Finite Group Databasebeta

← #11861112

Subgroups — #11861112

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 643 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64157C211yesmaximal, characteristic, complemented
2C3×#5822C211yesmaximal, characteristic
3C2×#63815C211yesmaximal, characteristic, complemented
4C3×#5236C211yesmaximal, characteristic, complemented
5#10591676C214yesmaximal, complemented
6#10591675C214yesmaximal, complemented
7#10591141C211yesmaximal, characteristic, complemented
8#10591111C211yesmaximal, characteristic, complemented
9#10591057C211yesmaximal, characteristic, complemented
10#83999—31nomaximal
11#78989—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14#64157—21no—
15#64157—21no—
16#64157C2212yescomplemented
17#64157C2212yescomplemented
18C2×#3748—21no—
19C2×#3748C2211yescharacteristic
20C22×C3⋊(C3⋊C8)—21no—
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#951C412yescomplemented
23C3×#950C2214yes—
24C3×#949C412yescomplemented
25C3×#942C412yescomplemented
26C3×#932C412yescomplemented
27C3×#926C2211yescharacteristic
28C2×C3×#208C2211yescharacteristic
29C2×C3×#208C2211yescharacteristic
30C2×#3711—21no—
31#63815—21no—
32#63815—21no—
33#63815C2212yescomplemented
34#63815C2212yescomplemented
35C2×D3×C3⋊C8—21no—
36C3×#837C2214yescomplemented
37#63577C2214yescomplemented
38#63569C2214yescomplemented
39#63554C2212yescomplemented
40Dic3×C3⋊C8C2212yescomplemented
41C3×#575—31no—
42#5822D311yescharacteristic
43C2×#948—31no—
44C2×#948—31no—
45C2×#948—31no—
46C2×#948—61no—
47C2×#907—31no—
48C3×#421—31no—
49#5236—31no—
50#5236D311yescharacteristic, complemented
51#5197—34no—
52#5196—34no—
53#5125—31no—
54#5124—31no—
55#5122—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×C3×#67—21no—
70C3×#235—21no—
71C3×#235—21no—
72C3×#235C2×C412yes—
73C3×#235C2312yes—
74C2×C3×D12C2×C411yescharacteristic
75C2×C3×C4×D3—21no—
76C2×C3×Dic6C2×C411yescharacteristic
77#3748—21no—
78#3748—22no—
79#3748—22no—
80#3748C2312yes—
81C2×C3⋊(C3⋊C8)—21no—
82C2×C3⋊(C3⋊C8)—22no—
83C2×C3⋊(C3⋊C8)—22no—
84C2×C3⋊(C3⋊C8)D411yescharacteristic
85C2×C3⋊(C3⋊C8)D411yescharacteristic
86C2×C3⋊(C3⋊C8)D411yescharacteristic
87C2×C3⋊(C3⋊C8)D411yescharacteristic
88C2×C3⋊(C3⋊C8)C2311yescharacteristic
89C2×C3⋊(C3⋊C8)C2311yescharacteristic
90C3×#217—21no—
91C3×#216C2×C414yes—
92C3×#215C2×C414yes—
93C3×#214C2×C414yes—
94C3×#213C2×C414yes—
95C3×C4⋊Dic3—21no—
96C3×C4×Dic3C2312yes—
97C3×#208—21no—
98C3×#208C2×C412yes—
99C3×#208C2×C412yes—
100C3×#208C2312yes—
101C2×C3×C3⋊C8—21no—
102C2×C3×C3⋊C8C2312yes—
103#3711—22no—
104#3711—22no—
105D3×C3⋊C8—22no—
106D3×C3⋊C8—22no—
107#2955—91noSylow
108C2×C3×#41—21no—
109C2×C3×#41—31no—
110C2×C3×#41C2×D311yescharacteristic
111C2×C3×#41C2×D311yescharacteristic
112C2×#235C2×D311yescharacteristic
