Finite Group Databasebeta

← #11792276

Subgroups — #11792276

Order 1152.

869 conjugacy classes of subgroups.

The subgroup lattice has 655 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64160C211yesmaximal, characteristic, complemented
2C3×#5833C211yesmaximal, characteristic
3C2×#63831C211yesmaximal, characteristic, complemented
4C2×C3×#837C211yesmaximal, characteristic, complemented
5#10591213C211yesmaximal, characteristic, complemented
6C2×#63569C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#71881—31nomaximal
9#70393—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13#64160—22no—
14#64160—22no—
15C2×#3756—21no—
16C2×#3754—21no—
17C2×#3748C2211yescharacteristic
18C3×#946—21no—
19C3×#939—22no—
20C3×#938—21no—
21C3×#930—21no—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C3×#924—21no—
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26C2×#3719—21no—
27#63831—22no—
28#63831—22no—
29C2×#3716—21no—
30C3×#837—22no—
31#63579—22no—
32#63569—22no—
33C3×#537—31no—
34#5833D311yescharacteristic
35C2×#951—31no—
36C2×#951—31no—
37C2×#951—31no—
38C2×#951—61no—
39C2×#909—31no—
40C2×C3×#104—31no—
41C2×#837—31no—
42C2×#837D311yescharacteristic, complemented
43#4973—31no—
44#4929—31no—
45C2×#805—31no—
46#4554—31no—
47#4530—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
57C22×C3⋊Dic3—21no—
58C2×#634—21no—
59C2×#634—21no—
60C2×#634—21no—
61C2×#634—21no—
62C2×#634—21no—
63C2×#634D412yescomplemented
64C2×C3×#67—21no—
65C2×C3×#67—22no—
66C22×C3×Dic3—21no—
67C22×C3×Dic3D412yes—
68C3×#235—21no—
69C3×#235—21no—
70C3×#235—21no—
71C3×#235—21no—
72C2×C3×D12D411yescharacteristic
73C2×C3×C4×D3—21no—
74C2×C3×Dic6D411yescharacteristic
75#3756—24no—
76#3754—24no—
77#3748—21no—
78#3748D412yescomplemented
79C2×C3⋊(C3⋊C8)—21no—
80C3×#217—22no—
81C3×(C2×D3)⋊C4—22no—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3—21no—
84C3×Dic3⋊C4—22no—
85C3×C4×Dic3—21no—
86C3×C4×Dic3—21no—
87C3×#208—21no—
88C3×#208D412yescomplemented
89C2×C3×C3⋊C8—21no—
90#3719—24no—
91#3716—24no—
92#2007—91noSylow
93C2×C3×#41—21no—
94C2×C3×#41—31no—
95C2×C3×#41C2×D311yescharacteristic
96C2×C3×#41C2×D311yescharacteristic
97C2×#235C2×D311yescharacteristic
98C22×Dic6—31no—
99C22×Dic6—31no—
100C22×Dic6—61no—
101C2×C3×M16—31no—
102C3×C22⋊Q8—61no—
103C3×C22⋊Q8—61no—
104C3×#121—61no—
105C3×#121—62no—
106C3×#121—61no—
107C2×C3×C4⋊C4—31no—
108C2×C3×C42—31no—
109#951—62no—
110#951—62no—
111#951—62no—
112#951—62no—
113#951—62no—
114#951—64no—
115#951—64no—
116#951—62no—
117#946—21no—
118C2×#216—61no—
119C2×#216—62no—
120C2×#216—61no—
121C2×#216—61no—
122#939—22no—
123#938—21no—
124C2×#214—61no—
125C2×#214—62no—
126C2×#214—61no—
127C2×#214—61no—
128#930—21no—
129C2×C4⋊Dic3C2×D311yescharacteristic
130#924—21no—
131C2×C4×Dic3C2×D311yescharacteristic
132C2×#208—31no—
133C2×#208—31no—
134C2×#208—61no—
135C2×#208C2×D311yescharacteristic
136#909—62no—
137#909—62no—
138C2×Dic12—61no—
139C2×#204—61no—
140C3×#104—62no—
141#837—22no—
142#837—62no—
143C3⋊#95—62no—
144C3⋊#95—62no—
145#805—62no—
146C23×C32—21no—
147C23×C32C2×D411yescharacteristic
148C22×C3×D3—21no—
149C32×Q8—21no—
150C32×Q8—21no—
151C32×D4—21no—
