Finite Group Databasebeta

← #11793184

Subgroups — #11793184

Order 1152.

801 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63908C211yesmaximal, characteristic
2C2×#63645C211yesmaximal, characteristic, complemented
3C2×C3×#821C211yesmaximal, characteristic, complemented
4C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
5#10591313C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#70175—31nomaximal
9#69934—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×C4×D3C2211yescharacteristic
12C22×#625—21no—
13C22×C32×C8C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×(C2×D3)⋊Dic3—21no—
19C2×(C2×D3)⋊Dic3—21no—
20#63908—22no—
21#63908—22no—
22#63645—22no—
23C3×#821—22no—
24C3×(C2×D3)⋊C8—22no—
25#63579—21no—
26#63563—22no—
27C2×#938—31no—
28C2×#930—31no—
29C2×C3×#102—31no—
30C2×C3×C22⋊C8—31no—
31C2×#832—31no—
32#5212—31no—
33C2×#821—31no—
34C2×#821D311yescharacteristic, complemented
35C2×(C2×D3)⋊C8D311yescharacteristic, complemented
36C2×#818—31no—
37C2×#818—31no—
38C2×#818—61no—
39#4987—31no—
40#4551—31no—
41#4529—31no—
42C23×C3×D3—21no—
43C23×C3×D3D411yescharacteristic
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C22×C3⋊Dic3—21no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3D411yescharacteristic
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12D412yes—
55C2×C3×C4×D3—21no—
56C2×C3×C4×D3—21no—
57C2×C3×C4×D3—21no—
58C2×C3×C4×D3—21no—
59C2×C3×C4×D3—21no—
60C2×C3×C4×D3—21no—
61C2×#625—24no—
62C2×#625—42no—
63C2×#625—42no—
64C2×C32×C8—21no—
65C2×C32×C8—21no—
66C2×C32×C8D412yescomplemented
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)—21no—
69C4⋊(C3⋊Dic3)—21no—
70C4⋊(C3⋊Dic3)D412yes—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76(C2×D3)⋊Dic3—24no—
77(C2×D3)⋊Dic3—42no—
78#2033—91noSylow
79C22×C3×D4—31no—
80C23×C3×C4—31no—
81C22×#67—61no—
82C22×#67—61no—
83C22×D12C2×D311yescharacteristic
84C22×C4×D3C2×D311yescharacteristic
85C22×C3×C8—21no—
86C22×C3×C8—31no—
87C22×C3×C8C2×D311yescharacteristic
88C22×C3×C8C2×D311yescharacteristic
89C2×C3×C4⋊C4—31no—
90C2×#217—61no—
91C2×#217—61no—
92#938—62no—
93#938—62no—
94#930—62no—
95#930—62no—
96C2×(C2×D3)⋊C4—61no—
97C2×(C2×D3)⋊C4—61no—
98C2×C4⋊Dic3—31no—
99C2×C4⋊Dic3—31no—
100C2×C4⋊Dic3—31no—
101C2×C4⋊Dic3—31no—
102C2×C4⋊Dic3—61no—
103C2×C4⋊Dic3—61no—
104C2×C4⋊Dic3C2×D311yescharacteristic
105C22×C3⋊C8C2×D311yescharacteristic
106C3×#102—62no—
107C3×C22⋊C8—62no—
108#832—62no—
109C3⋊#95—61no—
110C3⋊#95—61no—
111#821—22no—
112#821—62no—
113(C2×D3)⋊C8—22no—
114#818—62no—
115#818—62no—
116#818—64no—
117C23×C32C2×D411yescharacteristic
118C22×C3×D3—21no—
119C22×C3×D3—21no—
120C22×C3×D3—21no—
121C22×C3×D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3—21no—
124C22×C3×D3—22no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C22×C3×D3—41no—
129C22×C3×D3—41no—
130C22×C3×D3—41no—
131C22×C3×D3D812yes—
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—22no—
139C2×C3⋊Dic3—41no—
140C2×C3⋊Dic3—41no—
141C2×C3⋊Dic3—41no—
142C2×C3⋊Dic3—41no—
143C2×C3⋊Dic3—41no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C3×D12—22no—
151C3×D12—22no—
152C3×D12—41no—
153C3×D12—41no—
154C3×C4×D3—41no—
155C3×C4×D3—41no—
156C3×C4×D3—41no—
157C3×C4×D3—41no—
158#625—48no—
159C32×C8—22no—
160C3×C3⋊C8—41no—
161C2×#121—91no—
