Finite Group Databasebeta

← #11861113

Subgroups — #11861113

Order 1152.

1043 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596293C211yesmaximal, characteristic
2C2×C3×#948C211yesmaximal, characteristic, complemented
3C2×#63817C211yesmaximal, characteristic, complemented
4C3×#5236C211yesmaximal, characteristic, complemented
5#10591663C214yesmaximal, complemented
6#10591662C214yesmaximal, complemented
7#10591143C211yesmaximal, characteristic, complemented
8#10591113C211yesmaximal, characteristic, complemented
9#10591055C211yesmaximal, characteristic, complemented
10#83792—31nomaximal
11#78989—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C2×#3828C2211yescharacteristic
14#64160C412yescomplemented
15#64159C2214yes—
16#64158C412yescomplemented
17#64151C412yescomplemented
18#64141C412yescomplemented
19C2×#3748C2211yescharacteristic
20C3×#948—21no—
21C3×#948—21no—
22C3×#948C2212yescomplemented
23C3×#948C2212yescomplemented
24C3×#926C2211yescharacteristic
25C2×C3×#208—21no—
26C2×C3×#208C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28C22×C3×C3⋊C8—21no—
29C22×C3×C3⋊C8C2211yescharacteristic
30C2×#3712—21no—
31#63817—21no—
32#63817—21no—
33#63817C2212yescomplemented
34#63817C2212yescomplemented
35C2×#3710—21no—
36C3×#837C2214yescomplemented
37#63578C2214yescomplemented
38#63570C2214yescomplemented
39#63554C2212yescomplemented
40Dic3×C3⋊C8C2212yescomplemented
41C2×C3×#131—31no—
42#5822—31no—
43#5822—31no—
44#5822—61no—
45C2×#948D311yescharacteristic, complemented
46C2×#907—31no—
47C2×#901—31no—
48C3×#421—31no—
49#5236D311yescharacteristic, complemented
50#5145—34no—
51#5144—34no—
52#5139—31no—
53#5124—31no—
54#5124—31no—
55#5101—31no—
56#5005—31no—
57#4997—31no—
58#4824—34no—
59#4823—34no—
60C32×#41—21no—
61C32×#41—21no—
62C32×#41C2×C412yes—
63C32×#41C2312yes—
64C2×C32×Q8C2×C411yescharacteristic
65C2×C32×D4—21no—
66C2×C32×D4C2×C411yescharacteristic
67C22×C32×C4—21no—
68C22×C32×C4C2311yescharacteristic
69C2×#638—21no—
70#3828—21no—
71#3828—21no—
72#3828C2×C412yes—
73#3828C2312yes—
74C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
75C2×C4×C3⋊D3—21no—
76C2×#634C2×C411yescharacteristic
77#3756C2×C414yes—
78#3755C2×C414yes—
79#3754C2×C414yes—
80#3753C2×C414yes—
81#3748C2×C412yes—
82#3748C2×C412yes—
83C2×C3⋊(C3⋊C8)C2312yes—
84C3×#217—21no—
85C3×C4⋊Dic3—21no—
86C3×C4×Dic3C2312yes—
87C3×#208—21no—
88C3×#208—21no—
89C3×#208—22no—
90C3×#208—22no—
91C3×#208C2312yes—
92C3×#208C2312yes—
93C2×C3×C3⋊C8—21no—
94C2×C3×C3⋊C8—21no—
95C2×C3×C3⋊C8—22no—
96C2×C3×C3⋊C8—22no—
97C2×C3×C3⋊C8D411yescharacteristic
98C2×C3×C3⋊C8D411yescharacteristic
99C2×C3×C3⋊C8D411yescharacteristic
100C2×C3×C3⋊C8D411yescharacteristic
101C2×C3×C3⋊C8C2311yescharacteristic
102C2×C3×C3⋊C8C2311yescharacteristic
103#3712—22no—
104#3712—22no—
105#3710—22no—
106#3710—22no—
107#2955—91noSylow
