Finite Group Databasebeta

← #10703039

Subgroups — #10703039

Order 768.

962 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#825C211yesmaximal, characteristic
2C2×#5133C211yesmaximal, characteristic
3#82186C211yesmaximal, characteristic
4C2×C3×#343C211yesmaximal, characteristic, complemented
5#71985C211yesmaximal, characteristic, complemented
6C2×#4555C211yesmaximal, characteristic, complemented
7#71563C211yesmaximal, characteristic, complemented
8#11195—31nomaximal, Sylow
9C22×#235C2211yescharacteristic
10C22×C3×M16C2211yescharacteristic
11C22×C3×M16C2211yescharacteristic
12C22×C3×C4⋊C4C2211yescharacteristic
13C2×#926C2211yescharacteristic
14C22×C4⋊Dic3C2211yescharacteristic
15C22×C4×Dic3C2211yescharacteristic
16#5213—22no—
17C2×C3⋊#95—22no—
18C2×#825—22no—
19C2×#825—22no—
20C2×#825—22no—
21#5133—22no—
22#5133C414yescomplemented
23C2×#821—21no—
24C2×#816—21no—
25#4988—21no—
26#4987—21no—
27#4987—21no—
28#4973—21no—
29C3×#343—22no—
30#4555—22no—
31#4551—21no—
32#4551—21no—
33C22×#104—31no—
34C2×#417—31no—
35#2311—31no—
36C2×#343D311yescharacteristic, complemented
37#1736—31no—
38C2×#339—31no—
39C4⋊#95—31no—
40C23×C3×C4D412yes—
41C23×C3×C4C2311yescharacteristic
42C22×#67—21no—
43C23×Dic3—21no—
44C23×Dic3—21no—
45C2×#235—21no—
46C2×#235—21no—
47C2×#235—21no—
48C2×#235—21no—
49C2×#235—21no—
50C2×#235—21no—
51C2×#235—21no—
52C2×#235—21no—
53C2×#235—21no—
54C2×#235—21no—
55C2×#235C2×C412yes—
56C2×#235D412yes—
57C22×D12D411yescharacteristic
58C22×C4×D3—21no—
59C22×Dic6D411yescharacteristic
60C2×C3×M16—21no—
61C2×C3×M16—21no—
62C2×C3×M16—21no—
63C2×C3×M16—21no—
64C2×C3×M16—21no—
65C2×C3×M16—21no—
66C2×C3×M16—21no—
67C2×C3×M16—21no—
68C2×C3×M16—21no—
69C2×C3×M16—21no—
70C2×C3×M16C2×C412yes—
71C2×C3×M16D412yes—
72C22×C3×C8—21no—
73C22×C3×C8—21no—
74C2×C3×C4⋊C4—21no—
75C2×C3×C4⋊C4—21no—
76C2×C3×C4⋊C4—21no—
77C2×C3×C4⋊C4—21no—
78C2×C3×C4⋊C4—21no—
79C2×C3×C4⋊C4—21no—
80C2×#217—21no—
81C2×(C2×D3)⋊C4—22no—
82C2×(C2×D3)⋊C4—22no—
83#926—21no—
84#926—21no—
85#926—21no—
86#926—21no—
87C2×C4⋊Dic3—21no—
88C2×C4⋊Dic3—21no—
89C2×C4⋊Dic3—21no—
90C2×C4⋊Dic3—21no—
91C2×C4⋊Dic3—21no—
92C2×C4⋊Dic3C2×C412yes—
93C2×C4⋊Dic3D411yescharacteristic
94C2×C4⋊Dic3D411yescharacteristic
95C2×C4×Dic3—21no—
96C2×C4×Dic3—21no—
97C2×C4×Dic3—21no—
98C2×C4×Dic3—21no—
99C2×C4×Dic3—21no—
100C2×C4×Dic3—21no—
101C2×C4×Dic3D412yes—
102C3⋊#95—22no—
103C3⋊#95—22no—
104C3⋊#95—44no—
105#825—28no—
106#821—24no—
107#816—24no—
108C22×#41—31no—
109C22×M16C2×D311yescharacteristic
110C22×M16C2×D311yescharacteristic
111C2×#117—31no—
112C22×C4⋊C4—31no—
113C22×C4⋊C4C2×D311yescharacteristic
114C22×C42—31no—
115C2×#104—62no—
116C2×#104—62no—
117C2×#104—62no—
118#417—34no—
119#417—62no—
120C2×#103—61no—
121C2×#102—61no—
122#391—61no—
123#390—61no—
124#386—62no—
125#380—61no—
126#380—61no—
127C2×#95—62no—
128#343—22no—
129#340—61no—
130#340—61no—
131#339—62no—
132C24×C3C2×D411yescharacteristic
133C23×D3—21no—
134C22×C3×C4—22no—
135C22×C3×C4—22no—
136C22×C3×C4—22no—
137C22×C3×C4—42no—
