Finite Group Databasebeta

← #11783768

Subgroups — #11783768

Order 1152.

754 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 754 conjugacy classes of subgroups — too many to draw. Only its 89 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×#3811C211yesmaximal, characteristic
2C4×C22⋊#157C211yesmaximal, characteristic, complemented
3C2×#63738C212yesmaximal
4#10591260C211yesmaximal, characteristic, complemented
5#10590076C212yesmaximal, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×#3811C2211yescharacteristic
8C2×C4×D32C411yescharacteristic, complemented
9C2×C22⋊#157C2212yes—
10C2×C4×#157—21no—
11C3×C4×#67—21no—
12#63974C2211yescharacteristic
13#67⋊Dic3—21no—
14C2×#3722C2212yes—
15C2×Dic32—21no—
16#63921C411yescharacteristic, complemented
17C4×#626—21no—
18#63883C411yescharacteristic, complemented
19C4×#624C411yescharacteristic, complemented
20#63881—21no—
21#63781—21no—
22#63738C418yescomplemented
23C3×C3⋊#95—21no—
24C4×D3×D4—61no—
25#4666—61no—
26C23×C3⋊D3C2311yescharacteristic
27C22×D32C2×C411yescharacteristic
28C22×#157—22no—
29C22×C32×C4D411yescharacteristic
30C22×C3⋊Dic3D411yescharacteristic
31C2×C4×C3⋊D3—42no—
32C2×C4×C3⋊D3C2×C411yescharacteristic
33C2×C4×C3⋊D3C2×C411yescharacteristic
34C2×C4×C3⋊D3D411yescharacteristic
35C2×C4×C3⋊D3D411yescharacteristic
36C2×C3×#67—21no—
37C22×C3×Dic3—22no—
38C2×C3×C4×D3—21no—
39#3811—22no—
40#3811C2×C414yes—
41C2×#626—21no—
42C2×#624C2×C411yescharacteristic
43C2×#624C2×C411yescharacteristic
44C2×#624C2×C411yescharacteristic
45C2×D3×Dic3—21no—
46C4×D32—42no—
47C22⋊#157—22no—
48C22⋊#157C2×C414yescomplemented
49C4×#157—42no—
50C3×#217—21no—
51C3×(C2×D3)⋊C4—21no—
52C3×Dic3⋊C4—21no—
53C3×C4×Dic3—21no—
54Dic3⋊Dic3—21no—
55#3722—21no—
56#3722—22no—
57#3722C2×C414yescomplemented
58(C2×D3)⋊Dic3—21no—
59Dic32—21no—
60Dic32—42no—
61C4×#99—91nomaximal, Sylow
62C2×D3×D4—61no—
63C22×C4×D3—61no—
64C22×C4×D3—61no—
65C22×C4×D3—61no—
66C3×C4×D4—61no—
67D4×Dic3—61no—
68C4×#67—21no—
69C4×#67—61no—
70C2×(C2×D3)⋊C4—62no—
71C2×C4×Dic3—62no—
72#893—61no—
73D3×C4⋊C4—61no—
74#67⋊C4—61no—
75#67⋊C4—61no—
76D3×C22⋊C4—61no—
77D3×C22⋊C4—61no—
78C4×D12—61no—
79C42×D3—61no—
80C3×#95—61no—
81C3⋊#95—21no—
82C23×C32C2×D411yescharacteristic
83C22×C3⋊D3—41no—
84C22×C3⋊D3—41no—
85C22×C3⋊D3C22×C411yescharacteristic
86C22×C3⋊D3C22×C412yes—
87C22×C3⋊D3C2×D411yescharacteristic
88C22×C3⋊D3#4112yes—
89C22×C3×D3—21no—
90C2×D32—21no—
91C2×D32—41no—
92C2×D32—41no—