108C2×C3×#41—21no—
109C2×C3×#41C2×D311yescharacteristic
110C2×C3×#41C2×D311yescharacteristic
111C2×#235—31no—
112C2×#235—31no—
113C2×#235—61no—
114C3×#131—32no—
115C3×#131—32no—
116C3×#131—61no—
117C3×#131—61no—
118C2×C3×M16—31no—
119C2×C3×M16—31no—
120C2×C3×M16—61no—
121C22×C3×C8—31no—
122C22×C3×C8—61no—
123C3×#117—31no—
124#951—32no—
125#951—32no—
126#951—62no—
127#950—34no—
128#950—34no—
129#950—64no—
130#949—32no—
131#949—32no—
132#949—62no—
133#948—21no—
134#948—21no—
135#948C2×D312yescomplemented
136#948C2×D312yescomplemented
137#942—32no—
138#942—32no—
139#942—62no—
140#932—32no—
141#932—32no—
142#932—62no—
143#926C2×D311yescharacteristic
144C2×#208—21no—
145C2×#208—31no—
146C2×#208—31no—
147C2×#208—61no—
148C2×#208C2×D311yescharacteristic
149C2×#208C2×D311yescharacteristic
150C22×C3⋊C8—21no—
151C22×C3⋊C8C2×D311yescharacteristic
152#907—32no—
153#907—32no—
154#907—61no—
155#907—61no—
156#901—32no—
157#901—32no—
158#901—61no—
159#901—61no—
160C2×ΓL(1,𝔽25)—61no—
161C2×ΓL(1,𝔽25)—61no—
162C2×D3×C8—61no—
163C2×D3×C8—61no—
164C3×#104—34no—
165#837C2×D314yescomplemented
166#825—34no—
167#822—34no—
168#822—34no—
169#815—32no—
170C8×Dic3—32no—
171#805—34no—
172#803—32no—
173C4×C3⋊C8—32no—
174C23×C32—21no—
175C23×C32#4111yescharacteristic
176C22×C3⋊D3—21no—
177C32×Q8—21no—
178C32×Q8C22×C412yes—
179C32×D4—22no—
180C32×D4—22no—
181C32×D4—21no—
182C32×D4C22×C412yes—
183C2×C32×C4—21no—
184C2×C32×C4—22no—
185C2×C32×C4—22no—
186C2×C32×C4C22×C411yescharacteristic
187C2×C32×C4C22×C411yescharacteristic
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4#4111yescharacteristic
191C2×C32×C4C2411yescharacteristic
192#638—22no—
193#638—22no—
194C2×C3⋊Dic3—21no—
195C4⋊(C3⋊D3)—21no—
196C4⋊(C3⋊D3)C22×C412yes—
197C4×C3⋊D3—22no—
198C4×C3⋊D3—22no—
199#634—21no—
200#634C22×C412yes—
201C2×C3×Dic3—22no—
202C3⋊(C3⋊C8)C22×C414yes—
203C3×C3⋊C8—22no—
204C3×C3⋊C8—22no—
205C3×C3⋊C8C2×D411yescharacteristic
206C3×C3⋊C8C2×D411yescharacteristic
207C3×C3⋊C8C2×D411yescharacteristic
208C3×C3⋊C8C2×D411yescharacteristic
209#575—91no—
210C2×#131—31no—
211C2×#131—91no—
212#444—94no—
213#443—94no—
214#430—91no—
215#421—31no—
216#421—91no—
217#405—91no—
218C3×#41—21no—
219C3×#41—21no—
220C3×#41—21no—
221C3×#41—21no—
222C3×#41—22no—
223C3×#41—22no—
224C3×#41—41no—
225C3×#41—41no—
226C3×#41C4×D312yes—
227C3×#41C4×D312yes—
228C3×#41C22×D312yes—
229C3×#41C22×D312yes—
230C2×C3×Q8—21no—
231C2×C3×Q8C4×D311yescharacteristic
232C2×C3×Q8C4×D311yescharacteristic
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—41no—
237C2×C3×D4C4×D311yescharacteristic
238C2×C3×D4C4×D311yescharacteristic
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—41no—
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C2×#67—61no—
246C2×#67—61no—
247C2×#67—121no—
248#235—32no—
249#235—32no—
250#235—32no—
251#235—32no—
252#235—62no—
253#235—62no—
