Finite Group Databasebeta

← D3×#4806 #11863611

Subgroups — D3×#4806 #11863611

Order 1152.

1663 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D32×Q8C211yesmaximal, characteristic, complemented
2C2×D3×#215C211yesmaximal, characteristic, complemented
3C2×D3×#204C211yesmaximal, characteristic, complemented
4D3×#895C211yesmaximal, characteristic
5#10592505C211yesmaximal, characteristic, complemented
6C3×#4806C211yesmaximal, characteristic, complemented
7C3×D3×#103C211yesmaximal, characteristic, complemented
8#10591592C211yesmaximal, characteristic, complemented
9#10591584C211yesmaximal, characteristic, complemented
10#10590951C211yesmaximal, characteristic, complemented
11D3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
12#10590824C211yesmaximal, characteristic, complemented
13#10590606C211yesmaximal, characteristic, complemented
14#10590603C211yesmaximal, characteristic, complemented
15D3×#810C211yesmaximal, characteristic, complemented
16D3×#448—31nomaximal
17C2×#4806—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic, complemented
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic, complemented
21D32×Q8—24no—
22D32×Q8—24no—
23C2×D3×D12—21no—
24C2×D3×D12C2211yescharacteristic
25C2×C4×D32—21no—
26C2×C4×D32C2211yescharacteristic
27C2×#3797—21no—
28C2×#3797C2211yescharacteristic, complemented
29C2×D3×Dic6—21no—
30C2×D3×Dic6—21no—
31C2×D3×Dic6C2211yescharacteristic
32C2×D3×Dic6C2211yescharacteristic, complemented
33C2×#3755C2211yescharacteristic, complemented
34C2×#3744C2211yescharacteristic, complemented
35#64104C2211yescharacteristic
36C2×C3×#215C2211yescharacteristic, complemented
37C2×C3×#204C2211yescharacteristic, complemented
38C2×C3×D3×C8C2211yescharacteristic
39C3×#895C2211yescharacteristic
40C3×D3×C4⋊C4C2211yescharacteristic
41D3×#215—24no—
42D3×(C2×D3)⋊C4—21no—
43#63916C2211yescharacteristic
44#63910—21no—
45#63909C2211yescharacteristic
46#63886—21no—
47C2×#3717C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic, complemented
49C2×#3716C2211yescharacteristic, complemented
50C2×#3715C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic
52D3×#204—24no—
53C32×#103C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55#63637C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#810C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63565C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C22×D3×Q8—31no—
66C22×D3×Q8—31no—
67C22×#215—31no—
68C2×D3×SD16—31no—
69C2×D3×SD16—31no—
70C22×#204—31no—
71D3×#121—31no—
72C2×#895—31no—
73C3×#448—31no—
74C2×C3×#103—31no—
75#5227—31no—
76#5170—31no—
77#5170—31no—
78C2×(C2×D3)⋊C8—31no—
79#5040—31no—
80C2×#810—31no—
81#4806—31no—
82#4806—31no—
83#4806—31no—
84#4806—31no—
85#4806—31no—
86#4806—31no—
87#4806—31no—
88#4806—31no—
89#4806—31no—
