Finite Group Databasebeta

← C4×#63741 #11783889

Subgroups — C4×#63741 #11783889

Order 1152.

644 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C4×#3805C211yesmaximal, characteristic
2C4×#3792C211yesmaximal, characteristic, complemented
3C2×#63741C212yesmaximal
4C4×Dic32C211yesmaximal, characteristic, complemented
5#10590074C212yesmaximal, complemented
6C2×#3805C2211yescharacteristic
7C2×#3792C2212yes—
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C3×C4×#67—21no—
10C2×C3×C4×Dic3—21no—
11#67⋊Dic3—21no—
12#63957C2211yescharacteristic
13C2×Dic32—21no—
14C2×Dic32C2212yes—
15C4×#627C411yescharacteristic, complemented
16#63902C411yescharacteristic, complemented
17C4×#625C411yescharacteristic, complemented
18#63878—21no—
19C4×D3×Dic3—21no—
20#63838C411yescharacteristic, complemented
21#63777—21no—
22C4×#622—21no—
23#63741C418yesdirect product factor
24C4×#237—61no—
25C42×Dic3—61no—
26C22×C32×C4D411yescharacteristic
27C22×C3⋊Dic3D411yescharacteristic
28C22×C3⋊Dic3C2311yescharacteristic
29C2×C3×#67—21no—
30C22×C3×Dic3—22no—
31C2×C3×C4×D3—21no—
32C2×#627C2×C411yescharacteristic
33C2×#625C2×C411yescharacteristic
34#3805—22no—
35#3805C2×C414yes—
36C2×D3×Dic3—21no—
37C2×D3×Dic3—21no—
38#3792—22no—
39#3792C2×C414yescomplemented
40C2×#622—22no—
41C4×C3⋊Dic3C2×C411yescharacteristic
42C4×C3⋊Dic3C2×C411yescharacteristic
43C4×C3⋊Dic3D411yescharacteristic
44C4×C3⋊Dic3D411yescharacteristic
45C3×#217—21no—
46C3×(C2×D3)⋊C4—21no—
47C3×Dic3⋊C4—21no—
48C3×C4×Dic3—24no—
49C3×C4×Dic3—21no—
50#3724C2×C411yescharacteristic
51#3724C2×C411yescharacteristic
52Dic3⋊Dic3—21no—
53(C2×D3)⋊Dic3—21no—
54Dic32—24no—
55Dic32—21no—
56Dic32—21no—
57Dic32—22no—
58Dic32C2×C414yescomplemented
59C4×#104—91nomaximal, Sylow
60C2×#237—61no—
61C3×C4×D4—61no—
62C2×C3×C42—61no—
63D4×Dic3—61no—
64C4×#67—21no—
65C4×#67—61no—
66C2×C4×Dic3—21no—
67C2×C4×Dic3—62no—
68C2×C4×Dic3—61no—
69C2×C4×Dic3—61no—
70C2×C4×Dic3—61no—
71C2×C4×Dic3—62no—
72#892—61no—
73#887—61no—
74#67⋊C4—61no—
75#67⋊C4—61no—
76#877—61no—
77#877—61no—
78C42×D3—61no—
79C4×Dic6—61no—
80C23×C32C2×D411yescharacteristic
81C22×C3×D3—21no—
82C2×C32×C4—22no—
83C2×C32×C4C22⋊C411yescharacteristic
84C2×C32×C4C22⋊C411yescharacteristic
85C2×C3⋊Dic3—22no—
86C2×C3⋊Dic3C22⋊C411yescharacteristic
87C2×C3⋊Dic3C22⋊C411yescharacteristic
88C2×C3⋊Dic3C22×C411yescharacteristic
89C2×C3⋊Dic3C22×C412yes—
90C2×C3⋊Dic3C2×D411yescharacteristic
91C2×C3⋊Dic3#4112yes—
92C3×#67—24no—
93C2×C3×Dic3—24no—
94C2×C3×Dic3—24no—
95C2×C3×Dic3—21no—
96C2×C3×Dic3—24no—
97C2×C3×Dic3—21no—
98C2×C3×Dic3—21no—
99C3×C4×D3—42no—
100#627—21no—
101#627C4212yescomplemented
102#625—21no—
103#625C4212yescomplemented
104D3×Dic3—24no—
105D3×Dic3—42no—
106#622—24no—
107C4×#41—91no—
108C2×#104—92no—
