Finite Group Databasebeta

← C3×#500650 #72271677

Subgroups — C3×#500650 #72271677

Order 1536.

1558 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#61414C211yesmaximal, characteristic, complemented
2C3×#33595C211yesmaximal, characteristic, complemented
3C3×#33469C211yesmaximal, characteristic, complemented
4C3×#29271C211yesmaximal, characteristic, complemented
5C3×#13417C211yesmaximal, characteristic, complemented
6C3×#13416C211yesmaximal, characteristic, complemented
7C3×#13340C211yesmaximal, characteristic, complemented
8C3×#13334C211yesmaximal, characteristic, complemented
9C3×#13269C211yesmaximal, characteristic, complemented
10C3×#13215C211yesmaximal, characteristic, complemented
11C3×#13037C211yesmaximal, characteristic, complemented
12C3×#13030C211yesmaximal, characteristic, complemented
13C3×#12956C211yesmaximal, characteristic, complemented
14C3×#12949C211yesmaximal, characteristic, complemented
15C3×#12828C211yesmaximal, characteristic, complemented
16#500650C311yesmaximal, characteristic, direct product factor, Sylow
17C3×#3506—21no—
18C3×#3414C2211yescharacteristic
19C3×#3414C2211yescharacteristic
20C2×C3×#509C2211yescharacteristic
21C3×#3401—22no—
22C3×#3401—22no—
23C3×#3399—22no—
24C3×#3399—22no—
25C3×#3155C2211yescharacteristic
26C3×#3155C2211yescharacteristic
27C3×#3150C2211yescharacteristic
28C3×#3045—21no—
29C3×#3045—21no—
30C3×#3036—21no—
31C3×#2961C2211yescharacteristic
32C3×#2957C2211yescharacteristic
33C3×#2952C2211yescharacteristic
34C3×#2952C2211yescharacteristic
35C2×C3×#442C2211yescharacteristic
36C3×#2213—22no—
37C3×#2212—22no—
38C3×AGL(1,ℤ/16)—22no—
39C3×#2180—22no—
40C2×C3×#365C2211yescharacteristic
41C3×#2153C2211yescharacteristic
42C3×#2148C2211yescharacteristic
43C3×#2148C2211yescharacteristic
44C2×C3×#361C2211yescharacteristic
45C2×C3×#361C2211yescharacteristic
46C3×#2145C2211yescharacteristic
47C3×#2145C2211yescharacteristic
48C2×C3×#360C2211yescharacteristic
49C3×#2143C2211yescharacteristic
50C3×#2143C2211yescharacteristic
51C3×#2140C2211yescharacteristic
52C3×#2110C2211yescharacteristic
53C3×#2098—21no—
54C3×#2031—21no—
55C3×#1976C2211yescharacteristic
56C3×#1975C2211yescharacteristic
57C3×#1953C2211yescharacteristic
58C3×#1946C2211yescharacteristic
59C3×#1868—21no—
60C3×#1861—21no—
61C3×#1833C2211yescharacteristic
62C3×#1386C2211yescharacteristic
63C3×#1383C2211yescharacteristic
64C3×#1378C2211yescharacteristic
65C3×#1378C2211yescharacteristic
66C3×#1375C2211yescharacteristic
67C3×#1375C2211yescharacteristic
68#61414C2×C311yescharacteristic, complemented
69#33595C2×C311yescharacteristic, complemented
70#33469C2×C311yescharacteristic, complemented
71#29271C2×C311yescharacteristic, complemented
72#13417C2×C311yescharacteristic, complemented
73#13416C2×C311yescharacteristic, complemented
74#13340C2×C311yescharacteristic, complemented
75#13334C2×C311yescharacteristic, complemented
76#13269C2×C311yescharacteristic, complemented
77#13215C2×C311yescharacteristic, complemented
78#13037C2×C311yescharacteristic, complemented
79#13030C2×C311yescharacteristic, complemented
80#12956C2×C311yescharacteristic, complemented
81#12949C2×C311yescharacteristic, complemented
82#12828C2×C311yescharacteristic, complemented