152C32×D4—21no—
153C32×D4—41no—
154C32×D4—41no—
155C2×C32×C4—21no—
156C2×C32×C4—41no—
157C2×C32×C4—41no—
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4#4111yescharacteristic
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—41no—
166C2×C3⋊Dic3—41no—
167#634—22no—
168#634—22no—
169#634—41no—
170#634—41no—
171C3×#67—41no—
172C3×#67—41no—
173C3×#67—82no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—41no—
178C2×C3×Dic3—41no—
179C2×C3×Dic3—42no—
180C3×D12—21no—
181C3×D12—21no—
182C3×C4×D3—41no—
183C3×C4×D3—41no—
184C3×Dic6—21no—
185C3×Dic6—21no—
186C3⋊(C3⋊C8)—22no—
187C3×C3⋊C8—22no—
188C2×#137—91no—
189C2×#137—91no—
190#537—31no—
191C2×#104—31no—
192C2×#104—91no—
193#391—91no—
194#343—91no—
195C3×#41—22no—
196C3×#41—22no—
197C3×#41—21no—
198C3×#41—21no—
199C3×#41—21no—
200C3×#41—21no—
201C3×#41—21no—
202C3×#41—21no—
203C3×#41—21no—
204C3×#41—21no—
205C3×#41—41no—
206C3×#41—41no—
207C3×#41—61no—
208C3×#41—61no—
209C3×#41—61no—
210C3×#41—61no—
211C2×C3×Q8—21no—
212C2×C3×Q8—31no—
213C2×C3×Q8D1211yescharacteristic
214C2×C3×Q8#6711yescharacteristic
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—31no—
219C2×C3×D4—41no—
220C2×C3×D4—61no—
221C2×C3×D4—62no—
222C2×C3×D4D1211yescharacteristic
223C2×C3×D4#6711yescharacteristic
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—32no—
228C22×C3×C4—41no—
229C22×C3×C4—61no—
230C22×C3×C4—61no—
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C2×#67—21no—
234C2×#67—22no—
235C22×Dic3—21no—
236C22×Dic3—61no—
237C22×Dic3—61no—
238C22×Dic3—121no—
239C22×Dic3#6712yes—
240#235—21no—
241#235—21no—
242#235—21no—
243#235—21no—
244C2×D12#6711yescharacteristic
245C2×C4×D3—21no—
246C2×Dic6—32no—
247C2×Dic6—32no—
248C2×Dic6—62no—
249C2×Dic6—62no—
250C2×Dic6—62no—
251C2×Dic6—61no—
252C2×Dic6—61no—
253C2×Dic6—61no—
254C2×Dic6—61no—
255C2×Dic6—61no—
256C2×Dic6—61no—
257C2×Dic6—61no—
258C2×Dic6—61no—
259C2×Dic6—61no—
260C2×Dic6—61no—
261C2×Dic6—121no—
262C2×Dic6—121no—
263C2×Dic6—121no—
264C2×Dic6#6711yescharacteristic
265C3×M16—32no—
266C3×M16—61no—
267C2×C3×C8—61no—
268C3×C4⋊C4—62no—
269C3×C4⋊C4—61no—
270C3×C4⋊C4—61no—
271C3×C22⋊C4—62no—
272C3×C22⋊C4—62no—
273C3×C42—61no—
274C3×C42—61no—
275#217—22no—
276#216—64no—
277#216—68no—
278#216—64no—
279#216—64no—
280#214—64no—
281#214—68no—
282#214—64no—
283#214—64no—
284(C2×D3)⋊C4—22no—
285C4⋊Dic3—21no—
286C4⋊Dic3—21no—
287Dic3⋊C4—22no—
288C4×Dic3—21no—
289C4×Dic3—21no—
290#208—21no—
291#208—32no—
292#208—32no—
293#208—62no—
294#208—62no—
295#208—61no—
296#208—61no—
297#208#6712yescomplemented
298C2×C3⋊C8—21no—
299C2×C3⋊C8—62no—
300C2×C3⋊C8—61no—
301C2×C3⋊C8—61no—
302Dic12—64no—
303#204—64no—
304C22×C32—21no—
305C22×C32—21no—
306C22×C32—41no—
307C22×C32—41no—
308C22×C32—41no—
309C22×C32#12011yescharacteristic
310C22×C32#12111yescharacteristic
311C22×C32#12711yescharacteristic
312C2×C3×D3—41no—
313C2×C3×D3—41no—
314C2×C3×D3—41no—
315C32×C4—41no—
316C32×C4#12011yescharacteristic
317C32×C4#12011yescharacteristic
318C32×C4#12111yescharacteristic
319C32×C4#12111yescharacteristic
320C3⋊Dic3—42no—
321C3×Dic3—42no—
322C3×Dic3—41no—
323C3×Dic3—42no—
324C2×#41—31no—
325C2×#41D3211yescharacteristic
