Finite Group Databasebeta

← #16944656

Subgroups — #16944656

Order 4352.

456 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 87 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#14532043C211yesmaximal, characteristic
2#14527105C211yesmaximal, characteristic
3#14526807C212yesmaximal, complemented
4#14526783C212yesmaximal, complemented
5C4×C17×#99C211yesmaximal, characteristic
6C2×#10587612C411yescharacteristic, complemented
7#11762862—21no—
8#11762748C411yescharacteristic, complemented
9#11762745C2211yescharacteristic
10#11762739C411yescharacteristic, complemented
11#11762737—21no—
12#11762734C2211yescharacteristic
13#11762723—21no—
14C4×#63225—21no—
15C4×C22⋊Dic17—21no—
16C4×C22⋊Dic17C411yescharacteristic, complemented
17#11762533—21no—
18#11762533C2212yes—
19C2×C4×D4×C17C2211yescharacteristic
20C2×C17×#99—21no—
21C4×C22⋊C4×C17—21no—
22C17×#342C2212yes—
23C22×D4×C17D411yescharacteristic
24C23×C4×C17C2×C411yescharacteristic
25C23×C4×C17D411yescharacteristic
26C4×D4×C17—41no—
27C4×D4×C17—41no—
28C2×C4⋊C4×C17C2×C411yescharacteristic
29C2×C22⋊C4×C17—22no—
30C2×C22⋊C4×C17D411yescharacteristic
31C2×C22⋊C4×C17C2311yescharacteristic
32C2×C42×C17—41no—
33C2×C42×C17D411yescharacteristic
34C2×C22⋊Dic17—21no—
35C2×C22⋊Dic17—21no—
36C2×C22⋊Dic17—21no—
37C2×C22⋊Dic17—21no—
38#10587612—41no—
39#10587612—41no—
40C2×C4⋊Dic17C2×C411yescharacteristic
41C2×C4⋊Dic17C2×C411yescharacteristic
42C2×#63225—21no—
43C2×#63225—21no—
44C2×C4×Dic17—21no—
45C2×C4×Dic17—21no—
46C17×#99—24no—
47C17×#95—41no—
48#10587502—21no—
49#10587502—21no—
50#10587502—21no—
51#10587502—21no—
52#10587502C2×C411yescharacteristic
53#10587502C2×C411yescharacteristic
54C22⋊#3622—22no—
55C4⋊#3622—41no—
56C4×#3622—41no—
57C24×C17C22⋊C411yescharacteristic
58C24×C17C2×D411yescharacteristic
59C2×D4×C17—22no—
60C2×D4×C17—22no—
61C2×D4×C17—41no—
62C22×C4×C17—21no—
63C22×C4×C17—21no—
64C22×C4×C17—21no—
65C22×C4×C17—21no—
66C22×C4×C17—42no—
67C22×C4×C17—42no—
68C22×C4×C17—42no—
69C22×C4×C17C22⋊C411yescharacteristic
70C22×C4×C17C22⋊C411yescharacteristic
71C22×C4×C17C22⋊C411yescharacteristic
72C22×C4×C17C22×C411yescharacteristic
73C22×C4×C17C2×D411yescharacteristic
74C22×Dic17—21no—
75C22×Dic17—21no—
76C22×Dic17—21no—
77C22×Dic17—21no—
78C4⋊C4×C17—41no—
79C22⋊C4×C17—24no—
80C22⋊C4×C17—41no—
81C22⋊C4×C17—41no—
82C22⋊C4×C17—42no—
83C42×C17—21no—
84C42×C17—21no—
85C42×C17—82no—
86C22⋊Dic17—42no—
87C22⋊Dic17—42no—
88C22⋊Dic17—42no—
89C22⋊Dic17—42no—
90C4⋊Dic17—41no—
91C4⋊Dic17—41no—
92#63225—42no—
93#63225—42no—
94C4×Dic17—42no—
95C4×Dic17—41no—
96C4×Dic17—41no—
97C2×#3622—42no—
98#11727—171nomaximal, Sylow
99C23×C17—21no—
100C23×C17—21no—
101C23×C17—21no—
102C23×C17—21no—
103C23×C17—21no—
104C23×C17—41no—
105C23×C17—41no—
106C23×C17—41no—
107C23×C17—41no—
108C23×C17C2×C22⋊C411yescharacteristic
109C23×C17#13512yes—
110D4×C17—44no—
111C2×C4×C17—21no—
112C2×C4×C17—21no—
113C2×C4×C17—22no—
114C2×C4×C17—21no—
115C2×C4×C17—21no—
116C2×C4×C17—21no—
117C2×C4×C17—42no—
118C2×C4×C17—42no—
119C2×C4×C17—42no—
120C2×C4×C17—41no—
121C2×C4×C17—41no—
122C2×C4×C17—41no—
123C2×C4×C17—44no—
124C2×C4×C17—81no—
125C2×C4×C17—82no—
126C2×C4×C17—82no—
127C2×C4×C17#9911yescharacteristic
128C2×C4×C17#9911yescharacteristic
129C2×C4×C17#10412yes—
130C2×Dic17—22no—
131C2×Dic17—41no—
132C2×Dic17—41no—
133C2×Dic17—41no—
134C2×Dic17—41no—
135C2×Dic17—41no—
136C2×Dic17—41no—
137C2×Dic17—41no—
138C2×Dic17—41no—
139C2×Dic17—41no—
140C2×Dic17—41no—
141C2×Dic17—41no—
142#3622—82no—
143#2395—171no—
144C4×#99D1711yescharacteristic
145#1460—171no—
146#1352—172no—
147#1344—172no—
148C22×C17—21no—
149C22×C17—21no—
150C22×C17—22no—
151C22×C17—42no—
152C22×C17—41no—
153C22×C17—41no—
154C22×C17—41no—
155C22×C17—41no—
156C22×C17—41no—
157C22×C17—81no—
158C22×C17—81no—
159C22×C17—81no—
160C22×C17C2×#9911yescharacteristic
161C22×C17#41611yescharacteristic
