Finite Group Databasebeta

← #11864591

Subgroups — #11864591

Order 1152.

1627 conjugacy classes of subgroups.

The subgroup lattice has 1051 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1004C211yesmaximal, characteristic, complemented
2C2×#63935C211yesmaximal, characteristic, complemented
3C2×#63934C211yesmaximal, characteristic, complemented
4#10594894C211yesmaximal, characteristic, complemented
5#10592916C211yesmaximal, characteristic, complemented
6C3×#5218C211yesmaximal, characteristic, complemented
7#10591461C211yesmaximal, characteristic, complemented
8#10591458C211yesmaximal, characteristic, complemented
9#10591452C211yesmaximal, characteristic, complemented
10#10591448C211yesmaximal, characteristic, complemented
11#10591414C211yesmaximal, characteristic, complemented
12D3×#832C211yesmaximal, characteristic, complemented
13#10591170C211yesmaximal, characteristic, complemented
14#10591163C211yesmaximal, characteristic, complemented
15#10591145C211yesmaximal, characteristic, complemented
16#84102—31nomaximal
17#80149—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C22×C3×#67—21no—
20C22×C3×#67—21no—
21C3×#1004—24no—
22C3×#1004—24no—
23C2×C3×#237—21no—
24C2×C3×#237C2211yescharacteristic
25C2×C3×#237C2211yescharacteristic
26C2×C3×D3×D4—21no—
27C2×C3×D3×D4C2211yescharacteristic
28C2×C3×D3×D4C2211yescharacteristic
29C2×C3×#235C2211yescharacteristic
30C2×C3×#235C2211yescharacteristic
31C2×#3799C2211yescharacteristic, complemented
32C2×#3753C2211yescharacteristic, complemented
33C2×#3753C2211yescharacteristic, complemented
34#64139C2211yescharacteristic, complemented
35C2×C3×#214C2211yescharacteristic, complemented
36C2×C3×#214C2211yescharacteristic, complemented
37C3×#924C2211yescharacteristic, complemented
38#63971—21no—
39#63958—21no—
40#63935—24no—
41#63934—24no—
42#63909C2211yescharacteristic, complemented
43D3×C4⋊Dic3C2211yescharacteristic, complemented
44#63888—21no—
45#63886—21no—
46#63856C2211yescharacteristic, complemented
47C2×#3718C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52C2×D3×C3⋊C8C2211yescharacteristic, complemented
53#63659C2211yescharacteristic, complemented
54#63659C2211yescharacteristic, complemented
55#63657C2211yescharacteristic, complemented
56C3×#832C2211yescharacteristic, complemented
57C3×#832C2211yescharacteristic, complemented
58C3×#830C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×C3×H(5,𝔽2)—31no—
66C2×#1004D311yescharacteristic, complemented
67#5833—31no—
68C2×#950—31no—
69C2×#932—31no—
70C2×#916—31no—
71C2×#914—31no—
72#5629—31no—
73C3×#450—31no—
74#5239—31no—
75#5239—31no—
76#5238—31no—
77#5238—31no—
78#5234—31no—
79#5232—31no—
80#5218—31no—
81#5218D311yescharacteristic, complemented
82#5217—31no—
83#5217—31no—
84#5217—31no—
85#5217—61no—
