Finite Group Databasebeta

← #11904567

Subgroups — #11904567

Order 1152.

3469 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64367C211yesmaximal, characteristic, complemented
2C22×#3795C211yesmaximal, characteristic, complemented
3C3×#5830C211yesmaximal, characteristic, complemented
4C3×#5828C211yesmaximal, characteristic, complemented
5#10595362C214yesmaximal, complemented
6#10595239C214yesmaximal, complemented
7#10595164C214yesmaximal, complemented
8#10595160C214yesmaximal, complemented
9#10595042C211yesmaximal, characteristic, complemented
10#10595023C211yesmaximal, characteristic, complemented
11#10594919C214yesmaximal, complemented
12#10594918C214yesmaximal, complemented
13#10594828C211yesmaximal, characteristic, complemented
14#86315—31nomaximal
15#86023—31nomaximal
16C2×C32×#41C2211yescharacteristic
17#64367—28no—
18C2×Q8×C3⋊D3C2212yescomplemented
19C2×#3830C2214yes—
20C2×#3830C2212yescomplemented
21C2×#3828C2211yescharacteristic
22C2×#3828C2212yescomplemented
23C22×#634C2211yescharacteristic
24C22×#634C2212yescomplemented
25C22×C3×D12C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic
27C22×#625C2212yes—
28C22×D3×Dic3C2212yes—
29C2×#3795—28no—
30C2×#3795C2214yes—
31C2×#3795C2214yes—
32C3×#947C2212yescomplemented
33C3×#946C2212yescomplemented
34C3×#940C2212yescomplemented
35C3×#938C2212yescomplemented
36C3×#937C2212yes—
37C3×#937C2214yes—
38C3×#935C2212yes—
39C3×#930C2214yescomplemented
40C3×C4×#67C2214yescomplemented
41C3×#926C2211yescharacteristic
42C3×#926C2211yescharacteristic
43#63980C2218yescomplemented
44#63979C2218yescomplemented
45#63977C2214yes—
46#63977C2212yes—
47#67⋊Dic3C2218yescomplemented
48#63971C2218yescomplemented
49#63966C2212yes—
50#63957C2214yes—
51#63916C2214yescomplemented
52#63913C2218yescomplemented
53#63912C2218yescomplemented
54#63911C2212yescomplemented
55#63909C2212yescomplemented
56C4×#626C2214yescomplemented
57#63896C2218yescomplemented
58#63881C2218yescomplemented
59#63860C2212yescomplemented
60#63857C2212yescomplemented
61#63844C2214yescomplemented
62#63844C2214yescomplemented
63C2×#1010—31no—
64C2×#1010—31no—
65C2×#1010—61no—
66C22×#237—31no—
67C22×#235—31no—
68C3×#535—31no—
69C3×#525—31no—
70#5830D311yescharacteristic, complemented
71#5828D311yescharacteristic, complemented
72#5805—31no—
73#5791—31no—
74#5718—34no—
75#5677—34no—
76#5656—34no—
77#5633—34no—
78#5599—34no—
79#5599—34no—
80#5598—34no—
81#5592—34no—
82#5592—34no—
83#5586—34no—
84#5553—34no—
85#5552—34no—
86#5525—31no—
87#5524—31no—
