Finite Group Databasebeta

← #11865505

Subgroups — #11865505

Order 1152.

902 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 902 conjugacy classes of subgroups — too many to draw. Only its 129 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×#64227C212yesmaximal
2C4×#3802C211yesmaximal, characteristic
3#10593909C211yesmaximal, characteristic, complemented
4#10593726C211yesmaximal, characteristic, complemented
5#10593438C214yesmaximal, complemented
6#10593437C214yesmaximal, complemented
7#10593375C212yesmaximal, complemented
8C2×#3802C2211yescharacteristic
9C2×C4×D32—21no—
10C2×#3797C2212yes—
11C2×#3787C2212yes—
12C2×#3775C2218yes—
13#64227—28no—
14C42×C3⋊D3C2211yescharacteristic
15C3×C4×D12—21no—
16C3×#869—21no—
17#63921—21no—
18#63919C2212yescomplemented
19#63919C2212yescomplemented
20#63902C2212yes—
21C4×#625C2212yes—
22#63900—21no—
23#63900—21no—
24#63900C2211yescharacteristic
25#63898—21no—
26#63873—21no—
27#63779C2212yescomplemented
28C4⋊#622C2212yescomplemented
29#63740C2218yescomplemented
30D3×C4⋊Q8—61no—
31C4×D3×D4—61no—
32C22×D32—21no—
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C4×C3⋊D3D411yescharacteristic
35C2×C4×C3⋊D3C2311yescharacteristic
36C2×C3×D12—21no—
37C2×C3×C4×D3—22no—
38C2×C3×Dic6—22no—
39C2×#627C2314yes—
40C2×#625C2312yes—
41C2×#624—22no—
42C2×#624—21no—
43C2×D3×Dic3—22no—
44#3802—22no—
45#3802D414yes—
46C4×D32—44no—
47#3797—24no—
48#3797—24no—
49C2×#622C2314yes—
50#3787—24no—
51#3775—216no—
52C32×C42D411yescharacteristic
53C4×C3⋊Dic3D411yescharacteristic
54C4×C3⋊Dic3C2311yescharacteristic
55C4×C3⋊Dic3C2311yescharacteristic
56C3×(C2×D3)⋊C4—22no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—22no—
59C3×C4⋊Dic3—22no—
60#3724—22no—
61#3724—22no—
62#3724C2312yes—
63(C2×D3)⋊Dic3—22no—
64C2×#461—91nomaximal, Sylow
65C2×D3×Q8—62no—
66C2×D3×D4—61no—
67C22×C4×D3—62no—
68C3×C4⋊Q8—61no—
69C3×C4×D4—61no—
70#944—62no—
71D4×Dic3—61no—
72C4×#67—62no—
73#893—61no—
74D3×C4⋊C4—61no—
75D3×C4⋊C4—62no—
76D3×C4⋊C4—62no—
77#888—62no—
78#888—62no—
79#67⋊C4—62no—
80D3×C22⋊C4—62no—
81C4×D12—21no—
82C42×D3—61no—
83C42×D3—61no—
84#869—21no—
85C22×C3⋊D3C2×D411yescharacteristic
86C22×C3×D3—22no—
87C2×D32—24no—
88C2×D32—42no—
89C2×D32—42no—
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C3⋊Dic3C2×D411yescharacteristic
94C2×C3⋊Dic3C2×D411yescharacteristic
95C2×C3⋊Dic3C2411yescharacteristic
96C4×C3⋊D3—22no—
97C4×C3⋊D3SD1614yescomplemented
98C4×C3⋊D3C2×D412yes—
99C4×C3⋊D3#4112yes—
100C2×C3×Dic3—22no—
101C2×C3×Dic3—24no—
102C3×D12—24no—
103C3×C4×D3—44no—
104C3×Dic6—44no—
105#627—24no—
106#627—24no—
107#625—22no—
108#625C2×D414yes—
109#624—44no—
110#624—42no—
111D3×Dic3—44no—
