Finite Group Databasebeta

← #11859486

Subgroups — #11859486

Order 1152.

1067 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63803C212yesmaximal, complemented
2#10593968C211yesmaximal, characteristic
3C8×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4C3×C8×D12C211yesmaximal, characteristic, complemented
5C3×C4×D3×C8C211yesmaximal, characteristic, complemented
6#10590953C212yesmaximal, complemented
7#10590730C212yesmaximal, complemented
8C8×#626C212yesmaximal, complemented
9#10590338C211yesmaximal, characteristic, complemented
10#10590337C211yesmaximal, characteristic, complemented
11#10590336C211yesmaximal, characteristic, complemented
12#79422—31nomaximal
13#78458—31nomaximal
14C2×#3798C2212yes—
15C2×C8×C3⋊D3C2212yes—
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C3×D3×C8C2211yescharacteristic
18C2×C3×D3×C8C2212yes—
19C2×C3×D3×C8C2211yescharacteristic
20C3×C4×D12C2211yescharacteristic
21C3×C42×D3C2211yescharacteristic
22#63918C411yescharacteristic
23#63911C411yescharacteristic
24#63909C411yescharacteristic
25#63908C411yescharacteristic
26#63906C412yes—
27C4×#626C2212yes—
28#63852C412yes—
29C2×#3712C2212yes—
30C2×#3711C2212yes—
31C2×#3711C2212yes—
32#63803—28no—
33C32×C4×C8C2211yescharacteristic
34#63647C2212yes—
35C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
36C3×(C2×D3)⋊C8C2212yes—
37C3×C8×Dic3C2211yescharacteristic
38C3×C8×Dic3C2211yescharacteristic
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40C3×C4×C3⋊C8C2211yescharacteristic
41Dic3⋊(C3⋊C8)C2212yes—
42#63557C2212yes—
43(C2×D3)⋊(C3⋊C8)C2212yes—
44C2×#901—32no—
45C2×#901—32no—
46#5548—31no—
47#5477—31no—
48C3×C8×D4—31no—
49C2×C3×C4×C8—31no—
50#5110—32no—
51C8×#67—32no—
52#5012—31no—
53#4924—31no—
54#4838—31no—
55#4837—31no—
56#4729—32no—
57#4727—32no—
58#4688—31no—
59#4688—32no—
60#4688—31no—
61C8×D12—32no—
62C8×D12—31no—
63C8×D12—31no—
64C8×D12—61no—
65C8×D12D311yescharacteristic, complemented
66C4×D3×C8D311yescharacteristic, complemented
67C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
68C2×C4×C3⋊D3C2312yes—
69C2×C3×D12C2×C411yescharacteristic
70C2×C3×C4×D3C2×C411yescharacteristic
71C2×C3×C4×D3C2×C411yescharacteristic
72C2×C3×C4×D3C2312yes—
73C2×C3×C4×D3C2311yescharacteristic
74C2×#627C2×C412yes—
75C2×#626C2×C412yes—
76C2×#626C2×C412yes—
77C2×#626C2×C412yes—
78C2×#625C2×C412yes—
79#3798—24no—
80#3798—24no—
81C2×C32×C8C2311yescharacteristic
82C2×C32×C8C2311yescharacteristic
83C32×C42C2311yescharacteristic
84#3752C2×C412yes—
85C4⋊(C3⋊Dic3)C2×C411yescharacteristic
86C2×C3⋊(C3⋊C8)C2312yes—
87C8×C3⋊D3—24no—
88C3×(C2×D3)⋊C4C2×C412yes—
89C3×C4⋊Dic3C2×C411yescharacteristic
90C3×C4×Dic3C2×C411yescharacteristic
91C3×C4×Dic3C2×C411yescharacteristic