93C2×D32C4212yescomplemented
94C2×#157—24no—
95C2×#157—42no—
96C2×#157—42no—
97C2×C32×C4—41no—
98C2×C32×C4C22⋊C411yescharacteristic
99C2×C32×C4C22⋊C411yescharacteristic
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3C22⋊C411yescharacteristic
102C2×C3⋊Dic3C22⋊C411yescharacteristic
103C4×C3⋊D3—22no—
104C4×C3⋊D3—22no—
105C4×C3⋊D3—41no—
106C4×C3⋊D3—41no—
107C3×#67—24no—
108C2×C3×Dic3—21no—
109C2×C3×Dic3—21no—
110C2×C3×Dic3—21no—
111C2×C3×Dic3—24no—
112C2×C3×Dic3—42no—
113C2×C3×Dic3—42no—
114C3×C4×D3—42no—
115#626—24no—
116#624—21no—
117#624—41no—
118#624—41no—
119#624C4212yescomplemented
120D3×Dic3—42no—
121C2×C4×D4—91no—
122C2×#99—92no—
123C4×C22⋊C4—91no—
124C4×C22⋊C4—91no—
125#342—92no—
126C23×D3—61no—
127C23×D3—61no—
128C23×D3—61no—
129C2×C3×D4—61no—
130C22×C3×C4—21no—
131C22×C3×C4—21no—
132C22×C3×C4—61no—
133C22×C3×C4—62no—
134C2×#67—21no—
135C2×#67—61no—
136C22×Dic3—22no—
137C22×Dic3—61no—
138C22×Dic3—61no—
139C22×Dic3—61no—
140D3×D4—64no—
141D3×D4—64no—
142C2×D12—61no—
143C2×C4×D3—21no—
144C2×C4×D3—61no—
145C2×C4×D3—61no—
146C2×C4×D3—61no—
147C2×C4×D3—61no—
148C2×C4×D3—61no—
149C2×C4×D3—61no—
150C2×C4×D3—61no—
151C2×C4×D3—61no—
152C2×C4×D3—61no—
153C2×C4×D3—61no—
154C2×C4×D3—61no—
155C2×C4×D3—61no—
156C2×C4×D3—124no—
157C2×C4×D3—124no—
158C2×C4×D3—124no—
159C3×C4⋊C4—61no—
160C3×C22⋊C4—61no—
161C3×C22⋊C4—61no—
162C3×C42—61no—
163#217—21no—
164#217—61no—
165(C2×D3)⋊C4—21no—
166(C2×D3)⋊C4—64no—
167(C2×D3)⋊C4—61no—
168(C2×D3)⋊C4—61no—
169(C2×D3)⋊C4—64no—
170(C2×D3)⋊C4—61no—
171C4⋊Dic3—61no—
172Dic3⋊C4—21no—
173Dic3⋊C4—61no—
174C4×Dic3—21no—
175C4×Dic3—61no—
176C4×Dic3—61no—
177C4×Dic3—124no—
178C22×C32—21no—
179C22×C32—21no—
180C22×C32C2×C22⋊C411yescharacteristic
181C22×C32C4×D412yes—
182C2×C3⋊D3—21no—
183C2×C3⋊D3—21no—
184C2×C3⋊D3—21no—
185C2×C3⋊D3—21no—
186C2×C3⋊D3—42no—
187C2×C3⋊D3—42no—
188C2×C3⋊D3C2×C4211yescharacteristic
189C2×C3⋊D3#11711yescharacteristic
190C2×C3⋊D3C4×D412yes—
191C2×C3×D3—22no—
192C2×C3×D3—41no—
193C2×C3×D3—41no—
194D32—42no—
195D32—42no—
196#157—44no—
197C32×C4—21no—
198C32×C4—21no—
199C3⋊Dic3—21no—
200C3⋊Dic3#9912yescomplemented
201C3×Dic3—22no—
202C3×Dic3—44no—
203C3×Dic3—41no—
204C3×Dic3—41no—
205C22×D4—91no—
206C23×C4—91no—
207C23×C4—91no—
208C4×D4—61no—
209C4×D4—181no—
210C4×D4—181no—
211C4×D4—181no—
212C2×C4⋊C4—91no—
213C2×C22⋊C4—91no—
214C2×C22⋊C4—91no—
215C2×C22⋊C4—92no—
216C2×C22⋊C4—92no—
217C2×C42—91no—
218C2×C42—181no—
219C2×C42—181no—
220#99—98no—