112#622—24no—
113C22×SD16—92no—
114C2×C4⋊Q8—91no—
115C2×C4×D4—91no—
116#461—94no—
117#461—94no—
118C2×C4⋊C8—91no—
119C2×#103—92no—
120C23×D3—62no—
121C2×C3×Q8—62no—
122C2×C3×D4—61no—
123C22×C3×C4—62no—
124C2×#67—62no—
125C22×Dic3—62no—
126D3×Q8—124no—
127D3×Q8—124no—
128D3×D4—64no—
129D3×D4—64no—
130C2×D12—21no—
131C2×C4×D3—22no—
132C2×C4×D3—61no—
133C2×C4×D3—61no—
134C2×C4×D3—61no—
135C2×C4×D3—61no—
136C2×C4×D3—61no—
137C2×C4×D3—61no—
138C2×C4×D3—62no—
139C2×C4×D3—64no—
140C2×C4×D3—62no—
141C2×C4×D3—128no—
142C2×Dic6—22no—
143C2×Dic6—64no—
144C3×C4⋊C4—62no—
145C3×C4⋊C4—62no—
146C3×C4⋊C4—61no—
147C3×C22⋊C4—62no—
148C3×C42—21no—
149C3×C42—21no—
150#217—62no—
151(C2×D3)⋊C4—22no—
152(C2×D3)⋊C4—62no—
153C4⋊Dic3—22no—
154C4⋊Dic3—22no—
155C4⋊Dic3—21no—
156Dic3⋊C4—62no—
157Dic3⋊C4—64no—
158Dic3⋊C4—64no—
159C4×Dic3—61no—
160C4×Dic3—61no—
161C4×Dic3—61no—
162C4×Dic3—61no—
163C4×Dic3—61no—
164C4×Dic3—61no—
165C22×C32C22×D411yescharacteristic
166C2×C3⋊D3#12112yes—
167C2×C3⋊D3C2×SD1612yes—
168C2×C3⋊D3#13712yes—
169C2×C3×D3—24no—
170C2×C3×D3—42no—
171C2×C3×D3—42no—
172D32—48no—
173C32×C4—21no—
174C32×C4#12112yes—
175C32×C4C2×SD1612yescomplemented
176C3⋊Dic3—21no—
177C3⋊Dic3C2×SD1612yescomplemented
178C3⋊Dic3C22×D411yescharacteristic
179C3⋊Dic3C2×#4111yescharacteristic
180C3×Dic3—44no—
181C3×Dic3—42no—
182C22×Q8—92no—
183C22×D4—91no—
184C23×C4—181no—
185C2×SD16—98no—
186C2×SD16—188no—
187C22×C8—92no—
188C4⋊Q8—61no—
189C4⋊Q8—92no—
190C4⋊Q8—92no—
191C4⋊Q8—181no—
192C4×D4—61no—
193C4×D4—92no—
194C4×D4—92no—
195C4×D4—181no—
196C2×C4⋊C4—91no—
197C2×C4⋊C4—181no—
198C2×C4⋊C4—181no—
199C2×C22⋊C4—181no—
200C2×C42—91no—
201C4⋊C8—92no—
202C4⋊C8—92no—
203#103—98no—
204C23×C3—62no—
205C22×D3—22no—
206C22×D3—61no—
207C22×D3—61no—
208C22×D3—68no—
209C22×D3—124no—
210C22×D3—124no—
211C3×Q8—124no—
212C3×D4—64no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—64no—
220C2×C3×C4—62no—
221C2×C3×C4—124no—
222#67—64no—
223#67—64no—
224C2×Dic3—24no—
225C2×Dic3—22no—
226C2×Dic3—61no—
227C2×Dic3—61no—
228C2×Dic3—61no—
229C2×Dic3—61no—
230C2×Dic3—61no—
231C2×Dic3—61no—
232C2×Dic3—124no—
233D12—24no—
234C4×D3—44no—
235C4×D3—64no—
236C4×D3—64no—
237C4×D3—62no—
238C4×D3—62no—
239C4×D3—62no—
240C4×D3—62no—
241C4×D3—64no—
242C4×D3—122no—
243C4×D3—124no—
244C4×D3—128no—
245C4×D3—124no—
246Dic6—44no—
247Dic6—124no—
248Dic6—124no—
249C2×C32C2×#12111yescharacteristic
250C2×C32C22×SD1611yescharacteristic
251C2×C32C2×#13711yescharacteristic
252C3⋊D3#46114yescomplemented
253C3×D3—44no—
254C24—181no—
255C2×Q8—62no—
256C2×Q8—94no—
257C2×Q8—184no—
258C2×Q8—184no—
259C2×D4—61no—
260C2×D4—94no—
261C2×D4—92no—
262C2×D4—182no—
263C22×C4—62no—
264C22×C4—91no—
