Finite Group Databasebeta

← D3×#5725 #11900763

Subgroups — D3×#5725 #11900763

Order 1152.

3611 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#239C212yesmaximal, complemented
2#10596196C211yesmaximal, characteristic, complemented
3C3×#5725C211yesmaximal, characteristic, complemented
4C3×D3×C4⋊Q8C211yesmaximal, characteristic, complemented
5D3×#947C212yesmaximal, complemented
6#10595363C212yesmaximal, complemented
7#10595360C212yesmaximal, complemented
8D3×#895C214yesmaximal, complemented
9D3×#893C214yesmaximal, complemented
10#10594518C214yesmaximal, complemented
11#10594369C214yesmaximal, complemented
12D3×#874C211yesmaximal, characteristic, complemented
13C42×D32C211yesmaximal, characteristic, complemented
14#10593970C211yesmaximal, characteristic, complemented
15#10593907C211yesmaximal, characteristic, complemented
16D3×#532—31nomaximal
17C2×#5725—31nomaximal
18C2×#3832C2212yescomplemented
19C2×C3×#239C2212yescomplemented
20C2×C3×D3×Q8C2212yes—
21D3×#239—216no—
22C2×D3×D12C2214yes—
23C2×D3×D12C2214yes—
24C2×D3×D12C2212yes—
25C2×C4×D32C2214yes—
26C2×C4×D32C2212yes—
27C2×C4×D32C2211yescharacteristic
28C2×#3799C2212yescomplemented
29C2×#3799C2214yescomplemented
30C2×#3796C2212yescomplemented
31C2×#3796C2214yescomplemented
32C32×C4⋊Q8C2211yescharacteristic, complemented
33#64156C2212yescomplemented
34#64104C2214yescomplemented
35#64102C2214yescomplemented
36#64083C2211yescharacteristic, complemented
37C42×C3⋊D3C2211yescharacteristic, complemented
38C3×#947C2212yescomplemented
39C3×#944C2212yescomplemented
40C3×#895C2214yescomplemented
41C3×#893C2214yescomplemented
42C3×D3×C4⋊C4C2214yes—
43C3×#888C2214yescomplemented
44C3×#874C2211yescharacteristic, complemented
45C3×C42×D3C2211yescharacteristic
46C3×C42×D3C2211yescharacteristic, complemented
47C3×#869C2211yescharacteristic, complemented
48D3×(C2×D3)⋊C4C2218yes—
49#63916C2214yescomplemented
50#63911C2212yescomplemented
51#63911C2214yescomplemented
52#63910C2218yescomplemented
53#63909C2214yescomplemented
54#63907C2218yescomplemented
55#63904C2218yescomplemented
56#63898C2214yescomplemented
57#63894C2214yescomplemented
58#63886C2218yescomplemented
59C4×#624C2211yescharacteristic, complemented
60C4×#624C2212yescomplemented
61#63881C2218yescomplemented
62C4×D3×Dic3C2212yes—
63C4×D3×Dic3C2211yescharacteristic
64C4×D3×Dic3C2211yescharacteristic, complemented
65C4×D3×Dic3C2212yescomplemented
66#63864C2212yescomplemented
67#63863C2212yescomplemented
68C2×D3×#41—32no—
69C22×#239—32no—
70C3×#532—31no—
