Finite Group Databasebeta

← #17949720

Subgroups — #17949720

Order 4352.

606 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 606 conjugacy classes of subgroups — too many to draw. Only its 110 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#14544676C211yesmaximal, characteristic, complemented
2C4×#10587543C211yesmaximal, characteristic, complemented
3#14543603C212yesmaximal, complemented
4#14543600C212yesmaximal, complemented
5C4×#10587624C211yesmaximal, characteristic
6C2×#10587543—21no—
7C2×#10587543—21no—
8C2×C4×#3624—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587624C411yescharacteristic
13C2×C4×C22⋊D17—21no—
14C2×C42×D17C2211yescharacteristic
15#11762712C2211yescharacteristic
16#11762705C2211yescharacteristic
17#11762697—21no—
18#11762685—21no—
19#11762666C411yescharacteristic
20C4×C4⋊Dic17C411yescharacteristic
21C4×C22⋊Dic17—21no—
22C2×C4×D4×C17C411yescharacteristic
23C22×D4×C17C2×C411yescharacteristic
24C23×C4×C17—21no—
25C22×C22⋊D17—21no—
26C22×C4×D17C2×C411yescharacteristic
27C22×C4×D17D411yescharacteristic
28C22×C4×D17D411yescharacteristic
29C22×#3624—22no—
30C22×#3624—22no—
31C4×D4×C17—42no—
32C2×C4⋊C4×C17C2×C411yescharacteristic
33C2×C22⋊C4×C17—21no—
34C2×C42×C17C2×C411yescharacteristic
35C2×C22⋊Dic17—21no—
36C2×C22⋊Dic17—21no—
37C2×C22⋊Dic17—21no—
38#10587624—22no—
39#10587624C814yescomplemented
40C4×C22⋊D17—44no—
41C2×#63227—21no—
42C2×C4⋊Dic17C2×C411yescharacteristic
43C2×C4⋊Dic17C2×C411yescharacteristic
44C2×#63225—21no—
45C2×C4×Dic17—21no—
46C2×C4×Dic17D411yescharacteristic
47C2×C4×Dic17D411yescharacteristic
48C2×C4×Dic17C2311yescharacteristic
49C42×D17—42no—
50#10587543—24no—
51#10587543—42no—
52C4×#3624—42no—
53#10587502—21no—
54#10587502—21no—
55#10587502—21no—
56C24×C17—21no—
57C23×D17C22⋊C411yescharacteristic
58C2×D4×C17—21no—
59C2×D4×C17—41no—
60C2×D4×C17—41no—
61C2×D4×C17C2×C812yes—
62C22×C4×C17—21no—
63C22×C4×C17—42no—
64C22×C4×C17—42no—
65C22×C4×C17—42no—
66C22×C4×C17C22⋊C411yescharacteristic
67C22×C4×C17C22⋊C411yescharacteristic
68C22×C4×C17C22×C411yescharacteristic
69C2×C22⋊D17—24no—
70C2×C22⋊D17—42no—
71C2×C22⋊D17—42no—
72C22×Dic17—21no—
73C22×Dic17—21no—
74C22×Dic17C22⋊C411yescharacteristic
75C22×Dic17C2×D411yescharacteristic
76C22×Dic17C2×D411yescharacteristic
77C2×C4×D17—22no—
78C2×C4×D17—22no—
79C2×C4×D17—22no—
80C2×C4×D17—22no—
81C2×C4×D17—41no—
82C2×C4×D17—41no—
83C2×C4×D17—41no—
84C2×C4×D17—41no—
85C2×C4×D17C2×C812yes—
86C2×C4×D17M1612yes—
87C2×#3624—24no—
88C2×#3624—42no—
89C2×#3624—42no—
90C2×#3624—42no—
91C2×#3624—42no—
92C2×#3624—42no—
93C4⋊C4×C17—41no—
94C22⋊C4×C17—42no—
95C42×C17—22no—
96C22⋊Dic17—24no—
97C22⋊Dic17—42no—
98C22⋊Dic17—42no—
99#63227—42no—
100C4⋊Dic17—21no—
101C4⋊Dic17—41no—
102C4⋊Dic17C2×C812yes—
103#63225—42no—
104C4×Dic17—22no—
105C4×Dic17—41no—
106C4×Dic17—41no—
107C4×Dic17—42no—
108#7582—171nomaximal, Sylow
109C23×C17—22no—
110C23×C17—41no—
111C23×C17—41no—
