Finite Group Databasebeta

← #11790842

Subgroups — #11790842

Order 1152.

945 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 945 conjugacy classes of subgroups — too many to draw. Only its 134 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×#63980C211yesmaximal, characteristic
2C22⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#806C212yesmaximal, complemented
4#10591720C211yesmaximal, characteristic, complemented
5C2×#63580C212yesmaximal, complemented
6#70030—32nomaximal
7C23×C3⋊Dic3C2211yescharacteristic
8C22×C3×#67C2212yes—
9C22×#625C411yescharacteristic, complemented
10C2×C32×C22⋊C4C2211yescharacteristic
11C2×#3757C2211yescharacteristic
12C2×C4×C3⋊Dic3—21no—
13C2×C3×#217C2212yes—
14#63980—21no—
15#63980—21no—
16#63980—21no—
17#63980—21no—
18C2×#3724—21no—
19C2×#3724C411yescharacteristic, complemented
20C2×(C2×D3)⋊Dic3C412yescomplemented
21#63658—21no—
22C3×#806—24no—
23#63580—24no—
24#63579—21no—
25C2×#939—32no—
26C2×C3×#99—32no—
27C2×#834—32no—
28C2×#806—32no—
29C2×#806D312yescomplemented
30#4942—32no—
31Dic3×C22⋊C4—32no—
32Dic3×C22⋊C4—61no—
33C24×C32C2311yescharacteristic
34C23×C3×D3C2×C412yes—
35C22×C32×C4—21no—
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3—42no—
38C22×C3⋊Dic3C2×C411yescharacteristic
39C22×C3⋊Dic3C2×C411yescharacteristic
40C22×C3⋊Dic3D411yescharacteristic
41C22×C3⋊Dic3D411yescharacteristic
42C22×C3⋊Dic3D411yescharacteristic
43C22×C3⋊Dic3D411yescharacteristic
44C2×C3×#67—22no—
45C2×C3×#67—22no—
46C2×C3×#67—22no—
47C2×C3×#67—22no—
48C2×C3×#67—22no—
49C2×C3×#67—22no—
50C22×C3×Dic3—22no—
51C22×C3×Dic3C2×C412yes—
52C2×#625—21no—
53C2×#625—21no—
54C2×#625—42no—
55C32×C22⋊C4—21no—
56C32×C22⋊C4D412yescomplemented
57#3757—21no—
58#3757D412yescomplemented
59C4×C3⋊Dic3—42no—
60C3×#217—22no—
61C3×#217—22no—
62#3724—21no—
63#3724—21no—
64#3724—42no—
65(C2×D3)⋊Dic3—22no—
66(C2×D3)⋊Dic3—22no—
67#1964—91noSylow
68C22×C3×D4—32no—
69C22×#67—32no—
70C22×#67C2×D312yes—
71C23×Dic3—32no—
72C23×Dic3—61no—
73C2×C3×C22⋊C4—21no—
74C2×C3×C22⋊C4—32no—
75C2×C3×C22⋊C4C2×D312yes—
76C2×#217—32no—
77C2×#217—32no—
78C2×#217—61no—
79C2×#217C2×D312yes—
80#939—62no—
81#939—62no—
82#939—62no—
83#939—62no—
84C2×(C2×D3)⋊C4—32no—
85C2×Dic3⋊C4—32no—
86C2×Dic3⋊C4—62no—
87C2×C4×Dic3—62no—
88C2×C4×Dic3—62no—
89C3×#99—64no—
90#834—64no—
91C3⋊#95—62no—
92C3⋊#95—62no—
93C3⋊#95—62no—
94#806—24no—
95#806—64no—
96C23×C32—41no—
97C23×C32—41no—
98C23×C32C22×C411yescharacteristic
99C23×C32C2×D411yescharacteristic
100C23×C32C2×D411yescharacteristic
101C23×C32C2×D411yescharacteristic
102C23×C32C2×D411yescharacteristic
103C23×C32#4111yescharacteristic
104C23×C32#4111yescharacteristic
105C22×C3×D3—22no—
106C22×C3×D3—22no—
107C22×C3×D3—22no—
108C22×C3×D3—42no—
109C22×C3×D3—42no—
110C2×C32×C4—22no—
111C2×C32×C4—41no—
112C2×C32×C4—41no—
