Finite Group Databasebeta

← C4×#11763711 #17960813

Subgroups — C4×#11763711 #17960813

Order 4352.

576 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 106 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
5C4×#10587615C211yesmaximal, characteristic
6C2×#10587553C2212yes—
7C2×#10587551C2212yes—
8C4×#63247—21no—
9C4×C22⋊#595—21no—
10#11763711C418yesdirect product factor
11#11763689—21no—
12#11763687—21no—
13C2×#10587615C2211yescharacteristic
14C2×C4×C22⋊D17C2211yescharacteristic
15#11762700—21no—
16#11762693—21no—
17#11762688C2211yescharacteristic
18#11762682C411yescharacteristic, complemented
19#11762672C411yescharacteristic, complemented
20C4×#63225—21no—
21C4×#63227—21no—
22C4×C22⋊Dic17C411yescharacteristic, complemented
23C22×C42×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×C42×C17—21no—
33C2×C42×C17—21no—
34C2×C42×C17—41no—
35C2×C42×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—42no—
72C22×C4×C17—42no—
73C22×C4×C17—41no—
74C22×C4×C17—41no—
75C22×C4×C17—41no—
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—42no—
91C22⋊#595—24no—
92C22⋊#595—42no—
93#63247—24no—
94#63247—42no—
95C2×#3624—42no—
96C4×#595—82no—
97C42×C17—42no—
98C42×C17—41no—
99C42×C17—41no—
100C22⋊Dic17—21no—
101C22⋊Dic17—41no—
102C22⋊Dic17—41no—
103C22⋊Dic17C4212yescomplemented
104#63227—24no—
105#63227—41no—
106#63227—42no—
107#63225—24no—
108#63225—41no—
109#63225—42no—
110C4×Dic17—21no—
111C4×Dic17—21no—
112C4×Dic17—42no—
113C4×#352—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—22no—
131C2×C4×C17—22no—
132C2×C4×C17—21no—
133C2×C4×C17—42no—
134C2×C4×C17—41no—
135C2×C4×C17—42no—
136C2×C4×C17—42no—
137C2×C4×C17—41no—
138C2×C4×C17—41no—
139C2×C4×C17—41no—
140C2×C4×C17—42no—
141C2×C4×C17—42no—
142C2×C4×C17—41no—
143C2×C4×C17—42no—
144C2×C4×C17#9911yescharacteristic
145C2×C4×C17#9911yescharacteristic
146C22⋊D17—42no—
147C22⋊D17—42no—
148C2×Dic17—21no—
149C2×Dic17—21no—
150C2×Dic17—22no—
151C2×Dic17—21no—
152C2×Dic17—21no—
153C2×Dic17—41no—
154C2×Dic17—41no—
155C2×Dic17—41no—
156C2×Dic17—41no—
157C2×Dic17—41no—
158C2×Dic17—41no—
159C2×Dic17—41no—
160C2×Dic17C4×D412yes—
161C4×D17—42no—
162C4×D17—81no—
163#3624—44no—
164C4×#123—171no—
165C2×#352—172no—
166C4×#100—171no—
167C4×#99—171no—
168#1390—172no—
169C22×C17—21no—
170C22×C17—21no—
171C22×C17—21no—
172C22×C17—21no—
173C22×C17—41no—
174C22×C17—41no—
175C22×C17—42no—
176C22×C17—41no—
177C22×C17—41no—
178C22×C17C4×C22⋊C411yescharacteristic
179C22×C17C2×#9911yescharacteristic
180C22×C17#41011yescharacteristic
181C2×D17—22no—
182C2×D17—41no—
183C2×D17—41no—
184C2×D17—42no—
185C2×D17—81no—
186#595—84no—
187C4×C17—21no—
188C4×C17—41no—
189C4×C17—42no—
190C4×C17—42no—
191C4×C17#35212yescomplemented
192Dic17—22no—
193Dic17—42no—
194Dic17—41no—
195Dic17—41no—
196Dic17—81no—
197C2×#123—171no—
198C2×C4×D4—171no—
199C22×C42#59511yescharacteristic, complemented
200C2×#100—172no—
201C2×#99—172no—
202C4×M16—341no—
203#388—341no—
204#387—341no—
205#386—171no—
206#385—171no—
207#381—171no—
208C4×C4⋊C4—341no—
209C4×C22⋊C4—171no—
210C4×C22⋊C4—341no—
211C4×C22⋊C4—341no—
212#352—178no—
213#343—341no—
214#342—341no—
215C2×C17—21no—
216C2×C17—21no—
217C2×C17—41no—
218C2×C17—41no—
219C2×C17C4×#9911yescharacteristic
220C2×C17C2×#35211yescharacteristic
221C2×C17#212011yescharacteristic
222D17—42no—
223C22×D4—171no—
224C23×C4—171no—
225C23×C4C2×#59511yescharacteristic
226C23×C4C2×#59511yescharacteristic
