Finite Group Databasebeta

← C3×#499269 #72271618

Subgroups — C3×#499269 #72271618

Order 1536.

1638 conjugacy classes of subgroups.

The subgroup lattice has 1262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#60698C211yesmaximal, characteristic, complemented
2C3×#33468C211yesmaximal, characteristic, complemented
3C2×C3×AGL(1,ℤ/16)C211yesmaximal, characteristic, complemented
4C3×#21559C211yesmaximal, characteristic, complemented
5C3×#13460C211yesmaximal, characteristic, complemented
6C3×#13417C211yesmaximal, characteristic, complemented
7C3×#13400C211yesmaximal, characteristic, complemented
8C3×#13396C211yesmaximal, characteristic, complemented
9C3×#13374C211yesmaximal, characteristic, complemented
10C3×#13334C211yesmaximal, characteristic, complemented
11C3×#13318C211yesmaximal, characteristic, complemented
12C3×#13310C211yesmaximal, characteristic, complemented
13C3×#12649C211yesmaximal, characteristic, complemented
14C3×#12647C211yesmaximal, characteristic, complemented
15C3×#12609C211yesmaximal, characteristic, complemented
16#499269C311yesmaximal, characteristic, direct product factor, Sylow
17C3×#3460—21no—
18C3×#3414C2211yescharacteristic
19C2×C3×#509C2211yescharacteristic
20C3×#3184—21no—
21C3×#3183—21no—
22C3×#3180—22no—
23C3×#3179—22no—
24C3×#3176—21no—
25C3×#3173—21no—
26C3×#3163C2211yescharacteristic
27C3×#3155C2211yescharacteristic
28C3×#3136—21no—
29C3×#3067C2211yescharacteristic
30C3×#3062—21no—
31C3×#3060C2211yescharacteristic
32C3×#3058C2211yescharacteristic
33C3×#2955—21no—
34C2×C3×#444C2211yescharacteristic
35C3×C4×AGL(1,ℤ/8)—21no—
36C3×#2943C2211yescharacteristic
37C2×C3×#442C2211yescharacteristic
38C3×#2875C2211yescharacteristic
39C3×AGL(1,ℤ/16)—22no—
40C3×AGL(1,ℤ/16)—22no—
41C3×AGL(1,ℤ/16)—21no—
42C3×AGL(1,ℤ/16)—21no—
43C3×#2180—21no—
44C3×#2180—21no—
45C3×#2155C2211yescharacteristic
46C2×C3×#365C2211yescharacteristic
47C3×#2148C2211yescharacteristic
48C2×C3×#361C2211yescharacteristic
49C2×C3×#361C2211yescharacteristic
50C3×#2145C2211yescharacteristic
51C3×#2145C2211yescharacteristic
52C2×C3×#360C2211yescharacteristic
53C3×#2143C2211yescharacteristic
54C3×#2140C2211yescharacteristic
55C3×#2117C2211yescharacteristic
56C3×#2117C2211yescharacteristic
57C2×C3×#347C2211yescharacteristic
58C2×C3×#347C2211yescharacteristic
59C3×#1976C2211yescharacteristic
60C3×#1953C2211yescharacteristic
61C3×#1932—21no—
62C3×#1906—21no—
63C3×#1814C2211yescharacteristic
64C3×#1773C2211yescharacteristic
65C3×#1757—21no—
66C3×#1389C2211yescharacteristic
67C3×#1386C2211yescharacteristic
68C3×#1384C2211yescharacteristic
69C3×#1383C2211yescharacteristic
70C3×#1378C2211yescharacteristic
71C3×#1378C2211yescharacteristic
72#60698C2×C311yescharacteristic, complemented
73#33468C2×C311yescharacteristic, complemented
74C2×AGL(1,ℤ/16)C2×C311yescharacteristic, complemented
75#21559C2×C311yescharacteristic, complemented
76#13460C2×C311yescharacteristic, complemented
77#13417C2×C311yescharacteristic, complemented
78#13400C2×C311yescharacteristic, complemented
79#13396C2×C311yescharacteristic, complemented
80#13374C2×C311yescharacteristic, complemented
81#13334C2×C311yescharacteristic, complemented
82#13318C2×C311yescharacteristic, complemented
