Finite Group Databasebeta

← #11904568

Subgroups — #11904568

Order 1152.

3239 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C22×#3799C211yesmaximal, characteristic, complemented
3#10596301C211yesmaximal, characteristic, complemented
4C3×#5828C211yesmaximal, characteristic, complemented
5#10595402C214yesmaximal, complemented
6#10595238C214yesmaximal, complemented
7#10595236C214yesmaximal, complemented
8#10595159C214yesmaximal, complemented
9#10595045C211yesmaximal, characteristic, complemented
10#10595022C211yesmaximal, characteristic, complemented
11#10595007C214yesmaximal, complemented
12#10594902C214yesmaximal, complemented
13#10594818C211yesmaximal, characteristic, complemented
14#87290—31nomaximal
15#86023—31nomaximal
16C2×C32×#41C2211yescharacteristic
17C22×C4⋊(C3⋊D3)C2211yescharacteristic
18C3×#1010—28no—
19C2×C3×D3×Q8C2212yescomplemented
20C2×C3×#237C2214yes—
21C2×C3×#237C2212yescomplemented
22C2×C3×#235C2211yescharacteristic
23C2×C3×#235C2212yescomplemented
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×Dic6C2211yescharacteristic
26C22×C3×Dic6C2212yescomplemented
27C22×#626C2212yes—
28C22×#624C2212yes—
29C2×#3799—28no—
30C2×#3799C2214yes—
31C2×#3799C2214yes—
32#64156C2212yescomplemented
33#64149C2212yescomplemented
34#64146C2214yes—
35#64139C2214yescomplemented
36#64135C2211yescharacteristic
37C3×#946C2212yescomplemented
38C3×#938C2212yescomplemented
39C3×#937C2212yes—
40C3×#935C2212yes—
41C3×C4×#67C2214yescomplemented
42C3×#926C2211yescharacteristic
43#63981C2214yes—
44#63979C2218yescomplemented
45#63978C2218yescomplemented
46#63976C2212yes—
47#63961C2212yes—
48#63958C2218yescomplemented
49#63955C2214yes—
50#63952C2218yescomplemented
51#63911C2212yescomplemented
52#63909C2214yescomplemented
53#63908C2212yescomplemented
54#63907C2218yescomplemented
55#63906C2218yescomplemented
56#63904C2218yescomplemented
57C4×#625C2214yescomplemented
58#63888C2218yescomplemented
59#63864C2212yescomplemented
60#63856C2212yescomplemented
61#63843C2214yescomplemented
62Dic3×Dic6C2214yescomplemented
63C2×C3×2−1+4—31no—
64C2×#1010D311yescharacteristic, complemented
65C22×#239—31no—
66C22×#235—31no—
67C3×#525—31no—
68#5834—34no—
69#5834—34no—
70#5830—31no—
71#5830—31no—
72#5830—34no—
73#5830—31no—
74#5830—61no—
75#5828—31no—
76#5828—34no—
77#5828D311yescharacteristic, complemented
78#5817—34no—
79#5817—34no—
80#5812—31no—
81#5791—31no—
82#5656—34no—
83#5633—34no—
84#5599—34no—
85#5592—34no—
86#5553—34no—
87#5552—34no—
88#5525—31no—
89#5516—31no—
90C23×C3⋊D3C2312yes—