138C22×C3×C4—42no—
139C22×C3×C4C22×C411yescharacteristic
140C22×C3×C4C2×D411yescharacteristic
141C22×C3×C4C2×D411yescharacteristic
142C22×C3×C4C2×D411yescharacteristic
143C22×C3×C4C2×D411yescharacteristic
144C22×C3×C4C2×D411yescharacteristic
145C22×C3×C4#4111yescharacteristic
146C22×C3×C4#4111yescharacteristic
147C22×C3×C4#4111yescharacteristic
148C22×C3×C4#4111yescharacteristic
149C22×C3×C4#4111yescharacteristic
150C22×C3×C4#4111yescharacteristic
151C22×C3×C4#4111yescharacteristic
152C22×C3×C4#4111yescharacteristic
153C2×#67—22no—
154C2×#67—22no—
155C2×#67—41no—
156C2×#67—41no—
157C2×#67—41no—
158C2×#67—41no—
159C22×Dic3—22no—
160C22×Dic3—22no—
161C22×Dic3—21no—
162C22×Dic3—22no—
163C22×Dic3—22no—
164C22×Dic3—21no—
165C22×Dic3—21no—
166C22×Dic3—41no—
167C22×Dic3—41no—
168C22×Dic3—41no—
169C22×Dic3—41no—
170C22×Dic3—42no—
171C22×Dic3—42no—
172C22×Dic3—41no—
173C22×Dic3—41no—
174#235—22no—
175#235—22no—
176#235—22no—
177#235—22no—
178#235—22no—
179#235—22no—
180#235—22no—
181#235—22no—
182#235—41no—
183#235—41no—
184#235—41no—
185#235—41no—
186#235—41no—
187#235—41no—
188#235—41no—
189#235—41no—
190C2×D12—21no—
191C2×D12—21no—
192C2×D12—21no—
193C2×D12—21no—
194C2×D12—21no—
195C2×D12C22⋊C412yes—
196C2×C4×D3—22no—
197C2×C4×D3—22no—
198C2×C4×D3—41no—
199C2×C4×D3—41no—
200C2×C4×D3—41no—
201C2×C4×D3—41no—
202C2×Dic6—21no—
203C2×Dic6—21no—
204C2×Dic6—21no—
205C2×Dic6—21no—
206C2×Dic6—21no—
207C2×Dic6C22⋊C412yes—
208C3×M16—22no—
209C3×M16—22no—
210C3×M16—22no—
211C3×M16—22no—
212C3×M16—41no—
213C3×M16—41no—
214C3×M16—41no—
215C3×M16—41no—
216C2×C3×C8—22no—
217C2×C3×C8—22no—
218C2×C3×C8—41no—
219C2×C3×C8—41no—
220C2×C3×C8—41no—
221C2×C3×C8—41no—
222C3×C4⋊C4—41no—
223C3×C4⋊C4—41no—
224C3×C4⋊C4—41no—
225C3×C4⋊C4—41no—
226#217—41no—
227#217—41no—
228(C2×D3)⋊C4—82no—
229(C2×D3)⋊C4—82no—
230C4⋊Dic3—22no—
231C4⋊Dic3—22no—
232C4⋊Dic3—21no—
233C4⋊Dic3—21no—
234C4⋊Dic3—21no—
235C4⋊Dic3—21no—
236C4⋊Dic3—41no—
237C4⋊Dic3—41no—
238C4×Dic3—22no—
239C4×Dic3—22no—
240C4×Dic3—41no—
241C4×Dic3—41no—
242C4×Dic3—41no—
243C4×Dic3—41no—
244C2×#41—32no—
245C2×#41—32no—
246C2×#41—61no—
247C2×#41—61no—
248C2×#41—61no—
249C2×#41—61no—
250C2×#41—61no—
251C2×#41—61no—
252C2×#41—61no—
253C2×#41—61no—
254C2×#41—61no—
255C2×#41—61no—
256C22×Q8—31no—
257C22×D4—31no—
258C22×D4—61no—
259C23×C4—61no—
260C23×C4—61no—
261C23×C4—61no—
262C23×C4D1212yes—
263C23×C4C22×D311yescharacteristic
264C2×M16—21no—
265C2×M16—21no—
266C2×M16—21no—
267C2×M16—21no—
268C2×M16—21no—
269C2×M16—21no—
270C2×M16—21no—
271C2×M16—21no—
272C2×M16—21no—
273C2×M16—21no—
274C2×M16C4×D312yes—
275C2×M16#6712yes—
276C22×C8—21no—
277C22×C8—21no—
278#117—61no—
279#117—61no—
280#117—61no—
281#117—61no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—32no—
289C2×C4⋊C4—31no—
290C2×C4⋊C4—31no—
291C2×C4⋊C4—61no—
292C2×C4⋊C4—61no—
293C2×C4⋊C4—61no—
294C2×C4⋊C4—61no—
295C2×C4⋊C4—61no—
296C2×C22⋊C4—61no—
297C2×C22⋊C4—62no—
298C2×C22⋊C4—62no—
299C2×C42—32no—
300C2×C42—61no—
301C2×C42—61no—