113C3×#137—32no—
114C3×#137—32no—
115C3×AGL(1,ℤ/8)—32no—
116C3×AGL(1,ℤ/8)—32no—
117C3×#135—34no—
118C2×C3×M16—31no—
119C2×C3×M16—31no—
120C3×#117—31no—
121#951Dic312yescomplemented
122#950C2×D314yes—
123#949Dic312yescomplemented
124#948—32no—
125#948—32no—
126#948—32no—
127#948—32no—
128#948—32no—
129#948—32no—
130#948—62no—
131#948—62no—
132#948—61no—
133#948—61no—
134#948—61no—
135#948—61no—
136#948—61no—
137#948—61no—
138#948—62no—
139#948—62no—
140#942Dic312yescomplemented
141#932Dic312yescomplemented
142#926C2×D311yescharacteristic
143C2×#208—31no—
144C2×#208—31no—
145C2×#208—61no—
146C2×#208—61no—
147C2×#208—61no—
148C2×#208—61no—
149C2×#208—62no—
150C2×#208C2×D311yescharacteristic
151C2×#208C2×D311yescharacteristic
152C22×C3⋊C8—31no—
153C22×C3⋊C8—31no—
154C22×C3⋊C8—61no—
155C22×C3⋊C8—61no—
156C22×C3⋊C8—61no—
157C22×C3⋊C8—61no—
158C22×C3⋊C8—62no—
159#907—32no—
160#907—32no—
161#907—61no—
162#907—61no—
163C2×ΓL(1,𝔽25)—61no—
164C2×D3×C8—61no—
165C3×#104—34no—
166#837—34no—
167#837C2×D314yescomplemented
168#822—34no—
169#819—34no—
170#815—32no—
171C8×Dic3—32no—
172#805—34no—
173#803—32no—
174C4×C3⋊C8—32no—
175C23×C32—21no—
176C23×C32#4111yescharacteristic
177C22×C3×D3—21no—
178C32×Q8—21no—
179C32×Q8C22×C412yes—
180C32×D4—22no—
181C32×D4—22no—
182C32×D4—21no—
183C32×D4C22×C412yes—
184C2×C32×C4—21no—
185C2×C32×C4—22no—
186C2×C32×C4—22no—
187C2×C32×C4C22×C411yescharacteristic
188C2×C32×C4C22×C411yescharacteristic
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4#4111yescharacteristic
192C2×C32×C4C2411yescharacteristic
193C3×#67—22no—
194C3×#67—22no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—22no—
197C3×D12—21no—
198C3×D12C22×C412yes—
199C3×C4×D3—22no—
200C3×C4×D3—22no—
201C3×Dic6—21no—
202C3×Dic6C22×C412yes—
203C3⋊(C3⋊C8)—22no—
204C3⋊(C3⋊C8)C2×D411yescharacteristic
205C3⋊(C3⋊C8)C2×D411yescharacteristic
206C3⋊(C3⋊C8)C2×D411yescharacteristic
207C3⋊(C3⋊C8)C2×D411yescharacteristic
208C3×C3⋊C8—22no—
209C3×C3⋊C8C22×C414yes—
210#575—31no—
211C2×#131—91no—
212C2×#131—91no—
213#444—94no—
214#443—94no—
215#430—91no—
216#421—31no—
217#421—91no—
218#405—91no—
219C3×#41—22no—
220C3×#41—22no—
221C3×#41—21no—
222C3×#41—21no—
223C3×#41—21no—
224C3×#41—21no—
225C3×#41—22no—
226C3×#41—22no—
227C3×#41—32no—
228C3×#41—32no—
229C3×#41—61no—
230C3×#41—61no—
231C3×#41C4×D312yes—
232C3×#41C2×Dic312yes—
233C3×#41C22×D312yes—
234C3×#41C22×D312yes—
235C2×C3×Q8—21no—
236C2×C3×Q8—31no—
237C2×C3×Q8C4×D311yescharacteristic
238C2×C3×Q8C2×Dic311yescharacteristic
239C2×C3×D4—22no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—31no—
244C2×C3×D4—61no—
245C2×C3×D4C4×D311yescharacteristic
246C2×C3×D4C2×Dic311yescharacteristic
247C22×C3×C4—22no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—61no—
