Finite Group Databasebeta

← #11904566

Subgroups — #11904566

Order 1152.

3237 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C22×#3796C211yesmaximal, characteristic, complemented
3#10596299C211yesmaximal, characteristic, complemented
4C3×#5830C211yesmaximal, characteristic, complemented
5#10595401C214yesmaximal, complemented
6#10595238C214yesmaximal, complemented
7#10595158C214yesmaximal, complemented
8#10595154C214yesmaximal, complemented
9#10595040C211yesmaximal, characteristic, complemented
10#10595034C211yesmaximal, characteristic, complemented
11#10595006C214yesmaximal, complemented
12#10594900C214yesmaximal, complemented
13#10594818C211yesmaximal, characteristic, complemented
14#87290—31nomaximal
15#86315—31nomaximal
16C2×C32×#41C2211yescharacteristic
17C22×C4×C3⋊D3C2211yescharacteristic
18C3×#1010—28no—
19C2×C3×D3×Q8C2212yescomplemented
20C2×C3×#237C2214yes—
21C2×C3×#237C2212yescomplemented
22C2×C3×#235C2211yescharacteristic
23C2×C3×#235C2212yescomplemented
24C22×C3×D12C2211yescharacteristic
25C22×C3×Dic6C2211yescharacteristic
26C22×C3×Dic6C2212yescomplemented
27C22×#626C2212yes—
28C22×D3×Dic3C2212yes—
29C2×#3796—28no—
30C2×#3796C2214yes—
31C2×#3796C2214yes—
32#64155C2212yescomplemented
33#64147C2212yescomplemented
34#64146C2212yes—
35#64144C2212yes—
36C4×#638C2214yescomplemented
37#64135C2211yescharacteristic
38C3×#947C2212yescomplemented
39C3×#940C2212yescomplemented
40C3×#937C2214yes—
41C3×#930C2214yescomplemented
42C3×#926C2211yescharacteristic
43#63981C2212yes—
44#63979C2218yescomplemented
45#63978C2218yescomplemented
46#63976C2214yes—
47Dic3×#67C2218yescomplemented
48#63970C2218yescomplemented
49#63962C2212yes—
50#63955C2214yes—
51#63916C2212yescomplemented
52#63914C2212yescomplemented
53#63908C2214yescomplemented
54#63907C2218yescomplemented
55#63906C2218yescomplemented
56C4×#626C2214yescomplemented
57#63887C2218yescomplemented
58#63879C2218yescomplemented
59#63871C2212yescomplemented
60#63863C2212yescomplemented
61#63843C2214yescomplemented
62Dic3×Dic6C2214yescomplemented
63C2×C3×2−1+4—31no—
64C2×#1010D311yescharacteristic, complemented
65C22×#239—31no—
66C22×#237—31no—
67C3×#535—31no—
68#5834—34no—
69#5834—34no—
70#5830—31no—
71#5830—34no—
72#5830D311yescharacteristic, complemented
73#5828—31no—
74#5828—31no—
75#5828—34no—
76#5828—31no—
77#5828—61no—
78#5817—34no—
79#5817—34no—
80#5812—31no—
81#5805—31no—
82#5718—34no—
83#5677—34no—
84#5599—34no—
85#5598—34no—
86#5592—34no—
87#5586—34no—
