Finite Group Databasebeta

← #17949784

Subgroups — #17949784

Order 4352.

504 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 106 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
2#14544641C211yesmaximal, characteristic
3#14543605C212yesmaximal, complemented
4#14543602C212yesmaximal, complemented
5C4×#10587583C211yesmaximal, characteristic
6C2×#10587544—21no—
7C2×#10587543—21no—
8C2×#10587543—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587583C411yescharacteristic
13C2×C4×Dic34C411yescharacteristic
14C2×C42×D17C2211yescharacteristic
15#11762714C2211yescharacteristic
16#11762708C2211yescharacteristic
17#11762694—21no—
18#11762683—21no—
19#11762666C411yescharacteristic
20C4×C4⋊Dic17—21no—
21C4×#63227—21no—
22C4×C4⋊C4×C17C411yescharacteristic
23C22×C4×D17C2×C411yescharacteristic
24C22×C4×D17D411yescharacteristic
25C22×C4×D17D411yescharacteristic
26C22×Dic34C2×C411yescharacteristic
27C22×#3624—22no—
28C22×#3624—22no—
29C2×C4⋊C4×C17C2×C411yescharacteristic
30C2×C4⋊C4×C17C2×C411yescharacteristic
31C2×C42×C17—21no—
32C2×C42×C17C2×C411yescharacteristic
33C2×#63227—21no—
34C2×#63227—21no—
35C2×C4⋊Dic17—21no—
36C2×C4⋊Dic17—21no—
37C2×C4⋊Dic17C2×C411yescharacteristic
38C2×#63225—21no—
39C2×C4×Dic17—21no—
40C2×C4×Dic17D411yescharacteristic
41C2×C4×Dic17D411yescharacteristic
42C2×C4×Dic17C2311yescharacteristic
43#10587583—22no—
44#10587583C814yescomplemented
45C42×D17—42no—
46C4×Dic34—42no—
47#10587544—42no—
48#10587543—42no—
49#10587543—42no—
50C17×#95—21no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54#10587502—21no—
55C23×D17C22⋊C411yescharacteristic
56C22×C4×C17—21no—
57C22×C4×C17—21no—
58C22×C4×C17C22⋊C411yescharacteristic
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22×C411yescharacteristic
61C22×Dic17—21no—
62C22×Dic17—21no—
63C22×Dic17C22⋊C411yescharacteristic
64C22×Dic17C2×D411yescharacteristic
65C22×Dic17C2×D411yescharacteristic
66C2×C4×D17—22no—
67C2×C4×D17—21no—
68C2×C4×D17—22no—
69C2×C4×D17—21no—
70C2×C4×D17—41no—
71C2×C4×D17—41no—
72C2×C4×D17—41no—
73C2×C4×D17—41no—
74C2×C4×D17—41no—
75C2×C4×D17C2×C812yes—
76C2×C4×D17M1612yes—
77C2×Dic34—21no—
78C2×Dic34—41no—
79C2×Dic34—41no—
80C2×Dic34C2×C812yes—
81C2×#3624—42no—
82C2×#3624—42no—
83C2×#3624—42no—
84C2×#3624—42no—
85C2×#3624—42no—
86C2×#3624—42no—
87C4⋊C4×C17—21no—
88C4⋊C4×C17—41no—
89C4⋊C4×C17C2×C812yes—
90C42×C17—22no—
91C42×C17—42no—
92#63227—24no—
93#63227—42no—
94C4⋊Dic17—24no—
95C4⋊Dic17—41no—
96C4⋊Dic17—41no—
97C4⋊Dic17—41no—
98#63225—42no—
99C4×Dic17—22no—
100C4×Dic17—41no—
101C4×Dic17—41no—
102C4×Dic17—42no—
103#7600—171nomaximal, Sylow
104C23×C17C2×C22⋊C411yescharacteristic
105C22×D17—21no—
106C22×D17—21no—
107C22×D17—21no—
