Finite Group Databasebeta

← #11805509

Subgroups — #11805509

Order 1152.

1621 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic
2C2×#63952C212yesmaximal
3C3×#5212C211yesmaximal, characteristic, complemented
4C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
5#10591693C212yesmaximal, complemented
6#10591378C212yesmaximal, complemented
7#10591370C211yesmaximal, characteristic, complemented
8#10591360C211yesmaximal, characteristic, complemented
9#10591355C211yesmaximal, characteristic, complemented
10#10591264C212yesmaximal, complemented
11#10591257C211yesmaximal, characteristic, complemented
12#74011—31nomaximal
13#73369—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×#638C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C23×C3×Dic3C2212yes—
18C22×#624C2212yes—
19C2×#3757C2211yescharacteristic
20C4×#638C418yescomplemented
21C2×#3752C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C3×#217C2212yes—
25C2×C3×C4⋊Dic3C2212yes—
26C2×#3724C2212yes—
27C2×#3724C2212yes—
28C2×#3724C2212yes—
29C2×#3722C2212yes—
30C2×Dic32C2212yes—
31#63952—28no—
32C3×C3⋊#95C2211yescharacteristic
33C3×C3⋊#95C2211yescharacteristic
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2211yescharacteristic
36C3×C3⋊#95C2211yescharacteristic
37#63579C2212yes—
38#63579C2212yes—
39C2×C4×#67—31no—
40C2×C4×#67—31no—
41C2×C4×#67—32no—
42C2×C4×#67—61no—
43C2×#67⋊C4—32no—
44C3×#380—31no—
45C2×C3×#95—31no—
46#5212D311yescharacteristic, complemented
47#5210—32no—
48C2×C3⋊#95D311yescharacteristic, complemented
49#4989—32no—
50#4976—32no—
51#4946—32no—
52#4668—32no—
53#4667—31no—
54#4667—31no—
55D3×#95—31no—
56D3×#95—31no—
57#4650—31no—
58#4650—31no—
59#4649—31no—
60#4649—31no—
61#4647—32no—
62C24×C32C2311yescharacteristic
63C23×C3⋊D3C2311yescharacteristic
64C22×C32×C4—42no—
65C22×C32×C4C2×C414yescomplemented
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C2×#638C2×C414yes—
69C2×#638D414yes—
70C2×#638Q814yes—
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2311yescharacteristic
73C22×C3⋊Dic3C2311yescharacteristic
74C2×C4×C3⋊D3—42no—
75C2×C4×C3⋊D3C2×C414yescomplemented
76C22×C3×Dic3—24no—
77C22×C3×Dic3—24no—
78C22×C3×Dic3—42no—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2312yes—
83C2×#624—24no—
84C2×#624—24no—
85C2×#624—42no—
86#3757C2×C414yescomplemented
87#3752C2×C414yescomplemented
88#3750C2×C414yescomplemented
89C4×C3⋊Dic3C2×C414yescomplemented
90C3×#217—24no—
91C3×C4⋊Dic3—42no—
92#3724—24no—
93#3724—24no—
94#3724—42no—
95#3722—24no—
96Dic32—24no—
97#2349—91noSylow
98C23×C3×C4—21no—
99C23×C3×C4—32no—
100C23×C3×C4C2×D311yescharacteristic
101C23×C3×C4C2×D311yescharacteristic
102C22×#67—31no—
103C22×#67—31no—
104C22×#67—61no—
105C23×Dic3C2×D312yes—
106C22×C4×D3—31no—