88#5524—31no—
89#5516—31no—
90C23×C3⋊D3C2311yescharacteristic
91C23×C3×D3C2312yes—
92C32×#41—24no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2312yes—
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4C2312yes—
97C22×C32×C4C2311yescharacteristic
98C2×#638C2314yes—
99C22×C3⋊Dic3C2311yescharacteristic
100C2×C4×C3⋊D3—24no—
101C2×C4×C3⋊D3C2312yes—
102C2×C4×C3⋊D3C2312yes—
103C2×C3×#67C2312yes—
104C2×C3×#67C2314yes—
105C2×C3×#67C2318yes—
106C22×C3×Dic3C2314yes—
107C22×C3×Dic3C2312yes—
108C3×D3×Q8—28no—
109C3×#237—216no—
110C3×#237—28no—
111C3×#235—24no—
112C3×#235—28no—
113C2×C3×D12—24no—
114C2×C3×D12C2312yes—
115C2×C3×D12C2312yes—
116C2×C3×D12C2311yescharacteristic
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×#626C2314yes—
128C2×#625C2318yes—
129C2×D3×Dic3—28no—
130C2×D3×Dic3C2318yes—
131#3796—216no—
132#3796—216no—
133#3757C2312yes—
134#3757C2314yes—
135#3752C2314yes—
136C4⋊(C3⋊Dic3)C2312yes—
137#3750C2314yes—
138C4×C3⋊Dic3C2312yes—
139C3×#217C2312yes—
140C3×(C2×D3)⋊C4C2318yes—
141C3×C4⋊Dic3C2312yes—
142C3×C4×Dic3C2312yes—
143Dic3⋊Dic3C2318yes—
144Dic3⋊Dic3C2314yes—
145#3722C2314yes—
146(C2×D3)⋊Dic3C2318yes—
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—
161C22×C3×D4—31no—
162C22×#67—32no—
163C23×Dic3—32no—
164#1010—28no—
165C2×#239—34no—
166C2×#239—34no—
167C2×#239—68no—
168C2×D3×Q8C2×D312yescomplemented
169C2×#237—34no—
170C2×#237—34no—
171C2×#237—68no—
172C2×#237C2×D314yes—
173C2×#237C2×D312yescomplemented
174C2×#235C2×D311yescharacteristic
175C2×#235C2×D312yescomplemented
176C22×D12—32no—
177C22×D12C2×D311yescharacteristic
178C22×C4×D3—32no—
179C22×C4×D3—31no—
180C22×C4×D3—31no—
181C22×C4×D3—61no—
182C22×Dic6C2×D311yescharacteristic
183C22×Dic6C2×D312yescomplemented
184C3×#127—32no—
185C3×#124—32no—
186C3×#121—34no—
187C3×#120—34no—
188C3×#117—31no—
189#953—34no—
190#947—32no—
191#947—38no—
192#947C2×D312yescomplemented
193#946—32no—
194#946—32no—
195#946—38no—
196#946—32no—
197#946—62no—
198Q8×Dic3—34no—
199Q8×Dic3—34no—
200#940—38no—
201#940—38no—
202#940—32no—
203#940—32no—
204#940C2×D312yescomplemented
205#939—38no—
206#939—38no—
207#938—32no—
208#938—32no—
209#938—38no—
210#938—34no—
211#938—32no—
212#938—62no—
213#937—34no—
214#937—32no—
215#937—32no—
216#937—32no—
217#937—62no—
218#937C2×D314yes—
219#936—32no—
220#935—32no—
221#935—32no—
222#935—32no—
223#935—62no—
224D4×Dic3—38no—
225#930—38no—
226#930—34no—
227#930—38no—
228#930C2×D314yescomplemented
229C4×#67—34no—
