Finite Group Databasebeta

← #11774314

Subgroups — #11774314

Order 1152.

837 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 837 conjugacy classes of subgroups — too many to draw. Only its 122 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×D4×C3⋊D3C211yesmaximal, characteristic
2#10590297C211yesmaximal, characteristic, complemented
3#10590256C211yesmaximal, characteristic, complemented
4C3×D4⋊(C3⋊C8)C212yesmaximal, complemented
5#10589082C212yesmaximal, complemented
6#68167—32nomaximal
7C2×D4×C3⋊D3C411yescharacteristic
8C22×C4×C3⋊D3—21no—
9C32×C4×D4C2211yescharacteristic
10D4×C3⋊Dic3C411yescharacteristic
11C4×#638—21no—
12#64102C411yescharacteristic
13C4⋊C4×C3⋊D3C411yescharacteristic
14#64090—21no—
15C22⋊C4×C3⋊D3—21no—
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17C42×C3⋊D3C2211yescharacteristic
18C3×C4⋊(C3⋊C8)C2212yescomplemented
19C3×C4×C3⋊C8C2212yescomplemented
20#63572—21no—
21#63557—21no—
22#63557—21no—
23#63553—21no—
24C4×D3×D4—32no—
25C4×D3×D4—61no—
26#4833—32no—
27#4685—32no—
28C3×D4⋊C8—32no—
29D4⋊(C3⋊C8)D312yescomplemented
30#4483—32no—
31#4459—32no—
32C23×C3⋊D3—21no—
33C2×C32×D4C2×C411yescharacteristic
34C22×C32×C4—21no—
35C2×#638—21no—
36C22×C3⋊Dic3—21no—
37D4×C3⋊D3—22no—
38D4×C3⋊D3C814yescomplemented
39C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
40C2×C4×C3⋊D3—21no—
41C2×C4×C3⋊D3—21no—
42C2×C4×C3⋊D3—21no—
43C2×C4×C3⋊D3—44no—
44C2×C4×C3⋊D3C2×C411yescharacteristic
45C2×C4×C3⋊D3D411yescharacteristic
46C2×C4×C3⋊D3D411yescharacteristic
47C32×C4⋊C4C2×C411yescharacteristic
48C32×C22⋊C4—21no—
49C32×C42C2311yescharacteristic
50#3757—21no—
51#3752—21no—
52#3752—21no—
53C4⋊(C3⋊Dic3)C2×C411yescharacteristic
54#3750—21no—
55C4×C3⋊Dic3C2×C411yescharacteristic
56C4×C3⋊Dic3D411yescharacteristic
57C4×C3⋊Dic3D411yescharacteristic
58C2×C3×C3⋊C8—22no—
59C2×C3×C3⋊C8—22no—
60#1478—91noSylow
61C2×D3×D4—32no—
62C2×D3×D4—61no—
63C22×C4×D3—62no—
64C22×C4×D3—62no—
65C3×C4×D4—21no—
66C3×C4×D4C2×D312yes—
67D4×Dic3—32no—
68D4×Dic3—61no—
69C4×#67—62no—
70C4×#67—62no—
71#893—32no—
72#893—61no—
73D3×C4⋊C4—32no—
74D3×C4⋊C4—61no—
75#67⋊C4—62no—
76#67⋊C4—62no—
77D3×C22⋊C4—62no—
78D3×C22⋊C4—62no—
79C4×D12—32no—
80C4×D12—61no—
81C42×D3—32no—
82C42×D3—61no—
83C3×C4⋊C8—32no—
84C3×C4×C8—32no—
85(C2×D3)⋊C8—62no—
86(C2×D3)⋊C8—62no—
87Dic3⋊C8—62no—
88C8×Dic3—62no—
89C4⋊(C3⋊C8)C2×D312yescomplemented
90C4×C3⋊C8C2×D312yescomplemented
91C23×C32—21no—
92C22×C3⋊D3—21no—
93C22×C3⋊D3—24no—
94C22×C3⋊D3—42no—
95C22×C3⋊D3—42no—
96C22×C3⋊D3C22⋊C411yescharacteristic
97C32×D4—21no—
98C32×D4C2×C812yes—
99C2×C32×C4—21no—
100C2×C32×C4—42no—
101C2×C32×C4C22×C411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104#638—24no—
105C2×C3⋊Dic3—21no—
106C2×C3⋊Dic3—42no—
107C2×C3⋊Dic3C22⋊C411yescharacteristic
108C2×C3⋊Dic3C22⋊C411yescharacteristic
109C2×C3⋊Dic3C22⋊C411yescharacteristic
110C4⋊(C3⋊D3)—21no—
111C4⋊(C3⋊D3)C2×C812yes—
112C4×C3⋊D3—22no—
113C4×C3⋊D3—41no—
114C4×C3⋊D3—42no—
115C4×C3⋊D3—42no—
116C4×C3⋊D3—42no—
117C4×C3⋊D3C2×C812yes—
118C4×C3⋊D3M1612yes—
119C3×C3⋊C8—42no—
120C3×C3⋊C8—42no—
121C2×C4×D4—91no—