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—22no—
115C2×C3⋊Dic3—22no—
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3—41no—
118C2×C3⋊Dic3—41no—
119C2×C3⋊Dic3—41no—
120C2×C3⋊Dic3—41no—
121C2×C3⋊Dic3—41no—
122C2×C3⋊Dic3C22⋊C411yescharacteristic
123C2×C3⋊Dic3C22⋊C411yescharacteristic
124C2×C3⋊Dic3C22⋊C411yescharacteristic
125C2×C3⋊Dic3C22⋊C411yescharacteristic
126C3×#67—42no—
127C3×#67—42no—
128C3×#67—42no—
129C3×#67—42no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—42no—
134C2×C3×Dic3—42no—
135C2×C3×Dic3—42no—
136#625—42no—
137#625—42no—
138C2×#121—91no—
139C2×#99—32no—
140C2×#99—92no—
141#380—91no—
142C4×C22⋊C4—91no—
143C24×C3—21no—
144C24×C3—32no—
145C24×C3C22×D312yes—
146C23×D3C4×D312yes—
147C2×C3×D4—62no—
148C2×C3×D4—62no—
149C2×C3×D4—62no—
150C2×C3×D4—62no—
151C2×C3×D4—62no—
152C2×C3×D4—62no—
153C22×C3×C4—22no—
154C22×C3×C4—22no—
155C22×C3×C4—32no—
156C22×C3×C4—62no—
157C2×#67—22no—
158C2×#67—22no—
159C2×#67—22no—
160C2×#67—22no—
161C2×#67—22no—
162C2×#67—22no—
163C2×#67—62no—
164C2×#67—62no—
165C2×#67—124no—
166C22×Dic3—22no—
167C22×Dic3—32no—
168C22×Dic3—32no—
169C22×Dic3—32no—
170C22×Dic3—32no—
171C22×Dic3—32no—
172C22×Dic3—32no—
173C22×Dic3—61no—
174C22×Dic3—61no—
175C22×Dic3—61no—
176C22×Dic3—61no—
177C22×Dic3—61no—
178C22×Dic3—61no—
179C22×Dic3—62no—
180C22×Dic3—62no—
181C22×Dic3—124no—
182C22×Dic3—124no—
183C22×Dic3C4×D312yes—
184C3×C22⋊C4—22no—
185C3×C22⋊C4—22no—
186C3×C22⋊C4—22no—
187C3×C22⋊C4—62no—
188C3×C22⋊C4—62no—
189C3×C22⋊C4#6714yescomplemented
190#217—22no—
191#217—22no—
192#217—34no—
193#217—62no—
194#217—62no—
195#217—62no—
196#217—62no—
197#217—62no—
198(C2×D3)⋊C4—62no—
199(C2×D3)⋊C4—62no—
200Dic3⋊C4—62no—
201Dic3⋊C4—62no—
202Dic3⋊C4—124no—
203C4×Dic3—124no—
204C4×Dic3—124no—
205C22×C32—21no—
206C22×C32—21no—
207C22×C32—21no—
208C22×C32—21no—
209C22×C32—21no—
210C22×C32—21no—
211C22×C32—41no—
212C22×C32—41no—
213C22×C32—41no—
214C22×C32—41no—
215C22×C32C2×C22⋊C411yescharacteristic
216C22×C32C4×D411yescharacteristic
217C22×C32C4×D411yescharacteristic
218C22×C32#12111yescharacteristic
219C22×C32#12111yescharacteristic
220C22×C32#12411yescharacteristic
221C22×C32#12711yescharacteristic
222C2×C3×D3—42no—
223C2×C3×D3—42no—
224C2×C3×D3—42no—
225C2×C3×D3—82no—
226C2×C3×D3—82no—
227C32×C4—42no—
228C3⋊Dic3—21no—
229C3⋊Dic3—21no—
230C3⋊Dic3—21no—
231C3⋊Dic3—42no—
232C3⋊Dic3#9912yescomplemented
233C3×Dic3—42no—
234C3×Dic3—82no—
235C22×D4—32no—
236C22×D4—91no—
237C23×C4—91no—
238#121—181no—
239#121—181no—
240#121—181no—
241#121—181no—
242C2×C4⋊C4—91no—
243C2×C4⋊C4—181no—
244C2×C22⋊C4—32no—
245C2×C22⋊C4—91no—
246C2×C22⋊C4—92no—
247C2×C22⋊C4D3211yescharacteristic
248C2×C42—181no—
249#99—64no—
250#99—184no—
251#95—181no—
252#95—181no—
253C23×C3—21no—
254C23×C3—21no—
255C23×C3—21no—
256C23×C3—21no—