83C2×C3×AGL(1,ℤ/8)—21no—
84C2×C3×AGL(1,ℤ/8)—21no—
85C2×C3×#135—21no—
86C2×C3×#135C2311yescharacteristic
87C2×C3×#135C2311yescharacteristic
88C2×C3×#135C2311yescharacteristic
89C22×C3×D8C2311yescharacteristic
90C3×#568—21no—
91C3×#559—22no—
92C3×#559—22no—
93C3×#556—22no—
94C3×#555—41no—
95C3×#553—41no—
96C3×#553—41no—
97C3×#550—22no—
98C3×#547—41no—
99C3×#538—42no—
100C3×#535—21no—
101C3×#535—21no—
102C3×#533D411yescharacteristic
103C3×#532—21no—
104C3×#525—42no—
105C3×#520—21no—
106C3×#520—21no—
107C2×C3×C4×D4—21no—
108C3×#510—21no—
109C3×#510—21no—
110C3×#510—21no—
111C3×#510—21no—
112C3×#509—21no—
113C3×#509—21no—
114C3×#509—22no—
115C3×#509—21no—
116C3×#509—21no—
117C3×#509—41no—
118C3×#508—22no—
119C3×#508—41no—
120C2×C3×SD32—21no—
121C2×C3×D16—21no—
122C2×C3×M32C2311yescharacteristic
123C2×C3×M32C2311yescharacteristic
124C2×C3×M32C2311yescharacteristic
125C2×C3×M32C2311yescharacteristic
126C3×#497—21no—
127C3×#497—21no—
128C3×#496—21no—
129C3×#496—21no—
130C3×#496—22no—
131C3×#496—22no—
132C3×#495—21no—
133C3×#495D412yes—
134C3×#493—21no—
135C3×#493D412yes—
136C3×#464—22no—
137C3×#464—22no—
138C3×#463—22no—
139C3×#463—22no—
140C3×#463—22no—
141C3×#463—22no—
142C3×#461—22no—
143C3×#460—22no—
144C3×#460—22no—
145C3×#459—22no—
146C3×#459—22no—
147C3×#459—22no—
148C3×#446—22no—
149C3×#446—22no—
150C3×#444—22no—
151C3×#443—22no—
152C3×#442—21no—
153C3×#442—22no—
154C3×#442—22no—
155C3×#442D412yes—
156C3×#441—21no—
157C3×#441D412yes—
158C3×C4×SD16—22no—
159C3×C4×SD16—22no—
160C3×#430—21no—
161C2×C3×#108C2311yescharacteristic
162C2×C3×#108C2311yescharacteristic
163C3×#427C2311yescharacteristic
164C2×C3×#106C2311yescharacteristic
165C3×#424—21no—
166C3×#424D411yescharacteristic
167C3×#424D411yescharacteristic
168C3×#423D411yescharacteristic
169C3×#421—21no—
170C3×#421—21no—
171C2×C3×#104—21no—
172C3×#417—21no—
173C3×#417—21no—
174C2×C3×#102—21no—
175C3×#410—21no—
176C3×#408—21no—
177C3×#405C2311yescharacteristic
178C3×#405C2311yescharacteristic
179C2×C3×#97C2311yescharacteristic
180C3×#365—22no—
181C3×#364—22no—
182C3×#362—21no—
183C3×#362—21no—
184C3×#361—22no—
185C3×#361—21no—
186C3×#361—21no—
187C3×#361—41no—
188C3×#360—22no—
189C3×#360—41no—
190C3×#360—41no—
191C3×#359—22no—
192C3×#359—41no—
193C3×#357—22no—
194C3×#347—22no—
195C3×#344—21no—
196C3×#344—21no—
197C3×#339—21no—
198C3×H(3,ℤ/4)—21no—
199#3506—21no—
200#3414C22×C311yescharacteristic
201#3414C22×C311yescharacteristic
202C2×#509C22×C311yescharacteristic
203#3401—22no—
204#3401—22no—
205#3399—22no—
206#3399—22no—
207#3155C22×C311yescharacteristic
208#3155C22×C311yescharacteristic
209#3150C22×C311yescharacteristic
210#3045—21no—
211#3045—21no—
212#3036—21no—
213#2961C22×C311yescharacteristic
214#2957C22×C311yescharacteristic
215#2952C22×C311yescharacteristic
216#2952C22×C311yescharacteristic
217C2×#442C22×C311yescharacteristic
218#2213—22no—
219#2212—22no—
220AGL(1,ℤ/16)—22no—
221#2180—22no—
222C2×#365C22×C311yescharacteristic
223#2153C22×C311yescharacteristic
224#2148C22×C311yescharacteristic
225#2148C22×C311yescharacteristic
226C2×#361C22×C311yescharacteristic
227C2×#361C22×C311yescharacteristic
228#2145C22×C311yescharacteristic
229#2145C22×C311yescharacteristic
