Finite Group Databasebeta

← #11792277

Subgroups — #11792277

Order 1152.

887 conjugacy classes of subgroups.

The subgroup lattice has 669 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596304C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic, complemented
3C2×#63833C211yesmaximal, characteristic, complemented
4C2×C3×#837C211yesmaximal, characteristic, complemented
5#10591220C211yesmaximal, characteristic, complemented
6C2×#63570C211yesmaximal, characteristic, complemented
7#10589168C211yesmaximal, characteristic, complemented
8#72110—31nomaximal
9#70393—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13#64155—21no—
14#64148—22no—
15#64147—21no—
16#64139—21no—
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18#64133—21no—
19C3×#951—22no—
20C3×#951—22no—
21C2×C3×#216—21no—
22C2×C3×#214—21no—
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26C2×#3719—21no—
27#63833—22no—
28#63833—22no—
29C2×#3717—21no—
30C3×#837—22no—
31#63579—22no—
32#63570—22no—
33C2×C3×#137—31no—
34#5833—31no—
35#5833—31no—
36#5833—61no—
37C2×#951D311yescharacteristic, complemented
38C2×#942—31no—
39C2×#909—31no—
40C2×C3×#104—31no—
41C2×#837D311yescharacteristic, complemented
42#5229—31no—
43C2×#825—31no—
44#4929—31no—
45C2×#805—31no—
46#4554—31no—
47#4554—31no—
48C32×#41—21no—
49C32×#41—21no—
50C32×#41—21no—
51C32×#41—21no—
52C2×C32×Q8D411yescharacteristic
53C2×C32×D4—21no—
54C2×C32×D4D411yescharacteristic
55C22×C32×C4—21no—
56C22×C32×C4C2311yescharacteristic
57C2×#638—21no—
58C2×#638—22no—
59C22×C3⋊Dic3D412yes—
60#3828—21no—
61#3828—21no—
62#3828—21no—
63#3828—21no—
64C2×C4⋊(C3⋊D3)D411yescharacteristic
65C2×C4×C3⋊D3—21no—
66C2×#634D411yescharacteristic
67C22×C3×Dic3—21no—
68C22×C3×Dic3—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—21no—
73C2×C3×Dic6—21no—
74C2×C3×Dic6D412yescomplemented
75#3757—22no—
76#3752—22no—
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)—21no—
79#3750—22no—
80C3×#216—24no—
81C3×#214—24no—
82C3×C4×Dic3—21no—
83C3×C4×Dic3—21no—
84C3×#208—21no—
85C3×#208—21no—
86C3×#208D412yescomplemented
87C3×#208D412yescomplemented
88C2×C3×C3⋊C8—21no—
89C2×C3×C3⋊C8—21no—
90#3719—24no—
91#3717—24no—
92#2007—91noSylow
93C2×C3×#41—21no—
94C2×C3×#41C2×D311yescharacteristic
95C2×C3×#41C2×D311yescharacteristic
96C22×C3×Q8—31no—
97C2×#235—31no—
98C2×#235—31no—
99C2×#235—61no—
100C22×Dic6C2×D311yescharacteristic
101C3×#137—62no—
102C3×#137—62no—
103C2×C3×Q16—61no—
104C2×C3×SD16—61no—
105C2×C3×M16—31no—
106C2×C3×M16—31no—
107C2×C3×C42—31no—
108#951—22no—
109#951—22no—
110#946—62no—
111#946—61no—
112#946—61no—
113C2×#216—21no—
114C2×#216—61no—
115#942—62no—
116#942—62no—
117C2×#215—61no—
118#939—62no—