257C23×C3—21no—
258C23×C3—21no—
259C23×C3—21no—
260C23×C3—42no—
261C23×C3—42no—
262C23×C3—42no—
263C23×C3—42no—
264C23×C3—62no—
265C23×C3—62no—
266C23×C3—62no—
267C23×C3—122no—
268C23×C3—122no—
269C23×C3C2×C4×D312yes—
270C23×C3#23512yes—
271C23×C3D3×D412yes—
272C23×C3D3×D412yes—
273C23×C3D3×D412yes—
274C23×C3#23712yes—
275C23×C3C2×#6712yes—
276C22×D3—22no—
277C22×D3—22no—
278C22×D3—22no—
279C22×D3—42no—
280C22×D3—42no—
281C3×D4—122no—
282C3×D4—122no—
283C3×D4—122no—
284C3×D4—122no—
285C2×C3×C4—24no—
286C2×C3×C4—24no—
287C2×C3×C4—42no—
288C2×C3×C4—42no—
289C2×C3×C4—42no—
290C2×C3×C4—42no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—122no—
295C2×C3×C4—122no—
296C2×C3×C4—122no—
297#67—42no—
298#67—42no—
299#67—42no—
300#67—42no—
301#67—124no—
302#67—124no—
303C2×Dic3—22no—
304C2×Dic3—22no—
305C2×Dic3—22no—
306C2×Dic3—32no—
307C2×Dic3—32no—
308C2×Dic3—32no—
309C2×Dic3—32no—
310C2×Dic3—42no—
311C2×Dic3—42no—
312C2×Dic3—42no—
313C2×Dic3—61no—
314C2×Dic3—61no—
315C2×Dic3—61no—
316C2×Dic3—61no—
317C2×Dic3—64no—
318C2×Dic3—64no—
319C2×Dic3—64no—
320C2×Dic3—64no—
321C2×Dic3—64no—
322C2×Dic3—64no—
323C2×Dic3—122no—
324C2×Dic3—122no—
325C2×Dic3—122no—
326C2×Dic3—122no—
327C2×Dic3—122no—
328C2×Dic3—122no—
329C2×Dic3—122no—
330C2×Dic3—122no—
331C2×Dic3—122no—
332C2×Dic3—122no—
333C2×Dic3—122no—
334C2×Dic3—122no—
335C2×C32—21no—
336C2×C32—21no—
337C2×C32—21no—
338C2×C32—21no—
339C2×C32—21no—
340C2×C32—21no—
341C2×C32#39011yescharacteristic
342C2×C32C2×#9911yescharacteristic
343C2×C32#41011yescharacteristic
344C3×D3—82no—
345C24—32no—
346C24C2×D3211yescharacteristic
347C2×D4—62no—
348C2×D4—62no—
349C2×D4—62no—
350C2×D4—62no—
351C2×D4—62no—
352C2×D4—62no—
353C2×D4—181no—
354C2×D4—181no—
355C2×D4—362no—
356C22×C4—21no—
357C22×C4—32no—
358C22×C4—62no—
359C22×C4—91no—
360C22×C4—91no—
361C22×C4—91no—
362C22×C4—91no—
363C22×C4—91no—
364C22×C4—91no—
365C22×C4—181no—
366C22×C4—362no—
367C4⋊C4—181no—
368C4⋊C4—181no—
369C4⋊C4—362no—
370C22⋊C4—21no—
371C22⋊C4—62no—
372C22⋊C4—62no—
373C22⋊C4—92no—
374C22⋊C4—182no—
375C22⋊C4—182no—
376C22⋊C4—181no—
377C22⋊C4#62512yescomplemented
378C42—362no—
379C22×C3—22no—
380C22×C3—22no—
381C22×C3—22no—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3—22no—
385C22×C3—22no—
386C22×C3—22no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—41no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—42no—
399C22×C3—42no—
400C22×C3—42no—
401C22×C3—42no—
402C22×C3—42no—
403C22×C3—42no—
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—122no—
407C22×C3—122no—
408C22×C3—122no—
409C22×C3—242no—
410C22×C3—242no—
411C22×C3D3×C22⋊C412yes—
412C22×C3#67⋊C412yes—
413C22×C3#88412yes—
414C22×C3#88512yes—
415C22×C3C4×#6712yes—
416C22×C3#93912yes—
417C22×C3#94012yes—
418C2×D3—42no—
419C2×D3—42no—
420C2×D3—42no—
421C2×D3—82no—