88#5516—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×#638C2312yes—
99C2×#638C2314yes—
100C22×C3⋊Dic3C2314yes—
101C22×C3⋊Dic3C2312yes—
102Q8×C3⋊D3—28no—
103#3830—216no—
104#3830—28no—
105#3828—24no—
106#3828—28no—
107C2×C4⋊(C3⋊D3)C2311yescharacteristic
108C2×C4×C3⋊D3C2312yes—
109C2×C4×C3⋊D3C2314yes—
110C2×#634—28no—
111C2×#634D418yescomplemented
112C2×#634C2311yescharacteristic
113C2×#634C2314yes—
114C2×#634C2312yes—
115C2×#634C2312yes—
116C2×C3×#67C2314yes—
117C2×C3×#67C2318yes—
118C22×C3×Dic3C2311yescharacteristic
119C2×C3×D12—24no—
120C2×C3×D12C2312yes—
121C2×C3×D12C2312yes—
122C2×C3×C4×D3—24no—
123C2×C3×C4×D3C2312yes—
124C2×C3×C4×D3C2312yes—
125C2×#626C2318yes—
126C2×#626C2314yes—
127C2×#625—28no—
128C2×#625C2318yes—
129C2×D3×Dic3—28no—
130C2×D3×Dic3C2318yes—
131#3795—216no—
132#3795—216no—
133C3×#217C2312yes—
134C3×#217C2312yes—
135C3×#217C2314yes—
136C3×(C2×D3)⋊C4C2314yes—
137C3×(C2×D3)⋊C4C2318yes—
138C3×C4⋊Dic3C2312yes—
139C3×C4⋊Dic3C2312yes—
140C3×Dic3⋊C4C2314yes—
141C3×C4×Dic3C2312yes—
142C3×C4×Dic3C2312yes—
143#3724C2318yes—
144Dic3⋊Dic3C2314yes—
145#3722C2314yes—
146(C2×D3)⋊Dic3C2314yes—
147(C2×D3)⋊Dic3C2318yes—
148Dic32C2318yes—
149#3487—91noSylow
150C2×C3×#41—21no—
151C2×C3×#41C2×D311yescharacteristic
152C2×C3×#41C2×D311yescharacteristic
153C22×C3×D4—31no—
154C23×C3×C4—31no—
155C22×#67—32no—
156C22×#67—32no—
157C23×Dic3—32no—
158#1010—68no—
159#1010—68no—
160#1010—616no—
161C2×D3×Q8—32no—
162C2×D3×Q8—32no—
163C2×D3×Q8—62no—
164C2×#237—34no—
165C2×#237—32no—
166C2×#237—34no—
167C2×#237—32no—
168C2×#237—34no—
169C2×#237—34no—
170C2×#237—64no—
171C2×#237—62no—
172C2×#237—68no—
173C2×#235—31no—
174C2×#235—31no—
175C2×#235—32no—
176C2×#235—32no—
177C2×#235—34no—
178C2×#235—34no—
179C2×#235—61no—
180C2×#235—62no—
181C2×#235—68no—
182C22×D12C2×D311yescharacteristic
183C22×C4×D3—32no—
184C22×C4×D3C2×D311yescharacteristic
185C22×Dic6—31no—
186C22×Dic6—31no—
187C22×Dic6—32no—
188C22×Dic6—32no—
189C22×Dic6—61no—
190C22×Dic6—62no—
191C3×#127—32no—
192C3×#124—32no—
193C3×#123—32no—
194C3×C22⋊Q8—32no—
195C3×#121—32no—
196C3×#121—34no—
197C3×#120—34no—
198C3×#120—32no—
199C3×C4×D4—34no—
200C3×#117—31no—
201C3×#117—31no—
202#953—32no—
203#953—34no—
204#947C2×D312yescomplemented
205#946C2×D312yescomplemented
206#940—38no—
207#940—38no—
208#940—32no—
209#940C2×D312yescomplemented
210#939—38no—
211#939—38no—
212#939—38no—
213#938—34no—
214#938C2×D312yescomplemented
215#937C2×D314yes—
216#937C2×D312yes—
217#936—32no—
218#935C2×D312yes—
