Finite Group Databasebeta

← #17950173

Subgroups — #17950173

Order 4352.

570 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 94 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#14544638C211yesmaximal, characteristic, complemented
2#14544447C211yesmaximal, characteristic, complemented
3#14543605C212yesmaximal, complemented
4#14543600C212yesmaximal, complemented
5#14537083C211yesmaximal, characteristic
6C22×#63247—21no—
7C2×C4⋊#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
29C2×#63247—24no—
30C2×#63247—42no—
31C2×#63247—42no—
32C22×#3624—22no—
33C22×#3624—22no—
34C17×#121—42no—
35C2×C4⋊C4×C17C2×C411yescharacteristic
36C2×C22⋊C4×C17—21no—
37C2×C22⋊Dic17—21no—
38C2×C22⋊Dic17—21no—
39C2×C22⋊Dic17—21no—
40C2×C22⋊Dic17—21no—
41C2×C22⋊Dic17—21no—
42#10587622—42no—
43C2×C4⋊Dic17C2×C411yescharacteristic
44#10587610—42no—
45C2×#63225—21no—
46C2×C4×Dic17—42no—
47C2×C4×Dic17C2×C411yescharacteristic
48C2×C4×Dic17D411yescharacteristic
49C2×C4×Dic17D411yescharacteristic
50C2×C4×Dic17C2311yescharacteristic
51C22⋊#3624—42no—
52C4⋊#3624—42no—
53#10587502—21no—
54#10587502—21no—
55#10587502—21no—
56#10587502—21no—
57C24×C17—21no—
58C24×C17C22⋊C411yescharacteristic
59C2×D4×C17—22no—
60C2×D4×C17—41no—
61C2×D4×C17—41no—
62C2×D4×C17—42no—
63C2×D4×C17—42no—
64C2×D4×C17—42no—
65C22×C4×C17—22no—
66C22×C4×C17—22no—
67C22×C4×C17—21no—
68C22×C4×C17—41no—
69C22×C4×C17C22⋊C411yescharacteristic
70C22×C4×C17C22×C411yescharacteristic
71C22×Dic17—22no—
72C22×Dic17—22no—
73C22×Dic17—21no—
74C22×Dic17—21no—
75C22×Dic17—21no—
76C22×Dic17—21no—
77C22×Dic17—21no—
78C22×Dic17—21no—
79C22×Dic17—41no—
80C22×Dic17—41no—
81C22×Dic17C22⋊C411yescharacteristic
82C22×Dic17C22⋊C411yescharacteristic
83C22×Dic17C2×D411yescharacteristic
84C22×Dic17C2×D411yescharacteristic
85C2×Dic34—22no—
86C2×Dic34—41no—
87C2×Dic34—41no—
88#63247—48no—
89C2×#3624—24no—
90C2×#3624—42no—
91C2×#3624—42no—
92C2×#3624—42no—
93C2×#3624—42no—
94C2×#3624—42no—
95C4⋊C4×C17—41no—
96C22⋊C4×C17—42no—
97C22⋊Dic17—42no—
98C22⋊Dic17—42no—
99C22⋊Dic17—42no—
100C22⋊Dic17—41no—
101C22⋊Dic17—41no—
102C22⋊Dic17—41no—
103C22⋊Dic17—41no—
104C4⋊Dic17—41no—
105#63225—42no—
106C4×Dic17—22no—
107C4×Dic17—22no—
108C4×Dic17—41no—
109C4×Dic17—41no—
110#7710—171nomaximal, Sylow
111C23×C17—21no—
112C23×C17—21no—
113C23×C17—21no—
114C23×C17—21no—
115C23×C17—21no—
116C23×C17—21no—
117C23×C17—41no—
118C23×C17—41no—
119C23×C17—41no—
120C23×C17—41no—
121C23×C17—41no—
122C23×C17—41no—
123C23×C17—41no—
124C23×C17#10412yes—
125C23×C17C2×C22⋊C411yescharacteristic
126D4×C17—82no—
127D4×C17—84no—
128C2×C4×C17—21no—
129C2×C4×C17—21no—
130C2×C4×C17—21no—
131C2×C4×C17—21no—
132C2×C4×C17—44no—
133C2×C4×C17—41no—