162C2×#107—91no—
163C2×#102—31no—
164C2×#102—91no—
165C2×C22⋊C8—31no—
166#380—91no—
167#340—91no—
168C24×C3—31no—
169C24×C3—61no—
170C23×D3—21no—
171C23×D3D1211yescharacteristic
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—61no—
181C22×C3×C4—61no—
182C22×C3×C4—61no—
183C22×C3×C4—61no—
184C22×C3×C4—61no—
185C22×C3×C4—61no—
186C22×C3×C4—61no—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C2×#67—64no—
190C2×#67—64no—
191C2×#67—122no—
192C2×#67—122no—
193C2×#67—122no—
194C2×#67—122no—
195C22×Dic3—21no—
196C22×Dic3—61no—
197C22×Dic3—61no—
198C22×Dic3—61no—
199C22×Dic3—61no—
200C22×Dic3—121no—
201C22×Dic3—121no—
202C22×Dic3D1211yescharacteristic
203C2×D12—21no—
204C2×D12—21no—
205C2×D12—21no—
206C2×D12—21no—
207C2×D12—21no—
208C2×D12D1212yes—
209C2×C4×D3—21no—
210C2×C4×D3—21no—
211C2×C4×D3—21no—
212C2×C4×D3—21no—
213C2×C4×D3—21no—
214C2×C4×D3—21no—
215C2×C3×C8—22no—
216C2×C3×C8—22no—
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—21no—
220C2×C3×C8—21no—
221C2×C3×C8—22no—
222C2×C3×C8—61no—
223C2×C3×C8—61no—
224C2×C3×C8—61no—
225C2×C3×C8#6712yescomplemented
226C2×C3×C8#6712yescomplemented
227C3×C4⋊C4—61no—
228C3×C4⋊C4—61no—
229#217—64no—
230#217—122no—
231(C2×D3)⋊C4—64no—
232(C2×D3)⋊C4—122no—
233C4⋊Dic3—21no—
234C4⋊Dic3—21no—
235C4⋊Dic3—32no—
236C4⋊Dic3—32no—
237C4⋊Dic3—62no—
238C4⋊Dic3—61no—
239C4⋊Dic3—61no—
240C4⋊Dic3—62no—
241C4⋊Dic3—61no—
242C4⋊Dic3—61no—
243C4⋊Dic3—61no—
244C4⋊Dic3—61no—
245C4⋊Dic3—121no—
246C4⋊Dic3—121no—
247C2×C3⋊C8—21no—
248C2×C3⋊C8—21no—
249C2×C3⋊C8—21no—
250C22×C32#12011yescharacteristic
251C22×C32#12111yescharacteristic
252C22×C32#12311yescharacteristic
253C22×C32C2×D811yescharacteristic
254C22×C32#13511yescharacteristic
255C22×C32AGL(1,ℤ/8)11yescharacteristic
256C22×C32#13711yescharacteristic
257C2×C3×D3—22no—
258C2×C3×D3—22no—
259C2×C3×D3—22no—
260C2×C3×D3—41no—
261C2×C3×D3—41no—
262C2×C3×D3—41no—
263C2×C3×D3—41no—
264C2×C3×D3—42no—
265C2×C3×D3—42no—
266C2×C3×D3—42no—
267C2×C3×D3—81no—
268C2×C3×D3—81no—
269C2×C3×D3—81no—
270C2×C3×D3—81no—
271C32×C4#12111yescharacteristic
272C32×C4#12111yescharacteristic
273C32×C4#12311yescharacteristic
274C32×C4#12411yescharacteristic
275C3⋊Dic3—42no—
276C3⋊Dic3—81no—
277C3×Dic3—41no—
278C3×Dic3—81no—
279C22×D4—31no—
280C22×D4—181no—
281C23×C4—31no—
282C22×C8—31no—
283C22×C8D3211yescharacteristic
284#121—182no—
285#121—182no—
286C2×C4⋊C4—31no—
287C2×C4⋊C4—91no—
288C2×C4⋊C4—91no—
289C2×C22⋊C4—181no—
290C2×C22⋊C4—181no—
291#107—182no—
292#102—62no—
293#102—182no—
294C22⋊C8—62no—
295#95—181no—
296C23×C3—21no—
297C23×C3—32no—
298C23×C3—61no—
299C23×C3—61no—
300C23×C3—61no—
301C23×C3—61no—
302C23×C3—61no—
303C23×C3—61no—
304C23×C3—62no—
305C23×C3—121no—
306C23×C3—121no—
307C23×C3—121no—
308C23×C3—121no—
309C23×C3—121no—
310C23×C3—121no—
311C23×C3C2×D1211yescharacteristic
312C23×C3D3×D411yescharacteristic
313C22×D3—21no—
314C22×D3—21no—
315C22×D3—21no—
316C22×D3—21no—
317C22×D3—21no—
318C22×D3—21no—
319C22×D3—22no—
320C22×D3—41no—
321C22×D3—41no—
322C22×D3—41no—
323C22×D3—41no—
324C22×D3—41no—
325C22×D3—41no—
326C22×D3D2412yes—
327C3×D4—62no—
328C3×D4—62no—
329C3×D4—121no—
330C3×D4—121no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—61no—
338C2×C3×C4—61no—
339C2×C3×C4—61no—
340C2×C3×C4—121no—