230C4×#67—34no—
231C4×#67—38no—
232C4×#67—38no—
233C4×#67—34no—
234C4×#67—64no—
235#926—31no—
236#926—31no—
237#926—34no—
238#926—61no—
239#926C2×D311yescharacteristic
240#897—32no—
241#895—32no—
242#887—34no—
243#886—32no—
244#885—38no—
245#884—38no—
246#882—32no—
247#67⋊C4—38no—
248#878—38no—
249#877—34no—
250C4×D12—34no—
251C4×Dic6—34no—
252C23×C32C2412yes—
253C23×C32C2411yescharacteristic
254C22×C3⋊D3—22no—
255C22×C3⋊D3—42no—
256C22×C3⋊D3C2412yes—
257C22×C3×D3—24no—
258C22×C3×D3—44no—
259C22×C3×D3C2414yes—
260C22×C3×D3C2412yes—
261C32×Q8—22no—
262C32×D4—24no—
263C32×D4—22no—
264C2×C32×C4—24no—
265C2×C32×C4C2×D414yes—
266C2×C32×C4C2412yes—
267C2×C32×C4C2411yescharacteristic
268C2×C32×C4C2411yescharacteristic
269#638—44no—
270C2×C3⋊Dic3—22no—
271C2×C3⋊Dic3C2414yes—
272C2×C3⋊Dic3C2412yes—
273C4×C3⋊D3—24no—
274C4×C3⋊D3—24no—
275C3×#67—24no—
276C3×#67—28no—
277C3×#67—48no—
278C2×C3×Dic3—28no—
279C2×C3×Dic3C2×D418yes—
280C2×C3×Dic3C2414yes—
281C2×C3×Dic3C2412yes—
282C2×C3×Dic3C2414yes—
283C3×D12—24no—
284C3×D12—24no—
285C3×D12—22no—
286C3×C4×D3—24no—
287C3×C4×D3—28no—
288C3×Dic6—22no—
289C3×Dic6—28no—
290C3×Dic6C2×D418yes—
291C3×Dic6C2×D418yes—
292#626—216no—
293#626—44no—
294#625—48no—
295D3×Dic3—216no—
296C2×2−1+4—31no—
297C22×#41—91no—
298#550—94no—
299#550—94no—
300#548—94no—
301#548—94no—
302#535—31no—
303#535—94no—
304#535—91no—
305#525—91no—
306#525—94no—
307#525—91no—
308#519—91no—
309C24×C3—32no—
310C23×D3—31no—
311C23×D3—31no—
312C23×D3—61no—
313C23×D3C22×D312yes—
314C3×#41—24no—
315C3×#41—24no—
316C3×#41—44no—
317C3×#41—68no—
318C3×#41—616no—
319C3×#41—68no—
320C3×#41—64no—
321C2×C3×Q8—21no—
322C2×C3×Q8—38no—
323C2×C3×Q8—32no—
324C2×C3×Q8—32no—
325C2×C3×Q8—34no—
326C2×C3×Q8—31no—
327C2×C3×Q8—68no—
328C2×C3×Q8—68no—
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×D4—22no—
332C2×C3×D4—21no—
333C2×C3×D4—32no—
334C2×C3×D4—34no—
335C2×C3×D4—38no—
336C2×C3×D4—32no—
337C2×C3×D4—31no—
338C2×C3×D4—32no—
339C2×C3×D4—64no—
340C2×C3×D4C22×D312yes—
341C2×C3×D4C22×D312yes—
342C2×C3×D4C22×D311yescharacteristic
343C2×C3×D4C22×D311yescharacteristic
344C22×C3×C4—21no—
345C22×C3×C4—22no—
346C22×C3×C4—32no—
347C22×C3×C4—34no—
348C22×C3×C4—34no—
349C22×C3×C4—32no—
350C22×C3×C4C22×D312yes—
351C22×C3×C4C22×D312yes—
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C2×#67—34no—
355C2×#67—34no—
356C2×#67—38no—
357C2×#67—38no—
358C2×#67—38no—
359C2×#67—34no—
360C2×#67—64no—
361C2×#67—68no—
362C2×#67C22×D312yes—