219D4×Dic3—38no—
220#930—32no—
221#930C2×D314yescomplemented
222#929—32no—
223C4×#67—34no—
224C4×#67C2×D314yescomplemented
225#926C2×D311yescharacteristic
226#926C2×D311yescharacteristic
227#924—32no—
228#897—32no—
229#896—38no—
230#895—34no—
231#895—32no—
232#893—38no—
233#887—34no—
234#887—34no—
235#886—32no—
236#885—38no—
237#885—38no—
238#884—38no—
239#884—38no—
240#884—38no—
241#882—34no—
242#882—32no—
243#67⋊C4—38no—
244#67⋊C4—38no—
245#878—38no—
246#877—34no—
247#877—34no—
248#875—32no—
249#874—32no—
250C4×D12—34no—
251C4×Dic6—34no—
252C4×Dic6—34no—
253C23×C32C2412yes—
254C23×C32C2411yescharacteristic
255C22×C3⋊D3C2412yes—
256C22×C3×D3—24no—
257C22×C3×D3—22no—
258C22×C3×D3—42no—
259C22×C3×D3—44no—
260C22×C3×D3C2414yes—
261C22×C3×D3C2412yes—
262C32×Q8—22no—
263C32×D4—24no—
264C32×D4—22no—
265C2×C32×C4—24no—
266C2×C32×C4C2×D414yes—
267C2×C32×C4C2412yes—
268C2×C32×C4C2411yescharacteristic
269C2×C32×C4C2411yescharacteristic
270#638—24no—
271#638—28no—
272C2×C3⋊Dic3—28no—
273C2×C3⋊Dic3C2×D418yes—
274C2×C3⋊Dic3C2412yes—
275C2×C3⋊Dic3C2414yes—
276C4⋊(C3⋊D3)—22no—
277C4×C3⋊D3—24no—
278C4×C3⋊D3—28no—
279#634—22no—
280#634—28no—
281#634C2×D418yes—
282#634C2×D418yes—
283C3×#67—44no—
284C3×#67—48no—
285C2×C3×Dic3—22no—
286C2×C3×Dic3C2414yes—
287C2×C3×Dic3C2414yes—
288C2×C3×Dic3C2412yes—
289C3×D12—24no—
290C3×D12—24no—
291C3×C4×D3—24no—
292C3×C4×D3—24no—
293#626—48no—
294#626—44no—
295#625—216no—
296D3×Dic3—216no—
297C2×2−1+4—91no—
298C22×#41—91no—
299#550—94no—
300#550—94no—
301#548—94no—
302#548—94no—
303#535—31no—
304#535—91no—
305#535—94no—
306#525—31no—
307#525—91no—
308#525—94no—
309#519—91no—
310C24×C3—32no—
311C24×C3—31no—
312C23×D3C22×D312yes—
313C23×D3C22×D311yescharacteristic
314C3×#41—28no—
315C3×#41—24no—
316C3×#41—24no—
317C2×C3×Q8—21no—
318C2×C3×Q8C22×D311yescharacteristic
319C2×C3×Q8C22×D311yescharacteristic
320C2×C3×D4—22no—
321C2×C3×D4—21no—
322C2×C3×D4—38no—
323C2×C3×D4—34no—
324C2×C3×D4—32no—
325C2×C3×D4—32no—
326C2×C3×D4—64no—
327C2×C3×D4C22×D312yes—
328C2×C3×D4C22×D312yes—
329C2×C3×D4C22×D311yescharacteristic
330C2×C3×D4C22×D311yescharacteristic
331C22×C3×C4—22no—
332C22×C3×C4—21no—
333C22×C3×C4—31no—
334C22×C3×C4—32no—
335C22×C3×C4—32no—
336C22×C3×C4—64no—
337C22×C3×C4C22×D312yes—
338C22×C3×C4C22×D312yes—
339C22×C3×C4C22×D311yescharacteristic
340C22×C3×C4C22×D311yescharacteristic
341C2×#67—32no—
342C2×#67—32no—
343C2×#67—34no—
344C2×#67—34no—
345C2×#67—38no—
346C2×#67—38no—
347C2×#67—38no—
348C2×#67—34no—
349C2×#67—62no—
350C2×#67—64no—
