Finite Group Databasebeta

← #11802733

Subgroups — #11802733

Order 1152.

2205 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic
2C2×#63900C211yesmaximal, characteristic, complemented
3C2×#63849C211yesmaximal, characteristic, complemented
4C3×#5212C212yesmaximal, complemented
5#10591722C212yesmaximal, complemented
6#10591704C212yesmaximal, complemented
7#10591380C212yesmaximal, complemented
8#10591325C212yesmaximal, complemented
9#10591273C212yesmaximal, complemented
10#74003—32nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×#638C2211yescharacteristic
13C22×#638C2211yescharacteristic
14C2×#3828—24no—
15C2×#3828—24no—
16C2×#3828C418yescomplemented
17C22×C4⋊(C3⋊D3)C2211yescharacteristic
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×#634C2211yescharacteristic
21C22×#624C2212yes—
22C2×C3×#217C2214yes—
23C2×C3×C4⋊Dic3C2212yes—
24C2×C3×C4⋊Dic3C2212yes—
25C2×#3724C2212yes—
26C2×#3722C2212yes—
27C2×#3722C2214yes—
28C2×Dic32C2212yes—
29#63900—24no—
30#63849—24no—
31C3×C3⋊#95C2214yes—
32#63579C2214yes—
33C22×#235—32no—
34C22×#235—61no—
35C2×#892—32no—
36C2×D3×C4⋊C4—32no—
37C3×#380—32no—
38#5212D312yescomplemented
39#4987—32no—
40#4987—32no—
41#4957—34no—
42#4956—34no—
43#4665—34no—
44#4646—34no—
45C24×C32C2311yescharacteristic
46C23×C3⋊D3C2311yescharacteristic
47C23×C3⋊D3C2311yescharacteristic
48C22×C32×C4—22no—
49C22×C32×C4—22no—
50C22×C32×C4C2×C414yescomplemented
51C22×C32×C4C2311yescharacteristic
52C22×C32×C4C2311yescharacteristic
53C2×#638—22no—
54C2×#638—22no—
55C2×#638—22no—
56C2×#638—22no—
57C2×#638C2×C414yes—
58C2×#638C2×C414yescomplemented
59C22×C3⋊Dic3C2311yescharacteristic
60C22×C3⋊Dic3C2311yescharacteristic
61#3828—232no—
62C2×C4⋊(C3⋊D3)—22no—
63C2×C4⋊(C3⋊D3)—22no—
64C2×C4⋊(C3⋊D3)C2×C414yes—
65C2×C4×C3⋊D3—22no—
66C2×C4×C3⋊D3—22no—
67C2×C4×C3⋊D3C2×C414yes—
68C2×C4×C3⋊D3C2×C414yescomplemented
69C2×C4×C3⋊D3D414yes—
70C2×C4×C3⋊D3D414yes—
71C2×#634—22no—
72C2×#634—22no—
73C2×#634C2×C414yescomplemented
74C22×C3×Dic3C2314yes—
75C22×C3×Dic3C2314yes—
76C2×#624—24no—
77C2×#624—44no—
78C3×#217—44no—
79C3×C4⋊Dic3—24no—
80C3×C4⋊Dic3—24no—
81#3724—24no—
82#3722—24no—
83#3722—44no—
84Dic32—24no—
85#2311—91noSylow
86C23×C3×C4—21no—
87C23×C3×C4C2×D312yes—
88C22×#67—32no—
89C22×#67—32no—
90C22×#67—61no—
91C22×#67—61no—
92C2×#235—316no—
93C2×#235—68no—
94C2×#235—68no—
95C2×#235—68no—
96C2×#235—68no—
97C2×#235—68no—
98C22×D12—32no—
99C22×D12—61no—
100C22×C4×D3—32no—
101C22×C4×D3—32no—
102C22×C4×D3—34no—
103C22×C4×D3—61no—
104C22×C4×D3—61no—
105C22×Dic6—32no—
106C22×Dic6—61no—
107C2×C3×C4⋊C4—32no—
108C2×C3×C4⋊C4—32no—
109C2×C3×C22⋊C4—34no—
110C2×#217C2×D314yes—
111C2×(C2×D3)⋊C4—34no—
112C2×(C2×D3)⋊C4—34no—
113C2×(C2×D3)⋊C4—34no—
114C2×C4⋊Dic3C2×D312yes—
115C2×C4⋊Dic3C2×D312yes—
116C2×Dic3⋊C4—34no—
117C2×C4×Dic3—34no—
118#892—68no—
119D3×C4⋊C4—68no—
120C3×#95—34no—
121C3⋊#95—34no—
122C3⋊#95—34no—
123C3⋊#95C2×D314yes—
124C23×C32—21no—
125C23×C32—21no—
126C23×C32—22no—
127C23×C32—22no—
128C23×C32C22×C412yes—
129C23×C32C2411yescharacteristic