119#939—62no—
120#939—64no—
121#938—62no—
122#938—61no—
123#938—61no—
124C2×#214—21no—
125#930—61no—
126#930—61no—
127#930—62no—
128C2×C4⋊Dic3—31no—
129C2×C4⋊Dic3—31no—
130C2×C4⋊Dic3—61no—
131#924—61no—
132#924—61no—
133#924—62no—
134C2×C4×Dic3C2×D311yescharacteristic
135C2×#208C2×D311yescharacteristic
136C2×#208C2×D311yescharacteristic
137#909—62no—
138#909—62no—
139C2×Dic12—61no—
140C2×#204—61no—
141C3×#104—62no—
142#837—22no—
143C3⋊#95—62no—
144C3⋊#95—62no—
145#825—62no—
146#805—62no—
147C23×C32—21no—
148C23×C32C2×D411yescharacteristic
149C22×C3⋊D3—21no—
150C32×Q8—21no—
151C32×Q8—21no—
152C32×D4—21no—
153C32×D4—21no—
154C32×D4—41no—
155C32×D4—41no—
156C2×C32×C4—21no—
157C2×C32×C4—41no—
158C2×C32×C4—41no—
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4#4111yescharacteristic
165#638—41no—
166#638—41no—
167#638—82no—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—42no—
171C4⋊(C3⋊D3)—21no—
172C4⋊(C3⋊D3)—21no—
173C4×C3⋊D3—41no—
174C4×C3⋊D3—41no—
175#634—21no—
176#634—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—41no—
180C2×C3×Dic3—41no—
181C2×C3×Dic3—41no—
182C2×C3×Dic3—41no—
183C3×Dic6—22no—
184C3×Dic6—22no—
185C3×Dic6—41no—
186C3×Dic6—41no—
187C3×C3⋊C8—22no—
188C3×C3⋊C8—22no—
189C2×#137—31no—
190C2×#137—91no—
191#537—91no—
192C2×#104—31no—
193C2×#104—91no—
194#391—91no—
195#343—91no—
196C3×#41—21no—
197C3×#41—21no—
198C3×#41—21no—
199C3×#41—21no—
200C3×#41—21no—
201C3×#41—21no—
202C3×#41—21no—
203C3×#41—21no—
204C3×#41—41no—
205C3×#41—41no—
206C3×#41—41no—
207C3×#41—41no—
208C2×C3×Q8—21no—
209C2×C3×Q8—32no—
210C2×C3×Q8—61no—
211C2×C3×Q8—61no—
212C2×C3×Q8—61no—
213C2×C3×Q8—61no—
214C2×C3×Q8—61no—
215C2×C3×Q8D1211yescharacteristic
216C2×C3×Q8#6711yescharacteristic
217C2×C3×D4—22no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4D1211yescharacteristic
222C2×C3×D4#6711yescharacteristic
223C22×C3×C4—22no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—61no—
228C22×C3×C4—61no—
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C2×#67—62no—
232C2×#67—61no—
233C2×#67—61no—
234C2×#67—64no—
235C2×#67—62no—
236C2×#67—62no—
237C22×Dic3—21no—
238C22×Dic3—21no—
239C22×Dic3—32no—
240C22×Dic3—32no—
241C22×Dic3—62no—
242#235—61no—
243#235—61no—
244#235—61no—
245#235—61no—
246#235—61no—
247#235—61no—
248#235—61no—
249#235—61no—
250#235—121no—
251#235—121no—
252#235—121no—
253#235—121no—
254C2×D12—31no—
255C2×D12—31no—
256C2×D12—61no—
257C2×C4×D3—62no—
258C2×C4×D3—61no—
259C2×C4×D3—61no—
260C2×Dic6—21no—
261C2×Dic6—21no—
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6—31no—
266C2×Dic6—31no—
267C2×Dic6—61no—
268C2×Dic6#6712yescomplemented
269C3×Q16—64no—
270C3×SD16—64no—
271C3×M16—32no—
