Finite Group Databasebeta

← #11871308

Subgroups — #11871308

Order 1152.

856 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 856 conjugacy classes of subgroups — too many to draw. Only its 105 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×C4×#625C211yesmaximal, characteristic, complemented
2#10594929C211yesmaximal, characteristic, complemented
3#10593806C211yesmaximal, characteristic, complemented
4#10593519C212yesmaximal, complemented
5#10593497C212yesmaximal, complemented
6#10593419C214yesmaximal, complemented
7#10593417C212yesmaximal, complemented
8#10593359C212yesmaximal, complemented
9C22×C3×C4×D3—21no—
10C22×#625C2211yescharacteristic
11C2×#3805—21no—
12C2×#3774C2214yes—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C3×#930—21no—
15#63980C2212yes—
16C2×#3724C2211yescharacteristic
17C2×(C2×D3)⋊Dic3—21no—
18#63919C2211yescharacteristic, complemented
19#63915—21no—
20#63914C2211yescharacteristic, complemented
21#63902C2212yescomplemented
22C4×#625—21no—
23C4×#625—21no—
24C4×#625C2212yes—
25C4×#625C2212yes—
26#63898—21no—
27C22⋊#622C2212yes—
28#63777C2212yescomplemented
29C4⋊#622C2212yescomplemented
30#63742C2214yescomplemented
31#63739C2214yes—
32#63739C2214yescomplemented
33C2×C4×#67—61no—
34#5596—61no—
35C23×C3×D3—21no—
36C22×C32×C4D411yescharacteristic
37C22×C3⋊Dic3D411yescharacteristic
38C22×C3⋊Dic3C2311yescharacteristic
39C2×C3×#67—22no—
40C22×C3×Dic3—21no—
41C2×C3×D12—21no—
42C2×C3×C4×D3—22no—
43C2×C3×C4×D3—22no—
44C2×C3×C4×D3—44no—
45C2×#627—21no—
46C2×#625—21no—
47C2×#625—24no—
48C2×#625—21no—
49C2×#625C2312yes—
50C2×#625C2312yes—
51#3805—44no—
52C2×D3×Dic3—22no—
53C2×#622C2314yes—
54#3774—28no—
55C4×C3⋊Dic3D411yescharacteristic
56C4×C3⋊Dic3D411yescharacteristic
57C4×C3⋊Dic3C2311yescharacteristic
58C4×C3⋊Dic3C2311yescharacteristic
59C3×(C2×D3)⋊C4—22no—
60C3×C4⋊Dic3—21no—
61#3724—21no—
62#3724C2312yes—
63#3724C2312yes—
64(C2×D3)⋊Dic3—22no—
65(C2×D3)⋊Dic3—22no—
66(C2×D3)⋊Dic3—22no—
67#3109—91nomaximal, Sylow
68C23×C3×C4—61no—
69C22×#67—61no—
70C2×#237—62no—
71C22×C4×D3—21no—
72C3×#121—61no—
73C2×#217—61no—
74#940—61no—
75#939—62no—
76D4×Dic3—61no—
77#930—21no—
78C4×#67—62no—
79C4×#67—62no—
80C4×#67—62no—
81C4×#67—62no—
82C2×(C2×D3)⋊C4—61no—
83C2×Dic3⋊C4—61no—
84C2×C4×Dic3—61no—
85C2×C4×Dic3—61no—
86#893—61no—
87#888—61no—
88#885—62no—
89#67⋊C4—62no—
90C23×C32C2×D411yescharacteristic
91C22×C3×D3—24no—
92C22×C3×D3—22no—
93C22×C3×D3—22no—
94C22×C3×D3—42no—
95C22×C3×D3—42no—
96C2×C32×C4—22no—
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3C2×D411yescharacteristic
102C2×C3⋊Dic3C2×D411yescharacteristic
103C2×C3⋊Dic3C2×D411yescharacteristic
104C2×C3⋊Dic3C2411yescharacteristic
105C3×#67—44no—
106C2×C3×Dic3—22no—
107C2×C3×Dic3—22no—
108C2×C3×Dic3—42no—
109C3×D12—42no—
110C3×C4×D3—44no—
111C3×C4×D3—44no—
112#627—42no—
113#625—24no—
114#625—22no—
115#625—24no—
116#625—42no—
117#625#4114yescomplemented
