Finite Group Databasebeta

← #17949884

Subgroups — #17949884

Order 4352.

510 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 94 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#14544569C211yesmaximal, characteristic, complemented
2#14544501C211yesmaximal, characteristic, complemented
3#14543603C212yesmaximal, complemented
4#14543601C212yesmaximal
5#14531245C211yesmaximal, characteristic
6C2×#10587544—21no—
7C2×#10587542—21no—
8C2×#10587542—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×C4×D68C411yescharacteristic
13C2×#10587558—21no—
14#11762710C411yescharacteristic
15#11762710C2211yescharacteristic
16#11762705C411yescharacteristic
17#11762705C2211yescharacteristic
18#11762698—21no—
19#11762698—21no—
20C4×#63227—21no—
21C42×Dic17C2211yescharacteristic
22C4×C4⋊C4×C17C411yescharacteristic
23C22×D68C2×C411yescharacteristic
24C22×C4×D17—21no—
25C22×#3624—22no—
26C22×#3624—22no—
27C2×C4⋊C4×C17C2×C411yescharacteristic
28C2×C4⋊C4×C17C2×C411yescharacteristic
29C2×C42×C17—21no—
30C2×C42×C17C2×C411yescharacteristic
31C2×#63227—21no—
32C2×#63227—21no—
33C2×#63227—21no—
34C2×#63227—21no—
35C2×#63227—21no—
36C2×C4⋊Dic17C2×C411yescharacteristic
37C2×#63225—21no—
38C2×#63225—21no—
39C2×C4×Dic17C2×C411yescharacteristic
40C2×C4×Dic17D411yescharacteristic
41C2×C4×Dic17D411yescharacteristic
42C2×C4×Dic17D411yescharacteristic
43C2×C4×Dic17D411yescharacteristic
44C2×C4×Dic17C2311yescharacteristic
45C4×D68—22no—
46C4×D68—22no—
47#10587558—44no—
48#10587544—24no—
49#10587542—24no—
50#10587542—42no—
51C17×#95—21no—
52#10587502—21no—
53#10587502—21no—
54C23×D17—21no—
55C22×C4×C17—21no—
56C22×C4×C17—21no—
57C22×C4×C17C22⋊C411yescharacteristic
58C22×C4×C17C22⋊C411yescharacteristic
59C22×C4×C17C22×C411yescharacteristic
60C22×Dic17—21no—
61C22×Dic17C22⋊C411yescharacteristic
62C22×Dic17C22⋊C411yescharacteristic
63C22×Dic17C2×D411yescharacteristic
64C22×Dic17C2×D411yescharacteristic
65C2×D68—21no—
66C2×D68—41no—
67C2×D68—41no—
68C2×D68M1612yes—
69C2×C4×D17—24no—
70C2×C4×D17—42no—
71C2×C4×D17—42no—
72C2×#3624—24no—
73C2×#3624—24no—
74C2×#3624—42no—
75C2×#3624—42no—
76C2×#3624—42no—
77C2×#3624—42no—
78C4⋊C4×C17—41no—
79C4⋊C4×C17—41no—
80C42×C17—21no—
81C42×C17—21no—
82C42×C17—42no—
83#63227—24no—
84#63227—42no—
85#63227—42no—
86#63227—42no—
87#63227—41no—
88#63227—41no—
89C4⋊Dic17—21no—
90C4⋊Dic17M1612yes—
91#63225—42no—
92#63225—42no—
93C4×Dic17—22no—
94C4×Dic17—22no—
95C4×Dic17—21no—
96C4×Dic17—22no—
97C4×Dic17—21no—
98C4×Dic17—41no—
99C4×Dic17—41no—
100#7628—171nomaximal, Sylow
101C23×C17C2×C22⋊C411yescharacteristic
102C22×D17—22no—
103C22×D17—41no—
104C22×D17—41no—
105C22×D17—41no—
106C22×D17—41no—
107C22×D17—41no—
108C22×D17—41no—
109C2×C4×C17—21no—
110C2×C4×C17—21no—
111C2×C4×C17—21no—
112C2×C4×C17—21no—
113C2×C4×C17—21no—
114C2×C4×C17—21no—
115C2×C4×C17—21no—
116C2×C4×C17—41no—
117C2×C4×C17—41no—
118C2×C4×C17—41no—
119C2×C4×C17—41no—
120C2×C4×C17—41no—
121C2×C4×C17—41no—
122C2×C4×C17#10412yes—
123C2×C4×C17C2×M1611yescharacteristic
124C2×C4×C17C2×M1611yescharacteristic
125C2×Dic17—21no—
126C2×Dic17—21no—
127C2×Dic17—21no—
128C2×Dic17—21no—
129C2×Dic17—21no—
130C2×Dic17—21no—
131C2×Dic17—22no—
132C2×Dic17—21no—
133C2×Dic17—21no—
134C2×Dic17—21no—
135C2×Dic17—41no—
136C2×Dic17—41no—
137C2×Dic17#10412yes—
138C2×Dic17AGL(1,ℤ/8)11yescharacteristic
139C2×Dic17AGL(1,ℤ/8)12yes—
140C2×Dic17#13711yescharacteristic
141D68—42no—
142D68—42no—
143C4×D17—48no—
144#3624—44no—
145#3624—44no—
146#2293—171no—
147#1767—171no—
148#1745—171no—
149#1271—172no—
150#1270—172no—
151C22×C17#40711yescharacteristic
152C22×C17#41011yescharacteristic
153C22×C17#41311yescharacteristic
154C22×C17#41711yescharacteristic
155C22×C17#41811yescharacteristic
156C22×C17C2×#10411yescharacteristic
157C22×C17C2×#10411yescharacteristic
158C2×D17—42no—
159C2×D17—42no—
160C2×D17—42no—
161C2×D17—81no—
162C2×D17—81no—
163C2×D17—81no—
164C2×D17—81no—
165C4×C17—21no—
166C4×C17—21no—
167C4×C17—22no—
168C4×C17—41no—