254#235—61no—
255#235—61no—
256#235—61no—
257#235—61no—
258#235—121no—
259#235—121no—
260C2×D12—31no—
261C2×D12—31no—
262C2×D12—61no—
263C2×C4×D3—61no—
264C2×C4×D3—61no—
265C2×C4×D3—121no—
266C2×Dic6—31no—
267C2×Dic6—31no—
268C2×Dic6—61no—
269C3×M16—32no—
270C3×M16—32no—
271C3×M16—62no—
272C3×M16—62no—
273C3×M16—61no—
274C3×M16—61no—
275C2×C3×C8—31no—
276C2×C3×C8—31no—
277C2×C3×C8—31no—
278C2×C3×C8—31no—
279C2×C3×C8—31no—
280C2×C3×C8—31no—
281C2×C3×C8—62no—
282C2×C3×C8—62no—
283C2×C3×C8—61no—
284C2×C3×C8—61no—
285C3×C4⋊C4—61no—
286C3×C22⋊C4—61no—
287C3×C42—32no—
288#217—21no—
289#216—34no—
290#216—34no—
291#216—64no—
292#215—34no—
293#215—34no—
294#215—64no—
295#214—34no—
296#214—34no—
297#214—64no—
298#213—34no—
299#213—34no—
300#213—64no—
301C4⋊Dic3—21no—
302C4×Dic3C22×D312yes—
303#208—21no—
304#208—21no—
305#208—22no—
306#208—22no—
307#208—32no—
308#208—32no—
309#208—32no—
310#208—32no—
311#208—62no—
312#208—62no—
313#208C22×D312yes—
314#208C22×D312yes—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—22no—
318C2×C3⋊C8—22no—
319C2×C3⋊C8—32no—
320C2×C3⋊C8—32no—
321C2×C3⋊C8—62no—
322C2×C3⋊C8#6711yescharacteristic
323C2×C3⋊C8#6711yescharacteristic
324C2×C3⋊C8#6711yescharacteristic
325C2×C3⋊C8#6711yescharacteristic
326C2×C3⋊C8C22×D311yescharacteristic
327C2×C3⋊C8C22×D311yescharacteristic
328ΓL(1,𝔽25)—62no—
329ΓL(1,𝔽25)—62no—
330ΓL(1,𝔽25)—62no—
331ΓL(1,𝔽25)—62no—
332D3×C8—62no—
333D3×C8—62no—
334D3×C8—62no—
335D3×C8—62no—
336C22×C32—22no—
337C22×C32—41no—
338C22×C32—42no—
339C22×C32C4×D411yescharacteristic
340C22×C32C4×D411yescharacteristic
341C22×C32C2×#4111yescharacteristic
342C2×C3⋊D3—22no—
343C2×C3⋊D3—42no—
344C32×C4—22no—
345C32×C4C4×D411yescharacteristic
346C32×C4C4×D411yescharacteristic
347C32×C4C23×C411yescharacteristic
348C32×C4C22×D411yescharacteristic
349C3⋊Dic3—22no—
350C3×Dic3—42no—
351C2×#41—91no—
352C2×#41D3211yescharacteristic
353#137—92no—
354#137—92no—
355AGL(1,ℤ/8)—92no—
356AGL(1,ℤ/8)—92no—
357#135—94no—
358#131—32no—
359#131—32no—
360#131—61no—
361#131—61no—
362#131—92no—
363#131—92no—
364#131—181no—
365#131—181no—
366C2×M16—31no—
367C2×M16—31no—
368C2×M16—61no—
369C2×M16—91no—
370C2×M16—181no—
371C22×C8—31no—
372C22×C8—61no—
373C22×C8—181no—
374#117—31no—
375#108—94no—
376#104—34no—
377#104—94no—
378#97—92no—
379C4×C8—92no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—41no—
384C23×C3#23511yescharacteristic
385C23×C3#23711yescharacteristic
386C22×D3—61no—
387C22×D3—61no—
388C22×D3—121no—
389C3×Q8—21no—
390C3×Q8—21no—
391C3×Q8—22no—
392C3×Q8—41no—
393C3×Q8C2×C4×D312yes—
394C3×Q8C2×C4×D312yes—
395C3×D4—22no—
396C3×D4—22no—
397C3×D4—22no—
398C3×D4—22no—
399C3×D4—21no—
400C3×D4—21no—
401C3×D4—22no—
402C3×D4—41no—
403C3×D4—42no—
404C3×D4—42no—
405C3×D4C2×C4×D312yes—
406C3×D4C2×C4×D312yes—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—42no—