91C23×C3×D3C2311yescharacteristic
92C32×#41—24no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2312yes—
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4C2312yes—
97C22×C32×C4C2311yescharacteristic
98C2×#638C2318yes—
99C2×C4⋊(C3⋊D3)—24no—
100C2×C4⋊(C3⋊D3)C2312yes—
101C2×C4⋊(C3⋊D3)C2312yes—
102C2×C3×#67C2312yes—
103C2×C3×#67C2314yes—
104C2×C3×#67C2314yes—
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2314yes—
107C22×C3×Dic3C2312yes—
108C3×D3×Q8—28no—
109C3×#237—216no—
110C3×#237—28no—
111C3×#235—24no—
112C3×#235—28no—
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3—24no—
115C2×C3×C4×D3C2312yes—
116C2×C3×C4×D3C2312yes—
117C2×C3×C4×D3C2312yes—
118C2×C3×C4×D3C2314yes—
119C2×C3×Dic6—28no—
120C2×C3×Dic6D418yescomplemented
121C2×C3×Dic6C2311yescharacteristic
122C2×C3×Dic6C2314yes—
123C2×C3×Dic6C2312yes—
124C2×C3×Dic6C2312yes—
125C2×#626—28no—
126C2×#626C2318yes—
127C2×#626C2318yes—
128C2×#625C2314yes—
129C2×#624—28no—
130C2×#624C2318yes—
131#3799—216no—
132#3799—216no—
133#3757C2312yes—
134#3752C2318yes—
135C4⋊(C3⋊Dic3)C2312yes—
136C4×C3⋊Dic3C2312yes—
137C3×#217C2312yes—
138C3×#217C2314yes—
139C3×(C2×D3)⋊C4C2314yes—
140C3×C4⋊Dic3C2312yes—
141C3×Dic3⋊C4C2314yes—
142C3×C4×Dic3C2312yes—
143#3724C2314yes—
144Dic3⋊Dic3C2318yes—
145#3722C2318yes—
146(C2×D3)⋊Dic3C2314yes—
147(C2×D3)⋊Dic3C2314yes—
148Dic32C2318yes—
149#3487—91noSylow
150C3×2−1+4—68no—
151C2×C3×#41—21no—
152C2×C3×#41—34no—
153C2×C3×#41—32no—
154C2×C3×#41—31no—
155C2×C3×#41—32no—
156C2×C3×#41C2×D311yescharacteristic
157C2×C3×#41C2×D311yescharacteristic
158C22×C3×Q8—32no—
159C22×C3×Q8—31no—
160C22×C3×Q8—32no—
161C23×C3×C4—31no—
162C22×#67—32no—
163#1010—28no—
164C2×#239—34no—
165C2×#239—34no—
166C2×#239—68no—
167C2×D3×Q8C2×D312yescomplemented
168C2×#237C2×D314yes—
169C2×#237C2×D312yescomplemented
170C2×#235—34no—
171C2×#235—34no—
172C2×#235—68no—
173C2×#235C2×D311yescharacteristic
174C2×#235C2×D312yescomplemented
175C22×D12—32no—
176C22×D12—31no—
177C22×D12—31no—
178C22×D12—61no—
179C22×C4×D3—32no—
180C22×C4×D3—32no—
181C22×C4×D3C2×D311yescharacteristic
182C22×Dic6C2×D311yescharacteristic
183C22×Dic6C2×D312yescomplemented
184C3×#123—32no—
185C3×C22⋊Q8—32no—
186C3×#121—32no—
187C3×#120—32no—
188C3×C4×D4—34no—
189C3×#117—31no—
190#953—32no—
191#947—32no—
192#947—32no—
193#947—38no—
194#947—32no—
195#947—62no—
196#946—32no—
197#946—38no—
198#946C2×D312yescomplemented
199Q8×Dic3—34no—
200Q8×Dic3—34no—
201#940—32no—
202#940—32no—
203#940—38no—
204#940—38no—
205#940—32no—
206#940—62no—
207#939—38no—
