Finite Group Databasebeta

← #17950246

Subgroups — #17950246

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#14544676C211yesmaximal, characteristic, complemented
2#14544639C211yesmaximal, characteristic, complemented
3#14543605C212yesmaximal, complemented
4#14543601C212yesmaximal, complemented
5#14537086C211yesmaximal, characteristic
6C2×C4⋊#3624—21no—
7C2×#10587543—21no—
8C2×#10587543—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587561C411yescharacteristic
13C2×#10587583C411yescharacteristic
14C2×#10587581C411yescharacteristic
15C2×C42×D17C2211yescharacteristic
16#11762714C2211yescharacteristic
17#11762710C2211yescharacteristic
18#11762701—21no—
19#11762701—21no—
20#11762687—21no—
21#11762687—21no—
22C17×#382C411yescharacteristic
23C22×D68—21no—
24C22×D68C2×C411yescharacteristic
25C22×C4×D17C2×C411yescharacteristic
26C22×C4×D17D411yescharacteristic
27C22×C4×D17D411yescharacteristic
28C22×Dic34C2×C411yescharacteristic
29C22×#3624—22no—
30C22×#3624—22no—
31C2×C4⋊C4×C17C2×C411yescharacteristic
32C2×C4⋊C4×C17C2×C411yescharacteristic
33C2×C42×C17C2×C411yescharacteristic
34C2×#63227—21no—
35C2×#63227—21no—
36C2×#63227—21no—
37C2×#63227—21no—
38C2×#63227—21no—
39C2×#63227—21no—
40C2×C4⋊Dic17—21no—
41C2×C4×Dic17D411yescharacteristic
42C2×C4×Dic17D411yescharacteristic
43C2×C4×Dic17C2311yescharacteristic
44#10587583—42no—
45#10587581—42no—
46#10587561—42no—
47C42×D17—42no—
48#10587543—42no—
49#10587543—42no—
50C4⋊#3624—42no—
51C17×#95—21no—
52C17×#95—21no—
53#10587502—21no—
54#10587502—21no—
55C23×D17—21no—
56C23×D17C22⋊C411yescharacteristic
57C22×C4×C17—21no—
58C22×C4×C17—21no—
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22⋊C411yescharacteristic
61C22×C4×C17C22×C411yescharacteristic
62C22×Dic17—21no—
63C22×Dic17C22⋊C411yescharacteristic
64C22×Dic17C2×D411yescharacteristic
65C22×Dic17C2×D411yescharacteristic
66C2×D68—22no—
67C2×D68—41no—
68C2×D68—41no—
69C2×D68—42no—
70C2×D68—42no—
71C2×D68—42no—
72C2×C4×D17—22no—
73C2×C4×D17—22no—
74C2×C4×D17—22no—
75C2×C4×D17—22no—
76C2×C4×D17—21no—
77C2×C4×D17—21no—
78C2×C4×D17—41no—
79C2×C4×D17—41no—
80C2×C4×D17—41no—
81C2×C4×D17—41no—
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—
92C4⋊C4×C17—41no—
93C42×C17—22no—
94#63227—42no—
95#63227—42no—
96#63227—42no—
97#63227—42no—
98#63227—42no—
99#63227—41no—
100#63227—41no—
101C4⋊Dic17—42no—
102C4×Dic17—22no—
103C4×Dic17—41no—
104C4×Dic17—41no—
105#7730—171nomaximal, Sylow
106C23×C17C2×C22⋊C411yescharacteristic
107C22×D17—21no—
108C22×D17—21no—
109C22×D17—21no—
110C22×D17—21no—
111C22×D17—21no—
112C22×D17—21no—
113C22×D17—41no—
114C22×D17—41no—
115C22×D17—41no—
116C22×D17—41no—
117C22×D17—41no—
118C22×D17—41no—
119C22×D17—41no—
120C22×D17#10012yes—
121C2×C4×C17—21no—
122C2×C4×C17—21no—
123C2×C4×C17—21no—
124C2×C4×C17—21no—
125C2×C4×C17—21no—
126C2×C4×C17—21no—
127C2×C4×C17—21no—
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#9912yes—
135C2×C4×C17#13112yes—
136C2×Dic17—21no—
137C2×Dic17—21no—
138C2×Dic17—21no—
139C2×Dic17—21no—
140C2×Dic17—21no—
141C2×Dic17—21no—
142C2×Dic17—21no—
143C2×Dic17—41no—
144C2×Dic17—41no—
145C2×Dic17—41no—
146C2×Dic17#13512yes—
147C2×Dic17AGL(1,ℤ/8)11yescharacteristic
148C2×Dic17#13711yescharacteristic
149D68—82no—
150D68—84no—
151C4×D17—44no—
152C4×D17—42no—
153C4×D17—42no—
154C4×D17—44no—
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#40811yescharacteristic
164C22×C17C2×#9911yescharacteristic
165C22×C17C2×#10011yescharacteristic
166C22×C17#41611yescharacteristic
167C22×C17#41711yescharacteristic
168C22×C17#42111yescharacteristic
169C22×C17#42111yescharacteristic
170C2×D17—22no—
171C2×D17—22no—
172C2×D17—22no—
173C2×D17—41no—
174C2×D17—41no—
175C2×D17—41no—
176C2×D17—41no—