90#4806—61no—
91#4806D311yescharacteristic, direct product factor
92D3×#103—31no—
93D3×#103D311yescharacteristic, complemented
94#4738—31no—
95D3×C22⋊C8—31no—
96C22×D32—21no—
97C22×D32D411yescharacteristic
98C2×C32×Q8C2311yescharacteristic
99Q8×C3⋊D3—22no—
100Q8×C3⋊D3—22no—
101C2×C4⋊(C3⋊D3)—21no—
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4×C3⋊D3—21no—
104C2×C4×C3⋊D3C2311yescharacteristic
105C2×#634—21no—
106C2×#634C2311yescharacteristic
107C3×D3×Q8—22no—
108C3×D3×Q8—22no—
109C3×D3×Q8—22no—
110C3×D3×Q8D414yescomplemented
111C2×C3×D12—21no—
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×Dic6—21no—
119C2×C3×Dic6—21no—
120C2×C3×Dic6C2311yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122C2×#627—21no—
123C2×#627—21no—
124C2×#627—21no—
125C2×#626—21no—
126C2×#626—21no—
127C2×#626—21no—
128C2×#624—21no—
129C2×#624D411yescharacteristic
130C2×D3×Dic3—21no—
131C2×D3×Dic3—21no—
132C2×D3×Dic3D411yescharacteristic
133C2×D3×Dic3D411yescharacteristic
134D3×D12—22no—
135D3×D12—22no—
136D3×D12—44no—
137C4×D32—28no—
138C4×D32—22no—
139C4×D32—22no—
140#3797—28no—
141#3797—22no—
142#3797—22no—
143D3×Dic6—28no—
144D3×Dic6—28no—
145D3×Dic6—22no—
146D3×Dic6—22no—
147D3×Dic6—22no—
148D3×Dic6D414yescomplemented
149C2×C32×C8C2311yescharacteristic
150C32×C4⋊C4C2311yescharacteristic
151#3755—22no—
152#3752—21no—
153C2×C3⋊(C3⋊C8)C2311yescharacteristic
154#3744—22no—
155C3×#215—22no—
156C3×(C2×D3)⋊C4—21no—
157C3×C4⋊Dic3C2311yescharacteristic
158C3×Dic3⋊C4—21no—
159C2×C3×C3⋊C8C2311yescharacteristic
160C2×C3×C3⋊C8C2311yescharacteristic
161C3×#204—22no—
162C3×D3×C8—22no—
163#3722—21no—
164(C2×D3)⋊Dic3—21no—
165#3717—22no—
166#3717—22no—
167#3716—22no—
168#3715—22no—
169D3×C3⋊C8—22no—
170C2×#448—91noSylow
171C22×C3×Q8—31no—
172C22×C3×Q8—31no—
173C2×D3×Q8—31no—
174C2×D3×Q8—31no—
175C2×D3×Q8—31no—
176C2×D3×Q8—31no—
177C2×D3×Q8—31no—
178C2×D3×Q8—31no—
179C2×D3×Q8—61no—
180C2×D3×Q8—61no—
181C2×D3×Q8—61no—
182C2×D3×Q8—64no—
183C2×D3×Q8—61no—
184C2×D3×Q8—61no—
185C2×D3×Q8—64no—
186C2×D3×Q8—64no—
187C2×D3×Q8—64no—
188C2×D3×Q8C2×D311yescharacteristic
189C2×D3×Q8C2×D311yescharacteristic, complemented
190C2×D3×D4—31no—
191C2×D3×D4—61no—
192C22×D12—31no—
193C22×D12—61no—
194C22×C4×D3—31no—
195C22×C4×D3—31no—
196C22×C4×D3—61no—
197C22×C4×D3—61no—
198C22×Dic6—31no—
199C22×Dic6—31no—
200C22×Dic6—61no—
201C22×Dic6—61no—
202C2×C3×SD16—31no—
203C2×C3×SD16—31no—
204C22×C3×C8—31no—
205C3×#121—31no—
206C2×C3×C4⋊C4—31no—
207C2×#215—31no—
208C2×#215—31no—
209C2×#215—31no—
210C2×#215—31no—
211C2×#215—31no—
212C2×#215—61no—
213C2×#215—64no—
214C2×#215C2×D311yescharacteristic, complemented
215#939—61no—
216#938—31no—
217C2×#214—31no—
218C2×#214—31no—
219#930—31no—
220C2×(C2×D3)⋊C4—61no—
221C22×C3⋊C8—31no—
222D3×SD16—64no—
223D3×SD16—64no—
224C2×#204—31no—