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C22×D311yescharacteristic
254C2×#67—21no—
255#235—21no—
256#235—21no—
257#235C2×Dic312yes—
258#235C22×D312yes—
259C2×D12C2×Dic311yescharacteristic
260C2×C4×D3—21no—
261C2×Dic6C2×Dic311yescharacteristic
262C3×Q16—34no—
263C3×SD16—34no—
264C3×SD16—34no—
265C3×D8—34no—
266C3×M16—32no—
267C3×M16—32no—
268C3×M16—32no—
269C3×M16—61no—
270C2×C3×C8—32no—
271C2×C3×C8—61no—
272C3×C4⋊C4—61no—
273C3×C22⋊C4—61no—
274C3×C42—32no—
275#217—21no—
276#216C2×Dic314yes—
277#215C2×Dic314yes—
278#214C2×Dic314yes—
279#213C2×Dic314yes—
280C4⋊Dic3—21no—
281C4×Dic3C22×D312yes—
282#208—21no—
283#208—32no—
284#208—32no—
285#208—62no—
286#208—62no—
287#208—62no—
288#208—62no—
289#208—62no—
290#208—62no—
291#208—62no—
292#208—64no—
293#208—64no—
294#208—62no—
295#208—61no—
296#208—61no—
297#208C2×Dic312yes—
298#208C2×Dic312yes—
299#208C22×D312yes—
300C2×C3⋊C8—21no—
301C2×C3⋊C8—31no—
302C2×C3⋊C8—31no—
303C2×C3⋊C8—31no—
304C2×C3⋊C8—31no—
305C2×C3⋊C8—31no—
306C2×C3⋊C8—31no—
307C2×C3⋊C8—31no—
308C2×C3⋊C8—31no—
309C2×C3⋊C8—31no—
310C2×C3⋊C8—31no—
311C2×C3⋊C8—31no—
312C2×C3⋊C8—31no—
313C2×C3⋊C8—61no—
314C2×C3⋊C8—61no—
315C2×C3⋊C8—61no—
316C2×C3⋊C8—61no—
317C2×C3⋊C8—61no—
318C2×C3⋊C8—61no—
319C2×C3⋊C8—62no—
320C2×C3⋊C8—62no—
321C2×C3⋊C8—62no—
322C2×C3⋊C8—62no—
323C2×C3⋊C8—62no—
324C2×C3⋊C8—62no—
325C2×C3⋊C8—62no—
326C2×C3⋊C8—64no—
327C2×C3⋊C8—64no—
328C2×C3⋊C8—61no—
329C2×C3⋊C8—61no—
330C2×C3⋊C8C22×D312yes—
331ΓL(1,𝔽25)—62no—
332ΓL(1,𝔽25)—62no—
333D3×C8—62no—
334D3×C8—62no—
335C22×C32—22no—
336C22×C32—41no—
337C22×C32—42no—
338C22×C32C4×D411yescharacteristic
339C22×C32C4×D411yescharacteristic
340C22×C32C2×#4111yescharacteristic
341C2×C3×D3—22no—
342C2×C3×D3—42no—
343C32×C4—22no—
344C32×C4C4×D411yescharacteristic
345C32×C4C4×D411yescharacteristic
346C32×C4C23×C411yescharacteristic
347C32×C4C22×D411yescharacteristic
348C3×Dic3—22no—
349C3×Dic3—42no—
350C2×#41—31no—
351C2×#41D3211yescharacteristic
352#137—32no—
353#137—32no—
354AGL(1,ℤ/8)—32no—
355AGL(1,ℤ/8)—32no—
356#135—34no—
357#131—92no—
358#131—92no—
359#131—92no—
360#131—92no—
361#131—181no—
362#131—181no—
363#131—181no—
364#131—181no—
365C2×M16—31no—
366C2×M16—31no—
367C2×M16—91no—
368C2×M16—181no—
369C2×M16—181no—
370C22×C8—91no—
371C22×C8—181no—
372C22×C8—181no—
373#117—31no—
374#108—94no—
375#104—34no—
376#104—94no—
377#97—92no—
378C4×C8—92no—
379C23×C3—22no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—61no—
384C23×C3#23711yescharacteristic
385C23×C3#23711yescharacteristic
386C22×D3—21no—
387C3×Q8—22no—
388C3×Q8—21no—
389C3×Q8—21no—
390C3×Q8—22no—
391C3×Q8—32no—
392C3×Q8—61no—
393C3×Q8C2×C4×D312yes—
394C3×Q8C22×Dic312yes—
395C3×D4—24no—
396C3×D4—24no—
397C3×D4—22no—
398C3×D4—22no—
399C3×D4—22no—
400C3×D4—22no—
401C3×D4—22no—
402C3×D4—21no—
403C3×D4—21no—