71C2×C3×C4⋊Q8—31no—
72#5832—32no—
73C2×#947—32no—
74#5725—32no—
75#5725—31no—
76#5725—31no—
77#5725—32no—
78#5725—34no—
79#5725—34no—
80#5725—31no—
81#5725—31no—
82#5725—61no—
83#5725D311yescharacteristic, direct product factor
84D3×C4⋊Q8D311yescharacteristic, complemented
85#5716—31no—
86D3×#127—31no—
87D3×#124—32no—
88#5668—32no—
89D3×#121—34no—
90#5596—34no—
91#5548—34no—
92C4×D3×D4—34no—
93C2×#895—34no—
94C2×#893—34no—
95#5477—31no—
96C2×#874—31no—
97C2×C42×D3—31no—
98C2×C42×D3—31no—
99C22×D32C2314yes—
100C22×D32C2311yescharacteristic
101C2×C32×Q8C2312yes—
102#3832—28no—
103C2×C4⋊(C3⋊D3)C2312yes—
104C2×C4⋊(C3⋊D3)C2314yes—
105C2×C4⋊(C3⋊D3)C2314yes—
106C2×C4×C3⋊D3C2314yes—
107C2×C4×C3⋊D3C2312yes—
108C2×C4×C3⋊D3C2311yescharacteristic
109C3×#239—28no—
110C3×D3×Q8—28no—
111C2×C3×D12C2314yes—
112C2×C3×D12C2314yes—
113C2×C3×D12C2312yes—
114C2×C3×C4×D3C2314yes—
115C2×C3×C4×D3C2314yes—
116C2×C3×C4×D3C2312yes—
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×C4×D3C2311yescharacteristic
119C2×C3×C4×D3C2312yes—
120C2×C3×Dic6C2314yes—
121C2×C3×Dic6C2312yes—
122C2×#626C2314yes—
123C2×#626C2314yes—
124C2×#626C2314yes—
125C2×#626C2318yes—
126C2×#624C2314yes—
127C2×#624C2312yes—
128C2×#624C2311yescharacteristic
129C2×D3×Dic3C2314yes—
130C2×D3×Dic3C2312yes—
131C2×D3×Dic3C2312yes—
132C2×D3×Dic3C2311yescharacteristic
133C2×D3×Dic3C2311yescharacteristic
134D3×D12—216no—
135D3×D12—28no—
136D3×D12—216no—
137C4×D32—28no—
138C4×D32—216no—
139C4×D32D418yescomplemented
140#3799—28no—
141#3799—216no—
142#3796—28no—
143#3796—216no—
144C32×C4⋊C4C2314yes—
145C32×C42C2311yescharacteristic
146#3752C2318yes—
147C4×C3⋊Dic3C2312yes—
148C4×C3⋊Dic3C2311yescharacteristic
149C3×(C2×D3)⋊C4C2318yes—
150C3×C4⋊Dic3C2314yes—
151C3×Dic3⋊C4C2318yes—
152C3×C4×Dic3C2312yes—
153C3×C4×Dic3C2312yes—
154C3×C4×Dic3C2311yescharacteristic
155C3×C4×Dic3C2311yescharacteristic
156#3722C2318yes—
157(C2×D3)⋊Dic3C2318yes—
158Dic32C2312yes—
159Dic32C2312yes—
160Dic32C2312yes—
161C2×#532—91noSylow
162C2×C3×#41—32no—
163C22×C3×Q8—32no—
164D3×#41—616no—
165C2×#239—32no—
166C2×#239—32no—
167C2×#239—34no—
168C2×#239—32no—
169C2×#239—34no—
170C2×#239—32no—
171C2×#239—62no—
172C2×#239—616no—
173C2×#239C2×D312yescomplemented
174C2×D3×Q8C2×D312yes—
175C2×#237—32no—
176C2×#237—34no—
177C2×D3×D4—32no—
178C2×D3×D4—34no—
179C2×D3×D4—34no—
180C2×#235—32no—
181C2×#235—34no—
182C22×D12—32no—
183C22×D12—34no—
184C22×D12—34no—
185C22×C4×D3—31no—
186C22×C4×D3—31no—
187C22×C4×D3—34no—
188C22×C4×D3—34no—
189C22×C4×D3—32no—