86C2×#832—31no—
87#5173—31no—
88#5169—31no—
89#5047—31no—
90#4781—31no—
91#4773—31no—
92#4771—31no—
93D3×#102—31no—
94#4734—31no—
95#4727—31no—
96C24×C32—21no—
97C23×C3×D3—21no—
98C23×C3×D3—21no—
99C2×C32×D4—22no—
100C2×C32×D4—22no—
101C2×C32×D4—21no—
102C2×C32×D4C2311yescharacteristic
103C2×C32×D4C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C2×#638—21no—
106C2×C4⋊(C3⋊D3)C2311yescharacteristic
107C2×C3×#67—28no—
108C2×C3×#67—28no—
109C2×C3×#67—21no—
110C2×C3×#67—21no—
111C2×C3×#67—21no—
112C2×C3×#67—21no—
113C2×C3×#67—21no—
114C2×C3×#67D411yescharacteristic
115C2×C3×#67D411yescharacteristic
116C22×C3×Dic3—21no—
117C22×C3×Dic3—21no—
118C3×#237—28no—
119C3×#237—22no—
120C3×#237—22no—
121C3×#237—22no—
122C3×#237D414yescomplemented
123C3×D3×D4—28no—
124C3×D3×D4—22no—
125C3×D3×D4—22no—
126C3×D3×D4—22no—
127C3×D3×D4D414yescomplemented
128C3×#235—22no—
129C3×#235—22no—
130C3×#235—22no—
131C3×#235—22no—
132C2×C3×D12D411yescharacteristic
133C2×C3×D12C2311yescharacteristic
134C2×C3×C4×D3—21no—
135C2×C3×C4×D3C2311yescharacteristic
136C2×C3×C4×D3C2311yescharacteristic
137C2×C3×Dic6D411yescharacteristic
138C2×C3×Dic6C2311yescharacteristic
139C2×C3×Dic6C2311yescharacteristic
140C2×#626—21no—
141C2×#626—21no—
142C2×#624—21no—
143C2×D3×Dic3—21no—
144#3799—22no—
145#3799—22no—
146#3753—22no—
147#3753—22no—
148#3752—21no—
149C4⋊(C3⋊Dic3)C2311yescharacteristic
150C2×C3⋊(C3⋊C8)C2311yescharacteristic
151C2×C3⋊(C3⋊C8)C2311yescharacteristic
152C3×#217—21no—
153C3×#214—22no—
154C3×#214—22no—
155C3×C4⋊Dic3C2311yescharacteristic
156C3×Dic3⋊C4—21no—
157C2×C3×C3⋊C8C2311yescharacteristic
158C2×C3×C3⋊C8C2311yescharacteristic
159#3724—21no—
160Dic3⋊Dic3—21no—
161#3722—21no—
162(C2×D3)⋊Dic3—21no—
163#3718—22no—
164#3717—22no—
165#3715—22no—
166#3714—22no—
167#3711—22no—
168D3×C3⋊C8—22no—
169#3012—91noSylow
170C3×H(5,𝔽2)—64no—
171C3×H(5,𝔽2)—64no—
172C2×C3×#41—31no—
173C2×C3×#41—31no—
174C2×C3×#41—31no—
175C2×C3×#41—31no—
176C2×C3×#41—61no—
177C22×C3×D4—21no—
178C22×C3×D4—31no—
179C22×C3×D4—31no—
180C22×C3×D4—61no—
181C22×C3×D4—61no—
182C22×C3×D4—61no—
183C22×C3×D4C2×D311yescharacteristic
184C22×C3×D4C2×D311yescharacteristic
185C22×#67—21no—
186C22×#67—21no—
187C2×#239—31no—
188#1004—24no—
189#1004—24no—
190C2×#237—21no—
191C2×#237C2×D311yescharacteristic
192C2×#237C2×D311yescharacteristic
193C2×D3×D4—21no—
194C2×D3×D4C2×D311yescharacteristic
195C2×D3×D4C2×D311yescharacteristic
196C2×#235—31no—
197C2×#235C2×D311yescharacteristic
198C2×#235C2×D311yescharacteristic
199C2×C3×SD16—31no—
200C2×C3×SD16—31no—
201C3×C22⋊Q8—31no—
202#950—64no—
203#946—31no—
204#946—61no—
205C2×#216—31no—
206C2×#216—31no—
207C2×#215—31no—
208C2×#215—31no—
209#939—61no—
210#939—61no—
211#938—61no—
212C2×#214—31no—
213C2×#214C2×D311yescharacteristic, complemented