208#938—32no—
209#938—38no—
210#938C2×D312yescomplemented
211#937—32no—
212#937—34no—
213#937—34no—
214#937—34no—
215#937—64no—
216#937C2×D312yes—
217#935—32no—
218#935C2×D312yes—
219#930—34no—
220#930—34no—
221#930—38no—
222#930—32no—
223#930—38no—
224#930—34no—
225#930—64no—
226#929—32no—
227C4×#67—34no—
228C4×#67—34no—
229C4×#67—38no—
230C4×#67—38no—
231C4×#67C2×D314yescomplemented
232#926—31no—
233#926—31no—
234#926—34no—
235#926—61no—
236#926C2×D311yescharacteristic
237#924—32no—
238#896—38no—
239#895—34no—
240#893—38no—
241#887—34no—
242#885—38no—
243#884—38no—
244#884—38no—
245#882—34no—
246#67⋊C4—38no—
247#877—34no—
248#875—32no—
249#874—32no—
250C4×Dic6—34no—
251C23×C32C2412yes—
252C23×C32C2411yescharacteristic
253C22×C3⋊D3—24no—
254C22×C3⋊D3—44no—
255C22×C3⋊D3C2414yes—
256C22×C3×D3—22no—
257C22×C3×D3—42no—
258C22×C3×D3C2412yes—
259C22×C3×D3C2412yes—
260C32×Q8—22no—
261C32×D4—24no—
262C32×D4—22no—
263C2×C32×C4—24no—
264C2×C32×C4C2×D414yes—
265C2×C32×C4C2412yes—
266C2×C32×C4C2411yescharacteristic
267C2×C32×C4C2411yescharacteristic
268#638—48no—
269C2×C3⋊Dic3C2414yes—
270C4⋊(C3⋊D3)—24no—
271C4⋊(C3⋊D3)—24no—
272C3×#67—24no—
273C3×#67—28no—
274C3×#67—44no—
275C2×C3×Dic3—22no—
276C2×C3×Dic3—28no—
277C2×C3×Dic3C2×D418yes—
278C2×C3×Dic3C2414yes—
279C2×C3×Dic3C2412yes—
280C2×C3×Dic3C2412yes—
281C2×C3×Dic3C2414yes—
282C3×D12—22no—
283C3×C4×D3—24no—
284C3×C4×D3—24no—
285C3×C4×D3—24no—
286C3×C4×D3—28no—
287C3×Dic6—22no—
288C3×Dic6—28no—
289C3×Dic6C2×D418yes—
290C3×Dic6C2×D418yes—
291#626—216no—
292#626—48no—
293#625—44no—
294#624—216no—
295C2×2−1+4—31no—
296C22×#41—91no—
297#550—94no—
298#550—94no—
299#548—94no—
300#548—94no—
301#535—91no—
302#535—94no—
303#535—91no—
304#525—31no—
305#525—94no—
306#525—91no—
307#519—91no—
308C24×C3—31no—
309C23×D3—32no—
310C23×D3—32no—
311C23×D3—62no—
312C23×D3C22×D311yescharacteristic
313C3×#41—24no—
314C3×#41—24no—
315C3×#41—44no—
316C3×#41—68no—
317C3×#41—616no—
318C3×#41—68no—
319C3×#41—64no—
320C2×C3×Q8—21no—
321C2×C3×Q8—38no—
322C2×C3×Q8—32no—
323C2×C3×Q8—32no—
324C2×C3×Q8—34no—
325C2×C3×Q8—31no—
326C2×C3×Q8—68no—
327C2×C3×Q8—68no—
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×D4—22no—
331C2×C3×D4—21no—
332C2×C3×D4—32no—
333C2×C3×D4—34no—
334C2×C3×D4—34no—
335C2×C3×D4—31no—
336C2×C3×D4C22×D312yes—
337C2×C3×D4C22×D312yes—
338C2×C3×D4C22×D311yescharacteristic
339C2×C3×D4C22×D311yescharacteristic
340C22×C3×C4—21no—
341C22×C3×C4—22no—
342C22×C3×C4—32no—
343C22×C3×C4—34no—
344C22×C3×C4—31no—
345C22×C3×C4—32no—
346C22×C3×C4—34no—