190C22×C4×D3—32no—
191C3×C4⋊Q8—21no—
192C3×C4⋊Q8—32no—
193C3×C4⋊Q8—34no—
194C3×C4⋊Q8—31no—
195C3×C4⋊Q8C2×D311yescharacteristic, complemented
196C3×C4⋊Q8C2×D311yescharacteristic, complemented
197C3×#127—31no—
198C3×#124—32no—
199C3×#121—34no—
200C3×C4×D4—34no—
201C2×C3×C4⋊C4—34no—
202C2×C3×C42—31no—
203C2×C3×C42—31no—
204#947—32no—
205#947—32no—
206#947—32no—
207#947—38no—
208#947—32no—
209#947—62no—
210#947C2×D312yescomplemented
211#944C2×D312yescomplemented
212#940—32no—
213#940—34no—
214#939—38no—
215#938—34no—
216#936—32no—
217D4×Dic3—34no—
218#930—34no—
219C4×#67—38no—
220C2×(C2×D3)⋊C4—38no—
221C2×C4×Dic3—32no—
222C2×C4×Dic3—31no—
223C2×C4×Dic3—31no—
224C2×C4×Dic3—32no—
225#895—38no—
226#895—34no—
227#895—34no—
228#895—34no—
229#895—34no—
230#895—38no—
231#895—64no—
232#895C2×D314yescomplemented
233#893—34no—
234#893—38no—
235#893—34no—
236#893—34no—
237#893—38no—
238#893—34no—
239#893—64no—
240#893C2×D314yescomplemented
241D3×C4⋊C4C2×D314yes—
242#888C2×D314yescomplemented
243#885—38no—
244#884—38no—
245#67⋊C4—38no—
246D3×C22⋊C4—38no—
247#875—32no—
248#874—32no—
249#874—34no—
250#874—31no—
251#874—31no—
252#874—61no—
253#874C2×D311yescharacteristic, complemented
254C4×D12—34no—
255C42×D3—31no—
256C42×D3—32no—
257C42×D3—31no—
258C42×D3—32no—
259C42×D3—31no—
260C42×D3—31no—
261C42×D3—31no—
262C42×D3—31no—
263C42×D3—32no—
264C42×D3—32no—
265C42×D3—61no—
266C42×D3C2×D311yescharacteristic
267C42×D3C2×D311yescharacteristic, complemented
268#869C2×D311yescharacteristic, complemented
269C22×C3⋊D3C2414yes—
270C22×C3⋊D3C2411yescharacteristic
271C22×C3×D3C2414yes—
272C22×C3×D3C2411yescharacteristic
273C22×C3×D3C2411yescharacteristic
274C2×D32—24no—
275C2×D32—28no—
276C2×D32—216no—
277C2×D32C2×D414yes—
278C32×Q8—24no—
279C2×C32×C4C2414yes—
280C2×C32×C4C2411yescharacteristic
281C2×C32×C4C2412yes—
282C2×C3⋊Dic3C2412yes—
283C2×C3⋊Dic3C2411yescharacteristic
284C4⋊(C3⋊D3)—28no—
285C4⋊(C3⋊D3)—24no—
286C4⋊(C3⋊D3)—28no—
287C4×C3⋊D3—24no—
288C4×C3⋊D3—28no—
289C4×C3⋊D3C2×D414yescomplemented
290C2×C3×Dic3C2412yes—
291C2×C3×Dic3C2414yes—
292C2×C3×Dic3C2411yescharacteristic
293C2×C3×Dic3C2411yescharacteristic
294C2×C3×Dic3C2412yes—
295C3×D12—28no—
296C3×D12—24no—
297C3×D12—28no—
298C3×C4×D3—28no—
299C3×C4×D3—24no—
300C3×C4×D3—28no—
301C3×C4×D3C2×D414yes—
302C3×C4×D3C2×D414yescomplemented
303C3×C4×D3#4118yescomplemented
304C3×Dic6—24no—
305C3×Dic6—28no—
306#626—28no—
307#626—28no—
308#626—28no—
309#626—216no—
310#624—28no—
311#624—24no—
312#624C2×D414yescomplemented
