Finite Group Databasebeta

← D3×#5477 #11900769

Subgroups — D3×#5477 #11900769

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×#235C212yesmaximal, complemented
2#10595948C211yesmaximal, characteristic, complemented
3C3×#5477C211yesmaximal, characteristic, complemented
4C2×C3×C42×D3C211yesmaximal, characteristic, complemented
5D3×#930C214yesmaximal, complemented
6#10595029C212yesmaximal, complemented
7#10594910C214yesmaximal, complemented
8D3×#875C212yesmaximal, complemented
9D3×#874C211yesmaximal, characteristic, complemented
10C4×D3×D12C214yesmaximal, complemented
11#10593970C211yesmaximal, characteristic, complemented
12#10593969C212yesmaximal, complemented
13#10593968C214yesmaximal, complemented
14#10593897C211yesmaximal, characteristic, complemented
15D3×#869C211yesmaximal, characteristic, complemented
16D3×#532—31nomaximal
17C2×#5477—31nomaximal
18C2×#3828C2212yescomplemented
19C2×C3×#235C2212yescomplemented
20C22×C3×C4×D3C2212yes—
21C22×C3×C4×D3C2211yescharacteristic
22C2×D3×#67C2214yes—
23C2×#3804C2214yescomplemented
24D3×#235—216no—
25C2×D3×D12C2212yes—
26C2×D3×D12C2214yes—
27C2×C4×D32C2214yes—
28C2×#3799C2212yescomplemented
29C2×#3798C2214yescomplemented
30C2×#3795C2212yescomplemented
31C2×D3×Dic6C2212yes—
32C2×C32×C42C2211yescharacteristic, complemented
33#64139C2214yescomplemented
34#64084C2212yescomplemented
35#64083C2211yescharacteristic, complemented
36C4×C4⋊(C3⋊D3)C2214yescomplemented
37#64078C2211yescharacteristic, complemented
38C3×#930C2214yescomplemented
39C2×C3×C4×Dic3C2212yescomplemented
40C2×C3×C4×Dic3C2211yescharacteristic, complemented
41C3×#875C2212yescomplemented
42C3×#874C2211yescharacteristic, complemented
43C3×C4×D12C2214yescomplemented
44C3×C42×D3C2211yescharacteristic
45C3×C42×D3C2212yes—
46C3×C42×D3C2211yescharacteristic
47C3×C42×D3C2211yescharacteristic, complemented
48C3×C42×D3C2212yescomplemented
49C3×C42×D3C2211yescharacteristic, complemented
50C3×#869C2211yescharacteristic, complemented
51#63978C2218yescomplemented
52D3×(C2×D3)⋊C4C2218yes—
53#63918C2214yescomplemented
54#63911C2214yescomplemented
55#63911C2212yescomplemented
56#63909C2214yescomplemented
57#63908C2214yescomplemented
58#63906C2218yescomplemented
59C4×#626C2218yescomplemented
60#63894C2214yescomplemented
61Dic3×D12C2214yescomplemented
62D3×C4⋊Dic3C2214yes—
63#63880C2218yescomplemented
64#63866C2212yescomplemented
65#63864C2212yescomplemented
66#63860C2212yescomplemented
67#63852C2218yescomplemented
68C2×D3×#41—32no—
69C22×#235—32no—
70C3×#532—31no—
71C22×C3×C42—31no—
72#5832—32no—
73C2×#930—34no—
74#5725—31no—