221#95—61no—
222#95—181no—
223C23×C3—21no—
224C23×C3—21no—
225C23×C3—61no—
226C22×D3—21no—
227C22×D3—62no—
228C22×D3—61no—
229C22×D3—62no—
230C22×D3—61no—
231C22×D3—62no—
232C22×D3—61no—
233C22×D3—61no—
234C22×D3—62no—
235C22×D3—62no—
236C22×D3—62no—
237C22×D3—122no—
238C22×D3—122no—
239C22×D3—122no—
240C22×D3—122no—
241C22×D3—122no—
242C22×D3—121no—
243C22×D3—121no—
244C3×D4—64no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—42no—
250C2×C3×C4—42no—
251C2×C3×C4—61no—
252C2×C3×C4—61no—
253C2×C3×C4—61no—
254C2×C3×C4—64no—
255C2×C3×C4—122no—
256C2×C3×C4—122no—
257C2×C3×C4—122no—
258#67—24no—
259#67—64no—
260C2×Dic3—21no—
261C2×Dic3—21no—
262C2×Dic3—21no—
263C2×Dic3—24no—
264C2×Dic3—42no—
265C2×Dic3—42no—
266C2×Dic3—61no—
267C2×Dic3—61no—
268C2×Dic3—61no—
269C2×Dic3—61no—
270C2×Dic3—64no—
271C2×Dic3—122no—
272C2×Dic3—122no—
273D12—64no—
274C4×D3—42no—
275C4×D3—62no—
276C4×D3—62no—
277C4×D3—64no—
278C4×D3—122no—
279C4×D3—122no—
280C4×D3—122no—
281C4×D3—122no—
282C4×D3—122no—
283C4×D3—122no—
284C4×D3—122no—
285C4×D3—122no—
286C4×D3—122no—
287C4×D3—122no—
288C2×C32—22no—
289C2×C32C4×C22⋊C411yescharacteristic
290C2×C32C2×#9911yescharacteristic
291C2×C32#41011yescharacteristic
292C3⋊D3—21no—
293C3⋊D3—21no—
294C3⋊D3—22no—
295C3×D3—42no—
296C24—91no—
297C24—91no—
298C2×D4—61no—
299C2×D4—94no—
300C2×D4—181no—
301C2×D4—182no—
302C22×C4—62no—
303C22×C4—61no—
304C22×C4—91no—
305C22×C4—91no—
306C22×C4—91no—
307C22×C4—91no—
308C22×C4—91no—
309C22×C4—91no—
310C22×C4—91no—
311C22×C4—91no—
312C22×C4—181no—
313C22×C4—182no—
314C22×C4—362no—
315C22×C4—362no—
316C22×C4GO+(4,𝔽2)11yescharacteristic
317C4⋊C4—61no—
318C4⋊C4—181no—
319C22⋊C4—61no—
320C22⋊C4—61no—
321C22⋊C4—94no—
322C22⋊C4—94no—
323C22⋊C4—181no—
324C22⋊C4—182no—
325C22⋊C4—181no—
326C22⋊C4—182no—
327C42—61no—
328C42—181no—
329C42—362no—
330C42—362no—
331C22×C3—21no—
332C22×C3—22no—
333C22×C3—21no—
334C22×C3—22no—
335C22×C3—22no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—41no—
339C22×C3—41no—
340C22×C3—62no—
341C22×C3—121no—
342C22×C3—121no—
343C2×D3—22no—
344C2×D3—41no—
345C2×D3—41no—
346C2×D3—61no—
347C2×D3—61no—
348C2×D3—62no—
349C2×D3—61no—
350C2×D3—61no—
351C2×D3—62no—
352C2×D3—62no—
353C2×D3—62no—
354C2×D3—121no—
355C2×D3—121no—
356C2×D3—121no—
357C2×D3—121no—
358C2×D3—121no—
359C2×D3—121no—
360C2×D3—124no—
361C2×D3—124no—
362C2×D3—124no—
363C2×D3—124no—
364C2×D3—122no—
365C2×D3—122no—
366C2×D3—122no—
367C2×D3—122no—
368C3×C4—22no—