363C2×#67C22×D314yes—
364C2×#67C22×D318yes—
365C22×Dic3—31no—
366C22×Dic3—31no—
367C22×Dic3—38no—
368C22×Dic3—61no—
369C22×Dic3—68no—
370C22×Dic3C22×D314yes—
371C22×Dic3C22×D312yes—
372#239—616no—
373#239—616no—
374D3×Q8—28no—
375#237—216no—
376#237—28no—
377#237—616no—
378#237—616no—
379#235—24no—
380#235—28no—
381C2×D12—24no—
382C2×D12—38no—
383C2×D12—34no—
384C2×D12—68no—
385C2×D12C22×D311yescharacteristic
386C2×D12C22×D312yes—
387C2×D12C22×D312yes—
388C2×C4×D3—38no—
389C2×C4×D3—32no—
390C2×C4×D3—32no—
391C2×C4×D3—32no—
392C2×C4×D3—32no—
393C2×C4×D3—62no—
394C2×C4×D3—62no—
395C2×C4×D3—68no—
396C2×C4×D3—64no—
397C2×C4×D3—64no—
398C2×C4×D3—124no—
399C2×C4×D3C22×D312yes—
400C2×C4×D3C22×D314yes—
401C2×Dic6—28no—
402C2×Dic6#6718yescomplemented
403C2×Dic6C22×D314yes—
404C2×Dic6C22×D311yescharacteristic
405C2×Dic6C22×D312yes—
406C2×Dic6C22×D312yes—
407C3×C4⋊C4—32no—
408C3×C22⋊C4—32no—
409C3×C22⋊C4—38no—
410C3×C42—32no—
411#217—32no—
412#217—32no—
413#217—34no—
414#217—34no—
415#217—38no—
416#217—34no—
417#217—62no—
418#217—64no—
419#217C22×D312yes—
420(C2×D3)⋊C4—34no—
421(C2×D3)⋊C4—38no—
422(C2×D3)⋊C4—34no—
423(C2×D3)⋊C4—34no—
424(C2×D3)⋊C4—34no—
425(C2×D3)⋊C4—34no—
426(C2×D3)⋊C4—64no—
427(C2×D3)⋊C4C22×D318yes—
428C4⋊Dic3—32no—
429C4⋊Dic3—32no—
430C4⋊Dic3—34no—
431C4⋊Dic3—38no—
432C4⋊Dic3—62no—
433C4⋊Dic3C22×D312yes—
434Dic3⋊C4—34no—
435Dic3⋊C4—34no—
436Dic3⋊C4—38no—
437Dic3⋊C4—34no—
438Dic3⋊C4—64no—
439C4×Dic3—32no—
440C4×Dic3—32no—
441C4×Dic3—38no—
442C4×Dic3—38no—
443C4×Dic3—62no—
444C4×Dic3C22×D312yes—
445C22×C32—22no—
446C22×C32—22no—
447C22×C32—24no—
448C22×C32C22×D412yes—
449C22×C32C2511yescharacteristic
450C2×C3⋊D3—22no—
451C2×C3⋊D3—22no—
452C2×C3⋊D3—22no—
453C2×C3⋊D3—44no—
454C2×C3×D3—24no—
455C2×C3×D3—22no—
456C2×C3×D3—24no—
457C2×C3×D3—28no—
458C2×C3×D3—48no—
459C32×C4—22no—
460C32×C4C22×D412yes—
461C32×C4C22×D412yes—
462C3⋊Dic3—22no—
463C3⋊Dic3—24no—
464C3×Dic3—22no—
465C3×Dic3—24no—
466C3×Dic3C22×D418yes—
4672−1+4—68no—
468C2×#41—34no—
469C2×#41—32no—
470C2×#41—31no—
471C2×#41—32no—
472C2×#41—94no—
473C2×#41—94no—
474C2×#41—188no—
475C2×#41D3211yescharacteristic
476C22×Q8—32no—
477C22×Q8—31no—
478C22×Q8—32no—
479C22×D4—31no—
480C22×D4—92no—
481C23×C4—92no—
482C23×C4—91no—
483#127—32no—
484#127—98no—
485#127—92no—
486#124—32no—
487#124—98no—
488#124—92no—
489#123—92no—
490#123—92no—
491C22⋊Q8—98no—
492C22⋊Q8—92no—
493C22⋊Q8—92no—
494#121—34no—
495#121—98no—
496#121—92no—
497#121—94no—
498#121—98no—