130C22×C3⋊D3—21no—
131C22×C3⋊D3—21no—
132C22×C3⋊D3—22no—
133C22×C3⋊D3—22no—
134C22×C3⋊D3—22no—
135C22×C3⋊D3—22no—
136C22×C3⋊D3C22×C412yes—
137C22×C3⋊D3C22×C412yes—
138C22×C3⋊D3C2×D412yes—
139C22×C3⋊D3C2×D412yes—
140C2×C32×C4—21no—
141C2×C32×C4—21no—
142C2×C32×C4—28no—
143C2×C32×C4C22×C412yes—
144C2×C32×C4C22×C412yes—
145C2×C32×C4C2×D412yes—
146C2×C32×C4C2×D412yes—
147#638—28no—
148#638—28no—
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3—21no—
151C2×C3⋊Dic3C22×C412yes—
152C2×C3⋊Dic3C22×C412yes—
153C2×C3⋊Dic3C2×D412yes—
154C2×C3⋊Dic3C2×D412yes—
155C4⋊(C3⋊D3)—28no—
156C4×C3⋊D3—28no—
157C4×C3⋊D3C22⋊C4116yescomplemented
158#634—28no—
159C2×C3×Dic3—24no—
160C2×C3×Dic3—24no—
161C2×C3×Dic3—24no—
162C2×C3×Dic3—24no—
163C2×C3×Dic3—24no—
164C2×C3×Dic3—24no—
165#624—48no—
166C22×#41—91no—
167C2×#117—91no—
168C22×C4⋊C4—91no—
169#391—92no—
170#390—92no—
171#386—92no—
172#386—92no—
173#380—32no—
174#380—92no—
175C24×C3—21no—
176C24×C3C22×D312yes—
177C23×D3—32no—
178C23×D3—32no—
179C23×D3—61no—
180C23×D3—61no—
181C22×C3×C4—24no—
182C22×C3×C4—24no—
183C22×C3×C4—24no—
184C22×C3×C4—24no—
185C22×C3×C4—24no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—34no—
189C22×C3×C4—34no—
190C22×C3×C4C4×D318yescomplemented
191C22×C3×C4C22×D312yes—
192C22×C3×C4C22×D312yes—
193C2×#67—38no—
194C2×#67—38no—
195C2×#67—64no—
196C2×#67—64no—
197C2×#67—64no—
198C2×#67—64no—
199C2×#67—64no—
200C2×#67—64no—
201C2×#67—64no—
202C2×#67—64no—
203C2×#67—64no—
204C2×#67—64no—
205C22×Dic3—32no—
206C22×Dic3—32no—
207C22×Dic3—61no—
208C22×Dic3—61no—
209C22×Dic3C22×D314yes—
210C22×Dic3C22×D314yes—
211#235—664no—
212#235—664no—
213C2×D12—38no—
214C2×D12—64no—
215C2×D12—64no—
216C2×D12—64no—
217C2×D12—64no—
218C2×D12—64no—
219C2×C4×D3—38no—
220C2×C4×D3—38no—
221C2×C4×D3—38no—
222C2×C4×D3—38no—
223C2×C4×D3—64no—
224C2×C4×D3—64no—
225C2×C4×D3—64no—
226C2×C4×D3—64no—
227C2×C4×D3—64no—
228C2×C4×D3—64no—
229C2×C4×D3—64no—
230C2×C4×D3—64no—
231C2×C4×D3—68no—
232C2×C4×D3—124no—
233C2×C4×D3—124no—
234C2×Dic6—38no—
235C2×Dic6—64no—
236C2×Dic6—64no—
237C2×Dic6—64no—
238C2×Dic6—64no—
239C2×Dic6—64no—
240C3×C4⋊C4—64no—
241C3×C4⋊C4—64no—
242C3×C22⋊C4—124no—
243#217—44no—
244(C2×D3)⋊C4—68no—
245(C2×D3)⋊C4—124no—
246(C2×D3)⋊C4—124no—
247C4⋊Dic3—24no—
248C4⋊Dic3—24no—
249Dic3⋊C4—68no—
250C4×Dic3—68no—
251C22×C32—22no—
252C22×C32—24no—
253C22×C32—41no—
254C22×C32—41no—
255C22×C32—42no—
256C22×C32C23×C411yescharacteristic
257C22×C32C22×D411yescharacteristic
258C22×C32C22×D411yescharacteristic
259C22×C32H(5,𝔽2)12yes—
260C22×C322−1+412yes—
261C2×C3⋊D3—22no—
262C2×C3⋊D3—24no—
263C2×C3⋊D3—22no—
264C2×C3⋊D3—22no—
265C2×C3⋊D3—24no—
266C2×C3⋊D3—24no—
267C2×C3⋊D3—41no—
268C2×C3⋊D3—41no—
269C2×C3⋊D3—42no—
270C2×C3⋊D3C2×C22⋊C414yes—
271C32×C4—22no—
272C32×C4C2×C22⋊C414yes—
273C3⋊Dic3—22no—
274C3⋊Dic3C2×C22⋊C414yes—
275C3×Dic3—44no—
276C3×Dic3—44no—
277C2×#41—98no—
278C2×#41—184no—
279C2×#41—184no—
280C22×Q8—91no—
281C22×D4—91no—
282C22×D4—91no—
283C22×D4—91no—
284C23×C4—92no—
285C23×C4—91no—
286C23×C4—91no—
