Finite Group Databasebeta

← #11793168

Subgroups — #11793168

Order 1152.

949 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64139C211yesmaximal, characteristic
2C3×#5212C211yesmaximal, characteristic, complemented
3C2×C3×#830C211yesmaximal, characteristic, complemented
4C2×#63575C211yesmaximal, characteristic, complemented
5C2×#63564C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#69934—31nomaximal
9#69523—31nomaximal
10C23×C32×C4C2211yescharacteristic
11C22×#638—21no—
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13#64139—22no—
14#64139—22no—
15C2×#3752—21no—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C3×#217—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C3×C3⋊#95—21no—
23C3×#830—22no—
24#63575—22no—
25#63564—22no—
26#63564—22no—
27C2×#930—31no—
28C2×#930—31no—
29C2×#930—61no—
30C2×C3×C22⋊C8—31no—
31C3×#380—31no—
32#5212D311yescharacteristic, complemented
33C2×#830D311yescharacteristic, complemented
34C2×#821—31no—
35C2×#821—31no—
36C2×#818—31no—
37C2×#809—31no—
38C2×#809—31no—
39C2×#807—31no—
40#4551—31no—
41#4529—31no—
42C24×C32D411yescharacteristic
43C23×C3⋊D3—21no—
44C22×C32×C4—21no—
45C22×C32×C4—21no—
46C22×C32×C4—21no—
47C22×C32×C4—21no—
48C22×C32×C4—21no—
49C22×C32×C4—21no—
50C22×C32×C4D411yescharacteristic
51C22×C32×C4C2311yescharacteristic
52C2×#638—24no—
53C2×#638—42no—
54C2×#638—42no—
55C22×C3⋊Dic3—21no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)D412yes—
62C22×C3×Dic3—21no—
63C22×C3×Dic3—21no—
64#3752—24no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)D412yes—
67C3×#217—42no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8D412yescomplemented
78#2033—91noSylow
79C23×C3×C4—21no—
80C23×C3×C4C2×D311yescharacteristic
81C23×C3×C4C2×D311yescharacteristic
82C22×#67—62no—
83C22×#67—61no—
84C22×#67—61no—
85C22×D12—31no—
86C22×D12—31no—
87C22×D12—61no—
88C22×C3×C8—31no—
89C22×C3×C8—31no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C4⋊C4—31no—
92C2×C3×C22⋊C4—61no—
93C2×#217—21no—
94#930—62no—
95#930—62no—
96#930—62no—
97#930—62no—
98#930—64no—
99#930—64no—
100C2×(C2×D3)⋊C4—62no—
101C2×(C2×D3)⋊C4—61no—
102C2×(C2×D3)⋊C4—61no—
103C2×C4⋊Dic3—31no—
104C2×C4⋊Dic3—31no—
105C2×C4⋊Dic3—61no—
106C2×C4⋊Dic3C2×D311yescharacteristic
107C2×C4⋊Dic3C2×D311yescharacteristic
108C22×C3⋊C8C2×D311yescharacteristic
109C22×C3⋊C8C2×D311yescharacteristic
110C3×C22⋊C8—62no—
111C3×#95—61no—
112C3⋊#95—21no—
113#830—22no—
114#821—62no—
115#821—62no—
116#818—62no—
117#809—62no—
118#809—62no—
119#807—62no—
120C23×C32—21no—
121C23×C32—21no—
122C23×C32—21no—
123C23×C32—21no—
124C23×C32—21no—
125C23×C32—21no—
126C23×C32D812yes—
127C23×C32C2×D411yescharacteristic
128C22×C3⋊D3—22no—
129C22×C3⋊D3—41no—
130C22×C3⋊D3—41no—
131C22×C3⋊D3—41no—
