251C2×D4—341no—
252C2×D4—341no—
253C2×D4—341no—
254C2×D4—341no—
255C22×C4—341no—
256C22×C4—681no—
257C22×C4—681no—
258C22×C4—681no—
259C22×C4—681no—
260C22×C4—681no—
261C22×C4—681no—
262C22×C4—681no—
263C22×C4—681no—
264C22×C4C2×D6811yescharacteristic
265C22×C4D4×D1711yescharacteristic
266C22×C4#6325611yescharacteristic
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—681no—
278C2×C8—681no—
279C2×C8—681no—
280C2×C8#6321912yes—
281C2×C8D13612yes—
282C4⋊C4—341no—
283C4⋊C4—341no—
284C4⋊C4—681no—
285C4⋊C4—681no—
286C4⋊C4—681no—
287C4⋊C4—681no—
288C4⋊C4—681no—
289C4⋊C4—681no—
290C4⋊C4—681no—
291C4⋊C4—681no—
292C4⋊C4—1361no—
293C4⋊C4—1361no—
294C22⋊C4—681no—
295C22⋊C4—681no—
296C42#6325211yescharacteristic
297C42#6325211yescharacteristic
298C42#6325411yescharacteristic
299C42#6325411yescharacteristic
300C23—342no—
301C23—681no—
302C23—681no—
303C23—681no—
304C23—681no—
305C23—681no—
306C23—681no—
307C23#1058758111yescharacteristic
308D4—342no—
309D4—342no—
310D4—681no—
311D4—681no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—681no—
315C2×C4—681no—
316C2×C4—681no—
317C2×C4—1361no—
318C2×C4—1361no—
319C2×C4—1361no—
320C2×C4—1361no—
321C2×C4—1361no—
322C2×C4—1361no—
323C2×C4—1361no—
324C2×C4—1361no—
325C2×C4—1361no—
326C2×C4—1361no—
327C2×C4#1058756111yescharacteristic
328C2×C4#1058756911yescharacteristic
329C2×C4#1058756911yescharacteristic
330C2×C4#1058757211yescharacteristic
331C2×C4#1058758411yescharacteristic
332C2×C4#1058758411yescharacteristic
333C2×C4C2×#6321911yescharacteristic
334C2×C4C2×D13611yescharacteristic
335C2×C4#1058759411yescharacteristic
336C2×C4#1058759511yescharacteristic
337C2×C4#1058759711yescharacteristic
338C2×C4SD16×D1711yescharacteristic
339C2×C4#1058760211yescharacteristic
340C2×C4#1058760411yescharacteristic
341C8—22no—
342C8—22no—
343C8—81no—
344C8—81no—
345C8—1361no—
346C22—682no—
347C22—682no—
348C22—682no—
349C22—1361no—
350C22—1361no—
351C22—1361no—
352C22—1361no—
353C22#1176273611yescharacteristic
354C22#1176300511yescharacteristic
355C22#1176301511yescharacteristic
356C22#1176303911yescharacteristic
357C22#1176305611yescharacteristic
358C22#1176307311yescharacteristic
359C22#1176307311yescharacteristic
360C4—21no—
361C4—21no—
362C4—2721no—
363C4—2721no—
364C4—1361no—
365C4#1176312311yescharacteristic
366C4#1176312611yescharacteristic
367C4#1176312811yescharacteristic
368C4#1176313211yescharacteristic
369C4#1176313811yescharacteristic
370C4#1176314811yescharacteristic
371C4#1176315611yescharacteristic
372C4#1176316911yescharacteristic
373C2—1362no—
374C2#1452812611yescharacteristic
375C2#1452816011yescharacteristic
376C2#1452825011yescharacteristic
377C2#1452828411yescharacteristic
378C2#1453018911yescharacteristic
379C2#1453021911yescharacteristic
380C2#1453023111yescharacteristic
subgroupG/H
centerC23#10587581
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1277C2
socleC23×C17#121
prime radicalC22×D68D4
hypercenter#1277D17
hypocenterC17#10619
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
2. #14528941C2semidirect
5. #14526668C2semidirect
6. #14526668C2semidirect
7. C17×#1277C2semidirect
162. #1277D17semidirect
247. C17#10619semidirect

Maximal subgroups

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

subgroupindex
#145295782
#145289412
#145287852
#145266682
C17×#12772
#1061917