302C2×C42—61no—
303C2×C42—61no—
304C2×C42—61no—
305C2×C42—61no—
306#104—68no—
307#103—64no—
308#102—64no—
309#95—62no—
310#95—62no—
311#95—124no—
312C23×C3—21no—
313C23×C3—21no—
314C23×C3—21no—
315C23×C3—21no—
316C23×C3C4×D411yescharacteristic
317C23×C3#12011yescharacteristic
318C23×C3#12111yescharacteristic
319C23×C3#12111yescharacteristic
320C23×C3#12111yescharacteristic
321C23×C3#12311yescharacteristic
322C23×C3#12411yescharacteristic
323C22×D3—22no—
324C22×D3—41no—
325C22×D3—41no—
326C22×D3—41no—
327C22×D3—41no—
328C22×D3—41no—
329C22×D3—41no—
330C2×C3×C4—44no—
331C2×C3×C4—42no—
332C2×C3×C4—42no—
333C2×C3×C4—42no—
334C2×C3×C4—82no—
335C2×C3×C4C2×C22⋊C411yescharacteristic
336C2×C3×C4#11711yescharacteristic
337C2×C3×C4#11711yescharacteristic
338C2×C3×C4C4×D411yescharacteristic
339C2×C3×C4C4×D411yescharacteristic
340C2×C3×C4C4×D411yescharacteristic
341C2×C3×C4#12011yescharacteristic
342C2×C3×C4#12111yescharacteristic
343C2×C3×C4#12111yescharacteristic
344C2×C3×C4#12111yescharacteristic
345C2×C3×C4#12111yescharacteristic
346C2×C3×C4#12111yescharacteristic
347C2×C3×C4#12311yescharacteristic
348C2×C3×C4#12311yescharacteristic
349C2×C3×C4#12311yescharacteristic
350C2×C3×C4#12311yescharacteristic
351C2×C3×C4#12311yescharacteristic
352C2×C3×C4#12311yescharacteristic
353C2×C3×C4#12311yescharacteristic
354C2×C3×C4#12311yescharacteristic
355C2×C3×C4#12311yescharacteristic
356C2×C3×C4#12411yescharacteristic
357C2×C3×C4#12411yescharacteristic
358C2×C3×C4#12411yescharacteristic
359C2×C3×C4#12611yescharacteristic
360C2×C3×C4#12611yescharacteristic
361C2×C3×C4#12611yescharacteristic
362C2×C3×C4#12611yescharacteristic
363#67—42no—
364#67—42no—
365#67—42no—
366#67—42no—
367C2×Dic3—24no—
368C2×Dic3—22no—
369C2×Dic3—42no—
370C2×Dic3—42no—
371C2×Dic3—42no—
372C2×Dic3—42no—
373C2×Dic3—42no—
374C2×Dic3—42no—
375C2×Dic3—41no—
376C2×Dic3—41no—
377C2×Dic3—44no—
378C2×Dic3—42no—
379C2×Dic3—41no—
380C2×Dic3—41no—
381C2×Dic3—41no—
382C2×Dic3—41no—
383C2×Dic3—41no—
384C2×Dic3—41no—
385C2×Dic3—82no—
386C2×Dic3—81no—
387C2×Dic3—81no—
388D12—22no—
389D12—22no—
390D12—41no—
391D12—41no—
392C4×D3—42no—
393C4×D3—42no—
394C4×D3—42no—
395C4×D3—42no—
396Dic6—22no—
397Dic6—22no—
398Dic6—41no—
399Dic6—41no—
400C3×C8—42no—
401C3×C8—42no—
402C24—61no—
403C24C2×D1211yescharacteristic
404#41—62no—
405#41—62no—
406#41—62no—
407#41—62no—
408#41—62no—
409#41—62no—
410#41—62no—
411#41—62no—
412#41—121no—
413#41—121no—
414#41—121no—
415#41—121no—
416#41—121no—
417#41—121no—
418#41—121no—
419#41—121no—
420C2×Q8—32no—
421C2×Q8—61no—
422C2×Q8—61no—
423C2×Q8—61no—
424C2×Q8—61no—
425C2×Q8—61no—
426C2×D4—32no—
427C2×D4—62no—
428C2×D4—62no—
429C2×D4—61no—
430C2×D4—61no—
431C2×D4—61no—
432C2×D4—61no—
433C2×D4—61no—
434C2×D4—121no—
435C2×D4—121no—
436C2×D4—121no—
437C2×D4—121no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—62no—
444C22×C4—62no—
445C22×C4—61no—
446C22×C4—62no—
447C22×C4—62no—
448C22×C4—62no—
449C22×C4—62no—
450C22×C4—61no—
451C22×C4—61no—
452C22×C4—121no—