499#121—98no—
500#121—92no—
501#120—34no—
502#120—92no—
503#120—94no—
504#120—92no—
505C4×Q8—94no—
506C4×Q8—94no—
507C4×D4—94no—
508C4×D4—98no—
509C4×D4—98no—
510C4×D4—94no—
511#117—31no—
512#117—94no—
513#117—91no—
514C23×C3—21no—
515C23×C3—22no—
516C23×C3—34no—
517C23×C3—32no—
518C23×C3—64no—
519C23×C3—124no—
520C23×C3C23×D312yes—
521C23×C3C23×D312yes—
522C23×C3C23×D311yescharacteristic
523C23×C3C23×D311yescharacteristic
524C22×D3—24no—
525C22×D3—32no—
526C22×D3—32no—
527C22×D3—44no—
528C22×D3—62no—
529C22×D3—62no—
530C22×D3—62no—
531C22×D3—122no—
532C22×D3—122no—
533C22×D3—122no—
534C22×D3—124no—
535C22×D3C23×D314yes—
536C22×D3C23×D312yes—
537C3×Q8—22no—
538C3×Q8—22no—
539C3×Q8—38no—
540C3×Q8—38no—
541C3×Q8—42no—
542C3×Q8—68no—
543C3×Q8—62no—
544C3×D4—24no—
545C3×D4—24no—
546C3×D4—22no—
547C3×D4—22no—
548C3×D4—42no—
549C3×D4—44no—
550C3×D4—68no—
551C3×D4—64no—
552C3×D4—62no—
553C3×D4—64no—
554C3×D4—64no—
555C3×D4—128no—
556C2×C3×C4—24no—
557C2×C3×C4—24no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—22no—
561C2×C3×C4—24no—
562C2×C3×C4—38no—
563C2×C3×C4—34no—
564C2×C3×C4—34no—
565C2×C3×C4—32no—
566C2×C3×C4—44no—
567C2×C3×C4—68no—
568C2×C3×C4—68no—
569C2×C3×C4—64no—
570C2×C3×C4D3×D414yes—
571C2×C3×C4C2×#6714yes—
572C2×C3×C4C23×D312yes—
573C2×C3×C4C23×D312yes—
574C2×C3×C4C23×D311yescharacteristic
575C2×C3×C4C23×D311yescharacteristic
576C2×C3×C4C23×D311yescharacteristic
577C2×C3×C4C23×D311yescharacteristic
578#67—24no—
579#67—28no—
580#67—48no—
581#67—616no—
582#67—124no—
583#67—128no—
584#67—128no—
585#67—124no—
586#67—124no—
587#67—128no—
588C2×Dic3—28no—
589C2×Dic3—34no—
590C2×Dic3—34no—
591C2×Dic3—32no—
592C2×Dic3—32no—
593C2×Dic3—64no—
594C2×Dic3—62no—
595C2×Dic3—62no—
596C2×Dic3—62no—
597C2×Dic3—616no—
598C2×Dic3—122no—
599C2×Dic3C2×#6718yes—
600C2×Dic3C23×D314yes—
601C2×Dic3C23×D312yes—
602C2×Dic3C23×D314yes—
603D12—24no—
604D12—24no—
605D12—22no—
606D12—616no—
607D12—124no—
608C4×D3—24no—
609C4×D3—28no—
610C4×D3—616no—
611C4×D3—64no—
612C4×D3—64no—
613C4×D3—64no—
614C4×D3—64no—
615C4×D3—124no—
616C4×D3—124no—
617Dic6—22no—
618Dic6—28no—
619Dic6C2×#6718yes—
620Dic6C2×#6718yes—
621C2×C32—22no—
622C2×C32—42no—
623C2×C32C23×D411yescharacteristic
624C2×C32#58512yes—
625C3⋊D3—42no—
626C3×D3—42no—
627C3×D3—44no—
628C24—32no—
629C24—91no—
630#41—24no—
631#41—68no—
632#41—616no—
633#41—68no—
634#41—64no—
635#41—1816no—
636#41—1816no—
637C2×Q8—32no—
638C2×Q8—32no—
639C2×Q8—34no—
640C2×Q8—31no—
641C2×Q8—38no—