272C3×M16—32no—
273C3×M16—61no—
274C3×M16—61no—
275C2×C3×C8—61no—
276C2×C3×C8—61no—
277C3×C42—61no—
278C3×C42—61no—
279#217—64no—
280#217—62no—
281#217—62no—
282#216—24no—
283#216—64no—
284#215—64no—
285#214—24no—
286(C2×D3)⋊C4—64no—
287(C2×D3)⋊C4—62no—
288(C2×D3)⋊C4—62no—
289C4⋊Dic3—62no—
290C4⋊Dic3—62no—
291C4⋊Dic3—61no—
292C4⋊Dic3—61no—
293C4⋊Dic3—61no—
294C4⋊Dic3—61no—
295Dic3⋊C4—64no—
296Dic3⋊C4—62no—
297Dic3⋊C4—62no—
298C4×Dic3—21no—
299C4×Dic3—21no—
300#208—21no—
301#208—21no—
302#208#6712yescomplemented
303#208#6712yescomplemented
304C2×C3⋊C8—21no—
305C2×C3⋊C8—21no—
306Dic12—64no—
307#204—64no—
308C22×C32—21no—
309C22×C32—21no—
310C22×C32—41no—
311C22×C32—41no—
312C22×C32—41no—
313C22×C32#12011yescharacteristic
314C22×C32#12111yescharacteristic
315C22×C32#12711yescharacteristic
316C2×C3⋊D3—41no—
317C2×C3⋊D3—41no—
318C2×C3⋊D3—41no—
319C32×C4—41no—
320C32×C4#12011yescharacteristic
321C32×C4#12011yescharacteristic
322C32×C4#12111yescharacteristic
323C32×C4#12111yescharacteristic
324C3⋊Dic3—41no—
325C3⋊Dic3—42no—
326C3×Dic3—42no—
327C3×Dic3—42no—
328C2×#41—91no—
329C2×#41D3211yescharacteristic
330C22×Q8—31no—
331#137—62no—
332#137—62no—
333#137—182no—
334#137—182no—
335C2×Q16—61no—
336C2×Q16—181no—
337C2×SD16—61no—
338C2×SD16—181no—
339C2×M16—31no—
340C2×M16—31no—
341C22⋊Q8—181no—
342C22⋊Q8—181no—
343#121—181no—
344#121—182no—
345#121—181no—
346C2×C4⋊C4—91no—
347C2×C42—31no—
348#104—62no—
349#104—182no—
350#95—182no—
351C23×C3—22no—
352C23×C3—21no—
353C23×C3—21no—
354C23×C3—21no—
355C23×C3D3×D411yescharacteristic
356C23×C3D3×D411yescharacteristic
357C22×D3—62no—
358C22×D3—61no—
359C22×D3—61no—
360C3×Q8—21no—
361C3×Q8—21no—
362C3×Q8—21no—
363C3×Q8—21no—
364C3×Q8—41no—
365C3×Q8—41no—
366C3×Q8—62no—
367C3×Q8—62no—
368C3×Q8—121no—
369C3×Q8—121no—
370C3×D4—21no—
371C3×D4—21no—
372C3×D4—21no—
373C3×D4—21no—
374C3×D4—41no—
375C3×D4—41no—
376C3×D4—42no—
377C3×D4—42no—
378C3×D4—41no—
379C3×D4—41no—
380C3×D4—41no—
381C3×D4—41no—
382C2×C3×C4—22no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—42no—
392C2×C3×C4—42no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4—41no—
396C2×C3×C4—41no—
397C2×C3×C4—62no—
398C2×C3×C4—62no—
399C2×C3×C4—121no—
400C2×C3×C4—121no—
401C2×C3×C4—121no—
402C2×C3×C4—121no—
403C2×C3×C4C2×D1211yescharacteristic
404C2×C3×C4#23511yescharacteristic
405C2×C3×C4D3×D411yescharacteristic
406C2×C3×C4D3×D411yescharacteristic
407C2×C3×C4D3×D411yescharacteristic
408C2×C3×C4D3×D411yescharacteristic
409C2×C3×C4D3×D411yescharacteristic
410C2×C3×C4#23711yescharacteristic
411C2×C3×C4C2×#6711yescharacteristic
412C2×C3×C4C2×#6711yescharacteristic
413C2×C3×C4C2×#6711yescharacteristic
414C2×C3×C4C2×#6711yescharacteristic