422C2×D3—82no—
423C3×C4—44no—
424C3×C4—44no—
425C3×C4—122no—
426C3×C4—242no—
427Dic3—34no—
428Dic3—42no—
429Dic3—62no—
430Dic3—62no—
431Dic3—62no—
432Dic3—62no—
433Dic3—62no—
434Dic3—82no—
435Dic3—121no—
436Dic3—121no—
437Dic3—124no—
438Dic3—124no—
439C32#196411yescharacteristic, complemented, Sylow
440C23—41no—
441C23—41no—
442C23—62no—
443C23—62no—
444C23—62no—
445C23—122no—
446C23—122no—
447C23#379811yescharacteristic
448C23C4×D3211yescharacteristic
449C23#380211yescharacteristic
450C23#380211yescharacteristic
451C23#380511yescharacteristic
452C23C2×#62511yescharacteristic
453C23#381111yescharacteristic
454D4—122no—
455D4—122no—
456D4—122no—
457D4—122no—
458D4—362no—
459D4—362no—
460C2×C4—22no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—62no—
464C2×C4—62no—
465C2×C4—62no—
466C2×C4—91no—
467C2×C4—91no—
468C2×C4—91no—
469C2×C4—91no—
470C2×C4—122no—
471C2×C4—122no—
472C2×C4—122no—
473C2×C4—182no—
474C2×C4—182no—
475C2×C4—182no—
476C2×C4—182no—
477C2×C4—361no—
478C2×C4—361no—
479C2×C4—361no—
480C2×C4—361no—
481C2×C4—361no—
482C2×C3—22no—
483C2×C3—22no—
484C2×C3—22no—
485C2×C3—22no—
486C2×C3—22no—
487C2×C3—22no—
488C2×C3—22no—
489C2×C3—22no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—41no—
494C2×C3—41no—
495C2×C3—41no—
496C2×C3—41no—
497C2×C3—242no—
498C2×C3#474012yes—
499C2×C3D3×#9912yes—
500C2×C3#495712yes—
501D3—82no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—122no—
513C22—122no—
514C22—122no—
515C22—242no—
516C22—242no—
517C22C4×#62511yescharacteristic
518C22#6390211yescharacteristic
519C22#6391211yescharacteristic
520C22#6391411yescharacteristic
521C22#6391511yescharacteristic
522C22#6392111yescharacteristic
523C22#6398011yescharacteristic
524C4—42no—
525C4—92no—
526C4—122no—
527C4—181no—
528C4—181no—
529C4—181no—
530C4—242no—
531C4—362no—
532C3—21no—
533C3#7003012yescomplemented
534C2—21no—
535C2—21no—
536C2—21no—
537C2—21no—
538C2—21no—
539C2—21no—
540C2—242no—
541C2#1059040411yescharacteristic
542C2#1059040611yescharacteristic
543C2#1059138511yescharacteristic
subgroupG/H
centerC22#63921
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#63980C2
cosocleC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#1964
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22⋊C4×C3⋊Dic3C2semidirect
3. C2×C3×#806C2semidirect
4. #10591720C2semidirect
5. C2×#63580C2semidirect
9. C22×#625C4semidirect
19. C2×#3724C4semidirect
20. C2×(C2×D3)⋊Dic3C4semidirect
29. C2×#806D3semidirect
56. C32×C22⋊C4D4semidirect
58. #3757D4semidirect
189. C3×C22⋊C4#67semidirect
232. C3⋊Dic3#99semidirect
377. C22⋊C4#625semidirect
439. C32#1964semidirect
533. C3#70030semidirect

Maximal subgroups

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

subgroupindex
C2×#639802
C22⋊C4×C3⋊Dic32
C2×C3×#8062
#105917202
C2×#635802
#700303