230C2×#360C22×C311yescharacteristic
231#2143C22×C311yescharacteristic
232#2143C22×C311yescharacteristic
233#2140C22×C311yescharacteristic
234#2110C22×C311yescharacteristic
235#2098—21no—
236#2031—21no—
237#1976C22×C311yescharacteristic
238#1975C22×C311yescharacteristic
239#1953C22×C311yescharacteristic
240#1946C22×C311yescharacteristic
241#1868—21no—
242#1861—21no—
243#1833C22×C311yescharacteristic
244#1386C22×C311yescharacteristic
245#1383C22×C311yescharacteristic
246#1378C22×C311yescharacteristic
247#1378C22×C311yescharacteristic
248#1375C22×C311yescharacteristic
249#1375C22×C311yescharacteristic
250C2×C3×#41—21no—
251C2×C3×#41—21no—
252C2×C3×#41—21no—
253C2×C3×#41—42no—
254C22×C3×D4—21no—
255C23×C3×C4—41no—
256C3×AGL(1,ℤ/8)—81no—
257C3×AGL(1,ℤ/8)—81no—
258C3×AGL(1,ℤ/8)—81no—
259C3×AGL(1,ℤ/8)—81no—
260C3×#135—21no—
261C3×#135—21no—
262C3×#135—21no—
263C3×#135—21no—
264C3×#135—21no—
265C3×#135—21no—
266C3×#135—21no—
267C3×#135—21no—
268C3×#135—21no—
269C3×#135—21no—
270C3×#135—21no—
271C3×#135—21no—
272C3×#135—81no—
273C3×#135—81no—
274C2×C3×Q16—21no—
275C2×C3×Q16C2×D411yescharacteristic
276C2×C3×Q16C2×D411yescharacteristic
277C2×C3×Q16#4111yescharacteristic, complemented
278C2×C3×SD16—21no—
279C2×C3×SD16—21no—
280C2×C3×SD16—22no—
281C2×C3×SD16—22no—
282C2×C3×SD16—21no—
283C2×C3×SD16—21no—
284C2×C3×SD16—21no—
285C2×C3×D8—21no—
286C2×C3×D8—22no—
287C2×C3×D8—22no—
288C2×C3×D8—21no—
289C2×C3×D8—21no—
290C2×C3×D8—21no—
291C2×C3×D8—21no—
292C2×C3×D8—21no—
293C2×C3×D8C2×D412yes—
294C2×C3×D8C2×D411yescharacteristic
295C2×C3×D8C2×D411yescharacteristic
296C2×C3×D8#4111yescharacteristic, complemented
297C3×#131—42no—
298C3×#131—81no—
299C2×C3×M16—21no—
300C2×C3×M16—21no—
301C2×C3×M16—81no—
302C2×C3×M16C2×D411yescharacteristic
303C2×C3×M16C2×D411yescharacteristic
304C22×C3×C8C2×D411yescharacteristic
305C22×C3×C8C2411yescharacteristic
306C3×C4⋊Q8—21no—
307C3×C4⋊Q8—21no—
308C3×#127—22no—
309C3×#127—21no—
310C3×#127—22no—
311C3×#126—42no—
312C3×#126—42no—
313C3×#125—21no—
314C3×#124—21no—
315C3×#124—21no—
316C3×#124—22no—
317C3×#124—22no—
318C3×#124—42no—
319C3×#124—42no—
320C3×#123—42no—
321C3×#123—42no—
322C3×#123—42no—
323C3×#123—42no—
324C3×C22⋊Q8—22no—
325C3×C22⋊Q8—42no—
326C3×#121—42no—
327C3×#121—41no—
328C3×#121—41no—
329C3×#121—41no—
330C3×#121—41no—
331C3×#121—42no—
332C3×#121—42no—
333C3×#121—41no—
334C3×#121—41no—
335C3×#120—42no—
336C3×#120—42no—
337C3×C4×Q8—22no—
338C3×C4×Q8—22no—
339C3×C4×Q8—22no—
340C3×C4×D4—22no—
341C3×C4×D4—22no—
342C3×C4×D4—22no—
343C3×C4×D4—22no—
344C3×C4×D4—42no—
345C3×C4×D4—42no—
346C3×C4×D4—42no—
347C3×C4×D4—42no—
348C3×C4×D4—41no—
349C3×C4×D4—41no—
350C3×C4×D4—41no—
351C3×C4×D4—41no—
352C3×#117—21no—
353C3×#117—41no—
354C3×#117—41no—
355C3×#117—42no—
356C3×#117C2×D411yescharacteristic
357C3×#117C2×D411yescharacteristic
358C2×C3×C4⋊C4—21no—
359C2×C3×C4⋊C4—41no—
360C2×C3×C4⋊C4—41no—
361C2×C3×C22⋊C4—41no—
362C2×C3×C42C2×D411yescharacteristic
363C3×Q32—22no—
364C3×Q32—41no—
365C3×SD32—22no—
366C3×SD32—22no—
367C3×SD32—42no—
368C3×SD32—41no—
369C3×SD32—41no—
370C3×D16—22no—
371C3×D16—42no—
372C3×D16—41no—
373C3×M32—21no—
374C3×M32—21no—
375C3×M32—21no—
376C3×M32—21no—
377C3×M32—21no—
378C3×M32—21no—