214C2×#214C2×D311yescharacteristic, complemented
215#932—64no—
216C2×#213—31no—
217C2×#213—31no—
218C2×#213—31no—
219C2×#213—31no—
220C2×#213—31no—
221C2×#213—61no—
222C2×#213—61no—
223#930—31no—
224#930—31no—
225#930—31no—
226#930—61no—
227C2×C4⋊Dic3—31no—
228#924—31no—
229#924C2×D311yescharacteristic, complemented
230C2×#208—31no—
231C22×C3⋊C8—31no—
232#916—64no—
233#914—64no—
234C2×D24—31no—
235C2×#204—31no—
236C2×ΓL(1,𝔽25)—31no—
237C2×D3×C8—31no—
238#896—61no—
239#895—31no—
240#895—61no—
241D3×C4⋊C4—31no—
242#884—61no—
243#884—61no—
244C3×#102—31no—
245C3×#102—31no—
246C3×C22⋊C8—31no—
247#835—31no—
248#835—31no—
249#832—31no—
250#832—31no—
251#832—31no—
252#832—31no—
253#832—31no—
254#832—31no—
255#832—61no—
256#832—61no—
257#832C2×D311yescharacteristic, complemented
258#832C2×D311yescharacteristic, complemented
259#830—31no—
260#830—31no—
261#830—31no—
262#830—31no—
263#830—61no—
264#830C2×D311yescharacteristic, complemented
265#821—31no—
266(C2×D3)⋊C8—31no—
267(C2×D3)⋊C8—31no—
268#816—31no—
269#810—31no—
270#809—31no—
271C23×C32—24no—
272C23×C32—21no—
273C23×C32—21no—
274C23×C32—81no—
275C23×C32—81no—
276C23×C32C2×D411yescharacteristic
277C22×C3⋊D3—21no—
278C22×C3×D3—21no—
279C22×C3×D3—24no—
280C22×C3×D3—24no—
281C22×C3×D3—81no—
282C22×C3×D3—81no—
283C22×C3×D3—81no—
284C22×C3×D3—81no—
285C22×C3×D3C2×D411yescharacteristic
286C22×C3×D3C2×D411yescharacteristic
287C32×D4—24no—
288C32×D4—21no—
289C32×D4—21no—
290C32×D4C2×D412yes—
291C32×D4C2×D412yes—
292C2×C32×C4—21no—
293C2×C32×C4—21no—
294C2×C32×C4C2×D411yescharacteristic
295C2×C32×C4C2411yescharacteristic
296#638—81no—
297C2×C3⋊Dic3—21no—
298C4⋊(C3⋊D3)—21no—
299C4⋊(C3⋊D3)—21no—
300C3×#67—24no—
301C3×#67—24no—
302C3×#67—24no—
303C3×#67—22no—
304C3×#67—24no—
305C3×#67—22no—
306C3×#67—24no—
307C2×C3×Dic3—24no—
308C2×C3×Dic3—21no—
309C2×C3×Dic3—24no—
310C2×C3×Dic3—21no—
311C2×C3×Dic3—21no—
312C2×C3×Dic3C2×D411yescharacteristic
313C2×C3×Dic3C2×D411yescharacteristic
314C3×D12—22no—
315C3×D12—21no—
316C3×D12C2×D412yes—
317C3×C4×D3—24no—
318C3×C4×D3—21no—
319C3×C4×D3—21no—
320C3×C4×D3C2×D412yes—
321C3×C4×D3C2×D412yes—
322C3×Dic6—21no—
323C3×Dic6—22no—
324C3×Dic6—21no—
325C3×Dic6—21no—
326C3×Dic6C2×D412yes—
327#626—42no—
328#626—81no—
329#624—42no—
330D3×Dic3—81no—
331C3⋊(C3⋊C8)—21no—
332C3⋊(C3⋊C8)—21no—
333C3×C3⋊C8—21no—
334C3×C3⋊C8—21no—
335C2×H(5,𝔽2)—31no—
336C2×AGL(1,ℤ/8)—91no—
337C2×#135—91no—
338#537—91no—
339#452—91no—
340#452—91no—
341#450—31no—
342#450—91no—
343#449—91no—
344#449—91no—
345#447—91no—
346#447—91no—
347#417—91no—
348C2×#102—91no—
349#408—91no—
350C24×C3—21no—
351C24×C3—21no—
352C24×C3—41no—
353C24×C3—61no—
354C24×C3—61no—
355C23×D3—21no—
356C23×D3—21no—
357C3×#41—34no—
358C3×#41—62no—
359C3×#41—62no—
360C3×#41—62no—
361C3×#41—62no—