112C23×C17—41no—
113C23×C17—41no—
114C23×C17—41no—
115C23×C17—41no—
116C23×C17C2×C22⋊C411yescharacteristic
117C22×D17—21no—
118C22×D17—21no—
119C22×D17—21no—
120C22×D17—21no—
121C22×D17—21no—
122C22×D17—21no—
123C22×D17C22⋊C812yes—
124D4×C17—42no—
125D4×C17—42no—
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—84no—
136C2×C4×C17#9912yes—
137C2×C4×C17#10412yes—
138C2×C4×C17C22×C811yescharacteristic
139C2×C4×C17C2×M1611yescharacteristic
140C22⋊D17—48no—
141C2×Dic17—21no—
142C2×Dic17—21no—
143C2×Dic17—21no—
144C2×Dic17—21no—
145C2×Dic17—21no—
146C2×Dic17—21no—
147C2×Dic17—22no—
148C2×Dic17—41no—
149C2×Dic17—41no—
150C2×Dic17—41no—
151C2×Dic17—41no—
152C2×Dic17—41no—
153C2×Dic17C22⋊C812yes—
154C2×Dic17#13512yes—
155C2×Dic17AGL(1,ℤ/8)12yes—
156C4×D17—42no—
157C4×D17—42no—
158C4×D17—44no—
159C4×D17—44no—
160#3624—44no—
161#3624—82no—
162C4×#121—171no—
163#1817—171no—
164C4×C22⋊C8—171no—
165#1271—172no—
166#1270—172no—
167C22×C17—42no—
168C22×C17—42no—
169C22×C17—42no—
170C22×C17—81no—
171C22×C17—81no—
172C22×C17—81no—
173C22×C17—81no—
174C22×C17C2×C22⋊C811yescharacteristic
175C22×C17C2×#9911yescharacteristic
176C22×C17#41311yescharacteristic
177C22×C17#41611yescharacteristic
178C22×C17#41811yescharacteristic
179C22×C17C2×#10411yescharacteristic
180C22×C17#42111yescharacteristic
181C2×D17—22no—
182C2×D17—22no—
183C2×D17—22no—
184C2×D17—41no—
185C2×D17—41no—
186C2×D17—41no—
187C2×D17—41no—
188C4×C17—21no—
189C4×C17—21no—
190C4×C17—22no—
191C4×C17—22no—
192C4×C17—81no—
193Dic17—22no—
194Dic17—22no—
195Dic17—22no—
196Dic17—42no—
197Dic17—81no—
198C2×#121—171no—
199C2×C4×D4—341no—
200C2×C4×D4#59511yescharacteristic
201C22×C42—171no—
202C2×C22⋊C8—341no—
203C2×C22⋊C8—341no—
204C2×C4×C8—341no—
205#390—171no—
206#389—171no—
207#388—341no—
208#386—341no—
209#380—171no—
210C4×C4⋊C4—171no—
211C4×C22⋊C4—341no—
212#336—172no—
213#336—172no—
214#336—341no—
215C2×C17—82no—
216C2×C17#145911yescharacteristic
217C2×C17#147611yescharacteristic
218C2×C17#147811yescharacteristic
219C2×C17#150711yescharacteristic
220C2×C17#151611yescharacteristic
221C2×C17#152911yescharacteristic
222C2×C17#155311yescharacteristic
223D17—42no—
224C22×D4—341no—
225C22×D4C2×#59511yescharacteristic
226C23×C4—21no—
227C23×C4—171no—
228C23×C4—171no—
229C23×C4—171no—
230C22×C8—342no—
231C22×C8—342no—
232#121—174no—
233#121—342no—
234C4×D4—42no—
235C4×D4—684no—
236C2×C4⋊C4—171no—
237C2×C4⋊C4—171no—
238C2×C4⋊C4—341no—
239C2×C4⋊C4C2×#59511yescharacteristic
240C2×C22⋊C4—21no—
241C2×C22⋊C4—341no—
242C2×C22⋊C4—341no—
243C2×C22⋊C4—341no—
244C2×C22⋊C4—341no—
245C2×C42—171no—
246C2×C42—171no—
247C2×C42—171no—
248C2×C42—341no—
249C2×C42—682no—
250C2×C42C2×#59511yescharacteristic
251C22⋊C8—344no—
252C22⋊C8—682no—
253C4×C8—682no—
254#95—341no—
255#95—341no—
256#95—341no—
257C17#758211yescharacteristic, complemented, Sylow
258C24—21no—
259C24—171no—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—344no—