227C23×C4C2×#59511yescharacteristic
228C2×M16—342no—
229#123—174no—
230#123—342no—
231C4×D4—681no—
232C4×D4—681no—
233C2×C4⋊C4—171no—
234C2×C4⋊C4—341no—
235C2×C4⋊C4—341no—
236C2×C22⋊C4—171no—
237C2×C22⋊C4—171no—
238C2×C22⋊C4—171no—
239C2×C22⋊C4—171no—
240C2×C22⋊C4—341no—
241C2×C22⋊C4—342no—
242C2×C22⋊C4—341no—
243C2×C42—21no—
244C2×C42—21no—
245C2×C42—41no—
246C2×C42—41no—
247C2×C42—171no—
248C2×C42—341no—
249C2×C42—681no—
250#100—174no—
251#100—342no—
252#99—174no—
253#99—342no—
254#97—681no—
255C4×C8—681no—
256#95—341no—
257#95—341no—
258#95—341no—
259#95—341no—
260#95—341no—
261#95—681no—
262C17C4×#35211yescharacteristic, complemented, Sylow
263C24—171no—
264C24C22×#59511yescharacteristic
265C2×D4—172no—
266C2×D4—172no—
267C2×D4—681no—
268C2×D4—681no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—171no—
280C22×C4—171no—
281C22×C4—171no—
282C22×C4—341no—
283C22×C4—341no—
284C22×C4—341no—
285C22×C4—341no—
286C22×C4—682no—
287C22×C4—682no—
288C22×C4C4×#59512yescomplemented
289C22×C4C22⋊#59511yescharacteristic
290C22×C4C22⋊#59511yescharacteristic
291M16—344no—
292M16—682no—
293C2×C8—682no—
294C4⋊C4—344no—
295C4⋊C4—681no—
296C4⋊C4—682no—
297C22⋊C4—172no—
298C22⋊C4—344no—
299C22⋊C4—341no—
300C22⋊C4—344no—
301C22⋊C4—681no—
302C22⋊C4—682no—
303C22⋊C4—681no—
304C22⋊C4—682no—
305C22⋊C4—681no—
306C42—42no—
307C42—41no—
308C42—41no—
309C42—341no—
310C42—341no—
311C42—682no—
312C42—1362no—
313C23—21no—
314C23—21no—
315C23—41no—
316C23—41no—
317C23—172no—
318C23—341no—
319C23—341no—
320C23—681no—
321C23—681no—
322C23C2×C4×#59511yescharacteristic
323C23#1058767711yescharacteristic
324C23C2×C22⋊#59511yescharacteristic
325D4—682no—
326D4—682no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—172no—
343C2×C4—341no—
344C2×C4—341no—
345C2×C4—342no—
346C2×C4—341no—
347C2×C4—341no—
348C2×C4—681no—
349C2×C4—681no—
350C2×C4—682no—
351C2×C4—681no—
352C2×C4—681no—
353C2×C4—681no—
354C2×C4—681no—
355C2×C4—684no—
356C2×C4—681no—
357C2×C4—1361no—
358C2×C4—1362no—
359C2×C4—1362no—
360C2×C4#1058755111yescharacteristic
361C2×C4#1058755111yescharacteristic
362C8—684no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—41no—
368C22—41no—
369C22—42no—
370C22—41no—
371C22—41no—
372C22—342no—
373C22—682no—
374C22—681no—
375C22—681no—
376C22—1361no—
377C22C4×C22⋊#59511yescharacteristic
378C22C2×#1058755111yescharacteristic
379C22#1176378811yescharacteristic
380C4—21no—
381C4—41no—
382C4—42no—
383C4—42no—
384C4—342no—
385C4—682no—
386C4—681no—
387C4—681no—
388C4—1361no—
389C4—1364no—
390C4#1176371112yesdirect product factor
391C2—21no—
392C2—21no—
393C2—41no—
394C2—41no—
395C2—682no—
396C2C4×#1058755111yescharacteristic
397C2C2×#1176371111yescharacteristic
398C2#1454503511yescharacteristic
subgroupG/H
centerC2×C4#10587551
commutatorC23×C17C2×C42
FrattiniC24C22×#595
FittingC22×C42×C17C4
socleC22×C17C2×#99
prime radical, cosocleC22×C22⋊D17C23
hypercenterC22×C42#595
hypocenterC17C4×#352
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
10. #11763711C4direct (N × H)
18. #11762682C4semidirect
19. #11762672C4semidirect
22. C4×C22⋊Dic17C4semidirect
23. C22×C42×C17C4semidirect
76. C22×C4×C17C42semidirect
103. C22⋊Dic17C42semidirect
191. C4×C17#352semidirect
199. C22×C42#595semidirect
262. C17C4×#352semidirect
288. C22×C4C4×#595semidirect
390. C4#11763711direct (N × H)

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
C4×#105876152
C4×#35217