362C3×#41—62no—
363C3×#41—62no—
364C3×#41—68no—
365C3×#41—62no—
366C2×C3×Q8—31no—
367C2×C3×Q8—31no—
368C2×C3×Q8—31no—
369C2×C3×D4—22no—
370C2×C3×D4—22no—
371C2×C3×D4—22no—
372C2×C3×D4—22no—
373C2×C3×D4—21no—
374C2×C3×D4—21no—
375C2×C3×D4—21no—
376C2×C3×D4—21no—
377C2×C3×D4—34no—
378C2×C3×D4—31no—
379C2×C3×D4—31no—
380C2×C3×D4—31no—
381C2×C3×D4—31no—
382C2×C3×D4—41no—
383C2×C3×D4—42no—
384C2×C3×D4—42no—
385C2×C3×D4—62no—
386C2×C3×D4—61no—
387C2×C3×D4—61no—
388C2×C3×D4—62no—
389C2×C3×D4—68no—
390C2×C3×D4—61no—
391C2×C3×D4—61no—
392C2×C3×D4—68no—
393C2×C3×D4—68no—
394C2×C3×D4—61no—
395C2×C3×D4—62no—
396C2×C3×D4C22×D311yescharacteristic
397C2×C3×D4C22×D311yescharacteristic
398C2×C3×D4C22×D311yescharacteristic
399C2×C3×D4C22×D311yescharacteristic
400C22×C3×C4—21no—
401C22×C3×C4—31no—
402C22×C3×C4—31no—
403C22×C3×C4—61no—
404C22×C3×C4—61no—
405C22×C3×C4—61no—
406C22×C3×C4C22×D311yescharacteristic
407C22×C3×C4C22×D311yescharacteristic
408C2×#67—28no—
409C2×#67—28no—
410C2×#67—21no—
411C2×#67—21no—
412C2×#67—21no—
413C2×#67—21no—
414C2×#67—21no—
415C2×#67—61no—
416C2×#67—61no—
417C2×#67—61no—
418C2×#67—61no—
419C2×#67—121no—
420C2×#67#6711yescharacteristic
421C2×#67#6711yescharacteristic
422C22×Dic3—21no—
423C22×Dic3—21no—
424C22×Dic3—61no—
425#239—62no—
426#239—62no—
427#237—28no—
428#237—22no—
429#237—22no—
430#237—22no—
431#237#6714yescomplemented
432D3×D4—28no—
433D3×D4—22no—
434D3×D4—22no—
435D3×D4—22no—
436D3×D4#6714yescomplemented
437#235—22no—
438#235—22no—
439#235—22no—
440#235—22no—
441#235—62no—
442#235—62no—
443C2×D12—31no—
444C2×D12—31no—
445C2×D12—61no—
446C2×D12—61no—
447C2×D12—61no—
448C2×D12#6711yescharacteristic
449C2×D12C22×D311yescharacteristic
450C2×C4×D3—21no—
451C2×C4×D3—61no—
452C2×C4×D3—61no—
453C2×C4×D3—61no—
454C2×C4×D3C22×D311yescharacteristic
455C2×C4×D3C22×D311yescharacteristic
456C2×Dic6#6711yescharacteristic
457C2×Dic6C22×D311yescharacteristic
458C2×Dic6C22×D311yescharacteristic
459C3×SD16—62no—
460C3×SD16—62no—
461C2×C3×C8—31no—
462C2×C3×C8—31no—
463C3×C4⋊C4—31no—
464C3×C4⋊C4—61no—
465C3×C22⋊C4—61no—
466#217—21no—
467#217—61no—
468#216—62no—
469#216—62no—
470#215—62no—
471#215—62no—
472#214—22no—
473#214—22no—
474#214—62no—
475#213—62no—
476#213—62no—
477#213—62no—
478#213—62no—
479#213—62no—
480#213—122no—
481#213—122no—
482(C2×D3)⋊C4—61no—
483(C2×D3)⋊C4—61no—
484(C2×D3)⋊C4—61no—
485(C2×D3)⋊C4—61no—
486(C2×D3)⋊C4—61no—
487(C2×D3)⋊C4—121no—
488C4⋊Dic3—31no—
489C4⋊Dic3—31no—
490C4⋊Dic3—61no—
491C4⋊Dic3—61no—
492C4⋊Dic3C22×D311yescharacteristic
493Dic3⋊C4—21no—
494Dic3⋊C4—61no—
495Dic3⋊C4—61no—
496Dic3⋊C4—61no—
497#208—62no—
498C2×C3⋊C8—31no—
499C2×C3⋊C8—31no—
500C2×C3⋊C8—31no—
501C2×C3⋊C8—31no—
502C2×C3⋊C8—61no—
503C2×C3⋊C8—61no—
504C2×C3⋊C8—62no—
505C2×C3⋊C8C22×D311yescharacteristic