225C2×#204—31no—
226C2×#204—31no—
227C2×#204—31no—
228C2×#204—31no—
229C2×#204—61no—
230C2×#204—64no—
231C2×#204C2×D311yescharacteristic, complemented
232C2×D3×C8—31no—
233C2×D3×C8C2×D311yescharacteristic
234#895—31no—
235#895—31no—
236#895—31no—
237#895—31no—
238#895—61no—
239#895—61no—
240#895—61no—
241#895C2×D311yescharacteristic
242D3×C4⋊C4C2×D311yescharacteristic
243#884—61no—
244D3×C22⋊C4—61no—
245C3×#103—21no—
246C3×#103—31no—
247C3×#103—31no—
248C3×#103—31no—
249C3×#103—31no—
250C3×#103C2×D311yescharacteristic, complemented
251C3×#103C2×D311yescharacteristic, complemented
252C3×C22⋊C8—31no—
253#835—31no—
254#835C2×D311yescharacteristic, complemented
255#830—31no—
256(C2×D3)⋊C8—31no—
257(C2×D3)⋊C8—31no—
258(C2×D3)⋊C8—31no—
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—61no—
262(C2×D3)⋊C8C2×D311yescharacteristic, complemented
263#816—31no—
264#816C2×D311yescharacteristic, complemented
265#810—31no—
266#810—31no—
267#810—31no—
268#810—31no—
269#810—61no—
270#810C2×D311yescharacteristic, complemented
271#810C2×D311yescharacteristic, complemented
272C22×C3⋊D3—21no—
273C22×C3⋊D3C2×D411yescharacteristic
274C22×C3×D3—21no—
275C22×C3×D3C2×D411yescharacteristic
276C22×C3×D3C2×D411yescharacteristic
277C2×D32—22no—
278C2×D32—22no—
279C2×D32—42no—
280C2×D32—42no—
281C2×D32—42no—
282C2×D32SD1614yescomplemented
283C32×Q8—21no—
284C32×Q8C2×D412yescomplemented
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4C2411yescharacteristic
288C2×C3⋊Dic3—21no—
289C2×C3⋊Dic3C2×D411yescharacteristic
290C4⋊(C3⋊D3)—21no—
291C4⋊(C3⋊D3)—21no—
292C4⋊(C3⋊D3)—42no—
293C4×C3⋊D3—24no—
294C4×C3⋊D3—21no—
295C4×C3⋊D3—21no—
296#634—24no—
297#634—21no—
298#634C2×D412yescomplemented
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3C2×D411yescharacteristic
303C2×C3×Dic3C2×D411yescharacteristic
304C3×D12—21no—
305C3×D12—21no—
306C3×D12—42no—
307C3×C4×D3—24no—
308C3×C4×D3—24no—
309C3×C4×D3—21no—
310C3×C4×D3—21no—
311C3×C4×D3—42no—
312C3×C4×D3C2×D412yes—
313C3×C4×D3C2×D412yes—
314C3×Dic6—24no—
315C3×Dic6—21no—
316C3×Dic6—21no—
317C3×Dic6—24no—
318C3×Dic6C2×D412yescomplemented
319C3×Dic6C2×D412yescomplemented
320#627—24no—
321#627—24no—
322#627—24no—
323#626—42no—
324#626—42no—
325#626—42no—
326#624—24no—
327#624—22no—
328D3×Dic3—24no—
329D3×Dic3—22no—
330D3×Dic3—24no—
331D3×Dic3—22no—
332C32×C8—21no—
333C3⋊(C3⋊C8)—21no—
334C3×C3⋊C8—21no—
335C3×C3⋊C8—21no—
336C23×Q8—91no—
337C22×SD16—91no—
338C22×SD16—91no—
339C2×#121—91no—
340#448—31no—
341#448—91no—
342#448—91no—
343#448—91no—
344#448—91no—
345#448—91no—
346#448—91no—
347#448—91no—
348C2×#103—31no—
349C2×#103—91no—
350C2×C22⋊C8—91no—
351C23×D3—31no—
352C23×D3—31no—
353C23×D3—61no—
354C23×D3—61no—
355C2×C3×Q8—21no—
356C2×C3×Q8—34no—
357C2×C3×Q8—31no—
358C2×C3×Q8—31no—
359C2×C3×Q8—61no—