134C2×C4×C17—41no—
135C2×C4×C17—41no—
136C2×C4×C17#10012yes—
137C2×C4×C17#13112yes—
138C2×Dic17—24no—
139C2×Dic17—24no—
140C2×Dic17—21no—
141C2×Dic17—21no—
142C2×Dic17—21no—
143C2×Dic17—21no—
144C2×Dic17—21no—
145C2×Dic17—21no—
146C2×Dic17—21no—
147C2×Dic17—21no—
148C2×Dic17—21no—
149C2×Dic17—42no—
150C2×Dic17—42no—
151C2×Dic17—41no—
152C2×Dic17—41no—
153C2×Dic17—41no—
154C2×Dic17—41no—
155C2×Dic17—41no—
156C2×Dic17—41no—
157C2×Dic17#9912yes—
158C2×Dic17AGL(1,ℤ/8)11yescharacteristic
159C2×Dic17AGL(1,ℤ/8)11yescharacteristic
160C2×Dic17#13711yescharacteristic
161C2×Dic17#13711yescharacteristic
162Dic34—82no—
163#3624—44no—
164#3624—82no—
165#2850—171no—
166#1797—171no—
167#1728—171no—
168#1272—172no—
169#1270—172no—
170C22×C17—22no—
171C22×C17—22no—
172C22×C17—22no—
173C22×C17—41no—
174C22×C17—41no—
175C22×C17—41no—
176C22×C17—41no—
177C22×C17—81no—
178C22×C17—81no—
179C22×C17—81no—
180C22×C17—81no—
181C22×C17—81no—
182C22×C17—81no—
183C22×C17—81no—
184C22×C17#40811yescharacteristic
185C22×C17C2×#9911yescharacteristic
186C22×C17C2×#10011yescharacteristic
187C22×C17#41711yescharacteristic
188C22×C17#41711yescharacteristic
189C22×C17C2×#10411yescharacteristic
190C22×C17#42111yescharacteristic
191C4×C17—22no—
192C4×C17—22no—
193C4×C17—81no—
194Dic17—21no—
195Dic17—22no—
196Dic17—21no—
197Dic17—21no—
198Dic17—21no—
199Dic17—41no—
200Dic17—81no—
201Dic17—81no—
202C22×M16—341no—
203C2×#124—171no—
204C2×C22⋊Q8—171no—
205C2×#121#59511yescharacteristic
206C22×C42—171no—
207C2×C4⋊C8—341no—
208C2×C22⋊C8—341no—
209#391—171no—
210#390—171no—
211#388—341no—
212#388—341no—
213#386—341no—
214#386—341no—
215#382—171no—
216#336—172no—
217#336—172no—
218#336—341no—
219C2×C17—42no—
220C2×C17—161no—
221C2×C17#147111yescharacteristic
222C2×C17#148311yescharacteristic
223C2×C17#149511yescharacteristic
224C2×C17#150411yescharacteristic
225C2×C17#151311yescharacteristic
226C2×C17#152711yescharacteristic
227C2×C17#156011yescharacteristic
228C22×Q8—171no—
229C22×D4—21no—
230C22×D4C2×#59511yescharacteristic
231C23×C4—171no—
232C23×C4—171no—
233C23×C4C2×#59511yescharacteristic
234C2×M16—344no—
235C2×M16—682no—
236C2×M16—682no—
237C22×C8—342no—
238C22×C8—342no—
239#124—682no—
240C22⋊Q8—682no—
241#121—42no—
242C2×C4⋊C4—171no—
243C2×C4⋊C4—341no—
244C2×C4⋊C4C2×#59511yescharacteristic
245C2×C22⋊C4—21no—
246C2×C22⋊C4—341no—
247C2×C22⋊C4—341no—
248C2×C22⋊C4—341no—
249C2×C22⋊C4—341no—
250C2×C22⋊C4—341no—
251C2×C42—171no—
252C2×C42—171no—
253C2×C42—171no—
254C2×C42—171no—
255C2×C42—682no—
256C4⋊C8—682no—
257C22⋊C8—682no—
258#95—341no—
259#95—341no—
260#95—341no—
261#95—341no—
262C17#771011yescharacteristic, complemented, Sylow
263C24—21no—
264C24C22⋊#59511yescharacteristic