75D3×C4⋊Q8—31no—
76#5716—31no—
77D3×#127—31no—
78D3×#124—32no—
79#5668—32no—
80D3×#121—34no—
81#5596—34no—
82#5548—34no—
83C4×D3×D4—34no—
84#5477—32no—
85#5477—31no—
86#5477—31no—
87#5477—34no—
88#5477—32no—
89#5477—31no—
90#5477—34no—
91#5477—31no—
92#5477—61no—
93#5477D311yescharacteristic, direct product factor
94C2×#875—32no—
95C2×#874—31no—
96C2×C4×D12—34no—
97C2×C42×D3D311yescharacteristic, complemented
98C2×#869—31no—
99C23×C3×D3C2311yescharacteristic
100C22×D32C2314yes—
101C22×C32×C4C2312yes—
102C22×C32×C4C2311yescharacteristic
103C2×#638C2314yes—
104#3828—28no—
105C2×C4⋊(C3⋊D3)C2312yes—
106C2×C4⋊(C3⋊D3)C2314yes—
107C2×C4×C3⋊D3C2314yes—
108C2×#634C2312yes—
109C2×C3×#67C2314yes—
110C22×C3×Dic3C2312yes—
111C22×C3×Dic3C2311yescharacteristic
112C3×#235—28no—
113C2×C3×D12C2312yes—
114C2×C3×D12C2314yes—
115C2×C3×C4×D3—28no—
116C2×C3×C4×D3D418yescomplemented
117C2×C3×C4×D3C2314yes—
118C2×C3×C4×D3C2312yes—
119C2×C3×C4×D3C2312yes—
120C2×C3×C4×D3C2312yes—
121C2×C3×C4×D3C2311yescharacteristic
122C2×C3×C4×D3C2311yescharacteristic
123C2×C3×C4×D3C2311yescharacteristic
124C2×C3×C4×D3C2311yescharacteristic
125C2×C3×C4×D3C2312yes—
126C2×C3×Dic6C2312yes—
127D3×#67—216no—
128C2×#627C2314yes—
129C2×#626C2314yes—
130C2×#626C2314yes—
131C2×#626C2318yes—
132C2×#625C2314yes—
133C2×#624C2314yes—
134#3804—216no—
135C2×D3×Dic3C2314yes—
136C2×D3×Dic3C2314yes—
137D3×D12—28no—
138D3×D12—216no—
139C4×D32—216no—
140#3799—28no—
141#3798—216no—
142#3795—28no—
143D3×Dic6—28no—
144C32×C42C2311yescharacteristic
145C32×C42C2312yes—
146C32×C42C2311yescharacteristic
147#3752C2318yes—
148C4⋊(C3⋊Dic3)C2314yes—
149C3×(C2×D3)⋊C4C2318yes—
150C3×C4⋊Dic3C2314yes—
151C3×C4×Dic3C2312yes—
152C3×C4×Dic3C2311yescharacteristic
153C3×C4×Dic3C2311yescharacteristic
154C3×C4×Dic3C2312yes—
155C3×C4×Dic3C2312yes—
156C3×C4×Dic3C2312yes—
157C3×C4×Dic3C2312yes—
158Dic3⋊Dic3C2318yes—
159#3722C2318yes—
160(C2×D3)⋊Dic3C2318yes—
161C2×#532—91noSylow
162C2×C3×#41—32no—
163C23×C3×C4—31no—
164C23×C3×C4—32no—
165C22×#67—34no—
166D3×#41—616no—
167C2×#239—32no—
168C2×D3×Q8—32no—
169C2×#237—34no—
170C2×#237—32no—
171C2×D3×D4—34no—
172C2×D3×D4—32no—
173C2×D3×D4—34no—
174C2×#235—32no—
175C2×#235—32no—
176C2×#235—34no—
177C2×#235—32no—
178C2×#235—34no—
179C2×#235—34no—
180C2×#235—32no—
181C2×#235—62no—
182C2×#235—616no—
183C2×#235C2×D312yescomplemented
184C22×D12—32no—
185C22×D12—34no—
186C22×C4×D3—34no—
187C22×C4×D3—34no—
188C22×C4×D3C2×D312yes—
189C22×C4×D3C2×D311yescharacteristic
190C22×Dic6—32no—
191C3×C4⋊Q8—31no—
192C3×#127—31no—
193C3×#124—32no—
194C3×#121—34no—
195C3×C4×D4—34no—
