Finite Group Databasebeta

← #11792245

Subgroups — #11792245

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5833C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic, complemented
3C2×#63823C211yesmaximal, characteristic, complemented
4C2×#63664C211yesmaximal, characteristic, complemented
5#10591323C211yesmaximal, characteristic, complemented
6C2×#63568C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#72098—31nomaximal
9#71879—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C3×#949—22no—
16C3×#949—22no—
17C3×#946—21no—
18C2×C3×#215—21no—
19C3×#939—22no—
20C3×#938—21no—
21C2×C3×#213—21no—
22C3×#930—21no—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C3×#924—21no—
25C2×C3×#208C2211yescharacteristic
26C2×(C2×D3)⋊Dic3—22no—
27C2×#3715—21no—
28#63823—22no—
29#63823—22no—
30C2×#3713—21no—
31#63664—22no—
32#63568—22no—
33C2×C3×AGL(1,ℤ/8)—31no—
34C3×#537—31no—
35#5833D311yescharacteristic, complemented
36C2×#949—31no—
37C2×#949D311yescharacteristic, complemented
38C2×#932—31no—
39C2×#837—31no—
40C2×#837—31no—
41C2×#837—31no—
42C2×#837—61no—
43#5221—31no—
44C2×#825—31no—
45#4988—31no—
46#4554—31no—
47#4530—31no—
48C23×C3×D3—21no—
49C32×#41—21no—
50C32×#41—21no—
51C32×#41—21no—
52C32×#41—21no—
53C2×C32×Q8D411yescharacteristic
54C2×C32×D4—21no—
55C2×C32×D4D411yescharacteristic
56C22×C32×C4—21no—
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3—21no—
59C2×C3×#67—21no—
60C2×C3×#67—22no—
61C22×C3×Dic3D412yes—
62C3×#235—21no—
63C3×#235—21no—
64C3×#235—21no—
65C3×#235—21no—
66C2×C3×D12—21no—
67C2×C3×D12—21no—
68C2×C3×D12—21no—
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12D411yescharacteristic
72C2×C3×D12D412yescomplemented
73C2×C3×C4×D3—21no—
74C2×C3×Dic6D411yescharacteristic
75C4×C3⋊Dic3—21no—
76C4×C3⋊Dic3—21no—
77#3748—21no—
78#3748D412yescomplemented
79C2×C3⋊(C3⋊C8)—21no—
80C3×#217—22no—
81C3×#215—24no—
82C3×#213—24no—
83C3×(C2×D3)⋊C4—22no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—21no—
86C3×Dic3⋊C4—22no—
87C3×#208—21no—
88C3×#208D412yescomplemented
89C2×C3×C3⋊C8—21no—
90(C2×D3)⋊Dic3—44no—
91#3715—24no—
92#3713—24no—
93#2006—91noSylow
94C2×C3×#41—21no—
95C2×C3×#41—31no—
96C2×C3×#41C2×D311yescharacteristic
97C2×C3×#41C2×D311yescharacteristic
98C22×C3×D4—31no—
99C2×#235C2×D311yescharacteristic
100C22×D12C2×D311yescharacteristic
101C3×AGL(1,ℤ/8)—62no—
102C3×AGL(1,ℤ/8)—62no—
103C2×C3×SD16—61no—
104C2×C3×D8—61no—
105C2×C3×M16—31no—
106C3×C22⋊Q8—61no—
107C3×C22⋊Q8—61no—
108C3×#121—61no—
109C3×#121—62no—
110C3×#121—61no—
111C2×C3×C4⋊C4—31no—
112C2×#217—62no—
113#949—22no—
114#949—22no—
115#949—62no—
116#949—62no—
117#946—21no—
118C2×#215—21no—
119C2×#215—61no—
120#939—22no—
121#938—21no—
122C2×#214—61no—