169C4×C17—81no—
170C4×C17—81no—
171Dic17—22no—
172Dic17—21no—
173Dic17—21no—
174Dic17—22no—
175Dic17—41no—
176Dic17—42no—
177C2×C4×D4—171no—
178C2×#117—341no—
179C2×C4⋊C8—341no—
180C2×#97—341no—
181C2×#97—341no—
182#390—171no—
183#390—171no—
184#389—171no—
185#389—171no—
186#388—341no—
187#388—341no—
188C4×C4⋊C4#59511yescharacteristic
189C4×C22⋊C4—341no—
190C43—171no—
191#336—172no—
192#336—172no—
193#336—341no—
194C2×C17#146411yescharacteristic
195C2×C17#148911yescharacteristic
196C2×C17#149011yescharacteristic
197C2×C17#150511yescharacteristic
198C2×C17#150911yescharacteristic
199C2×C17#152411yescharacteristic
200C2×C17#155711yescharacteristic
201D17—82no—
202C22×D4—171no—
203C23×C4—341no—
204C22×C8—342no—
205C22×C8—342no—
206C4×D4—342no—
207C4×D4—342no—
208#117—684no—
209C2×C4⋊C4—171no—
210C2×C4⋊C4—341no—
211C2×C4⋊C4—341no—
212C2×C4⋊C4C2×#59511yescharacteristic
213C2×C4⋊C4C2×#59511yescharacteristic
214C2×C22⋊C4—341no—
215C2×C22⋊C4—341no—
216C2×C22⋊C4—341no—
217C2×C22⋊C4—341no—
218C2×C22⋊C4—341no—
219C2×C42—21no—
220C2×C42—171no—
221C2×C42—171no—
222C2×C42—171no—
223C2×C42—171no—
224C2×C42—171no—
225C2×C42—171no—
226C2×C42C2×#59511yescharacteristic
227C4⋊C8—344no—
228#97—344no—
229#97—682no—
230#95—21no—
231#95—341no—
232#95—341no—
233C17#762811yescharacteristic, complemented, Sylow
234C24—341no—
235C2×D4—172no—
236C2×D4—341no—
237C2×D4—681no—
238C2×D4—681no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—171no—
242C22×C4—171no—
243C22×C4—171no—
244C22×C4—171no—
245C22×C4—344no—
246C22×C4—341no—
247C22×C4—682no—
248C22×C4—682no—
249C22×C4C22⋊#59511yescharacteristic
250C22×C4C22⋊#59511yescharacteristic
251C22×C4C22×#59511yescharacteristic
252C2×C8—344no—
253C2×C8—344no—
254C2×C8—682no—
255C2×C8—682no—
256C2×C8—682no—
257C2×C8—682no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—172no—
261C4⋊C4—341no—
262C4⋊C4—682no—
263C4⋊C4—682no—
264C22⋊C4—344no—
265C22⋊C4—682no—
266C22⋊C4—681no—
267C22⋊C4—681no—
268C22⋊C4—682no—
269C22⋊C4—682no—
270C42—21no—
271C42—21no—
272C42—42no—
273C42—342no—
274C42—341no—
275C42—342no—
276C42—341no—
277C42—342no—
278C42—681no—
279C42—681no—
280C23—342no—
281C23—681no—
282C23—681no—
283C23—681no—
284C23—681no—
285C23—681no—
286C23—681no—
287C23C2×C22⋊#59511yescharacteristic
288D4—682no—
289D4—682no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—171no—
304C2×C4—171no—
305C2×C4—172no—
306C2×C4—172no—
307C2×C4—341no—
308C2×C4—341no—
309C2×C4—341no—
310C2×C4—341no—
311C2×C4—341no—
312C2×C4—341no—
313C2×C4—342no—
314C2×C4—341no—
315C2×C4—341no—
316C2×C4—341no—
317C2×C4—688no—
318C2×C4—681no—
319C2×C4—681no—
320C2×C4#1058755012yes—
321C2×C4D17⋊M1611yescharacteristic
322C2×C4D17⋊M1611yescharacteristic
323C8—684no—
324C8—684no—
325C22—682no—
326C22—682no—
327C22—682no—
328C22—1361no—
329C22—1361no—
330C22—1361no—
331C22—1361no—
332C22#1176378111yescharacteristic
333C22#1176378811yescharacteristic
334C22#1176379511yescharacteristic
335C22#1176380011yescharacteristic
336C22#1176380111yescharacteristic
337C22D17⋊#10411yescharacteristic
338C22C2×#1058755011yescharacteristic
339C4—21no—
340C4—21no—
341C4—22no—
342C4—41no—
343C4—81no—
344C4—81no—
345C4—342no—
346C4—341no—
347C4—341no—
348C4—342no—
349C4—681no—
350C4—682no—
351C2—1362no—
352C2#1454403711yescharacteristic
353C2#1454412111yescharacteristic
354C2#1454412511yescharacteristic
355C2#1454417411yescharacteristic
356C2#1454418811yescharacteristic
357C2#1454423611yescharacteristic
358C2#1454431511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC4×C4⋊C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC22×D68C2×C4
cosocleC2×C4×Dic17C23
hypercenterC4×C4⋊C4#595
hypocenterC17#7628
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #14544569C2semidirect
2. #14544501C2semidirect
3. #14543603C2semidirect
233. C17#7628semidirect

Maximal subgroups

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

subgroupindex
#145445692
#145445012
#145436032
#145436012
#145312452
#762817