Finite Group Databasebeta

← #17949882

Subgroups — #17949882

Order 4352.

510 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 98 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#14543602C212yesmaximal, complemented
4#14543600C212yesmaximal
5#14531249C211yesmaximal, characteristic
6C2×#10587544—21no—
7C2×#10587542—21no—
8C2×#10587542—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587612—21no—
13#11762712C411yescharacteristic
14#11762712C2211yescharacteristic
15#11762708C411yescharacteristic
16#11762708C2211yescharacteristic
17#11762702—21no—
18#11762702—21no—
19C4×C4⋊Dic17C411yescharacteristic
20C4×C22⋊Dic17—21no—
21C42×Dic17C2211yescharacteristic
22C2×C4×D4×C17C411yescharacteristic
23C22×D4×C17C2×C411yescharacteristic
24C23×C4×C17—21no—
25C22×#3624—22no—
26C22×#3624—22no—
27C4×D4×C17—22no—
28C4×D4×C17—22no—
29C2×C4⋊C4×C17C2×C411yescharacteristic
30C2×C22⋊C4×C17—21no—
31C2×C42×C17C2×C411yescharacteristic
32C2×C22⋊Dic17—21no—
33C2×C22⋊Dic17—21no—
34C2×C22⋊Dic17—21no—
35C2×C22⋊Dic17—21no—
36#10587612—44no—
37C2×C4⋊Dic17—21no—
38C2×C4⋊Dic17—21no—
39C2×C4⋊Dic17C2×C411yescharacteristic
40C2×C4⋊Dic17C2×C411yescharacteristic
41C2×C4×Dic17—21no—
42C2×C4×Dic17C2×C411yescharacteristic
43C2×C4×Dic17D411yescharacteristic
44C2×C4×Dic17D411yescharacteristic
45C2×C4×Dic17D411yescharacteristic
46C2×C4×Dic17D411yescharacteristic
47C2×C4×Dic17C2311yescharacteristic
48#10587544—24no—
49#10587542—24no—
50#10587542—42no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54C24×C17—21no—
55C2×D4×C17—21no—
56C2×D4×C17—41no—
57C2×D4×C17—41no—
58C2×D4×C17M1612yes—
59C22×C4×C17—24no—
60C22×C4×C17—21no—
61C22×C4×C17—42no—
62C22×C4×C17—42no—
63C22×C4×C17C22⋊C411yescharacteristic
64C22×C4×C17C22⋊C411yescharacteristic
65C22×C4×C17C22×C411yescharacteristic
66C22×Dic17—21no—
67C22×Dic17—21no—
68C22×Dic17C22⋊C411yescharacteristic
69C22×Dic17C22⋊C411yescharacteristic
70C22×Dic17C2×D411yescharacteristic
71C22×Dic17C2×D411yescharacteristic
72C2×#3624—24no—
73C2×#3624—24no—
74C2×#3624—42no—
75C2×#3624—42no—
76C2×#3624—42no—
77C2×#3624—42no—
78C4⋊C4×C17—21no—
79C4⋊C4×C17M1612yes—
80C22⋊C4×C17—24no—
81C42×C17—21no—
82C42×C17—21no—
83C22⋊Dic17—42no—
84C22⋊Dic17—42no—
85C22⋊Dic17—42no—
86C22⋊Dic17—41no—
87C22⋊Dic17—41no—
88C4⋊Dic17—42no—
89C4⋊Dic17—42no—
90C4⋊Dic17—41no—
91C4⋊Dic17—41no—
92C4×Dic17—22no—
93C4×Dic17—22no—
94C4×Dic17—21no—
95C4×Dic17—22no—
96C4×Dic17—21no—
97C4×Dic17—41no—
98C4×Dic17—41no—
99C4×Dic17—42no—
100#7628—171nomaximal, Sylow
101C23×C17—22no—
102C23×C17—41no—
103C23×C17—41no—
104C23×C17—41no—
105C23×C17—41no—
106C23×C17—41no—
107C23×C17—41no—
108C23×C17C2×C22⋊C411yescharacteristic
109D4×C17—42no—
110D4×C17—42no—
111C2×C4×C17—21no—
112C2×C4×C17—21no—
113C2×C4×C17—21no—
114C2×C4×C17—21no—
115C2×C4×C17—21no—
116C2×C4×C17—22no—
117C2×C4×C17—21no—
118C2×C4×C17—21no—
119C2×C4×C17—48no—
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—21no—
132C2×Dic17—21no—
133C2×Dic17—21no—
134C2×Dic17—41no—
135C2×Dic17—41no—
136C2×Dic17—41no—
137C2×Dic17—41no—
138C2×Dic17—41no—
139C2×Dic17—41no—
140C2×Dic17#10412yes—
141C2×Dic17AGL(1,ℤ/8)11yescharacteristic
142C2×Dic17AGL(1,ℤ/8)12yes—
143C2×Dic17#13711yescharacteristic
144#3624—44no—
145#3624—44no—
146#2293—171no—
147#1767—171no—
148#1745—171no—
149#1271—172no—
150#1270—172no—
151C22×C17—42no—
152C22×C17—42no—
153C22×C17—42no—
154C22×C17—81no—
155C22×C17—81no—
156C22×C17—81no—
157C22×C17—81no—
158C22×C17#40711yescharacteristic
159C22×C17#41011yescharacteristic
160C22×C17#41311yescharacteristic
161C22×C17#41711yescharacteristic
162C22×C17#41811yescharacteristic
163C22×C17C2×#10411yescharacteristic
164C22×C17C2×#10411yescharacteristic