341C2×C3×C4—121no—
342C2×C3×C4—121no—
343C2×C3×C4—121no—
344C2×C3×C4—121no—
345C2×C3×C4—121no—
346C2×C3×C4—121no—
347C2×C3×C4C2×D1211yescharacteristic
348C2×C3×C4#23511yescharacteristic
349C2×C3×C4#23511yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4#23711yescharacteristic
354C2×C3×C4#23711yescharacteristic
355C2×C3×C4#23711yescharacteristic
356C2×C3×C4#23711yescharacteristic
357C2×C3×C4C2×#6711yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359#67—128no—
360#67—128no—
361C2×Dic3—21no—
362C2×Dic3—21no—
363C2×Dic3—21no—
364C2×Dic3—41no—
365C2×Dic3—41no—
366C2×Dic3—41no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—122no—
370C2×Dic3—121no—
371C2×Dic3—121no—
372C2×Dic3—121no—
373C2×Dic3—121no—
374C2×Dic3—122no—
375C2×Dic3—121no—
376C2×Dic3—121no—
377C2×Dic3—121no—
378C2×Dic3—121no—
379C2×Dic3—121no—
380C2×Dic3—121no—
381C2×Dic3—241no—
382C2×Dic3—241no—
383C2×Dic3—241no—
384C2×Dic3—241no—
385D12—22no—
386D12—22no—
387D12—41no—
388D12—41no—
389C4×D3—41no—
390C4×D3—41no—
391C4×D3—41no—
392C4×D3—41no—
393C3×C8—24no—
394C3×C8—22no—
395C3×C8—22no—
396C3×C8—121no—
397C3⋊C8—41no—
398C2×C32#39411yescharacteristic
399C2×C32#44711yescharacteristic
400C2×C32#45211yescharacteristic
401C2×C32#46611yescharacteristic
402C2×C32#46811yescharacteristic
403C2×C32#48011yescharacteristic
404C2×C32#48211yescharacteristic
405C3×D3—42no—
406C3×D3—82no—
407C24—31no—
408C24—61no—
409C2×D4—32no—
410C2×D4—61no—
411C2×D4—61no—
412C2×D4—61no—
413C2×D4—61no—
414C2×D4—61no—
415C2×D4—184no—
416C2×D4—362no—
417C2×D4—362no—
418C22×C4—31no—
419C22×C4—61no—
420C22×C4—61no—
421C22×C4—61no—
422C22×C4—61no—
423C22×C4—61no—
424C22×C4—61no—
425C22×C4—61no—
426C22×C4—181no—
427C22×C4—181no—
428C22×C4C2×D3211yescharacteristic
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—61no—
432C2×C8—61no—
433C2×C8—61no—
434C2×C8#62512yescomplemented
435C4⋊C4—61no—
436C4⋊C4—61no—
437C4⋊C4—92no—
438C4⋊C4—181no—
439C4⋊C4—181no—
440C4⋊C4—181no—
441C22⋊C4—184no—
442C22⋊C4—362no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—62no—
451C22×C3—62no—
452C22×C3—62no—
453C22×C3—121no—
454C22×C3—121no—
455C22×C3—121no—
456C22×C3—121no—
457C22×C3—122no—
458C22×C3—122no—
459C22×C3—122no—
460C22×C3—241no—
461C22×C3—241no—
462C22×C3—241no—
463C22×C3—241no—
464C22×C3#88211yescharacteristic
465C22×C3#88211yescharacteristic
466C22×C3#88311yescharacteristic
467C22×C3#88611yescharacteristic
468C22×C3C2×D2411yescharacteristic
469C22×C3#90411yescharacteristic
470C22×C3#90811yescharacteristic
471C22×C3#90911yescharacteristic
472C22×C3D3×D811yescharacteristic
473C22×C3#91211yescharacteristic
474C22×C3#91411yescharacteristic
475C22×C3#91511yescharacteristic
476C22×C3#93011yescharacteristic
477C22×C3#93811yescharacteristic
478C2×D3—22no—
479C2×D3—22no—
480C2×D3—22no—
481C2×D3—41no—
482C2×D3—41no—
483C2×D3—41no—
484C2×D3—41no—
485C2×D3—42no—
486C2×D3—42no—
487C2×D3—42no—
488C2×D3—81no—
489C2×D3—81no—
490C2×D3—81no—
491C2×D3—81no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—21no—
496C3×C4—121no—
497C3×C4—241no—
498C3×C4#88311yescharacteristic
499C3×C4#88511yescharacteristic
500C3×C4#88511yescharacteristic
501C3×C4#88611yescharacteristic
502C3×C4#93011yescharacteristic
503C3×C4#93811yescharacteristic
504C3×C4#93911yescharacteristic