123#932—62no—
124#932—62no—
125C2×#213—21no—
126C2×#213—61no—
127C2×#213—61no—
128#930—21no—
129C2×(C2×D3)⋊C4—62no—
130C2×C4⋊Dic3C2×D311yescharacteristic
131#924—21no—
132C2×C4×Dic3—31no—
133C2×C4×Dic3—31no—
134C2×C4×Dic3—61no—
135C2×#208—31no—
136C2×#208—31no—
137C2×#208—61no—
138C2×#208C2×D311yescharacteristic
139#837—62no—
140#837—62no—
141#837—64no—
142#837—62no—
143#825—62no—
144C23×C32—21no—
145C23×C32C2×D411yescharacteristic
146C22×C3×D3—21no—
147C22×C3×D3—22no—
148C22×C3×D3—42no—
149C22×C3×D3—42no—
150C22×C3×D3—41no—
151C22×C3×D3—41no—
152C32×Q8—21no—
153C32×Q8—21no—
154C32×D4—21no—
155C32×D4—21no—
156C32×D4—41no—
157C32×D4—41no—
158C2×C32×C4—21no—
159C2×C32×C4—41no—
160C2×C32×C4—41no—
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4#4111yescharacteristic
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—41no—
169C2×C3⋊Dic3—41no—
170C3×#67—41no—
171C3×#67—41no—
172C3×#67—82no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—42no—
176C3×D12—21no—
177C3×D12—22no—
178C3×D12—22no—
179C3×D12—21no—
180C3×D12—41no—
181C3×D12—41no—
182C3×C4×D3—41no—
183C3×C4×D3—41no—
184C3×Dic6—21no—
185C3×Dic6—21no—
186C3⋊(C3⋊C8)—22no—
187C3×C3⋊C8—22no—
188C2×AGL(1,ℤ/8)—31no—
189C2×AGL(1,ℤ/8)—91no—
190#537—31no—
191C2×#104—91no—
192C2×#104—91no—
193#390—91no—
194#343—91no—
195C24×C3—61no—
196C23×D3—21no—
197C3×#41—22no—
198C3×#41—22no—
199C3×#41—21no—
200C3×#41—21no—
201C3×#41—21no—
202C3×#41—21no—
203C3×#41—21no—
204C3×#41—21no—
205C3×#41—21no—
206C3×#41—21no—
207C3×#41—41no—
208C3×#41—41no—
209C3×#41—61no—
210C3×#41—61no—
211C3×#41—61no—
212C3×#41—61no—
213C2×C3×Q8—21no—
214C2×C3×Q8—31no—
215C2×C3×Q8#6711yescharacteristic
216C2×C3×Q8#6711yescharacteristic
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—31no—
221C2×C3×D4—32no—
222C2×C3×D4—41no—
223C2×C3×D4—61no—
224C2×C3×D4—62no—
225C2×C3×D4—61no—
226C2×C3×D4—61no—
227C2×C3×D4—61no—
228C2×C3×D4—61no—
229C2×C3×D4—61no—
230C2×C3×D4#6711yescharacteristic
231C2×C3×D4#6711yescharacteristic
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—32no—
236C22×C3×C4—41no—
237C22×C3×C4—61no—
238C22×C3×C4C22×D311yescharacteristic
239C22×C3×C4C22×D311yescharacteristic
240C2×#67—21no—
241C2×#67—22no—
242C22×Dic3—61no—
243C22×Dic3—61no—
244C22×Dic3—121no—
245C22×Dic3#6712yes—
246#235—21no—
247#235—21no—
248#235—21no—
249#235—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12#6711yescharacteristic
256C2×D12#6712yescomplemented
257C2×C4×D3—21no—
258C2×Dic6#6711yescharacteristic
259C3×SD16—64no—
260C3×D8—64no—
261C3×M16—32no—
262C3×M16—61no—
263C2×C3×C8—61no—
264C3×C4⋊C4—62no—
265C3×C4⋊C4—61no—
266C3×C4⋊C4—61no—
267C3×C22⋊C4—62no—
268C3×C22⋊C4—62no—
269#217—22no—
270#217—124no—
271#215—24no—