109C4×M16—91no—
110C43—91no—
111#339—92no—
112C2×C3×D4—61no—
113C22×C3×C4—21no—
114C22×C3×C4—21no—
115C22×C3×C4—61no—
116C22×C3×C4—62no—
117C2×#67—21no—
118C2×#67—61no—
119C22×Dic3—22no—
120C22×Dic3—61no—
121C22×Dic3—61no—
122C22×Dic3—61no—
123C22×Dic3—61no—
124C22×Dic3—61no—
125C22×Dic3—61no—
126#237—64no—
127#237—64no—
128C2×C4×D3—21no—
129C2×C4×D3—61no—
130C2×C4×D3—61no—
131C2×Dic6—61no—
132C3×C4⋊C4—61no—
133C3×C22⋊C4—61no—
134C3×C22⋊C4—61no—
135C3×C42—61no—
136C3×C42—64no—
137#217—21no—
138#217—61no—
139(C2×D3)⋊C4—21no—
140(C2×D3)⋊C4—61no—
141C4⋊Dic3—61no—
142Dic3⋊C4—21no—
143Dic3⋊C4—61no—
144Dic3⋊C4—61no—
145Dic3⋊C4—61no—
146C4×Dic3—21no—
147C4×Dic3—24no—
148C4×Dic3—64no—
149C4×Dic3—61no—
150C4×Dic3—61no—
151C4×Dic3—61no—
152C4×Dic3—61no—
153C4×Dic3—61no—
154C4×Dic3—61no—
155C4×Dic3—61no—
156C4×Dic3—61no—
157C4×Dic3—61no—
158C4×Dic3—61no—
159C4×Dic3—61no—
160C4×Dic3—61no—
161C4×Dic3—64no—
162C4×Dic3—68no—
163C22×C32—21no—
164C22×C32—21no—
165C22×C32C2×C22⋊C411yescharacteristic
166C22×C32C4×D412yes—
167C2×C3×D3—22no—
168C2×C3×D3—41no—
169C2×C3×D3—41no—
170C32×C4—21no—
171C32×C4#10412yescomplemented
172C3⋊Dic3—21no—
173C3⋊Dic3#10412yescomplemented
174C3⋊Dic3C2×C4211yescharacteristic
175C3⋊Dic3#11711yescharacteristic
176C3⋊Dic3C4×D412yes—
177C3×Dic3—28no—
178C3×Dic3—22no—
179C3×Dic3—41no—
180C3×Dic3—41no—
181C2×#41—91no—
182C2×M16—92no—
183C4×Q8—91no—
184C4×Q8—91no—
185C4×D4—61no—
186C4×D4—91no—
187C4×D4—91no—
188C4×D4—181no—
189#117—91no—
190#117—181no—
191C2×C42—61no—
192C2×C42—91no—
193C2×C42—92no—
194C2×C42—181no—
195C2×C42—181no—
196#104—98no—
197#97—181no—
198C4×C8—181no—
199C23×C3—21no—
200C23×C3—21no—
201C23×C3—61no—
202C22×D3—21no—
203C3×D4—64no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—42no—
211C2×C3×C4—64no—
212C2×C3×C4—64no—
213C2×C3×C4—61no—
214C2×C3×C4—64no—
215C2×C3×C4—61no—
216C2×C3×C4—61no—
217C2×C3×C4—122no—
218#67—24no—
219#67—62no—
220#67—62no—
221C2×Dic3—24no—
222C2×Dic3—21no—
223C2×Dic3—24no—
224C2×Dic3—24no—
225C2×Dic3—21no—
226C2×Dic3—21no—
227C2×Dic3—61no—
228C2×Dic3—61no—
229C2×Dic3—61no—
230C2×Dic3—61no—
231C2×Dic3—62no—
232C2×Dic3—61no—
233C2×Dic3—62no—
234C2×Dic3—61no—
235C2×Dic3—61no—
236C2×Dic3—62no—
237C2×Dic3—62no—
238C2×Dic3—61no—
239C2×Dic3—64no—
240C2×Dic3—64no—
241C2×Dic3—122no—
242C2×Dic3—122no—
243C4×D3—42no—
244C4×D3—64no—
245C4×D3—122no—
246Dic6—62no—
247Dic6—62no—
248C2×C32—22no—
249C2×C32C4×C22⋊C411yescharacteristic
250C2×C32C2×#10411yescharacteristic
251C2×C32C2×#10411yescharacteristic
252C3×D3—42no—
253#41—94no—
254#41—182no—
255C2×Q8—91no—
256C2×D4—61no—
257C2×D4—91no—
258C22×C4—62no—
259C22×C4—61no—
260C22×C4—91no—
261C22×C4—91no—
262C22×C4—181no—
263C22×C4—181no—
264C22×C4GO+(4,𝔽2)11yescharacteristic