196C2×C3×C42—21no—
197C2×C3×C42—32no—
198C2×C3×C42—31no—
199C2×C3×C42—31no—
200C2×C3×C42—32no—
201C2×C3×C42—31no—
202C2×C3×C42—31no—
203C2×C3×C42—32no—
204C2×C3×C42—31no—
205C2×C3×C42C2×D311yescharacteristic, complemented
206C2×C3×C42C2×D311yescharacteristic, complemented
207#947—32no—
208#944—32no—
209#940—32no—
210#940—34no—
211#939—38no—
212#938—34no—
213#936—32no—
214D4×Dic3—34no—
215#930—34no—
216#930—34no—
217#930—38no—
218#930—34no—
219#930—38no—
220#930—34no—
221#930—64no—
222#930C2×D314yescomplemented
223C4×#67—38no—
224C2×(C2×D3)⋊C4—38no—
225C2×C4⋊Dic3—34no—
226C2×C4×Dic3C2×D311yescharacteristic, complemented
227C2×C4×Dic3C2×D312yescomplemented
228#895—34no—
229#893—34no—
230D3×C4⋊C4—34no—
231#888—34no—
232#885—38no—
233#884—38no—
234#67⋊C4—38no—
235D3×C22⋊C4—38no—
236#875—32no—
237#875—32no—
238#875—32no—
239#875—32no—
240#875—38no—
241#875—62no—
242#875C2×D312yescomplemented
243#874—32no—
244#874—34no—
245#874—31no—
246#874—31no—
247#874—61no—
248#874C2×D311yescharacteristic, complemented
249C4×D12—34no—
250C4×D12—38no—
251C4×D12—34no—
252C4×D12—34no—
253C4×D12—38no—
254C4×D12—34no—
255C4×D12—64no—
256C4×D12C2×D314yescomplemented
257C42×D3C2×D311yescharacteristic
258C42×D3C2×D311yescharacteristic
259C42×D3C2×D312yes—
260C42×D3C2×D311yescharacteristic, complemented
261C42×D3C2×D311yescharacteristic, complemented
262C42×D3C2×D312yescomplemented
263#869—32no—
264#869—31no—
265#869—31no—
266#869—34no—
267#869—61no—
268#869C2×D311yescharacteristic, complemented
269C23×C32C2411yescharacteristic
270C22×C3⋊D3C2414yes—
271C22×C3×D3—24no—
272C22×C3×D3C2×D414yes—
273C22×C3×D3C2414yes—
274C22×C3×D3C2411yescharacteristic
275C22×C3×D3C2411yescharacteristic
276C2×D32—28no—
277C2×D32—216no—
278C2×C32×C4—24no—
279C2×C32×C4C2×D414yescomplemented
280C2×C32×C4C2412yes—
281C2×C32×C4C2411yescharacteristic
282C2×C32×C4C2411yescharacteristic
283C2×C32×C4C2412yes—
284#638—28no—
285C2×C3⋊Dic3C2414yes—
286C4⋊(C3⋊D3)—24no—
287C4⋊(C3⋊D3)—28no—
288C4×C3⋊D3—28no—
289#634—24no—
290C3×#67—28no—
291C2×C3×Dic3—24no—
292C2×C3×Dic3C2×D414yescomplemented
293C2×C3×Dic3C2412yes—
294C2×C3×Dic3C2414yes—
295C2×C3×Dic3C2411yescharacteristic
296C2×C3×Dic3C2411yescharacteristic
297C2×C3×Dic3C2412yes—
298C3×D12—24no—
299C3×D12—28no—
300C3×C4×D3—24no—
301C3×C4×D3—28no—
302C3×C4×D3—24no—
303C3×C4×D3—24no—
304C3×C4×D3C2×D414yes—
305C3×C4×D3C2×D414yes—
306C3×C4×D3C2×D414yescomplemented
307C3×C4×D3C2×D414yescomplemented
308C3×C4×D3#4118yescomplemented
309C3×Dic6—24no—
310#627—28no—
311#626—28no—
312#626—28no—
313#626—216no—
314#625—28no—
315#624—28no—
316D3×Dic3—28no—
