Finite Group Databasebeta

← #11794021

Subgroups — #11794021

Order 1152.

821 conjugacy classes of subgroups.

The subgroup lattice has 641 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3714C211yesmaximal, characteristic
2C2×#63648C211yesmaximal, characteristic, complemented
3C2×C3×#821C211yesmaximal, characteristic, complemented
4C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
5#10591320C211yesmaximal, characteristic, complemented
6#10591318C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#70481—31nomaximal
9#70212—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3722—21no—
18C2×#3722—21no—
19C2×(C2×D3)⋊Dic3—21no—
20C2×(C2×D3)⋊Dic3—21no—
21C2×#3714—22no—
22C2×#3714—22no—
23C2×#3714—22no—
24#63648—22no—
25C3×#821—22no—
26C3×Dic3⋊C8—22no—
27C22×#213—31no—
28C22×D24—31no—
29C2×C3×C4⋊C8—31no—
30C2×C3×#102—31no—
31#5221—31no—
32C2×#821—31no—
33C2×#821—31no—
34C2×#821—61no—
35C2×#821D311yescharacteristic, complemented
36C2×Dic3⋊C8D311yescharacteristic, complemented
37#4988—31no—
38#4939—31no—
39#4939—31no—
40#4551—31no—
41#4529—31no—
42C23×C3⋊D3—21no—
43C23×C3×D3—21no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)D412yes—
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C22×C3×Dic3D411yescharacteristic
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12D412yes—
61C2×C32×C8—21no—
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4×Dic3—21no—
69C3×C4×Dic3—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8D412yes—
73#3722—42no—
74#3722—42no—
75(C2×D3)⋊Dic3—42no—
76(C2×D3)⋊Dic3—42no—
77#3714—28no—
78#2054—91noSylow
79C22×C3×D4—31no—
80C22×D12—31no—
81C22×D12—31no—
82C22×D12—61no—
83C22×D12C2×D311yescharacteristic
84C22×C3×C8—21no—
85C22×C3×C8—31no—
86C22×C3×C8C2×D311yescharacteristic
87C22×C3×C8C2×D311yescharacteristic
88C2×C3×C4⋊C4—31no—
89C2×C3×C42—31no—
90C2×#217—61no—
91C2×#217—61no—
92C2×#213—62no—
93C2×#213—62no—
94C2×#213—62no—
95C2×(C2×D3)⋊C4—61no—
96C2×(C2×D3)⋊C4—61no—
97C2×(C2×D3)⋊C4—61no—
98C2×(C2×D3)⋊C4—61no—
99C2×(C2×D3)⋊C4—61no—
100C2×(C2×D3)⋊C4—61no—
101C2×C4⋊Dic3—31no—
102C2×C4⋊Dic3—31no—
103C2×C4⋊Dic3—61no—
104C2×C4⋊Dic3C2×D311yescharacteristic
105C2×C4×Dic3C2×D311yescharacteristic
106C22×C3⋊C8C2×D311yescharacteristic
107C2×D24—62no—
108C2×D24—62no—
109C2×D24—62no—
110C3×C4⋊C8—62no—
111C3×#102—62no—
112#821—22no—
113#821—62no—
114#821—62no—
115#821—64no—
116Dic3⋊C8—22no—
117C23×C32C2×D411yescharacteristic
118C22×C3⋊D3—22no—
119C22×C3⋊D3—41no—
120C22×C3⋊D3—41no—
121C22×C3⋊D3—41no—
122C22×C3⋊D3—41no—
123C22×C3⋊D3—41no—
124C22×C3⋊D3—41no—
125C22×C3×D3—22no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C22×C3×D3—41no—
129C22×C3×D3—41no—
130C22×C3×D3—41no—
131C22×C3×D3—41no—
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C3⋊Dic3—41no—
139C2×C3⋊Dic3—41no—
140C2×C3⋊Dic3—41no—
141C4⋊(C3⋊D3)—22no—
142C4⋊(C3⋊D3)—22no—
143C4⋊(C3⋊D3)—41no—
144C4⋊(C3⋊D3)—41no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3D812yescomplemented
154C3×D12—22no—
155C3×D12—22no—
156C3×D12—41no—
157C3×D12—41no—
158C32×C8—41no—
159C3×C3⋊C8—22no—
160C22×D8—91no—
161C2×C4⋊C8—31no—
162C2×#102—31no—
163C2×#102—91no—
164#390—91no—
165#390—91no—
166#340—91no—
167C24×C3—61no—
168C23×D3—21no—
169C23×D3—61no—
170C23×D3—61no—
171C23×D3—121no—
172C2×C3×D4—32no—
