Finite Group Databasebeta

← #17950245

Subgroups — #17950245

Order 4352.

520 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 90 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#14544674C211yesmaximal, characteristic, complemented
2#14544640C211yesmaximal, characteristic, complemented
3#14543605C212yesmaximal, complemented
4#14543600C212yesmaximal, complemented
5#14537083C211yesmaximal, characteristic
6C2×#10587544—21no—
7C2×C22⋊#3624—21no—
8C2×C22⋊#3624—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587622C411yescharacteristic
13C2×#10587610C411yescharacteristic
14C22×C4×Dic17C2211yescharacteristic
15#11762714C2211yescharacteristic
16#11762712C2211yescharacteristic
17#11762703—21no—
18#11762703—21no—
19#11762689—21no—
20#11762689—21no—
21#11762674C411yescharacteristic
22C2×C17×#121C411yescharacteristic
23C22×D4×C17—21no—
24C22×D4×C17C2×C411yescharacteristic
25C23×C4×C17C2×C411yescharacteristic
26C23×Dic17D411yescharacteristic
27C23×Dic17D411yescharacteristic
28C22×Dic34C2×C411yescharacteristic
29C22×#3624—22no—
30C22×#3624—22no—
31C17×#121—42no—
32C2×C4⋊C4×C17C2×C411yescharacteristic
33C2×C22⋊C4×C17—21no—
34C2×C22⋊Dic17—21no—
35C2×C22⋊Dic17—21no—
36C2×C22⋊Dic17—21no—
37C2×C22⋊Dic17—21no—
38C2×C22⋊Dic17—21no—
39#10587622—42no—
40C2×C4⋊Dic17C2×C411yescharacteristic
41#10587610—42no—
42C2×#63225—21no—
43C2×C4×Dic17—42no—
44C2×C4×Dic17C2×C411yescharacteristic
45C2×C4×Dic17D411yescharacteristic
46C2×C4×Dic17D411yescharacteristic
47C2×C4×Dic17C2311yescharacteristic
48C22⋊#3624—42no—
49C22⋊#3624—42no—
50#10587544—42no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54#10587502—21no—
55C24×C17—21no—
56C24×C17C22⋊C411yescharacteristic
57C2×D4×C17—22no—
58C2×D4×C17—41no—
59C2×D4×C17—41no—
60C2×D4×C17—42no—
61C2×D4×C17—42no—
62C2×D4×C17—42no—
63C22×C4×C17—22no—
64C22×C4×C17—22no—
65C22×C4×C17—21no—
66C22×C4×C17—41no—
67C22×C4×C17C22⋊C411yescharacteristic
68C22×C4×C17C22×C411yescharacteristic
69C22×Dic17—22no—
70C22×Dic17—22no—
71C22×Dic17—21no—
72C22×Dic17—21no—
73C22×Dic17—21no—
74C22×Dic17—21no—
75C22×Dic17—41no—
76C22×Dic17—41no—
77C22×Dic17—41no—
78C22×Dic17C22⋊C411yescharacteristic
79C22×Dic17C22⋊C411yescharacteristic
80C22×Dic17C2×D411yescharacteristic
81C22×Dic17C2×D411yescharacteristic
82C2×Dic34—22no—
83C2×Dic34—41no—
84C2×Dic34—41no—
85C2×#3624—42no—
86C2×#3624—42no—
87C2×#3624—42no—
88C2×#3624—42no—
89C2×#3624—42no—
90C2×#3624—42no—
91C4⋊C4×C17—41no—
92C22⋊C4×C17—42no—
93C22⋊Dic17—42no—
94C22⋊Dic17—42no—
95C22⋊Dic17—42no—
96C22⋊Dic17—42no—
97C22⋊Dic17—41no—
98C22⋊Dic17—41no—
99C4⋊Dic17—41no—
100#63225—42no—
101C4×Dic17—22no—
102C4×Dic17—22no—
103C4×Dic17—41no—
104C4×Dic17—41no—
105#7730—171nomaximal, Sylow
106C23×C17—21no—
107C23×C17—21no—
108C23×C17—21no—
109C23×C17—21no—
110C23×C17—21no—
111C23×C17—21no—
