Finite Group Databasebeta

← #17949880

Subgroups — #17949880

Order 4352.

594 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 102 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#14544511C211yesmaximal, characteristic
2#14544511C211yesmaximal, characteristic
3#14543603C212yesmaximal, complemented
4#14543602C212yesmaximal, complemented
5D17×#389C211yesmaximal, characteristic
6C2×#10587543—21no—
7C2×#10587543—21no—
8C2×#10587542—21no—
9C2×#10587542—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×C4⋊C4×D17—21no—
13C2×C4⋊C4×D17C411yescharacteristic
14C2×C4⋊C4×D17C411yescharacteristic
15C2×C42×D17C2211yescharacteristic
16#11762708C2211yescharacteristic
17#11762707C411yescharacteristic
18#11762706—21no—
19#11762705C2211yescharacteristic
20#11762704—21no—
21#95×D17—21no—
22C17×#389C411yescharacteristic
23C22×C4×D17—21no—
24C22×C4×D17—21no—
25C22×C4×D17C2×C411yescharacteristic
26C22×C4×D17D411yescharacteristic
27C22×C4×D17D411yescharacteristic
28C22×#3624—22no—
29C22×#3624—22no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17C2×C411yescharacteristic
32C2×C4⋊C4×C17C2×C411yescharacteristic
33C2×C42×C17C2×C411yescharacteristic
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17C2×C411yescharacteristic
36C2×C4⋊Dic17C2×C411yescharacteristic
37C2×#63225—21no—
38C2×#63225—21no—
39C2×#63225—21no—
40C2×#63225—21no—
41C2×C4×Dic17D411yescharacteristic
42C2×C4×Dic17D411yescharacteristic
43C2×C4×Dic17C2311yescharacteristic
44C4⋊C4×D17—22no—
45C4⋊C4×D17—22no—
46C4⋊C4×D17—44no—
47C4⋊C4×D17—42no—
48C42×D17—42no—
49#10587543—24no—
50#10587543—24no—
51#10587542—42no—
52#10587542—42no—
53C17×#95—21no—
54#10587502—21no—
55#10587502—21no—
56#10587502—21no—
57C23×D17C22⋊C411yescharacteristic
58C22×C4×C17—21no—
59C22×C4×C17—21no—
60C22×C4×C17C22⋊C411yescharacteristic
61C22×C4×C17C22⋊C411yescharacteristic
62C22×C4×C17C22×C411yescharacteristic
63C22×Dic17—21no—
64C22×Dic17—21no—
65C22×Dic17C22⋊C411yescharacteristic
66C22×Dic17C2×D411yescharacteristic
67C22×Dic17C2×D411yescharacteristic
68C2×C4×D17—22no—
69C2×C4×D17—21no—
70C2×C4×D17—21no—
71C2×C4×D17—22no—
72C2×C4×D17—24no—
73C2×C4×D17—22no—
74C2×C4×D17—22no—
75C2×C4×D17—22no—
76C2×C4×D17—22no—
77C2×C4×D17—41no—
78C2×C4×D17—41no—
79C2×C4×D17—42no—
80C2×C4×D17—42no—
81C2×C4×D17—42no—
82C2×C4×D17—42no—
83C2×C4×D17—42no—
84C2×#3624—24no—
85C2×#3624—24no—
86C2×#3624—42no—
87C2×#3624—42no—
88C2×#3624—42no—
89C2×#3624—42no—
90C4⋊C4×C17—21no—
91C4⋊C4×C17—41no—
92C4⋊C4×C17—42no—
93C4⋊C4×C17M1612yes—
94C42×C17—41no—
95C4⋊Dic17—21no—
96C4⋊Dic17—42no—
97C4⋊Dic17—41no—
98C4⋊Dic17M1612yes—
99#63225—24no—
100#63225—42no—
101#63225—42no—
102#63225—42no—
103C4×Dic17—22no—
104C4×Dic17—22no—
105C4×Dic17—41no—
106#7627—171nomaximal, Sylow