83#13310C2×C311yescharacteristic, complemented
84#12649C2×C311yescharacteristic, complemented
85#12647C2×C311yescharacteristic, complemented
86#12609C2×C311yescharacteristic, complemented
87C3×#575—21no—
88C2×C3×AGL(1,ℤ/8)—21no—
89C2×C3×#135C2311yescharacteristic
90C2×C3×#135C2311yescharacteristic
91C22×C3×D8C2311yescharacteristic
92C2×C3×#131—21no—
93C2×C3×#131D411yescharacteristic
94C2×C3×#131C2311yescharacteristic
95C3×#544—21no—
96C3×#542—22no—
97C3×#542—41no—
98C3×#540—22no—
99C3×#540—41no—
100C3×#538—42no—
101C3×#537—21no—
102C3×#535—21no—
103C3×#535—21no—
104C3×#532—22no—
105C3×#532—41no—
106C3×#529—22no—
107C3×#529—41no—
108C3×#525—42no—
109C3×C4×#41—21no—
110C3×C4×#41D411yescharacteristic
111C2×C3×C4×D4—21no—
112C3×#510—21no—
113C3×#510—21no—
114C3×#509—22no—
115C3×#509—21no—
116C3×#509—21no—
117C3×#509—22no—
118C3×#508—22no—
119C2×C3×SD32—21no—
120C2×C3×D16—21no—
121C2×C3×M32C2311yescharacteristic
122C2×C3×M32C2311yescharacteristic
123C2×C3×M32C2311yescharacteristic
124C2×C3×M32C2311yescharacteristic
125C3×#501—22no—
126C3×#499—21no—
127C3×#498—21no—
128C3×#496—22no—
129C3×#495—21no—
130C3×#493—21no—
131C3×#490—22no—
132C3×#489—22no—
133C3×#488—22no—
134C3×#486—22no—
135C3×#473—21no—
136C3×#472—21no—
137C3×#471—22no—
138C3×#470—21no—
139C3×#469—22no—
140C3×#469—21no—
141C3×#469—21no—
142C3×#469—21no—
143C3×#468—22no—
144C3×#466—22no—
145C3×#466—22no—
146C3×#465—22no—
147C3×#465—22no—
148C3×#444—21no—
149C3×#444—21no—
150C3×#444—21no—
151C3×#444—21no—
152C3×#444—42no—
153C3×#443—42no—
154C3×#442—22no—
155C3×#442—21no—
156C3×#442—21no—
157C3×#442D411yescharacteristic
158C3×#442D412yes—
159C3×#442D412yes—
160C3×#442D411yescharacteristic
161C3×#441D411yescharacteristic
162C3×#441D411yescharacteristic
163C3×#440—22no—
164C3×#440—21no—
165C3×#440—21no—
166C3×C4×SD16—22no—
167C3×C4×D8—22no—
168C3×#430—21no—
169C2×C3×#108C2311yescharacteristic
170C2×C3×#108C2311yescharacteristic
171C3×#428—21no—
172C3×#427C2311yescharacteristic
173C3×#427C2311yescharacteristic
174C2×C3×#106C2311yescharacteristic
175C3×#421—21no—
176C3×#421—21no—
177C2×C3×#104—21no—
178C3×#418—21no—
179C3×#417—21no—
180C3×#416—21no—
181C2×C3×#102—21no—
182C3×#413—21no—
183C3×#410—21no—
184C3×#405—21no—
185C3×#405—21no—
186C3×#405—21no—
187C3×#405D411yescharacteristic
188C3×#405C2311yescharacteristic
189C3×C4×M16—21no—
190C3×C4×M16D411yescharacteristic
191C2×C3×#97—21no—
192C2×C3×#97C2311yescharacteristic
193C3×#365—22no—
194C3×#365—21no—
195C3×#365—21no—
196C3×#362—21no—
197C3×#361—22no—
198C3×#361—21no—
199C3×#361—22no—
200C3×#360—22no—
201C3×#360—22no—
202C3×#360—21no—
203C3×#360—21no—
204C3×#359—22no—
205C3×#357—22no—
206C3×#350—22no—
207C3×#350—22no—
208C3×#347—21no—
209C3×#347—21no—
210C3×#347—21no—
211C3×#347—21no—
212C3×#344—21no—
213C3×#344—21no—
214C3×#339—21no—
215#3460—21no—
216#3414C22×C311yescharacteristic
217C2×#509C22×C311yescharacteristic
218#3184—21no—
219#3183—21no—
220#3180—22no—
221#3179—22no—
222#3176—21no—
223#3173—21no—
224#3163C22×C311yescharacteristic
225#3155C22×C311yescharacteristic
226#3136—21no—
227#3067C22×C311yescharacteristic
228#3062—21no—
229#3060C22×C311yescharacteristic
230#3058C22×C311yescharacteristic
231#2955—21no—
232C2×#444C22×C311yescharacteristic