506C2×C3⋊C8C22×D311yescharacteristic
507D24—62no—
508#204—62no—
509ΓL(1,𝔽25)—62no—
510D3×C8—62no—
511C22×C32—21no—
512C22×C32—22no—
513C22×C32—22no—
514C22×C32—21no—
515C22×C32—21no—
516C22×C32—41no—
517C22×C32—41no—
518C22×C32—41no—
519C22×C32—41no—
520C22×C32—84no—
521C22×C32C22×D411yescharacteristic
522C2×C3⋊D3—41no—
523C2×C3⋊D3—41no—
524C2×C3⋊D3—41no—
525C2×C3×D3—21no—
526C2×C3×D3—21no—
527C2×C3×D3—21no—
528C2×C3×D3—22no—
529C2×C3×D3—21no—
530C2×C3×D3—21no—
531C2×C3×D3—41no—
532C2×C3×D3—41no—
533C2×C3×D3—84no—
534C2×C3×D3—84no—
535C2×C3×D3#12012yes—
536C32×C4—21no—
537C32×C4C22×D411yescharacteristic
538C32×C4C22×D411yescharacteristic
539C3⋊Dic3—41no—
540C3×Dic3—21no—
541C3×Dic3—22no—
542C3×Dic3—41no—
543C3×Dic3—41no—
544C3×Dic3#12012yes—
545H(5,𝔽2)—64no—
546H(5,𝔽2)—64no—
547C2×#41—31no—
548C2×#41—31no—
549C2×#41—31no—
550C2×#41—31no—
551C2×#41—61no—
552C2×#41—91no—
553C22×D4—31no—
554C22×D4—31no—
555C22×D4—61no—
556C22×D4—61no—
557C22×D4—61no—
558C22×D4D3211yescharacteristic
559AGL(1,ℤ/8)—184no—
560#135—184no—
561C2×Q16—91no—
562C2×SD16—31no—
563C2×SD16—31no—
564C2×SD16—91no—
565C2×SD16—91no—
566C2×D8—91no—
567C2×D8—91no—
568C2×D8—91no—
569C2×M16—91no—
570C22×C8—91no—
571C22⋊Q8—31no—
572C22⋊Q8—91no—
573C22⋊Q8—181no—
574#121—91no—
575#121—91no—
576#121—181no—
577#121—181no—
578#121—181no—
579C2×C4⋊C4—91no—
580#103—91no—
581#103—91no—
582#102—31no—
583#102—31no—
584#102—91no—
585#102—91no—
586#102—91no—
587#102—91no—
588C22⋊C8—31no—
589C22⋊C8—91no—
590C22⋊C8—91no—
591C22⋊C8—91no—
592C23×C3—24no—
593C23×C3—24no—
594C23×C3—21no—
595C23×C3—21no—
596C23×C3—21no—
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—31no—
600C23×C3—31no—
601C23×C3—41no—
602C23×C3—41no—
603C23×C3—44no—
604C23×C3—64no—
605C23×C3—64no—
606C23×C3—61no—
607C23×C3—81no—
608C23×C3—81no—
609C23×C3—81no—
610C23×C3—81no—
611C23×C3—82no—
612C23×C3—82no—
613C23×C3—241no—
614C23×C3—241no—
615C23×C3—241no—
616C23×C3—241no—
617C23×C3D3×D411yescharacteristic
618C23×C3C2×#6711yescharacteristic
619C22×D3—21no—
620C22×D3—24no—
621C22×D3—24no—
622C22×D3—61no—
623C22×D3—61no—
624C22×D3—81no—
625C22×D3—81no—
626C22×D3—81no—
627C22×D3—81no—
628C22×D3—121no—
629C22×D3C2×#6711yescharacteristic
630C22×D3C2×#6711yescharacteristic
631C3×Q8—32no—
632C3×Q8—62no—
633C3×Q8—61no—
634C3×Q8—61no—
635C3×Q8—61no—
636C3×D4—24no—
637C3×D4—24no—
638C3×D4—21no—
639C3×D4—21no—
640C3×D4—21no—
641C3×D4—21no—
642C3×D4—22no—
643C3×D4—22no—
644C3×D4—32no—
645C3×D4—41no—
646C3×D4—41no—
647C3×D4—44no—
648C3×D4—62no—
649C3×D4—62no—
650C3×D4—64no—
651C3×D4—62no—
652C3×D4—64no—
653C3×D4—64no—
654C3×D4—64no—
655C3×D4—64no—
656C3×D4—61no—
657C3×D4D3×D412yes—
658C3×D4D3×D412yes—
659C3×D4C2×#6712yes—
660C3×D4C2×#6712yes—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—31no—
