Finite Group Databasebeta

← #16939067

Subgroups — #16939067

Order 4352.

402 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14529577C211yesmaximal, characteristic
2#14528911C211yesmaximal, characteristic, complemented
3#14528785C211yesmaximal, characteristic
4#14528781C211yesmaximal, characteristic
5#14526668C211yesmaximal, characteristic, complemented
6#14526618C211yesmaximal, characteristic, complemented
7C17×#1296C211yesmaximal, characteristic, complemented
8C2×C4×D68C2211yescharacteristic
9C2×C4⋊#3622C2211yescharacteristic
10C2×#10587492—21no—
11C2×#10587480—21no—
12C2×#10587491—21no—
13C2×#10587491—21no—
14C2×C4×#3622C2211yescharacteristic
15#11762679C2211yescharacteristic
16#11762572—21no—
17#11762571—21no—
18#11762571—21no—
19#11762571—21no—
20C2×C17×C4⋊C8C2211yescharacteristic
21C2×C17×C4⋊C8C2211yescharacteristic
22C17×#384C2211yescharacteristic
23C22×D68D411yescharacteristic
24C22×C4×D17—21no—
25C22×C8×C17—21no—
26C22×C8×C17—21no—
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17—21no—
30C2×C42×C17C2311yescharacteristic
31C2×#63227—21no—
32C2×C4⋊Dic17—21no—
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17D411yescharacteristic
36C22×#3622—21no—
37C22×#3622D411yescharacteristic
38C22×#3622D411yescharacteristic
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—
47#10587492—42no—
48#10587491—42no—
49#10587491—42no—
50#10587480—42no—
51C4⋊#3622—21no—
52C4⋊#3622—21no—
53C4×#3622—21no—
54C4×#3622—21no—
55C23×D17—21no—
56C22×C4×C17—41no—
57C22×C4×C17C2×D411yescharacteristic
58C22×C4×C17C2×D411yescharacteristic
59C22×C4×C17#4111yescharacteristic
60C22×Dic17—21no—
61C22×Dic17—41no—
62C2×D68—21no—
63C2×D68—21no—
64C2×D68—21no—
65C2×D68—21no—
66C2×D68—21no—
67C2×D68Q1612yes—
68C2×C4×D17—41no—
69C2×C4×D17—41no—
70C2×C4×D17—41no—
71C2×C4×D17—41no—
72C2×C4×D17—41no—
73C2×C4×D17—41no—
74C2×C8×C17—41no—
75C2×C8×C17—41no—
76C2×C8×C17—41no—
77C2×C8×C17—41no—
78C2×C8×C17—41no—
79C2×C8×C17—41no—
80C4⋊C4×C17—41no—
81C4⋊C4×C17—41no—
82C4⋊C4×C17—41no—
83C4⋊C4×C17—41no—
84C4⋊C4×C17—81no—
85C42×C17#4111yescharacteristic
86C42×C17#4111yescharacteristic
87C42×C17#4111yescharacteristic
88C42×C17#4111yescharacteristic
89#63227—41no—
90#63227—41no—
91C4⋊Dic17—21no—
92C4⋊Dic17—21no—
93C4⋊Dic17—41no—
94C4⋊Dic17—41no—
95C4⋊Dic17—41no—
96C4⋊Dic17—41no—
97C4⋊Dic17—81no—
98C2×#3622—21no—
99C2×#3622—21no—
100C2×#3622—21no—
101C2×#3622—21no—
102C2×#3622—21no—
103C2×#3622—21no—
104C2×#3622—41no—
105C2×#3622—41no—
106C2×#3622—41no—
107#10622—171nomaximal, Sylow
108C23×C17#12111yescharacteristic
109C22×D17—22no—
110C22×D17—41no—
111C22×D17—41no—
112C22×D17—41no—
113C22×D17—41no—
114C22×D17—41no—
115C22×D17—41no—
116C2×C4×C17—21no—
117C2×C4×C17—21no—
118C2×C4×C17—81no—
119C2×C4×C17—81no—
120C2×C4×C17—81no—
121C2×C4×C17#12311yescharacteristic
122C2×C4×C17#12311yescharacteristic
123C2×C4×C17#12311yescharacteristic
124C2×C4×C17#12411yescharacteristic
125C2×C4×C17#12611yescharacteristic
