Finite Group Databasebeta

← #17960818

Subgroups — #17960818

Order 4352.

548 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 102 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
1C2×#11763711C212yesmaximal
2C4×#10587553C211yesmaximal, characteristic
3C4×#10587551C211yesmaximal, characteristic
4#14543868C212yesmaximal
5#14531453C211yesmaximal, characteristic
6C2×#10587553C2212yes—
7C2×#10587551C2212yes—
8C4×#63247—21no—
9C4×C22⋊#595—21no—
10#11763711C418yescomplemented
11#11763689—21no—
12#11763687—21no—
13C2×#10587615C2211yescharacteristic
14C2×C4×C22⋊D17C2211yescharacteristic
15#11762704—21no—
16#11762699—21no—
17#11762690—21no—
18#11762688C2211yescharacteristic
19#11762682C411yescharacteristic, complemented
20#11762680—21no—
21#11762672C411yescharacteristic, complemented
22C4×C22⋊Dic17C411yescharacteristic, complemented
23C22×C4⋊C4×C17C411yescharacteristic, complemented
24C23×C4×C17C2×C411yescharacteristic
25C23×C4×C17C2×C411yescharacteristic
26C23×C4×C17C2×C411yescharacteristic
27C22×C22⋊D17C2311yescharacteristic
28C22×C4×D17D411yescharacteristic
29C2×C22⋊#595—22no—
30C2×#63247—22no—
31C2×C4×#595—41no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17—21no—
34C2×C4⋊C4×C17—41no—
35C2×C4⋊C4×C17—41no—
36C2×C22⋊Dic17C2×C411yescharacteristic
37C2×C22⋊Dic17C2×C411yescharacteristic
38C2×C22⋊Dic17C2×C411yescharacteristic
39#10587615—22no—
40#10587615C2×C414yes—
41C4×C22⋊D17—41no—
42C4×C22⋊D17—41no—
43C2×#63227—21no—
44C2×#63227—21no—
45C2×#63227D411yescharacteristic
46C2×#63225—21no—
47C2×#63225—21no—
48C2×#63225D411yescharacteristic
49C2×C4×Dic17—21no—
50C2×C4×Dic17D411yescharacteristic
51#10587553—22no—
52#10587553C2×C414yes—
53#10587551—22no—
54#10587551C2×C414yes—
55(C2×#595)⋊C4—41no—
56#10587542—41no—
57C4×#3624—41no—
58#10587502—21no—
59#10587502—21no—
60#10587502—21no—
61#10587502—21no—
62#10587502—21no—
63C24×C17C22×C411yescharacteristic
64C23×D17C2×D411yescharacteristic
65C22×#595—42no—
66C22×C4×C17—21no—
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17—21no—
70C22×C4×C17—21no—
71C22×C4×C17—41no—
72C22×C4×C17—41no—
73C22×C4×C17—41no—
74C22×C4×C17—81no—
75C22×C4×C17—81no—
76C22×C4×C17C4212yescomplemented
77C22×C4×C17C22⋊C411yescharacteristic
78C22×C4×C17C22⋊C411yescharacteristic
79C2×C22⋊D17—41no—
80C2×C22⋊D17—41no—
81C2×C22⋊D17C22×C412yes—
82C2×C22⋊D17#4112yes—
83C22×Dic17—21no—
84C22×Dic17—21no—
85C22×Dic17C22⋊C411yescharacteristic
86C22×Dic17C22⋊C411yescharacteristic
87C22×Dic17C2×D411yescharacteristic
88C2×C4×D17—21no—
89C2×C4×D17—21no—
90C2×C4×D17—81no—
91C22⋊#595—24no—
92C22⋊#595—42no—
93#63247—24no—
94#63247—42no—
95C2×#3624—42no—
96C4×#595—82no—
97C4⋊C4×C17—42no—
98C4⋊C4×C17—41no—
99C4⋊C4×C17—41no—
100C22⋊Dic17—21no—
101C22⋊Dic17—41no—
102C22⋊Dic17—41no—
103C22⋊Dic17C4212yescomplemented
104#63227—24no—
105#63227—41no—
106#63227—81no—
107#63225—24no—
108#63225—41no—
109#63225—81no—