326C22×Q8—91no—
327#137—182no—
328#137—182no—
329#137—182no—
330#137—182no—
331C2×Q16—181no—
332C2×Q16—181no—
333C2×SD16—181no—
334C2×SD16—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×C42—31no—
344#104—62no—
345#104—182no—
346#95—182no—
347C23×C3—21no—
348C23×C3—21no—
349C23×C3—21no—
350C23×C3—41no—
351C23×C3—61no—
352C23×C3D3×D411yescharacteristic
353C23×C3C2×#6711yescharacteristic
354C22×D3—21no—
355C3×Q8—22no—
356C3×Q8—21no—
357C3×Q8—21no—
358C3×Q8—21no—
359C3×Q8—21no—
360C3×Q8—41no—
361C3×Q8—61no—
362C3×Q8—61no—
363C3×D4—22no—
364C3×D4—21no—
365C3×D4—21no—
366C3×D4—21no—
367C3×D4—21no—
368C3×D4—41no—
369C3×D4—42no—
370C3×D4—42no—
371C3×D4—41no—
372C3×D4—41no—
373C3×D4—41no—
374C3×D4—41no—
375C3×D4—61no—
376C3×D4—61no—
377C3×D4—121no—
378C3×D4—121no—
379C3×D4—242no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—41no—
389C2×C3×C4—42no—
390C2×C3×C4—42no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4—62no—
396C2×C3×C4—62no—
397C2×C3×C4—61no—
398C2×C3×C4—121no—
399C2×C3×C4—121no—
400C2×C3×C4—121no—
401C2×C3×C4—121no—
402C2×C3×C4—122no—
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×C4D3×D411yescharacteristic
411C2×C3×C4#23711yescharacteristic
412C2×C3×C4C2×#6711yescharacteristic
413C2×C3×C4C2×#6711yescharacteristic
414C2×C3×C4C2×#6711yescharacteristic
415#67—41no—
416#67—41no—
417#67—82no—
418C2×Dic3—22no—
419C2×Dic3—21no—
420C2×Dic3—22no—
421C2×Dic3—41no—
422C2×Dic3—41no—
423C2×Dic3—42no—
424C2×Dic3—62no—
425C2×Dic3—62no—
426C2×Dic3—122no—
427C2×Dic3—122no—
428C2×Dic3—122no—
429C2×Dic3—121no—
430C2×Dic3—121no—
431C2×Dic3—121no—
432C2×Dic3—121no—
433D12—21no—
434D12—21no—
435C4×D3—41no—
436C4×D3—41no—
437Dic6—21no—
438Dic6—21no—
439Dic6—64no—
440Dic6—62no—
441Dic6—62no—
442Dic6—62no—
443Dic6—62no—
444Dic6—122no—
445Dic6—122no—
446Dic6—122no—
447Dic6—121no—
448Dic6—121no—
449Dic6—121no—
450Dic6—121no—
451C3×C8—62no—
452C3⋊C8—22no—
453C3⋊C8—64no—
454C3⋊C8—62no—
455C3⋊C8—62no—
456C2×C32—21no—
457C2×C32—21no—
458C2×C32—81no—
459C2×C32#39211yescharacteristic
460C2×C32#45511yescharacteristic
461C2×C32#45611yescharacteristic
462C3×D3—81no—
463#41—21no—
464#41—21no—
465#41—21no—
466#41—21no—
467#41—61no—
468#41—61no—
469#41—61no—
470#41—61no—
471C2×Q8—31no—
472C2×Q8—92no—
473C2×Q8—181no—
474C2×Q8—181no—
475C2×Q8—181no—
476C2×Q8—181no—
477C2×Q8—181no—
478C2×Q8#62611yescharacteristic
479C2×D4—21no—
480C2×D4—31no—
481C2×D4—61no—
482C2×D4—62no—
483C2×D4#62611yescharacteristic
484C22×C4—21no—
485C22×C4—32no—
486C22×C4—61no—
487C22×C4—61no—
488C22×C4—181no—
489C22×C4C2×D3211yescharacteristic
490Q16—184no—
491Q16—184no—
492SD16—184no—
493SD16—184no—
494M16—32no—
495M16—61no—
496M16—92no—
497M16—181no—
498C2×C8—61no—
499C2×C8—181no—
500C4⋊C4—62no—
501C4⋊C4—61no—
502C4⋊C4—61no—
503C22⋊C4—62no—
504C22⋊C4—62no—
505C42—61no—
506C42—61no—
507C22×C3—21no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—41no—
515C22×C3—41no—
516C22×C3—42no—
517C22×C3—41no—
518C22×C3—41no—
519C22×C3—41no—
520C22×C3—41no—
521C22×C3—41no—
522C22×C3—41no—
523C22×C3—81no—
524C22×C3—81no—
525C22×C3—121no—
526C22×C3—121no—
527C22×C3—121no—
528C22×C3#88211yescharacteristic