317D3×Dic3—28no—
318C22×#41—92no—
319#532—31no—
320#532—94no—
321#532—94no—
322#532—92no—
323#532—91no—
324#532—91no—
325#532—92no—
326#532—91no—
327C2×C4⋊Q8—91no—
328C2×#127—91no—
329C2×#124—92no—
330C2×#121—94no—
331C2×C4×D4—94no—
332C22×C42—31no—
333C24×C3—31no—
334C23×D3—34no—
335C23×D3—34no—
336C23×D3C22×D311yescharacteristic
337C3×#41—68no—
338C2×C3×Q8—32no—
339C2×C3×D4—34no—
340C2×C3×D4—34no—
341C2×C3×D4—32no—
342C22×C3×C4—21no—
343C22×C3×C4—22no—
344C22×C3×C4—31no—
345C22×C3×C4—38no—
346C22×C3×C4—32no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—32no—
352C22×C3×C4—32no—
353C22×C3×C4—34no—
354C22×C3×C4—32no—
355C22×C3×C4—32no—
356C22×C3×C4—68no—
357C22×C3×C4C22×D312yes—
358C22×C3×C4C22×D312yes—
359C22×C3×C4C22×D311yescharacteristic
360C22×C3×C4C22×D311yescharacteristic
361C2×#67—34no—
362C2×#67—34no—
363C2×#67—34no—
364C2×#67—34no—
365C2×#67—38no—
366C2×#67—34no—
367C2×#67—34no—
368C2×#67—64no—
369C2×#67—616no—
370C2×#67C22×D314yes—
371C22×Dic3—34no—
372C22×Dic3—34no—
373C22×Dic3C22×D312yes—
374C22×Dic3C22×D311yescharacteristic
375#239—68no—
376D3×Q8—68no—
377#237—616no—
378#237—68no—
379D3×D4—616no—
380D3×D4—68no—
381D3×D4—616no—
382#235—28no—
383#235—68no—
384#235—616no—
385#235—68no—
386#235—616no—
387#235—68no—
388#235—68no—
389#235—616no—
390#235—128no—
391C2×D12—38no—
392C2×D12—34no—
393C2×D12—34no—
394C2×D12—34no—
395C2×D12—34no—
396C2×D12—32no—
397C2×D12—32no—
398C2×D12—64no—
399C2×D12—62no—
400C2×D12—616no—
401C2×D12—68no—
402C2×D12C22×D314yes—
403C2×D12C22×D312yes—
404C2×C4×D3—28no—
405C2×C4×D3—34no—
406C2×C4×D3—34no—
407C2×C4×D3—34no—
408C2×C4×D3—34no—
409C2×C4×D3—34no—
410C2×C4×D3—34no—
411C2×C4×D3—64no—
412C2×C4×D3—616no—
413C2×C4×D3—616no—
414C2×C4×D3D1218yescomplemented
415C2×C4×D3C22×D312yes—
416C2×C4×D3C22×D312yes—
417C2×C4×D3C22×D312yes—
418C2×C4×D3C22×D314yes—
419C2×C4×D3C22×D311yescharacteristic
420C2×C4×D3C22×D311yescharacteristic
421C2×C4×D3C22×D311yescharacteristic
422C2×C4×D3C22×D311yescharacteristic
423C2×C4×D3C22×D312yes—
424C2×Dic6—32no—
425C2×Dic6—32no—
426C2×Dic6—34no—
427C2×Dic6—34no—
428C2×Dic6—62no—
429C2×Dic6—68no—
430C2×Dic6C22×D312yes—
431C3×C4⋊C4—34no—
432C3×C22⋊C4—38no—
433C3×C42—21no—
434C3×C42—22no—
435C3×C42—21no—
436C3×C42—31no—
437C3×C42—32no—
438C3×C42—32no—
439C3×C42—32no—
440C3×C42—32no—
441C3×C42—32no—
442C3×C42—31no—
443C3×C42C22×D311yescharacteristic
444C3×C42C22×D311yescharacteristic
445C3×C42C22×D312yes—
446C3×C42C22×D311yescharacteristic
447C3×C42C22×D312yes—
448C3×C42C22×D311yescharacteristic
449#217—38no—
450(C2×D3)⋊C4—38no—
451(C2×D3)⋊C4—38no—
452(C2×D3)⋊C4—38no—