265M16—94no—
266M16—182no—
267C2×C8—182no—
268C4⋊C4—61no—
269C4⋊C4—91no—
270C4⋊C4—91no—
271C4⋊C4—181no—
272C22⋊C4—61no—
273C22⋊C4—61no—
274C22⋊C4—181no—
275C42—64no—
276C42—61no—
277C42—94no—
278C42—91no—
279C42—91no—
280C42—91no—
281C42—91no—
282C42—182no—
283C42—181no—
284C42—181no—
285C42—184no—
286C22×C3—21no—
287C22×C3—22no—
288C22×C3—21no—
289C22×C3—22no—
290C22×C3—22no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3—41no—
294C22×C3—41no—
295C22×C3—62no—
296C22×C3—121no—
297C22×C3—121no—
298C2×D3—22no—
299C2×D3—41no—
300C2×D3—41no—
301C3×C4—22no—
302C3×C4—22no—
303C3×C4—22no—
304C3×C4—41no—
305C3×C4—62no—
306C3×C4—68no—
307C3×C4—121no—
308C3×C4—121no—
309Dic3—22no—
310Dic3—28no—
311Dic3—41no—
312Dic3—41no—
313Dic3—61no—
314Dic3—61no—
315Dic3—62no—
316Dic3—62no—
317Dic3—62no—
318Dic3—61no—
319Dic3—61no—
320Dic3—62no—
321Dic3—62no—
322Dic3—121no—
323C32C4×#10411yescharacteristic, complemented, Sylow
324C23—61no—
325C23C2×GO+(4,𝔽2)11yescharacteristic
326Q8—92no—
327Q8—181no—
328D4—64no—
329D4—92no—
330D4—181no—
331C2×C4—22no—
332C2×C4—64no—
333C2×C4—64no—
334C2×C4—64no—
335C2×C4—61no—
336C2×C4—61no—
337C2×C4—61no—
338C2×C4—92no—
339C2×C4—92no—
340C2×C4—91no—
341C2×C4—91no—
342C2×C4—91no—
343C2×C4—91no—
344C2×C4—122no—
345C2×C4—184no—
346C2×C4—182no—
347C2×C4—362no—
348C2×C4D32⋊C411yescharacteristic
349C2×C4D32⋊C411yescharacteristic
350C8—184no—
351C2×C3—22no—
352C2×C3—22no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—21no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—42no—
360C2×C3—122no—
361D3—42no—
362C22—21no—
363C22—21no—
364C22—62no—
365C22—121no—
366C22—121no—
367C22C4×GO+(4,𝔽2)12yes—
368C22C2×D32⋊C411yescharacteristic
369C4—21no—
370C4—68no—
371C4—62no—
372C4—92no—
373C4—92no—
374C4—91no—
375C4—91no—
376C4—121no—
377C4—121no—
378C4—181no—
379C4#6374112yesdirect product factor
380C3—21no—
381C3—21no—
382C2—22no—
383C2—122no—
384C2#1059338011yescharacteristic
385C2C4×D32⋊C411yescharacteristic
386C2C2×#6374111yescharacteristic
subgroupG/H
centerC2×C4D32⋊C4
commutatorC3⋊Dic3C2×C42
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3805C22
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C4×#104
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C4×#3792C2semidirect
4. C4×Dic32C2semidirect
5. #10590074C2semidirect
15. C4×#627C4semidirect
16. #63902C4semidirect
17. C4×#625C4semidirect
20. #63838C4semidirect
23. #63741C4direct (N × H)
39. #3792C2×C4semidirect
58. Dic32C2×C4semidirect
101. #627C42semidirect
103. #625C42semidirect
171. C32×C4#104semidirect
173. C3⋊Dic3#104semidirect
323. C32C4×#104semidirect
379. C4#63741direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#38052
C4×#37922
C2×#637412
C4×Dic322
#105900742
C4×#1049