108C22×D17—21no—
109C22×D17—21no—
110C22×D17—21no—
111C22×D17C22⋊C812yes—
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—21no—
120C2×C4×C17—41no—
121C2×C4×C17—41no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17#9912yes—
126C2×C4×C17C22×C811yescharacteristic
127C2×C4×C17C2×M1611yescharacteristic
128C2×Dic17—21no—
129C2×Dic17—21no—
130C2×Dic17—21no—
131C2×Dic17—21no—
132C2×Dic17—21no—
133C2×Dic17—21no—
134C2×Dic17—22no—
135C2×Dic17—41no—
136C2×Dic17—41no—
137C2×Dic17—41no—
138C2×Dic17—41no—
139C2×Dic17—41no—
140C2×Dic17C22⋊C812yes—
141C2×Dic17AGL(1,ℤ/8)11yescharacteristic
142C2×Dic17#13711yescharacteristic
143C2×Dic17#13712yes—
144C4×D17—42no—
145C4×D17—42no—
146C4×D17—44no—
147C4×D17—42no—
148C4×D17—42no—
149Dic34—42no—
150Dic34—42no—
151#3624—82no—
152#3624—82no—
153C4×C22⋊Q8—171no—
154#1817—171no—
155#1797—171no—
156#1272—172no—
157#1271—172no—
158C22×C17C2×C22⋊C811yescharacteristic
159C22×C17C2×#9911yescharacteristic
160C22×C17#41311yescharacteristic
161C22×C17#41711yescharacteristic
162C22×C17#41911yescharacteristic
163C22×C17#42111yescharacteristic
164C22×C17#42111yescharacteristic
165C2×D17—22no—
166C2×D17—22no—
167C2×D17—22no—
168C2×D17—41no—
169C2×D17—41no—
170C2×D17—41no—
171C2×D17—41no—
172C4×C17—21no—
173C4×C17—21no—
174C4×C17—22no—
175C4×C17—42no—
176C4×C17—41no—
177C4×C17—81no—
178Dic17—22no—
179Dic17—22no—
180Dic17—21no—
181Dic17—21no—
182Dic17—42no—
183Dic17—81no—
184C2×C22⋊Q8—171no—
185C2×C4×Q8—171no—
186C22×C42—171no—
187C2×C4⋊C8—341no—
188C2×C22⋊C8—341no—
189C2×C22⋊C8—341no—
190#391—171no—
191#389—171no—
192#387—341no—
193#385—341no—
194#380—171no—
195C4×C4⋊C4—341no—
196C4×C4⋊C4#59511yescharacteristic
197C4×C22⋊C4—341no—
198#336—172no—
199#336—172no—
200#336—341no—
201C2×C17#145911yescharacteristic
202C2×C17#147711yescharacteristic
203C2×C17#147911yescharacteristic
204C2×C17#151111yescharacteristic
205C2×C17#151311yescharacteristic
206C2×C17#153511yescharacteristic
207C2×C17#155911yescharacteristic
208D17—42no—
209C22×Q8—171no—
210C23×C4—171no—
211C23×C4—171no—
212C23×C4—171no—
213C22×C8—342no—
214C22×C8—342no—
215C22⋊Q8—174no—
216C22⋊Q8—342no—
217C4×Q8—682no—
218C2×C4⋊C4—171no—
219C2×C4⋊C4—341no—
220C2×C4⋊C4—341no—
221C2×C4⋊C4—341no—
222C2×C4⋊C4C2×#59511yescharacteristic
223C2×C4⋊C4C2×#59511yescharacteristic
224C2×C22⋊C4—341no—
225C2×C22⋊C4—341no—
226C2×C42—21no—
227C2×C42—171no—
228C2×C42—171no—
229C2×C42—171no—
230C2×C42—341no—
231C2×C42—682no—
232C2×C42C2×#59511yescharacteristic
233C4⋊C8—682no—
234C22⋊C8—682no—
235C22⋊C8—682no—
236#95—21no—
237#95—341no—
238#95—341no—
239#95—341no—
240#95—341no—
241C17#760011yescharacteristic, complemented, Sylow
242C24—171no—
243C2×Q8—172no—
244C2×Q8—341no—
