Finite Group Databasebeta

← #17950247

Subgroups — #17950247

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#14543604C212yesmaximal, complemented
4#14543601C212yesmaximal, complemented
5#14537087C211yesmaximal, characteristic
6C2×#10587544—21no—
7C2×C22⋊#3624—21no—
8C2×C22⋊#3624—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587633C411yescharacteristic
13C2×#10587616C411yescharacteristic
14C22×C4×Dic17C2211yescharacteristic
15#11762716C2211yescharacteristic
16#11762710C2211yescharacteristic
17#11762699—21no—
18#11762699—21no—
19#11762686—21no—
20#11762686—21no—
21#11762674C411yescharacteristic
22C2×C17×C22⋊Q8C411yescharacteristic
23C22×Q8×C17C2×C411yescharacteristic
24C23×C4×C17C2×C411yescharacteristic
25C22×C22⋊D17—21no—
26C23×Dic17D411yescharacteristic
27C23×Dic17D411yescharacteristic
28C22×D68C2×C411yescharacteristic
29C22×#3624—22no—
30C22×#3624—22no—
31C17×C22⋊Q8—42no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17C2×C411yescharacteristic
34C2×C22⋊C4×C17—21no—
35#10587633—42no—
36#10587616—42no—
37C2×#63227—21no—
38C2×#63227—21no—
39C2×#63227—21no—
40C2×#63227—21no—
41C2×#63227—21no—
42C2×C4⋊Dic17C2×C411yescharacteristic
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×C17C22⋊C411yescharacteristic
56C23×D17—21no—
57C2×Q8×C17—22no—
58C2×Q8×C17—41no—
59C2×Q8×C17—41no—
60C22×C4×C17—22no—
61C22×C4×C17—22no—
62C22×C4×C17—21no—
63C22×C4×C17—21no—
64C22×C4×C17—41no—
65C22×C4×C17C22⋊C411yescharacteristic
66C22×C4×C17C22×C411yescharacteristic
67C2×C22⋊D17—42no—
68C2×C22⋊D17—42no—
69C2×C22⋊D17—42no—
70C22×Dic17—22no—
71C22×Dic17—22no—
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×D68—22no—
83C2×D68—41no—
84C2×D68—41no—
85C2×#3624—42no—
86C2×#3624—42no—
87C2×#3624—42no—
88C2×#3624—42no—
89C2×#3624—42no—
90C2×#3624—42no—
91C4⋊C4×C17—41no—
92C4⋊C4×C17—42no—
93C22⋊C4×C17—42no—
94#63227—42no—
95#63227—42no—
96#63227—42no—
97#63227—42no—
98#63227—41no—
99#63227—41no—
100C4⋊Dic17—41no—
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#10012yes—
113C23×C17C2×C22⋊C411yescharacteristic
114C22×D17—41no—
115C22×D17—41no—
116C22×D17—41no—
117C22×D17—41no—
118C22×D17—41no—
119C22×D17—41no—
120C22×D17—41no—
121Q8×C17—82no—
122C2×C4×C17—21no—
123C2×C4×C17—21no—
124C2×C4×C17—21no—
125C2×C4×C17—21no—
126C2×C4×C17—21no—
127C2×C4×C17—44no—
128C2×C4×C17—41no—
129C2×C4×C17—41no—
130C2×C4×C17—41no—
131C2×C4×C17—41no—
132C2×C4×C17—41no—
133C2×C4×C17—41no—
134C2×C4×C17#13112yes—
135C22⋊D17—84no—
136C2×Dic17—21no—
137C2×Dic17—21no—
138C2×Dic17—21no—
139C2×Dic17—21no—
140C2×Dic17—21no—
141C2×Dic17—21no—
142C2×Dic17—21no—
143C2×Dic17—21no—
144C2×Dic17—21no—
145C2×Dic17—44no—
146C2×Dic17—42no—
147C2×Dic17—42no—
148C2×Dic17—41no—
149C2×Dic17—41no—
150C2×Dic17—41no—
151C2×Dic17#9912yes—
152C2×Dic17#13512yes—
153C2×Dic17AGL(1,ℤ/8)11yescharacteristic
154C2×Dic17#13711yescharacteristic
155D68—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#40811yescharacteristic
171C22×C17C2×#9911yescharacteristic
172C22×C17C2×#10011yescharacteristic
173C22×C17#41611yescharacteristic
174C22×C17#41711yescharacteristic
175C22×C17#42111yescharacteristic
176C22×C17#42111yescharacteristic
177C2×D17—81no—
178C2×D17—81no—
179C2×D17—81no—
180C2×D17—81no—
181C2×D17—81no—
182C2×D17—81no—
183C2×D17—81no—
184C4×C17—22no—