264C2×D4—682no—
265C2×D4—682no—
266C2×D4#6324212yes—
267C22×C4—21no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—171no—
272C22×C4—171no—
273C22×C4—171no—
274C22×C4—172no—
275C22×C4—172no—
276C22×C4—342no—
277C22×C4—342no—
278C22×C4—341no—
279C22×C4—342no—
280C22×C4—342no—
281C22×C4—341no—
282C22×C4—681no—
283C22×C4—681no—
284C22×C4—681no—
285C22×C4—681no—
286C22×C4C22⋊#59511yescharacteristic
287C22×C4C22⋊#59511yescharacteristic
288C22×C4C22×#59511yescharacteristic
289C2×C8—344no—
290C2×C8—682no—
291C2×C8—682no—
292C2×C8—682no—
293C2×C8—682no—
294C2×C8—682no—
295C4⋊C4—41no—
296C4⋊C4—172no—
297C4⋊C4—341no—
298C4⋊C4—681no—
299C4⋊C4—682no—
300C22⋊C4—42no—
301C22⋊C4—344no—
302C22⋊C4—682no—
303C22⋊C4—682no—
304C22⋊C4—682no—
305C42—22no—
306C42—342no—
307C42—681no—
308C42—681no—
309C42—682no—
310C23—22no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—172no—
318C23—341no—
319C23—341no—
320C23—341no—
321C23—341no—
322C23—341no—
323C23—341no—
324C23C2×C22⋊#59511yescharacteristic
325D4—42no—
326D4—42no—
327D4—688no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—84no—
338C2×C4—172no—
339C2×C4—172no—
340C2×C4—172no—
341C2×C4—341no—
342C2×C4—341no—
343C2×C4—341no—
344C2×C4—341no—
345C2×C4—341no—
346C2×C4—341no—
347C2×C4—342no—
348C2×C4—682no—
349C2×C4—682no—
350C2×C4—684no—
351C2×C4—684no—
352C2×C4—681no—
353C2×C4—681no—
354C2×C4—681no—
355C2×C4—681no—
356C2×C4—681no—
357C2×C4#1058754812yes—
358C2×C4#1058755112yes—
359C2×C4C2×#6324211yescharacteristic
360C2×C4D17⋊M1611yescharacteristic
361C8—684no—
362C8—1362no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—342no—
371C22—342no—
372C22—342no—
373C22—681no—
374C22—681no—
375C22—681no—
376C22—681no—
377C22#1176377711yescharacteristic
378C22C2×#1058755111yescharacteristic
379C22#1176379511yescharacteristic
380C22#1176379911yescharacteristic
381C22#1176380111yescharacteristic
382C22C2×#1058754811yescharacteristic
383C22#1176380611yescharacteristic
384C4—22no—
385C4—22no—
386C4—21no—
387C4—21no—
388C4—81no—
389C4—342no—
390C4—342no—
391C4—342no—
392C4—682no—
393C4—1361no—
394C2—82no—
395C2—682no—
396C2#1454401911yescharacteristic
397C2#1454407611yescharacteristic
398C2#1454408411yescharacteristic
399C2#1454418011yescharacteristic
400C2#1454421011yescharacteristic
401C2#1454424911yescharacteristic
402C2#1454430711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC2×C4×D4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC2×#10587624C4
cosocleC2×C4×Dic17C23
hypercenterC2×C4×D4#595
hypocenterC17#7582
LCSG ▷ C2×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. #14544676C2semidirect
2. C4×#10587543C2semidirect
3. #14543603C2semidirect
4. #14543600C2semidirect
39. #10587624C8semidirect
257. C17#7582semidirect

Maximal subgroups

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

subgroupindex
#145446762
C4×#105875432
#145436032
#145436002
C4×#105876242
#758217