453C22×C4—121no—
454C22×C4—121no—
455C22×C4—121no—
456C22×C4—121no—
457C22×C4—121no—
458C22×C4—121no—
459C22×C4—121no—
460C22×C4—122no—
461C22×C4—122no—
462C22×C4—121no—
463C22×C4—121no—
464C22×C4C2×C4×D311yescharacteristic
465C22×C4#23511yescharacteristic
466C22×C4#23511yescharacteristic
467C22×C4#23511yescharacteristic
468C22×C4#23511yescharacteristic
469C22×C4D3×D411yescharacteristic
470C22×C4D3×D411yescharacteristic
471C22×C4D3×D411yescharacteristic
472C22×C4D3×D411yescharacteristic
473C22×C4#23711yescharacteristic
474C22×C4#23711yescharacteristic
475C22×C4#23911yescharacteristic
476C22×C4#23911yescharacteristic
477C22×C4C2×#6711yescharacteristic
478M16—22no—
479M16—22no—
480M16—22no—
481M16—22no—
482M16—41no—
483M16—41no—
484M16—41no—
485M16—41no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4—62no—
497C4⋊C4—61no—
498C4⋊C4—61no—
499C4⋊C4—62no—
500C4⋊C4—61no—
501C4⋊C4—61no—
502C4⋊C4—121no—
503C4⋊C4—121no—
504C22⋊C4—121no—
505C22⋊C4—121no—
506C22⋊C4—242no—
507C22⋊C4—242no—
508C42—62no—
509C42—62no—
510C42—121no—
511C42—121no—
512C42—121no—
513C42—121no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—21no—
520C22×C3—21no—
521C22×C3—21no—
522C22×C3—21no—
523C22×C3—21no—
524C22×C3—21no—
525C22×C3—21no—
526C22×C3#38611yescharacteristic
527C22×C3#38811yescharacteristic
528C22×C3#38811yescharacteristic
529C22×C3#39411yescharacteristic
530C22×C3#39411yescharacteristic
531C22×C3#39411yescharacteristic
532C22×C3#39711yescharacteristic
533C22×C3#45311yescharacteristic
534C22×C3#45411yescharacteristic
535C22×C3#45511yescharacteristic
536C22×C3#45611yescharacteristic
537C2×D3—42no—
538C2×D3—42no—
539C2×D3—42no—
540C2×D3—81no—
541C2×D3—81no—
542C2×D3—81no—
543C2×D3—81no—
544C3×C4—82no—
545C3×C4#38111yescharacteristic
546C3×C4#38611yescharacteristic
547C3×C4#38811yescharacteristic
548C3×C4#38811yescharacteristic
549C3×C4#39411yescharacteristic
550C3×C4#39711yescharacteristic
551C3×C4#39711yescharacteristic
552C3×C4#39711yescharacteristic
553Dic3—44no—
554Dic3—42no—
555Dic3—82no—
556Dic3—81no—
557Dic3—81no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—62no—
563C23—121no—
564C23—121no—
565C23—121no—
566C23—121no—
567C23—121no—
568C23—121no—
569C23C4×D1211yescharacteristic
570C23#87511yescharacteristic
571C23#88211yescharacteristic
572C23#88611yescharacteristic
573C23#89511yescharacteristic
574C23#89511yescharacteristic
575C23#93011yescharacteristic
576Q8—62no—
577Q8—62no—
578Q8—121no—
579Q8—121no—
580D4—62no—
581D4—62no—
582D4—122no—
583D4—122no—
584D4—122no—
585D4—122no—
586D4—121no—
587D4—121no—
588C2×C4—44no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—64no—
593C2×C4—62no—
594C2×C4—82no—
595C2×C4—122no—
596C2×C4—122no—
597C2×C4—122no—
598C2×C4—122no—
599C2×C4—122no—
600C2×C4—121no—
601C2×C4—121no—
602C2×C4—122no—
603C2×C4—122no—
604C2×C4—122no—
605C2×C4—122no—
606C2×C4—122no—
607C2×C4—124no—
608C2×C4—122no—
609C2×C4—121no—
610C2×C4—121no—
611C2×C4—121no—
612C2×C4—121no—
613C2×C4—121no—
614C2×C4—121no—
615C2×C4—242no—