668C2×C3×C4—32no—
669C2×C3×C4—32no—
670C2×C3×C4—31no—
671C2×C3×C4—41no—
672C2×C3×C4—41no—
673C2×C3×C4—64no—
674C2×C3×C4—64no—
675C2×C3×C4—64no—
676C2×C3×C4—61no—
677C2×C3×C4—61no—
678C2×C3×C4—61no—
679C2×C3×C4—61no—
680C2×C3×C4—61no—
681C2×C3×C4D3×D411yescharacteristic
682C2×C3×C4C2×#6711yescharacteristic
683C2×C3×C4C23×D311yescharacteristic
684C2×C3×C4C23×D311yescharacteristic
685#67—24no—
686#67—24no—
687#67—24no—
688#67—22no—
689#67—24no—
690#67—22no—
691#67—24no—
692#67—122no—
693#67—241no—
694#67—241no—
695#67—241no—
696#67—242no—
697C2×Dic3—24no—
698C2×Dic3—21no—
699C2×Dic3—24no—
700C2×Dic3—21no—
701C2×Dic3—21no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—121no—
705C2×Dic3—241no—
706C2×Dic3C2×#6711yescharacteristic
707C2×Dic3C2×#6711yescharacteristic
708D12—22no—
709D12—21no—
710D12—61no—
711D12—61no—
712D12—61no—
713D12—61no—
714D12—121no—
715D12—121no—
716D12—122no—
717D12—241no—
718D12C2×#6712yes—
719C4×D3—24no—
720C4×D3—21no—
721C4×D3—21no—
722C4×D3—122no—
723C4×D3—122no—
724C4×D3—241no—
725C4×D3C2×#6712yes—
726C4×D3C2×#6712yes—
727Dic6—21no—
728Dic6—22no—
729Dic6—21no—
730Dic6—21no—
731Dic6C2×#6712yes—
732C3×C8—61no—
733C3×C8—61no—
734C3⋊C8—21no—
735C3⋊C8—21no—
736C3⋊C8—61no—
737C3⋊C8—61no—
738C3⋊C8—61no—
739C3⋊C8—61no—
740C3⋊C8—121no—
741C3⋊C8—121no—
742C2×C32—41no—
743C2×C32—42no—
744C2×C32—42no—
745C2×C32C2×#12011yescharacteristic
746C2×C32#57611yescharacteristic
747C2×C32#57711yescharacteristic
748C3⋊D3—81no—
749C3×D3—22no—
750C3×D3—41no—
751C3×D3—42no—
752C24—21no—
753C24—61no—
754C24—61no—
755#41—34no—
756#41—62no—
757#41—62no—
758#41—62no—
759#41—62no—
760#41—62no—
761#41—62no—
762#41—68no—
763#41—62no—
764#41—182no—
765#41—182no—
766C2×Q8—31no—
767C2×Q8—31no—
768C2×Q8—31no—
769C2×D4—22no—
770C2×D4—22no—
771C2×D4—21no—
772C2×D4—34no—
773C2×D4—31no—
774C2×D4—31no—
775C2×D4—31no—
776C2×D4—31no—
777C2×D4—62no—
778C2×D4—61no—
779C2×D4—61no—
780C2×D4—62no—
781C2×D4—68no—
782C2×D4—61no—
783C2×D4—61no—
784C2×D4—68no—
785C2×D4—68no—
786C2×D4—61no—
787C2×D4—62no—
788C2×D4—91no—
789C2×D4—181no—
790C2×D4—181no—
791C2×D4—181no—
792C2×D4C2×D3211yescharacteristic
793C2×D4C2×D3211yescharacteristic
794C22×C4—31no—
795C22×C4—31no—
796C22×C4—61no—
797C22×C4—61no—
798C22×C4—61no—
799C22×C4—181no—
800C22×C4—181no—
801C22×C4C2×D3211yescharacteristic
802Q16—182no—
803SD16—62no—
804SD16—62no—
805SD16—182no—
806SD16—182no—
807D8—182no—
808D8—182no—
809D8—182no—
810M16—182no—
811C2×C8—31no—
812C2×C8—31no—
813C2×C8—91no—
814C2×C8—91no—
815C2×C8—182no—
816C4⋊C4—31no—
817C4⋊C4—61no—
818C4⋊C4—91no—
819C4⋊C4—181no—
820C4⋊C4—181no—
821C22⋊C4—61no—
822C22⋊C4—181no—
823C22⋊C4—181no—
824C22⋊C4—181no—
825C22×C3—22no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—21no—
829C22×C3—21no—
830C22×C3—22no—