118D3×Dic3—44no—
119#622—24no—
120#532—91no—
121C2×C4×D4—91no—
122#481—92no—
123#476—92no—
124#459—92no—
125#447—92no—
126#442—94no—
127#432—91no—
128C24×C3—61no—
129C23×D3—21no—
130C2×C3×D4—61no—
131C2×C3×D4—62no—
132C22×C3×C4—21no—
133C22×C3×C4—21no—
134C22×C3×C4—62no—
135C22×C3×C4—62no—
136C22×C3×C4—61no—
137C22×C3×C4—124no—
138C2×#67—22no—
139C2×#67—62no—
140C2×#67—62no—
141C2×#67—62no—
142C2×#67—68no—
143C2×#67—62no—
144C22×Dic3—21no—
145C22×Dic3—61no—
146C22×Dic3—61no—
147C22×Dic3—61no—
148C22×Dic3—61no—
149C22×Dic3—62no—
150#237—128no—
151C2×D12—21no—
152C2×C4×D3—22no—
153C2×C4×D3—22no—
154C2×C4×D3—44no—
155C2×C4×D3—62no—
156C2×Dic6—62no—
157C3×C4⋊C4—61no—
158C3×C22⋊C4—62no—
159#217—62no—
160#217—62no—
161#217—62no—
162(C2×D3)⋊C4—22no—
163(C2×D3)⋊C4—62no—
164(C2×D3)⋊C4—62no—
165(C2×D3)⋊C4—62no—
166C4⋊Dic3—21no—
167Dic3⋊C4—62no—
168Dic3⋊C4—62no—
169Dic3⋊C4—62no—
170C4×Dic3—61no—
171C4×Dic3—61no—
172C4×Dic3—61no—
173C4×Dic3—61no—
174C4×Dic3—61no—
175C4×Dic3—61no—
176C4×Dic3—61no—
177C4×Dic3—61no—
178C22×C32—21no—
179C22×C32—21no—
180C22×C32AGL(1,ℤ/8)12yes—
181C22×C32C22×D411yescharacteristic
182C2×C3×D3—24no—
183C2×C3×D3—48no—
184C2×C3×D3—42no—
185C2×C3×D3—42no—
186C2×C3×D3—42no—
187C2×C3×D3—42no—
188C2×C3×D3—42no—
189C32×C4—21no—
190C32×C4AGL(1,ℤ/8)12yes—
191C3⋊Dic3—21no—
192C3⋊Dic3—21no—
193C3⋊Dic3—21no—
194C3⋊Dic3C2×#4112yes—
195C3×Dic3—42no—
196C3×Dic3—42no—
197C2×#41—181no—
198C22×D4—91no—
199C23×C4—61no—
200C2×D8—94no—
201C4⋊Q8—91no—
202#127—91no—
203#124—181no—
204#121—61no—
205#121—92no—
206C4×D4—92no—
207C4×D4—92no—
208C4×D4—92no—
209C4×D4—181no—
210C4×D4—181no—
211C4×D4—181no—
212C2×C4⋊C4—91no—
213C2×C22⋊C4—181no—
214C2×C42—91no—
215#106—94no—
216C4⋊C8—92no—
217#102—94no—
218#102—94no—
219C22⋊C8—92no—
220#97—92no—
221C23×C3—21no—
222C23×C3—21no—
223C23×C3—62no—
224C23×C3—64no—
225C23×C3—62no—
226C23×C3—122no—
227C23×C3—122no—
228C22×D3—22no—
229C22×D3—24no—
230C22×D3—22no—
231C22×D3—42no—
232C22×D3—42no—
233C3×D4—122no—
234C3×D4—124no—
235C2×C3×C4—24no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—42no—
241C2×C3×C4—62no—
242C2×C3×C4—62no—
243C2×C3×C4—124no—
244C2×C3×C4—124no—
245C2×C3×C4—122no—
246#67—44no—
247#67—64no—
248#67—64no—
249#67—68no—
250#67—124no—
251#67—124no—
252C2×Dic3—22no—
253C2×Dic3—22no—
254C2×Dic3—42no—
255C2×Dic3—61no—
256C2×Dic3—61no—
257C2×Dic3—61no—
258C2×Dic3—61no—
259C2×Dic3—61no—
260C2×Dic3—61no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—64no—
264C2×Dic3—64no—
265C2×Dic3—122no—
266C2×Dic3—122no—
267C2×Dic3—124no—
268D12—42no—
269C4×D3—44no—
270C4×D3—44no—
271C4×D3—124no—
272Dic6—124no—
273C2×C32—22no—
274C2×C32#52511yescharacteristic
275C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
276C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
277C3×D3—44no—
278C3×D3—82no—
279C24—61no—
280#41—364no—
281C2×Q8—181no—
282C2×D4—62no—
283C2×D4—61no—