351C2×#67—68no—
352C2×#67—68no—
353C2×#67C22×D318yes—
354C2×#67C22×D314yes—
355C22×Dic3—32no—
356C22×Dic3—32no—
357C22×Dic3—34no—
358C22×Dic3—34no—
359C22×Dic3—38no—
360C22×Dic3—62no—
361C22×Dic3—64no—
362C22×Dic3—68no—
363C22×Dic3C22×D311yescharacteristic
364D3×Q8—68no—
365D3×Q8—68no—
366D3×Q8—616no—
367#237—616no—
368#237—616no—
369#237—68no—
370#237—68no—
371#237—616no—
372#237—616no—
373#237—632no—
374#237—616no—
375#235—616no—
376#235—616no—
377#235—68no—
378#235—68no—
379#235—616no—
380#235—68no—
381#235—64no—
382#235—64no—
383C2×D12—24no—
384C2×D12—31no—
385C2×D12—31no—
386C2×D12—34no—
387C2×D12—38no—
388C2×D12—61no—
389C2×D12C22×D312yes—
390C2×D12C22×D312yes—
391C2×C4×D3—24no—
392C2×C4×D3—38no—
393C2×C4×D3—32no—
394C2×C4×D3—34no—
395C2×C4×D3—34no—
396C2×C4×D3—32no—
397C2×C4×D3—62no—
398C2×C4×D3—64no—
399C2×C4×D3—68no—
400C2×C4×D3C22×D312yes—
401C2×C4×D3C22×D312yes—
402C2×Dic6—38no—
403C2×Dic6—38no—
404C2×Dic6—32no—
405C2×Dic6—32no—
406C2×Dic6—32no—
407C2×Dic6—32no—
408C2×Dic6—31no—
409C2×Dic6—34no—
410C2×Dic6—34no—
411C2×Dic6—31no—
412C2×Dic6—62no—
413C2×Dic6—61no—
414C2×Dic6—62no—
415C2×Dic6—64no—
416C2×Dic6—68no—
417C2×Dic6—68no—
418C2×Dic6—68no—
419C2×Dic6—616no—
420C3×C4⋊C4—32no—
421C3×C4⋊C4—32no—
422C3×C4⋊C4—34no—
423C3×C22⋊C4—32no—
424C3×C22⋊C4—32no—
425C3×C22⋊C4—34no—
426C3×C22⋊C4—38no—
427C3×C22⋊C4—34no—
428C3×C42—32no—
429C3×C42—32no—
430#217—38no—
431#217—34no—
432#217C22×D312yes—
433#217C22×D312yes—
434#217C22×D314yes—
435(C2×D3)⋊C4—34no—
436(C2×D3)⋊C4—38no—
437(C2×D3)⋊C4—34no—
438(C2×D3)⋊C4—34no—
439(C2×D3)⋊C4C22×D314yes—
440(C2×D3)⋊C4C22×D318yes—
441C4⋊Dic3—34no—
442C4⋊Dic3C22×D312yes—
443C4⋊Dic3C22×D312yes—
444Dic3⋊C4—38no—
445Dic3⋊C4—38no—
446Dic3⋊C4—34no—
447Dic3⋊C4C22×D314yes—
448C4×Dic3—38no—
449C4×Dic3—38no—
450C4×Dic3C22×D312yes—
451C4×Dic3C22×D312yes—
452C22×C32—22no—
453C22×C32—22no—
454C22×C32—24no—
455C22×C32C22×D412yes—
456C22×C32C2511yescharacteristic
457C2×C3⋊D3—22no—
458C2×C3⋊D3—24no—
459C2×C3×D3—24no—
460C2×C3×D3—22no—
461C2×C3×D3—22no—
462C2×C3×D3—28no—
463C2×C3×D3—22no—
464C2×C3×D3—48no—
465C2×C3×D3—44no—
466C32×C4—22no—
467C32×C4C22×D412yes—
468C32×C4C22×D412yes—
469C3⋊Dic3—22no—
470C3⋊Dic3C22×D418yes—
471C3×Dic3—22no—
472C3×Dic3—24no—
473C3×Dic3—24no—
4742−1+4—188no—
475C2×#41—94no—
476C2×#41—94no—
477C2×#41—94no—
478C2×#41—92no—
479C2×#41—91no—
480C2×#41—92no—
481C2×#41—188no—
482C2×#41D3211yescharacteristic
483C22×Q8—92no—
484C22×Q8—91no—
485C22×Q8—92no—
486C22×D4—31no—
487C22×D4—92no—
488C23×C4—31no—