132C22×C3⋊D3—41no—
133C22×C3⋊D3—41no—
134C22×C3⋊D3—41no—
135C2×C32×C4—21no—
136C2×C32×C4—21no—
137C2×C32×C4—21no—
138C2×C32×C4—41no—
139C2×C32×C4—41no—
140C2×C32×C4—41no—
141C2×C32×C4—41no—
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4#4111yescharacteristic
146C2×C32×C4#4111yescharacteristic
147C2×C32×C4#4111yescharacteristic
148#638—48no—
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—41no—
151C2×C3⋊Dic3—41no—
152C4⋊(C3⋊D3)—22no—
153C4⋊(C3⋊D3)—22no—
154C4⋊(C3⋊D3)—41no—
155C4⋊(C3⋊D3)—41no—
156C2×C3×Dic3—41no—
157C2×C3×Dic3—41no—
158C2×C3×Dic3—41no—
159C2×C3×Dic3—41no—
160C2×C3×Dic3—41no—
161C2×C3×Dic3—41no—
162C3×C3⋊C8—22no—
163C3×C3⋊C8—41no—
164C2×#121—91no—
165C2×#107—91no—
166C2×#102—91no—
167C2×#102—91no—
168C2×C22⋊C8—31no—
169#380—31no—
170#340—91no—
171C24×C3—21no—
172C24×C3D1211yescharacteristic
173C24×C3#6711yescharacteristic
174C23×D3—62no—
175C23×D3—61no—
176C23×D3—61no—
177C22×C3×C4—22no—
178C22×C3×C4—22no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—41no—
194C22×C3×C4—41no—
195C22×C3×C4—41no—
196C22×C3×C4—41no—
197C22×C3×C4—61no—
198C22×C3×C4—61no—
199C22×C3×C4D1211yescharacteristic
200C22×C3×C4#6711yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C2×#67—68no—
204C2×#67—64no—
205C2×#67—64no—
206C2×#67—124no—
207C2×#67—122no—
208C2×#67—122no—
209C2×#67—124no—
210C2×#67—122no—
211C2×#67—122no—
212C22×Dic3—21no—
213C22×Dic3—21no—
214C22×Dic3—62no—
215C22×Dic3—61no—
216C22×Dic3—61no—
217C2×D12—32no—
218C2×D12—32no—
219C2×D12—62no—
220C2×D12—61no—
221C2×D12—61no—
222C2×D12—61no—
223C2×D12—61no—
224C2×D12—61no—
225C2×D12—61no—
226C2×D12—61no—
227C2×D12—61no—
228C2×D12—62no—
229C2×D12—61no—
230C2×D12—61no—
231C2×D12—121no—
232C2×D12—121no—
233C2×D12—121no—
234C2×D12—121no—
235C2×C3×C8—32no—
236C2×C3×C8—61no—
237C2×C3×C8—61no—
238C2×C3×C8—61no—
239C2×C3×C8—61no—
240C2×C3×C8—61no—
241C3×C4⋊C4—61no—
242C3×C4⋊C4—61no—
243C3×C4⋊C4—61no—
244C3×C4⋊C4—61no—
245C3×C22⋊C4—122no—
246#217—42no—
247(C2×D3)⋊C4—68no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—64no—
250C4⋊Dic3—21no—
251C4⋊Dic3—21no—
252C4⋊Dic3—21no—
253C4⋊Dic3—21no—
254C4⋊Dic3—32no—
255C4⋊Dic3—32no—
256C4⋊Dic3—62no—
257C4⋊Dic3—62no—
258C4⋊Dic3—61no—
259C4⋊Dic3—61no—
260C2×C3⋊C8—21no—
261C2×C3⋊C8—21no—
262C2×C3⋊C8—21no—
263C2×C3⋊C8—21no—
264C2×C3⋊C8—21no—
265C2×C3⋊C8#6712yescomplemented
266C22×C32—22no—
267C22×C32—22no—
268C22×C32—22no—
269C22×C32—41no—
270C22×C32—41no—
271C22×C32—41no—
272C22×C32—41no—
273C22×C32#12011yescharacteristic
274C22×C32#12111yescharacteristic
275C22×C32#12311yescharacteristic
276C22×C32C2×D811yescharacteristic
277C22×C32#13511yescharacteristic
278C22×C32AGL(1,ℤ/8)11yescharacteristic
279C22×C32#13711yescharacteristic
280C2×C3⋊D3—42no—
281C2×C3⋊D3—42no—