616C2×C4—241no—
617C2×C4—241no—
618C2×C4#87211yescharacteristic
619C2×C4#87611yescharacteristic
620C2×C4D3×C22⋊C411yescharacteristic
621C2×C4#67⋊C411yescharacteristic
622C2×C4#88311yescharacteristic
623C2×C4#88311yescharacteristic
624C2×C4#88311yescharacteristic
625C2×C4#88411yescharacteristic
626C2×C4#88411yescharacteristic
627C2×C4#88411yescharacteristic
628C2×C4#88511yescharacteristic
629C2×C4#88511yescharacteristic
630C2×C4#89211yescharacteristic
631C2×C4#89311yescharacteristic
632C2×C4#89411yescharacteristic
633C2×C4#89411yescharacteristic
634C2×C4#89411yescharacteristic
635C2×C4#89411yescharacteristic
636C2×C4#89411yescharacteristic
637C2×C4#89811yescharacteristic
638C2×C4#89811yescharacteristic
639C2×C4#89811yescharacteristic
640C2×C4C4×#6711yescharacteristic
641C2×C4#92911yescharacteristic
642C2×C4#93711yescharacteristic
643C2×C4#93811yescharacteristic
644C2×C4#93911yescharacteristic
645C2×C4#94711yescharacteristic
646C8—42no—
647C8—42no—
648C2×C3—21no—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3#144011yescharacteristic
653C2×C3#188211yescharacteristic
654C2×C3#188311yescharacteristic
655C2×C3#203711yescharacteristic
656C2×C3#203811yescharacteristic
657C2×C3#203911yescharacteristic
658C2×C3#204011yescharacteristic
659D3—82no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—122no—
673C22—122no—
674C22—122no—
675C22—241no—
676C22—241no—
677C22—241no—
678C22—241no—
679C22#466511yescharacteristic
680C22#467011yescharacteristic
681C22#467211yescharacteristic
682C22#467411yescharacteristic
683C22#474611yescharacteristic
684C22#474711yescharacteristic
685C22#475211yescharacteristic
686C22#475311yescharacteristic
687C22#494011yescharacteristic
688C22#496111yescharacteristic
689C22#499111yescharacteristic
690C4—82no—
691C4—124no—
692C4—122no—
693C4—241no—
694C4—241no—
695C4—242no—
696C4#466411yescharacteristic
697C4#466911yescharacteristic
698C4#467511yescharacteristic
699C4#467511yescharacteristic
700C4#495611yescharacteristic
701C4#495911yescharacteristic
702C4#499011yescharacteristic
703C4#499211yescharacteristic
704C3#1119511yescharacteristic, complemented, Sylow
705C2—21no—
706C2—21no—
707C2—21no—
708C2—21no—
709C2—242no—
710C2#6897611yescharacteristic
711C2#6897711yescharacteristic
712C2#6900411yescharacteristic
713C2#6900511yescharacteristic
714C2#6942911yescharacteristic
715C2#7006611yescharacteristic
716C2#7010011yescharacteristic
subgroupG/H
centerC23#882
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC2×C3×#343C2
socleC23×C3#120
prime radicalC22×#235C22
cosocleC23×C3×C4C23
hypercenterC2×#343D3
hypocenterC3#11195
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
4. C2×C3×#343C2semidirect
5. #71985C2semidirect
6. C2×#4555C2semidirect
7. #71563C2semidirect
22. #5133C4semidirect
36. C2×#343D3semidirect
704. C3#11195semidirect

Maximal subgroups

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

subgroupindex
C22×#8252
C2×#51332
#821862
C2×C3×#3432
#719852
C2×#45552
#715632
#111953