404C3×D4—22no—
405C3×D4—32no—
406C3×D4—62no—
407C3×D4—62no—
408C3×D4—61no—
409C3×D4C2×C4×D312yes—
410C3×D4C22×Dic312yes—
411C2×C3×C4—24no—
412C2×C3×C4—22no—
413C2×C3×C4—24no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—61no—
427C2×C3×C4—62no—
428C2×C3×C4—62no—
429C2×C3×C4—62no—
430C2×C3×C4C2×C4×D311yescharacteristic
431C2×C3×C4C2×C4×D311yescharacteristic
432C2×C3×C4D3×D411yescharacteristic
433C2×C3×C4D3×D411yescharacteristic
434C2×C3×C4D3×D411yescharacteristic
435C2×C3×C4D3×D411yescharacteristic
436C2×C3×C4#23711yescharacteristic
437C2×C3×C4#23711yescharacteristic
438C2×C3×C4C22×Dic311yescharacteristic
439C2×C3×C4C22×Dic311yescharacteristic
440C2×C3×C4C23×D311yescharacteristic
441C2×C3×C4C23×D311yescharacteristic
442#67—22no—
443#67—22no—
444C2×Dic3—21no—
445C2×Dic3—22no—
446D12—21no—
447D12C22×Dic312yes—
448C4×D3—22no—
449C4×D3—22no—
450Dic6—21no—
451Dic6C22×Dic312yes—
452C3×C8—34no—
453C3×C8—62no—
454C3⋊C8—22no—
455C3⋊C8—31no—
456C3⋊C8—31no—
457C3⋊C8—31no—
458C3⋊C8—31no—
459C3⋊C8—31no—
460C3⋊C8—31no—
461C3⋊C8—31no—
462C3⋊C8—31no—
463C3⋊C8—61no—
464C3⋊C8—61no—
465C3⋊C8—61no—
466C3⋊C8—61no—
467C3⋊C8—64no—
468C3⋊C8—62no—
469C3⋊C8—62no—
470C3⋊C8C22×Dic314yes—
471C2×C32—21no—
472C2×C32—21no—
473C2×C32—21no—
474C2×C32—42no—
475C2×C32C2×C4×D411yescharacteristic
476C3×D3—42no—
477#41—21no—
478#41—21no—
479#41—32no—
480#41—32no—
481#41—61no—
482#41—61no—
483#41D3×Dic312yes—
484#41C2×D3212yes—
485C2×Q8—31no—
486C2×Q8D3×Dic311yescharacteristic
487C2×D4—21no—
488C2×D4—31no—
489C2×D4—61no—
490C2×D4D3×Dic311yescharacteristic
491C22×C4—21no—
492C22×C4—61no—
493C22×C4C2×D3211yescharacteristic
494Q16—34no—
495SD16—34no—
496SD16—34no—
497D8—34no—
498M16—32no—
499M16—32no—
500M16—32no—
501M16—61no—
502M16—92no—
503M16—182no—
504M16—182no—
505M16—182no—
506M16—182no—
507M16—181no—
508C2×C8—32no—
509C2×C8—61no—
510C2×C8—91no—
511C2×C8—91no—
512C2×C8—91no—
513C2×C8—91no—
514C2×C8—91no—
515C2×C8—91no—
516C2×C8—182no—
517C2×C8—182no—
518C2×C8—182no—
519C2×C8—182no—
520C2×C8—181no—
521C4⋊C4—61no—
522C22⋊C4—61no—
523C42—32no—
524C22×C3—24no—
525C22×C3—22no—
526C22×C3—22no—
527C22×C3—21no—
528C22×C3—21no—
529C22×C3—21no—
530C22×C3—41no—
531C22×C3—41no—
532C22×C3—42no—
533C22×C3—44no—
534C22×C3—42no—
535C22×C3—42no—
536C22×C3—62no—
537C22×C3—122no—
538C22×C3#67⋊C411yescharacteristic
539C22×C3#67⋊C411yescharacteristic
540C22×C3D4×Dic311yescharacteristic
541C22×C3D4×Dic311yescharacteristic
542C22×C3C2×#23711yescharacteristic
543C22×C3C2×#23711yescharacteristic
544C2×D3—22no—
545C2×D3—42no—
546C3×C4—24no—
547C3×C4—22no—
548C3×C4—22no—
549C3×C4—21no—
550C3×C4—21no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4—62no—
554C3×C4—122no—
555C3×C4#67⋊C411yescharacteristic
556C3×C4#67⋊C411yescharacteristic
557C3×C4D4×Dic311yescharacteristic