112C23×C17—41no—
113C23×C17—41no—
114C23×C17—41no—
115C23×C17—41no—
116C23×C17—41no—
117C23×C17—41no—
118C23×C17—41no—
119C23×C17#10012yes—
120C23×C17C2×C22⋊C411yescharacteristic
121D4×C17—82no—
122D4×C17—84no—
123C2×C4×C17—21no—
124C2×C4×C17—21no—
125C2×C4×C17—21no—
126C2×C4×C17—21no—
127C2×C4×C17—21no—
128C2×C4×C17—44no—
129C2×C4×C17—41no—
130C2×C4×C17—41no—
131C2×C4×C17—41no—
132C2×C4×C17#13112yes—
133C2×Dic17—21no—
134C2×Dic17—21no—
135C2×Dic17—21no—
136C2×Dic17—21no—
137C2×Dic17—21no—
138C2×Dic17—21no—
139C2×Dic17—21no—
140C2×Dic17—21no—
141C2×Dic17—21no—
142C2×Dic17—44no—
143C2×Dic17—42no—
144C2×Dic17—42no—
145C2×Dic17—41no—
146C2×Dic17—41no—
147C2×Dic17—41no—
148C2×Dic17—41no—
149C2×Dic17—41no—
150C2×Dic17—41no—
151C2×Dic17#9912yes—
152C2×Dic17#13512yes—
153C2×Dic17AGL(1,ℤ/8)11yescharacteristic
154C2×Dic17#13711yescharacteristic
155Dic34—82no—
156#3624—82no—
157#3624—82no—
158#2850—171no—
159#1817—171no—
160#1797—171no—
161#1272—172no—
162#1270—172no—
163C22×C17—22no—
164C22×C17—22no—
165C22×C17—22no—
166C22×C17—41no—
167C22×C17—41no—
168C22×C17—41no—
169C22×C17—41no—
170C22×C17—81no—
171C22×C17—81no—
172C22×C17—81no—
173C22×C17—81no—
174C22×C17—81no—
175C22×C17—81no—
176C22×C17—81no—
177C22×C17#40811yescharacteristic
178C22×C17C2×#9911yescharacteristic
179C22×C17C2×#10011yescharacteristic
180C22×C17#41611yescharacteristic
181C22×C17#41711yescharacteristic
182C22×C17#42111yescharacteristic
183C22×C17#42111yescharacteristic
184C4×C17—22no—
185C4×C17—41no—
186C4×C17—81no—
187Dic17—21no—
188Dic17—21no—
189Dic17—22no—
190Dic17—22no—
191Dic17—41no—
192Dic17—81no—
193Dic17—81no—
194C2×#124—171no—
195C2×C22⋊Q8—171no—
196C2×#121#59511yescharacteristic
197C22×C42—171no—
198C2×C4⋊C8—341no—
199C2×C22⋊C8—341no—
200C2×C22⋊C8—341no—
201#391—171no—
202#390—171no—
203#388—341no—
204#388—341no—
205#386—341no—
206#386—341no—
207#382—171no—
208#336—172no—
209#336—172no—
210#336—341no—
211C2×C17—42no—
212C2×C17—161no—
213C2×C17#147111yescharacteristic
214C2×C17#148211yescharacteristic
215C2×C17#149511yescharacteristic
216C2×C17#151311yescharacteristic
217C2×C17#151611yescharacteristic
218C2×C17#153311yescharacteristic
219C2×C17#155111yescharacteristic
220C22×Q8—171no—
221C22×D4—21no—
222C22×D4C2×#59511yescharacteristic
223C23×C4—171no—
224C23×C4—171no—
225C23×C4C2×#59511yescharacteristic
226C22×C8—342no—
227C22×C8—342no—
228#124—682no—
229C22⋊Q8—682no—
230#121—42no—
231C2×C4⋊C4—171no—
232C2×C4⋊C4—341no—
233C2×C4⋊C4C2×#59511yescharacteristic
234C2×C22⋊C4—21no—
235C2×C22⋊C4—341no—
236C2×C22⋊C4—341no—
237C2×C22⋊C4—341no—
238C2×C22⋊C4—341no—
239C2×C22⋊C4—341no—
240C2×C42—171no—
241C2×C42—171no—
242C2×C42—171no—
243C2×C42—171no—
244C2×C42—682no—
245C4⋊C8—682no—
246C22⋊C8—682no—
247C22⋊C8—682no—
248#95—341no—
249#95—341no—
250#95—341no—
251#95—341no—
