Finite Group Databasebeta

← #16939079

Subgroups — #16939079

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#14529578C211yesmaximal, characteristic
2#14528781C211yesmaximal, characteristic
3#14528781C211yesmaximal, characteristic
4#14526667C211yesmaximal, characteristic, complemented
5#14526667C211yesmaximal, characteristic, complemented
6#14526619C211yesmaximal, characteristic, complemented
7C17×#1834C211yesmaximal, characteristic, complemented
8C2×C4×D68C2211yescharacteristic
9C2×C4⋊#3622C2211yescharacteristic
10C2×C4⋊#3622C2211yescharacteristic
11C2×C4⋊#3622C2211yescharacteristic
12C2×#10587480—21no—
13C2×#10587480—21no—
14C2×#10587491—21no—
15C2×#10587491—21no—
16#11762571—21no—
17#11762571—21no—
18C2×C4×C8×C17C2211yescharacteristic
19C17×#384C2211yescharacteristic
20C17×#384C2211yescharacteristic
21C17×#340—21no—
22C17×#340—21no—
23C22×D68D411yescharacteristic
24C22×C4×D17—21no—
25C22×C8×C17D411yescharacteristic
26C22×C8×C17D411yescharacteristic
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17—21no—
33C2×C42×C17C2311yescharacteristic
34C2×#63227—21no—
35C2×C4⋊Dic17D411yescharacteristic
36C22×#3622—21no—
37C22×#3622—21no—
38C22×#3622—21no—
39C4×D68—21no—
40C4×D68—21no—
41C4×D68—21no—
42C4×D68—21no—
43C4×C8×C17—21no—
44C4×C8×C17—21no—
45#10587491—42no—
46#10587491—42no—
47#10587480—42no—
48#10587480—42no—
49C4⋊#3622—21no—
50C4⋊#3622—21no—
51C4⋊#3622—21no—
52C4⋊#3622—21no—
53C4⋊#3622—21no—
54C4⋊#3622—21no—
55C23×D17—21no—
56C22×C4×C17—41no—
57C22×C4×C17—41no—
58C22×C4×C17C2×D411yescharacteristic
59C22×C4×C17C2×D411yescharacteristic
60C22×C4×C17#4111yescharacteristic
61C22×Dic17—21no—
62C2×D68—21no—
63C2×D68—21no—
64C2×D68—21no—
65C2×D68—21no—
66C2×D68—21no—
67C2×D68SD1612yes—
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—21no—
75C2×C8×C17—21no—
76C2×C8×C17—21no—
77C2×C8×C17—21no—
78C2×C8×C17—21no—
79C2×C8×C17—21no—
80C4⋊C4×C17—41no—
81C4⋊C4×C17—41no—
82C4⋊C4×C17—41no—
83C4⋊C4×C17—41no—
84C4⋊C4×C17—41no—
85C4⋊C4×C17—41no—
86C4⋊C4×C17—41no—
87C4⋊C4×C17—41no—
88C4⋊C4×C17—81no—
89C4⋊C4×C17—81no—
90C42×C17#4111yescharacteristic
91C42×C17#4111yescharacteristic
92C42×C17#4111yescharacteristic
93C42×C17#4111yescharacteristic
94#63227—41no—
95#63227—41no—
96C4⋊Dic17—21no—
97C4⋊Dic17—21no—
98C2×#3622—41no—
99C2×#3622—41no—
100C2×#3622—41no—
101C2×#3622—41no—
102C2×#3622—41no—
103C2×#3622—41no—
104C2×#3622—41no—
105C2×#3622—41no—
106C2×#3622—41no—
107#10625—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—81no—
122C2×C4×C17—81no—
123C2×C4×C17—81no—
124C2×C4×C17#12311yescharacteristic
125C2×C4×C17#12311yescharacteristic
126C2×C4×C17#12311yescharacteristic
127C2×C4×C17#12411yescharacteristic
128C2×C4×C17#12611yescharacteristic
129C2×C4×C17#12611yescharacteristic
130C2×C4×C17C2×SD1611yescharacteristic
131C2×C4×C17#13511yescharacteristic
132C2×C4×C17#13511yescharacteristic
133C2×C4×C17#13511yescharacteristic
134C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C17#13711yescharacteristic
138C2×Dic17—41no—
139C2×Dic17—41no—
140C2×Dic17—41no—
141D68—22no—
142D68—22no—
143D68—41no—
144D68—41no—
145C4×D17—81no—
146C4×D17—81no—
147C4×D17—81no—
148C4×D17—81no—
149C8×C17—41no—
150C8×C17—41no—
151#3622—81no—
152#3622—81no—
153#3622—81no—
154#1954—171no—
155#1834D1711yescharacteristic, complemented
156#1802—171no—
157#1802—171no—
158#1296—171no—
159#1296—171no—
160#1277—171no—
161C22×C17#39711yescharacteristic
162C22×C17#46311yescharacteristic
163C22×C17#46311yescharacteristic
164C22×C17#46511yescharacteristic
165C22×C17#46811yescharacteristic
166C22×C17#47211yescharacteristic
167C22×C17#47311yescharacteristic
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—161no—
179C4×C17#48111yescharacteristic
180C4×C17#48211yescharacteristic
181C4×C17#48211yescharacteristic
182C4×C17#48211yescharacteristic
183C4×C17#48311yescharacteristic
184C4×C17#48511yescharacteristic
185C4×C17#48811yescharacteristic
186C4×C17#49011yescharacteristic
187Dic17—81no—
188C2×C4×D4—171no—
189C2×C4⋊C8—171no—
190C2×C4⋊C8—171no—
191C2×C4⋊C8—171no—
192C2×#102—341no—
193C2×#102—341no—
194C2×C22⋊C8—341no—
195C2×C22⋊C8—341no—
196C2×C4×C8C2×D1711yescharacteristic