92C3×C4×Dic3C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2312yes—
95C2×C3×C3⋊C8C2311yescharacteristic
96C3×D3×C8—22no—
97C3×D3×C8—24no—
98C3×D3×C8D414yescomplemented
99Dic3⋊Dic3C2×C412yes—
100#3722C2×C412yes—
101(C2×D3)⋊Dic3C2×C412yes—
102#3712—24no—
103#3711—24no—
104#3711—24no—
105#2931—91noSylow
106C2×#235—32no—
107C2×#235—32no—
108C22×C3×C8—31no—
109C22×C3×C8—32no—
110C22×C3×C8—31no—
111C3×C4×D4—31no—
112C2×C3×C42—31no—
113#940—31no—
114#938—31no—
115#930—31no—
116#930—32no—
117#930—31no—
118C4×#67—32no—
119C2×#208—32no—
120C2×#208—32no—
121#901—68no—
122#901—68no—
123C2×ΓL(1,𝔽25)—32no—
124C2×ΓL(1,𝔽25)—32no—
125C2×ΓL(1,𝔽25)—32no—
126C2×ΓL(1,𝔽25)—32no—
127C2×D3×C8—32no—
128C2×D3×C8—32no—
129C2×D3×C8—62no—
130C2×D3×C8C2×D311yescharacteristic
131C2×D3×C8C2×D312yes—
132C2×D3×C8C2×D311yescharacteristic
133#895—31no—
134#888—31no—
135#885—32no—
136#884—32no—
137#875—32no—
138#874—31no—
139C4×D12—32no—
140C4×D12—31no—
141C4×D12—31no—
142C4×D12—61no—
143C4×D12C2×D311yescharacteristic
144C42×D3C2×D311yescharacteristic
145#869—31no—
146C3×C4⋊C8—31no—
147C3×C22⋊C8—32no—
148C3×C4×C8—21no—
149C3×C4×C8—31no—
150C3×C4×C8—31no—
151C3×C4×C8—31no—
152C3×C4×C8C2×D311yescharacteristic
153C3×C4×C8C2×D311yescharacteristic
154#830—32no—
155(C2×D3)⋊C8—32no—
156(C2×D3)⋊C8—32no—
157(C2×D3)⋊C8—32no—
158(C2×D3)⋊C8—32no—
159(C2×D3)⋊C8—32no—
160(C2×D3)⋊C8—62no—
161(C2×D3)⋊C8C2×D312yes—
162Dic3⋊C8—32no—
163C8×Dic3C2×D311yescharacteristic
164C8×Dic3C2×D311yescharacteristic
165C4⋊(C3⋊C8)—31no—
166C4⋊(C3⋊C8)—31no—
167C4⋊(C3⋊C8)—32no—
168C4⋊(C3⋊C8)—61no—
169C4⋊(C3⋊C8)C2×D311yescharacteristic
170C4×C3⋊C8C2×D311yescharacteristic
171C22×C3⋊D3C22×C412yes—
172C22×C3×D3C22×C412yes—
173C22×C3×D3C22×C411yescharacteristic
174C2×C32×C4C22×C411yescharacteristic
175C2×C32×C4C22×C411yescharacteristic
176C2×C32×C4C2411yescharacteristic
177C2×C3⋊Dic3C22×C412yes—
178C4⋊(C3⋊D3)—22no—
179C4×C3⋊D3—22no—
180C4×C3⋊D3—22no—
181C2×C3×Dic3C22×C411yescharacteristic
182C2×C3×Dic3C22×C412yes—
183C2×C3×Dic3C22×C411yescharacteristic
184C2×C3×Dic3C22×C411yescharacteristic
185C3×D12—22no—
186C3×C4×D3—22no—
187C3×C4×D3—22no—
188C3×C4×D3—22no—
189C3×C4×D3—22no—
190C3×C4×D3C2×D412yes—
191C3×C4×D3#4112yes—
192#627—24no—
193#626—24no—
194#626—24no—
195#626—24no—
196#625—24no—
197C32×C8—21no—
198C32×C8C2×D412yes—
199C3⋊(C3⋊C8)—22no—
200C3×C3⋊C8—22no—
201C3×C3⋊C8—21no—
202C3×C3⋊C8C2×D412yes—
203C2×#131—92no—
204#532—91no—
205#436—92no—
206#436—91no—
207#436—91no—
208C8×D4—31no—
209C8×D4—92no—
210C8×D4—91no—
211#423—91no—
212#408—92no—
213C2×C4×C8—31no—
214C2×C3×D4—31no—
215C22×C3×C4—31no—
216C22×C3×C4—31no—
217C22×C3×C4—31no—
218C22×C3×C4—32no—
219C2×#67—32no—
220C2×#67—32no—
221C2×#67—32no—
222C2×#67—32no—
223C2×#67—32no—
