Finite Group Databasebeta

← #11922510

Subgroups — #11922510

Order 1152.

822 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 822 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C22×C3⋊SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
2C2×C3×GL(2,ℤ/4)C211yesmaximal, characteristic
3A4×#217C211yesmaximal, characteristic, complemented
4(C2×S4)⋊Dic3C212yesmaximal, complemented
5Dic3⋊SL(2,ℤ/4)C212yesmaximal, complemented
6#85301—31nomaximal
7#82584—31nomaximal
8C23×C3×A4C2211yescharacteristic
9C22×C3×S4C2211yescharacteristic
10C2×Dic3×A4C2212yes—
11C2×C3⋊SL(2,ℤ/4)—22no—
12C2×C3⋊SL(2,ℤ/4)C2212yes—
13C3×GL(2,ℤ/4)—22no—
14C2×C3×SL(2,ℤ/4)C2211yescharacteristic
15#63962—41nomaximal
16C2×GL(2,ℤ/4)D311yescharacteristic
17C22×SL(2,ℤ/4)—31no—
18C22×SL(2,ℤ/4)—61no—
19C2×C3×#120—31no—
20C22×#217—31no—
21C22×#217D311yescharacteristic, complemented
22C2×#935—31no—
23A4×C22⋊C4—31no—
24(C2×S4)⋊C4—32no—
25C4⋊SL(2,ℤ/4)—32no—
26#5222—32no—
27#5220—31no—
28#5220—32no—
29#4952—32no—
30#4946—31no—
31#4943—31no—
32#4942—32no—
33C22×C3×A4—22no—
34C22×C3×A4D412yes—
35C22×C3×A4C2311yescharacteristic
36C2×C3×S4—21no—
37C2×C3×S4—22no—
38C22×C3⋊Dic3—41no—
39C2×C3×#67—41no—
40Dic3×A4—22no—
41C3⋊SL(2,ℤ/4)—22no—
42C3×SL(2,ℤ/4)—21no—
43C3×#217—41no—
44Dic3⋊Dic3—42no—
45(C2×D3)⋊Dic3—42no—
46#2412—91noSylow
47C25×C3C2×D311yescharacteristic
48C23×A4—21no—
49C23×A4C2×D311yescharacteristic
50C22×S4C2×D311yescharacteristic
51C22×C3×D4—31no—
52C22×C3×D4—31no—
53C22×C3×D4—31no—
54C23×Dic3—31no—
55C23×Dic3—31no—
56C23×Dic3C2×D312yes—
57C2×C4×A4—32no—
58GL(2,ℤ/4)—22no—
59C2×SL(2,ℤ/4)—32no—
60C2×SL(2,ℤ/4)—62no—
61C2×SL(2,ℤ/4)—64no—
62C2×SL(2,ℤ/4)—62no—
63C2×SL(2,ℤ/4)C2×D311yescharacteristic
64C3×#120—62no—
65C3×#120—62no—
66C2×C3×C22⋊C4—31no—
67C2×C3×C22⋊C4—31no—
68C2×C3×C22⋊C4—31no—
69C2×#217—31no—
70C2×#217—31no—
71C2×#217—32no—
72C2×#217—32no—
73C2×#217—32no—
74C2×#217—32no—
75C2×#217—32no—
76C2×#217—62no—
77C2×#217—62no—
78#935—61no—
79#935—62no—
80#935—61no—
81C2×Dic3⋊C4—32no—
82C2×Dic3⋊C4—32no—
83#886—121no—
84C3⋊#95—32no—
85C3⋊#95—32no—
86C3⋊#95—32no—
87C3⋊#95—32no—
88C23×C32—41no—
89C22×C3×D3—41no—
90C2×C3×A4—22no—
91C2×C3×A4C2×D411yescharacteristic
92C2×C3×A4#4112yes—
93C3×S4—41no—
94C2×C3⋊Dic3—42no—
95C2×C3⋊Dic3—82no—
96C3×#67—82no—
97C2×C3×Dic3—41no—
98C2×C3×Dic3—42no—
99C2×#123—91no—
100C2×#120—31no—
101C22×C22⋊C4—31no—
102C22×C22⋊C4—91no—
103#397—92no—
104#394—92no—
105#386—92no—
106#386—91no—