252C17#773011yescharacteristic, complemented, Sylow
253C24—21no—
254C24C22⋊#59511yescharacteristic
255C2×Q8—342no—
256C2×Q8—681no—
257C2×Q8—681no—
258C2×D4—22no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4—42no—
262C2×D4—42no—
263C2×D4—42no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—41no—
268C22×C4—171no—
269C22×C4—171no—
270C22×C4—171no—
271C22×C4—171no—
272C22×C4—341no—
273C22×C4—342no—
274C22×C4—342no—
275C22×C4—341no—
276C22×C4—341no—
277C22×C4—341no—
278C22×C4—681no—
279C22×C4—681no—
280C22×C4—681no—
281C22×C4C22⋊#59511yescharacteristic
282C22×C4C22×#59511yescharacteristic
283C2×C8—682no—
284C2×C8—682no—
285C2×C8—682no—
286C2×C8—682no—
287C2×C8—682no—
288C2×C8—682no—
289C4⋊C4—41no—
290C4⋊C4—681no—
291C4⋊C4—682no—
292C22⋊C4—42no—
293C22⋊C4—682no—
294C22⋊C4—681no—
295C22⋊C4—681no—
296C22⋊C4—682no—
297C22⋊C4—682no—
298C22⋊C4—682no—
299C42—342no—
300C42—342no—
301C42—681no—
302C42—681no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23#1058755312yes—
317C23C2×C22⋊#59511yescharacteristic
318Q8—1362no—
319D4—82no—
320D4—84no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—44no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—172no—
331C2×C4—172no—
332C2×C4—171no—
333C2×C4—171no—
334C2×C4—341no—
335C2×C4—341no—
336C2×C4—341no—
337C2×C4—341no—
338C2×C4—341no—
339C2×C4—341no—
340C2×C4—341no—
341C2×C4—341no—
342C2×C4—341no—
343C2×C4—684no—
344C2×C4—682no—
345C2×C4—682no—
346C2×C4—681no—
347C2×C4—681no—
348C2×C4—681no—
349C2×C4—681no—
350C2×C4—681no—
351C2×C4—681no—
352C2×C4#1058767812yes—
353C8—1362no—
354C8—1362no—
355C22—22no—
356C22—22no—
357C22—22no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22#1176378211yescharacteristic
370C22D17⋊#9911yescharacteristic
371C22C2×#1058755311yescharacteristic
372C22#1176379911yescharacteristic
373C22#1176380011yescharacteristic
374C22#1176380711yescharacteristic
375C22#1176380711yescharacteristic
376C4—22no—
377C4—41no—
378C4—81no—
379C4—341no—
380C4—341no—
381C4—342no—
382C4—342no—
383C4—681no—
384C4—1361no—
385C4—1361no—
386C2—42no—
387C2—161no—
388C2#1454406011yescharacteristic
389C2#1454409511yescharacteristic
390C2#1454413911yescharacteristic
391C2#1454420011yescharacteristic
392C2#1454420911yescharacteristic
393C2#1454426311yescharacteristic
394C2#1454430311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
Fitting, prime radicalC2×C17×#121C4
socleC23×C17C2×C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC2×#121#595
hypocenterC17#7730
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #14544674C2semidirect
2. #14544640C2semidirect
3. #14543605C2semidirect
4. #14543600C2semidirect
252. C17#7730semidirect

Maximal subgroups

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

subgroupindex
#145446742
#145446402
#145436052
#145436002
#145370832
#773017