122#431—91no—
123#431—91no—
124D4⋊C8—32no—
125D4⋊C8—92no—
126C23×D3—62no—
127C23×D3—62no—
128C2×C3×D4—21no—
129C2×C3×D4C4×D312yes—
130C22×C3×C4—22no—
131C22×C3×C4—22no—
132C2×#67—62no—
133C2×#67—62no—
134C22×Dic3—62no—
135C22×Dic3—62no—
136D3×D4—38no—
137D3×D4—64no—
138D3×D4—64no—
139D3×D4—64no—
140C2×D12—32no—
141C2×D12—61no—
142C2×C4×D3—32no—
143C2×C4×D3—32no—
144C2×C4×D3—32no—
145C2×C4×D3—61no—
146C2×C4×D3—61no—
147C2×C4×D3—61no—
148C2×C4×D3—62no—
149C2×C4×D3—62no—
150C2×C4×D3—62no—
151C2×C4×D3—62no—
152C2×C4×D3—62no—
153C2×C4×D3—62no—
154C2×C4×D3—128no—
155C2×C4×D3—124no—
156C2×C4×D3—124no—
157C2×C3×C8—62no—
158C2×C3×C8—62no—
159C3×C4⋊C4—21no—
160C3×C4⋊C4C4×D312yes—
161C3×C22⋊C4—22no—
162C3×C22⋊C4—22no—
163C3×C42—21no—
164C3×C42C22×D312yes—
165#217—62no—
166#217—62no—
167(C2×D3)⋊C4—62no—
168(C2×D3)⋊C4—62no—
169(C2×D3)⋊C4—62no—
170(C2×D3)⋊C4—62no—
171C4⋊Dic3—32no—
172C4⋊Dic3—61no—
173Dic3⋊C4—62no—
174Dic3⋊C4—62no—
175C4×Dic3—32no—
176C4×Dic3—32no—
177C4×Dic3—32no—
178C4×Dic3—61no—
179C4×Dic3—61no—
180C4×Dic3—61no—
181C2×C3⋊C8—22no—
182C2×C3⋊C8—22no—
183C22×C32—22no—
184C22×C32—41no—
185C22×C32—41no—
186C22×C32C2×C22⋊C411yescharacteristic
187C2×C3⋊D3—21no—
188C2×C3⋊D3—21no—
189C2×C3⋊D3—22no—
190C2×C3⋊D3—48no—
191C2×C3⋊D3—41no—
192C2×C3⋊D3—41no—
193C2×C3⋊D3C22⋊C812yes—
194C32×C4—21no—
195C32×C4—41no—
196C32×C4C22×C811yescharacteristic
197C32×C4C2×M1611yescharacteristic
198C32×C4AGL(1,ℤ/8)12yes—
199C3⋊Dic3—21no—
200C3⋊Dic3—21no—
201C3⋊Dic3—41no—
202C3⋊Dic3C22⋊C812yes—
203C22×D4—91no—
204C23×C4—181no—
205C4×D4—91no—
206C4×D4—91no—
207C4×D4—91no—
208C4×D4—181no—
209C4×D4—181no—
210C4×D4D3211yescharacteristic
211C2×C4⋊C4—91no—
212C2×C22⋊C4—181no—
213C2×C42—91no—
214C4⋊C8—32no—
215C4⋊C8—181no—
216C22⋊C8—181no—
217C22⋊C8—181no—
218C4×C8—32no—
219C4×C8—181no—
220C23×C3—22no—
221C23×C3—22no—
222C22×D3—32no—
223C22×D3—61no—
224C22×D3—68no—
225C22×D3—62no—
226C22×D3—68no—
227C22×D3—62no—
228C22×D3—124no—
229C22×D3—124no—
230C22×D3—124no—
231C22×D3—124no—
232C3×D4—22no—
233C3×D4—22no—
234C3×D4—22no—
235C3×D4D3×C814yes—
236C2×C3×C4—22no—
237C2×C3×C4—22no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—44no—
242C2×C3×C4—42no—
243C2×C3×C4—42no—
244C2×C3×C4C2×C4×D312yes—
245C2×C3×C4D3×D412yes—
246C2×C3×C4D3×D412yes—
247#67—68no—
248#67—68no—
249C2×Dic3—32no—
250C2×Dic3—32no—
251C2×Dic3—32no—
252C2×Dic3—61no—
253C2×Dic3—61no—
254C2×Dic3—61no—
255C2×Dic3—62no—
256C2×Dic3—62no—
257C2×Dic3—124no—
258C2×Dic3—124no—
259D12—34no—
260D12—62no—
261D12—62no—
262D12—62no—
263C4×D3—34no—
264C4×D3—34no—
265C4×D3—62no—
266C4×D3—62no—
267C4×D3—64no—
268C4×D3—62no—
269C4×D3—62no—
270C4×D3—122no—
271C4×D3—124no—
272C4×D3—124no—
273C4×D3—124no—
274C4×D3—122no—
275C4×D3—124no—
276C4×D3—124no—
277C4×D3—122no—
278C4×D3—122no—
279C3×C8—122no—
280C3×C8—122no—
281C3⋊C8—42no—
282C3⋊C8—42no—
283C2×C32—42no—
284C2×C32C2×C22⋊C811yescharacteristic
285C2×C32#41811yescharacteristic
286C2×C32#42111yescharacteristic
287C3⋊D3—22no—
288C3⋊D3—42no—
289C24—181no—
290C2×D4—94no—
291C2×D4—91no—
292C2×D4—182no—
293C2×D4—181no—