272#215—64no—
273#214—64no—
274#213—24no—
275#213—64no—
276#213—64no—
277(C2×D3)⋊C4—22no—
278(C2×D3)⋊C4—124no—
279C4⋊Dic3—21no—
280C4⋊Dic3—21no—
281Dic3⋊C4—22no—
282C4×Dic3—62no—
283C4×Dic3—61no—
284C4×Dic3—61no—
285C4×Dic3—61no—
286C4×Dic3—61no—
287C4×Dic3—121no—
288#208—21no—
289#208—32no—
290#208—32no—
291#208—62no—
292#208—61no—
293#208—61no—
294#208—121no—
295#208#6712yescomplemented
296C2×C3⋊C8—21no—
297C2×C3⋊C8—61no—
298C2×C3⋊C8—61no—
299C2×C3⋊C8—121no—
300C22×C32—21no—
301C22×C32—21no—
302C22×C32—41no—
303C22×C32—41no—
304C22×C32—41no—
305C22×C32#12011yescharacteristic
306C22×C32#12111yescharacteristic
307C22×C32#12711yescharacteristic
308C2×C3×D3—44no—
309C2×C3×D3—41no—
310C2×C3×D3—42no—
311C2×C3×D3—41no—
312C2×C3×D3—41no—
313C2×C3×D3—82no—
314C2×C3×D3—81no—
315C2×C3×D3—81no—
316C32×C4—41no—
317C32×C4#12011yescharacteristic
318C32×C4#12011yescharacteristic
319C32×C4#12111yescharacteristic
320C32×C4#12111yescharacteristic
321C3⋊Dic3—42no—
322C3×Dic3—41no—
323C3×Dic3—42no—
324C2×#41—31no—
325C2×#41D3211yescharacteristic
326C22×D4—31no—
327AGL(1,ℤ/8)—62no—
328AGL(1,ℤ/8)—62no—
329AGL(1,ℤ/8)—182no—
330AGL(1,ℤ/8)—182no—
331C2×SD16—61no—
332C2×SD16—181no—
333C2×D8—61no—
334C2×D8—181no—
335C2×M16—31no—
336C2×M16—91no—
337C22⋊Q8—61no—
338C22⋊Q8—61no—
339#121—61no—
340#121—62no—
341#121—61no—
342C2×C4⋊C4—31no—
343C2×C22⋊C4—182no—
344C2×C42—91no—
345#104—182no—
346#104—182no—
347C23×C3—21no—
348C23×C3—21no—
349C23×C3—21no—
350C23×C3—41no—
351C23×C3—61no—
352C23×C3—62no—
353C23×C3—122no—
354C23×C3—122no—
355C23×C3—121no—
356C23×C3—121no—
357C23×C3D3×D411yescharacteristic
358C23×C3C2×#6711yescharacteristic
359C22×D3—22no—
360C22×D3—21no—
361C22×D3—42no—
362C22×D3—42no—
363C22×D3—41no—
364C22×D3—41no—
365C3×Q8—22no—
366C3×Q8—21no—
367C3×Q8—21no—
368C3×Q8—21no—
369C3×Q8—21no—
370C3×Q8—41no—
371C3×Q8—61no—
372C3×Q8—61no—
373C3×D4—22no—
374C3×D4—21no—
375C3×D4—21no—
376C3×D4—21no—
377C3×D4—21no—
378C3×D4—41no—
379C3×D4—42no—
380C3×D4—42no—
381C3×D4—41no—
382C3×D4—41no—
383C3×D4—41no—
384C3×D4—41no—
385C3×D4—61no—
386C3×D4—62no—
387C3×D4—62no—
388C3×D4—61no—
389C3×D4—121no—
390C3×D4—121no—
391C3×D4—121no—
392C3×D4—121no—
393C3×D4—242no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—41no—
403C2×C3×C4—42no—
404C2×C3×C4—42no—
405C2×C3×C4—41no—
406C2×C3×C4—41no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4—62no—
410C2×C3×C4—61no—
411C2×C3×C4—121no—
412C2×C3×C4—121no—
413C2×C3×C4—122no—
414C2×C3×C4D3×D411yescharacteristic
415C2×C3×C4D3×D411yescharacteristic
416C2×C3×C4D3×D411yescharacteristic
417C2×C3×C4D3×D411yescharacteristic
418C2×C3×C4D3×D411yescharacteristic
419C2×C3×C4#23711yescharacteristic
420C2×C3×C4#23711yescharacteristic
