Finite Group Databasebeta

← #16944786

Subgroups — #16944786

Order 4352.

500 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14534350C211yesmaximal, characteristic
2#14528517C211yesmaximal, characteristic, complemented
3#14526809C212yesmaximal, complemented
4#14526782C212yesmaximal
5C17×#1464C211yesmaximal, characteristic, complemented
6C2×C4×D68C411yescharacteristic, complemented
7C2×#10587612—21no—
8#11762748C411yescharacteristic, complemented
9#11762745C2211yescharacteristic
10#11762726C411yescharacteristic, complemented
11#11762718C2211yescharacteristic
12#11762700—21no—
13#11762688—21no—
14#11762685—21no—
15#11762680—21no—
16#11762677C411yescharacteristic, complemented
17#11762576—21no—
18#11762576C2212yes—
19C2×C17×#117C2211yescharacteristic
20C17×#432—21no—
21C17×#324—21no—
22C17×#323C2212yes—
23C23×C4×C17D411yescharacteristic
24C22×C22⋊D17—21no—
25C22×D68C2×C411yescharacteristic
26C22×C4×D17—21no—
27C17×#117—41no—
28C17×#117—41no—
29C2×C4⋊C4×C17C2×C411yescharacteristic
30C2×C4⋊C4×C17D411yescharacteristic
31C2×C22⋊C4×C17D411yescharacteristic
32C2×C22⋊C4×C17C2311yescharacteristic
33C2×C42×C17C2×C411yescharacteristic
34C2×C42×C17D411yescharacteristic
35C2×C22⋊Dic17—22no—
36C2×C22⋊Dic17—21no—
37C2×#63227—21no—
38C2×#63227—21no—
39C2×#63227—21no—
40C2×#63227—21no—
41#10587612—24no—
42#10587612—42no—
43C2×C4⋊Dic17—41no—
44C2×C4⋊Dic17C2×C411yescharacteristic
45C2×#63225—21no—
46C2×C4×Dic17—41no—
47C4×D68—41no—
48C4×D68—41no—
49C17×C4⋊C8—41no—
50C17×C22⋊C8—22no—
51C17×#97—41no—
52#10587502—21no—
53#10587502—21no—
54#10587502—21no—
55#10587502—21no—
56#10587502C2×C411yescharacteristic
57#10587502C2×C411yescharacteristic
58C24×C17C2×D411yescharacteristic
59C23×D17—21no—
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17—21no—
63C22×C4×C17—21no—
64C22×C4×C17—22no—
65C22×C4×C17C22⋊C411yescharacteristic
66C22×C4×C17C22⋊C411yescharacteristic
67C22×C4×C17C22⋊C411yescharacteristic
68C22×C4×C17C22⋊C411yescharacteristic
69C22×C4×C17C22×C411yescharacteristic
70C22×C4×C17C2×D411yescharacteristic
71C2×C22⋊D17—42no—
72C2×C22⋊D17—41no—
73C2×C22⋊D17—41no—
74C2×C22⋊D17—81no—
75C22×Dic17—21no—
76C22×Dic17—21no—
77C22×Dic17—21no—
78C22×Dic17—42no—
79C2×D68—41no—
80C2×D68—42no—
81C2×C4×D17—42no—
82C2×C4×D17—81no—
83C2×C4×D17—81no—
84C2×C8×C17—42no—
85C4⋊C4×C17—41no—
86C4⋊C4×C17—41no—
87C22⋊C4×C17—41no—
88C22⋊C4×C17—41no—
89C42×C17—21no—
90C42×C17—21no—
91C42×C17—21no—
92C42×C17—21no—
93C22⋊Dic17—24no—
94C22⋊Dic17—42no—
95C22⋊Dic17—81no—
96#63227—42no—
97#63227—41no—
98#63227—41no—
99#63227—42no—
100#63227—81no—
101C4⋊Dic17—44no—
102C4⋊Dic17—41no—
103#63225—81no—
104C4×Dic17—44no—
105#11754—171nomaximal, Sylow
106C23×C17—21no—
107C23×C17—21no—
108C23×C17—41no—
109C23×C17—41no—
110C23×C17C2×C22⋊C411yescharacteristic