107C22×C4×D3—31no—
108C22×C4×D3—32no—
109C22×C4×D3—32no—
110C22×C4×D3—61no—
111C2×C3×C4⋊C4—32no—
112C2×C3×C22⋊C4—32no—
113C2×#217—31no—
114C2×#217—31no—
115C2×#217—61no—
116C2×#217C2×D312yes—
117C4×#67—38no—
118C4×#67—38no—
119C4×#67—68no—
120C4×#67—68no—
121C2×(C2×D3)⋊C4—31no—
122C2×(C2×D3)⋊C4—31no—
123C2×(C2×D3)⋊C4—32no—
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4—61no—
126C2×C4⋊Dic3C2×D312yes—
127C2×Dic3⋊C4—31no—
128C2×Dic3⋊C4—31no—
129C2×Dic3⋊C4—32no—
130C2×Dic3⋊C4—32no—
131C2×Dic3⋊C4—32no—
132C2×Dic3⋊C4—32no—
133C2×Dic3⋊C4—32no—
134C2×Dic3⋊C4—32no—
135C2×Dic3⋊C4—61no—
136C2×C4×Dic3—31no—
137C2×C4×Dic3—31no—
138C2×C4×Dic3—32no—
139C2×C4×Dic3—32no—
140C2×C4×Dic3—61no—
141#67⋊C4—68no—
142C3×#95—32no—
143C3×#95—31no—
144C3×#95—31no—
145C3×#95—31no—
146C3×#95—31no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95—32no—
150C3⋊#95—32no—
151C3⋊#95C2×D311yescharacteristic
152C3⋊#95C2×D311yescharacteristic
153C3⋊#95C2×D311yescharacteristic
154C3⋊#95C2×D311yescharacteristic
155C3⋊#95C2×D312yes—
156C23×C32—22no—
157C23×C32—22no—
158C23×C32C22×C412yes—
159C23×C32C2×D412yes—
160C23×C32C2×Q812yes—
161C23×C32C2411yescharacteristic
162C22×C3⋊D3—22no—
163C22×C3⋊D3—22no—
164C22×C3⋊D3C22×C412yes—
165C22×C3⋊D3C2×D412yes—
166C22×C3⋊D3C2×Q812yes—
167C2×C32×C4—22no—
168C2×C32×C4—22no—
169C2×C32×C4—44no—
170C2×C32×C4C22×C412yes—
171C2×C32×C4C22×C412yes—
172#638C4⋊C4116yescomplemented
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3—22no—
175C2×C3⋊Dic3C22×C412yes—
176C2×C3⋊Dic3C22×C412yes—
177C2×C3⋊Dic3C22×C412yes—
178C2×C3⋊Dic3C2×D412yes—
179C2×C3⋊Dic3C2×Q812yes—
180C4×C3⋊D3—44no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—48no—
193C2×C3×Dic3#4114yes—
194#624—48no—
195C2×C4×D4—92no—
196C2×C4×D4—91no—
197#389—92no—
198#385—92no—
199#385—92no—
200#382—91no—
201#380—31no—
202#380—91no—
203C4×C4⋊C4—91no—
204C2×#95—31no—
205C2×#95—91no—
206C24×C3—21no—
207C24×C3C22×D311yescharacteristic
208C24×C3C22×D311yescharacteristic
209C23×D3—31no—
210C23×D3—31no—
211C23×D3—61no—
212C22×C3×C4—24no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—32no—
216C22×C3×C4—32no—
217C22×C3×C4—32no—
218C22×C3×C4—32no—
219C22×C3×C4—42no—
220C22×C3×C4—42no—
221C22×C3×C4—44no—
222C22×C3×C4—64no—
223C22×C3×C4—64no—
224C22×C3×C4—122no—
225C22×C3×C4C4×D314yescomplemented
226C22×C3×C4C4×D314yescomplemented
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C2×#67—34no—
232C2×#67—34no—
233C2×#67—34no—
234C2×#67—34no—
235C2×#67—34no—
236C2×#67—34no—
237C2×#67—64no—
238C2×#67—64no—
239C2×#67—64no—
240C22×Dic3—24no—
241C22×Dic3—24no—
242C22×Dic3—31no—
243C22×Dic3—31no—
244C22×Dic3—31no—
245C22×Dic3—31no—
246C22×Dic3—31no—
247C22×Dic3—31no—
248C22×Dic3—42no—
249C22×Dic3—61no—
250C22×Dic3—61no—
251C22×Dic3—61no—
