Finite Group Databasebeta

← #17950188

Subgroups — #17950188

Order 4352.

526 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 98 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#14544640C211yesmaximal, characteristic, complemented
2#14544638C211yesmaximal, characteristic, complemented
3#14543603C212yesmaximal, complemented
4#14543600C212yesmaximal, complemented
5#14537110C211yesmaximal, characteristic
6C2×#10587544—21no—
7C2×C4⋊#3624—21no—
8C2×C22⋊#3624—21no—
9C2×C22⋊#3624—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587621—21no—
13C22×C4×Dic17C2211yescharacteristic
14#11762712C411yescharacteristic
15#11762712C2211yescharacteristic
16#11762705C411yescharacteristic
17#11762705C2211yescharacteristic
18#11762697—21no—
19#11762697—21no—
20#11762689—21no—
21#11762669C411yescharacteristic
22C2×C17×#121C411yescharacteristic
23C22×D4×C17—21no—
24C22×D4×C17C2×C411yescharacteristic
25C23×C4×C17C2×C411yescharacteristic
26C23×Dic17D411yescharacteristic
27C23×Dic17D411yescharacteristic
28C22×#3624—22no—
29C22×#3624—22no—
30C17×#121—42no—
31C2×C4⋊C4×C17C2×C411yescharacteristic
32C2×C22⋊C4×C17—21no—
33C2×C22⋊Dic17—21no—
34C2×C22⋊Dic17—21no—
35C2×C22⋊Dic17—21no—
36C2×C22⋊Dic17—21no—
37C2×C22⋊Dic17—21no—
38#10587621—42no—
39#10587621—42no—
40C2×C4⋊Dic17C2×C411yescharacteristic
41C2×C4⋊Dic17C2×C411yescharacteristic
42C2×#63225—21no—
43C2×#63225—21no—
44C2×C4×Dic17—42no—
45C2×C4×Dic17C2×C411yescharacteristic
46C2×C4×Dic17D411yescharacteristic
47C2×C4×Dic17D411yescharacteristic
48C2×C4×Dic17C2311yescharacteristic
49C22⋊#3624—42no—
50C22⋊#3624—42no—
51#10587544—42no—
52C4⋊#3624—42no—
53#10587502—21no—
54#10587502—21no—
55#10587502—21no—
56C24×C17—21no—
57C24×C17C22⋊C411yescharacteristic
58C2×D4×C17—22no—
59C2×D4×C17—41no—
60C2×D4×C17—41no—
61C2×D4×C17—42no—
62C2×D4×C17—42no—
63C2×D4×C17—42no—
64C22×C4×C17—22no—
65C22×C4×C17—22no—
66C22×C4×C17—21no—
67C22×C4×C17—41no—
68C22×C4×C17C22⋊C411yescharacteristic
69C22×C4×C17C22×C411yescharacteristic
70C22×Dic17—21no—
71C22×Dic17—21no—
72C22×Dic17—21no—
73C22×Dic17—21no—
74C22×Dic17—41no—
75C22×Dic17—41no—
76C22×Dic17—41no—
77C22×Dic17—41no—
78C22×Dic17C22⋊C411yescharacteristic
79C22×Dic17C22⋊C411yescharacteristic
80C22×Dic17D812yes—
81C22×Dic17SD1612yes—
82C22×Dic17C2×D411yescharacteristic
83C22×Dic17C2×D411yescharacteristic
84C2×#3624—42no—
85C2×#3624—42no—
86C2×#3624—42no—
87C2×#3624—42no—
88C2×#3624—42no—
89C2×#3624—42no—
90C4⋊C4×C17—41no—
91C22⋊C4×C17—42no—
92C22⋊Dic17—42no—
93C22⋊Dic17—42no—
94C22⋊Dic17—42no—
95C22⋊Dic17—41no—
96C22⋊Dic17—41no—
97C22⋊Dic17—41no—
98C22⋊Dic17—41no—
99C4⋊Dic17—22no—
100C4⋊Dic17—41no—
101#63225—42no—
102#63225—41no—
103#63225—41no—
104C4×Dic17—22no—
105C4×Dic17—22no—
106C4×Dic17—41no—
107C4×Dic17—41no—
108#7714—171nomaximal, Sylow
109C23×C17—21no—