265C2×Q8—342no—
266C2×Q8—681no—
267C2×Q8—681no—
268C2×D4—22no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—42no—
272C2×D4—42no—
273C2×D4—42no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—21no—
277C22×C4—41no—
278C22×C4—171no—
279C22×C4—171no—
280C22×C4—171no—
281C22×C4—171no—
282C22×C4—342no—
283C22×C4—341no—
284C22×C4—341no—
285C22×C4—341no—
286C22×C4—341no—
287C22×C4—342no—
288C22×C4—341no—
289C22×C4—341no—
290C22×C4—681no—
291C22×C4—681no—
292C22×C4C22⋊#59511yescharacteristic
293C22×C4C22×#59511yescharacteristic
294M16—688no—
295C2×C8—344no—
296C2×C8—682no—
297C2×C8—682no—
298C2×C8—682no—
299C2×C8—682no—
300C2×C8—682no—
301C4⋊C4—41no—
302C4⋊C4—681no—
303C4⋊C4—682no—
304C22⋊C4—42no—
305C22⋊C4—681no—
306C22⋊C4—681no—
307C22⋊C4—681no—
308C22⋊C4—681no—
309C22⋊C4—682no—
310C22⋊C4—682no—
311C22⋊C4—682no—
312C42—342no—
313C42—342no—
314C42—681no—
315C42—681no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23#1058754812yes—
330C23C2×C22⋊#59511yescharacteristic
331Q8—1362no—
332D4—82no—
333D4—84no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—44no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—172no—
343C2×C4—171no—
344C2×C4—171no—
345C2×C4—171no—
346C2×C4—171no—
347C2×C4—344no—
348C2×C4—344no—
349C2×C4—341no—
350C2×C4—341no—
351C2×C4—341no—
352C2×C4—341no—
353C2×C4—341no—
354C2×C4—341no—
355C2×C4—341no—
356C2×C4—341no—
357C2×C4—341no—
358C2×C4—682no—
359C2×C4—682no—
360C2×C4—681no—
361C2×C4—681no—
362C2×C4—681no—
363C2×C4—681no—
364C2×C4—681no—
365C2×C4—681no—
366C2×C4#1058755312yes—
367C2×C4#1058767812yes—
368C8—684no—
369C8—1362no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22#1176378211yescharacteristic
385C22D17⋊#9911yescharacteristic
386C22C2×#1058755311yescharacteristic
387C22#1176380011yescharacteristic
388C22#1176380011yescharacteristic
389C22C2×#1058754811yescharacteristic
390C22#1176380711yescharacteristic
391C4—22no—
392C4—22no—
393C4—81no—
394C4—341no—
395C4—342no—
396C4—341no—
397C4—341no—
398C4—341no—
399C4—681no—
400C4—1361no—
401C4—1361no—
402C2—42no—
403C2—161no—
404C2#1454406011yescharacteristic
405C2#1454409911yescharacteristic
406C2#1454413911yescharacteristic
407C2#1454416911yescharacteristic
408C2#1454420011yescharacteristic
409C2#1454424311yescharacteristic
410C2#1454432111yescharacteristic
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#7710
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. #14544638C2semidirect
2. #14544447C2semidirect
3. #14543605C2semidirect
4. #14543600C2semidirect
262. C17#7710semidirect

Maximal subgroups

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

subgroupindex
#145446382
#145444472
#145436052
#145436002
#145370832
#771017