107#385—91no—
108#381—91no—
109#380—92no—
110C24×C3—22no—
111C24×C3—31no—
112C24×C3—31no—
113C24×C3—32no—
114C24×C3—31no—
115C24×C3—62no—
116C24×C3D1212yes—
117C24×C3C22×D311yescharacteristic
118C22×A4—24no—
119C22×A4—22no—
120C22×A4—22no—
121C22×A4—21no—
122C22×A4#6712yes—
123C22×A4C22×D311yescharacteristic
124C2×S4—22no—
125C2×S4—21no—
126C2×C3×D4—61no—
127C2×C3×D4—61no—
128C2×C3×D4—62no—
129C2×C3×D4—62no—
130C2×C3×D4—62no—
131C2×C3×D4—62no—
132C2×C3×D4—61no—
133C2×C3×D4—62no—
134C2×C3×D4—61no—
135C2×C3×D4—122no—
136C22×C3×C4—31no—
137C22×C3×C4—31no—
138C22×C3×C4—31no—
139C2×#67—41no—
140C22×Dic3—22no—
141C22×Dic3—32no—
142C22×Dic3—32no—
143C22×Dic3—32no—
144C22×Dic3—32no—
145C22×Dic3—62no—
146C22×Dic3—61no—
147C22×Dic3—62no—
148C22×Dic3—62no—
149C22×Dic3—62no—
150C22×Dic3—61no—
151C22×Dic3—121no—
152C22×Dic3—122no—
153C22×Dic3—241no—
154C4×A4—62no—
155SL(2,ℤ/4)—21no—
156SL(2,ℤ/4)—64no—
157SL(2,ℤ/4)—62no—
158C3×C22⋊C4—61no—
159C3×C22⋊C4—62no—
160C3×C22⋊C4—62no—
161C3×C22⋊C4—61no—
162C3×C22⋊C4—121no—
163#217—31no—
164#217—32no—
165#217—61no—
166#217—62no—
167#217—62no—
168#217—64no—
169#217—62no—
170#217—62no—
171#217—122no—
172#217S411yescharacteristic, complemented
173(C2×D3)⋊C4—122no—
174C4⋊Dic3—122no—
175Dic3⋊C4—62no—
176Dic3⋊C4—62no—
177Dic3⋊C4—122no—
178C22×C32—42no—
179C22×C32—41no—
180C22×C32—82no—
181C2×C3×D3—81no—
182C2×C3×D3—82no—
183C3×A4#12311yescharacteristic, complemented
184C3⋊Dic3—82no—
185C3×Dic3—82no—
186C3×Dic3—81no—
187C25D3211yescharacteristic
188C22×D4—31no—
189C22×D4—31no—
190C22×D4—31no—
191C23×C4—32no—
192C23×C4—91no—
193C23×C4—91no—
194#123—181no—
195#123—182no—
196#123—181no—
197#120—62no—
198#120—62no—
199C2×C4⋊C4—92no—
200C2×C4⋊C4—92no—
201C2×C22⋊C4—31no—
202C2×C22⋊C4—31no—
203C2×C22⋊C4—31no—
204C2×C22⋊C4—91no—
205C2×C22⋊C4—91no—
206C2×C22⋊C4—92no—
207C2×C22⋊C4—92no—
208C2×C22⋊C4—92no—
209C2×C22⋊C4—92no—
210C2×C22⋊C4—92no—
211C2×C22⋊C4—182no—
212C2×C22⋊C4—182no—
213#95—92no—
214#95—92no—
215#95—92no—
216#95—92no—
217C23×C3—22no—
218C23×C3—31no—
219C23×C3—31no—
220C23×C3—32no—
221C23×C3—32no—
222C23×C3—32no—
223C23×C3—32no—
224C23×C3—31no—
225C23×C3—41no—
226C23×C3—62no—
227C23×C3—62no—
228C23×C3—61no—
229C23×C3—62no—
230C23×C3—62no—
231C23×C3—64no—
232C23×C3—62no—
233C23×C3—62no—
234C23×C3—61no—
235C23×C3—61no—
236C23×C3—62no—
237C23×C3—61no—
238C23×C3—81no—
239C23×C3—122no—
240C23×C3C2×D1211yescharacteristic
241C23×C3#23712yes—
242C23×C3C2×S411yescharacteristic