126C2×C4×C17#12611yescharacteristic
127C2×C4×C17C2×Q1611yescharacteristic
128C2×C4×C17#13511yescharacteristic
129C2×C4×C17#13511yescharacteristic
130C2×C4×C17#13511yescharacteristic
131C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
135C2×Dic17—41no—
136C2×Dic17—41no—
137C2×Dic17—41no—
138C2×Dic17—81no—
139C2×Dic17—81no—
140C2×Dic17—81no—
141D68—22no—
142D68—22no—
143D68—41no—
144D68—41no—
145C4×D17—81no—
146C4×D17—81no—
147C4×D17—81no—
148C4×D17—81no—
149C8×C17—81no—
150C8×C17—81no—
151#3622—41no—
152#3622—41no—
153#3622—81no—
154#1954—171no—
155#1834—171no—
156#1802—171no—
157#1802—171no—
158#1296—171no—
159#1296D1711yescharacteristic, complemented
160#1277—171no—
161C22×C17#39711yescharacteristic
162C22×C17#46311yescharacteristic
163C22×C17#46311yescharacteristic
164C22×C17#46711yescharacteristic
165C22×C17#46911yescharacteristic
166C22×C17#47111yescharacteristic
167C22×C17#47111yescharacteristic
168C2×D17—42no—
169C2×D17—42no—
170C2×D17—42no—
171C2×D17—81no—
172C2×D17—81no—
173C2×D17—81no—
174C2×D17—81no—
175C4×C17—21no—
176C4×C17—21no—
177C4×C17—161no—
178C4×C17#48211yescharacteristic
179C4×C17#48211yescharacteristic
180C4×C17#48211yescharacteristic
181C4×C17#48211yescharacteristic
182C4×C17#48411yescharacteristic
183C4×C17#48411yescharacteristic
184C4×C17#48811yescharacteristic
185C4×C17#49011yescharacteristic
186Dic17—81no—
187Dic17—161no—
188C2×C4×D4—171no—
189C2×C4⋊C8—171no—
190C2×C4⋊C8C2×D1711yescharacteristic
191C2×C4⋊C8C2×D1711yescharacteristic
192C2×#102—341no—
193C2×#102—341no—
194C2×C22⋊C8—341no—
195C2×C22⋊C8—341no—
196C2×C4×C8—171no—
197#384—171no—
198#384C2×D1711yescharacteristic
199#340—341no—
200#340—341no—
201#340—341no—
202#340—341no—
203C2×C17#168311yescharacteristic
204C2×C17#168311yescharacteristic
205C2×C17#170111yescharacteristic
206C2×C17#170111yescharacteristic
207C2×C17#207311yescharacteristic
208C2×C17#207611yescharacteristic
209C2×C17#207911yescharacteristic
210D17—82no—
211C22×D4—171no—
212C23×C4—341no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—171no—
216C22×C8—171no—
217C22×C8—341no—
218C4×D4—341no—
219C4×D4—341no—
220C4×D4—341no—
221C4×D4—341no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—171no—
226C2×C4⋊C4—341no—
227C2×C4⋊C4—341no—
228C2×C4⋊C4—341no—
229C2×C22⋊C4—341no—
230C2×C42C22×D1711yescharacteristic
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—341no—
236C4⋊C8—341no—
237#102—682no—
238#102—682no—
239C22⋊C8—682no—
240C22⋊C8—682no—
241C4×C8—341no—
242C4×C8—341no—
243C17#1062211yescharacteristic, complemented, Sylow
244C24—341no—
245C2×D4—172no—
246C2×D4—341no—
247C2×D4—341no—
248C2×D4—341no—
249C2×D4—341no—
250C2×D4—341no—
251C22×C4—41no—
252C22×C4—341no—
253C22×C4—681no—
254C22×C4—681no—
255C22×C4—681no—
256C22×C4—681no—
257C22×C4—681no—
258C22×C4—681no—
259C22×C4—681no—
260C22×C4#6325211yescharacteristic
261C22×C4D4×D1711yescharacteristic
262C22×C4D4×D1711yescharacteristic
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—341no—