415#67—122no—
416#67—122no—
417#67—121no—
418#67—121no—
419#67—121no—
420#67—121no—
421#67—244no—
422#67—242no—
423#67—242no—
424C2×Dic3—22no—
425C2×Dic3—22no—
426C2×Dic3—41no—
427C2×Dic3—41no—
428C2×Dic3—41no—
429C2×Dic3—41no—
430C2×Dic3—62no—
431C2×Dic3—64no—
432C2×Dic3—61no—
433C2×Dic3—62no—
434C2×Dic3—61no—
435C2×Dic3—62no—
436C2×Dic3—122no—
437C2×Dic3—122no—
438C2×Dic3—242no—
439D12—61no—
440D12—61no—
441D12—61no—
442D12—61no—
443D12—121no—
444D12—121no—
445C4×D3—122no—
446C4×D3—122no—
447C4×D3—121no—
448C4×D3—121no—
449C4×D3—121no—
450C4×D3—121no—
451Dic6—22no—
452Dic6—22no—
453Dic6—41no—
454Dic6—41no—
455Dic6—61no—
456Dic6—61no—
457Dic6—61no—
458Dic6—61no—
459Dic6—121no—
460Dic6—121no—
461C3×C8—62no—
462C3×C8—62no—
463C3⋊C8—22no—
464C3⋊C8—22no—
465C2×C32—21no—
466C2×C32—21no—
467C2×C32—81no—
468C2×C32#39211yescharacteristic
469C2×C32#45511yescharacteristic
470C2×C32#45611yescharacteristic
471C3⋊D3—81no—
472#41—21no—
473#41—21no—
474#41—21no—
475#41—21no—
476#41—181no—
477#41—181no—
478#41—181no—
479#41—181no—
480C2×Q8—32no—
481C2×Q8—61no—
482C2×Q8—61no—
483C2×Q8—61no—
484C2×Q8—61no—
485C2×Q8—61no—
486C2×Q8—91no—
487C2×Q8#62611yescharacteristic
488C2×D4—21no—
489C2×D4—91no—
490C2×D4—181no—
491C2×D4—182no—
492C2×D4#62611yescharacteristic
493C22×C4—21no—
494C22×C4—61no—
495C22×C4—61no—
496C22×C4—92no—
497C22×C4—181no—
498C22×C4C2×D3211yescharacteristic
499Q16—64no—
500Q16—184no—
501SD16—64no—
502SD16—184no—
503M16—32no—
504M16—32no—
505M16—61no—
506M16—61no—
507C2×C8—61no—
508C2×C8—61no—
509C4⋊C4—182no—
510C4⋊C4—181no—
511C4⋊C4—181no—
512C22⋊C4—182no—
513C22⋊C4—182no—
514C42—61no—
515C42—61no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—21no—
520C22×C3—21no—
521C22×C3—21no—
522C22×C3—21no—
523C22×C3—41no—
524C22×C3—41no—
525C22×C3—42no—
526C22×C3—42no—
527C22×C3—42no—
528C22×C3—41no—
529C22×C3—41no—
530C22×C3—41no—
531C22×C3—41no—
532C22×C3—41no—
533C22×C3—41no—
534C22×C3#88211yescharacteristic
535C22×C3#88411yescharacteristic
536C22×C3#93711yescharacteristic
537C22×C3#93911yescharacteristic
538C22×C3#94011yescharacteristic
539C22×C3#94011yescharacteristic
540C2×D3—122no—
541C2×D3—122no—
542C2×D3—122no—
543C2×D3—121no—
544C2×D3—121no—
545C2×D3—121no—
546C2×D3—121no—
547C2×D3—121no—
548C2×D3—121no—
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—122no—
558C3×C4#88211yescharacteristic
559C3×C4#88411yescharacteristic
560C3×C4#93011yescharacteristic
561C3×C4#93711yescharacteristic
562C3×C4#93711yescharacteristic
563C3×C4#93811yescharacteristic
564C3×C4#93911yescharacteristic
565C3×C4#95311yescharacteristic
566Dic3—42no—
567Dic3—42no—
568Dic3—122no—
569Dic3—124no—
570Dic3—122no—