107C23×C17C2×C22⋊C411yescharacteristic
108C22×D17—21no—
109C22×D17—21no—
110C22×D17—21no—
111C22×D17—21no—
112C22×D17#10112yes—
113C22×D17#10412yes—
114C22×D17#10412yes—
115C2×C4×C17—21no—
116C2×C4×C17—21no—
117C2×C4×C17—22no—
118C2×C4×C17—21no—
119C2×C4×C17—21no—
120C2×C4×C17—21no—
121C2×C4×C17—21no—
122C2×C4×C17—21no—
123C2×C4×C17—21no—
124C2×C4×C17—41no—
125C2×C4×C17—41no—
126C2×C4×C17—41no—
127C2×C4×C17—41no—
128C2×C4×C17—41no—
129C2×C4×C17C2×M1611yescharacteristic
130C2×C4×C17C2×M1611yescharacteristic
131C2×Dic17—21no—
132C2×Dic17—21no—
133C2×Dic17—21no—
134C2×Dic17—21no—
135C2×Dic17—21no—
136C2×Dic17—21no—
137C2×Dic17—22no—
138C2×Dic17—41no—
139C2×Dic17—41no—
140C2×Dic17—41no—
141C2×Dic17—41no—
142C2×Dic17—41no—
143C2×Dic17#9912yes—
144C2×Dic17AGL(1,ℤ/8)12yes—
145C2×Dic17#13712yes—
146C4×D17—24no—
147C4×D17—24no—
148C4×D17—44no—
149C4×D17—44no—
150C4×D17—48no—
151C4×D17—84no—
152#3624—44no—
153#3624—44no—
154C2×#389—171no—
155#1749—171no—
156#1749—171no—
157#1271—172no—
158#1271—172no—
159C22×C17#40711yescharacteristic
160C22×C17C2×#9911yescharacteristic
161C22×C17C2×#10111yescharacteristic
162C22×C17#41811yescharacteristic
163C22×C17#41911yescharacteristic
164C22×C17C2×#10411yescharacteristic
165C22×C17C2×#10411yescharacteristic
166C2×D17—22no—
167C2×D17—22no—
168C2×D17—22no—
169C2×D17—22no—
170C2×D17—22no—
171C2×D17—22no—
172C2×D17#33014yes—
173C4×C17—21no—
174C4×C17—21no—
175C4×C17—42no—
176C4×C17—41no—
177C4×C17—41no—
178C4×C17—81no—
179Dic17—22no—
180Dic17—22no—
181Dic17—22no—
182Dic17—42no—
183Dic17—81no—
184C22×C4⋊C4—171no—
185C22×C4⋊C4—171no—
186C22×C4⋊C4—341no—
187C22×C42—171no—
188C2×C22⋊C8—341no—
189C2×C22⋊C8—341no—
190C2×#97—341no—
191C2×#97—341no—
192#389—171no—
193#389—171no—
194#389—171no—
195#389—341no—
196#389—341no—
197#389#59511yescharacteristic
198C2×#95—341no—
199#336—172no—
200#336—172no—
201C2×C17#146311yescharacteristic
202C2×C17#149011yescharacteristic
203C2×C17#149111yescharacteristic
204C2×C17#150711yescharacteristic
205C2×C17#150811yescharacteristic
206C2×C17C2×#33011yescharacteristic
207C2×C17#155611yescharacteristic
208D17—24no—
209C23×C4—171no—
210C23×C4—171no—
211C23×C4—171no—
212C23×C4—341no—
213C23×C4—341no—
214C22×C8—342no—
215C22×C8—342no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—171no—
218C2×C4⋊C4—171no—
219C2×C4⋊C4—342no—
220C2×C4⋊C4—341no—
221C2×C4⋊C4—342no—
222C2×C4⋊C4—341no—
223C2×C4⋊C4—341no—
224C2×C4⋊C4—341no—
225C2×C4⋊C4—341no—
226C2×C4⋊C4—684no—
227C2×C4⋊C4—682no—
228C2×C4⋊C4C2×#59511yescharacteristic
229C2×C4⋊C4C2×#59511yescharacteristic
230C2×C42—171no—
231C2×C42—171no—
232C2×C42—171no—
233C2×C42—682no—
234C2×C42C2×#59511yescharacteristic
235C22⋊C8—344no—
236C22⋊C8—344no—
237#97—682no—
238#97—682no—