252C22×Dic3C22×D312yes—
253C22×Dic3C22×D312yes—
254C22×Dic3C22×D312yes—
255C22×Dic3C22×D312yes—
256C2×C4×D3—34no—
257C2×C4×D3—34no—
258C2×C4×D3—64no—
259C2×C4×D3—64no—
260C2×C4×D3—64no—
261C2×C4×D3—64no—
262C2×C4×D3—64no—
263C2×C4×D3—122no—
264C2×C4×D3—122no—
265C2×C4×D3—122no—
266C2×C4×D3—122no—
267C2×C4×D3—124no—
268C3×C4⋊C4—122no—
269C3×C22⋊C4—64no—
270#217—24no—
271#217—34no—
272#217—34no—
273#217—64no—
274(C2×D3)⋊C4—34no—
275(C2×D3)⋊C4—34no—
276(C2×D3)⋊C4—64no—
277(C2×D3)⋊C4—64no—
278(C2×D3)⋊C4—64no—
279C4⋊Dic3—42no—
280Dic3⋊C4—34no—
281Dic3⋊C4—34no—
282Dic3⋊C4—64no—
283Dic3⋊C4—64no—
284Dic3⋊C4—64no—
285Dic3⋊C4—64no—
286Dic3⋊C4—64no—
287Dic3⋊C4—122no—
288Dic3⋊C4—122no—
289C4×Dic3—34no—
290C4×Dic3—34no—
291C4×Dic3—64no—
292C4×Dic3—64no—
293C4×Dic3—64no—
294C22×C32—22no—
295C22×C32—22no—
296C22×C32—24no—
297C22×C32—24no—
298C22×C32C2×C4⋊C414yes—
299C22×C32C23×C411yescharacteristic
300C22×C32C22×D411yescharacteristic
301C22×C32C22×Q811yescharacteristic
302C22×C32C2×#4112yes—
303C22×C32H(5,𝔽2)12yes—
304C2×C3⋊D3—22no—
305C2×C3⋊D3—22no—
306C2×C3⋊D3—24no—
307C2×C3⋊D3—24no—
308C2×C3⋊D3C2×C4⋊C414yes—
309C32×C4—22no—
310C32×C4—22no—
311C3⋊Dic3—22no—
312C3⋊Dic3—22no—
313C3⋊Dic3C2×C4⋊C414yes—
314C3×Dic3—24no—
315C3×Dic3—42no—
316C3×Dic3—42no—
317C3×Dic3—42no—
318C22×D4—91no—
319C23×C4—32no—
320C23×C4—92no—
321C23×C4—91no—
322C23×C4D3211yescharacteristic
323C4×D4—98no—
324C4×D4—188no—
325C2×C4⋊C4—32no—
326C2×C4⋊C4—91no—
327C2×C4⋊C4—92no—
328C2×C4⋊C4—92no—
329C2×C4⋊C4—92no—
330C2×C22⋊C4—32no—
331C2×C22⋊C4—91no—
332C2×C22⋊C4—91no—
333C2×C22⋊C4—92no—
334C2×C42—91no—
335C2×C42—92no—
336#95—31no—
337#95—31no—
338#95—32no—
339#95—31no—
340#95—31no—
341#95—92no—
342#95—92no—
343C23×C3—22no—
344C23×C3—22no—
345C23×C3—22no—
346C23×C3—22no—
347C23×C3—21no—
348C23×C3—22no—
349C23×C3—22no—
350C23×C3—22no—
351C23×C3—42no—
352C23×C3—42no—
353C23×C3C2×C4×D312yes—
354C23×C3C2×C4×D312yes—
355C23×C3D3×D412yes—
356C23×C3D3×D412yes—
357C23×C3D3×Q812yes—
358C23×C3D3×Q812yes—
359C23×C3C23×D311yescharacteristic
360C23×C3C23×D311yescharacteristic
361C22×D3—32no—
362C22×D3—32no—
363C22×D3—32no—
364C22×D3—32no—
365C22×D3—32no—
366C22×D3—32no—
367C22×D3—62no—
368C22×D3—62no—
369C22×D3—62no—
370C22×D3—62no—
371C22×D3—62no—
372C22×D3—62no—
373C22×D3—62no—
374C22×D3—122no—
375C22×D3—122no—
376C2×C3×C4—24no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—34no—
384C2×C3×C4—42no—
385C2×C3×C4—44no—
386C2×C3×C4—44no—
387C2×C3×C4—48no—
388C2×C3×C4—62no—
389C2×C3×C4—62no—
390C2×C3×C4—62no—
391C2×C3×C4—62no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4—62no—
395C2×C3×C4—62no—
396C2×C3×C4—62no—
397C2×C3×C4—62no—
398C2×C3×C4—62no—
399C2×C3×C4—128no—
400C2×C3×C4C2×C4×D312yes—
401C2×C3×C4C2×C4×D312yes—