379C3×M32—21no—
380C3×M32—21no—
381C2×C3×C16—21no—
382C2×C3×C16—21no—
383C2×C3×C16—21no—
384C2×C3×C16#4112yescomplemented
385C3×#108—21no—
386C3×#108—21no—
387C3×#108—21no—
388C3×#108—21no—
389C3×#108—81no—
390C3×#107—21no—
391C3×#106—21no—
392C3×#106—21no—
393C3×#106C2×D412yes—
394C3×C4⋊C8—22no—
395C3×C4⋊C8—22no—
396C3×C4⋊C8—22no—
397C3×C4⋊C8—81no—
398C3×#104—42no—
399C3×#104—41no—
400C3×#104—41no—
401C3×#104—81no—
402C3×#103—22no—
403C3×#103—22no—
404C3×#102—22no—
405C3×#102—22no—
406C3×#102—22no—
407C3×#102—22no—
408C3×#99—42no—
409C3×C22⋊C8—81no—
410C3×#97—21no—
411C3×#97—21no—
412C3×#97—21no—
413C3×#97C2×D412yes—
414C3×C4×C8—21no—
415C3×C4×C8C2×D412yes—
416C2×AGL(1,ℤ/8)—21no—
417C2×AGL(1,ℤ/8)—21no—
418C2×#135—21no—
419C2×#135C23×C311yescharacteristic
420C2×#135C23×C311yescharacteristic
421C2×#135C23×C311yescharacteristic
422C22×D8C23×C311yescharacteristic
423#568—21no—
424#559—22no—
425#559—22no—
426#556—22no—
427#555—41no—
428#553—41no—
429#553—41no—
430#550—22no—
431#547—41no—
432#538—42no—
433#535—21no—
434#535—21no—
435#533C3×D411yescharacteristic
436#532—21no—
437#525—42no—
438#520—21no—
439#520—21no—
440C2×C4×D4—21no—
441#510—21no—
442#510—21no—
443#510—21no—
444#510—21no—
445#509—21no—
446#509—21no—
447#509—22no—
448#509—21no—
449#509—21no—
450#509—41no—
451#508—22no—
452#508—41no—
453C2×SD32—21no—
454C2×D16—21no—
455C2×M32C23×C311yescharacteristic
456C2×M32C23×C311yescharacteristic
457C2×M32C23×C311yescharacteristic
458C2×M32C23×C311yescharacteristic
459#497—21no—
460#497—21no—
461#496—21no—
462#496—21no—
463#496—22no—
464#496—22no—
465#495—21no—
466#495C3×D412yes—
467#493—21no—
468#493C3×D412yes—
469#464—22no—
470#464—22no—
471#463—22no—
472#463—22no—
473#463—22no—
474#463—22no—
475#461—22no—
476#460—22no—
477#460—22no—
478#459—22no—
479#459—22no—
480#459—22no—
481#446—22no—
482#446—22no—
483#444—22no—
484#443—22no—
485#442—21no—
486#442—22no—
487#442—22no—
488#442C3×D412yes—
489#441—21no—
490#441C3×D412yes—
491C4×SD16—22no—
492C4×SD16—22no—
493#430—21no—
494C2×#108C23×C311yescharacteristic
495C2×#108C23×C311yescharacteristic
496#427C23×C311yescharacteristic
497C2×#106C23×C311yescharacteristic
498#424—21no—
499#424C3×D411yescharacteristic
500#424C3×D411yescharacteristic
501#423C3×D411yescharacteristic
502#421—21no—
503#421—21no—
504C2×#104—21no—
505#417—21no—
506#417—21no—
507C2×#102—21no—
508#410—21no—
509#408—21no—
510#405C23×C311yescharacteristic
511#405C23×C311yescharacteristic
512C2×#97C23×C311yescharacteristic
513#365—22no—
514#364—22no—
515#362—21no—
516#362—21no—
517#361—22no—
518#361—21no—
519#361—21no—
520#361—41no—
521#360—22no—
522#360—41no—
523#360—41no—
524#359—22no—
525#359—41no—
526#357—22no—
527#347—22no—
528#344—21no—
529#344—21no—
530#339—21no—
531H(3,ℤ/4)—21no—
532C24×C3—41no—
533C3×#41—41no—
534C3×#41—41no—
535C3×#41—41no—
536C3×#41—41no—
537C3×#41—41no—
538C3×#41—41no—
539C3×#41—41no—
540C3×#41—41no—
541C3×#41—41no—
542C3×#41—41no—
543C3×#41—41no—
544C3×#41—41no—
545C3×#41—164no—
546C2×C3×Q8—22no—
547C2×C3×Q8—21no—
548C2×C3×Q8—21no—
549C2×C3×Q8—21no—
550C2×C3×D4—22no—
551C2×C3×D4—21no—
552C2×C3×D4—21no—
553C2×C3×D4—21no—
554C2×C3×D4—41no—
555C2×C3×D4—42no—
556C2×C3×D4—42no—
557C2×C3×D4—41no—