294C2×D4#62411yescharacteristic
295C22×C4—21no—
296C22×C4—91no—
297C22×C4—91no—
298C22×C4—91no—
299C22×C4—181no—
300C22×C4—181no—
301C22×C4—181no—
302C22×C4—181no—
303C22×C4—364no—
304C2×C8—62no—
305C2×C8—62no—
306C4⋊C4—91no—
307C4⋊C4—181no—
308C4⋊C4#62411yescharacteristic
309C22⋊C4—21no—
310C22⋊C4—181no—
311C22⋊C4—181no—
312C22⋊C4—181no—
313C42—91no—
314C42—91no—
315C42—91no—
316C42C2×D3211yescharacteristic
317C22×C3—24no—
318C22×C3—24no—
319C22×C3—21no—
320C22×C3—42no—
321C22×C3—42no—
322C22×C3—42no—
323C22×C3—42no—
324C22×C3D3×C22⋊C412yes—
325C2×D3—34no—
326C2×D3—62no—
327C2×D3—62no—
328C2×D3—62no—
329C2×D3—62no—
330C2×D3—62no—
331C2×D3—64no—
332C2×D3—64no—
333C2×D3—1216no—
334C2×D3—1216no—
335C2×D3—122no—
336C2×D3—122no—
337C2×D3—122no—
338C2×D3—122no—
339C3×C4—22no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—22no—
343C3×C4—41no—
344C3×C4—42no—
345C3×C4—42no—
346C3×C4C2×D3×C812yes—
347C3×C4D3×M1612yes—
348C3×C4#91112yes—
349C3×C4#91412yes—
350Dic3—34no—
351Dic3—62no—
352Dic3—62no—
353Dic3—62no—
354Dic3—62no—
355Dic3—121no—
356Dic3—122no—
357Dic3—122no—
358C32#147811yescharacteristic, complemented, Sylow
359C23—21no—
360C23—91no—
361C23—184no—
362C23—181no—
363C23—362no—
364C23—362no—
365D4—21no—
366D4—92no—
367D4—184no—
368D4—181no—
369D4#371012yes—
370C2×C4—21no—
371C2×C4—42no—
372C2×C4—91no—
373C2×C4—92no—
374C2×C4—92no—
375C2×C4—91no—
376C2×C4—91no—
377C2×C4—182no—
378C2×C4—181no—
379C2×C4—361no—
380C2×C4—362no—
381C2×C4—362no—
382C2×C4—362no—
383C2×C4—362no—
384C2×C4C2×#62411yescharacteristic
385C2×C4#381111yescharacteristic
386C2×C4#381111yescharacteristic
387C8—122no—
388C8—122no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—44no—
393C2×C3—44no—
394C2×C3D3×C22⋊C812yes—
395C2×C3#477012yes—
396C2×C3#482112yes—
397D3—64no—
398D3—64no—
399D3—124no—
400D3—124no—
401C22—22no—
402C22—41no—
403C22—41no—
404C22—92no—
405C22—181no—
406C22—181no—
407C22—182no—
408C22—368no—
409C22—361no—
410C22—361no—
411C22#6397411yescharacteristic
412C4—21no—
413C4—41no—
414C4—92no—
415C4—181no—
416C4—181no—
417C4—361no—
418C4C2×#371011yescharacteristic
419C4#6381811yescharacteristic
420C4#6393712yes—
421C3—21no—
422C3#6816712yescomplemented
423C2—42no—
424C2—182no—
425C2—362no—
426C2#1059115211yescharacteristic
427C2#1059142611yescharacteristic
428C2#1059167211yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC32×C4C22×C8
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32C2×C22⋊C4
prime radicalC2×D4×C3⋊D3C4
cosocleC32×C42C23
hypercenterC4×D4D32
hypocenterC32#1478
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10590297C2semidirect
3. #10590256C2semidirect
4. C3×D4⋊(C3⋊C8)C2semidirect
5. #10589082C2semidirect
18. C3×C4⋊(C3⋊C8)C22semidirect
19. C3×C4×C3⋊C8C22semidirect
29. D4⋊(C3⋊C8)D3semidirect
38. D4×C3⋊D3C8semidirect
89. C4⋊(C3⋊C8)C2×D3semidirect
90. C4×C3⋊C8C2×D3semidirect
358. C32#1478semidirect
422. C3#68167semidirect

Maximal subgroups

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

subgroupindex
C4×D4×C3⋊D32
#105902972
#105902562
C3×D4⋊(C3⋊C8)2
#105890822
#681673