224#235—64no—
225#235—64no—
226#235—64no—
227#235—64no—
228C2×D12—32no—
229C2×D12—32no—
230C2×D12—32no—
231C2×D12—31no—
232C2×D12—31no—
233C2×D12—61no—
234C2×D12C4×D311yescharacteristic
235C2×C4×D3—32no—
236C2×C4×D3—32no—
237C2×C4×D3—62no—
238C2×C4×D3C4×D311yescharacteristic
239C2×C4×D3C4×D311yescharacteristic
240C2×C4×D3C22×D312yes—
241C2×C4×D3C22×D311yescharacteristic
242C2×Dic6—32no—
243C2×Dic6—32no—
244C2×C3×C8—21no—
245C2×C3×C8—21no—
246C2×C3×C8—31no—
247C2×C3×C8—34no—
248C2×C3×C8—32no—
249C2×C3×C8—31no—
250C2×C3×C8—62no—
251C2×C3×C8—64no—
252C2×C3×C8C22×D311yescharacteristic
253C2×C3×C8C22×D311yescharacteristic
254C2×C3×C8C22×D311yescharacteristic
255C2×C3×C8C22×D311yescharacteristic
256C3×C4⋊C4—31no—
257C3×C22⋊C4—32no—
258C3×C42—21no—
259C3×C42—31no—
260C3×C42—31no—
261C3×C42—31no—
262C3×C42C22×D311yescharacteristic
263C3×C42C22×D311yescharacteristic
264#217—32no—
265(C2×D3)⋊C4—32no—
266(C2×D3)⋊C4—32no—
267(C2×D3)⋊C4—32no—
268(C2×D3)⋊C4—32no—
269(C2×D3)⋊C4—32no—
270(C2×D3)⋊C4—62no—
271(C2×D3)⋊C4C4×D312yes—
272C4⋊Dic3—31no—
273C4⋊Dic3—31no—
274C4⋊Dic3—32no—
275C4⋊Dic3—61no—
276C4⋊Dic3C4×D311yescharacteristic
277Dic3⋊C4—32no—
278C4×Dic3C4×D311yescharacteristic
279C4×Dic3C4×D311yescharacteristic
280C4×Dic3C22×D311yescharacteristic
281#208—64no—
282#208—64no—
283C2×C3⋊C8—32no—
284C2×C3⋊C8—32no—
285C2×C3⋊C8—62no—
286C2×C3⋊C8C22×D311yescharacteristic
287C2×C3⋊C8C22×D312yes—
288C2×C3⋊C8C22×D311yescharacteristic
289ΓL(1,𝔽25)—64no—
290ΓL(1,𝔽25)—64no—
291ΓL(1,𝔽25)—64no—
292ΓL(1,𝔽25)—64no—
293D3×C8—22no—
294D3×C8—24no—
295D3×C8—64no—
296D3×C8—64no—
297D3×C8—124no—
298D3×C8D1214yescomplemented
299C22×C32C23×C411yescharacteristic
300C2×C3⋊D3—22no—
301C2×C3⋊D3—22no—
302C2×C3⋊D3—22no—
303C2×C3×D3—21no—
304C2×C3×D3—21no—
305C2×C3×D3—22no—
306C2×C3×D3—22no—
307C2×C3×D3—22no—
308C2×C3×D3C4×D412yes—
309C32×C4—21no—
310C32×C4#13112yescomplemented
311C32×C4C22×D411yescharacteristic
312C32×C4C2×#4111yescharacteristic
313C3⋊Dic3—22no—
314C3×Dic3—22no—
315C3×Dic3—21no—
316C3×Dic3C4×D412yes—
317C3×Dic3#13112yescomplemented
318C2×#41—92no—
319#131—188no—
320C2×M16—92no—
321C2×M16—92no—
322C2×M16—92no—
323C22×C8—31no—
324C22×C8—31no—
325C22×C8—32no—
326C22×C8—92no—
327C4⋊Q8—91no—
328#127—91no—
329#124—92no—
330#121—92no—
331#121—91no—
332#121—91no—
333C4×D4—31no—
334C4×D4—92no—
335C4×D4—91no—
336C2×C42—31no—
337C4⋊C8—31no—
338C4⋊C8—92no—
339C4⋊C8—91no—
340C22⋊C8—32no—
341C22⋊C8—92no—
342C22⋊C8—92no—
343C22⋊C8—92no—
344C4×C8—31no—
345C4×C8—31no—
346C4×C8—31no—
347C4×C8D3211yescharacteristic
348C23×C3—31no—
349C23×C3—32no—
350C22×D3—32no—
351C22×D3—32no—
352C22×D3—62no—
353C22×D3C2×C4×D312yes—
354C22×D3C2×C4×D311yescharacteristic