558C2×C3×D4—42no—
559C2×C3×D4—42no—
560C2×C3×D4—41no—
561C2×C3×D4—41no—
562C2×C3×D4—41no—
563C2×C3×D4—41no—
564C2×C3×D4—41no—
565C2×C3×D4—41no—
566C2×C3×D4—41no—
567C2×C3×D4—41no—
568C22×C3×C4—21no—
569C22×C3×C4—42no—
570C22×C3×C4—42no—
571C22×C3×C4—42no—
572C22×C3×C4—42no—
573C22×C3×C4—41no—
574C22×C3×C4—41no—
575C22×C3×C4—41no—
576C22×C3×C4—41no—
577C22×C3×C4—162no—
578C22×C3×C4C22×D411yescharacteristic
579C3×Q16—21no—
580C3×Q16—21no—
581C3×Q16—21no—
582C3×Q16—21no—
583C3×Q16—21no—
584C3×Q16—21no—
585C3×Q16—81no—
586C3×SD16—41no—
587C3×SD16—41no—
588C3×SD16—41no—
589C3×SD16—41no—
590C3×SD16—41no—
591C3×SD16—41no—
592C3×SD16—82no—
593C3×SD16—81no—
594C3×SD16—81no—
595C3×SD16—82no—
596C3×D8—21no—
597C3×D8—21no—
598C3×D8—21no—
599C3×D8—21no—
600C3×D8—22no—
601C3×D8—21no—
602C3×D8—22no—
603C3×D8—21no—
604C3×D8—41no—
605C3×D8—41no—
606C3×D8—82no—
607C3×D8—81no—
608C3×D8—82no—
609C3×M16—21no—
610C3×M16—21no—
611C3×M16—21no—
612C3×M16—21no—
613C3×M16—41no—
614C3×M16—41no—
615C3×M16—41no—
616C3×M16—41no—
617C3×M16—82no—
618C2×C3×C8—21no—
619C2×C3×C8—21no—
620C2×C3×C8—21no—
621C2×C3×C8—21no—
622C2×C3×C8—41no—
623C2×C3×C8—41no—
624C2×C3×C8—82no—
625C2×C3×C8#12012yes—
626C2×C3×C8C22×D411yescharacteristic
627C2×C3×C8C22×D411yescharacteristic
628C2×C3×C8C2×#4111yescharacteristic
629C2×C3×C8C2×#4111yescharacteristic
630C2×C3×C8H(5,𝔽2)11yescharacteristic
631C2×C3×C82−1+411yescharacteristic
632C3×C4⋊C4—22no—
633C3×C4⋊C4—22no—
634C3×C4⋊C4—22no—
635C3×C4⋊C4—21no—
636C3×C4⋊C4—21no—
637C3×C4⋊C4—22no—
638C3×C4⋊C4—42no—
639C3×C4⋊C4—42no—
640C3×C4⋊C4—41no—
641C3×C4⋊C4—41no—
642C3×C4⋊C4—41no—
643C3×C4⋊C4—41no—
644C3×C22⋊C4—21no—
645C3×C22⋊C4—42no—
646C3×C22⋊C4—42no—
647C3×C22⋊C4—42no—
648C3×C22⋊C4—42no—
649C3×C22⋊C4—42no—
650C3×C22⋊C4—42no—
651C3×C22⋊C4—41no—
652C3×C22⋊C4—41no—
653C3×C22⋊C4—42no—
654C3×C22⋊C4—42no—
655C3×C22⋊C4—41no—
656C3×C22⋊C4—41no—
657C3×C22⋊C4—41no—
658C3×C22⋊C4AGL(1,ℤ/8)12yes—
659C3×C42—21no—
660C3×C42—21no—
661C3×C42—42no—
662C3×C42—42no—
663C3×C42—41no—
664C3×C42#12012yes—
665C3×C42AGL(1,ℤ/8)11yescharacteristic
666C3×C42AGL(1,ℤ/8)11yescharacteristic
667C3×C16—22no—
668C3×C16—41no—
669C3×C16—41no—
670C3×C16—41no—
671C2×#41—21no—
672C2×#41—21no—
673C2×#41—21no—
674C2×#41—42no—
675C22×D4—21no—
676C23×C4—41no—
677AGL(1,ℤ/8)—81no—
678AGL(1,ℤ/8)—81no—
679AGL(1,ℤ/8)—81no—
680AGL(1,ℤ/8)—81no—
681#135—21no—
682#135—21no—
683#135—21no—
684#135—21no—
685#135—21no—
686#135—21no—
687#135—21no—
688#135—21no—
689#135—21no—
690#135—21no—
691#135—21no—
692#135—21no—
693#135—81no—
694#135—81no—
695C2×Q16—21no—
696C2×Q16C2×C3×D411yescharacteristic
697C2×Q16C2×C3×D411yescharacteristic
698C2×Q16C3×#4111yescharacteristic, complemented
699C2×SD16—21no—
700C2×SD16—21no—
701C2×SD16—22no—
702C2×SD16—22no—
703C2×SD16—21no—
704C2×SD16—21no—
705C2×SD16—21no—
706C2×D8—21no—
707C2×D8—22no—
708C2×D8—22no—
709C2×D8—21no—
710C2×D8—21no—
711C2×D8—21no—
712C2×D8—21no—
713C2×D8—21no—
714C2×D8C2×C3×D412yes—
715C2×D8C2×C3×D411yescharacteristic
716C2×D8C2×C3×D411yescharacteristic
717C2×D8C3×#4111yescharacteristic, complemented
718#131—42no—
719#131—81no—
720C2×M16—21no—
721C2×M16—21no—
722C2×M16—81no—
723C2×M16C2×C3×D411yescharacteristic
724C2×M16C2×C3×D411yescharacteristic