110C4×Dic17—21no—
111C4×Dic17—21no—
112C4×Dic17—81no—
113#12621—171nomaximal, Sylow
114C23×C17—21no—
115C23×C17—21no—
116C23×C17—41no—
117C23×C17—41no—
118C23×C17C2×C4211yescharacteristic
119C23×C17C2×C22⋊C411yescharacteristic
120C23×C17#11711yescharacteristic
121C22×D17—21no—
122C22×D17—21no—
123C22×D17—41no—
124C22×D17—41no—
125C22×D17C4×D412yes—
126C2×#595—44no—
127C2×#595—82no—
128C2×#595—82no—
129C2×C4×C17—22no—
130C2×C4×C17—21no—
131C2×C4×C17—41no—
132C2×C4×C17—42no—
133C2×C4×C17—41no—
134C2×C4×C17—41no—
135C2×C4×C17—42no—
136C2×C4×C17—41no—
137C2×C4×C17—41no—
138C2×C4×C17—41no—
139C2×C4×C17—41no—
140C2×C4×C17—81no—
141C2×C4×C17—81no—
142C2×C4×C17—82no—
143C2×C4×C17#9911yescharacteristic
144C2×C4×C17#9911yescharacteristic
145C22⋊D17—42no—
146C22⋊D17—42no—
147C2×Dic17—21no—
148C2×Dic17—21no—
149C2×Dic17—22no—
150C2×Dic17—21no—
151C2×Dic17—21no—
152C2×Dic17—41no—
153C2×Dic17—41no—
154C2×Dic17—41no—
155C2×Dic17—41no—
156C2×Dic17—41no—
157C2×Dic17—41no—
158C2×Dic17—41no—
159C2×Dic17C4×D412yes—
160C4×D17—42no—
161C4×D17—81no—
162#3624—44no—
163#2322—171no—
164C2×#352—172no—
165C4×#100—171no—
166C4×#99—171no—
167#1390—172no—
168C22×C17—21no—
169C22×C17—21no—
170C22×C17—21no—
171C22×C17—21no—
172C22×C17—41no—
173C22×C17—41no—
174C22×C17—42no—
175C22×C17—41no—
176C22×C17—41no—
177C22×C17C4×C22⋊C411yescharacteristic
178C22×C17C2×#9911yescharacteristic
179C22×C17#41011yescharacteristic
180C2×D17—22no—
181C2×D17—41no—
182C2×D17—41no—
183C2×D17—42no—
184C2×D17—81no—
185#595—84no—
186C4×C17—21no—
187C4×C17—21no—
188C4×C17—41no—
189C4×C17—42no—
190C4×C17—81no—
191Dic17—22no—
192Dic17—42no—
193Dic17—41no—
194Dic17—41no—
195Dic17—81no—
196C2×#123—171no—
197C2×C4×D4—171no—
198C22×C4⋊C4#59511yescharacteristic, complemented
199C2×#100—172no—
200C2×#99—172no—
201C4×M16—341no—
202#389—341no—
203#388—341no—
204#387—341no—
205#386—171no—
206#385—171no—
207#385—341no—
208#381—171no—
209C4×C22⋊C4—171no—
210C4×C22⋊C4—341no—
211#352—178no—
212#343—341no—
213#342—341no—
214C2×C17—21no—
215C2×C17—21no—
216C2×C17—41no—
217C2×C17—41no—
218C2×C17C4×#9911yescharacteristic
219C2×C17#212111yescharacteristic
220C2×C17#212311yescharacteristic
221D17—42no—
222C22×D4—171no—
223C23×C4—171no—
224C23×C4C2×#59511yescharacteristic
225C23×C4C2×#59511yescharacteristic
226C23×C4C2×#59511yescharacteristic
227C2×M16—342no—
228#123—174no—
229#123—342no—
230C4×D4—681no—
231C4×D4—681no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—41no—
235C2×C4⋊C4—41no—
236C2×C4⋊C4—171no—
237C2×C4⋊C4—341no—
238C2×C4⋊C4—341no—
239C2×C22⋊C4—171no—
240C2×C22⋊C4—171no—
241C2×C22⋊C4—171no—
242C2×C22⋊C4—171no—
243C2×C22⋊C4—341no—
244C2×C22⋊C4—342no—
245C2×C22⋊C4—341no—
246C2×C42—171no—
247C2×C42—341no—
248C2×C42—681no—
249#100—174no—
250#100—342no—
251#99—174no—
252#99—342no—
253#97—681no—
254C4×C8—681no—
255#95—341no—
256#95—341no—
257#95—341no—
258#95—341no—
259#95—341no—