313D3×Dic3—24no—
314D3×Dic3—28no—
315D3×Dic3—24no—
316D3×Dic3C2×D414yes—
317D3×Dic3C2×D414yescomplemented
318C22×#41—92no—
319#532—31no—
320#532—91no—
321#532—94no—
322#532—94no—
323#532—92no—
324#532—91no—
325#532—92no—
326#532—91no—
327C2×C4⋊Q8—31no—
328C2×#127—91no—
329C2×#124—92no—
330C2×#121—94no—
331C2×C4×D4—94no—
332C22×C42—91no—
333C23×D3—31no—
334C23×D3—31no—
335C23×D3—34no—
336C23×D3—34no—
337C3×#41—68no—
338C2×C3×Q8—22no—
339C2×C3×Q8—34no—
340C2×C3×Q8—32no—
341C2×C3×Q8—68no—
342C2×C3×Q8C22×D312yes—
343C2×C3×Q8C22×D312yes—
344C2×C3×D4—34no—
345C2×C3×D4—32no—
346C2×C3×D4—34no—
347C22×C3×C4—32no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—32no—
351C22×C3×C4—34no—
352C22×C3×C4—34no—
353C2×#67—38no—
354C2×#67—34no—
355C2×#67—34no—
356C2×#67—34no—
357C22×Dic3—31no—
358C22×Dic3—31no—
359C22×Dic3—34no—
360C22×Dic3—32no—
361C22×Dic3—32no—
362#239—28no—
363#239—616no—
364#239—616no—
365#239—68no—
366#239—68no—
367#239—68no—
368#239—68no—
369#239—128no—
370D3×Q8—28no—
371#237—68no—
372#237—616no—
373D3×D4—616no—
374D3×D4—68no—
375D3×D4—616no—
376#235—616no—
377#235—68no—
378C2×D12—38no—
379C2×D12—34no—
380C2×D12—34no—
381C2×D12—34no—
382C2×D12—34no—
383C2×D12—34no—
384C2×D12—32no—
385C2×D12—32no—
386C2×D12—34no—
387C2×D12—34no—
388C2×D12—64no—
389C2×D12—62no—
390C2×D12—64no—
391C2×D12—616no—
392C2×D12—68no—
393C2×D12—616no—
394C2×D12C22×D314yes—
395C2×D12C22×D312yes—
396C2×D12C22×D314yes—
397C2×C4×D3—31no—
398C2×C4×D3—31no—
399C2×C4×D3—31no—
400C2×C4×D3—31no—
401C2×C4×D3—31no—
402C2×C4×D3—31no—
403C2×C4×D3—38no—
404C2×C4×D3—38no—
405C2×C4×D3—32no—
406C2×C4×D3—32no—
407C2×C4×D3—34no—
408C2×C4×D3—32no—
409C2×C4×D3—32no—
410C2×C4×D3—34no—
411C2×C4×D3—34no—
412C2×C4×D3—32no—
413C2×C4×D3—32no—
414C2×C4×D3—34no—
415C2×C4×D3—34no—
416C2×C4×D3—61no—
417C2×C4×D3—62no—
418C2×C4×D3—64no—
419C2×C4×D3—616no—
420C2×C4×D3—616no—
421C2×C4×D3—68no—
422C2×C4×D3—68no—
423C2×C4×D3C22×D312yes—
424C2×C4×D3C22×D314yes—
425C2×C4×D3C22×D314yes—
426C2×C4×D3C22×D311yescharacteristic
427C2×C4×D3C22×D311yescharacteristic
428C2×C4×D3C22×D312yes—
429C2×Dic6C22×D312yes—
430C2×Dic6C22×D314yes—
431C3×C4⋊C4—24no—
432C3×C4⋊C4—38no—
433C3×C4⋊C4—34no—
434C3×C4⋊C4C22×D314yes—
435C3×C4⋊C4C22×D314yes—
436C3×C22⋊C4—38no—
437C3×C42—21no—
438C3×C42—32no—
439C3×C42—31no—
440C3×C42—32no—
441C3×C42—31no—
442C3×C42C22×D311yescharacteristic
443C3×C42C22×D311yescharacteristic
444#217—38no—
445(C2×D3)⋊C4—38no—
446(C2×D3)⋊C4—38no—
447(C2×D3)⋊C4—38no—
448(C2×D3)⋊C4—38no—
449(C2×D3)⋊C4—38no—