420C2×C3×C4—42no—
421C2×C3×C4—41no—
422C2×C3×C4—62no—
423C2×C3×C4C2×C4×D311yescharacteristic
424C2×C3×C4C2×C4×D311yescharacteristic
425C2×C3×C4C2×C4×D311yescharacteristic
426C2×C3×C4C2×C4×D311yescharacteristic
427C2×C3×C4#23511yescharacteristic
428C2×C3×C4D3×D411yescharacteristic
429C2×C3×C4D3×D411yescharacteristic
430C2×C3×C4#23711yescharacteristic
431C2×C3×C4C2×#6711yescharacteristic
432C2×C3×C4C2×#6711yescharacteristic
433C2×C3×C4C23×D311yescharacteristic
434C2×C3×C4C23×D311yescharacteristic
435#67—62no—
436#67—62no—
437#67—62no—
438#67—62no—
439#67—122no—
440#67—122no—
441C2×Dic3—22no—
442C2×Dic3—61no—
443C2×Dic3—61no—
444C2×Dic3—121no—
445D12—32no—
446D12—32no—
447D12—62no—
448D12—61no—
449D12—61no—
450D12—121no—
451C4×D3—62no—
452C4×D3—62no—
453C4×D3—62no—
454C4×D3—62no—
455C4×D3—122no—
456C4×D3—122no—
457Dic6—32no—
458Dic6—32no—
459Dic6—62no—
460Dic6—61no—
461Dic6—61no—
462Dic6—121no—
463C3×C8—31no—
464C3×C8—31no—
465C3×C8—31no—
466C3×C8—31no—
467C3×C8—62no—
468C3×C8—62no—
469C3⋊C8—22no—
470C3⋊C8—22no—
471C3⋊C8—34no—
472C3⋊C8—34no—
473C3⋊C8—64no—
474C3⋊C8C2×#6711yescharacteristic
475C3⋊C8C2×#6711yescharacteristic
476C3⋊C8C2×#6711yescharacteristic
477C3⋊C8C2×#6711yescharacteristic
478C2×C32—21no—
479C2×C32—21no—
480C2×C32—21no—
481C2×C32—42no—
482C2×C32C2×C4×D411yescharacteristic
483C3⋊D3—42no—
484#41—21no—
485#41—21no—
486#41—92no—
487#41—92no—
488#41—181no—
489#41—181no—
490#41#62412yes—
491#41C2×D3212yes—
492C2×Q8—91no—
493C2×Q8#62411yescharacteristic
494C2×D4—21no—
495C2×D4—91no—
496C2×D4—181no—
497C2×D4#62411yescharacteristic
498C22×C4—21no—
499C22×C4—181no—
500C22×C4C2×D3211yescharacteristic
501Q16—94no—
502SD16—94no—
503SD16—94no—
504D8—94no—
505M16—32no—
506M16—32no—
507M16—62no—
508M16—62no—
509M16—61no—
510M16—61no—
511M16—92no—
512M16—92no—
513M16—182no—
514M16—182no—
515C2×C8—31no—
516C2×C8—31no—
517C2×C8—31no—
518C2×C8—31no—
519C2×C8—31no—
520C2×C8—31no—
521C2×C8—62no—
522C2×C8—62no—
523C2×C8—61no—
524C2×C8—61no—
525C2×C8—92no—
526C2×C8—182no—
527C2×C8—182no—
528C4⋊C4—61no—
529C22⋊C4—61no—
530C42—32no—
531C22×C3—22no—
532C22×C3—22no—
533C22×C3—21no—
534C22×C3—21no—
535C22×C3—21no—
536C22×C3—42no—
537C22×C3—41no—
538C22×C3—41no—
539C22×C3—42no—
540C22×C3—42no—
541C22×C3—81no—
542C22×C3—82no—
543C22×C3#67⋊C411yescharacteristic
544C22×C3#67⋊C411yescharacteristic
545C22×C3C4×#6711yescharacteristic
546C22×C3C4×#6711yescharacteristic
547C22×C3C2×#23511yescharacteristic
548C22×C3C2×#23711yescharacteristic
549C2×D3—62no—
550C2×D3—62no—
551C2×D3—122no—
552C2×D3—122no—
553C2×D3—122no—
554C2×D3—242no—
555C3×C4—22no—
556C3×C4—22no—
557C3×C4—21no—
558C3×C4—21no—
559C3×C4—21no—
560C3×C4—21no—
561C3×C4—42no—
562C3×C4—122no—
563C3×C4#67⋊C411yescharacteristic
564C3×C4#67⋊C411yescharacteristic
565C3×C4C4×#6711yescharacteristic
566C3×C4C4×#6711yescharacteristic