642C2×Q8—68no—
643C2×Q8—68no—
644C2×Q8C2×D3211yescharacteristic
645C2×D4—32no—
646C2×D4—34no—
647C2×D4—38no—
648C2×D4—32no—
649C2×D4—32no—
650C2×D4—31no—
651C2×D4—64no—
652C2×D4—98no—
653C2×D4—94no—
654C2×D4—98no—
655C2×D4—94no—
656C2×D4—188no—
657C2×D4C2×D3212yes—
658C2×D4C2×D3211yescharacteristic
659C22×C4—32no—
660C22×C4—34no—
661C22×C4—34no—
662C22×C4—32no—
663C22×C4—98no—
664C22×C4—91no—
665C22×C4—92no—
666C22×C4—92no—
667C22×C4—188no—
668C22×C4—184no—
669C22×C4C2×D3212yes—
670C22×C4C2×D3211yescharacteristic
671C4⋊C4—32no—
672C4⋊C4—98no—
673C4⋊C4—94no—
674C4⋊C4—92no—
675C4⋊C4—94no—
676C22⋊C4—32no—
677C22⋊C4—38no—
678C22⋊C4—94no—
679C22⋊C4—94no—
680C22⋊C4—98no—
681C22⋊C4—92no—
682C22⋊C4—94no—
683C22⋊C4—94no—
684C42—32no—
685C42—98no—
686C42—92no—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—22no—
690C22×C3—24no—
691C22×C3—24no—
692C22×C3—22no—
693C22×C3—22no—
694C22×C3—21no—
695C22×C3—42no—
696C22×C3—44no—
697C22×C3—42no—
698C22×C3—62no—
699C22×C3—64no—
700C22×C3—68no—
701C22×C3—64no—
702C22×C3—128no—
703C22×C3C2×D3×D412yes—
704C22×C3C22×#6712yes—
705C22×C3C24×D311yescharacteristic
706C22×C3C24×D311yescharacteristic
707C2×D3—24no—
708C2×D3—28no—
709C2×D3—24no—
710C2×D3—22no—
711C2×D3—48no—
712C2×D3—64no—
713C2×D3—62no—
714C2×D3—62no—
715C2×D3—62no—
716C2×D3—62no—
717C2×D3—62no—
718C2×D3—62no—
719C2×D3—122no—
720C2×D3—122no—
721C2×D3—124no—
722C2×D3—124no—
723C2×D3—128no—
724C3×C4—22no—
725C3×C4—22no—
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—38no—
729C3×C4—42no—
730C3×C4—62no—
731C3×C4—64no—
732C3×C4C2×D3×D412yes—
733C3×C4C2×D3×D412yes—
734C3×C4C22×#6712yes—
735C3×C4C22×#6712yes—
736Dic3—24no—
737Dic3—22no—
738Dic3—62no—
739Dic3—64no—
740Dic3—64no—
741Dic3—62no—
742Dic3—122no—
743Dic3—124no—
744Dic3C22×#6718yes—
745C32#348711yescharacteristic, complemented, Sylow
746C23—34no—
747C23—32no—
748C23—64no—
749C23—92no—
750C23—124no—
751C23—182no—
752C23—362no—
753C23C22×D3212yes—
754C23C22×D3211yescharacteristic
755Q8—22no—
756Q8—38no—
757Q8—38no—
758Q8—68no—
759Q8—62no—
760D4—24no—
761D4—22no—
762D4—68no—
763D4—64no—
764D4—64no—
765D4—64no—
766D4—62no—
767D4—128no—
768D4—1816no—
769D4—364no—
770D4—364no—
771D4—368no—
772C2×C4—24no—
773C2×C4—38no—
774C2×C4—34no—
775C2×C4—34no—
776C2×C4—32no—
777C2×C4—68no—
778C2×C4—68no—
779C2×C4—64no—
780C2×C4—94no—
781C2×C4—92no—
782C2×C4—1816no—
783C2×C4—182no—
784C2×C4—184no—
785C2×C4—184no—
786C2×C4D3×#6714yes—
787C2×C4C22×D3212yes—