453(C2×D3)⋊C4—38no—
454(C2×D3)⋊C4—38no—
455(C2×D3)⋊C4—68no—
456(C2×D3)⋊C4C22×D318yes—
457C4⋊Dic3—34no—
458C4⋊Dic3—34no—
459C4⋊Dic3—38no—
460C4⋊Dic3—64no—
461C4⋊Dic3C22×D314yes—
462Dic3⋊C4—38no—
463C4×Dic3C22×D312yes—
464C4×Dic3C22×D312yes—
465C4×Dic3C22×D312yes—
466C4×Dic3C22×D312yes—
467C4×Dic3C22×D312yes—
468C4×Dic3C22×D311yescharacteristic
469C4×Dic3C22×D311yescharacteristic
470C22×C32—22no—
471C22×C32C22×D412yes—
472C22×C32C2511yescharacteristic
473C2×C3⋊D3—24no—
474C2×C3⋊D3—28no—
475C2×C3×D3—22no—
476C2×C3×D3—28no—
477C2×C3×D3—24no—
478C2×C3×D3—28no—
479C2×C3×D3C22×D412yes—
480C2×C3×D3C22×D412yes—
481C2×C3×D3C2×#4114yes—
482D32—416no—
483C32×C4—22no—
484C32×C4C22×D412yes—
485C32×C4C22×D412yes—
486C32×C4C2×#4114yescomplemented
487C3⋊Dic3—24no—
488C3×Dic3—24no—
489C3×Dic3—22no—
490C3×Dic3C22×D412yes—
491C3×Dic3C22×D412yes—
492C3×Dic3C2×#4114yescomplemented
493C2×#41—32no—
494C2×#41—94no—
495C2×#41—94no—
496C2×#41—92no—
497C2×#41—92no—
498C2×#41—92no—
499C2×#41—1816no—
500C22×Q8—92no—
501C22×D4—94no—
502C22×D4—92no—
503C22×D4—94no—
504C23×C4—31no—
505C23×C4—32no—
506C23×C4—94no—
507C4⋊Q8—31no—
508C4⋊Q8—94no—
509C4⋊Q8—92no—
510C4⋊Q8—91no—
511#127—31no—
512#127—94no—
513#127—92no—
514#127—91no—
515#124—32no—
516#124—98no—
517#124—92no—
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—98no—
528C4×D4—94no—
529C4×D4—98no—
530C4×D4—94no—
531C4×D4—94no—
532C2×C4⋊C4—94no—
533C2×C22⋊C4—98no—
534C2×C42—32no—
535C2×C42—31no—
536C2×C42—32no—
537C2×C42—31no—
538C2×C42—31no—
539C2×C42—31no—
540C2×C42—31no—
541C2×C42—32no—
542C2×C42D3211yescharacteristic, complemented
543C23×C3—21no—
544C23×C3—31no—
545C23×C3—34no—
546C23×C3—31no—
547C23×C3—34no—
548C23×C3—64no—
549C23×C3C23×D311yescharacteristic
550C23×C3C23×D311yescharacteristic
551C22×D3—24no—
552C22×D3—34no—
553C22×D3—34no—
554C22×D3—64no—
555C22×D3—68no—
556C22×D3—616no—
557C22×D3—68no—
558C22×D3—616no—
559C22×D3C2×D1214yes—
560C22×D3C23×D314yes—
561C22×D3C23×D311yescharacteristic
562C22×D3C23×D311yescharacteristic
563C3×Q8—64no—
564C3×D4—68no—
565C3×D4—64no—
566C3×D4—68no—
567C2×C3×C4—24no—
568C2×C3×C4—24no—
569C2×C3×C4—22no—
570C2×C3×C4—21no—
571C2×C3×C4—22no—
572C2×C3×C4—21no—
573C2×C3×C4—24no—
574C2×C3×C4—34no—
575C2×C3×C4—32no—
576C2×C3×C4—31no—
577C2×C3×C4—31no—
578C2×C3×C4—34no—
579C2×C3×C4—34no—
580C2×C3×C4—34no—
581C2×C3×C4—34no—
582C2×C3×C4—38no—
583C2×C3×C4—34no—
584C2×C3×C4—32no—
585C2×C3×C4—44no—
586C2×C3×C4—64no—
587C2×C3×C4—64no—
588C2×C3×C4—64no—
589C2×C3×C4—68no—
590C2×C3×C4—64no—
591C2×C3×C4C2×D1214yescomplemented
592C2×C3×C4D3×D414yescomplemented