173C2×C3×D4—61no—
174C2×C3×D4—61no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C22×C3×C4—21no—
179C22×C3×C4—31no—
180C22×C3×C4—31no—
181C22×C3×C4—61no—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C22×Dic3—21no—
185C22×Dic3—61no—
186C22×Dic3—61no—
187C22×Dic3—121no—
188C22×Dic3D1211yescharacteristic
189C22×Dic3D1211yescharacteristic
190C2×D12—21no—
191C2×D12—21no—
192C2×D12—21no—
193C2×D12—21no—
194C2×D12—21no—
195C2×D12—32no—
196C2×D12—32no—
197C2×D12—62no—
198C2×D12—62no—
199C2×D12—62no—
200C2×D12—61no—
201C2×D12—61no—
202C2×D12—61no—
203C2×D12—61no—
204C2×D12—61no—
205C2×D12—61no—
206C2×D12—61no—
207C2×D12—61no—
208C2×D12—61no—
209C2×D12—61no—
210C2×D12—121no—
211C2×D12—121no—
212C2×D12—121no—
213C2×D12#6712yes—
214C2×C3×C8—22no—
215C2×C3×C8—21no—
216C2×C3×C8—21no—
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—21no—
220C2×C3×C8—21no—
221C2×C3×C8—32no—
222C2×C3×C8—41no—
223C2×C3×C8—41no—
224C2×C3×C8—61no—
225C2×C3×C8—61no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4—61no—
228C3×C42—61no—
229C3×C42—61no—
230#217—122no—
231#217—122no—
232#213—68no—
233(C2×D3)⋊C4—122no—
234(C2×D3)⋊C4—122no—
235(C2×D3)⋊C4—122no—
236(C2×D3)⋊C4—122no—
237(C2×D3)⋊C4—122no—
238(C2×D3)⋊C4—122no—
239C4⋊Dic3—21no—
240C4⋊Dic3—21no—
241C4⋊Dic3—62no—
242C4⋊Dic3—61no—
243C4⋊Dic3—61no—
244C4⋊Dic3—61no—
245C4⋊Dic3—61no—
246C4⋊Dic3—121no—
247C4×Dic3—21no—
248C4×Dic3—21no—
249C2×C3⋊C8—21no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8#6712yes—
252D24—68no—
253C22×C32#12111yescharacteristic
254C22×C32#12111yescharacteristic
255C22×C32#12111yescharacteristic
256C22×C32C2×D811yescharacteristic
257C22×C32#13511yescharacteristic
258C22×C32AGL(1,ℤ/8)11yescharacteristic
259C22×C32AGL(1,ℤ/8)11yescharacteristic
260C2×C3⋊D3—42no—
261C2×C3⋊D3—42no—
262C2×C3⋊D3—42no—
263C2×C3⋊D3—81no—
264C2×C3⋊D3—81no—
265C2×C3⋊D3—81no—
266C2×C3⋊D3—81no—
267C2×C3×D3—42no—
268C2×C3×D3—42no—
269C2×C3×D3—42no—
270C2×C3×D3—81no—
271C2×C3×D3—81no—
272C2×C3×D3—81no—
273C2×C3×D3—81no—
274C32×C4#12011yescharacteristic
275C32×C4#12311yescharacteristic
276C32×C4#12311yescharacteristic
277C32×C4#12411yescharacteristic
278C3⋊Dic3—81no—
279C3×Dic3—22no—
280C3×Dic3—41no—
281C3×Dic3—81no—
282C22×D4—31no—
283C22×D4—91no—
284C2×D8—182no—
285C2×D8—182no—
286C2×D8—182no—
287C22×C8—31no—
288C22×C8D3211yescharacteristic
289C2×C4⋊C4—31no—
290C2×C4⋊C4—91no—
291C2×C22⋊C4—181no—
292C2×C22⋊C4—181no—
293C2×C22⋊C4—181no—
294C2×C22⋊C4—181no—
295C2×C42—31no—
296C4⋊C8—62no—
297#102—62no—
298#102—182no—
299C23×C3—21no—
300C23×C3—62no—
301C23×C3—121no—
302C23×C3—121no—
303C23×C3—121no—
304C23×C3—121no—
305C23×C3—121no—
306C23×C3—121no—
307C23×C3C2×D1211yescharacteristic
308C23×C3D3×D411yescharacteristic
309C22×D3—22no—
310C22×D3—41no—
311C22×D3—41no—
312C22×D3—41no—
313C22×D3—41no—
314C22×D3—41no—
315C22×D3—41no—
316C22×D3—62no—
317C22×D3—62no—
318C22×D3—122no—
319C22×D3—122no—
320C22×D3—122no—
321C22×D3—121no—
322C22×D3—121no—
323C22×D3—121no—
324C22×D3—121no—
325C22×D3—121no—
326C22×D3—121no—
327C22×D3—121no—
328C22×D3—121no—
329C22×D3—121no—
330C22×D3—121no—
331C22×D3—121no—
332C22×D3—121no—
333C22×D3—241no—
334C22×D3—241no—
335C22×D3—241no—
336C22×D3—241no—
337C3×D4—62no—
338C3×D4—62no—
339C3×D4—121no—