489C23×C4—92no—
490#127—32no—
491#127—92no—
492#127—98no—
493#124—32no—
494#124—92no—
495#124—98no—
496#123—32no—
497#123—92no—
498C22⋊Q8—32no—
499C22⋊Q8—98no—
500C22⋊Q8—92no—
501#121—32no—
502#121—34no—
503#121—98no—
504#121—98no—
505#121—92no—
506#121—94no—
507#121—98no—
508#120—32no—
509#120—34no—
510#120—92no—
511#120—94no—
512C4×Q8—94no—
513C4×Q8—94no—
514C4×D4—34no—
515C4×D4—94no—
516C4×D4—98no—
517C4×D4—98no—
518#117—31no—
519#117—31no—
520#117—94no—
521C23×C3—22no—
522C23×C3—21no—
523C23×C3—34no—
524C23×C3—32no—
525C23×C3—64no—
526C23×C3—62no—
527C23×C3—124no—
528C23×C3—122no—
529C23×C3C23×D312yes—
530C23×C3C23×D312yes—
531C23×C3C23×D311yescharacteristic
532C23×C3C23×D311yescharacteristic
533C22×D3—22no—
534C22×D3—24no—
535C22×D3—32no—
536C22×D3—32no—
537C22×D3—42no—
538C22×D3—44no—
539C22×D3—62no—
540C22×D3C23×D314yes—
541C22×D3C23×D312yes—
542C3×Q8—24no—
543C3×Q8—22no—
544C3×Q8—22no—
545C3×D4—28no—
546C3×D4—24no—
547C3×D4—24no—
548C3×D4—24no—
549C3×D4—22no—
550C3×D4—22no—
551C3×D4—64no—
552C3×D4—64no—
553C3×D4—128no—
554C3×D4—124no—
555C2×C3×C4—28no—
556C2×C3×C4—24no—
557C2×C3×C4—24no—
558C2×C3×C4—21no—
559C2×C3×C4—22no—
560C2×C3×C4—21no—
561C2×C3×C4—24no—
562C2×C3×C4—34no—
563C2×C3×C4—34no—
564C2×C3×C4—32no—
565C2×C3×C4—62no—
566C2×C3×C4—64no—
567C2×C3×C4—64no—
568C2×C3×C4D3×D414yes—
569C2×C3×C4D3×D414yes—
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—44no—
577#67—48no—
578#67—616no—
579#67—616no—
580#67—68no—
581#67—68no—
582#67—616no—
583#67—68no—
584#67—64no—
585#67—64no—
586#67—128no—
587#67—124no—
588C2×Dic3—22no—
589C2×Dic3—38no—
590C2×Dic3—38no—
591C2×Dic3—34no—
592C2×Dic3—34no—
593C2×Dic3—32no—
594C2×Dic3—32no—
595C2×Dic3—68no—
596C2×Dic3—64no—
597C2×Dic3—62no—
598C2×Dic3—616no—
599C2×Dic3—68no—
600C2×Dic3—68no—
601C2×Dic3—616no—
602C2×Dic3C23×D314yes—
603C2×Dic3C23×D314yes—
604C2×Dic3C23×D312yes—
605D12—24no—
606D12—24no—
607D12—64no—
608D12—62no—
609D12—62no—
610D12—124no—
611D12—128no—
612C4×D3—24no—
613C4×D3—24no—
614C4×D3—68no—
615C4×D3—68no—
616C4×D3—616no—
617C4×D3—616no—
618C4×D3—68no—
619C4×D3—64no—
620C4×D3—64no—
621Dic6—38no—
622Dic6—38no—
623Dic6—38no—
624Dic6—38no—
625Dic6—68no—
626Dic6—68no—
627Dic6—68no—
628Dic6—68no—
629Dic6—64no—
630Dic6—616no—
631Dic6—62no—
632Dic6—62no—
633C2×C32—22no—
634C2×C32—42no—
635C2×C32C23×D411yescharacteristic
636C2×C32#58512yes—
637C3⋊D3—42no—
638C3×D3—42no—
639C3×D3—44no—
640C24—31no—
641C24—32no—
642#41—24no—
643#41—188no—
644#41—1816no—
645#41—1816no—
646#41—1816no—