197#384C2×D1711yescharacteristic
198#384C2×D1711yescharacteristic
199#340—21no—
200#340—21no—
201#340—341no—
202#340—341no—
203C2×C17#167711yescharacteristic
204C2×C17#167911yescharacteristic
205C2×C17#169711yescharacteristic
206C2×C17#169911yescharacteristic
207C2×C17#207311yescharacteristic
208C2×C17#207711yescharacteristic
209C2×C17#207811yescharacteristic
210D17—82no—
211C22×D4—171no—
212C23×C4—341no—
213C22×C8—341no—
214C22×C8—341no—
215C22×C8—341no—
216C22×C8C22⋊D1711yescharacteristic
217C22×C8C22⋊D1711yescharacteristic
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—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—171no—
229C2×C22⋊C4—341no—
230C2×C42C22×D1711yescharacteristic
231C4⋊C8—341no—
232C4⋊C8—341no—
233C4⋊C8—341no—
234C4⋊C8—341no—
235C4⋊C8—341no—
236C4⋊C8—341no—
237#102—682no—
238#102—682no—
239C22⋊C8—682no—
240C22⋊C8—682no—
241C4×C8—21no—
242C4×C8—21no—
243C17#1062511yescharacteristic, 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—41no—
253C22×C4—341no—
254C22×C4—681no—
255C22×C4—681no—
256C22×C4—681no—
257C22×C4—681no—
258C22×C4—681no—
259C22×C4—681no—
260C22×C4D4×D1711yescharacteristic
261C22×C4#6325411yescharacteristic
262C22×C4C2×C22⋊D1711yescharacteristic
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—681no—
270C2×C8—681no—
271C2×C8—681no—
272C2×C8—681no—
273C2×C8—681no—
274C2×C8—681no—
275C2×C8—681no—
276C2×C8—681no—
277C2×C8—681no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—81no—
287C4⋊C4—81no—
288C4⋊C4—341no—
289C4⋊C4—341no—
290C22⋊C4—681no—
291C22⋊C4—681no—
292C42#6325211yescharacteristic
293C42#6325211yescharacteristic
294C42#6325611yescharacteristic
295C42#6325611yescharacteristic
296C23—342no—
297C23—681no—
298C23—681no—
299C23—681no—
300C23—681no—
301C23—681no—
302C23—681no—
303C23#1058762411yescharacteristic
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—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—681no—
317C2×C4—681no—
318C2×C4—681no—
319C2×C4—1361no—
320C2×C4—1361no—
321C2×C4—1361no—
322C2×C4—1361no—
323C2×C4#1058758011yescharacteristic
324C2×C4#1058758011yescharacteristic
325C2×C4#1058758411yescharacteristic
326C2×C4#1058758411yescharacteristic
327C2×C4SD16×D1711yescharacteristic
328C2×C4#1058760011yescharacteristic
329C2×C4#1058760111yescharacteristic
330C2×C4#1058760211yescharacteristic
331C2×C4#1058761511yescharacteristic
332C2×C4#1058763311yescharacteristic
333C2×C4#1058763511yescharacteristic
334C2×C4#1058763511yescharacteristic
335C2×C4#1058763611yescharacteristic
336C2×C4#1058763611yescharacteristic
337C8—41no—
338C8—41no—
339C8—1361no—
340C8—1361no—
341C8—1361no—
342C22—682no—
343C22—682no—
344C22—682no—
345C22—1361no—
346C22—1361no—
347C22—1361no—
348C22—1361no—
349C22#1176273511yescharacteristic
350C22#1176302111yescharacteristic
351C22#1176302111yescharacteristic
352C22#1176303511yescharacteristic
353C22#1176305211yescharacteristic
354C22#1176307611yescharacteristic
355C22#1176308111yescharacteristic
356C4—21no—
357C4—21no—
358C4—161no—
359C4—161no—
360C4—1361no—
361C4#1176312911yescharacteristic
362C4#1176313311yescharacteristic
363C4#1176313311yescharacteristic
364C4#1176313511yescharacteristic
365C4#1176314111yescharacteristic
366C4#1176315311yescharacteristic
367C4#1176316611yescharacteristic
368C4#1176317511yescharacteristic
369C2—1362no—
370C2#1452819011yescharacteristic
371C2#1452820411yescharacteristic
372C2#1452831411yescharacteristic
373C2#1452832811yescharacteristic
374C2#1453019811yescharacteristic
375C2#1453021811yescharacteristic
376C2#1453022511yescharacteristic
subgroupG/H
centerC23#10587624
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1834C2
socleC23×C17#121
prime radicalC22×D68D4
hypercenter#1834D17
hypocenterC17#10625
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

Complements

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

NH ≅ G/Ntype
4. #14526667C2semidirect
5. #14526667C2semidirect
6. #14526619C2semidirect
7. C17×#1834C2semidirect
155. #1834D17semidirect
243. C17#10625semidirect

Maximal subgroups

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

subgroupindex
#145295782
#145287812
#145266672
#145266192
C17×#18342
#1062517