529C22×C3#88411yescharacteristic
530C22×C3#93811yescharacteristic
531C22×C3#94011yescharacteristic
532C22×C3#94011yescharacteristic
533C22×C3#95311yescharacteristic
534C2×D3—41no—
535C2×D3—41no—
536C2×D3—41no—
537C3×C4—21no—
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—21no—
541C3×C4—42no—
542C3×C4—41no—
543C3×C4—41no—
544C3×C4—122no—
545C3×C4—121no—
546C3×C4—122no—
547C3×C4#88211yescharacteristic
548C3×C4#88411yescharacteristic
549C3×C4#93011yescharacteristic
550C3×C4#93711yescharacteristic
551C3×C4#93711yescharacteristic
552C3×C4#93711yescharacteristic
553C3×C4#93911yescharacteristic
554C3×C4#93911yescharacteristic
555Dic3—42no—
556Dic3—41no—
557Dic3—42no—
558Dic3—124no—
559Dic3—122no—
560Dic3—122no—
561C32#200711yescharacteristic, complemented, Sylow
562C23—21no—
563C23—61no—
564C23D3×#6711yescharacteristic
565Q8—21no—
566Q8—21no—
567Q8—61no—
568Q8—61no—
569Q8—182no—
570Q8—182no—
571Q8—361no—
572Q8—361no—
573D4—21no—
574D4—21no—
575D4—41no—
576D4—41no—
577D4—61no—
578D4—61no—
579D4—121no—
580D4—121no—
581D4—242no—
582C2×C4—21no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—62no—
586C2×C4—62no—
587C2×C4—61no—
588C2×C4—121no—
589C2×C4—121no—
590C2×C4—121no—
591C2×C4—121no—
592C2×C4—122no—
593C2×C4—182no—
594C2×C4—361no—
595C2×C4—361no—
596C2×C4#380411yescharacteristic
597C2×C4C2×#62611yescharacteristic
598C2×C4D3×#6711yescharacteristic
599C2×C4D3×#6711yescharacteristic
600C2×C4#381111yescharacteristic
601C2×C4#381111yescharacteristic
602C8—62no—
603C8—182no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—41no—
612C2×C3—41no—
613C2×C3—82no—
614C2×C3—81no—
615C2×C3—81no—
616C2×C3—241no—
617C2×C3#482511yescharacteristic
618C2×C3#482611yescharacteristic
619C2×C3#496011yescharacteristic
620C2×C3#522311yescharacteristic
621C2×C3#524211yescharacteristic
622C2×C3#524611yescharacteristic
623D3—81no—
624C22—21no—
625C22—21no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—121no—
630C22—121no—
631C22—121no—
632C22#6395811yescharacteristic
633C22#6397711yescharacteristic
634C22#6397911yescharacteristic
635C4—41no—
636C4—122no—
637C4—122no—
638C4—121no—
639C4—362no—
640C4#6397111yescharacteristic
641C4#6397811yescharacteristic
642C4#6398111yescharacteristic
643C4#6398311yescharacteristic
644C3—21no—
645C3#7039311yescharacteristic, complemented
646C3#7188111yescharacteristic, complemented
647C2—21no—
648C2—21no—
649C2—81no—
650C2—241no—
651C2#1059168811yescharacteristic
652C2#1059168911yescharacteristic
653C2#1059172411yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC22×C32#120
prime radicalC3×#5833C2
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
1. C2×#64160C2semidirect
3. C2×#63831C2semidirect
4. C2×C3×#837C2semidirect
5. #10591213C2semidirect
6. C2×#63569C2semidirect
7. #10589167C2semidirect
42. C2×#837D3semidirect
63. C2×#634D4semidirect
78. #3748D4semidirect
88. C3×#208D4semidirect
297. #208#67semidirect
561. C32#2007semidirect
645. C3#70393semidirect
646. C3#71881semidirect

Maximal subgroups

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

subgroupindex
C2×#641602
C3×#58332
C2×#638312
C2×C3×#8372
#105912132
C2×#635692
#105891672
#718813
#703933