243C22×D3—41no—
244C2×A4—24no—
245C2×A4—22no—
246C2×A4—22no—
247C2×A4—21no—
248C2×A4#23712yes—
249C2×A4C2×#6711yescharacteristic
250S4—41no—
251C3×D4—121no—
252C3×D4—122no—
253C3×D4—122no—
254C3×D4—124no—
255C3×D4—121no—
256C3×D4—122no—
257C2×C3×C4—62no—
258C2×C3×C4—61no—
259C2×C3×C4—61no—
260C2×C3×C4—61no—
261C2×C3×C4—62no—
262C2×C3×C4—61no—
263C2×C3×C4—61no—
264C2×C3×C4—122no—
265#67—82no—
266C2×Dic3—32no—
267C2×Dic3—41no—
268C2×Dic3—62no—
269C2×Dic3—62no—
270C2×Dic3—62no—
271C2×Dic3—62no—
272C2×Dic3—62no—
273C2×Dic3—62no—
274C2×Dic3—62no—
275C2×Dic3—62no—
276C2×Dic3—62no—
277C2×Dic3—62no—
278C2×Dic3—122no—
279C2×Dic3—122no—
280C2×Dic3—124no—
281C2×Dic3—122no—
282C2×Dic3—242no—
283C2×Dic3—242no—
284C2×Dic3—244no—
285C2×Dic3C2×S412yes—
286C2×C32—41no—
287C2×C32—42no—
288C2×C32—82no—
289C3×D3—161no—
290C24—22no—
291C24—31no—
292C24—31no—
293C24—32no—
294C24—31no—
295C24—62no—
296C24#62612yes—
297C24C2×D3211yescharacteristic
298C2×D4—61no—
299C2×D4—62no—
300C2×D4—62no—
301C2×D4—61no—
302C2×D4—62no—
303C2×D4—62no—
304C2×D4—61no—
305C2×D4—62no—
306C2×D4—61no—
307C2×D4—122no—
308C22×C4—31no—
309C22×C4—31no—
310C22×C4—31no—
311C22×C4—62no—
312C22×C4—92no—
313C22×C4—92no—
314C22×C4—92no—
315C22×C4—92no—
316C22×C4—182no—
317C22×C4—182no—
318C22×C4—182no—
319C22×C4—181no—
320C22×C4—182no—
321C22×C4—181no—
322C22×C4—362no—
323C4⋊C4—182no—
324C4⋊C4—182no—
325C4⋊C4—362no—
326C22⋊C4—31no—
327C22⋊C4—61no—
328C22⋊C4—62no—
329C22⋊C4—62no—
330C22⋊C4—61no—
331C22⋊C4—92no—
332C22⋊C4—91no—
333C22⋊C4—182no—
334C22⋊C4—181no—
335C22⋊C4—182no—
336C22⋊C4—182no—
337C22⋊C4—184no—
338C22⋊C4—182no—
339C22⋊C4—362no—
340C22×C3—22no—
341C22×C3—31no—
342C22×C3—32no—
343C22×C3—31no—
344C22×C3—31no—
345C22×C3—32no—
346C22×C3—32no—
347C22×C3—32no—
348C22×C3—41no—
349C22×C3—42no—
350C22×C3—62no—
351C22×C3—62no—
352C22×C3—64no—
353C22×C3—61no—
354C22×C3—62no—
355C22×C3—62no—
356C22×C3—62no—
357C22×C3—82no—
358C22×C3—84no—
359C22×C3—81no—
360C22×C3—82no—
361C22×C3—122no—
362C22×C3—121no—
363C22×C3—121no—
364C22×C3—122no—
365C22×C3—121no—
366C22×C3—122no—
367C22×C3#88611yescharacteristic, complemented
368C22×C3C4⋊S412yes—
369C22×C3C22×S411yescharacteristic
370C2×D3—81no—
371C2×D3—82no—
372A4—21no—
373A4#93511yescharacteristic, complemented
374C3×C4—121no—
375C3×C4—121no—
376C3×C4—121no—
377C3×C4—242no—
378Dic3—22no—
379Dic3—62no—
380Dic3—81no—
381Dic3—122no—
382Dic3—122no—
383Dic3—242no—
384Dic3—244no—