831C22×C3—22no—
832C22×C3—21no—
833C22×C3—21no—
834C22×C3—22no—
835C22×C3—22no—
836C22×C3—21no—
837C22×C3—32no—
838C22×C3—41no—
839C22×C3—41no—
840C22×C3—42no—
841C22×C3—42no—
842C22×C3—41no—
843C22×C3—41no—
844C22×C3—41no—
845C22×C3—41no—
846C22×C3—41no—
847C22×C3—41no—
848C22×C3—41no—
849C22×C3—41no—
850C22×C3—61no—
851C22×C3—61no—
852C22×C3—61no—
853C22×C3—61no—
854C22×C3—62no—
855C22×C3—61no—
856C22×C3—81no—
857C22×C3—81no—
858C22×C3—81no—
859C22×C3—81no—
860C22×C3—84no—
861C22×C3—84no—
862C22×C3—88no—
863C22×C3—121no—
864C22×C3—121no—
865C22×C3—244no—
866C22×C3—244no—
867C22×C3C2×D3×D411yescharacteristic
868C22×C3C22×#6711yescharacteristic
869C2×D3—21no—
870C2×D3—21no—
871C2×D3—21no—
872C2×D3—21no—
873C2×D3—21no—
874C2×D3—22no—
875C2×D3—41no—
876C2×D3—41no—
877C2×D3—84no—
878C2×D3—84no—
879C2×D3—121no—
880C2×D3—121no—
881C2×D3—121no—
882C2×D3—121no—
883C2×D3—121no—
884C2×D3—121no—
885C2×D3—241no—
886C2×D3—241no—
887C2×D3—241no—
888C2×D3#95312yes—
889C3×C4—21no—
890C3×C4—21no—
891C3×C4—21no—
892C3×C4—21no—
893C3×C4—32no—
894C3×C4—41no—
895C3×C4—61no—
896C3×C4—62no—
897C3×C4—121no—
898C3×C4—121no—
899C3×C4C2×D3×D411yescharacteristic
900C3×C4C2×D3×D411yescharacteristic
901C3×C4C22×#6711yescharacteristic
902C3×C4C22×#6711yescharacteristic
903Dic3—21no—
904Dic3—22no—
905Dic3—41no—
906Dic3—41no—
907Dic3—121no—
908Dic3—121no—
909Dic3—241no—
910Dic3#95312yes—
911C32#301211yescharacteristic, complemented, Sylow
912C23—24no—
913C23—21no—
914C23—21no—
915C23—31no—
916C23—31no—
917C23—64no—
918C23—64no—
919C23—61no—
920C23—81no—
921C23—81no—
922C23—181no—
923C23—241no—
924C23—241no—
925C23—241no—
926C23—241no—
927C23D3×#6711yescharacteristic
928Q8—32no—
929Q8—62no—
930Q8—61no—
931Q8—61no—
932Q8—61no—
933D4—24no—
934D4—21no—
935D4—21no—
936D4—32no—
937D4—62no—
938D4—62no—
939D4—64no—
940D4—62no—
941D4—64no—
942D4—64no—
943D4—64no—
944D4—64no—
945D4—61no—
946D4—181no—
947D4—181no—
948D4—362no—
949D4—721no—
950D4—721no—
951D4D3×#6712yes—
952D4D3×#6712yes—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—31no—
956C2×C4—32no—
957C2×C4—32no—
958C2×C4—31no—
959C2×C4—64no—
960C2×C4—64no—
961C2×C4—64no—
962C2×C4—61no—
963C2×C4—61no—
964C2×C4—61no—
965C2×C4—61no—
966C2×C4—61no—
967C2×C4—181no—
968C2×C4—362no—
969C2×C4—721no—
970C2×C4D3×#6711yescharacteristic
971C2×C4C22×D3211yescharacteristic
972C8—61no—
973C8—61no—
974C8—181no—
975C8—181no—
976C2×C3—21no—
977C2×C3—21no—
978C2×C3—21no—
979C2×C3—42no—
980C2×C3—41no—
981C2×C3—42no—
982C2×C3—42no—
983C2×C3—42no—
984C2×C3—42no—
985C2×C3—41no—
986C2×C3—62no—
987C2×C3—82no—
988C2×C3—82no—
989C2×C3—121no—
990C2×C3—122no—
991C2×C3D3×#12011yescharacteristic
992C2×C3#576211yescharacteristic
993C2×C3#577411yescharacteristic
994C2×C3#583511yescharacteristic
995C2×C3#583611yescharacteristic