111C23×C17AGL(1,ℤ/8)11yescharacteristic
112C23×C17#13711yescharacteristic
113C22×D17—22no—
114C22×D17—41no—
115C22×D17—41no—
116C22×D17—41no—
117C22×D17—41no—
118C22×D17—41no—
119C22×D17—41no—
120C2×C4×C17—22no—
121C2×C4×C17—22no—
122C2×C4×C17—22no—
123C2×C4×C17—22no—
124C2×C4×C17—21no—
125C2×C4×C17—21no—
126C2×C4×C17—21no—
127C2×C4×C17—21no—
128C2×C4×C17—21no—
129C2×C4×C17—21no—
130C2×C4×C17—21no—
131C2×C4×C17—21no—
132C2×C4×C17—41no—
133C2×C4×C17—41no—
134C2×C4×C17—41no—
135C2×C4×C17—41no—
136C2×C4×C17#9911yescharacteristic
137C2×C4×C17#9911yescharacteristic
138C2×C4×C17#10412yes—
139C22⋊D17—82no—
140C22⋊D17—82no—
141C2×Dic17—44no—
142C2×Dic17—41no—
143C2×Dic17—41no—
144C2×Dic17—41no—
145C2×Dic17—41no—
146C2×Dic17—41no—
147C2×Dic17—41no—
148C2×Dic17—41no—
149C2×Dic17—41no—
150C2×Dic17—41no—
151C2×Dic17—82no—
152C2×Dic17—82no—
153D68—42no—
154D68—42no—
155C4×D17—84no—
156C8×C17—82no—
157#2598—171no—
158#1740—171no—
159#1464D1711yescharacteristic, complemented
160#1352—172no—
161#1343—172no—
162C22×C17—21no—
163C22×C17—21no—
164C22×C17—21no—
165C22×C17—21no—
166C22×C17—41no—
167C22×C17—41no—
168C22×C17—41no—
169C22×C17—41no—
170C22×C17—81no—
171C22×C17C2×#9911yescharacteristic
172C22×C17#41711yescharacteristic
173C22×C17C2×#10411yescharacteristic
174C2×D17—42no—
175C2×D17—42no—
176C2×D17—42no—
177C2×D17—81no—
178C2×D17—81no—
179C2×D17—81no—
180C2×D17—81no—
181C4×C17—21no—
182C4×C17—21no—
183C4×C17—22no—
184C4×C17—41no—
185C4×C17—41no—
186C4×C17—41no—
187C4×C17—41no—
188Dic17—81no—
189Dic17—81no—
190Dic17—84no—
191Dic17—81no—
192C2×C4×D4—171no—
193C2×#117—341no—
194C2×#117C2×D1711yescharacteristic
195#432—21no—
196#400—171no—
197#399—171no—
198#394—171no—
199#392—171no—
200#388—341no—
201#386—341no—
202#386—341no—
203#385—341no—
204#383—171no—
205#342—172no—
206#342—341no—
207#324—21no—
208#323C2×D1712yes—
209C2×C17—21no—
210C2×C17—21no—
211C2×C17—41no—
212C2×C17—41no—
213C2×C17#150411yescharacteristic
214C2×C17#212011yescharacteristic
215C2×C17#212811yescharacteristic
216D17—82no—
217C22×D4—171no—
218C22×D4—341no—
219C23×C4—341no—
220C23×C4D6811yescharacteristic
221C4×D4—681no—
222C4×D4—681no—
223#117—41no—
224#117—41no—
225#117—344no—
226#117—682no—
227C2×C4⋊C4—171no—
228C2×C4⋊C4—341no—
229C2×C4⋊C4—681no—
230C2×C4⋊C4C4×D1711yescharacteristic
231C2×C4⋊C4C22⋊D1711yescharacteristic
232C2×C22⋊C4—342no—
233C2×C22⋊C4—341no—
234C2×C22⋊C4—341no—
235C2×C22⋊C4—341no—
236C2×C22⋊C4—341no—
237C2×C22⋊C4—341no—
238C2×C22⋊C4D6811yescharacteristic
239C2×C22⋊C4C22×D1711yescharacteristic
240C2×C42—681no—
241C2×C42C4×D1711yescharacteristic
242C2×C42C22⋊D1711yescharacteristic
243C4⋊C8—41no—
244C22⋊C8—22no—
245#97—41no—
246#95—171no—
247#95—171no—
248#95—341no—
249#95—341no—
250#95—341no—
251#95—341no—