355C3×D4—62no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—31no—
360C2×C3×C4—31no—
361C2×C3×C4—32no—
362C2×C3×C4—32no—
363C2×C3×C4—32no—
364C2×C3×C4—31no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4—62no—
369C2×C3×C4C2×C4×D311yescharacteristic
370C2×C3×C4C2×C4×D311yescharacteristic
371C2×C3×C4C2×C4×D311yescharacteristic
372C2×C3×C4C2×C4×D311yescharacteristic
373C2×C3×C4C23×D311yescharacteristic
374C2×C3×C4C23×D311yescharacteristic
375#67—64no—
376#67—64no—
377#67—64no—
378#67—64no—
379#67—64no—
380C2×Dic3—32no—
381C2×Dic3—32no—
382C2×Dic3—62no—
383C2×Dic3C2×C4×D311yescharacteristic
384C2×Dic3C2×C4×D312yes—
385C2×Dic3C2×C4×D311yescharacteristic
386C2×Dic3C2×C4×D311yescharacteristic
387D12—22no—
388D12—64no—
389D12—64no—
390D12—64no—
391D12—64no—
392D12—62no—
393D12—62no—
394C4×D3—22no—
395C4×D3—22no—
396C4×D3—22no—
397C4×D3—22no—
398C4×D3—62no—
399C4×D3—62no—
400C4×D3—62no—
401C4×D3—62no—
402C4×D3—122no—
403C4×D3—122no—
404C4×D3C2×D1212yes—
405C4×D3#23512yes—
406Dic6—64no—
407Dic6—64no—
408C3×C8—21no—
409C3×C8—21no—
410C3×C8—22no—
411C3×C8—32no—
412C3×C8—41no—
413C3×C8—62no—
414C3×C8—61no—
415C3×C8C2×D1212yes—
416C3×C8D3×D412yes—
417C3⋊C8—21no—
418C3⋊C8—22no—
419C3⋊C8—62no—
420C3⋊C8—62no—
421C3⋊C8—122no—
422C3⋊C8C2×D1212yes—
423C2×C32C2×C4×D411yescharacteristic
424C2×C32C2×#13111yescharacteristic
425C2×C32C2×#13111yescharacteristic
426C3⋊D3—42no—
427C3×D3—22no—
428C3×D3—42no—
429#41—184no—
430#41—184no—
431C2×Q8—92no—
432C2×D4—31no—
433C2×D4—92no—
434C2×D4—92no—
435C2×D4—92no—
436C2×D4—92no—
437C2×D4—91no—
438C22×C4—31no—
439C22×C4—32no—
440C22×C4—31no—
441C22×C4—31no—
442C22×C4—92no—
443M16—184no—
444M16—184no—
445M16—184no—
446C2×C8—31no—
447C2×C8—34no—
448C2×C8—31no—
449C2×C8—32no—
450C2×C8—62no—
451C2×C8—64no—
452C2×C8—92no—
453C2×C8—184no—
454C2×C8C2×D3211yescharacteristic
455C2×C8C2×D3211yescharacteristic
456C4⋊C4—31no—
457C4⋊C4—92no—
458C4⋊C4—91no—
459C22⋊C4—32no—
460C22⋊C4—92no—
461C22⋊C4—92no—
462C22⋊C4—92no—
463C42—31no—
464C42—31no—
465C42—31no—
466C42C2×D3211yescharacteristic
467C22×C3—21no—
468C22×C3—32no—
469C22×C3—61no—
470C22×C3—61no—
471C22×C3—62no—
472C22×C3—62no—
473C22×C3—62no—
474C22×C3C22×C4×D311yescharacteristic
475C22×C3C22×C4×D311yescharacteristic
476C2×D3—21no—
477C2×D3—21no—
478C2×D3—22no—
479C2×D3—22no—
480C2×D3—22no—
481C2×D3—64no—
482C2×D3—62no—
483C2×D3—62no—
484C2×D3—62no—
485C2×D3—62no—
486C2×D3—62no—
487C2×D3—62no—
488C2×D3—122no—
489C2×D3—122no—
490C2×D3C4×D1212yes—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—22no—
496C3×C4—32no—
497C3×C4—32no—
498C3×C4—41no—
499C3×C4—62no—
500C3×C4—61no—
501C3×C4#90112yescomplemented
502C3×C4#90112yescomplemented
503C3×C4C22×D1211yescharacteristic
504C3×C4C2×#23511yescharacteristic