270C2×C8—341no—
271C2×C8—341no—
272C2×C8—341no—
273C2×C8—341no—
274C2×C8—341no—
275C2×C8—681no—
276C2×C8—681no—
277C2×C8—681no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—81no—
283C4⋊C4—341no—
284C4⋊C4—341no—
285C4⋊C4—681no—
286C4⋊C4—681no—
287C4⋊C4—681no—
288C4⋊C4—681no—
289C4⋊C4—1361no—
290C22⋊C4—681no—
291C22⋊C4—681no—
292C42#6325211yescharacteristic
293C42#6325211yescharacteristic
294C42#6325411yescharacteristic
295C42#6325611yescharacteristic
296C23—342no—
297C23—681no—
298C23—681no—
299C23—681no—
300C23—681no—
301C23—681no—
302C23—681no—
303C23#1058757011yescharacteristic
304D4—342no—
305D4—342no—
306D4—681no—
307D4—681no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—681no—
314C2×C4—681no—
315C2×C4—681no—
316C2×C4—1361no—
317C2×C4—1361no—
318C2×C4—1361no—
319C2×C4—1361no—
320C2×C4—1361no—
321C2×C4—1361no—
322C2×C4—1361no—
323C2×C4#1058756211yescharacteristic
324C2×C4#1058756911yescharacteristic
325C2×C4#1058757111yescharacteristic
326C2×C4#1058758011yescharacteristic
327C2×C4#1058758011yescharacteristic
328C2×C4#1058758411yescharacteristic
329C2×C4#1058759711yescharacteristic
330C2×C4#1058759711yescharacteristic
331C2×C4#1058760011yescharacteristic
332C2×C4#1058760011yescharacteristic
333C2×C4#1058760211yescharacteristic
334C2×C4#1058760211yescharacteristic
335C2×C4Q16×D1711yescharacteristic
336C2×C4#1058760511yescharacteristic
337C8—81no—
338C8—81no—
339C8—681no—
340C8—681no—
341C8—1361no—
342C22—682no—
343C22—682no—
344C22—682no—
345C22—1361no—
346C22—1361no—
347C22—1361no—
348C22—1361no—
349C22#1176273811yescharacteristic
350C22#1176302311yescharacteristic
351C22#1176302711yescharacteristic
352C22#1176304911yescharacteristic
353C22#1176306111yescharacteristic
354C22#1176307111yescharacteristic
355C22#1176307511yescharacteristic
356C4—21no—
357C4—21no—
358C4—161no—
359C4—2721no—
360C4—1361no—
361C4#1176313211yescharacteristic
362C4#1176313511yescharacteristic
363C4#1176313511yescharacteristic
364C4#1176313611yescharacteristic
365C4#1176314311yescharacteristic
366C4#1176314611yescharacteristic
367C4#1176316511yescharacteristic
368C4#1176317211yescharacteristic
369C2—1362no—
370C2#1452823411yescharacteristic
371C2#1452823811yescharacteristic
372C2#1452834411yescharacteristic
373C2#1452834811yescharacteristic
374C2#1453020111yescharacteristic
375C2#1453021611yescharacteristic
376C2#1453023311yescharacteristic
subgroupG/H
centerC23#10587570
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1296C2
socleC23×C17#121
prime radicalC22×D68D4
hypercenter#1296D17
hypocenterC17#10622
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #14528911C2semidirect
5. #14526668C2semidirect
6. #14526618C2semidirect
7. C17×#1296C2semidirect
159. #1296D17semidirect
243. C17#10622semidirect

Maximal subgroups

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

subgroupindex
#145295772
#145289112
#145287852
#145287812
#145266682
#145266182
C17×#12962
#1062217