647#41—188no—
648#41—184no—
649C2×Q8—92no—
650C2×Q8—92no—
651C2×Q8—94no—
652C2×Q8—91no—
653C2×Q8—98no—
654C2×Q8—188no—
655C2×Q8—188no—
656C2×Q8C2×D3211yescharacteristic
657C2×D4—34no—
658C2×D4—38no—
659C2×D4—32no—
660C2×D4—32no—
661C2×D4—64no—
662C2×D4—98no—
663C2×D4—94no—
664C2×D4—98no—
665C2×D4—92no—
666C2×D4—94no—
667C2×D4—91no—
668C2×D4—188no—
669C2×D4C2×D3212yes—
670C2×D4C2×D3211yescharacteristic
671C22×C4—31no—
672C22×C4—32no—
673C22×C4—32no—
674C22×C4—64no—
675C22×C4—98no—
676C22×C4—92no—
677C22×C4—94no—
678C22×C4—94no—
679C22×C4—92no—
680C22×C4—188no—
681C22×C4C2×D3212yes—
682C22×C4C2×D3211yescharacteristic
683C4⋊C4—32no—
684C4⋊C4—32no—
685C4⋊C4—34no—
686C4⋊C4—98no—
687C4⋊C4—94no—
688C22⋊C4—32no—
689C22⋊C4—32no—
690C22⋊C4—34no—
691C22⋊C4—34no—
692C22⋊C4—38no—
693C22⋊C4—94no—
694C22⋊C4—98no—
695C22⋊C4—94no—
696C42—32no—
697C42—32no—
698C42—98no—
699C22×C3—22no—
700C22×C3—22no—
701C22×C3—24no—
702C22×C3—22no—
703C22×C3—22no—
704C22×C3—24no—
705C22×C3—24no—
706C22×C3—22no—
707C22×C3—21no—
708C22×C3—42no—
709C22×C3—44no—
710C22×C3—64no—
711C22×C3—62no—
712C22×C3—68no—
713C22×C3—62no—
714C22×C3—62no—
715C22×C3—128no—
716C22×C3—124no—
717C22×C3C2×D3×D412yes—
718C22×C3C2×D3×D412yes—
719C22×C3C24×D311yescharacteristic
720C22×C3C24×D311yescharacteristic
721C2×D3—22no—
722C2×D3—24no—
723C2×D3—22no—
724C2×D3—22no—
725C2×D3—28no—
726C2×D3—44no—
727C2×D3—48no—
728C2×D3—64no—
729C2×D3—62no—
730C2×D3—62no—
731C2×D3—64no—
732C2×D3—64no—
733C2×D3—124no—
734C3×C4—24no—
735C3×C4—22no—
736C3×C4—22no—
737C3×C4—22no—
738C3×C4—22no—
739C3×C4—62no—
740C3×C4—64no—
741C3×C4—64no—
742C3×C4C2×D3×D412yes—
743C3×C4C2×D3×D412yes—
744C3×C4C2×D3×D412yes—
745C3×C4C2×D3×D412yes—
746Dic3—22no—
747Dic3—24no—
748Dic3—24no—
749Dic3—38no—
750Dic3—38no—
751Dic3—68no—
752Dic3—64no—
753Dic3—62no—
754Dic3—62no—
755C32#348711yescharacteristic, complemented, Sylow
756C23—32no—
757C23—34no—
758C23—62no—
759C23—64no—
760C23—92no—
761C23—122no—
762C23—124no—
763C23C22×D3212yes—
764C23C22×D3211yescharacteristic
765Q8—22no—
766Q8—98no—
767Q8—98no—
768Q8—188no—
769Q8—182no—
770D4—24no—
771D4—22no—
772D4—64no—
773D4—64no—
774D4—128no—
775D4—124no—
776D4—188no—
777D4—1816no—
778D4—184no—
779D4—182no—
780D4—364no—
781D4—368no—
782C2×C4—24no—
783C2×C4—34no—
784C2×C4—34no—
785C2×C4—32no—
786C2×C4—62no—
787C2×C4—64no—
788C2×C4—64no—
789C2×C4—98no—
790C2×C4—94no—
791C2×C4—92no—
792C2×C4—188no—
793C2×C4—1816no—
794C2×C4—188no—
795C2×C4—184no—
796C2×C4#381114yes—
797C2×C4C22×D3212yes—