505C3×C4C2×D3×D411yescharacteristic
506C3×C4D3×#4111yescharacteristic
507Dic3—21no—
508Dic3—22no—
509Dic3—62no—
510Dic3—62no—
511Dic3—122no—
512Dic3C4×D1212yes—
513Dic3#90112yescomplemented
514C32#293111yescharacteristic, complemented, Sylow
515C23—31no—
516C23—32no—
517C23—92no—
518Q8—184no—
519D4—62no—
520D4—184no—
521D4—184no—
522D4—184no—
523D4—184no—
524D4—182no—
525C2×C4—31no—
526C2×C4—31no—
527C2×C4—32no—
528C2×C4—32no—
529C2×C4—31no—
530C2×C4—32no—
531C2×C4—62no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—92no—
536C2×C4—182no—
537C2×C4—182no—
538C2×C4C4×D3211yescharacteristic
539C2×C4C4×D3211yescharacteristic
540C2×C4C22×D3211yescharacteristic
541C8—21no—
542C8—32no—
543C8—62no—
544C8—61no—
545C8—182no—
546C8D3×D1212yes—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—62no—
551C2×C3—122no—
552C2×C3C2×C4×D1211yescharacteristic
553C2×C3C4×D3×D411yescharacteristic
554C2×C3C2×#90111yescharacteristic
555C2×C3C2×#90111yescharacteristic
556C2×C3C2×#90111yescharacteristic
557C2×C3D3×#13111yescharacteristic
558D3—22no—
559D3—42no—
560D3—124no—
561D3—122no—
562D3—122no—
563C22—32no—
564C22—61no—
565C22—61no—
566C22—62no—
567C22—62no—
568C22—62no—
569C22—182no—
570C22—182no—
571C22—182no—
572C22C2×C4×D3211yescharacteristic
573C4—21no—
574C4—32no—
575C4—32no—
576C4—61no—
577C4—62no—
578C4—182no—
579C4#6380312yescomplemented
580C4C2×D3×D1211yescharacteristic
581C4D3×#23511yescharacteristic
582C3—21no—
583C3#7845811yescharacteristic, complemented
584C3#7942211yescharacteristic, complemented
585C2—62no—
586C2—122no—
587C2—362no—
588C2C4×D3×D1211yescharacteristic
589C2D3×#90111yescharacteristic
590C2C2×#6380311yescharacteristic
subgroupG/H
centerC2×C8C2×D32
commutator, socleC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
prime radical#10593968C2
cosocleC2×C32×C4C24
hypercenterC4×C8D32
hypocenterC32#2931
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. C2×#63803C2semidirect
3. C8×C4⋊(C3⋊D3)C2semidirect
4. C3×C8×D12C2semidirect
5. C3×C4×D3×C8C2semidirect
6. #10590953C2semidirect
7. #10590730C2semidirect
8. C8×#626C2semidirect
9. #10590338C2semidirect
10. #10590337C2semidirect
11. #10590336C2semidirect
65. C8×D12D3semidirect
66. C4×D3×C8D3semidirect
98. C3×D3×C8D4semidirect
298. D3×C8D12semidirect
310. C32×C4#131semidirect
317. C3×Dic3#131semidirect
501. C3×C4#901semidirect
502. C3×C4#901semidirect
513. Dic3#901semidirect
514. C32#2931semidirect
579. C4#63803semidirect
583. C3#78458semidirect
584. C3#79422semidirect

Maximal subgroups

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

subgroupindex
C2×#638032
#105939682
C8×C4⋊(C3⋊D3)2
C3×C8×D122
C3×C4×D3×C82
#105909532
#105907302
C8×#6262
#105903382
#105903372
#105903362
#794223
#784583