110C23×C17—21no—
111C23×C17—21no—
112C23×C17—21no—
113C23×C17—21no—
114C23×C17—21no—
115C23×C17—41no—
116C23×C17—41no—
117C23×C17—41no—
118C23×C17—41no—
119C23×C17—41no—
120C23×C17—41no—
121C23×C17—41no—
122C23×C17#10212yes—
123C23×C17C2×C22⋊C411yescharacteristic
124D4×C17—82no—
125D4×C17—84no—
126C2×C4×C17—21no—
127C2×C4×C17—21no—
128C2×C4×C17—21no—
129C2×C4×C17—21no—
130C2×C4×C17—44no—
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—21no—
144C2×Dic17—21no—
145C2×Dic17—42no—
146C2×Dic17—42no—
147C2×Dic17—42no—
148C2×Dic17—42no—
149C2×Dic17—41no—
150C2×Dic17—41no—
151C2×Dic17—41no—
152C2×Dic17—41no—
153C2×Dic17—41no—
154C2×Dic17—41no—
155C2×Dic17#10212yes—
156C2×Dic17C2×D811yescharacteristic
157C2×Dic17C2×SD1611yescharacteristic
158C2×Dic17AGL(1,ℤ/8)11yescharacteristic
159C2×Dic17#13711yescharacteristic
160#3624—82no—
161#3624—82no—
162#2854—171no—
163#1797—171no—
164#1797—171no—
165#1271—172no—
166#1270—172no—
167C22×C17—22no—
168C22×C17—22no—
169C22×C17—22no—
170C22×C17—41no—
171C22×C17—41no—
172C22×C17—41no—
173C22×C17—41no—
174C22×C17—81no—
175C22×C17—81no—
176C22×C17—81no—
177C22×C17—81no—
178C22×C17—81no—
179C22×C17—81no—
180C22×C17—81no—
181C22×C17#40811yescharacteristic
182C22×C17C2×#9911yescharacteristic
183C22×C17#41311yescharacteristic
184C22×C17C2×#10211yescharacteristic
185C22×C17#41711yescharacteristic
186C22×C17#42111yescharacteristic
187C22×C17#42111yescharacteristic
188C4×C17—22no—
189C4×C17—22no—
190C4×C17—81no—
191Dic17—21no—
192Dic17—21no—
193Dic17—21no—
194Dic17—22no—
195Dic17—21no—
196Dic17—41no—
197Dic17—81no—
198Dic17—81no—
199C2×#123—341no—
200C2×#121#59511yescharacteristic
201C22×C42—171no—
202C2×C4⋊C8—341no—
203C2×C4⋊C8—341no—
204C2×C22⋊C8—341no—
205C2×C22⋊C8—341no—
206#390—171no—
207#390—171no—
208#389—171no—
209#389—171no—
210#388—341no—
211#388—341no—
212#386—341no—
213#380—171no—
214#336—172no—
215#336—172no—
216C2×C17—42no—
217C2×C17—161no—
218C2×C17#146811yescharacteristic
219C2×C17#148011yescharacteristic
220C2×C17#149511yescharacteristic
221C2×C17#151311yescharacteristic
222C2×C17#151911yescharacteristic
223C2×C17#153511yescharacteristic
224C2×C17#154711yescharacteristic
225C22×D4—21no—
226C22×D4C2×#59511yescharacteristic
227C23×C4—171no—
228C23×C4—171no—
229C23×C4C2×#59511yescharacteristic
230C22×C8—342no—
231C22×C8—342no—
232#123—682no—
233#123—682no—
234#121—42no—
235C2×C4⋊C4—171no—
236C2×C4⋊C4—171no—
237C2×C4⋊C4—341no—
238C2×C4⋊C4—341no—
239C2×C4⋊C4C2×#59511yescharacteristic
240C2×C22⋊C4—21no—
241C2×C22⋊C4—341no—
242C2×C22⋊C4—341no—
243C2×C22⋊C4—341no—
244C2×C22⋊C4—341no—
245C2×C22⋊C4—341no—
246C2×C42—171no—
247C2×C42—171no—
248C2×C42—171no—
249C2×C42—171no—
250C2×C42—682no—
251C4⋊C8—682no—
252C4⋊C8—682no—
253C22⋊C8—682no—
254C22⋊C8—682no—
255#95—341no—
256#95—341no—
