Finite Group Databasebeta

← #17949688

Subgroups — #17949688

Order 4352.

604 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 126 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#14544641C211yesmaximal, characteristic
2C4×#10587543C211yesmaximal, characteristic
3#14543603C212yesmaximal, complemented
4#14543602C212yesmaximal, complemented
5D17×#389C211yesmaximal, characteristic
6C2×#10587544—21no—
7C2×#10587543—21no—
8C2×#10587543—21no—
9C2×C4×#3624—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—42no—
46C4⋊C4×D17—42no—
47C4⋊C4×D17—42no—
48C4⋊C4×D17C814yescomplemented
49C42×D17—42no—
50#10587544—42no—
51#10587543—24no—
52#10587543—42no—
53C4×#3624—42no—
54C17×#95—21no—
55#10587502—21no—
56#10587502—21no—
57#10587502—21no—
58C23×D17C22⋊C411yescharacteristic
59C22×C4×C17—21no—
60C22×C4×C17—21no—
61C22×C4×C17C22⋊C411yescharacteristic
62C22×C4×C17C22⋊C411yescharacteristic
63C22×C4×C17C22×C411yescharacteristic
64C22×Dic17—21no—
65C22×Dic17—21no—
66C22×Dic17C22⋊C411yescharacteristic
67C22×Dic17C2×D411yescharacteristic
68C22×Dic17C2×D411yescharacteristic
69C2×C4×D17—22no—
70C2×C4×D17—22no—
71C2×C4×D17—24no—
72C2×C4×D17—22no—
73C2×C4×D17—22no—
74C2×C4×D17—41no—
75C2×C4×D17—41no—
76C2×C4×D17—41no—
77C2×C4×D17—42no—
78C2×C4×D17—42no—
79C2×C4×D17—42no—
80C2×C4×D17—42no—
81C2×C4×D17—42no—
82C2×C4×D17C2×C812yes—
83C2×C4×D17M1612yes—
84C2×C4×D17D812yes—
85C2×C4×D17SD1612yes—
86C2×#3624—24no—
87C2×#3624—42no—
88C2×#3624—42no—
89C2×#3624—42no—
90C2×#3624—42no—
91C2×#3624—42no—
92C4⋊C4×C17—21no—
93C4⋊C4×C17—41no—
94C4⋊C4×C17—42no—
95C4⋊C4×C17C2×C812yes—
96C42×C17—41no—
97C4⋊Dic17—21no—
98C4⋊Dic17—41no—
99C4⋊Dic17—41no—
100C4⋊Dic17—41no—
101C4⋊Dic17C2×C812yes—
102#63225—24no—
103#63225—42no—
104#63225—42no—
105#63225—41no—
106#63225—41no—
107C4×Dic17—22no—
108C4×Dic17—22no—
109C4×Dic17—41no—
110#7573—171nomaximal, Sylow
111C23×C17C2×C22⋊C411yescharacteristic
112C22×D17—21no—
113C22×D17—21no—
114C22×D17—21no—
115C22×D17—21no—
116C22×D17C22⋊C812yes—
117C22×D17#10212yes—
118C22×D17#10412yes—
119C2×C4×C17—21no—
120C2×C4×C17—21no—
121C2×C4×C17—21no—
122C2×C4×C17—21no—
123C2×C4×C17—22no—
124C2×C4×C17—21no—
125C2×C4×C17—21no—
126C2×C4×C17—21no—
127C2×C4×C17—41no—
128C2×C4×C17—41no—
129C2×C4×C17—41no—
130C2×C4×C17—41no—
131C2×C4×C17—41no—
132C2×C4×C17#10212yes—
133C2×C4×C17C22×C811yescharacteristic
134C2×C4×C17C2×M1611yescharacteristic
135C2×Dic17—21no—
136C2×Dic17—21no—
137C2×Dic17—21no—
138C2×Dic17—21no—
139C2×Dic17—22no—
140C2×Dic17—41no—
141C2×Dic17—41no—
142C2×Dic17—41no—
143C2×Dic17—41no—
144C2×Dic17—41no—
145C2×Dic17C22⋊C812yes—
146C2×Dic17#9912yes—
147C2×Dic17#10112yes—
148C2×Dic17C2×D811yescharacteristic
149C2×Dic17C2×SD1611yescharacteristic
150C2×Dic17#13712yes—
151C4×D17—24no—
152C4×D17—24no—
153C4×D17—42no—
154C4×D17—42no—
155C4×D17—44no—
156C4×D17—48no—
157C4×D17—84no—
158#3624—44no—
159#3624—82no—
160C2×#389—171no—
161#1797—171no—
162C4×C22⋊C8—171no—
163#1271—172no—
164#1271—172no—
165C22×C17C2×C22⋊C811yescharacteristic
166C22×C17C2×#9911yescharacteristic
167C22×C17C2×#10111yescharacteristic
168C22×C17C2×#10211yescharacteristic
169C22×C17#41911yescharacteristic
170C22×C17C2×#10411yescharacteristic
171C22×C17#42111yescharacteristic
172C2×D17—22no—
173C2×D17—22no—
174C2×D17—22no—
175C2×D17—22no—
176C2×D17—22no—
177C2×D17—22no—
178C2×D17D4⋊C814yes—
179C4×C17—21no—
180C4×C17—21no—
181C4×C17—22no—
182C4×C17—42no—
183C4×C17—41no—
184C4×C17—81no—
185Dic17—22no—
186Dic17—21no—
187Dic17—21no—
188Dic17—42no—
189Dic17—81no—
190Dic17#32414yes—
191C22×C4⋊C4—171no—
192C22×C4⋊C4—171no—
193C22×C4⋊C4—341no—
194C22×C42—171no—
195C2×C4⋊C8—341no—
196C2×C22⋊C8—341no—
197C2×C22⋊C8—341no—
198C2×C4×C8—341no—
199#389—171no—
200#389—171no—
201#389—171no—
202#389—341no—
203#389—341no—
204#389#59511yescharacteristic
205C2×#95—341no—