347C22×C3×C4—32no—
348C22×C3×C4—32no—
349C22×C3×C4—64no—
350C22×C3×C4C22×D312yes—
351C22×C3×C4C22×D312yes—
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C2×#67—38no—
355C2×#67—38no—
356C2×#67—34no—
357C2×#67—34no—
358C2×#67—38no—
359C2×#67—38no—
360C2×#67—68no—
361C2×#67—68no—
362C2×#67C22×D312yes—
363C2×#67C22×D314yes—
364C2×#67C22×D314yes—
365C22×Dic3C22×D314yes—
366C22×Dic3C22×D311yescharacteristic
367C22×Dic3C22×D312yes—
368#239—616no—
369#239—616no—
370D3×Q8—28no—
371#237—216no—
372#237—28no—
373#235—24no—
374#235—28no—
375#235—616no—
376#235—616no—
377C2×D12—38no—
378C2×D12—32no—
379C2×D12—32no—
380C2×D12—32no—
381C2×D12—32no—
382C2×D12—38no—
383C2×D12—62no—
384C2×D12—62no—
385C2×D12—68no—
386C2×D12—64no—
387C2×D12—64no—
388C2×D12—124no—
389C2×D12C22×D311yescharacteristic
390C2×C4×D3—24no—
391C2×C4×D3—38no—
392C2×C4×D3—38no—
393C2×C4×D3—68no—
394C2×C4×D3—68no—
395C2×C4×D3C22×D314yes—
396C2×C4×D3C22×D312yes—
397C2×C4×D3C22×D312yes—
398C2×C4×D3C22×D312yes—
399C2×Dic6—28no—
400C2×Dic6#6718yescomplemented
401C2×Dic6C22×D311yescharacteristic
402C2×Dic6C22×D314yes—
403C2×Dic6C22×D312yes—
404C2×Dic6C22×D312yes—
405C3×C4⋊C4—32no—
406C3×C4⋊C4—34no—
407C3×C22⋊C4—32no—
408C3×C22⋊C4—34no—
409C3×C22⋊C4—34no—
410C3×C42—32no—
411#217—32no—
412#217—32no—
413#217—34no—
414#217—34no—
415#217—62no—
416#217C22×D312yes—
417#217C22×D314yes—
418(C2×D3)⋊C4—34no—
419(C2×D3)⋊C4—34no—
420(C2×D3)⋊C4—38no—
421(C2×D3)⋊C4—38no—
422(C2×D3)⋊C4—38no—
423(C2×D3)⋊C4—38no—
424(C2×D3)⋊C4—68no—
425(C2×D3)⋊C4C22×D314yes—
426C4⋊Dic3—32no—
427C4⋊Dic3—32no—
428C4⋊Dic3—38no—
429C4⋊Dic3—62no—
430C4⋊Dic3C22×D312yes—
431Dic3⋊C4—38no—
432Dic3⋊C4—34no—
433Dic3⋊C4—34no—
434Dic3⋊C4C22×D314yes—
435C4×Dic3—32no—
436C4×Dic3—32no—
437C4×Dic3—38no—
438C4×Dic3—38no—
439C4×Dic3—62no—
440C4×Dic3C22×D312yes—
441C22×C32—22no—
442C22×C32—22no—
443C22×C32—24no—
444C22×C32C22×D412yes—
445C22×C32C2511yescharacteristic
446C2×C3⋊D3—24no—
447C2×C3⋊D3—28no—
448C2×C3⋊D3—48no—
449C2×C3×D3—22no—
450C2×C3×D3—22no—
451C2×C3×D3—22no—
452C2×C3×D3—24no—
453C2×C3×D3—22no—
454C2×C3×D3—44no—
455C32×C4—22no—
456C32×C4C22×D412yes—
457C32×C4C22×D412yes—
458C3⋊Dic3—24no—
459C3×Dic3—22no—
460C3×Dic3—22no—
461C3×Dic3—24no—
462C3×Dic3C22×D418yes—
4632−1+4—68no—
464C2×#41—34no—
465C2×#41—32no—
466C2×#41—31no—
467C2×#41—32no—
468C2×#41—94no—
469C2×#41—94no—
470C2×#41—188no—
471C2×#41D3211yescharacteristic
472C22×Q8—32no—
473C22×Q8—31no—
474C22×Q8—32no—
475C22×D4—92no—
476C22×D4—91no—
477C23×C4—31no—
478C23×C4—92no—
479#127—92no—
480#127—98no—