402C2×C3×C4C2×C4×D312yes—
403C2×C3×C4C2×C4×D312yes—
404#67—316no—
405#67—316no—
406#67—616no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—22no—
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—32no—
419C2×Dic3—32no—
420C2×Dic3—32no—
421C2×Dic3—32no—
422C2×Dic3—32no—
423C2×Dic3—32no—
424C2×Dic3—32no—
425C2×Dic3—32no—
426C2×Dic3—32no—
427C2×Dic3—32no—
428C2×Dic3—48no—
429C2×Dic3—62no—
430C2×Dic3—62no—
431C2×Dic3—62no—
432C2×Dic3—62no—
433C2×Dic3—62no—
434C2×Dic3—62no—
435C2×Dic3—62no—
436C2×Dic3—62no—
437C2×Dic3—62no—
438C2×Dic3—122no—
439C2×Dic3—122no—
440C2×Dic3#23514yes—
441C4×D3—128no—
442C4×D3—128no—
443C4×D3—124no—
444C4×D3—124no—
445C4×D3—128no—
446C2×C32—24no—
447C2×C32C22×C4⋊C411yescharacteristic
448C2×C32C4×#4111yescharacteristic
449C2×C32#51811yescharacteristic
450C2×C32#54612yes—
451C2×C32#55412yes—
452C3⋊D3—24no—
453C24—91no—
454C24C2×D3211yescharacteristic
455C2×D4—94no—
456C2×D4—94no—
457C2×D4—94no—
458C22×C4—32no—
459C22×C4—32no—
460C22×C4—32no—
461C22×C4—32no—
462C22×C4—42no—
463C22×C4—64no—
464C22×C4—64no—
465C22×C4—91no—
466C22×C4—91no—
467C22×C4—91no—
468C22×C4—94no—
469C22×C4—122no—
470C22×C4—184no—
471C22×C4—184no—
472C22×C4—362no—
473C22×C4—362no—
474C22×C4#62414yescomplemented
475C22×C4C2×D3211yescharacteristic
476C22×C4C2×D3211yescharacteristic
477C4⋊C4—94no—
478C4⋊C4—122no—
479C4⋊C4—184no—
480C4⋊C4—184no—
481C4⋊C4—362no—
482C22⋊C4—64no—
483C22⋊C4—94no—
484C22⋊C4—94no—
485C22⋊C4—184no—
486C42—94no—
487C42—184no—
488C22×C3—24no—
489C22×C3—22no—
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—24no—
493C22×C3—24no—
494C22×C3—22no—
495C22×C3—24no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—22no—
499C22×C3—21no—
500C22×C3—22no—
501C22×C3—24no—
502C22×C3—42no—
503C22×C3—44no—
504C22×C3—42no—
505C22×C3—44no—
506C22×C3D3×C4⋊C414yes—
507C22×C3D3×C4⋊C414yes—
508C22×C3C22×C4×D311yescharacteristic
509C22×C3C22×C4×D311yescharacteristic
510C22×C3C2×#23512yes—
511C22×C3C2×D3×D411yescharacteristic
512C22×C3C2×D3×D411yescharacteristic
513C22×C3#100412yes—
514C22×C3#100412yes—
515C22×C3C2×D3×Q811yescharacteristic
516C22×C3C2×D3×Q811yescharacteristic
517C22×C3D3×#4112yes—
518C2×D3—34no—
519C2×D3—34no—
520C2×D3—64no—
521C2×D3—64no—
522C2×D3—62no—
523C2×D3—62no—
524C2×D3—62no—
525C2×D3—64no—
526C2×D3—64no—
527C2×D3—62no—
528C2×D3—64no—
529C2×D3—122no—
530C2×D3—124no—
531C2×D3—122no—
532C2×D3—124no—
533C3×C4—24no—
534C3×C4—22no—
535C3×C4—22no—
536C3×C4—22no—
537C3×C4—22no—
538C3×C4—42no—
539C3×C4—64no—
540C3×C4—122no—
541C3×C4—122no—
542C3×C4—122no—
543Dic3—24no—
544Dic3—34no—
545Dic3—34no—
546Dic3—42no—
547Dic3—42no—
548Dic3—42no—
549Dic3—64no—
550Dic3—62no—
551Dic3—62no—
552Dic3—62no—
553Dic3—62no—
554Dic3—122no—
555Dic3—122no—