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—22no—
186C4×C17—41no—
187C4×C17—81no—
188C4×C17—81no—
189Dic17—21no—
190Dic17—21no—
191Dic17—22no—
192Dic17—41no—
193Dic17—81no—
194C2×#124—171no—
195C2×C22⋊Q8—171no—
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#59511yescharacteristic
208#336—172no—
209#336—172no—
210#336—341no—
211C2×C17#147111yescharacteristic
212C2×C17#148211yescharacteristic
213C2×C17#149511yescharacteristic
214C2×C17#151311yescharacteristic
215C2×C17#151611yescharacteristic
216C2×C17#153311yescharacteristic
217C2×C17#155111yescharacteristic
218D17—42no—
219D17—161no—
220C22×Q8—171no—
221C22×D4—171no—
222C22×D4—341no—
223C23×C4—171no—
224C23×C4—171no—
225C23×C4—171no—
226C22×C8—342no—
227C22×C8—342no—
228#124—682no—
229C22⋊Q8—682no—
230#121—682no—
231C2×C4⋊C4—341no—
232C2×C4⋊C4C2×#59511yescharacteristic
233C2×C4⋊C4C2×#59511yescharacteristic
234C2×C22⋊C4—341no—
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—682no—
244C2×C42C2×#59511yescharacteristic
245C4⋊C8—682no—
246C22⋊C8—682no—
247C22⋊C8—682no—
248#95—21no—
249#95—21no—
250#95—341no—
251#95—341no—
252C17#773011yescharacteristic, complemented, Sylow
253C24—171no—
254C24—341no—
255C2×Q8—342no—
256C2×Q8—681no—
257C2×Q8—681no—
258C2×D4—342no—
259C2×D4—681no—
260C2×D4—681no—
261C2×D4—682no—
262C2×D4—682no—
263C2×D4—682no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—171no—
267C22×C4—171no—
268C22×C4—171no—
269C22×C4—341no—
270C22×C4—342no—
271C22×C4—341no—
272C22×C4—342no—
273C22×C4—342no—
274C22×C4—342no—
275C22×C4—341no—
276C22×C4—681no—
277C22×C4—681no—
278C22×C4—681no—
279C22×C4—681no—
280C22×C4C22⋊#59511yescharacteristic
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—41no—
291C4⋊C4—682no—
292C22⋊C4—682no—
293C22⋊C4—682no—
294C22⋊C4—681no—
295C22⋊C4—681no—
296C22⋊C4—682no—
297C22⋊C4—682no—
298C22⋊C4—682no—
299C42—22no—
300C42—342no—
301C42—681no—
302C42—681no—
303C23—172no—
304C23—341no—
305C23—341no—
306C23—341no—
307C23—341no—
308C23—341no—
309C23—341no—
310C23—681no—
311C23—681no—
312C23—681no—
313C23—681no—
314C23—681no—
315C23—681no—
316C23—681no—
317C23C2×C22⋊#59511yescharacteristic
318Q8—1362no—
319D4—1362no—
320D4—1364no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
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—684no—
345C2×C4—684no—
346C2×C4—682no—
347C2×C4—682no—
348C2×C4—681no—
349C2×C4—681no—
350C2×C4—681no—
351C2×C4#1058753912yes—
352C2×C4#1058768012yes—
353C8—1362no—
354C8—1362no—
355C22—342no—
356C22—342no—
357C22—342no—
358C22—681no—
359C22—681no—
360C22—681no—
361C22—681no—
362C22—1361no—
363C22—1361no—
364C22—1361no—
365C22—1361no—
366C22—1361no—
367C22—1361no—
368C22—1361no—
369C22#1176378411yescharacteristic
370C22C2×#1058753911yescharacteristic
371C22D17⋊#10011yescharacteristic
372C22#1176379911yescharacteristic
373C22#1176380011yescharacteristic
374C22#1176380611yescharacteristic
375C22#1176380611yescharacteristic
376C4—22no—
377C4—22no—
378C4—41no—
379C4—81no—
380C4—81no—
381C4—341no—
382C4—341no—
383C4—342no—
384C4—681no—
385C4—1361no—
386C2—2721no—
387C2—682no—
388C2#1454406111yescharacteristic
389C2#1454409811yescharacteristic
390C2#1454414211yescharacteristic
391C2#1454420111yescharacteristic
392C2#1454421211yescharacteristic
393C2#1454426411yescharacteristic
394C2#1454430411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#382C4
socleC23×C17C2×C22⋊C4
prime radicalC2×#10587581C4
cosocleC2×C4×Dic17C23
hypercenter#382#595
hypocenterC17#7730
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
1. #14544676C2semidirect
2. #14544639C2semidirect
3. #14543605C2semidirect
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
#145446762
#145446392
#145436052
#145436012
#145370862
#773017