725C22×C8C2×C3×D411yescharacteristic
726C22×C8C24×C311yescharacteristic
727C4⋊Q8—21no—
728C4⋊Q8—21no—
729#127—21no—
730#127—22no—
731#127—22no—
732#126—42no—
733#126—42no—
734#125—21no—
735#124—21no—
736#124—21no—
737#124—22no—
738#124—22no—
739#124—42no—
740#124—42no—
741#123—42no—
742#123—42no—
743#123—42no—
744#123—42no—
745C22⋊Q8—22no—
746C22⋊Q8—42no—
747#121—42no—
748#121—41no—
749#121—41no—
750#121—41no—
751#121—41no—
752#121—42no—
753#121—42no—
754#121—41no—
755#121—41no—
756#120—42no—
757#120—42no—
758C4×Q8—22no—
759C4×Q8—22no—
760C4×Q8—22no—
761C4×D4—22no—
762C4×D4—22no—
763C4×D4—22no—
764C4×D4—22no—
765C4×D4—42no—
766C4×D4—42no—
767C4×D4—42no—
768C4×D4—42no—
769C4×D4—41no—
770C4×D4—41no—
771C4×D4—41no—
772C4×D4—41no—
773#117—21no—
774#117—41no—
775#117—41no—
776#117—42no—
777#117C2×C3×D411yescharacteristic
778#117C2×C3×D411yescharacteristic
779C2×C4⋊C4—21no—
780C2×C4⋊C4—41no—
781C2×C4⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C42C2×C3×D411yescharacteristic
784Q32—22no—
785Q32—41no—
786SD32—22no—
787SD32—22no—
788SD32—42no—
789SD32—41no—
790SD32—41no—
791D16—22no—
792D16—42no—
793D16—41no—
794M32—21no—
795M32—21no—
796M32—21no—
797M32—21no—
798M32—21no—
799M32—21no—
800M32—21no—
801M32—21no—
802C2×C16—21no—
803C2×C16—21no—
804C2×C16—21no—
805C2×C16C3×#4112yescomplemented
806#108—21no—
807#108—21no—
808#108—21no—
809#108—21no—
810#108—81no—
811#107—21no—
812#106—21no—
813#106—21no—
814#106C2×C3×D412yes—
815C4⋊C8—22no—
816C4⋊C8—22no—
817C4⋊C8—22no—
818C4⋊C8—81no—
819#104—42no—
820#104—41no—
821#104—41no—
822#104—81no—
823#103—22no—
824#103—22no—
825#102—22no—
826#102—22no—
827#102—22no—
828#102—22no—
829#99—42no—
830C22⋊C8—81no—
831#97—21no—
832#97—21no—
833#97—21no—
834#97C2×C3×D412yes—
835C4×C8—21no—
836C4×C8C2×C3×D412yes—
837C23×C3—42no—
838C23×C3—41no—
839C23×C3—41no—
840C23×C3—41no—
841C23×C3—81no—
842C23×C3—81no—
843C23×C3—161no—
844C23×C3—161no—
845C23×C3C2×AGL(1,ℤ/8)11yescharacteristic
846C3×Q8—41no—
847C3×Q8—41no—
848C3×Q8—41no—
849C3×Q8—41no—
850C3×Q8—41no—
851C3×Q8—41no—
852C3×Q8—82no—
853C3×D4—41no—
854C3×D4—42no—
855C3×D4—41no—
856C3×D4—41no—
857C3×D4—41no—
858C3×D4—41no—
859C3×D4—41no—
860C3×D4—42no—
861C3×D4—82no—
862C3×D4—81no—
863C3×D4—81no—
864C3×D4—81no—
865C3×D4—81no—
866C3×D4—81no—
867C3×D4—81no—
868C3×D4—81no—
869C3×D4—81no—
870C3×D4—161no—
871C3×D4—162no—
872C3×D4—162no—
873C3×D4—162no—
874C3×D4—162no—
875C2×C3×C4—22no—
876C2×C3×C4—21no—
877C2×C3×C4—21no—
878C2×C3×C4—22no—
879C2×C3×C4—41no—
880C2×C3×C4—41no—
881C2×C3×C4—41no—
882C2×C3×C4—42no—
883C2×C3×C4—81no—
884C2×C3×C4—84no—
885C2×C3×C4—81no—
886C2×C3×C4—81no—
887C2×C3×C4—81no—
888C2×C3×C4—81no—
889C2×C3×C4—81no—
890C2×C3×C4—81no—
891C2×C3×C4—81no—
892C2×C3×C4—162no—
893C2×C3×C4—162no—
894C2×C3×C4—162no—
895C2×C3×C4—161no—
896C2×C3×C4C2×#12011yescharacteristic
897C2×C3×C4#54811yescharacteristic
898C2×C3×C4#55011yescharacteristic
899C2×C3×C4C2×AGL(1,ℤ/8)11yescharacteristic
900C2×C3×C4#57611yescharacteristic
901C2×C3×C4#57611yescharacteristic
902C3×C8—22no—
903C3×C8—41no—
904C3×C8—41no—
905C3×C8—81no—
906C3×C8—81no—
907C3×C8#52511yescharacteristic
908C3×C8#53711yescharacteristic
909C3×C8#54611yescharacteristic
910C3×C8#54711yescharacteristic