571Dic3—121no—
572Dic3—121no—
573Dic3—122no—
574C32#200711yescharacteristic, complemented, Sylow
575C23—21no—
576C23—181no—
577C23#381111yescharacteristic
578Q8—21no—
579Q8—21no—
580Q8—62no—
581Q8—62no—
582Q8—121no—
583Q8—121no—
584Q8—181no—
585Q8—181no—
586D4—21no—
587D4—21no—
588D4—41no—
589D4—41no—
590D4—181no—
591D4—181no—
592D4—361no—
593D4—361no—
594D4—722no—
595C2×C4—21no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—62no—
599C2×C4—62no—
600C2×C4—121no—
601C2×C4—121no—
602C2×C4—121no—
603C2×C4—121no—
604C2×C4—182no—
605C2×C4—181no—
606C2×C4—361no—
607C2×C4—361no—
608C2×C4—362no—
609C2×C4#380411yescharacteristic
610C2×C4C2×#62611yescharacteristic
611C2×C4D3×#6711yescharacteristic
612C2×C4D3×#6711yescharacteristic
613C2×C4D3×#6711yescharacteristic
614C2×C4#381111yescharacteristic
615C8—62no—
616C8—62no—
617C2×C3—21no—
618C2×C3—21no—
619C2×C3—21no—
620C2×C3—21no—
621C2×C3—21no—
622C2×C3—21no—
623C2×C3—21no—
624C2×C3—41no—
625C2×C3—41no—
626C2×C3—82no—
627C2×C3—81no—
628C2×C3—81no—
629C2×C3#482511yescharacteristic
630C2×C3#482611yescharacteristic
631C2×C3#496011yescharacteristic
632C2×C3#520211yescharacteristic
633C2×C3#520511yescharacteristic
634C2×C3#522311yescharacteristic
635D3—242no—
636D3—241no—
637D3—241no—
638C22—21no—
639C22—21no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—361no—
644C22—361no—
645C22—361no—
646C22#6397111yescharacteristic
647C22#6397911yescharacteristic
648C22#6398111yescharacteristic
649C4—41no—
650C4—122no—
651C4—122no—
652C4—362no—
653C4—361no—
654C4#6395811yescharacteristic
655C4#6397711yescharacteristic
656C4#6397811yescharacteristic
657C4#6398311yescharacteristic
658C3—21no—
659C3#7039311yescharacteristic, complemented
660C3#7211011yescharacteristic, complemented
661C2—21no—
662C2—21no—
663C2—81no—
664C2—721no—
665C2#1059166811yescharacteristic
666C2#1059169011yescharacteristic
667C2#1059172411yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC22×C32#120
prime radical#10596304C2
hypercenterC2×#41D32
hypocenterC32#2007
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
2. C2×C3×#951C2semidirect
3. C2×#63833C2semidirect
4. C2×C3×#837C2semidirect
5. #10591220C2semidirect
6. C2×#63570C2semidirect
7. #10589168C2semidirect
37. C2×#951D3semidirect
41. C2×#837D3semidirect
74. C2×C3×Dic6D4semidirect
86. C3×#208D4semidirect
87. C3×#208D4semidirect
268. C2×Dic6#67semidirect
302. #208#67semidirect
303. #208#67semidirect
574. C32#2007semidirect
659. C3#70393semidirect
660. C3#72110semidirect

Maximal subgroups

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

subgroupindex
#105963042
C2×C3×#9512
C2×#638332
C2×C3×#8372
#105912202
C2×#635702
#105891682
#721103
#703933