450(C2×D3)⋊C4—68no—
451(C2×D3)⋊C4C22×D318yes—
452C4⋊Dic3C22×D314yes—
453Dic3⋊C4C22×D318yes—
454C4×Dic3—32no—
455C4×Dic3—32no—
456C4×Dic3—31no—
457C4×Dic3—31no—
458C4×Dic3—32no—
459C4×Dic3—32no—
460C4×Dic3—32no—
461C4×Dic3—32no—
462C4×Dic3—32no—
463C4×Dic3—32no—
464C4×Dic3—62no—
465C4×Dic3—61no—
466C4×Dic3C22×D312yes—
467C4×Dic3C22×D311yescharacteristic
468C4×Dic3C22×D312yes—
469C4×Dic3C22×D311yescharacteristic
470C22×C32C2511yescharacteristic
471C2×C3⋊D3—22no—
472C2×C3⋊D3—24no—
473C2×C3⋊D3—28no—
474C2×C3⋊D3C22×D412yes—
475C2×C3×D3—22no—
476C2×C3×D3—24no—
477C2×C3×D3—28no—
478C2×C3×D3C22×D412yes—
479C2×C3×D3C22×D412yes—
480C2×C3×D3C2×#4114yes—
481D32—28no—
482D32—416no—
483C32×C4—24no—
484C32×C4C22×D412yes—
485C32×C4C2×#4114yescomplemented
486C3⋊Dic3—22no—
487C3⋊Dic3C22×D412yes—
488C3×Dic3—24no—
489C3×Dic3—22no—
490C3×Dic3C22×D412yes—
491C3×Dic3C22×D412yes—
492C3×Dic3C2×#4114yescomplemented
493C2×#41—32no—
494C2×#41—92no—
495C2×#41—94no—
496C2×#41—94no—
497C2×#41—92no—
498C2×#41—92no—
499C2×#41—1816no—
500C22×Q8—32no—
501C22×D4—94no—
502C22×D4—94no—
503C22×D4—92no—
504C23×C4—91no—
505C23×C4—94no—
506C23×C4—92no—
507C4⋊Q8—32no—
508C4⋊Q8—34no—
509C4⋊Q8—31no—
510C4⋊Q8D3211yescharacteristic, complemented
511#127—31no—
512#127—94no—
513#127—92no—
514#127—91no—
515#124—32no—
516#124—92no—
517#124—98no—
518#124—92no—
519#124—92no—
520#121—34no—
521#121—98no—
522#121—94no—
523#121—94no—
524#121—98no—
525#121—94no—
526C4×D4—34no—
527C4×D4—94no—
528C4×D4—98no—
529C4×D4—98no—
530C4×D4—94no—
531C4×D4—94no—
532C2×C4⋊C4—34no—
533C2×C22⋊C4—98no—
534C2×C42—31no—
535C2×C42—31no—
536C2×C42—92no—
537C2×C42—91no—
538C2×C42—92no—
539C2×C42—91no—
540C2×C42—91no—
541C2×C42—92no—
542C2×C42—91no—
543C23×C3—31no—
544C23×C3—31no—
545C23×C3—34no—
546C22×D3—31no—
547C22×D3—31no—
548C22×D3—34no—
549C22×D3—34no—
550C22×D3—34no—
551C22×D3—34no—
552C22×D3—61no—
553C22×D3—64no—
554C22×D3—64no—
555C22×D3—68no—
556C22×D3—616no—
557C22×D3—64no—
558C22×D3—68no—
559C22×D3—616no—
560C22×D3C23×D314yes—
561C22×D3C23×D311yescharacteristic
562C22×D3C23×D311yescharacteristic
563C3×Q8—24no—
564C3×Q8—24no—
565C3×Q8—44no—
566C3×Q8—68no—
567C3×Q8—64no—
568C3×D4—68no—
569C3×D4—64no—
570C3×D4—68no—
571C2×C3×C4—22no—
572C2×C3×C4—21no—
573C2×C3×C4—24no—
574C2×C3×C4—32no—
575C2×C3×C4—31no—
576C2×C3×C4—31no—
577C2×C3×C4—34no—
578C2×C3×C4—34no—
579C2×C3×C4—38no—
580C2×C3×C4—32no—
581C2×C3×C4—34no—
582C2×C3×C4—68no—
583C2×C3×C4—68no—
584C2×C3×C4—64no—
585C2×C3×C4C23×D314yes—
586C2×C3×C4C23×D314yes—