282C2×C3⋊D3—42no—
283C2×C3⋊D3—81no—
284C2×C3⋊D3—81no—
285C2×C3⋊D3—81no—
286C2×C3⋊D3—81no—
287C32×C4—41no—
288C32×C4#12111yescharacteristic
289C32×C4#12111yescharacteristic
290C32×C4#12311yescharacteristic
291C32×C4#12411yescharacteristic
292C3⋊Dic3—42no—
293C3×Dic3—81no—
294C3×Dic3—81no—
295C22×D4—91no—
296C22×D4—181no—
297C23×C4D3211yescharacteristic
298C22×C8—31no—
299C22×C8—31no—
300#121—182no—
301#121—182no—
302C2×C4⋊C4—31no—
303C2×C4⋊C4—31no—
304C2×C4⋊C4—91no—
305C2×C22⋊C4—61no—
306C2×C22⋊C4—181no—
307#107—182no—
308#102—182no—
309#102—182no—
310C22⋊C8—62no—
311#95—61no—
312C23×C3—22no—
313C23×C3—22no—
314C23×C3—21no—
315C23×C3—21no—
316C23×C3—21no—
317C23×C3—21no—
318C23×C3—21no—
319C23×C3—21no—
320C23×C3—21no—
321C23×C3—21no—
322C23×C3—21no—
323C23×C3—21no—
324C23×C3—21no—
325C23×C3—21no—
326C23×C3—22no—
327C23×C3—21no—
328C23×C3—41no—
329C23×C3—41no—
330C23×C3—41no—
331C23×C3—41no—
332C23×C3D2412yes—
333C23×C3#21312yes—
334C23×C3C2×D1211yescharacteristic
335C23×C3C2×#6711yescharacteristic
336C22×D3—64no—
337C22×D3—62no—
338C22×D3—62no—
339C22×D3—122no—
340C22×D3—122no—
341C22×D3—122no—
342C22×D3—122no—
343C22×D3—122no—
344C22×D3—122no—
345C22×D3—121no—
346C22×D3—121no—
347C22×D3—121no—
348C22×D3—121no—
349C22×D3—121no—
350C22×D3—121no—
351C22×D3—121no—
352C22×D3—121no—
353C22×D3—121no—
354C22×D3—121no—
355C22×D3—121no—
356C22×D3—121no—
357C2×C3×C4—22no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—41no—
371C2×C3×C4—41no—
372C2×C3×C4—42no—
373C2×C3×C4—42no—
374C2×C3×C4—42no—
375C2×C3×C4—42no—
376C2×C3×C4—41no—
377C2×C3×C4—41no—
378C2×C3×C4—41no—
379C2×C3×C4—41no—
380C2×C3×C4—41no—
381C2×C3×C4—41no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—121no—
385C2×C3×C4—121no—
386C2×C3×C4—121no—
387C2×C3×C4—121no—
388C2×C3×C4—121no—
389C2×C3×C4—121no—
390C2×C3×C4#23511yescharacteristic
391C2×C3×C4#23511yescharacteristic
392C2×C3×C4#23511yescharacteristic
393C2×C3×C4D3×D411yescharacteristic
394C2×C3×C4D3×D411yescharacteristic
395C2×C3×C4D3×D411yescharacteristic
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4#23711yescharacteristic
399C2×C3×C4#23711yescharacteristic
400C2×C3×C4#23711yescharacteristic
401C2×C3×C4C2×#6711yescharacteristic
402#67—1216no—
403#67—128no—
404#67—128no—
405C2×Dic3—41no—
406C2×Dic3—41no—
407C2×Dic3—41no—
408C2×Dic3—41no—
409C2×Dic3—41no—
410C2×Dic3—41no—
411C2×Dic3—64no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—122no—
415C2×Dic3—122no—
416C2×Dic3—121no—
417C2×Dic3—121no—
418C2×Dic3—121no—
419C2×Dic3—121no—
420D12—62no—
421D12—62no—
422D12—62no—
423D12—62no—
424D12—122no—
425D12—122no—
426D12—122no—
427D12—122no—
428D12—121no—
429D12—121no—
430D12—121no—
431D12—121no—
432C3×C8—62no—
433C3×C8—121no—
434C3⋊C8—22no—
435C3⋊C8—41no—