287C23×C4D3211yescharacteristic
288#117—184no—
289C2×C4⋊C4—32no—
290C2×C4⋊C4—32no—
291C2×C4⋊C4—92no—
292C2×C4⋊C4—184no—
293C2×C22⋊C4—34no—
294C2×C22⋊C4—92no—
295C2×C22⋊C4—94no—
296C2×C42—92no—
297#95—34no—
298#95—94no—
299C23×C3—22no—
300C23×C3—22no—
301C23×C3—22no—
302C23×C3—22no—
303C23×C3—22no—
304C23×C3—22no—
305C23×C3—22no—
306C23×C3—22no—
307C23×C3—21no—
308C23×C3—22no—
309C23×C3—42no—
310C23×C3—42no—
311C23×C3C2×C4×D314yes—
312C23×C3C23×D312yes—
313C22×D3—34no—
314C22×D3—34no—
315C22×D3—34no—
316C22×D3—34no—
317C22×D3—62no—
318C22×D3—62no—
319C22×D3—62no—
320C22×D3—62no—
321C22×D3—62no—
322C22×D3—62no—
323C22×D3—62no—
324C22×D3—62no—
325C22×D3—62no—
326C22×D3—62no—
327C22×D3—62no—
328C22×D3—62no—
329C22×D3—62no—
330C22×D3—62no—
331C22×D3—62no—
332C22×D3—62no—
333C22×D3—122no—
334C22×D3—122no—
335C22×D3—122no—
336C22×D3—122no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—216no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—216no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—64no—
348C2×C3×C4—64no—
349C2×C3×C4—64no—
350C2×C3×C4—64no—
351C2×C3×C4—64no—
352C2×C3×C4—64no—
353C2×C3×C4C2×C4×D314yes—
354C2×C3×C4C2×C4×D314yes—
355C2×C3×C4D3×D414yes—
356C2×C3×C4D3×D414yes—
357#67—616no—
358#67—616no—
359#67—616no—
360#67—616no—
361C2×Dic3—24no—
362C2×Dic3—24no—
363C2×Dic3—24no—
364C2×Dic3—24no—
365C2×Dic3—24no—
366C2×Dic3—24no—
367C2×Dic3—34no—
368C2×Dic3—34no—
369C2×Dic3—34no—
370C2×Dic3—34no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379D12—616no—
380D12—616no—
381C4×D3—332no—
382C4×D3—616no—
383C4×D3—616no—
384C4×D3—616no—
385C4×D3—1216no—
386Dic6—616no—
387Dic6—616no—
388C2×C32—42no—
389C2×C32C22×C22⋊C411yescharacteristic
390C2×C32#52012yes—
391C2×C32#53511yescharacteristic
392C2×C32#53611yescharacteristic
393C2×C32#53712yes—
394C3⋊D3—24no—
395C3⋊D3—42no—
396C24—91no—
397C24—91no—
398C24C2×D3211yescharacteristic
399#41—1832no—
400C2×Q8—94no—
401C2×Q8—182no—
402C2×Q8—182no—
403C2×D4—94no—
404C2×D4—94no—
405C2×D4—94no—
406C2×D4—182no—
407C2×D4—182no—
408C2×D4—182no—
409C2×D4—182no—
410C2×D4—182no—
411C2×D4—182no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—34no—
415C22×C4—34no—
416C22×C4—91no—
417C22×C4—94no—
418C22×C4—94no—
419C22×C4—94no—
420C22×C4—91no—
421C22×C4—94no—
422C22×C4—184no—
423C22×C4—182no—
424C22×C4—182no—
425C22×C4—364no—
426C22×C4#62414yescomplemented
427C22×C4C2×D3211yescharacteristic
428C22×C4C2×D3211yescharacteristic
429C4⋊C4—64no—
430C4⋊C4—64no—
431C4⋊C4—184no—
432C22⋊C4—124no—
433C22⋊C4—184no—
434C22⋊C4—364no—
435C42—184no—
436C22×C3—24no—
437C22×C3—24no—
438C22×C3—24no—
439C22×C3—24no—
440C22×C3—22no—
441C22×C3—22no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—44no—
446C22×C3—42no—
447C22×C3—44no—
448C22×C3—42no—
449C22×C3—42no—
450C22×C3—42no—
451C22×C3—42no—
452C22×C3—42no—
453C22×C3C22×C4×D312yes—
454C22×C3C2×D3×D412yes—
455C22×C3C2×D3×D412yes—
456C22×C3#100412yes—
457C22×C3#100712yes—
458C22×C3#100912yes—
459C22×C3#101012yes—
460C2×D3—38no—
461C2×D3—64no—
462C2×D3—64no—
463C2×D3—64no—