165C4×C17—21no—
166C4×C17—21no—
167C4×C17—22no—
168C4×C17—41no—
169C4×C17—42no—
170Dic17—22no—
171Dic17—21no—
172Dic17—21no—
173Dic17—22no—
174Dic17—41no—
175Dic17—81no—
176Dic17—81no—
177C2×C4×D4#59511yescharacteristic
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—171no—
189C4×C22⋊C4—341no—
190C43—171no—
191#336—172no—
192#336—172no—
193#336—341no—
194C2×C17—82no—
195C2×C17#146411yescharacteristic
196C2×C17#148911yescharacteristic
197C2×C17#149011yescharacteristic
198C2×C17#150511yescharacteristic
199C2×C17#150911yescharacteristic
200C2×C17#152411yescharacteristic
201C2×C17#155711yescharacteristic
202C22×D4C2×#59511yescharacteristic
203C23×C4—21no—
204C22×C8—342no—
205C22×C8—342no—
206C4×D4—22no—
207C4×D4—22no—
208#117—684no—
209C2×C4⋊C4—171no—
210C2×C4⋊C4—171no—
211C2×C4⋊C4—341no—
212C2×C4⋊C4—341no—
213C2×C4⋊C4C2×#59511yescharacteristic
214C2×C22⋊C4—21no—
215C2×C22⋊C4—341no—
216C2×C22⋊C4—341no—
217C2×C22⋊C4—341no—
218C2×C22⋊C4—341no—
219C2×C42—171no—
220C2×C42—171no—
221C2×C42—171no—
222C2×C42—171no—
223C2×C42—171no—
224C2×C42—171no—
225C2×C42—341no—
226C2×C42C2×#59511yescharacteristic
227C4⋊C8—344no—
228#97—344no—
229#97—682no—
230#95—341no—
231#95—341no—
232#95—341no—
233C17#762811yescharacteristic, complemented, Sylow
234C24—21no—
235C2×D4—21no—
236C2×D4—41no—
237C2×D4—41no—
238C2×D4#6324712yes—
239C22×C4—24no—
240C22×C4—21no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—171no—
244C22×C4—171no—
245C22×C4—171no—
246C22×C4—171no—
247C22×C4—341no—
248C22×C4—341no—
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—21no—
259C4⋊C4—681no—
260C4⋊C4—681no—
261C4⋊C4—682no—
262C4⋊C4—682no—
263C4⋊C4#6324712yes—
264C22⋊C4—24no—
265C22⋊C4—681no—
266C22⋊C4—681no—
267C22⋊C4—682no—
268C22⋊C4—682no—
269C22⋊C4—682no—
270C42—21no—
271C42—21no—
272C42—342no—
273C42—341no—
274C42—342no—
275C42—341no—
276C42—342no—
277C42—681no—
278C42—681no—
279C42—682no—
280C23—22no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23C2×C22⋊#59511yescharacteristic
288D4—42no—
289D4—42no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—48no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—171no—
302C2×C4—171no—
303C2×C4—172no—
304C2×C4—172no—
305C2×C4—341no—
306C2×C4—341no—
307C2×C4—341no—
308C2×C4—341no—
309C2×C4—341no—
310C2×C4—341no—
311C2×C4—341no—
312C2×C4—341no—
313C2×C4—341no—
314C2×C4—681no—
315C2×C4—681no—
316C2×C4—681no—
317C2×C4—681no—
318C2×C4—681no—
319C2×C4—681no—
320C2×C4#1058754812yes—
321C2×C4C2×#6324711yescharacteristic
322C2×C4C2×#6324711yescharacteristic
323C8—684no—
324C8—684no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22#1176377911yescharacteristic
333C22#1176378811yescharacteristic
334C22#1176379511yescharacteristic
335C22#1176380011yescharacteristic
336C22#1176380111yescharacteristic
337C22C2×#1058754811yescharacteristic
338C22D17⋊#10411yescharacteristic
339C4—21no—
340C4—21no—
341C4—22no—
342C4—41no—
343C4—42no—
344C4—342no—
345C4—341no—
346C4—341no—
347C4—342no—
348C4—681no—
349C4—1361no—
350C4—1361no—
351C2—82no—
352C2#1454403511yescharacteristic
353C2#1454411911yescharacteristic
354C2#1454412311yescharacteristic
355C2#1454417411yescharacteristic
356C2#1454418611yescharacteristic
357C2#1454423411yescharacteristic
358C2#1454431511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C4×D4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC22×D4×C17C2×C4
cosocleC2×C4×Dic17C23
hypercenterC2×C4×D4#595
hypocenterC17#7628
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #14544569C2semidirect
2. #14544501C2semidirect
3. #14543602C2semidirect
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
#145436022
#145436002
#145312492
#762817