798C2×C4C22×D3211yescharacteristic
799C2×C4C22×D3211yescharacteristic
800C2×C3—22no—
801C2×C3—22no—
802C2×C3—22no—
803C2×C3—21no—
804C2×C3—42no—
805C2×C3—44no—
806C2×C3—42no—
807C2×C3—42no—
808C2×C3—124no—
809C2×C3—122no—
810C2×C3C22×D3×D411yescharacteristic
811C2×C3C22×D3×D411yescharacteristic
812C2×C3#596412yes—
813C2×C3#596612yes—
814D3—42no—
815D3—44no—
816D3—124no—
817D3—122no—
818D3—122no—
819C22—22no—
820C22—24no—
821C22—22no—
822C22—62no—
823C22—68no—
824C22—62no—
825C22—62no—
826C22—64no—
827C22—124no—
828C22—128no—
829C22—184no—
830C22—182no—
831C22C2×#381112yes—
832C22C23×D3211yescharacteristic
833C4—22no—
834C4—64no—
835C4—64no—
836C4—62no—
837C4—98no—
838C4—182no—
839C4C2×#381112yes—
840C4C2×#381112yes—
841C3—21no—
842C3#8602311yescharacteristic, complemented
843C3#8631511yescharacteristic, complemented
844C2—22no—
845C2—42no—
846C2—122no—
847C2—124no—
848C2—362no—
849C2#1059669612yes—
850C2C22×#381111yescharacteristic
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×#64367C2semidirect
2. C22×#3795C2semidirect
3. C3×#5830C2semidirect
4. C3×#5828C2semidirect
5. #10595362C2semidirect
6. #10595239C2semidirect
7. #10595164C2semidirect
8. #10595160C2semidirect
9. #10595042C2semidirect
10. #10595023C2semidirect
11. #10594919C2semidirect
12. #10594918C2semidirect
13. #10594828C2semidirect
18. C2×Q8×C3⋊D3C22semidirect
20. C2×#3830C22semidirect
22. C2×#3828C22semidirect
24. C22×#634C22semidirect
32. C3×#947C22semidirect
33. C3×#946C22semidirect
34. C3×#940C22semidirect
35. C3×#938C22semidirect
39. C3×#930C22semidirect
40. C3×C4×#67C22semidirect
43. #63980C22semidirect
44. #63979C22semidirect
47. #67⋊Dic3C22semidirect
48. #63971C22semidirect
51. #63916C22semidirect
52. #63913C22semidirect
53. #63912C22semidirect
54. #63911C22semidirect
55. #63909C22semidirect
56. C4×#626C22semidirect
57. #63896C22semidirect
58. #63881C22semidirect
59. #63860C22semidirect
60. #63857C22semidirect
61. #63844C22semidirect
62. #63844C22semidirect
70. #5830D3semidirect
71. #5828D3semidirect
111. C2×#634D4semidirect
204. #947C2×D3semidirect
205. #946C2×D3semidirect
209. #940C2×D3semidirect
214. #938C2×D3semidirect
221. #930C2×D3semidirect
224. C4×#67C2×D3semidirect
755. C32#3487semidirect
842. C3#86023semidirect
843. C3#86315semidirect

Maximal subgroups

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

subgroupindex
C2×#643672
C22×#37952
C3×#58302
C3×#58282
#105953622
#105952392
#105951642
#105951602
#105950422
#105950232
#105949192
#105949182
#105948282
#863153
#860233