239#95—21no—
240#95—341no—
241#95—341no—
242#95—341no—
243C17#762711yescharacteristic, complemented, Sylow
244C24—171no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—171no—
248C22×C4—171no—
249C22×C4—171no—
250C22×C4—342no—
251C22×C4—342no—
252C22×C4—342no—
253C22×C4—342no—
254C22×C4—342no—
255C22×C4—342no—
256C22×C4—344no—
257C22×C4—341no—
258C22×C4—341no—
259C22×C4—341no—
260C22×C4—341no—
261C22×C4—681no—
262C22×C4—681no—
263C22×C4—682no—
264C22×C4—682no—
265C22×C4—682no—
266C22×C4—682no—
267C22×C4—682no—
268C22×C4C22⋊#59511yescharacteristic
269C22×C4C22⋊#59511yescharacteristic
270C22×C4C22×#59511yescharacteristic
271C2×C8—344no—
272C2×C8—344no—
273C2×C8—682no—
274C2×C8—682no—
275C2×C8—682no—
276C2×C8—682no—
277C4⋊C4—21no—
278C4⋊C4—41no—
279C4⋊C4—42no—
280C4⋊C4—172no—
281C4⋊C4—344no—
282C4⋊C4—341no—
283C4⋊C4—681no—
284C4⋊C4—682no—
285C4⋊C4—682no—
286C4⋊C4—682no—
287C4⋊C4—682no—
288C4⋊C4#6324312yes—
289C42—41no—
290C42—342no—
291C42—342no—
292C42—681no—
293C23—172no—
294C23—172no—
295C23—172no—
296C23—341no—
297C23—341no—
298C23—341no—
299C23—341no—
300C23C2×C22⋊#59511yescharacteristic
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—172no—
316C2×C4—172no—
317C2×C4—172no—
318C2×C4—344no—
319C2×C4—344no—
320C2×C4—341no—
321C2×C4—341no—
322C2×C4—341no—
323C2×C4—341no—
324C2×C4—341no—
325C2×C4—341no—
326C2×C4—342no—
327C2×C4—684no—
328C2×C4—684no—
329C2×C4—688no—
330C2×C4—681no—
331C2×C4—681no—
332C2×C4—681no—
333C2×C4—681no—
334C2×C4—681no—
335C2×C4—1364no—
336C2×C4C2×#6324311yescharacteristic
337C2×C4D17⋊M1611yescharacteristic
338C8—684no—
339C8—684no—
340C22—174no—
341C22—342no—
342C22—342no—
343C22—342no—
344C22—342no—
345C22—342no—
346C22—342no—
347C22#1176378011yescharacteristic
348C22D17⋊#9911yescharacteristic
349C22D17⋊#10111yescharacteristic
350C22#1176380111yescharacteristic
351C22#1176380211yescharacteristic
352C22D17⋊#10411yescharacteristic
353C22D17⋊#10411yescharacteristic
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—42no—
359C4—81no—
360C4—342no—
361C4—342no—
362C4—342no—
363C4—682no—
364C4—1361no—
365C2—344no—
366C2#1454403311yescharacteristic
367C2#1454412411yescharacteristic
368C2#1454412711yescharacteristic
369C2#1454417911yescharacteristic
370C2#1454418211yescharacteristic
371C2D17⋊#33011yescharacteristic
372C2#1454431411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#389C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenter#389#595
hypocenterC17#7627
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
3. #14543603C2semidirect
4. #14543602C2semidirect
243. C17#7627semidirect

Maximal subgroups

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

subgroupindex
#145445112
#145436032
#145436022
D17×#3892
#762717