558C3×C4D4×Dic311yescharacteristic
559C3×C4C22×C4×D311yescharacteristic
560C3×C4C2×D3×D411yescharacteristic
561C3×C4C2×D3×D411yescharacteristic
562C3×C4C23×Dic311yescharacteristic
563Dic3—22no—
564Dic3—42no—
565C32#295511yescharacteristic, complemented, Sylow
566C23—21no—
567C23—61no—
568C23#380511yescharacteristic
569Q8—21no—
570Q8—32no—
571Q8—61no—
572Q8C2×D3×Dic312yes—
573D4—22no—
574D4—22no—
575D4—21no—
576D4—32no—
577D4—62no—
578D4—62no—
579D4—61no—
580D4C2×D3×Dic312yes—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—61no—
585C2×C4—62no—
586C2×C4—62no—
587C2×C4—62no—
588C2×C4C2×D3×Dic311yescharacteristic
589C2×C4C2×D3×Dic311yescharacteristic
590C2×C4#380511yescharacteristic
591C2×C4#381111yescharacteristic
592C2×C4#381111yescharacteristic
593C2×C4C22×D3211yescharacteristic
594C8—34no—
595C8—62no—
596C8—91no—
597C8—91no—
598C8—91no—
599C8—91no—
600C8—182no—
601C2×C3—22no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—41no—
610C2×C3—41no—
611C2×C3—44no—
612C2×C3—42no—
613C2×C3—42no—
614C2×C3—122no—
615C2×C3C2×#67⋊C411yescharacteristic
616C2×C3C2×D4×Dic311yescharacteristic
617D3—42no—
618C22—22no—
619C22—41no—
620C22—42no—
621C22—62no—
622C22—122no—
623C22#67⋊Dic311yescharacteristic
624C22#67⋊Dic311yescharacteristic
625C22C2×#380511yescharacteristic
626C4—22no—
627C4—62no—
628C4—122no—
629C4#67⋊Dic311yescharacteristic
630C4#67⋊Dic311yescharacteristic
631C4C22×D3×Dic311yescharacteristic
632C4C2×#381111yescharacteristic
633C3—21no—
634C3#7898911yescharacteristic, complemented
635C3#8399911yescharacteristic, complemented
636C2—21no—
637C2—21no—
638C2—21no—
639C2—42no—
640C2—122no—
641C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
centerC4C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×C4×D4
prime radicalC3×#5822C2
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
1. C2×#64157C2semidirect
3. C2×#63815C2semidirect
4. C3×#5236C2semidirect
5. #10591676C2semidirect
6. #10591675C2semidirect
7. #10591141C2semidirect
8. #10591111C2semidirect
9. #10591057C2semidirect
16. #64157C22semidirect
17. #64157C22semidirect
22. C3×#951C4semidirect
24. C3×#949C4semidirect
25. C3×#942C4semidirect
26. C3×#932C4semidirect
33. #63815C22semidirect
34. #63815C22semidirect
36. C3×#837C22semidirect
37. #63577C22semidirect
38. #63569C22semidirect
39. #63554C22semidirect
40. Dic3×C3⋊C8C22semidirect
50. #5236D3semidirect
121. #951Dic3semidirect
123. #949Dic3semidirect
140. #942Dic3semidirect
141. #932Dic3semidirect
167. #837C2×D3semidirect
565. C32#2955semidirect
634. C3#78989semidirect
635. C3#83999semidirect

Maximal subgroups

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

subgroupindex
C2×#641572
C3×#58222
C2×#638152
C3×#52362
#105916762
#105916752
#105911412
#105911112
#105910572
#839993
#789893