360C2×C3×Q8—61no—
361C2×C3×Q8—62no—
362C2×C3×Q8—62no—
363C2×C3×Q8—62no—
364C2×C3×Q8C22×D311yescharacteristic
365C2×C3×Q8C22×D311yescharacteristic
366C2×C3×D4—31no—
367C2×C3×D4—61no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—61no—
371C22×C3×C4—61no—
372C22×C3×C4—61no—
373C2×#67—61no—
374C2×#67—61no—
375C2×#67—61no—
376C22×Dic3—31no—
377C22×Dic3—31no—
378C22×Dic3—61no—
379C22×Dic3—61no—
380D3×Q8—22no—
381D3×Q8—22no—
382D3×Q8—22no—
383D3×Q8—34no—
384D3×Q8—62no—
385D3×Q8—62no—
386D3×Q8—68no—
387D3×Q8—68no—
388D3×Q8—62no—
389D3×Q8—62no—
390D3×Q8—62no—
391D3×Q8—62no—
392D3×Q8—68no—
393D3×Q8—68no—
394D3×Q8—62no—
395D3×Q8—62no—
396D3×Q8—62no—
397D3×Q8—62no—
398D3×Q8—62no—
399D3×Q8—122no—
400D3×Q8—122no—
401D3×Q8D1214yescomplemented
402D3×D4—62no—
403D3×D4—62no—
404D3×D4—124no—
405C2×D12—21no—
406C2×D12—31no—
407C2×D12—31no—
408C2×D12—61no—
409C2×D12—62no—
410C2×D12—62no—
411C2×D12—61no—
412C2×D12—61no—
413C2×D12—61no—
414C2×D12—61no—
415C2×D12—61no—
416C2×D12—121no—
417C2×D12—124no—
418C2×D12C22×D311yescharacteristic
419C2×C4×D3—21no—
420C2×C4×D3—21no—
421C2×C4×D3—21no—
422C2×C4×D3—31no—
423C2×C4×D3—31no—
424C2×C4×D3—31no—
425C2×C4×D3—31no—
426C2×C4×D3—31no—
427C2×C4×D3—31no—
428C2×C4×D3—61no—
429C2×C4×D3—62no—
430C2×C4×D3—62no—
431C2×C4×D3—68no—
432C2×C4×D3—68no—
433C2×C4×D3—61no—
434C2×C4×D3—61no—
435C2×C4×D3—61no—
436C2×C4×D3—61no—
437C2×C4×D3—61no—
438C2×C4×D3—61no—
439C2×C4×D3—62no—
440C2×C4×D3—62no—
441C2×C4×D3—121no—
442C2×C4×D3C22×D311yescharacteristic
443C2×C4×D3C22×D311yescharacteristic
444C2×Dic6—21no—
445C2×Dic6—21no—
446C2×Dic6—31no—
447C2×Dic6—31no—
448C2×Dic6—34no—
449C2×Dic6—61no—
450C2×Dic6—62no—
451C2×Dic6—62no—
452C2×Dic6—68no—
453C2×Dic6—68no—
454C2×Dic6—61no—
455C2×Dic6—61no—
456C2×Dic6—61no—
457C2×Dic6—61no—
458C2×Dic6—61no—
459C2×Dic6—61no—
460C2×Dic6—61no—
461C2×Dic6—61no—
462C2×Dic6—62no—
463C2×Dic6—121no—
464C2×Dic6C22×D311yescharacteristic
465C2×Dic6C22×D311yescharacteristic
466C3×SD16—62no—
467C3×SD16—62no—
468C2×C3×C8—21no—
469C2×C3×C8—31no—
470C2×C3×C8—31no—
471C2×C3×C8—62no—
472C2×C3×C8C22×D311yescharacteristic
473C2×C3×C8C22×D311yescharacteristic
474C3×C4⋊C4—21no—
475C3×C4⋊C4—31no—
476C3×C4⋊C4—61no—
477C3×C4⋊C4C22×D311yescharacteristic
478C3×C4⋊C4C22×D311yescharacteristic
479C3×C22⋊C4—61no—
480#217—61no—
481#215—22no—
482#215—62no—
483#215—62no—
484#215—62no—
485#215—62no—
486#215—62no—
487#215—122no—
488#214—62no—
489#214—62no—
490(C2×D3)⋊C4—21no—
491(C2×D3)⋊C4—61no—
492(C2×D3)⋊C4—61no—
493(C2×D3)⋊C4—61no—
494(C2×D3)⋊C4—61no—
495(C2×D3)⋊C4—61no—
496(C2×D3)⋊C4—121no—
497C4⋊Dic3C22×D311yescharacteristic
498Dic3⋊C4—21no—
499C2×C3⋊C8—31no—
500C2×C3⋊C8—31no—
501C2×C3⋊C8—61no—
502C2×C3⋊C8—62no—
503C2×C3⋊C8C22×D311yescharacteristic
504C2×C3⋊C8C22×D311yescharacteristic
505#204—22no—