587C2×C3×C4C23×D311yescharacteristic
588C2×C3×C4C23×D311yescharacteristic
589C2×C3×C4C23×D312yes—
590C2×C3×C4C23×D312yes—
591#67—68no—
592#67—68no—
593#67—68no—
594#67—616no—
595C2×Dic3—31no—
596C2×Dic3—31no—
597C2×Dic3—34no—
598C2×Dic3—34no—
599C2×Dic3—32no—
600C2×Dic3—32no—
601C2×Dic3—61no—
602C2×Dic3—62no—
603C2×Dic3—68no—
604C2×Dic3—64no—
605C2×Dic3—64no—
606C2×Dic3C23×D312yes—
607C2×Dic3C23×D314yes—
608C2×Dic3C23×D311yescharacteristic
609C2×Dic3C23×D311yescharacteristic
610C2×Dic3C23×D312yes—
611D12—28no—
612D12—24no—
613D12—28no—
614D12—68no—
615D12—68no—
616D12—616no—
617D12—68no—
618D12—68no—
619D12—68no—
620D12—64no—
621D12—64no—
622D12—68no—
623D12—68no—
624D12—128no—
625D12—124no—
626D12—128no—
627C4×D3—28no—
628C4×D3—24no—
629C4×D3—28no—
630C4×D3—34no—
631C4×D3—34no—
632C4×D3—34no—
633C4×D3—34no—
634C4×D3—34no—
635C4×D3—34no—
636C4×D3—64no—
637C4×D3—64no—
638C4×D3—68no—
639C4×D3—68no—
640C4×D3—68no—
641C4×D3—68no—
642C4×D3—64no—
643C4×D3—64no—
644C4×D3—64no—
645C4×D3—64no—
646C4×D3—68no—
647C4×D3—64no—
648C4×D3—128no—
649C4×D3—124no—
650C4×D3D3×D414yes—
651C4×D3D3×D414yescomplemented
652C4×D3#23918yescomplemented
653Dic6—24no—
654Dic6—28no—
655C2×C32C23×D411yescharacteristic
656C2×C32C22×#4112yes—
657C3⋊D3—22no—
658C3⋊D3—44no—
659C3×D3—22no—
660C3×D3—44no—
661C3×D3#53214yescomplemented
662C24—91no—
663C24—94no—
664#41—68no—
665#41—188no—
666#41—1816no—
667#41—1816no—
668#41—188no—
669#41—188no—
670C2×Q8—34no—
671C2×Q8—32no—
672C2×Q8—68no—
673C2×Q8C2×D3212yes—
674C2×D4—34no—
675C2×D4—34no—
676C2×D4—32no—
677C2×D4—98no—
678C2×D4—94no—
679C2×D4—94no—
680C2×D4—94no—
681C2×D4—94no—
682C2×D4—94no—
683C2×D4—92no—
684C2×D4—188no—
685C2×D4—1816no—
686C2×D4—1816no—
687C22×C4—32no—
688C22×C4—31no—
689C22×C4—31no—
690C22×C4—32no—
691C22×C4—34no—
692C22×C4—34no—
693C22×C4—91no—
694C22×C4—98no—
695C22×C4—92no—
696C22×C4—94no—
697C22×C4—91no—
698C22×C4—91no—
699C22×C4—92no—
700C22×C4—92no—
701C22×C4—94no—
702C22×C4—91no—
703C22×C4—92no—
704C22×C4—94no—
705C22×C4—188no—
706C22×C4—1816no—
707C4⋊C4—38no—
708C4⋊C4—34no—
709C4⋊C4C2×D3214yes—
710C22⋊C4—38no—
711C22⋊C4—98no—
712C22⋊C4—98no—
713C22⋊C4—98no—
714C42—32no—
715C42—31no—
716C42—31no—
717C42—32no—
718C42—92no—
719C42—92no—
720C42—92no—
721C42—92no—
722C42—91no—
723C42C2×D3211yescharacteristic
724C22×C3—21no—
725C22×C3—32no—
726C22×C3—34no—
727C22×C3—32no—
728C22×C3—62no—
729C22×C3—64no—
730C22×C3—68no—
731C22×C3C24×D311yescharacteristic
732C22×C3C24×D311yescharacteristic
733C2×D3—22no—
734C2×D3—24no—