505C3×C4#93911yescharacteristic
506Dic3—41no—
507Dic3—81no—
508Dic3—122no—
509Dic3—122no—
510Dic3—242no—
511Dic3—242no—
512Dic3—241no—
513Dic3—241no—
514C32#203311yescharacteristic, complemented, Sylow
515C23—32no—
516C23—61no—
517C23—61no—
518C23—61no—
519C23—61no—
520C23—61no—
521C23—61no—
522C23—62no—
523C23—121no—
524C23—121no—
525C23—121no—
526C23—121no—
527C23—121no—
528C23—121no—
529C23D3×D1211yescharacteristic
530D4—62no—
531D4—62no—
532D4—121no—
533D4—121no—
534D4—368no—
535C2×C4—61no—
536C2×C4—61no—
537C2×C4—61no—
538C2×C4—121no—
539C2×C4—121no—
540C2×C4—121no—
541C2×C4—121no—
542C2×C4—121no—
543C2×C4—121no—
544C2×C4—121no—
545C2×C4—182no—
546C2×C4—361no—
547C2×C4—361no—
548C2×C4—361no—
549C2×C4—361no—
550C2×C4—361no—
551C2×C4#379511yescharacteristic
552C2×C4#379511yescharacteristic
553C2×C4D3×D1211yescharacteristic
554C2×C4#380511yescharacteristic
555C2×C4C2×#62511yescharacteristic
556C2×C4#381111yescharacteristic
557C8—22no—
558C8—121no—
559C2×C3—21no—
560C2×C3—21no—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—122no—
567C2×C3—242no—
568C2×C3#473211yescharacteristic
569C2×C3#473311yescharacteristic
570C2×C3#473611yescharacteristic
571C2×C3#473711yescharacteristic
572C2×C3#477311yescharacteristic
573C2×C3#477411yescharacteristic
574C2×C3#478311yescharacteristic
575C2×C3#478411yescharacteristic
576C2×C3#496111yescharacteristic
577C2×C3#496111yescharacteristic
578C2×C3#511511yescharacteristic
579C2×C3#513411yescharacteristic
580C2×C3#515711yescharacteristic
581C2×C3#517411yescharacteristic
582D3—42no—
583D3—82no—
584C22—62no—
585C22—62no—
586C22—62no—
587C22—121no—
588C22—121no—
589C22—121no—
590C22—121no—
591C22—122no—
592C22—122no—
593C22—122no—
594C22—241no—
595C22—241no—
596C22—241no—
597C22—241no—
598C22D3×D2411yescharacteristic
599C22#6379411yescharacteristic
600C22#6380011yescharacteristic
601C22#6380711yescharacteristic
602C22#6389111yescharacteristic
603C22#6390811yescharacteristic
604C22#6392311yescharacteristic
605C4—121no—
606C4—241no—
607C4—362no—
608C4—721no—
609C4#6389111yescharacteristic
610C4#6390811yescharacteristic
611C4#6391311yescharacteristic
612C4#6398011yescharacteristic
613C3—21no—
614C3#6993411yescharacteristic, complemented
615C3#7017511yescharacteristic, complemented
616C2—122no—
617C2—242no—
618C2#1059068011yescharacteristic
619C2#1059083111yescharacteristic
620C2#1059083311yescharacteristic
621C2#1059083411yescharacteristic
622C2#1059094711yescharacteristic
623C2#1059096911yescharacteristic
624C2#1059139411yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC2×#63908C2
hypercenterC22×C8D32
hypocenterC32#2033
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×#63645C2semidirect
3. C2×C3×#821C2semidirect
4. C2×C3×(C2×D3)⋊C8C2semidirect
5. #10591313C2semidirect
6. C2×#63563C2semidirect
7. #10589164C2semidirect
34. C2×#821D3semidirect
35. C2×(C2×D3)⋊C8D3semidirect
66. C2×C32×C8D4semidirect
225. C2×C3×C8#67semidirect
226. C2×C3×C8#67semidirect
434. C2×C8#625semidirect
514. C32#2033semidirect
614. C3#69934semidirect
615. C3#70175semidirect

Maximal subgroups

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

subgroupindex
C2×#639082
C2×#636452
C2×C3×#8212
C2×C3×(C2×D3)⋊C82
#105913132
C2×#635632
#105891642
#701753
#699343