506#204—62no—
507#204—62no—
508#204—62no—
509#204—62no—
510#204—62no—
511#204—122no—
512D3×C8—22no—
513D3×C8—62no—
514C22×C32C22×D411yescharacteristic
515C2×C3⋊D3—21no—
516C2×C3⋊D3—21no—
517C2×C3⋊D3—41no—
518C2×C3⋊D3—41no—
519C2×C3⋊D3—41no—
520C2×C3⋊D3C2×SD1612yescomplemented
521C2×C3×D3—21no—
522C2×C3×D3—21no—
523C2×C3×D3—41no—
524C2×C3×D3—41no—
525C2×C3×D3—41no—
526C2×C3×D3#12012yes—
527C2×C3×D3C2×SD1612yes—
528C2×C3×D3C2×SD1612yescomplemented
529C2×C3×D3#13712yes—
530D32—28no—
531D32—84no—
532C32×C4—22no—
533C32×C4—41no—
534C32×C4C22×D411yescharacteristic
535C32×C4C22×D411yescharacteristic
536C3⋊Dic3—21no—
537C3⋊Dic3—22no—
538C3×Dic3—21no—
539C3×Dic3—22no—
540C3×Dic3—22no—
541C3×Dic3—41no—
542C3×Dic3#12012yes—
543C22×Q8—31no—
544C22×Q8—31no—
545C22×Q8—91no—
546C22×Q8—91no—
547C22×Q8—91no—
548C22×Q8—91no—
549C22×Q8—181no—
550C22×Q8—181no—
551C22×Q8—181no—
552C22×Q8—184no—
553C22×Q8—184no—
554C22×D4—91no—
555C22×D4—181no—
556C23×C4—91no—
557C23×C4—181no—
558C2×SD16—31no—
559C2×SD16—31no—
560C2×SD16—91no—
561C2×SD16—91no—
562C2×SD16—91no—
563C2×SD16—91no—
564C2×SD16—91no—
565C2×SD16—91no—
566C2×SD16—184no—
567C2×SD16—184no—
568C22×C8—31no—
569C22×C8—91no—
570#121—31no—
571#121—91no—
572#121—91no—
573#121—91no—
574#121—181no—
575#121—181no—
576C2×C4⋊C4—31no—
577C2×C22⋊C4—181no—
578#103—31no—
579#103—31no—
580#103—31no—
581#103—31no—
582#103—91no—
583#103—91no—
584#103—91no—
585#103D3211yescharacteristic, complemented
586C22⋊C8—31no—
587C22⋊C8—91no—
588C22⋊C8—91no—
589C22⋊C8—91no—
590C23×C3—31no—
591C23×C3—31no—
592C23×C3—61no—
593C22×D3—21no—
594C22×D3—31no—
595C22×D3—31no—
596C22×D3—34no—
597C22×D3—34no—
598C22×D3—61no—
599C22×D3—62no—
600C22×D3—62no—
601C22×D3—62no—
602C22×D3—62no—
603C22×D3—61no—
604C22×D3—61no—
605C22×D3—121no—
606C22×D3—122no—
607C22×D3—122no—
608C22×D3—122no—
609C22×D3—122no—
610C22×D3—122no—
611C22×D3—122no—
612C22×D3D3×D411yescharacteristic
613C22×D3D3×D411yescharacteristic
614C3×Q8—21no—
615C3×Q8—21no—
616C3×Q8—22no—
617C3×Q8—32no—
618C3×Q8—32no—
619C3×Q8—41no—
620C3×Q8—64no—
621C3×Q8—64no—
622C3×Q8—61no—
623C3×Q8—61no—
624C3×Q8C2×D1212yescomplemented
625C3×Q8D3×D412yescomplemented
626C3×D4—61no—
627C3×D4—61no—
628C3×D4—122no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—31no—
635C2×C3×C4—32no—
636C2×C3×C4—32no—
637C2×C3×C4—31no—
638C2×C3×C4—41no—
639C2×C3×C4—41no—
640C2×C3×C4—64no—
641C2×C3×C4—64no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4—61no—
645C2×C3×C4—61no—
646C2×C3×C4—61no—
647C2×C3×C4—122no—
648C2×C3×C4C23×D311yescharacteristic
649C2×C3×C4C23×D311yescharacteristic
650#67—122no—
651#67—122no—
652#67—122no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—21no—
656C2×Dic3—31no—
657C2×Dic3—31no—
658C2×Dic3—61no—
659C2×Dic3—64no—
660C2×Dic3—62no—
661C2×Dic3—64no—