735C2×D3—28no—
736C2×D3—32no—
737C2×D3—32no—
738C2×D3—62no—
739C2×D3—68no—
740C2×D3—62no—
741C2×D3—62no—
742C2×D3—68no—
743C2×D3—64no—
744C2×D3—64no—
745C2×D3—68no—
746C2×D3—68no—
747C2×D3—122no—
748C2×D3—124no—
749C2×D3—128no—
750C2×D3—1216no—
751C2×D3—1216no—
752C2×D3C2×D3×D412yes—
753C2×D3C2×D3×D412yes—
754C2×D3C2×#23914yes—
755C3×C4—24no—
756C3×C4—24no—
757C3×C4—22no—
758C3×C4—24no—
759C3×C4—32no—
760C3×C4—32no—
761C3×C4—34no—
762C3×C4—44no—
763C3×C4—64no—
764C3×C4—62no—
765C3×C4C2×D3×D412yes—
766C3×C4C2×D3×D412yes—
767C3×C4C2×#23914yescomplemented
768C3×C4D3×#4114yescomplemented
769Dic3—24no—
770Dic3—22no—
771Dic3—32no—
772Dic3—32no—
773Dic3—62no—
774Dic3—62no—
775Dic3—62no—
776Dic3—122no—
777Dic3C2×D3×D412yes—
778Dic3C2×D3×D412yes—
779Dic3C2×#23914yescomplemented
780C32C2×#53211yescharacteristic, complemented, Sylow
781C23—31no—
782C23—31no—
783C23—34no—
784C23—94no—
785C23—91no—
786C23—94no—
787C23—184no—
788C23—188no—
789C23—1816no—
790Q8—24no—
791Q8—68no—
792Q8—64no—
793D4—68no—
794D4—64no—
795D4—68no—
796D4—188no—
797D4—188no—
798D4—1816no—
799D4—188no—
800D4—188no—
801D4—184no—
802D4—188no—
803C2×C4—32no—
804C2×C4—31no—
805C2×C4—31no—
806C2×C4—34no—
807C2×C4—34no—
808C2×C4—38no—
809C2×C4—32no—
810C2×C4—34no—
811C2×C4—68no—
812C2×C4—68no—
813C2×C4—64no—
814C2×C4—94no—
815C2×C4—94no—
816C2×C4—94no—
817C2×C4—91no—
818C2×C4—94no—
819C2×C4—92no—
820C2×C4—188no—
821C2×C4—188no—
822C2×C4—184no—
823C2×C4—184no—
824C2×C4—188no—
825C2×C4—184no—
826C2×C4—184no—
827C2×C4C22×D3214yes—
828C2×C4C22×D3211yescharacteristic
829C2×C4C22×D3212yes—
830C2×C3—21no—
831C2×C3—22no—
832C2×C3—34no—
833C2×C3—62no—
834C2×C3—124no—
835C2×C3C22×D3×D411yescharacteristic
836C2×C3C22×D3×D411yescharacteristic
837C2×C3C22×#23912yes—
838C2×C3C2×D3×#4112yes—
839D3—22no—
840D3—44no—
841D3—62no—
842D3—62no—
843D3—122no—
844D3—124no—
845D3—124no—
846D3—244no—
847D3#572514yesdirect product factor
848C22—32no—
849C22—34no—
850C22—32no—
851C22—62no—
852C22—64no—
853C22—68no—
854C22—92no—
855C22—188no—
856C22—182no—
857C22—184no—
858C22—188no—
859C22—3616no—
860C22C23×D3211yescharacteristic
861C4—24no—
862C4—32no—
863C4—32no—
864C4—34no—
865C4—64no—
866C4—62no—
867C4—92no—
868C4—182no—
869C4D32×D412yes—
870C4D3×#23914yescomplemented
871C3—21no—
872C3C2×#572511yescharacteristic, complemented
873C3D3×#53211yescharacteristic, complemented
874C2—34no—
875C2—62no—
876C2—124no—
877C2—182no—
878C2—364no—
879C2C2×D32×D411yescharacteristic
880C2C2×D3×#23912yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