340C3×D4—121no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—32no—
348C2×C3×C4—61no—
349C2×C3×C4—61no—
350C2×C3×C4—61no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—121no—
354C2×C3×C4—121no—
355C2×C3×C4—121no—
356C2×C3×C4#23511yescharacteristic
357C2×C3×C4#23511yescharacteristic
358C2×C3×C4#23511yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4#23711yescharacteristic
364C2×C3×C4#23911yescharacteristic
365C2×C3×C4#23911yescharacteristic
366C2×C3×C4C2×#6711yescharacteristic
367C2×C3×C4C2×#6711yescharacteristic
368C2×Dic3—21no—
369C2×Dic3—21no—
370C2×Dic3—21no—
371C2×Dic3—21no—
372C2×Dic3—21no—
373C2×Dic3—41no—
374C2×Dic3—41no—
375C2×Dic3—41no—
376C2×Dic3—122no—
377C2×Dic3—121no—
378C2×Dic3—121no—
379C2×Dic3—121no—
380C2×Dic3—121no—
381C2×Dic3—121no—
382C2×Dic3—121no—
383C2×Dic3—241no—
384C2×Dic3—241no—
385C2×Dic3D2412yescomplemented
386D12—22no—
387D12—22no—
388D12—41no—
389D12—41no—
390D12—64no—
391D12—62no—
392D12—62no—
393D12—62no—
394D12—62no—
395D12—122no—
396D12—122no—
397D12—122no—
398D12—121no—
399D12—121no—
400D12—121no—
401D12—121no—
402C3×C8—42no—
403C3×C8—41no—
404C3×C8—41no—
405C3×C8—62no—
406C3⋊C8—22no—
407C2×C32#39411yescharacteristic
408C2×C32#45911yescharacteristic
409C2×C32#45911yescharacteristic
410C2×C32#46311yescharacteristic
411C2×C32#46311yescharacteristic
412C2×C32#46611yescharacteristic
413C2×C32#46911yescharacteristic
414C3⋊D3—82no—
415C3×D3—82no—
416C24—61no—
417C24—181no—
418C2×D4—32no—
419C2×D4—61no—
420C2×D4—61no—
421C2×D4—61no—
422C2×D4—61no—
423C2×D4—61no—
424C2×D4—92no—
425C2×D4—181no—
426C2×D4—181no—
427C2×D4—181no—
428C2×D4—181no—
429C2×D4—181no—
430C22×C4—31no—
431C22×C4—31no—
432C22×C4—61no—
433C22×C4—181no—
434C22×C4C2×D3211yescharacteristic
435D8—188no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—32no—
440C2×C8—61no—
441C2×C8—61no—
442C4⋊C4—61no—
443C4⋊C4—61no—
444C4⋊C4—181no—
445C4⋊C4—181no—
446C22⋊C4—362no—
447C22⋊C4—362no—
448C22⋊C4—362no—
449C22⋊C4—362no—
450C42—61no—
451C42—61no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—122no—
460C22×C3—122no—
461C22×C3—122no—
462C22×C3—241no—
463C22×C3—241no—
464C22×C3—241no—
465C22×C3—241no—
466C22×C3#88411yescharacteristic
467C22×C3#88411yescharacteristic
468C22×C3#89511yescharacteristic
469C22×C3#89511yescharacteristic
470C22×C3C2×D2411yescharacteristic
471C22×C3#90411yescharacteristic
472C22×C3#90811yescharacteristic
473C22×C3#90811yescharacteristic
474C22×C3D3×D811yescharacteristic
475C22×C3#91111yescharacteristic
476C22×C3#91411yescharacteristic
477C22×C3#91611yescharacteristic
478C22×C3#93011yescharacteristic
479C22×C3#93911yescharacteristic
480C2×D3—42no—
481C2×D3—42no—
482C2×D3—42no—
483C2×D3—81no—
484C2×D3—81no—
485C2×D3—81no—
486C2×D3—81no—
487C2×D3—124no—
488C2×D3—122no—
489C2×D3—122no—
490C2×D3—122no—
491C2×D3—122no—
492C2×D3—122no—
493C2×D3—122no—
494C2×D3—242no—
495C2×D3—242no—
496C2×D3—242no—
497C2×D3—242no—
498C2×D3—242no—
499C2×D3—242no—
500C2×D3—241no—
501C2×D3—241no—
502C2×D3—241no—
503C2×D3—241no—
504C2×D3—241no—
505C2×D3—241no—
506C2×D3—241no—
507C2×D3—241no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—62no—
513C3×C4—121no—
514C3×C4—241no—
515C3×C4#88311yescharacteristic
516C3×C4#88511yescharacteristic
517C3×C4#89411yescharacteristic
518C3×C4#89411yescharacteristic