662C2×Dic3—61no—
663C2×Dic3—61no—
664C2×Dic3—62no—
665C2×Dic3—121no—
666C2×Dic3D3×D411yescharacteristic
667C2×Dic3D3×D411yescharacteristic
668D12—21no—
669D12—21no—
670D12—42no—
671D12—61no—
672D12—61no—
673D12—61no—
674D12—61no—
675D12—121no—
676D12—121no—
677D12—122no—
678D12—122no—
679D12—122no—
680D12—122no—
681D12—122no—
682D12—242no—
683C4×D3—24no—
684C4×D3—24no—
685C4×D3—21no—
686C4×D3—21no—
687C4×D3—42no—
688C4×D3—62no—
689C4×D3—64no—
690C4×D3—64no—
691C4×D3—64no—
692C4×D3—64no—
693C4×D3—62no—
694C4×D3—64no—
695C4×D3—62no—
696C4×D3—64no—
697C4×D3—61no—
698C4×D3—61no—
699C4×D3—61no—
700C4×D3—61no—
701C4×D3—62no—
702C4×D3—121no—
703C4×D3—121no—
704C4×D3—124no—
705C4×D3C2×D1212yes—
706C4×D3D3×D412yes—
707Dic6—24no—
708Dic6—21no—
709Dic6—21no—
710Dic6—24no—
711Dic6—32no—
712Dic6—32no—
713Dic6—62no—
714Dic6—64no—
715Dic6—64no—
716Dic6—64no—
717Dic6—64no—
718Dic6—64no—
719Dic6—64no—
720Dic6—64no—
721Dic6—61no—
722Dic6—61no—
723Dic6—64no—
724Dic6—121no—
725Dic6—124no—
726Dic6C2×D1212yescomplemented
727Dic6D3×D412yescomplemented
728C3×C8—21no—
729C3×C8—21no—
730C3×C8—41no—
731C3×C8—61no—
732C3×C8—61no—
733C3⋊C8—21no—
734C3⋊C8—21no—
735C3⋊C8—61no—
736C3⋊C8—61no—
737C3⋊C8—121no—
738C2×C32C2×#12011yescharacteristic
739C2×C32C22×SD1611yescharacteristic
740C2×C32C2×#13711yescharacteristic
741C3⋊D3—22no—
742C3⋊D3—81no—
743C3×D3—22no—
744C3×D3—81no—
745C3×D3#44814yescomplemented
746C24—91no—
747C24—181no—
748C2×Q8—34no—
749C2×Q8—31no—
750C2×Q8—31no—
751C2×Q8—61no—
752C2×Q8—61no—
753C2×Q8—62no—
754C2×Q8—62no—
755C2×Q8—62no—
756C2×Q8—94no—
757C2×Q8—91no—
758C2×Q8—181no—
759C2×Q8—181no—
760C2×Q8—181no—
761C2×Q8—182no—
762C2×Q8—181no—
763C2×Q8—182no—
764C2×Q8—182no—
765C2×Q8—188no—
766C2×Q8—188no—
767C2×Q8—182no—
768C2×Q8—182no—
769C2×Q8—182no—
770C2×Q8—188no—
771C2×Q8—182no—
772C2×Q8C2×D3211yescharacteristic
773C2×D4—31no—
774C2×D4—61no—
775C2×D4—91no—
776C2×D4—181no—
777C2×D4—182no—
778C2×D4—182no—
779C2×D4—181no—
780C2×D4—181no—
781C2×D4—181no—
782C2×D4—364no—
783C22×C4—31no—
784C22×C4—31no—
785C22×C4—61no—
786C22×C4—61no—
787C22×C4—61no—
788C22×C4—91no—
789C22×C4—91no—
790C22×C4—91no—
791C22×C4—91no—
792C22×C4—181no—
793C22×C4—182no—
794C22×C4—182no—
795C22×C4—181no—
796C22×C4—188no—
797C22×C4—181no—
798C22×C4—181no—
799SD16—62no—
800SD16—62no—
801SD16—182no—
802SD16—182no—
803SD16—182no—
804SD16—182no—
805SD16—182no—
806SD16—182no—
807C2×C8—31no—
808C2×C8—31no—
809C2×C8—62no—
810C2×C8—91no—
811C2×C8—182no—
812C2×C8C2×D3211yescharacteristic
813C4⋊C4—31no—
814C4⋊C4—61no—
815C4⋊C4C2×D3211yescharacteristic
816C22⋊C4—61no—
817C22⋊C4—181no—
818C22⋊C4—181no—
819C22⋊C4—181no—
820C22×C3—21no—
821C22×C3—32no—
822C22×C3—32no—
823C22×C3—32no—
824C22×C3—32no—
825C22×C3—61no—
826C22×C3—61no—
827C22×C3—121no—
828C22×C3—121no—
829C22×C3—121no—