567C3×C4C22×C4×D311yescharacteristic
568C3×C4C22×C4×D311yescharacteristic
569C3×C4C2×D3×D411yescharacteristic
570C3×C4C22×#6711yescharacteristic
571Dic3—42no—
572Dic3—62no—
573Dic3—62no—
574Dic3—122no—
575C32#295511yescharacteristic, complemented, Sylow
576C23—21no—
577C23—181no—
578C23#380411yescharacteristic
579Q8—21no—
580Q8—92no—
581Q8—181no—
582Q8C2×#62412yes—
583D4—22no—
584D4—22no—
585D4—21no—
586D4—92no—
587D4—182no—
588D4—182no—
589D4—181no—
590D4C2×#62412yes—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—62no—
595C2×C4—181no—
596C2×C4—182no—
597C2×C4—182no—
598C2×C4#380411yescharacteristic
599C2×C4C2×#62411yescharacteristic
600C2×C4C2×#62411yescharacteristic
601C2×C4D3×#6711yescharacteristic
602C2×C4D3×#6711yescharacteristic
603C2×C4C22×D3211yescharacteristic
604C8—31no—
605C8—31no—
606C8—31no—
607C8—31no—
608C8—62no—
609C8—62no—
610C8—94no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—21no—
616C2×C3—21no—
617C2×C3—21no—
618C2×C3—41no—
619C2×C3—41no—
620C2×C3—41no—
621C2×C3—42no—
622C2×C3—42no—
623C2×C3—82no—
624C2×C3C2×#67⋊C411yescharacteristic
625C2×C3C2×C4×#6711yescharacteristic
626D3—122no—
627D3—122no—
628D3—242no—
629C22—22no—
630C22—41no—
631C22—42no—
632C22—182no—
633C22—362no—
634C22#6395211yescharacteristic
635C22#6395211yescharacteristic
636C22C2×#380411yescharacteristic
637C4—22no—
638C4—122no—
639C4—182no—
640C4#6395211yescharacteristic
641C4#6395211yescharacteristic
642C4C22×#62411yescharacteristic
643C4C2×D3×#6711yescharacteristic
644C3—21no—
645C3#7898911yescharacteristic, complemented
646C3#8379211yescharacteristic, complemented
647C2—21no—
648C2—21no—
649C2—21no—
650C2—42no—
651C2—362no—
652C2C2×#6395211yescharacteristic
subgroupG/H
centerC4C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×C4×D4
prime radical#10596293C2
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32#2955
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×C3×#948C2semidirect
3. C2×#63817C2semidirect
4. C3×#5236C2semidirect
5. #10591663C2semidirect
6. #10591662C2semidirect
7. #10591143C2semidirect
8. #10591113C2semidirect
9. #10591055C2semidirect
14. #64160C4semidirect
16. #64158C4semidirect
17. #64151C4semidirect
18. #64141C4semidirect
22. C3×#948C22semidirect
23. C3×#948C22semidirect
33. #63817C22semidirect
34. #63817C22semidirect
36. C3×#837C22semidirect
37. #63578C22semidirect
38. #63570C22semidirect
39. #63554C22semidirect
40. Dic3×C3⋊C8C22semidirect
45. C2×#948D3semidirect
49. #5236D3semidirect
135. #948C2×D3semidirect
136. #948C2×D3semidirect
165. #837C2×D3semidirect
575. C32#2955semidirect
645. C3#78989semidirect
646. C3#83792semidirect

Maximal subgroups

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

subgroupindex
#105962932
C2×C3×#9482
C2×#638172
C3×#52362
#105916632
#105916622
#105911432
#105911132
#105910552
#837923
#789893