436C2×C32—42no—
437C2×C32#39411yescharacteristic
438C2×C32#44711yescharacteristic
439C2×C32#45211yescharacteristic
440C2×C32#46611yescharacteristic
441C2×C32#46811yescharacteristic
442C2×C32#48011yescharacteristic
443C2×C32#48211yescharacteristic
444C3⋊D3—82no—
445C24—181no—
446C24#62611yescharacteristic
447C2×D4—92no—
448C2×D4—184no—
449C2×D4—181no—
450C2×D4—181no—
451C2×D4—181no—
452C2×D4—181no—
453C2×D4—181no—
454C2×D4—362no—
455C2×D4—362no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—61no—
463C22×C4—61no—
464C22×C4—181no—
465C22×C4#62611yescharacteristic
466C22×C4C2×D3211yescharacteristic
467C2×C8—32no—
468C2×C8—61no—
469C2×C8—61no—
470C2×C8—61no—
471C2×C8—61no—
472C2×C8—61no—
473C4⋊C4—61no—
474C4⋊C4—61no—
475C4⋊C4—61no—
476C4⋊C4—61no—
477C4⋊C4—92no—
478C4⋊C4—181no—
479C22⋊C4—122no—
480C22⋊C4—184no—
481C22×C3—24no—
482C22×C3—22no—
483C22×C3—22no—
484C22×C3—22no—
485C22×C3—22no—
486C22×C3—22no—
487C22×C3—22no—
488C22×C3—21no—
489C22×C3—21no—
490C22×C3—21no—
491C22×C3—21no—
492C22×C3—21no—
493C22×C3—21no—
494C22×C3—21no—
495C22×C3—42no—
496C22×C3—42no—
497C22×C3—42no—
498C22×C3—42no—
499C22×C3—42no—
500C22×C3—42no—
501C22×C3—41no—
502C22×C3—41no—
503C22×C3—41no—
504C22×C3—41no—
505C22×C3—41no—
506C22×C3—41no—
507C22×C3—41no—
508C22×C3—41no—
509C22×C3#88211yescharacteristic
510C22×C3#88611yescharacteristic
511C22×C3C2×D2411yescharacteristic
512C22×C3#90411yescharacteristic
513C22×C3#90811yescharacteristic
514C22×C3#90911yescharacteristic
515C22×C3#92911yescharacteristic
516C22×C3#93011yescharacteristic
517C22×C3C2×#21311yescharacteristic
518C22×C3#93711yescharacteristic
519C22×C3#93911yescharacteristic
520C22×C3#94211yescharacteristic
521C22×C3#94911yescharacteristic
522C22×C3#95011yescharacteristic
523C2×D3—124no—
524C2×D3—124no—
525C2×D3—124no—
526C2×D3—122no—
527C2×D3—122no—
528C2×D3—122no—
529C2×D3—122no—
530C2×D3—122no—
531C2×D3—122no—
532C2×D3—242no—
533C2×D3—242no—
534C2×D3—242no—
535C2×D3—242no—
536C2×D3—241no—
537C2×D3—241no—
538C2×D3—241no—
539C2×D3—241no—
540C2×D3—241no—
541C2×D3—241no—
542C2×D3—241no—
543C2×D3—241no—
544C3×C4—21no—
545C3×C4—21no—
546C3×C4—21no—
547C3×C4—21no—
548C3×C4—42no—
549C3×C4—41no—
550C3×C4—41no—
551C3×C4—241no—
552C3×C4—241no—
553C3×C4#88311yescharacteristic
554C3×C4#88311yescharacteristic
555C3×C4#88411yescharacteristic
556C3×C4#88411yescharacteristic
557C3×C4#88511yescharacteristic
558C3×C4#88511yescharacteristic
559C3×C4#93811yescharacteristic
560C3×C4#93911yescharacteristic
561Dic3—81no—
562Dic3—81no—
563Dic3—124no—
564Dic3—122no—
565Dic3—122no—
566C32#203311yescharacteristic, complemented, Sylow
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—182no—
574C23—361no—
575C23—361no—
576C23—361no—
577C23—361no—
578C23—361no—