481#127—92no—
482#124—92no—
483#124—98no—
484#124—92no—
485#123—32no—
486#123—92no—
487C22⋊Q8—32no—
488C22⋊Q8—98no—
489C22⋊Q8—92no—
490#121—32no—
491#121—98no—
492#121—98no—
493#121—94no—
494#121—92no—
495#121—98no—
496#121—94no—
497#120—32no—
498#120—94no—
499#120—92no—
500#120—94no—
501C4×Q8—94no—
502C4×Q8—94no—
503C4×D4—34no—
504C4×D4—98no—
505C4×D4—98no—
506C4×D4—94no—
507#117—31no—
508#117—94no—
509#117—91no—
510C23×C3—21no—
511C23×C3—22no—
512C23×C3—32no—
513C23×C3—32no—
514C23×C3—62no—
515C23×C3—122no—
516C23×C3C23×D312yes—
517C23×C3C23×D312yes—
518C23×C3C23×D311yescharacteristic
519C23×C3C23×D311yescharacteristic
520C22×D3—22no—
521C22×D3—34no—
522C22×D3—34no—
523C22×D3—42no—
524C22×D3—64no—
525C22×D3—64no—
526C22×D3—64no—
527C22×D3—124no—
528C22×D3—124no—
529C22×D3—124no—
530C22×D3—244no—
531C22×D3C23×D312yes—
532C22×D3C23×D312yes—
533C3×Q8—22no—
534C3×Q8—22no—
535C3×Q8—38no—
536C3×Q8—38no—
537C3×Q8—42no—
538C3×Q8—68no—
539C3×Q8—62no—
540C3×D4—24no—
541C3×D4—24no—
542C3×D4—22no—
543C3×D4—22no—
544C3×D4—42no—
545C3×D4—44no—
546C3×D4—68no—
547C3×D4—64no—
548C3×D4—62no—
549C3×D4—124no—
550C2×C3×C4—24no—
551C2×C3×C4—24no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—22no—
555C2×C3×C4—24no—
556C2×C3×C4—38no—
557C2×C3×C4—34no—
558C2×C3×C4—34no—
559C2×C3×C4—32no—
560C2×C3×C4—32no—
561C2×C3×C4—44no—
562C2×C3×C4—68no—
563C2×C3×C4—68no—
564C2×C3×C4—62no—
565C2×C3×C4—64no—
566C2×C3×C4—64no—
567C2×C3×C4—64no—
568C2×C3×C4D3×D414yes—
569C2×C3×C4C2×#6714yes—
570C2×C3×C4C23×D312yes—
571C2×C3×C4C23×D312yes—
572C2×C3×C4C23×D311yescharacteristic
573C2×C3×C4C23×D311yescharacteristic
574C2×C3×C4C23×D311yescharacteristic
575C2×C3×C4C23×D311yescharacteristic
576#67—24no—
577#67—28no—
578#67—44no—
579#67—616no—
580#67—128no—
581#67—124no—
582#67—124no—
583#67—128no—
584#67—128no—
585#67—248no—
586C2×Dic3—22no—
587C2×Dic3—28no—
588C2×Dic3—34no—
589C2×Dic3—34no—
590C2×Dic3—64no—
591C2×Dic3C2×#6718yes—
592C2×Dic3C23×D314yes—
593C2×Dic3C23×D312yes—
594C2×Dic3C23×D312yes—
595C2×Dic3C23×D314yes—
596D12—22no—
597D12—616no—
598D12—64no—
599D12—64no—
600D12—64no—
601D12—64no—
602D12—124no—
603D12—124no—
604D12—128no—
605C4×D3—24no—
606C4×D3—24no—
607C4×D3—24no—
608C4×D3—28no—
609C4×D3—616no—
610C4×D3—616no—
611Dic6—22no—
612Dic6—28no—
613Dic6C2×#6718yes—
614Dic6C2×#6718yes—
615C2×C32—22no—
616C2×C32—42no—
617C2×C32C23×D411yescharacteristic
618C2×C32#58512yes—
619C3⋊D3—44no—
620C3×D3—42no—
621C3×D3—42no—
622C24—31no—
623C24—92no—
624#41—24no—
625#41—68no—
626#41—616no—
627#41—68no—