206#336—172no—
207#336—172no—
208C2×C17C2×#32411yescharacteristic
209C2×C17C2×D4⋊C811yescharacteristic
210C2×C17#147911yescharacteristic
211C2×C17#150811yescharacteristic
212C2×C17#151911yescharacteristic
213C2×C17#152811yescharacteristic
214C2×C17#154611yescharacteristic
215D17—24no—
216C23×C4—171no—
217C23×C4—171no—
218C23×C4—171no—
219C23×C4—341no—
220C23×C4—341no—
221C22×C8—342no—
222C22×C8—342no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—171no—
225C2×C4⋊C4—174no—
226C2×C4⋊C4—171no—
227C2×C4⋊C4—342no—
228C2×C4⋊C4—341no—
229C2×C4⋊C4—341no—
230C2×C4⋊C4—341no—
231C2×C4⋊C4—341no—
232C2×C4⋊C4—341no—
233C2×C4⋊C4—682no—
234C2×C4⋊C4—682no—
235C2×C4⋊C4—682no—
236C2×C4⋊C4C2×#59511yescharacteristic
237C2×C4⋊C4C2×#59511yescharacteristic
238C2×C42—171no—
239C2×C42—171no—
240C2×C42—171no—
241C2×C42—682no—
242C2×C42C2×#59511yescharacteristic
243C4⋊C8—682no—
244C22⋊C8—344no—
245C22⋊C8—682no—
246C4×C8—682no—
247#95—21no—
248#95—341no—
249#95—341no—
250#95—341no—
251C17#757311yescharacteristic, complemented, Sylow
252C24—171no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—171no—
256C22×C4—171no—
257C22×C4—171no—
258C22×C4—172no—
259C22×C4—172no—
260C22×C4—172no—
261C22×C4—172no—
262C22×C4—342no—
263C22×C4—342no—
264C22×C4—342no—
265C22×C4—342no—
266C22×C4—344no—
267C22×C4—341no—
268C22×C4—341no—
269C22×C4—681no—
270C22×C4—681no—
271C22×C4—681no—
272C22×C4—682no—
273C22×C4—682no—
274C22×C4—682no—
275C22×C4—682no—
276C22×C4—682no—
277C22×C4C22⋊#59511yescharacteristic
278C22×C4C22⋊#59511yescharacteristic
279C22×C4C22×#59511yescharacteristic
280C2×C8—344no—
281C2×C8—682no—
282C2×C8—682no—
283C2×C8—682no—
284C2×C8—682no—
285C2×C8—682no—
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—42no—
289C4⋊C4—172no—
290C4⋊C4—344no—
291C4⋊C4—341no—
292C4⋊C4—681no—
293C4⋊C4—681no—
294C4⋊C4—681no—
295C4⋊C4—681no—
296C4⋊C4—681no—
297C4⋊C4—682no—
298C4⋊C4—682no—
299C4⋊C4#6324212yes—
300C42—41no—
301C42—342no—
302C42—342no—
303C42—681no—
304C23—172no—
305C23—172no—
306C23—172no—
307C23—341no—
308C23—341no—
309C23—341no—
310C23—341no—
311C23C2×C22⋊#59511yescharacteristic
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—172no—
326C2×C4—172no—
327C2×C4—172no—
328C2×C4—171no—
329C2×C4—171no—
330C2×C4—172no—
331C2×C4—344no—
332C2×C4—344no—
333C2×C4—341no—
334C2×C4—341no—
335C2×C4—341no—
336C2×C4—341no—
337C2×C4—342no—
338C2×C4—682no—
339C2×C4—682no—
340C2×C4—684no—
341C2×C4—688no—
342C2×C4—681no—
343C2×C4—681no—
344C2×C4—681no—
345C2×C4—681no—
346C2×C4—681no—
347C2×C4—1364no—
348C2×C4#1058754712yes—
349C2×C4C2×#6324211yescharacteristic
350C2×C4D17⋊M1611yescharacteristic
351C8—684no—
352C8—1362no—
353C22—174no—
354C22—342no—
355C22—342no—
356C22—342no—
357C22—342no—
358C22—342no—
359C22—342no—
360C22#1176377711yescharacteristic
361C22D17⋊#9911yescharacteristic
362C22D17⋊#10111yescharacteristic
363C22C2×#1058754711yescharacteristic
364C22#1176380211yescharacteristic
365C22D17⋊#10411yescharacteristic
366C22#1176380611yescharacteristic
367C4—22no—
368C4—21no—
369C4—21no—
370C4—41no—
371C4—42no—
372C4—81no—
373C4—174no—
374C4—342no—
375C4—341no—
376C4—341no—
377C4—682no—
378C4—1361no—
379C2—344no—
380C2#1454401311yescharacteristic
381C2#1454407011yescharacteristic
382C2#1454408711yescharacteristic
383C2#1454418211yescharacteristic
384C2#1454421911yescharacteristic
385C2#1454424711yescharacteristic
386C2#1454429411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#389C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenter#389#595
hypocenterC17#7573
LCSG ▷ C2×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
48. C4⋊C4×D17C8semidirect
251. C17#7573semidirect

Maximal subgroups

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

subgroupindex
#145446412
C4×#105875432
#145436032
#145436022
D17×#3892
#757317