hypercenterC4⋊Q8D32
hypocenterC32C2×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×D3×#239C2semidirect
2. #10596196C2semidirect
3. C3×#5725C2semidirect
4. C3×D3×C4⋊Q8C2semidirect
5. D3×#947C2semidirect
6. #10595363C2semidirect
7. #10595360C2semidirect
8. D3×#895C2semidirect
9. D3×#893C2semidirect
10. #10594518C2semidirect
11. #10594369C2semidirect
12. D3×#874C2semidirect
13. C42×D32C2semidirect
14. #10593970C2semidirect
15. #10593907C2semidirect
18. C2×#3832C22semidirect
19. C2×C3×#239C22semidirect
28. C2×#3799C22semidirect
29. C2×#3799C22semidirect
30. C2×#3796C22semidirect
31. C2×#3796C22semidirect
32. C32×C4⋊Q8C22semidirect
33. #64156C22semidirect
34. #64104C22semidirect
35. #64102C22semidirect
36. #64083C22semidirect
37. C42×C3⋊D3C22semidirect
38. C3×#947C22semidirect
39. C3×#944C22semidirect
40. C3×#895C22semidirect
41. C3×#893C22semidirect
43. C3×#888C22semidirect
44. C3×#874C22semidirect
46. C3×C42×D3C22semidirect
47. C3×#869C22semidirect
49. #63916C22semidirect
50. #63911C22semidirect
51. #63911C22semidirect
52. #63910C22semidirect
53. #63909C22semidirect
54. #63907C22semidirect
55. #63904C22semidirect
56. #63898C22semidirect
57. #63894C22semidirect
58. #63886C22semidirect
59. C4×#624C22semidirect
60. C4×#624C22semidirect
61. #63881C22semidirect
64. C4×D3×Dic3C22semidirect
65. C4×D3×Dic3C22semidirect
66. #63864C22semidirect
67. #63863C22semidirect
83. #5725D3direct (N × H)
84. D3×C4⋊Q8D3semidirect
139. C4×D32D4semidirect
173. C2×#239C2×D3semidirect
195. C3×C4⋊Q8C2×D3semidirect
196. C3×C4⋊Q8C2×D3semidirect
210. #947C2×D3semidirect
211. #944C2×D3semidirect
232. #895C2×D3semidirect
240. #893C2×D3semidirect
242. #888C2×D3semidirect
253. #874C2×D3semidirect
267. C42×D3C2×D3semidirect
268. #869C2×D3semidirect
289. C4×C3⋊D3C2×D4semidirect
302. C3×C4×D3C2×D4semidirect
303. C3×C4×D3#41semidirect
312. #624C2×D4semidirect
317. D3×Dic3C2×D4semidirect
485. C32×C4C2×#41semidirect
492. C3×Dic3C2×#41semidirect
510. C4⋊Q8D32semidirect
651. C4×D3D3×D4semidirect
652. C4×D3#239semidirect
661. C3×D3#532semidirect
767. C3×C4C2×#239semidirect
768. C3×C4D3×#41semidirect
779. Dic3C2×#239semidirect
780. C32C2×#532semidirect
847. D3#5725direct (N × H)
870. C4D3×#239semidirect
872. C3C2×#5725semidirect
873. C3D3×#532semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2392
#105961962
C3×#57252
C3×D3×C4⋊Q82
D3×#9472
#105953632
#105953602
D3×#8952
D3×#8932
#105945182
#105943692
D3×#8742
C42×D322
#105939702
#105939072
D3×#5323
C2×#57253