628#41—64no—
629#41—1816no—
630#41—1816no—
631C2×Q8—32no—
632C2×Q8—32no—
633C2×Q8—34no—
634C2×Q8—31no—
635C2×Q8—38no—
636C2×Q8—68no—
637C2×Q8—68no—
638C2×Q8C2×D3211yescharacteristic
639C2×D4—32no—
640C2×D4—34no—
641C2×D4—34no—
642C2×D4—31no—
643C2×D4—98no—
644C2×D4—98no—
645C2×D4—94no—
646C2×D4—98no—
647C2×D4—92no—
648C2×D4—92no—
649C2×D4—188no—
650C2×D4—184no—
651C2×D4C2×D3212yes—
652C2×D4C2×D3211yescharacteristic
653C22×C4—32no—
654C22×C4—34no—
655C22×C4—31no—
656C22×C4—32no—
657C22×C4—32no—
658C22×C4—34no—
659C22×C4—32no—
660C22×C4—64no—
661C22×C4—98no—
662C22×C4—188no—
663C22×C4C2×D3212yes—
664C22×C4C2×D3211yescharacteristic
665C4⋊C4—32no—
666C4⋊C4—34no—
667C4⋊C4—98no—
668C4⋊C4—94no—
669C4⋊C4—92no—
670C22⋊C4—32no—
671C22⋊C4—34no—
672C22⋊C4—34no—
673C22⋊C4—98no—
674C22⋊C4—94no—
675C22⋊C4—94no—
676C22⋊C4—92no—
677C22⋊C4—98no—
678C42—32no—
679C42—98no—
680C42—92no—
681C22×C3—22no—
682C22×C3—22no—
683C22×C3—22no—
684C22×C3—24no—
685C22×C3—24no—
686C22×C3—22no—
687C22×C3—22no—
688C22×C3—21no—
689C22×C3—42no—
690C22×C3—44no—
691C22×C3—42no—
692C22×C3—62no—
693C22×C3—64no—
694C22×C3—62no—
695C22×C3—62no—
696C22×C3—62no—
697C22×C3—124no—
698C22×C3C2×D3×D412yes—
699C22×C3C22×#6712yes—
700C22×C3C24×D311yescharacteristic
701C22×C3C24×D311yescharacteristic
702C2×D3—22no—
703C2×D3—22no—
704C2×D3—22no—
705C2×D3—24no—
706C2×D3—22no—
707C2×D3—44no—
708C2×D3—64no—
709C2×D3—68no—
710C2×D3—68no—
711C2×D3—64no—
712C2×D3—124no—
713C2×D3—128no—
714C2×D3—128no—
715C2×D3—128no—
716C2×D3—248no—
717C3×C4—22no—
718C3×C4—22no—
719C3×C4—22no—
720C3×C4—22no—
721C3×C4—38no—
722C3×C4—42no—
723C3×C4—62no—
724C3×C4—64no—
725C3×C4—62no—
726C3×C4C2×D3×D412yes—
727C3×C4C2×D3×D412yes—
728C3×C4C22×#6712yes—
729C3×C4C22×#6712yes—
730Dic3—22no—
731Dic3—24no—
732Dic3—22no—
733Dic3—64no—
734Dic3—64no—
735Dic3—124no—
736Dic3C22×#6718yes—
737C32#348711yescharacteristic, complemented, Sylow
738C23—32no—
739C23—32no—
740C23—62no—
741C23—94no—
742C23—122no—
743C23—184no—
744C23—364no—
745C23C22×D3212yes—
746C23C22×D3211yescharacteristic
747Q8—22no—
748Q8—38no—
749Q8—38no—
750Q8—68no—
751Q8—62no—
752D4—24no—
753D4—22no—
754D4—68no—
755D4—64no—
756D4—62no—
757D4—124no—
758D4—1816no—
759D4—184no—
760D4—184no—
761D4—368no—
762D4—368no—
763D4—364no—
764C2×C4—24no—
765C2×C4—38no—
766C2×C4—34no—
767C2×C4—34no—
768C2×C4—32no—
769C2×C4—32no—
770C2×C4—68no—
771C2×C4—68no—
772C2×C4—62no—
773C2×C4—64no—
774C2×C4—64no—
775C2×C4—64no—
776C2×C4—94no—
777C2×C4—1816no—
778C2×C4D3×#6714yes—
779C2×C4C22×D3212yes—
780C2×C4C22×D3211yescharacteristic