464C2×D3—64no—
465C2×D3—64no—
466C2×D3—64no—
467C2×D3—64no—
468C2×D3—64no—
469C2×D3—64no—
470C2×D3—64no—
471C2×D3—64no—
472C2×D3—122no—
473C2×D3—124no—
474C2×D3—124no—
475C2×D3—122no—
476C2×D3—124no—
477C2×D3—122no—
478C2×D3—124no—
479C2×D3—122no—
480C2×D3—122no—
481C2×D3—122no—
482C2×D3—122no—
483C2×D3—122no—
484C3×C4—24no—
485C3×C4—24no—
486C3×C4—24no—
487C3×C4—124no—
488C3×C4—124no—
489C3×C4D3×C22⋊C418yes—
490Dic3—38no—
491Dic3—44no—
492Dic3—44no—
493Dic3—64no—
494Dic3—64no—
495Dic3—64no—
496C32#231111yescharacteristic, complemented, Sylow
497C23—22no—
498C23—22no—
499C23—21no—
500C23—21no—
501C23—92no—
502C23—92no—
503C23—92no—
504C23—92no—
505C23—182no—
506C23—182no—
507C23—182no—
508C23—182no—
509C23—181no—
510C23—181no—
511C23C2×#62412yes—
512C23C22×D3211yescharacteristic
513Q8—188no—
514D4—188no—
515D4—188no—
516D4—188no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—28no—
520C2×C4—64no—
521C2×C4—64no—
522C2×C4—64no—
523C2×C4—64no—
524C2×C4—64no—
525C2×C4—64no—
526C2×C4—92no—
527C2×C4—92no—
528C2×C4—92no—
529C2×C4—916no—
530C2×C4—92no—
531C2×C4—181no—
532C2×C4—181no—
533C2×C4—188no—
534C2×C4—368no—
535C2×C4C2×#62412yes—
536C2×C4C2×#62412yes—
537C2×C4#381112yes—
538C2×C4#381112yes—
539C2×C3—21no—
540C2×C3—22no—
541C2×C3—22no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—44no—
545C2×C3—44no—
546C2×C3C2×D3×C22⋊C412yes—
547C2×C3#550412yes—
548C2×C3#552312yes—
549C2×C3#560712yes—
550C2×C3#560812yes—
551C2×C3#562812yes—
552C2×C3#562912yes—
553D3—68no—
554D3—124no—
555D3—124no—
556D3—124no—
557C22—24no—
558C22—22no—
559C22—41no—
560C22—42no—
561C22—41no—
562C22—94no—
563C22—182no—
564C22—184no—
565C22—184no—
566C22—182no—
567C22—184no—
568C22—182no—
569C22—361no—
570C22—362no—
571C22—361no—
572C22#6429712yes—
573C22#6430712yes—
574C22C22×#62411yescharacteristic
575C22C2×#381111yescharacteristic
576C22C2×#381111yescharacteristic
577C4—22no—
578C4—94no—
579C4—124no—
580C4—124no—
581C4—182no—
582C4#6397414yes—
583C3—21no—
584C3#7400312yescomplemented
585C2—42no—
586C2—184no—
587C2—362no—
588C2#1059480511yescharacteristic
589C2#1059492312yes—
590C2#1059499012yes—
591C2#1059508211yescharacteristic
592C2C2×#6397411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×#3828C2
hypercenterC23×C4D32
hypocenterC32#2311
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63900C2semidirect
3. C2×#63849C2semidirect
4. C3×#5212C2semidirect
5. #10591722C2semidirect
6. #10591704C2semidirect
7. #10591380C2semidirect
8. #10591325C2semidirect
9. #10591273C2semidirect
16. C2×#3828C4semidirect
38. #5212D3semidirect
50. C22×C32×C4C2×C4semidirect
58. C2×#638C2×C4semidirect
68. C2×C4×C3⋊D3C2×C4semidirect
73. C2×#634C2×C4semidirect
157. C4×C3⋊D3C22⋊C4semidirect
190. C22×C3×C4C4×D3semidirect
426. C22×C4#624semidirect
496. C32#2311semidirect
584. C3#74003semidirect

Maximal subgroups

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

subgroupindex
C22×#38282
C2×#639002
C2×#638492
C3×#52122
#105917222
#105917042
#105913802
#105913252
#105912732
#740033