421C2×C3×C4C2×#6711yescharacteristic
422C2×C3×C4C2×#6711yescharacteristic
423C2×C3×C4C2×#6711yescharacteristic
424C2×C3×C4C2×#6711yescharacteristic
425C2×C3×C4C2×#6711yescharacteristic
426#67—41no—
427#67—41no—
428#67—82no—
429C2×Dic3—21no—
430C2×Dic3—22no—
431C2×Dic3—42no—
432C2×Dic3—62no—
433C2×Dic3—62no—
434C2×Dic3—122no—
435C2×Dic3—122no—
436C2×Dic3—121no—
437C2×Dic3—121no—
438C2×Dic3—122no—
439C2×Dic3—121no—
440C2×Dic3—121no—
441D12—21no—
442D12—22no—
443D12—21no—
444D12—22no—
445D12—41no—
446D12—41no—
447C4×D3—41no—
448C4×D3—41no—
449Dic6—21no—
450Dic6—21no—
451C3×C8—62no—
452C3⋊C8—22no—
453C3⋊C8—62no—
454C3⋊C8—62no—
455C3⋊C8—122no—
456C2×C32—21no—
457C2×C32—21no—
458C2×C32—81no—
459C2×C32#39211yescharacteristic
460C2×C32#45311yescharacteristic
461C2×C32#45411yescharacteristic
462C3×D3—81no—
463C3×D3—82no—
464C24—61no—
465#41—21no—
466#41—21no—
467#41—21no—
468#41—21no—
469#41—61no—
470#41—61no—
471#41—61no—
472#41—61no—
473C2×Q8—31no—
474C2×Q8#62511yescharacteristic
475C2×D4—21no—
476C2×D4—31no—
477C2×D4—32no—
478C2×D4—61no—
479C2×D4—62no—
480C2×D4—61no—
481C2×D4—61no—
482C2×D4—61no—
483C2×D4—61no—
484C2×D4—61no—
485C2×D4#62511yescharacteristic
486C22×C4—21no—
487C22×C4—32no—
488C22×C4—61no—
489C22×C4—181no—
490C22×C4C2×D3211yescharacteristic
491SD16—64no—
492SD16—184no—
493D8—64no—
494D8—184no—
495M16—32no—
496M16—61no—
497M16—92no—
498M16—181no—
499C2×C8—61no—
500C2×C8—181no—
501C4⋊C4—62no—
502C4⋊C4—61no—
503C4⋊C4—61no—
504C22⋊C4—62no—
505C22⋊C4—62no—
506C22⋊C4—364no—
507C42—181no—
508C42—181no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—41no—
517C22×C3—41no—
518C22×C3—42no—
519C22×C3—41no—
520C22×C3—41no—
521C22×C3—41no—
522C22×C3—41no—
523C22×C3—41no—
524C22×C3—41no—
525C22×C3—81no—
526C22×C3—81no—
527C22×C3—124no—
528C22×C3—121no—
529C22×C3—121no—
530C22×C3—121no—
531C22×C3—122no—
532C22×C3—242no—
533C22×C3—241no—
534C22×C3—241no—
535C22×C3#93711yescharacteristic
536C22×C3#93811yescharacteristic
537C22×C3#93911yescharacteristic
538C22×C3#94011yescharacteristic
539C22×C3#94011yescharacteristic
540C22×C3#95311yescharacteristic
541C2×D3—44no—
542C2×D3—41no—
543C2×D3—42no—
544C2×D3—41no—
545C2×D3—41no—
546C2×D3—82no—
547C2×D3—81no—
548C2×D3—81no—
549C3×C4—21no—
550C3×C4—21no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4—42no—
554C3×C4—41no—
555C3×C4—41no—
556C3×C4—122no—
557C3×C4—121no—
558C3×C4#93711yescharacteristic
559C3×C4#93711yescharacteristic
560C3×C4#93711yescharacteristic
561C3×C4#93811yescharacteristic
562C3×C4#93911yescharacteristic
563C3×C4#93911yescharacteristic
564C3×C4#93911yescharacteristic
565C3×C4#95311yescharacteristic
566Dic3—41no—
567Dic3—42no—
568Dic3—122no—
569Dic3—122no—
570Dic3—124no—