260#95—681no—
261C17#1262111yescharacteristic, complemented, Sylow
262C24—171no—
263C24C22×#59511yescharacteristic
264C2×D4—172no—
265C2×D4—172no—
266C2×D4—681no—
267C2×D4—681no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—81no—
277C22×C4—81no—
278C22×C4—171no—
279C22×C4—171no—
280C22×C4—171no—
281C22×C4—341no—
282C22×C4—341no—
283C22×C4—341no—
284C22×C4—341no—
285C22×C4—682no—
286C22×C4—1361no—
287C22×C4C4×#59512yescomplemented
288C22×C4C22⋊#59511yescharacteristic
289C22×C4C22⋊#59511yescharacteristic
290M16—344no—
291M16—682no—
292C2×C8—682no—
293C4⋊C4—42no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—344no—
297C4⋊C4—681no—
298C4⋊C4—1361no—
299C22⋊C4—172no—
300C22⋊C4—344no—
301C22⋊C4—341no—
302C22⋊C4—344no—
303C22⋊C4—681no—
304C22⋊C4—681no—
305C22⋊C4—682no—
306C22⋊C4—681no—
307C22⋊C4—1361no—
308C42—341no—
309C42—341no—
310C42—1361no—
311C42—1362no—
312C23—21no—
313C23—21no—
314C23—41no—
315C23—41no—
316C23—172no—
317C23—341no—
318C23—341no—
319C23—681no—
320C23—681no—
321C23C2×C4×#59511yescharacteristic
322C23#1058767711yescharacteristic
323C23C2×C22⋊#59511yescharacteristic
324D4—682no—
325D4—682no—
326C2×C4—22no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—82no—
340C2×C4—172no—
341C2×C4—341no—
342C2×C4—341no—
343C2×C4—342no—
344C2×C4—341no—
345C2×C4—341no—
346C2×C4—682no—
347C2×C4—681no—
348C2×C4—681no—
349C2×C4—681no—
350C2×C4—681no—
351C2×C4—681no—
352C2×C4—681no—
353C2×C4—684no—
354C2×C4—681no—
355C2×C4—1361no—
356C2×C4—1362no—
357C2×C4—1362no—
358C2×C4#1058755111yescharacteristic
359C2×C4#1058755111yescharacteristic
360C8—684no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—41no—
366C22—41no—
367C22—42no—
368C22—41no—
369C22—41no—
370C22—342no—
371C22—682no—
372C22—681no—
373C22—681no—
374C22—1361no—
375C22C4×C22⋊#59511yescharacteristic
376C22C2×#1058755111yescharacteristic
377C22#1176378811yescharacteristic
378C4—21no—
379C4—21no—
380C4—41no—
381C4—42no—
382C4—81no—
383C4—342no—
384C4—682no—
385C4—681no—
386C4—681no—
387C4—1361no—
388C4—1364no—
389C2—21no—
390C2—21no—
391C2—41no—
392C2—41no—
393C2—682no—
394C2C4×#1058755111yescharacteristic
395C2#1454503911yescharacteristic
396C2#1454504611yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC23×C17C2×C42
FrattiniC24C22×#595
FittingC22×C4⋊C4×C17C4
socleC22×C17C2×#99
prime radical, cosocleC22×C22⋊D17C23
hypercenterC22×C4⋊C4#595
hypocenterC17#12621
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
10. #11763711C4semidirect
19. #11762682C4semidirect
21. #11762672C4semidirect
22. C4×C22⋊Dic17C4semidirect
23. C22×C4⋊C4×C17C4semidirect
76. C22×C4×C17C42semidirect
103. C22⋊Dic17C42semidirect
198. C22×C4⋊C4#595semidirect
261. C17#12621semidirect
287. C22×C4C4×#595semidirect

Maximal subgroups

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

subgroupindex
C2×#117637112
C4×#105875532
C4×#105875512
#145438682
#145314532
#1262117