284C2×D4—92no—
285C2×D4—92no—
286C2×D4—181no—
287C2×D4—181no—
288C2×D4—184no—
289C22×C4—61no—
290C22×C4—62no—
291C22×C4—62no—
292C22×C4—91no—
293C22×C4—91no—
294C22×C4—124no—
295C22×C4—182no—
296C22×C4GO+(4,𝔽2)11yescharacteristic
297D8—188no—
298C2×C8—94no—
299C4⋊C4—61no—
300C4⋊C4—92no—
301C4⋊C4—92no—
302C4⋊C4—181no—
303C22⋊C4—62no—
304C22⋊C4—182no—
305C22⋊C4—182no—
306C22⋊C4—182no—
307C42—91no—
308C42—91no—
309C42—91no—
310C42—91no—
311C22×C3—22no—
312C22×C3—22no—
313C22×C3—21no—
314C22×C3—21no—
315C22×C3—22no—
316C22×C3—22no—
317C22×C3—41no—
318C22×C3—41no—
319C22×C3—64no—
320C22×C3—122no—
321C22×C3—128no—
322C22×C3—122no—
323C22×C3—122no—
324C22×C3—122no—
325C22×C3—122no—
326C2×D3—24no—
327C2×D3—42no—
328C2×D3—48no—
329C2×D3—42no—
330C2×D3—42no—
331C2×D3—42no—
332C2×D3—42no—
333C3×C4—22no—
334C3×C4—22no—
335C3×C4—22no—
336C3×C4—41no—
337C3×C4—122no—
338C3×C4—122no—
339Dic3—42no—
340Dic3—42no—
341Dic3—62no—
342Dic3—62no—
343Dic3—62no—
344Dic3—62no—
345Dic3—62no—
346Dic3—121no—
347Dic3—121no—
348Dic3—121no—
349C32#310911yescharacteristic, complemented, Sylow
350C23—64no—
351C23—62no—
352C23—62no—
353C23—122no—
354C23—122no—
355C23C2×GO+(4,𝔽2)11yescharacteristic
356Q8—362no—
357D4—94no—
358D4—124no—
359D4—122no—
360D4—182no—
361D4—184no—
362D4—184no—
363D4—362no—
364C2×C4—22no—
365C2×C4—62no—
366C2×C4—62no—
367C2×C4—91no—
368C2×C4—91no—
369C2×C4—91no—
370C2×C4—91no—
371C2×C4—124no—
372C2×C4—122no—
373C2×C4—124no—
374C2×C4—182no—
375C2×C4—182no—
376C2×C4—364no—
377C2×C4C2×GO+(4,𝔽2)11yescharacteristic
378C2×C4C2×GO+(4,𝔽2)11yescharacteristic
379C8—184no—
380C2×C3—24no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—42no—
388C2×C3—124no—
389C2×C3—242no—
390D3—44no—
391D3—82no—
392C22—21no—
393C22—21no—
394C22—64no—
395C22—128no—
396C22—122no—
397C22—122no—
398C22—122no—
399C22—122no—
400C22—122no—
401C22#6422412yes—
402C22C22×GO+(4,𝔽2)11yescharacteristic
403C4—21no—
404C4—92no—
405C4—122no—
406C4—122no—
407C4—181no—
408C4—181no—
409C4—181no—
410C4#6423612yes—
411C3—21no—
412C3—21no—
413C2—22no—
414C2—124no—
415C2—242no—
416C2C2×#6422411yescharacteristic
417C2#1059651011yescharacteristic
418C2C2×#6423611yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC22×C32×C4D4
socleC22×C32C22×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#3109
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×#625C2semidirect
2. #10594929C2semidirect
3. #10593806C2semidirect
4. #10593519C2semidirect
5. #10593497C2semidirect
6. #10593419C2semidirect
7. #10593417C2semidirect
8. #10593359C2semidirect
18. #63919C22semidirect
20. #63914C22semidirect
21. #63902C22semidirect
28. #63777C22semidirect
29. C4⋊#622C22semidirect
30. #63742C22semidirect
32. #63739C22semidirect
117. #625#41semidirect
349. C32#3109semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6252
#105949292
#105938062
#105935192
#105934972
#105934192
#105934172
#105933592
#31099