571C32#200611yescharacteristic, complemented, Sylow
572C23—21no—
573C23—62no—
574C23—61no—
575C23—122no—
576C23—122no—
577C23—121no—
578C23—121no—
579C23D3×#6711yescharacteristic
580Q8—21no—
581Q8—21no—
582Q8—61no—
583Q8—61no—
584D4—21no—
585D4—21no—
586D4—41no—
587D4—41no—
588D4—61no—
589D4—62no—
590D4—61no—
591D4—62no—
592D4—121no—
593D4—121no—
594D4—121no—
595D4—121no—
596D4—242no—
597C2×C4—21no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—62no—
601C2×C4—61no—
602C2×C4—121no—
603C2×C4—121no—
604C2×C4—122no—
605C2×C4—182no—
606C2×C4—361no—
607C2×C4—361no—
608C2×C4#380511yescharacteristic
609C2×C4C2×#62511yescharacteristic
610C2×C4D3×#6711yescharacteristic
611C2×C4D3×#6711yescharacteristic
612C2×C4D3×#6711yescharacteristic
613C2×C4#381111yescharacteristic
614C8—62no—
615C8—182no—
616C2×C3—21no—
617C2×C3—21no—
618C2×C3—21no—
619C2×C3—21no—
620C2×C3—21no—
621C2×C3—21no—
622C2×C3—21no—
623C2×C3—41no—
624C2×C3—41no—
625C2×C3—82no—
626C2×C3—81no—
627C2×C3—81no—
628C2×C3—241no—
629C2×C3—242no—
630C2×C3#519811yescharacteristic
631C2×C3#520111yescharacteristic
632C2×C3#522311yescharacteristic
633C2×C3#522311yescharacteristic
634C2×C3#524111yescharacteristic
635C2×C3#524511yescharacteristic
636D3—82no—
637D3—81no—
638C22—21no—
639C22—21no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—124no—
644C22—121no—
645C22—121no—
646C22—121no—
647C22—122no—
648C22—242no—
649C22—241no—
650C22—241no—
651C22#6397011yescharacteristic
652C22#6397611yescharacteristic
653C22#6397911yescharacteristic
654C4—41no—
655C4—122no—
656C4—121no—
657C4—362no—
658C4#6397011yescharacteristic
659C4#6397611yescharacteristic
660C4#6398011yescharacteristic
661C4#6398311yescharacteristic
662C3—21no—
663C3#7187911yescharacteristic, complemented
664C3#7209811yescharacteristic, complemented
665C2—21no—
666C2—21no—
667C2—81no—
668C2—242no—
669C2—241no—
670C2#1059166511yescharacteristic
671C2#1059168411yescharacteristic
672C2#1059172311yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC22×C32#120
hypercenterC2×#41D32
hypocenterC32#2006
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C3×#5833C2semidirect
2. C2×C3×#949C2semidirect
3. C2×#63823C2semidirect
4. C2×#63664C2semidirect
5. #10591323C2semidirect
6. C2×#63568C2semidirect
7. #10589167C2semidirect
35. #5833D3semidirect
37. C2×#949D3semidirect
72. C2×C3×D12D4semidirect
78. #3748D4semidirect
88. C3×#208D4semidirect
256. C2×D12#67semidirect
295. #208#67semidirect
571. C32#2006semidirect
663. C3#71879semidirect
664. C3#72098semidirect

Maximal subgroups

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

subgroupindex
C3×#58332
C2×C3×#9492
C2×#638232
C2×#636642
#105913232
C2×#635682
#105891672
#720983
#718793