593C2×C3×C4C23×D312yes—
594C2×C3×C4C23×D312yes—
595C2×C3×C4C23×D311yescharacteristic
596C2×C3×C4C23×D312yes—
597C2×C3×C4C23×D311yescharacteristic
598C2×C3×C4C23×D312yes—
599C2×C3×C4C23×D311yescharacteristic
600C2×C3×C4C23×D311yescharacteristic
601#67—28no—
602#67—68no—
603#67—68no—
604#67—68no—
605#67—68no—
606#67—68no—
607#67—68no—
608#67—616no—
609#67—128no—
610C2×Dic3—24no—
611C2×Dic3—34no—
612C2×Dic3—34no—
613C2×Dic3—64no—
614C2×Dic3—68no—
615C2×Dic3—68no—
616C2×Dic3C2×D1214yescomplemented
617C2×Dic3C23×D312yes—
618C2×Dic3C23×D314yes—
619C2×Dic3C23×D311yescharacteristic
620C2×Dic3C23×D311yescharacteristic
621C2×Dic3C23×D312yes—
622D12—24no—
623D12—28no—
624D12—616no—
625D12—68no—
626D12—68no—
627D12—64no—
628D12—68no—
629D12—64no—
630D12—68no—
631D12—128no—
632D12—124no—
633C4×D3—24no—
634C4×D3—24no—
635C4×D3—28no—
636C4×D3—24no—
637C4×D3—68no—
638C4×D3—68no—
639C4×D3—68no—
640C4×D3—68no—
641C4×D3—68no—
642C4×D3—68no—
643C4×D3—128no—
644C4×D3C2×D1214yes—
645C4×D3C2×D1214yes—
646C4×D3C2×D1214yescomplemented
647C4×D3C2×D1214yescomplemented
648C4×D3#23518yescomplemented
649Dic6—24no—
650Dic6—68no—
651Dic6—64no—
652Dic6—64no—
653Dic6—68no—
654Dic6—124no—
655C2×C32—22no—
656C2×C32C23×D411yescharacteristic
657C2×C32C22×#4112yes—
658C3⋊D3—44no—
659C3×D3—22no—
660C3×D3—44no—
661C3×D3#53214yescomplemented
662C24—31no—
663C24—94no—
664#41—68no—
665#41—1816no—
666#41—1816no—
667#41—188no—
668#41—188no—
669#41—188no—
670C2×Q8—32no—
671C2×Q8—94no—
672C2×Q8—92no—
673C2×Q8—188no—
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—31no—
688C22×C4—32no—
689C22×C4—31no—
690C22×C4—31no—
691C22×C4—31no—
692C22×C4—31no—
693C22×C4—38no—
694C22×C4—32no—
695C22×C4—32no—
696C22×C4—32no—
697C22×C4—32no—
698C22×C4—34no—
699C22×C4—68no—
700C22×C4—94no—
701C22×C4—94no—
702C22×C4—94no—
703C22×C4—94no—
704C22×C4—1816no—
705C22×C4C2×D3212yes—
706C22×C4C2×D3211yescharacteristic
707C4⋊C4—34no—
708C4⋊C4—98no—
709C4⋊C4—94no—
710C22⋊C4—38no—
711C22⋊C4—98no—
712C22⋊C4—98no—
713C22⋊C4—98no—
714C42—32no—
715C42—32no—
716C42—32no—
717C42—31no—
718C42—31no—
719C42—32no—
720C42—32no—
721C42C2×D3211yescharacteristic
722C42C2×D3211yescharacteristic
723C42C2×D3212yes—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—21no—
728C22×C3—32no—
729C22×C3—34no—
730C22×C3—32no—
731C22×C3—42no—
732C22×C3—68no—
733C22×C3—62no—
734C22×C3—64no—
735C22×C3—68no—
736C22×C3C22×D1212yes—
737C22×C3C2×D3×D412yes—
738C22×C3C24×D311yescharacteristic
739C22×C3C24×D311yescharacteristic
740C2×D3—22no—
741C2×D3—28no—
742C2×D3—24no—
743C2×D3—28no—
744C2×D3—64no—
745C2×D3—68no—