162C22×C17C2×#10411yescharacteristic
163C4×C17—21no—
164C4×C17—22no—
165C4×C17—41no—
166C4×C17—41no—
167C4×C17—41no—
168C4×C17—84no—
169C4×C17#35212yes—
170Dic17—42no—
171Dic17—81no—
172Dic17—81no—
173Dic17—81no—
174C2×C4×D4C2×D1711yescharacteristic
175C2×#117—171no—
176#431—341no—
177C2×#99—21no—
178#400—171no—
179#399—171no—
180#398—171no—
181#397—171no—
182#397—341no—
183#394—341no—
184C4×C4⋊C4—341no—
185C4×C22⋊C4—21no—
186C4×C22⋊C4—171no—
187C4×C22⋊C4—341no—
188#342C2×D1712yes—
189#323—172no—
190#323—341no—
191C2×C17—21no—
192C2×C17—21no—
193C2×C17—42no—
194C2×C17—81no—
195C2×C17#150111yescharacteristic
196C2×C17C2×#35211yescharacteristic
197C2×C17#212611yescharacteristic
198C22×D4C22⋊D1711yescharacteristic
199C23×C4C4×D1711yescharacteristic
200C23×C4C22⋊D1711yescharacteristic
201C4×D4—41no—
202C4×D4—41no—
203#117—681no—
204#117—681no—
205C2×C4⋊C4—171no—
206C2×C4⋊C4—171no—
207C2×C4⋊C4—341no—
208C2×C4⋊C4—341no—
209C2×C4⋊C4C4×D1711yescharacteristic
210C2×C22⋊C4—22no—
211C2×C22⋊C4—341no—
212C2×C22⋊C4—341no—
213C2×C22⋊C4—341no—
214C2×C22⋊C4—341no—
215C2×C22⋊C4D6811yescharacteristic
216C2×C22⋊C4C22×D1711yescharacteristic
217C2×C42—41no—
218C2×C42—341no—
219C2×C42—341no—
220C2×C42D6811yescharacteristic
221C4⋊C8—681no—
222#99—24no—
223C22⋊C8—342no—
224C4×C8—681no—
225#95—41no—
226#95—171no—
227#95—171no—
228#95—341no—
229#95—341no—
230#95—341no—
231#95—341no—
232C17#1172711yescharacteristic, complemented, Sylow
233C24#6322711yescharacteristic
234C24C2×C22⋊D1711yescharacteristic
235C2×D4—22no—
236C2×D4—22no—
237C2×D4—41no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—341no—
246C22×C4—341no—
247C22×C4—341no—
248C22×C4—341no—
249C22×C4#6322711yescharacteristic
250C22×C4#6322711yescharacteristic
251C22×C4#6322711yescharacteristic
252C22×C4C2×C4×D1711yescharacteristic
253C22×C4C2×D6811yescharacteristic
254C2×C8—682no—
255C4⋊C4—41no—
256C4⋊C4—681no—
257C4⋊C4—681no—
258C4⋊C4—682no—
259C4⋊C4—682no—
260C22⋊C4—24no—
261C22⋊C4—41no—
262C22⋊C4—41no—
263C22⋊C4—42no—
264C22⋊C4—682no—
265C22⋊C4—682no—
266C22⋊C4—682no—
267C22⋊C4—682no—
268C42—21no—
269C42—21no—
270C42—82no—
271C42—682no—
272C42—681no—
273C42—681no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23C2×#6322711yescharacteristic
284C23#1058763612yes—
285D4—44no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—44no—
299C2×C4—81no—
300C2×C4—82no—
301C2×C4—82no—
302C2×C4—342no—
303C2×C4—681no—
304C2×C4—681no—
305C2×C4—681no—
306C2×C4—681no—
307C2×C4—681no—
308C2×C4—681no—
309C2×C4—681no—
310C2×C4—681no—
311C2×C4—681no—
312C2×C4—681no—
313C2×C4—681no—
314C2×C4#1058747612yes—
315C2×C4#1058747711yescharacteristic
316C2×C4#1058747711yescharacteristic
317C8—1362no—
318C22—21no—
319C22—21no—
320C22—22no—
321C22—42no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—81no—
328C22—81no—
329C22—81no—
330C22C2×#1058747711yescharacteristic
331C22#1176280311yescharacteristic
332C22C2×#1058747611yescharacteristic
333C4—22no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—84no—
339C4—682no—
340C4—1361no—
341C4—1361no—
342C4—1361no—
343C4#1176259812yes—
344C2—21no—
345C2—21no—
346C2—42no—
347C2—81no—
348C2#1452727311yescharacteristic
349C2C2×#1176259811yescharacteristic
350C2#1453044711yescharacteristic
subgroupG/H
centerC2×C4#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC4×C17×#99C2
socleC22×C17C2×#99
prime radicalC22×D4×C17D4
cosocleC2×C22⋊C4×C17C23
hypercenterC4×#99D17
hypocenterC17#11727
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. #14526807C2semidirect
4. #14526783C2semidirect
6. C2×#10587612C4semidirect
8. #11762748C4semidirect
10. #11762739C4semidirect
16. C4×C22⋊Dic17C4semidirect
232. C17#11727semidirect

Maximal subgroups

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

subgroupindex
#145320432
#145271052
#145268072
#145267832
C4×C17×#992
#1172717