830C22×C3C2×D3×D411yescharacteristic
831C22×C3C2×D3×D411yescharacteristic
832C2×D3—21no—
833C2×D3—21no—
834C2×D3—32no—
835C2×D3—32no—
836C2×D3—41no—
837C2×D3—41no—
838C2×D3—41no—
839C2×D3—62no—
840C2×D3—68no—
841C2×D3—61no—
842C2×D3—61no—
843C2×D3—61no—
844C2×D3—61no—
845C2×D3—68no—
846C2×D3—121no—
847C2×D3—121no—
848C2×D3—121no—
849C2×D3—121no—
850C2×D3—121no—
851C2×D3—121no—
852C2×D3—121no—
853C2×D3—121no—
854C2×D3—241no—
855C2×D3—241no—
856C2×D3—241no—
857C2×D3—244no—
858C2×D3—244no—
859C2×D3#88212yes—
860C2×D3D3×SD1612yes—
861C2×D3D3×SD1612yescomplemented
862C2×D3#91812yes—
863C3×C4—22no—
864C3×C4—22no—
865C3×C4—21no—
866C3×C4—21no—
867C3×C4—32no—
868C3×C4—42no—
869C3×C4—41no—
870C3×C4—41no—
871C3×C4—61no—
872C3×C4—62no—
873C3×C4—62no—
874C3×C4—81no—
875C3×C4—121no—
876C3×C4C22×D1211yescharacteristic
877C3×C4C2×D3×D411yescharacteristic
878C3×C4C2×D3×D411yescharacteristic
879C3×C4C2×D3×D411yescharacteristic
880Dic3—22no—
881Dic3—21no—
882Dic3—22no—
883Dic3—41no—
884Dic3—62no—
885Dic3—61no—
886Dic3—62no—
887Dic3—61no—
888Dic3—122no—
889Dic3—121no—
890Dic3#88212yes—
891C32C2×#44811yescharacteristic, complemented, Sylow
892C23—31no—
893C23—31no—
894C23—61no—
895C23—94no—
896C23—91no—
897C23—182no—
898C23—182no—
899C23—181no—
900C23—362no—
901C23—362no—
902C23—362no—
903Q8—21no—
904Q8—32no—
905Q8—32no—
906Q8—64no—
907Q8—64no—
908Q8—61no—
909Q8—61no—
910Q8—92no—
911Q8—184no—
912Q8—184no—
913Q8—184no—
914Q8—184no—
915Q8—181no—
916Q8D3×D1212yescomplemented
917D4—61no—
918D4—61no—
919D4—122no—
920D4—181no—
921D4—181no—
922D4—362no—
923D4—362no—
924D4—362no—
925D4—362no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—31no—
929C2×C4—32no—
930C2×C4—32no—
931C2×C4—31no—
932C2×C4—64no—
933C2×C4—64no—
934C2×C4—61no—
935C2×C4—61no—
936C2×C4—61no—
937C2×C4—61no—
938C2×C4—61no—
939C2×C4—91no—
940C2×C4—122no—
941C2×C4—184no—
942C2×C4—182no—
943C2×C4—182no—
944C2×C4—184no—
945C2×C4—182no—
946C2×C4—184no—
947C2×C4—184no—
948C2×C4—181no—
949C2×C4—181no—
950C2×C4—181no—
951C2×C4C22×D3211yescharacteristic
952C8—21no—
953C8—61no—
954C8—61no—
955C8—181no—
956C2×C3—21no—
957C2×C3—21no—
958C2×C3—21no—
959C2×C3—34no—
960C2×C3—62no—
961C2×C3—241no—
962C2×C3C2×#88211yescharacteristic
963C2×C3D3×#12011yescharacteristic
964C2×C3C2×D3×SD1611yescharacteristic
965C2×C3C2×D3×SD1611yescharacteristic
966C2×C3C2×#91811yescharacteristic
967C2×C3D3×#13711yescharacteristic
968D3—22no—
969D3—62no—
970D3—62no—
971D3—81no—
972D3—122no—
973D3—241no—
974D3—241no—
975D3—481no—
976D3#480614yesdirect product factor
977C22—32no—
978C22—32no—
979C22—32no—
980C22—32no—
981C22—61no—
982C22—61no—
983C22—92no—
984C22—121no—
985C22—121no—
986C22—121no—
987C22—188no—
988C22—181no—
989C22—181no—
990C22—361no—
991C22—361no—
992C22—361no—
993C22—724no—