252C17#1175411yescharacteristic, complemented, Sylow
253C24—341no—
254C24C2×D6811yescharacteristic
255C2×D4—681no—
256C2×D4—682no—
257C2×D4—682no—
258C2×D4—681no—
259C2×D4—681no—
260C2×D4—1361no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—341no—
267C22×C4—341no—
268C22×C4—341no—
269C22×C4—682no—
270C22×C4—682no—
271C22×C4—1361no—
272C22×C4—1361no—
273C22×C4#6322711yescharacteristic
274C22×C4#6322711yescharacteristic
275C22×C4#6322711yescharacteristic
276C22×C4#6322711yescharacteristic
277C22×C4C2×C4×D1711yescharacteristic
278C22×C4C2×C22⋊D1711yescharacteristic
279C2×C8—42no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—681no—
283C4⋊C4—684no—
284C4⋊C4—1361no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—344no—
288C22⋊C4—682no—
289C22⋊C4—682no—
290C22⋊C4—681no—
291C22⋊C4—681no—
292C22⋊C4—682no—
293C22⋊C4—1361no—
294C22⋊C4—1361no—
295C42—21no—
296C42—21no—
297C42—21no—
298C42—21no—
299C42—684no—
300C23—21no—
301C23—21no—
302C23—41no—
303C23—41no—
304C23—342no—
305C23—681no—
306C23—681no—
307C23—681no—
308C23—681no—
309C23—681no—
310C23—681no—
311C23#1058759411yescharacteristic
312C23#1058759511yescharacteristic
313C23C2×#6322711yescharacteristic
314D4—682no—
315D4—682no—
316D4—1362no—
317D4—1362no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—684no—
335C2×C4—681no—
336C2×C4—681no—
337C2×C4—681no—
338C2×C4—681no—
339C2×C4—681no—
340C2×C4—681no—
341C2×C4—681no—
342C2×C4—681no—
343C2×C4—681no—
344C2×C4—1364no—
345C2×C4—1362no—
346C2×C4—1362no—
347C2×C4#1058747711yescharacteristic
348C2×C4#1058747711yescharacteristic
349C2×C4#1058749612yes—
350C8—82no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—81no—
360C22—682no—
361C22—682no—
362C22—682no—
363C22—1361no—
364C22—1361no—
365C22—1361no—
366C22—1361no—
367C22C2×#1058747711yescharacteristic
368C22#1176281111yescharacteristic
369C22C2×#1058749611yescharacteristic
370C4—21no—
371C4—21no—
372C4—22no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—1361no—
378C4—1361no—
379C4—1364no—
380C4—1361no—
381C2—21no—
382C2—21no—
383C2—41no—
384C2—41no—
385C2—1362no—
386C2#1452728911yescharacteristic
387C2#1453042611yescharacteristic
388C2#1453045511yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC17×#1464C2
socleC22×C17C2×#99
prime radical#11762718C22
cosocleC2×C22⋊C4×C17C23
hypercenter#1464D17
hypocenterC17#11754
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #14528517C2semidirect
3. #14526809C2semidirect
5. C17×#1464C2semidirect
6. C2×C4×D68C4semidirect
8. #11762748C4semidirect
10. #11762726C4semidirect
16. #11762677C4semidirect
159. #1464D17semidirect
252. C17#11754semidirect

Maximal subgroups

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

subgroupindex
#145343502
#145285172
#145268092
#145267822
C17×#14642
#1175417