911C24—41no—
912#41—41no—
913#41—41no—
914#41—41no—
915#41—41no—
916#41—41no—
917#41—41no—
918#41—41no—
919#41—41no—
920#41—41no—
921#41—41no—
922#41—41no—
923#41—41no—
924#41—164no—
925C2×Q8—22no—
926C2×Q8—21no—
927C2×Q8—21no—
928C2×Q8—21no—
929C2×D4—22no—
930C2×D4—21no—
931C2×D4—21no—
932C2×D4—21no—
933C2×D4—41no—
934C2×D4—42no—
935C2×D4—42no—
936C2×D4—41no—
937C2×D4—42no—
938C2×D4—42no—
939C2×D4—41no—
940C2×D4—41no—
941C2×D4—41no—
942C2×D4—41no—
943C2×D4—41no—
944C2×D4—41no—
945C2×D4—41no—
946C2×D4—41no—
947C22×C4—21no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—41no—
953C22×C4—41no—
954C22×C4—41no—
955C22×C4—41no—
956C22×C4—162no—
957C22×C4C22×C3×D411yescharacteristic
958Q16—21no—
959Q16—21no—
960Q16—21no—
961Q16—21no—
962Q16—21no—
963Q16—21no—
964Q16—81no—
965SD16—41no—
966SD16—41no—
967SD16—41no—
968SD16—41no—
969SD16—41no—
970SD16—41no—
971SD16—82no—
972SD16—81no—
973SD16—81no—
974SD16—82no—
975D8—21no—
976D8—21no—
977D8—21no—
978D8—21no—
979D8—22no—
980D8—21no—
981D8—22no—
982D8—21no—
983D8—41no—
984D8—41no—
985D8—82no—
986D8—81no—
987D8—82no—
988M16—21no—
989M16—21no—
990M16—21no—
991M16—21no—
992M16—41no—
993M16—41no—
994M16—41no—
995M16—41no—
996M16—82no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—41no—
1002C2×C8—41no—
1003C2×C8—82no—
1004C2×C8C3×#12012yes—
1005C2×C8C22×C3×D411yescharacteristic
1006C2×C8C22×C3×D411yescharacteristic
1007C2×C8C2×C3×#4111yescharacteristic
1008C2×C8C2×C3×#4111yescharacteristic
1009C2×C8C3×H(5,𝔽2)11yescharacteristic
1010C2×C8C3×2−1+411yescharacteristic
1011C4⋊C4—22no—
1012C4⋊C4—22no—
1013C4⋊C4—22no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—22no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—41no—
1020C4⋊C4—41no—
1021C4⋊C4—41no—
1022C4⋊C4—41no—
1023C22⋊C4—21no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—41no—
1035C22⋊C4—41no—
1036C22⋊C4—41no—
1037C22⋊C4C3×AGL(1,ℤ/8)12yes—
1038C42—21no—
1039C42—21no—
1040C42—42no—
1041C42—42no—
1042C42—41no—
1043C42C3×#12012yes—
1044C42C3×AGL(1,ℤ/8)11yescharacteristic
1045C42C3×AGL(1,ℤ/8)11yescharacteristic
1046C16—22no—
1047C16—41no—
1048C16—41no—
1049C16—41no—
1050C22×C3—41no—
1051C22×C3—82no—
1052C22×C3—81no—
1053C22×C3—81no—
1054C22×C3—81no—
1055C22×C3—81no—
1056C22×C3—82no—
1057C22×C3—81no—
1058C22×C3—81no—
1059C22×C3—81no—
1060C22×C3—82no—
1061C22×C3—161no—
1062C22×C3—162no—
1063C22×C3—162no—
1064C22×C3#300311yescharacteristic
1065C22×C3#336611yescharacteristic
1066C22×C3#339911yescharacteristic
1067C3×C4—41no—
1068C3×C4—41no—
1069C3×C4—42no—
1070C3×C4—42no—
1071C3×C4—82no—
1072C3×C4—81no—
1073C3×C4—81no—
1074C3×C4—81no—
1075C3×C4—161no—
1076C3×C4#240711yescharacteristic
1077C3×C4#300811yescharacteristic
1078C3×C4#336611yescharacteristic
1079C3×C4#339911yescharacteristic
1080C23—42no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—81no—
1085C23—81no—
1086C23—161no—
1087C23—161no—
1088C23C2×C3×AGL(1,ℤ/8)11yescharacteristic
1089Q8—41no—
1090Q8—41no—
1091Q8—41no—
1092Q8—41no—
1093Q8—41no—
1094Q8—41no—
1095Q8—82no—
1096D4—42no—
1097D4—41no—
1098D4—41no—
1099D4—41no—
1100D4—41no—
1101D4—41no—
1102D4—42no—
1103D4—41no—
1104D4—82no—
1105D4—81no—
1106D4—81no—
1107D4—81no—
1108D4—81no—
1109D4—81no—