519C3×C4#92911yescharacteristic
520C3×C4#93711yescharacteristic
521C3×C4#93711yescharacteristic
522C3×C4#94711yescharacteristic
523Dic3—22no—
524Dic3—41no—
525Dic3—81no—
526Dic3—242no—
527Dic3—241no—
528Dic3—241no—
529C32#205411yescharacteristic, complemented, Sylow
530C23—62no—
531C23—121no—
532C23—121no—
533C23—121no—
534C23—121no—
535C23—121no—
536C23—121no—
537C23—182no—
538C23—361no—
539C23—361no—
540C23—361no—
541C23—361no—
542C23—361no—
543C23—361no—
544C23D3×D1211yescharacteristic
545D4—62no—
546D4—62no—
547D4—121no—
548D4—121no—
549D4—182no—
550D4—182no—
551D4—361no—
552D4—361no—
553C2×C4—32no—
554C2×C4—61no—
555C2×C4—61no—
556C2×C4—61no—
557C2×C4—61no—
558C2×C4—61no—
559C2×C4—121no—
560C2×C4—121no—
561C2×C4—121no—
562C2×C4—361no—
563C2×C4—361no—
564C2×C4—361no—
565C2×C4#379611yescharacteristic
566C2×C4#379811yescharacteristic
567C2×C4#379911yescharacteristic
568C2×C4D3×#6711yescharacteristic
569C2×C4D3×#6711yescharacteristic
570C2×C4#381111yescharacteristic
571C8—41no—
572C8—62no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—21no—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—242no—
581C2×C3#477511yescharacteristic
582C2×C3#478211yescharacteristic
583C2×C3#478611yescharacteristic
584C2×C3#478711yescharacteristic
585C2×C3#484311yescharacteristic
586C2×C3#484311yescharacteristic
587C2×C3#484411yescharacteristic
588C2×C3#484411yescharacteristic
589C2×C3#495911yescharacteristic
590C2×C3#499111yescharacteristic
591C2×C3#511511yescharacteristic
592C2×C3#513511yescharacteristic
593C2×C3#515011yescharacteristic
594C2×C3#516511yescharacteristic
595D3—82no—
596D3—244no—
597D3—242no—
598D3—242no—
599C22—122no—
600C22—122no—
601C22—122no—
602C22—241no—
603C22—241no—
604C22—241no—
605C22—241no—
606C22—362no—
607C22—362no—
608C22—362no—
609C22—721no—
610C22—721no—
611C22—721no—
612C22—721no—
613C22D3×D2411yescharacteristic
614C22#6379411yescharacteristic
615C22#6379511yescharacteristic
616C22#6380611yescharacteristic
617C22#6388611yescharacteristic
618C22#6390611yescharacteristic
619C22#6391011yescharacteristic
620C4—62no—
621C4—121no—
622C4—241no—
623C4—721no—
624C4#6385011yescharacteristic
625C4#6385311yescharacteristic
626C4#6390711yescharacteristic
627C4#6398311yescharacteristic
628C3—21no—
629C3#7021211yescharacteristic, complemented
630C3#7048111yescharacteristic, complemented
631C2—242no—
632C2—722no—
633C2#1059075311yescharacteristic
634C2#1059075411yescharacteristic
635C2#1059076511yescharacteristic
636C2#1059082611yescharacteristic
637C2#1059082711yescharacteristic
638C2#1059086011yescharacteristic
639C2#1059129111yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×#3714C2
hypercenterC22×C8D32
hypocenterC32#2054
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63648C2semidirect
3. C2×C3×#821C2semidirect
4. C2×C3×Dic3⋊C8C2semidirect
5. #10591320C2semidirect
6. #10591318C2semidirect
7. #10589164C2semidirect
35. C2×#821D3semidirect
36. C2×Dic3⋊C8D3semidirect
153. C2×C3×Dic3D8semidirect
385. C2×Dic3D24semidirect
529. C32#2054semidirect
629. C3#70212semidirect
630. C3#70481semidirect

Maximal subgroups

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

subgroupindex
C22×#37142
C2×#636482
C2×C3×#8212
C2×C3×Dic3⋊C82
#105913202
#105913182
#105891642
#704813
#702123