556C32#234911yescharacteristic, complemented, Sylow
557C23—22no—
558C23—22no—
559C23—92no—
560C23—92no—
561C23—92no—
562C23—182no—
563C23—182no—
564C23#379712yes—
565C23#380212yes—
566C23C2×#62412yes—
567C23C22×D3211yescharacteristic
568D4—916no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—34no—
572C2×C4—44no—
573C2×C4—62no—
574C2×C4—62no—
575C2×C4—62no—
576C2×C4—62no—
577C2×C4—62no—
578C2×C4—62no—
579C2×C4—62no—
580C2×C4—62no—
581C2×C4—62no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4—92no—
585C2×C4—92no—
586C2×C4—92no—
587C2×C4—92no—
588C2×C4—92no—
589C2×C4—128no—
590C2×C4—182no—
591C2×C4—182no—
592C2×C4—364no—
593C2×C4—368no—
594C2×C4C2×#62412yes—
595C2×C4C2×#62412yes—
596C2×C3—24no—
597C2×C3—24no—
598C2×C3—22no—
599C2×C3—21no—
600C2×C3—21no—
601C2×C3—22no—
602C2×C3—21no—
603C2×C3—44no—
604C2×C3C4×#23511yescharacteristic
605C2×C3#548611yescharacteristic
606C2×C3#548611yescharacteristic
607C2×C3#549012yes—
608C2×C3C2×D3×C4⋊C411yescharacteristic
609C2×C3C2×D3×C4⋊C411yescharacteristic
610C2×C3#551112yes—
611C2×C3#552211yescharacteristic
612C2×C3#561012yes—
613C2×C3#563612yes—
614D3—64no—
615D3—64no—
616D3—124no—
617C22—24no—
618C22—22no—
619C22—24no—
620C22—22no—
621C22—94no—
622C22—184no—
623C22—182no—
624C22—184no—
625C22—182no—
626C22#6390014yes—
627C22C2×#379711yescharacteristic
628C22C2×#380211yescharacteristic
629C22D3×#23512yes—
630C22C22×#62411yescharacteristic
631C22#6433012yes—
632C4—22no—
633C4—22no—
634C4—64no—
635C4—94no—
636C4—122no—
637C4—122no—
638C4—122no—
639C4—182no—
640C4—182no—
641C3—21no—
642C3#7336911yescharacteristic, complemented
643C3#7401111yescharacteristic, complemented
644C2—24no—
645C2—184no—
646C2C2×#6390011yescharacteristic
647C2#1059495411yescharacteristic
648C2#1059495612yes—
649C2#1059508312yes—
650C2#1059551011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC23×C4D32
hypocenterC32#2349
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C3×#5212C2semidirect
4. C2×C3×C3⋊#95C2semidirect
5. #10591693C2semidirect
6. #10591378C2semidirect
7. #10591370C2semidirect
8. #10591360C2semidirect
9. #10591355C2semidirect
10. #10591264C2semidirect
11. #10591257C2semidirect
20. C4×#638C4semidirect
46. #5212D3semidirect
48. C2×C3⋊#95D3semidirect
65. C22×C32×C4C2×C4semidirect
75. C2×C4×C3⋊D3C2×C4semidirect
86. #3757C2×C4semidirect
87. #3752C2×C4semidirect
88. #3750C2×C4semidirect
89. C4×C3⋊Dic3C2×C4semidirect
172. #638C4⋊C4semidirect
225. C22×C3×C4C4×D3semidirect
226. C22×C3×C4C4×D3semidirect
474. C22×C4#624semidirect
556. C32#2349semidirect
642. C3#73369semidirect
643. C3#74011semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C2×#639522
C3×#52122
C2×C3×C3⋊#952
#105916932
#105913782
#105913702
#105913602
#105913552
#105912642
#105912572
#740113
#733693