265C22×C4—91no—
266C22×C4—91no—
267C22×C4—181no—
268C22×C4—182no—
269C22×C4—182no—
270C22×C4—364no—
271SD16—1816no—
272C2×C8—94no—
273C2×C8—184no—
274C4⋊C4—61no—
275C4⋊C4—62no—
276C4⋊C4—62no—
277C4⋊C4—92no—
278C4⋊C4—182no—
279C4⋊C4—182no—
280C22⋊C4—62no—
281C22⋊C4—182no—
282C42—91no—
283C42—91no—
284C42—91no—
285C42GO+(4,𝔽2)11yescharacteristic
286C22×C3—21no—
287C22×C3—21no—
288C22×C3—64no—
289C22×C3—122no—
290C22×C3—122no—
291C2×D3—24no—
292C2×D3—42no—
293C2×D3—42no—
294C2×D3—62no—
295C2×D3—62no—
296C2×D3—62no—
297C2×D3—62no—
298C2×D3—62no—
299C2×D3—62no—
300C2×D3—1216no—
301C3×C4—22no—
302C3×C4—22no—
303C3×C4—22no—
304C3×C4—22no—
305C3×C4—22no—
306C3×C4—41no—
307C3×C4—124no—
308C3×C4—122no—
309Dic3—44no—
310Dic3—42no—
311Dic3—61no—
312Dic3—61no—
313Dic3—62no—
314Dic3—61no—
315Dic3—61no—
316Dic3—62no—
317Dic3—62no—
318Dic3—121no—
319C32C2×#46111yescharacteristic, complemented, Sylow
320C23—62no—
321C23—91no—
322C23—184no—
323C23—362no—
324C23—362no—
325Q8—124no—
326Q8—184no—
327Q8—184no—
328D4—64no—
329D4—94no—
330D4—182no—
331C2×C4—62no—
332C2×C4—64no—
333C2×C4—91no—
334C2×C4—91no—
335C2×C4—94no—
336C2×C4—92no—
337C2×C4—92no—
338C2×C4—91no—
339C2×C4—124no—
340C2×C4—182no—
341C2×C4—364no—
342C2×C4—362no—
343C2×C4—364no—
344C2×C4C2×GO+(4,𝔽2)11yescharacteristic
345C2×C4C2×GO+(4,𝔽2)11yescharacteristic
346C2×C4C2×GO+(4,𝔽2)11yescharacteristic
347C8—184no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—124no—
355D3—44no—
356D3—64no—
357D3—64no—
358C22—64no—
359C22—92no—
360C22—92no—
361C22—92no—
362C22—122no—
363C22—122no—
364C22—368no—
365C22C22×GO+(4,𝔽2)11yescharacteristic
366C4—21no—
367C4—92no—
368C4—91no—
369C4—91no—
370C4—122no—
371C4—124no—
372C4—181no—
373C4#6422712yescomplemented
374C4#6423012yes—
375C3—21no—
376C3—21no—
377C2—94no—
378C2—124no—
379C2C2×#6422711yescharacteristic
380C2#1059650511yescharacteristic
381C2C2×#6423011yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC32×C42D4
socleC22×C32C22×D4
prime radicalC2×#3802C22
hypercenterC42GO+(4,𝔽2)
hypocenterC32C2×#461
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
3. #10593909C2semidirect
4. #10593726C2semidirect
5. #10593438C2semidirect
6. #10593437C2semidirect
7. #10593375C2semidirect
18. #63919C22semidirect
19. #63919C22semidirect
27. #63779C22semidirect
28. C4⋊#622C22semidirect
29. #63740C22semidirect
97. C4×C3⋊D3SD16semidirect
175. C32×C4C2×SD16semidirect
177. C3⋊Dic3C2×SD16semidirect
252. C3⋊D3#461semidirect
319. C32C2×#461semidirect
373. C4#64227semidirect

Maximal subgroups

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

subgroupindex
C2×#642272
C4×#38022
#105939092
#105937262
#105934382
#105934372
#105933752
C2×#4619