781C2×C4C22×D3211yescharacteristic
782C2×C3—22no—
783C2×C3—22no—
784C2×C3—22no—
785C2×C3—21no—
786C2×C3—42no—
787C2×C3—42no—
788C2×C3—42no—
789C2×C3—82no—
790C2×C3—122no—
791C2×C3—122no—
792C2×C3C22×D3×D411yescharacteristic
793C2×C3#596412yes—
794C2×C3#596812yes—
795C2×C3C23×#6711yescharacteristic
796D3—42no—
797D3—42no—
798D3—124no—
799D3—124no—
800D3—244no—
801C22—22no—
802C22—24no—
803C22—22no—
804C22—62no—
805C22—64no—
806C22—62no—
807C22—62no—
808C22—62no—
809C22—124no—
810C22—188no—
811C22—184no—
812C22—368no—
813C22C2×D3×#6712yes—
814C22C23×D3211yescharacteristic
815C4—22no—
816C4—38no—
817C4—64no—
818C4—62no—
819C4—62no—
820C4—184no—
821C4C2×D3×#6712yes—
822C4C2×D3×#6712yes—
823C3—21no—
824C3#8602311yescharacteristic, complemented
825C3#8729011yescharacteristic, complemented
826C2—22no—
827C2—42no—
828C2—122no—
829C2—122no—
830C2—364no—
831C2#1059669712yes—
832C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3487
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. C22×#3799C2semidirect
3. #10596301C2semidirect
4. C3×#5828C2semidirect
5. #10595402C2semidirect
6. #10595238C2semidirect
7. #10595236C2semidirect
8. #10595159C2semidirect
9. #10595045C2semidirect
10. #10595022C2semidirect
11. #10595007C2semidirect
12. #10594902C2semidirect
13. #10594818C2semidirect
19. C2×C3×D3×Q8C22semidirect
21. C2×C3×#237C22semidirect
23. C2×C3×#235C22semidirect
26. C22×C3×Dic6C22semidirect
32. #64156C22semidirect
33. #64149C22semidirect
35. #64139C22semidirect
37. C3×#946C22semidirect
38. C3×#938C22semidirect
41. C3×C4×#67C22semidirect
44. #63979C22semidirect
45. #63978C22semidirect
48. #63958C22semidirect
50. #63952C22semidirect
51. #63911C22semidirect
52. #63909C22semidirect
53. #63908C22semidirect
54. #63907C22semidirect
55. #63906C22semidirect
56. #63904C22semidirect
57. C4×#625C22semidirect
58. #63888C22semidirect
59. #63864C22semidirect
60. #63856C22semidirect
61. #63843C22semidirect
62. Dic3×Dic6C22semidirect
64. C2×#1010D3semidirect
77. #5828D3semidirect
120. C2×C3×Dic6D4semidirect
167. C2×D3×Q8C2×D3semidirect
169. C2×#237C2×D3semidirect
174. C2×#235C2×D3semidirect
183. C22×Dic6C2×D3semidirect
198. #946C2×D3semidirect
210. #938C2×D3semidirect
231. C4×#67C2×D3semidirect
400. C2×Dic6#67semidirect
737. C32#3487semidirect
824. C3#86023semidirect
825. C3#87290semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C22×#37992
#105963012
C3×#58282
#105954022
#105952382
#105952362
#105951592
#105950452
#105950222
#105950072
#105949022
#105948182
#872903
#860233