369C3×C4—41no—
370C3×C4—41no—
371C3×C4—41no—
372C3×C4—62no—
373C3×C4—121no—
374C3×C4—121no—
375C3×C4—124no—
376Dic3—22no—
377Dic3—41no—
378Dic3—41no—
379Dic3—44no—
380Dic3—62no—
381Dic3—62no—
382Dic3—62no—
383Dic3—121no—
384C32C4×#9911yescharacteristic, complemented, Sylow
385C23—61no—
386C23—92no—
387C23—91no—
388C23—91no—
389C23—92no—
390C23—92no—
391C23—181no—
392C23—361no—
393C23—361no—
394C23—361no—
395C23—361no—
396C23C2×GO+(4,𝔽2)11yescharacteristic
397D4—64no—
398D4—184no—
399C2×C4—41no—
400C2×C4—61no—
401C2×C4—64no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—92no—
405C2×C4—91no—
406C2×C4—91no—
407C2×C4—122no—
408C2×C4—122no—
409C2×C4—122no—
410C2×C4—182no—
411C2×C4—182no—
412C2×C4—181no—
413C2×C4—182no—
414C2×C4—184no—
415C2×C4—361no—
416C2×C4—361no—
417C2×C4—362no—
418C2×C4—361no—
419C2×C4—361no—
420C2×C4—362no—
421C2×C4—362no—
422C2×C4D32⋊C411yescharacteristic
423C2×C4D32⋊C411yescharacteristic
424C2×C3—22no—
425C2×C3—22no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—42no—
433C2×C3—122no—
434D3—42no—
435D3—62no—
436D3—62no—
437D3—122no—
438D3—122no—
439D3—121no—
440D3—121no—
441C22—21no—
442C22—21no—
443C22—62no—
444C22—91no—
445C22—92no—
446C22—91no—
447C22—121no—
448C22—121no—
449C22—181no—
450C22—181no—
451C22—181no—
452C22—181no—
453C22—362no—
454C22—362no—
455C22—362no—
456C22—362no—
457C22C4×GO+(4,𝔽2)12yes—
458C22C2×D32⋊C411yescharacteristic
459C4—21no—
460C4—21no—
461C4—62no—
462C4—92no—
463C4—124no—
464C4—121no—
465C4—121no—
466C4—181no—
467C4—364no—
468C3—21no—
469C3—21no—
470C2—22no—
471C2—122no—
472C2—182no—
473C2—181no—
474C2—181no—
475C2#1059334611yescharacteristic
476C2C4×D32⋊C411yescharacteristic
477C2#1059349011yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊D3C2×C42
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3811C22
cosocleC23×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C4×#99
LCSG ▷ C2×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊#157C2semidirect
4. #10591260C2semidirect
5. #10590076C2semidirect
8. C2×C4×D32C4semidirect
16. #63921C4semidirect
18. #63883C4semidirect
19. C4×#624C4semidirect
22. #63738C4semidirect
48. C22⋊#157C2×C4semidirect
57. #3722C2×C4semidirect
93. C2×D32C42semidirect
119. #624C42semidirect
200. C3⋊Dic3#99semidirect
384. C32C4×#99semidirect

Maximal subgroups

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

subgroupindex
C4×#38112
C4×C22⋊#1572
C2×#637382
#105912602
#105900762
C4×#999