746C2×D3—64no—
747C2×D3—68no—
748C2×D3—124no—
749C2×D3—128no—
750C2×D3—1216no—
751C2×D3—1216no—
752C2×D3C22×D1212yes—
753C2×D3C22×D1212yes—
754C2×D3C2×#23514yes—
755C3×C4—22no—
756C3×C4—22no—
757C3×C4—22no—
758C3×C4—22no—
759C3×C4—24no—
760C3×C4—32no—
761C3×C4—32no—
762C3×C4—34no—
763C3×C4—42no—
764C3×C4—64no—
765C3×C4—62no—
766C3×C4C22×D1212yes—
767C3×C4C22×D1212yes—
768C3×C4C2×#23514yescomplemented
769C3×C4C2×D3×D412yes—
770C3×C4C2×D3×D412yes—
771C3×C4D3×#4114yescomplemented
772Dic3—22no—
773Dic3—24no—
774Dic3—64no—
775Dic3—64no—
776Dic3—124no—
777Dic3C22×D1212yes—
778Dic3C22×D1212yes—
779Dic3C2×#23514yescomplemented
780C32C2×#53211yescharacteristic, complemented, Sylow
781C23—31no—
782C23—34no—
783C23—31no—
784C23—34no—
785C23—64no—
786C23—94no—
787C23—188no—
788C23—1816no—
789C23C22×D3211yescharacteristic
790Q8—64no—
791Q8—188no—
792Q8—184no—
793D4—68no—
794D4—64no—
795D4—68no—
796D4—188no—
797D4—1816no—
798D4—188no—
799D4—188no—
800D4—188no—
801D4—184no—
802D4—188no—
803C2×C4—24no—
804C2×C4—34no—
805C2×C4—32no—
806C2×C4—31no—
807C2×C4—31no—
808C2×C4—34no—
809C2×C4—34no—
810C2×C4—34no—
811C2×C4—34no—
812C2×C4—38no—
813C2×C4—32no—
814C2×C4—34no—
815C2×C4—64no—
816C2×C4—64no—
817C2×C4—64no—
818C2×C4—68no—
819C2×C4—64no—
820C2×C4—94no—
821C2×C4—188no—
822C2×C4—188no—
823C2×C4—188no—
824C2×C4—188no—
825C2×C4D3×D1214yescomplemented
826C2×C4C22×D3212yes—
827C2×C4C22×D3211yescharacteristic
828C2×C4C22×D3212yes—
829C2×C4C22×D3211yescharacteristic
830C2×C3—22no—
831C2×C3—22no—
832C2×C3—21no—
833C2×C3—22no—
834C2×C3—34no—
835C2×C3—42no—
836C2×C3—62no—
837C2×C3—124no—
838C2×C3C23×D1211yescharacteristic
839C2×C3C22×#23512yes—
840C2×C3C22×D3×D411yescharacteristic
841C2×C3C2×D3×#4112yes—
842D3—22no—
843D3—44no—
844D3—124no—
845D3—124no—
846D3—244no—
847D3#547714yesdirect product factor
848C22—22no—
849C22—32no—
850C22—34no—
851C22—32no—
852C22—68no—
853C22—62no—
854C22—64no—
855C22—68no—
856C22—184no—
857C22—188no—
858C22—3616no—
859C22C2×D3×D1212yes—
860C22C23×D3211yescharacteristic
861C4—22no—
862C4—32no—
863C4—32no—
864C4—34no—
865C4—64no—
866C4—62no—
867C4—184no—
868C4C2×D3×D1212yes—
869C4C2×D3×D1212yes—
870C4D3×#23514yescomplemented
871C3—21no—
872C3C2×#547711yescharacteristic, complemented
873C3D3×#53211yescharacteristic, complemented
874C2—22no—
875C2—34no—
876C2—62no—
877C2—124no—
878C2—364no—
879C2C22×D3×D1211yescharacteristic
880C2C2×D3×#23512yes—
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32C2×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×D3×#235C2semidirect
2. #10595948C2semidirect
3. C3×#5477C2semidirect