579C23—361no—
580C23#371412yes—
581C23C2×#62611yescharacteristic
582D4—182no—
583D4—182no—
584D4—368no—
585D4—361no—
586D4—361no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—121no—
595C2×C4—121no—
596C2×C4—121no—
597C2×C4—121no—
598C2×C4—121no—
599C2×C4—121no—
600C2×C4—182no—
601C2×C4—361no—
602C2×C4—361no—
603C2×C4#380411yescharacteristic
604C2×C4#380411yescharacteristic
605C2×C4#380411yescharacteristic
606C2×C4D3×#6711yescharacteristic
607C2×C4#381111yescharacteristic
608C2×C4#381111yescharacteristic
609C8—62no—
610C8—121no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—21no—
616C2×C3—21no—
617C2×C3—21no—
618C2×C3—44no—
619C2×C3—42no—
620C2×C3—42no—
621C2×C3#473211yescharacteristic
622C2×C3#473311yescharacteristic
623C2×C3#473611yescharacteristic
624C2×C3#473711yescharacteristic
625C2×C3#495911yescharacteristic
626C2×C3#496111yescharacteristic
627C2×C3#496711yescharacteristic
628C2×C3#500311yescharacteristic
629C2×C3#503611yescharacteristic
630C2×C3#503811yescharacteristic
631C2×C3#504711yescharacteristic
632C2×C3#504911yescharacteristic
633C2×C3#511511yescharacteristic
634C2×C3#513411yescharacteristic
635D3—244no—
636D3—242no—
637D3—242no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—362no—
646C22—362no—
647C22—362no—
648C22—721no—
649C22—721no—
650C22—721no—
651C22—721no—
652C22C2×#371411yescharacteristic
653C22#6382511yescharacteristic
654C22#6382911yescharacteristic
655C22#6383311yescharacteristic
656C22#6396611yescharacteristic
657C22#6397811yescharacteristic
658C22#6398111yescharacteristic
659C4—41no—
660C4—241no—
661C4—241no—
662C4—362no—
663C4#6395311yescharacteristic
664C4#6395811yescharacteristic
665C4#6397111yescharacteristic
666C4#6397511yescharacteristic
667C3—21no—
668C3#6952311yescharacteristic, complemented
669C3#6993411yescharacteristic, complemented
670C2—42no—
671C2—722no—
672C2#1059113311yescharacteristic
673C2#1059113611yescharacteristic
674C2#1059116411yescharacteristic
675C2#1059116811yescharacteristic
676C2#1059117811yescharacteristic
677C2#1059118411yescharacteristic
678C2#1059171211yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC2×#64139C2
hypercenterC23×C4D32
hypocenterC32#2033
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C3×#5212C2semidirect
3. C2×C3×#830C2semidirect
4. C2×#63575C2semidirect
5. C2×#63564C2semidirect
6. C2×#63564C2semidirect
7. #10589164C2semidirect
32. #5212D3semidirect
33. C2×#830D3semidirect
77. C2×C3×C3⋊C8D4semidirect
265. C2×C3⋊C8#67semidirect
566. C32#2033semidirect
668. C3#69523semidirect
669. C3#69934semidirect

Maximal subgroups

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

subgroupindex
C2×#641392
C3×#52122
C2×C3×#8302
C2×#635752
C2×#635642
#105891642
#699343
#695233