245C2×Q8—681no—
246C2×Q8—681no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—171no—
250C22×C4—171no—
251C22×C4—171no—
252C22×C4—172no—
253C22×C4—172no—
254C22×C4—341no—
255C22×C4—342no—
256C22×C4—341no—
257C22×C4—341no—
258C22×C4—342no—
259C22×C4—341no—
260C22×C4—681no—
261C22×C4—681no—
262C22×C4—681no—
263C22×C4—681no—
264C22×C4—681no—
265C22×C4C22⋊#59511yescharacteristic
266C22×C4C22⋊#59511yescharacteristic
267C22×C4C22×#59511yescharacteristic
268C2×C8—682no—
269C2×C8—682no—
270C2×C8—682no—
271C2×C8—682no—
272C2×C8—682no—
273C2×C8—682no—
274C4⋊C4—21no—
275C4⋊C4—41no—
276C4⋊C4—344no—
277C4⋊C4—681no—
278C4⋊C4—682no—
279C4⋊C4—681no—
280C4⋊C4—681no—
281C4⋊C4#6324212yes—
282C22⋊C4—344no—
283C22⋊C4—682no—
284C42—22no—
285C42—42no—
286C42—342no—
287C42—681no—
288C42—681no—
289C42—682no—
290C23—172no—
291C23—341no—
292C23—341no—
293C23—341no—
294C23—341no—
295C23—341no—
296C23—341no—
297C23C2×C22⋊#59511yescharacteristic
298Q8—682no—
299Q8—682no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—172no—
314C2×C4—171no—
315C2×C4—171no—
316C2×C4—172no—
317C2×C4—341no—
318C2×C4—341no—
319C2×C4—341no—
320C2×C4—341no—
321C2×C4—341no—
322C2×C4—341no—
323C2×C4—342no—
324C2×C4—682no—
325C2×C4—682no—
326C2×C4—684no—
327C2×C4—682no—
328C2×C4—682no—
329C2×C4—681no—
330C2×C4—681no—
331C2×C4—681no—
332C2×C4—681no—
333C2×C4—681no—
334C2×C4#1058753912yes—
335C2×C4C2×#6324211yescharacteristic
336C2×C4D17⋊M1611yescharacteristic
337C8—1362no—
338C8—1362no—
339C22—342no—
340C22—342no—
341C22—342no—
342C22—681no—
343C22—681no—
344C22—681no—
345C22—681no—
346C22#1176377711yescharacteristic
347C22C2×#1058753911yescharacteristic
348C22#1176379511yescharacteristic
349C22#1176380011yescharacteristic
350C22#1176380211yescharacteristic
351C22#1176380611yescharacteristic
352C22#1176380711yescharacteristic
353C4—22no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—42no—
358C4—81no—
359C4—342no—
360C4—341no—
361C4—341no—
362C4—342no—
363C4—682no—
364C4—1361no—
365C2—682no—
366C2#1454402111yescharacteristic
367C2#1454408011yescharacteristic
368C2#1454408711yescharacteristic
369C2#1454419211yescharacteristic
370C2#1454420111yescharacteristic
371C2#1454426811yescharacteristic
372C2#1454431911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC4×C4⋊C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC4×C4⋊C4#595
hypocenterC17#7600
LCSG ▷ C2×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
3. #14543605C2semidirect
4. #14543602C2semidirect
44. #10587583C8semidirect
241. C17#7600semidirect

Maximal subgroups

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

subgroupindex
#145446762
#145446412
#145436052
#145436022
C4×#105875832
#760017