257#95—341no—
258C17#771411yescharacteristic, complemented, Sylow
259C24—21no—
260C24C22⋊#59511yescharacteristic
261C2×D4—22no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—42no—
265C2×D4—42no—
266C2×D4—42no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—21no—
270C22×C4—41no—
271C22×C4—171no—
272C22×C4—171no—
273C22×C4—171no—
274C22×C4—172no—
275C22×C4—172no—
276C22×C4—171no—
277C22×C4—341no—
278C22×C4—341no—
279C22×C4—341no—
280C22×C4—341no—
281C22×C4—681no—
282C22×C4—681no—
283C22×C4—681no—
284C22×C4—681no—
285C22×C4C22⋊#59511yescharacteristic
286C22×C4C22×#59511yescharacteristic
287C2×C8—682no—
288C2×C8—682no—
289C2×C8—682no—
290C2×C8—682no—
291C2×C8—682no—
292C2×C8—682no—
293C4⋊C4—41no—
294C4⋊C4—342no—
295C4⋊C4—681no—
296C4⋊C4—681no—
297C4⋊C4—682no—
298C4⋊C4—681no—
299C22⋊C4—42no—
300C22⋊C4—681no—
301C22⋊C4—681no—
302C22⋊C4—681no—
303C22⋊C4—682no—
304C22⋊C4—681no—
305C22⋊C4—682no—
306C22⋊C4—682no—
307C42—342no—
308C42—342no—
309C42—681no—
310C42—681no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23#1058754712yes—
325C23C2×C22⋊#59511yescharacteristic
326D4—82no—
327D4—84no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—44no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—171no—
337C2×C4—172no—
338C2×C4—171no—
339C2×C4—171no—
340C2×C4—171no—
341C2×C4—341no—
342C2×C4—341no—
343C2×C4—341no—
344C2×C4—341no—
345C2×C4—341no—
346C2×C4—341no—
347C2×C4—341no—
348C2×C4—341no—
349C2×C4—341no—
350C2×C4—682no—
351C2×C4—682no—
352C2×C4—682no—
353C2×C4—682no—
354C2×C4—681no—
355C2×C4—681no—
356C2×C4—681no—
357C2×C4—681no—
358C2×C4—681no—
359C2×C4—681no—
360C2×C4#1058755112yes—
361C2×C4#1058767812yes—
362C8—1362no—
363C8—1362no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22#1176378211yescharacteristic
379C22C2×#1058755111yescharacteristic
380C22#1176379611yescharacteristic
381C22C2×#1058754711yescharacteristic
382C22#1176380011yescharacteristic
383C22#1176380611yescharacteristic
384C22#1176380711yescharacteristic
385C4—22no—
386C4—22no—
387C4—81no—
388C4—341no—
389C4—341no—
390C4—341no—
391C4—342no—
392C4—341no—
393C4—681no—
394C4—1361no—
395C4—1361no—
396C2—42no—
397C2—161no—
398C2#1454404911yescharacteristic
399C2#1454408911yescharacteristic
400C2#1454413911yescharacteristic
401C2#1454419911yescharacteristic
402C2#1454422011yescharacteristic
403C2#1454426911yescharacteristic
404C2#1454429611yescharacteristic
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#7714
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. #14544640C2semidirect
2. #14544638C2semidirect
3. #14543603C2semidirect
4. #14543600C2semidirect
258. C17#7714semidirect

Maximal subgroups

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

subgroupindex
#145446402
#145446382
#145436032
#145436002
#145371102
#771417