996C2×C3C2×#95311yescharacteristic
997D3—22no—
998D3—41no—
999D3—42no—
1000D3—241no—
1001D3—241no—
1002D3—481no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—22no—
1007C22—22no—
1008C22—32no—
1009C22—41no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—61no—
1014C22—61no—
1015C22—61no—
1016C22—61no—
1017C22—62no—
1018C22—61no—
1019C22—84no—
1020C22—121no—
1021C22—121no—
1022C22—244no—
1023C22—244no—
1024C22—361no—
1025C22—361no—
1026C22—361no—
1027C22C2×D3×#6711yescharacteristic
1028C4—21no—
1029C4—32no—
1030C4—61no—
1031C4—62no—
1032C4—121no—
1033C4—121no—
1034C4—361no—
1035C4C2×D3×#6711yescharacteristic
1036C4C2×D3×#6711yescharacteristic
1037C3—21no—
1038C3#8014911yescharacteristic, complemented
1039C3#8410211yescharacteristic, complemented
1040C2—41no—
1041C2—42no—
1042C2—42no—
1043C2—62no—
1044C2—121no—
1045C2—122no—
1046C2—721no—
1047C2#1059509711yescharacteristic
1048C2#1059510511yescharacteristic
1049C2D3×#95311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3012
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1004C2semidirect
2. C2×#63935C2semidirect
3. C2×#63934C2semidirect
4. #10594894C2semidirect
5. #10592916C2semidirect
6. C3×#5218C2semidirect
7. #10591461C2semidirect
8. #10591458C2semidirect
9. #10591452C2semidirect
10. #10591448C2semidirect
11. #10591414C2semidirect
12. D3×#832C2semidirect
13. #10591170C2semidirect
14. #10591163C2semidirect
15. #10591145C2semidirect
31. C2×#3799C22semidirect
32. C2×#3753C22semidirect
33. C2×#3753C22semidirect
34. #64139C22semidirect
35. C2×C3×#214C22semidirect
36. C2×C3×#214C22semidirect
37. C3×#924C22semidirect
42. #63909C22semidirect
43. D3×C4⋊Dic3C22semidirect
46. #63856C22semidirect
47. C2×#3718C22semidirect
48. C2×#3717C22semidirect
49. C2×#3715C22semidirect
50. C2×#3714C22semidirect
51. C2×#3711C22semidirect
52. C2×D3×C3⋊C8C22semidirect
53. #63659C22semidirect
54. #63659C22semidirect
55. #63657C22semidirect
56. C3×#832C22semidirect
57. C3×#832C22semidirect
58. C3×#830C22semidirect
59. #63566C22semidirect
60. #63565C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
63. (C2×D3)⋊(C3⋊C8)C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
66. C2×#1004D3semidirect
81. #5218D3semidirect
122. C3×#237D4semidirect
127. C3×D3×D4D4semidirect
213. C2×#214C2×D3semidirect
214. C2×#214C2×D3semidirect
229. #924C2×D3semidirect
257. #832C2×D3semidirect
258. #832C2×D3semidirect
264. #830C2×D3semidirect
431. #237#67semidirect
436. D3×D4#67semidirect
911. C32#3012semidirect
1038. C3#80149semidirect
1039. C3#84102semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10042
C2×#639352
C2×#639342
#105948942
#105929162
C3×#52182
#105914612
#105914582
#105914522
#105914482
#105914142
D3×#8322
#105911702
#105911632
#105911452
#841023
#801493