1110D4—81no—
1111D4—81no—
1112D4—81no—
1113D4—162no—
1114D4—162no—
1115D4—161no—
1116D4—162no—
1117D4—162no—
1118C2×C4—22no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—22no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—42no—
1125C2×C4—41no—
1126C2×C4—81no—
1127C2×C4—84no—
1128C2×C4—81no—
1129C2×C4—81no—
1130C2×C4—81no—
1131C2×C4—81no—
1132C2×C4—81no—
1133C2×C4—81no—
1134C2×C4—81no—
1135C2×C4—162no—
1136C2×C4—162no—
1137C2×C4—162no—
1138C2×C4—161no—
1139C2×C4C2×C3×#12011yescharacteristic
1140C2×C4C3×#54811yescharacteristic
1141C2×C4C3×#55011yescharacteristic
1142C2×C4C2×C3×AGL(1,ℤ/8)11yescharacteristic
1143C2×C4C3×#57611yescharacteristic
1144C2×C4C3×#57611yescharacteristic
1145C8—22no—
1146C8—41no—
1147C8—41no—
1148C8—81no—
1149C8—81no—
1150C8C3×#52511yescharacteristic
1151C8C3×#53711yescharacteristic
1152C8C3×#54611yescharacteristic
1153C8C3×#54711yescharacteristic
1154C2×C3—21no—
1155C2×C3—21no—
1156C2×C3—21no—
1157C2×C3—161no—
1158C2×C3—161no—
1159C2×C3—162no—
1160C2×C3—161no—
1161C2×C3#2419611yescharacteristic
1162C22—41no—
1163C22—82no—
1164C22—81no—
1165C22—81no—
1166C22—81no—
1167C22—81no—
1168C22—82no—
1169C22—81no—
1170C22—81no—
1171C22—81no—
1172C22—82no—
1173C22—161no—
1174C22—162no—
1175C22—162no—
1176C22C3×#300311yescharacteristic
1177C22C3×#336611yescharacteristic
1178C22C3×#339911yescharacteristic
1179C4—41no—
1180C4—41no—
1181C4—42no—
1182C4—42no—
1183C4—82no—
1184C4—81no—
1185C4—81no—
1186C4—81no—
1187C4—161no—
1188C4C3×#240711yescharacteristic
1189C4C3×#300811yescharacteristic
1190C4C3×#336611yescharacteristic
1191C4C3×#339911yescharacteristic
1192C3#50065011yescharacteristic, direct product factor, Sylow
1193C2—21no—
1194C2—21no—
1195C2—21no—
1196C2—162no—
1197C2—161no—
1198C2—161no—
1199C2—161no—
1200C2C3×#2419611yescharacteristic
subgroupG/H
center, socleC2×C3#24196
commutator, Frattini, cosocleC22×C8C24×C3
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#2961 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#61414C2semidirect
2. C3×#33595C2semidirect
3. C3×#33469C2semidirect
4. C3×#29271C2semidirect
5. C3×#13417C2semidirect
6. C3×#13416C2semidirect
7. C3×#13340C2semidirect
8. C3×#13334C2semidirect
9. C3×#13269C2semidirect
10. C3×#13215C2semidirect
11. C3×#13037C2semidirect
12. C3×#13030C2semidirect
13. C3×#12956C2semidirect
14. C3×#12949C2semidirect
15. C3×#12828C2semidirect
16. #500650C3direct (N × H)
68. #61414C2×C3semidirect
69. #33595C2×C3semidirect
70. #33469C2×C3semidirect
71. #29271C2×C3semidirect
72. #13417C2×C3semidirect
73. #13416C2×C3semidirect
74. #13340C2×C3semidirect
75. #13334C2×C3semidirect
76. #13269C2×C3semidirect
77. #13215C2×C3semidirect
78. #13037C2×C3semidirect
79. #13030C2×C3semidirect
80. #12956C2×C3semidirect
81. #12949C2×C3semidirect
82. #12828C2×C3semidirect
277. C2×C3×Q16#41semidirect
296. C2×C3×D8#41semidirect
384. C2×C3×C16#41semidirect
698. C2×Q16C3×#41semidirect
717. C2×D8C3×#41semidirect
805. C2×C16C3×#41semidirect
1192. C3#500650direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#614142
C3×#335952
C3×#334692
C3×#292712
C3×#134172
C3×#134162
C3×#133402
C3×#133342
C3×#132692
C3×#132152
C3×#130372
C3×#130302
C3×#129562
C3×#129492
C3×#128282
#5006503