788C2×C4C22×D3211yescharacteristic
789C2×C4C22×D3211yescharacteristic
790C2×C3—22no—
791C2×C3—22no—
792C2×C3—22no—
793C2×C3—21no—
794C2×C3—42no—
795C2×C3—42no—
796C2×C3—42no—
797C2×C3—82no—
798C2×C3—122no—
799C2×C3—124no—
800C2×C3C22×D3×D411yescharacteristic
801C2×C3#596612yes—
802C2×C3#596812yes—
803C2×C3C23×#6711yescharacteristic
804D3—44no—
805D3—42no—
806D3—124no—
807D3—122no—
808D3—122no—
809C22—22no—
810C22—24no—
811C22—22no—
812C22—68no—
813C22—64no—
814C22—62no—
815C22—64no—
816C22—128no—
817C22—182no—
818C22—182no—
819C22—182no—
820C22—364no—
821C22C2×D3×#6712yes—
822C22C23×D3211yescharacteristic
823C4—22no—
824C4—38no—
825C4—64no—
826C4—62no—
827C4—184no—
828C4—182no—
829C4C2×D3×#6712yes—
830C4C2×D3×#6712yes—
831C3—21no—
832C3#8631511yescharacteristic, complemented
833C3#8729011yescharacteristic, complemented
834C2—22no—
835C2—42no—
836C2—124no—
837C2—122no—
838C2—362no—
839C2#1059669812yes—
840C2C22×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×#3796C2semidirect
3. #10596299C2semidirect
4. C3×#5830C2semidirect
5. #10595401C2semidirect
6. #10595238C2semidirect
7. #10595158C2semidirect
8. #10595154C2semidirect
9. #10595040C2semidirect
10. #10595034C2semidirect
11. #10595006C2semidirect
12. #10594900C2semidirect
13. #10594818C2semidirect
19. C2×C3×D3×Q8C22semidirect
21. C2×C3×#237C22semidirect
23. C2×C3×#235C22semidirect
26. C22×C3×Dic6C22semidirect
32. #64155C22semidirect
33. #64147C22semidirect
36. C4×#638C22semidirect
38. C3×#947C22semidirect
39. C3×#940C22semidirect
41. C3×#930C22semidirect
44. #63979C22semidirect
45. #63978C22semidirect
47. Dic3×#67C22semidirect
48. #63970C22semidirect
51. #63916C22semidirect
52. #63914C22semidirect
53. #63908C22semidirect
54. #63907C22semidirect
55. #63906C22semidirect
56. C4×#626C22semidirect
57. #63887C22semidirect
58. #63879C22semidirect
59. #63871C22semidirect
60. #63863C22semidirect
61. #63843C22semidirect
62. Dic3×Dic6C22semidirect
64. C2×#1010D3semidirect
72. #5830D3semidirect
120. C2×C3×Dic6D4semidirect
168. C2×D3×Q8C2×D3semidirect
173. C2×#237C2×D3semidirect
175. C2×#235C2×D3semidirect
183. C22×Dic6C2×D3semidirect
192. #947C2×D3semidirect
204. #940C2×D3semidirect
228. #930C2×D3semidirect
402. C2×Dic6#67semidirect
745. C32#3487semidirect
832. C3#86315semidirect
833. 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×#37962
#105962992
C3×#58302
#105954012
#105952382
#105951582
#105951542
#105950402
#105950342
#105950062
#105949002
#105948182
#872903
#863153