385C32—41noSylow
386C23—22no—
387C23—31no—
388C23—31no—
389C23—32no—
390C23—32no—
391C23—31no—
392C23—32no—
393C23—32no—
394C23—62no—
395C23—62no—
396C23—61no—
397C23—62no—
398C23—62no—
399C23—64no—
400C23—62no—
401C23—62no—
402C23—61no—
403C23—61no—
404C23—62no—
405C23—61no—
406C23—122no—
407C23#380512yes—
408C23C2×#62611yescharacteristic
409C23D3×S411yescharacteristic
410D4—122no—
411D4—121no—
412D4—122no—
413D4—124no—
414D4—122no—
415D4—121no—
416C2×C4—32no—
417C2×C4—61no—
418C2×C4—61no—
419C2×C4—61no—
420C2×C4—62no—
421C2×C4—62no—
422C2×C4—61no—
423C2×C4—61no—
424C2×C4—92no—
425C2×C4—182no—
426C2×C4—182no—
427C2×C4—182no—
428C2×C4—182no—
429C2×C4—182no—
430C2×C4—182no—
431C2×C4—182no—
432C2×C4—182no—
433C2×C4—182no—
434C2×C4—182no—
435C2×C4—362no—
436C2×C4—364no—
437C2×C4—362no—
438C2×C3—22no—
439C2×C3—31no—
440C2×C3—31no—
441C2×C3—32no—
442C2×C3—41no—
443C2×C3—42no—
444C2×C3—62no—
445C2×C3—82no—
446C2×C3—84no—
447C2×C3—81no—
448C2×C3—82no—
449C2×C3—241no—
450C2×C3C2×C4⋊S411yescharacteristic
451C2×C3#591412yes—
452D3—161no—
453C22—22no—
454C22—32no—
455C22—31no—
456C22—31no—
457C22—31no—
458C22—32no—
459C22—32no—
460C22—32no—
461C22—62no—
462C22—62no—
463C22—64no—
464C22—61no—
465C22—62no—
466C22—62no—
467C22—62no—
468C22—122no—
469C22—121no—
470C22—121no—
471C22—122no—
472C22—121no—
473C22—122no—
474C22#6396211yescharacteristic, complemented
475C22#6420712yes—
476C22C2×D3×S411yescharacteristic
477C4—62no—
478C4—121no—
479C4—121no—
480C4—121no—
481C4—182no—
482C4—362no—
483C4—362no—
484C3—41no—
485C3—81no—
486C3#8530111yescharacteristic, complemented
487C2—22no—
488C2—31no—
489C2—31no—
490C2—32no—
491C2—62no—
492C2—241no—
493C2C2×#6420711yescharacteristic
494C2#1059646812yes—
subgroupG/H
center, FrattiniC22C2×D3×S4
commutator, cosocleC22×C3×A4C23
FittingC25×C3C2×D3
socleC24×C3C22×D3
prime radicalC2×C3×GL(2,ℤ/4)C2
hypercenterC23D3×S4
hypocenterC3×A4#123
LCSG ▷ C22×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C22×C3⋊SL(2,ℤ/4)C2semidirect
3. A4×#217C2semidirect
4. (C2×S4)⋊Dic3C2semidirect
5. Dic3⋊SL(2,ℤ/4)C2semidirect
21. C22×#217D3semidirect
172. #217S4semidirect
183. C3×A4#123semidirect
367. C22×C3#886semidirect
373. A4#935semidirect
474. C22#63962semidirect
486. C3#85301semidirect

Maximal subgroups

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

subgroupindex
C22×C3⋊SL(2,ℤ/4)2
C2×C3×GL(2,ℤ/4)2
A4×#2172
(C2×S4)⋊Dic32
Dic3⋊SL(2,ℤ/4)2
#853013
#825843
#639624