994C22D32×D411yescharacteristic
995C4—22no—
996C4—32no—
997C4—41no—
998C4—61no—
999C4—62no—
1000C4—62no—
1001C4—121no—
1002C4—181no—
1003C4—182no—
1004C4C2×D3×D1211yescharacteristic
1005C4D32×D411yescharacteristic
1006C3—21no—
1007C3C2×#480611yescharacteristic, complemented
1008C3D3×#44811yescharacteristic, complemented
1009C2—34no—
1010C2—62no—
1011C2—182no—
1012C2—241no—
1013C2—721no—
1014C2D3×#88211yescharacteristic
1015C2D32×SD1611yescharacteristic
1016C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalD3×#895C2
hypercenter#103D32
hypocenterC32C2×#448
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. C2×D32×Q8C2semidirect
2. C2×D3×#215C2semidirect
3. C2×D3×#204C2semidirect
5. #10592505C2semidirect
6. C3×#4806C2semidirect
7. C3×D3×#103C2semidirect
8. #10591592C2semidirect
9. #10591584C2semidirect
10. #10590951C2semidirect
11. D3×(C2×D3)⋊C8C2semidirect
12. #10590824C2semidirect
13. #10590606C2semidirect
14. #10590603C2semidirect
15. D3×#810C2semidirect
18. C2×Q8×C3⋊D3C22semidirect
20. C2×C3×D3×Q8C22semidirect
28. C2×#3797C22semidirect
32. C2×D3×Dic6C22semidirect
33. C2×#3755C22semidirect
34. C2×#3744C22semidirect
36. C2×C3×#215C22semidirect
37. C2×C3×#204C22semidirect
47. C2×#3717C22semidirect
48. C2×#3717C22semidirect
49. C2×#3716C22semidirect
50. C2×#3715C22semidirect
53. C32×#103C22semidirect
54. #63647C22semidirect
55. #63637C22semidirect
56. C3×#835C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#816C22semidirect
59. C3×#810C22semidirect
60. C3×#810C22semidirect
61. #63567C22semidirect
62. #63565C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
91. #4806D3direct (N × H)
93. D3×#103D3semidirect
110. C3×D3×Q8D4semidirect
148. D3×Dic6D4semidirect
189. C2×D3×Q8C2×D3semidirect
214. C2×#215C2×D3semidirect
231. C2×#204C2×D3semidirect
250. C3×#103C2×D3semidirect
251. C3×#103C2×D3semidirect
254. #835C2×D3semidirect
262. (C2×D3)⋊C8C2×D3semidirect
264. #816C2×D3semidirect
270. #810C2×D3semidirect
271. #810C2×D3semidirect
282. C2×D32SD16semidirect
284. C32×Q8C2×D4semidirect
298. #634C2×D4semidirect
318. C3×Dic6C2×D4semidirect
319. C3×Dic6C2×D4semidirect
401. D3×Q8D12semidirect
520. C2×C3⋊D3C2×SD16semidirect
528. C2×C3×D3C2×SD16semidirect
585. #103D32semidirect
624. C3×Q8C2×D12semidirect
625. C3×Q8D3×D4semidirect
726. Dic6C2×D12semidirect
727. Dic6D3×D4semidirect
745. C3×D3#448semidirect
861. C2×D3D3×SD16semidirect
891. C32C2×#448semidirect
916. Q8D3×D12semidirect
976. D3#4806direct (N × H)
1007. C3C2×#4806semidirect
1008. C3D3×#448semidirect

Maximal subgroups

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

subgroupindex
C2×D32×Q82
C2×D3×#2152
C2×D3×#2042
D3×#8952
#105925052
C3×#48062
C3×D3×#1032
#105915922
#105915842
#105909512
D3×(C2×D3)⋊C82
#105908242
#105906062
#105906032
D3×#8102
D3×#4483
C2×#48063