4. C2×C3×C42×D3C2semidirect
5. D3×#930C2semidirect
6. #10595029C2semidirect
7. #10594910C2semidirect
8. D3×#875C2semidirect
9. D3×#874C2semidirect
10. C4×D3×D12C2semidirect
11. #10593970C2semidirect
12. #10593969C2semidirect
13. #10593968C2semidirect
14. #10593897C2semidirect
15. D3×#869C2semidirect
18. C2×#3828C22semidirect
19. C2×C3×#235C22semidirect
23. C2×#3804C22semidirect
28. C2×#3799C22semidirect
29. C2×#3798C22semidirect
30. C2×#3795C22semidirect
32. C2×C32×C42C22semidirect
33. #64139C22semidirect
34. #64084C22semidirect
35. #64083C22semidirect
36. C4×C4⋊(C3⋊D3)C22semidirect
37. #64078C22semidirect
38. C3×#930C22semidirect
39. C2×C3×C4×Dic3C22semidirect
40. C2×C3×C4×Dic3C22semidirect
41. C3×#875C22semidirect
42. C3×#874C22semidirect
43. C3×C4×D12C22semidirect
47. C3×C42×D3C22semidirect
48. C3×C42×D3C22semidirect
49. C3×C42×D3C22semidirect
50. C3×#869C22semidirect
51. #63978C22semidirect
53. #63918C22semidirect
54. #63911C22semidirect
55. #63911C22semidirect
56. #63909C22semidirect
57. #63908C22semidirect
58. #63906C22semidirect
59. C4×#626C22semidirect
60. #63894C22semidirect
61. Dic3×D12C22semidirect
63. #63880C22semidirect
64. #63866C22semidirect
65. #63864C22semidirect
66. #63860C22semidirect
67. #63852C22semidirect
93. #5477D3direct (N × H)
97. C2×C42×D3D3semidirect
116. C2×C3×C4×D3D4semidirect
183. C2×#235C2×D3semidirect
205. C2×C3×C42C2×D3semidirect
206. C2×C3×C42C2×D3semidirect
222. #930C2×D3semidirect
226. C2×C4×Dic3C2×D3semidirect
227. C2×C4×Dic3C2×D3semidirect
242. #875C2×D3semidirect
248. #874C2×D3semidirect
256. C4×D12C2×D3semidirect
260. C42×D3C2×D3semidirect
261. C42×D3C2×D3semidirect
262. C42×D3C2×D3semidirect
268. #869C2×D3semidirect
279. C2×C32×C4C2×D4semidirect
292. C2×C3×Dic3C2×D4semidirect
306. C3×C4×D3C2×D4semidirect
307. C3×C4×D3C2×D4semidirect
308. C3×C4×D3#41semidirect
414. C2×C4×D3D12semidirect
486. C32×C4C2×#41semidirect
492. C3×Dic3C2×#41semidirect
542. C2×C42D32semidirect
591. C2×C3×C4C2×D12semidirect
592. C2×C3×C4D3×D4semidirect
616. C2×Dic3C2×D12semidirect
646. C4×D3C2×D12semidirect
647. C4×D3C2×D12semidirect
648. C4×D3#235semidirect
661. C3×D3#532semidirect
768. C3×C4C2×#235semidirect
771. C3×C4D3×#41semidirect
779. Dic3C2×#235semidirect
780. C32C2×#532semidirect
825. C2×C4D3×D12semidirect
847. D3#5477direct (N × H)
870. C4D3×#235semidirect
872. C3C2×#5477semidirect
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×#2352
#105959482
C3×#54772
C2×C3×C42×D32
D3×#9302
#105950292
#105949102
D3×#8752
D3×#8742
C4×D3×D122
#105939702
#105939692
#105939682
#105938972
D3×#8692
D3×#5323
C2×#54773