185C4×C17—41no—
186C4×C17—81no—
187C4×C17—81no—
188Dic17—21no—
189Dic17—21no—
190Dic17—22no—
191Dic17—22no—
192Dic17—41no—
193Dic17—81no—
194C2×#124—171no—
195C2×C22⋊Q8#59511yescharacteristic
196C2×#121—171no—
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#147111yescharacteristic
213C2×C17#148211yescharacteristic
214C2×C17#149511yescharacteristic
215C2×C17#151311yescharacteristic
216C2×C17#151611yescharacteristic
217C2×C17#153311yescharacteristic
218C2×C17#155111yescharacteristic
219D17—161no—
220C22×Q8C2×#59511yescharacteristic
221C22×D4—171no—
222C22×D4—341no—
223C23×C4—171no—
224C23×C4—171no—
225C23×C4C2×#59511yescharacteristic
226C22×C8—342no—
227C22×C8—342no—
228#124—682no—
229C22⋊Q8—42no—
230#121—682no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—171no—
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—341no—
254C24C22⋊#59511yescharacteristic
255C2×Q8—22no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×D4—342no—
259C2×D4—681no—
260C2×D4—681no—
261C2×D4—682no—
262C2×D4—682no—
263C2×D4—682no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—41no—
269C22×C4—171no—
270C22×C4—171no—
271C22×C4—171no—
272C22×C4—171no—
273C22×C4—341no—
274C22×C4—342no—
275C22×C4—342no—
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—42no—
291C4⋊C4—681no—
292C22⋊C4—42no—
293C22⋊C4—682no—
294C22⋊C4—682no—
295C22⋊C4—682no—
296C22⋊C4—681no—
297C22⋊C4—681no—
298C22⋊C4—682no—
299C42—342no—
300C42—342no—
301C42—681no—
302C42—681no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—681no—
310C23—681no—
311C23—681no—
312C23—681no—
313C23—681no—
314C23—681no—
315C23—681no—
316C23#1058755312yes—
317C23C2×C22⋊#59511yescharacteristic
318Q8—82no—
319D4—1362no—
320D4—1364no—
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—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—172no—
334C2×C4—172no—
335C2×C4—171no—
336C2×C4—171no—
337C2×C4—341no—
338C2×C4—341no—
339C2×C4—341no—
340C2×C4—341no—
341C2×C4—341no—
342C2×C4—341no—
343C2×C4—341no—
344C2×C4—341no—
345C2×C4—341no—
346C2×C4—684no—
347C2×C4—682no—
348C2×C4—682no—
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—1361no—
363C22—1361no—
364C22—1361no—
365C22—1361no—
366C22—1361no—
367C22—1361no—
368C22—1361no—
369C22#1176378211yescharacteristic
370C22D17⋊#9911yescharacteristic
371C22C2×#1058755311yescharacteristic
372C22#1176379911yescharacteristic
373C22#1176380011yescharacteristic
374C22#1176380811yescharacteristic
375C22#1176380811yescharacteristic
376C4—22no—
377C4—41no—
378C4—81no—
379C4—81no—
380C4—341no—
381C4—341no—
382C4—342no—
383C4—342no—
384C4—681no—
385C4—1361no—
386C2—42no—
387C2—2721no—
388C2#1454406011yescharacteristic
389C2#1454409711yescharacteristic
390C2#1454414111yescharacteristic
391C2#1454420211yescharacteristic
392C2#1454421111yescharacteristic
393C2#1454426511yescharacteristic
394C2#1454430311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×C22⋊Q8C4
socleC23×C17C2×C22⋊C4
prime radicalC2×#10587616C4
cosocleC2×C4×Dic17C23
hypercenterC2×C22⋊Q8#595
hypocenterC17#7730
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #14544674C2semidirect
2. #14544640C2semidirect
3. #14543604C2semidirect
4. #14543601C2semidirect
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
#145436042
#145436012
#145370872
#773017