233C4×AGL(1,ℤ/8)—21no—
234#2943C22×C311yescharacteristic
235C2×#442C22×C311yescharacteristic
236#2875C22×C311yescharacteristic
237AGL(1,ℤ/16)—22no—
238AGL(1,ℤ/16)—22no—
239AGL(1,ℤ/16)—21no—
240AGL(1,ℤ/16)—21no—
241#2180—21no—
242#2180—21no—
243#2155C22×C311yescharacteristic
244C2×#365C22×C311yescharacteristic
245#2148C22×C311yescharacteristic
246C2×#361C22×C311yescharacteristic
247C2×#361C22×C311yescharacteristic
248#2145C22×C311yescharacteristic
249#2145C22×C311yescharacteristic
250C2×#360C22×C311yescharacteristic
251#2143C22×C311yescharacteristic
252#2140C22×C311yescharacteristic
253#2117C22×C311yescharacteristic
254#2117C22×C311yescharacteristic
255C2×#347C22×C311yescharacteristic
256C2×#347C22×C311yescharacteristic
257#1976C22×C311yescharacteristic
258#1953C22×C311yescharacteristic
259#1932—21no—
260#1906—21no—
261#1814C22×C311yescharacteristic
262#1773C22×C311yescharacteristic
263#1757—21no—
264#1389C22×C311yescharacteristic
265#1386C22×C311yescharacteristic
266#1384C22×C311yescharacteristic
267#1383C22×C311yescharacteristic
268#1378C22×C311yescharacteristic
269#1378C22×C311yescharacteristic
270C2×C3×#41—21no—
271C2×C3×#41—21no—
272C2×C3×#41—42no—
273C2×C3×#41C2×D411yescharacteristic
274C22×C3×D4—21no—
275C23×C3×C4—41no—
276C3×#137—22no—
277C3×#137—41no—
278C3×AGL(1,ℤ/8)—22no—
279C3×AGL(1,ℤ/8)—42no—
280C3×AGL(1,ℤ/8)—41no—
281C3×AGL(1,ℤ/8)—42no—
282C3×#135—21no—
283C3×#135—21no—
284C3×#135—21no—
285C3×#135—21no—
286C3×#135—21no—
287C3×#135—21no—
288C3×#135—21no—
289C3×#135—21no—
290C3×#135—42no—
291C2×C3×Q16C2×D411yescharacteristic
292C2×C3×Q16#4111yescharacteristic, complemented
293C2×C3×SD16—22no—
294C2×C3×SD16—21no—
295C2×C3×SD16—21no—
296C2×C3×D8—22no—
297C2×C3×D8—21no—
298C2×C3×D8—21no—
299C2×C3×D8—21no—
300C2×C3×D8—21no—
301C2×C3×D8—21no—
302C2×C3×D8C2×D412yes—
303C2×C3×D8C2×D411yescharacteristic
304C2×C3×D8#4111yescharacteristic, complemented
305C3×#131—22no—
306C3×#131—21no—
307C3×#131—21no—
308C3×#131—21no—
309C3×#131—21no—
310C3×#131—41no—
311C3×#131—41no—
312C3×#131—41no—
313C3×#131—41no—
314C3×#131—41no—
315C2×C3×M16—21no—
316C2×C3×M16—21no—
317C2×C3×M16—21no—
318C2×C3×M16—21no—
319C2×C3×M16—41no—
320C2×C3×M16C2×D411yescharacteristic
321C2×C3×M16C2×D411yescharacteristic
322C22×C3×C8—21no—
323C22×C3×C8—21no—
324C22×C3×C8—41no—
325C22×C3×C8C2×D411yescharacteristic
326C22×C3×C8C2411yescharacteristic
327C3×C4⋊Q8—22no—
328C3×C4⋊Q8—41no—
329C3×#127—22no—
330C3×#127—41no—
331C3×#126—42no—
332C3×#126—42no—
333C3×#125—22no—
334C3×#125—41no—
335C3×#124—22no—
336C3×#124—42no—
337C3×#124—42no—
338C3×#124—41no—
339C3×#123—42no—
340C3×#123—42no—
341C3×#123—42no—
342C3×#123—42no—
343C3×C22⋊Q8—22no—
344C3×C22⋊Q8—42no—
345C3×C22⋊Q8—41no—
346C3×C22⋊Q8—42no—
347C3×#121—22no—
348C3×#121—22no—
349C3×#121—22no—
350C3×#121—42no—
351C3×#121—42no—
352C3×#121—41no—
353C3×#121—41no—
354C3×#121—42no—
355C3×#121—42no—
356C3×#121—41no—
357C3×#120—42no—
358C3×#120—42no—
359C3×C4×Q8—21no—
360C3×C4×Q8—21no—
361C3×C4×Q8—21no—
362C3×C4×D4—21no—
363C3×C4×D4—22no—
364C3×C4×D4—21no—
365C3×C4×D4—22no—
366C3×C4×D4—22no—
367C3×C4×D4—21no—
368C3×C4×D4—41no—
369C3×C4×D4—41no—
370C3×C4×D4—42no—
371C3×C4×D4—41no—
372C3×C4×D4—41no—
373C3×C4×D4—42no—
374C3×#117—21no—
375C3×#117—21no—
376C3×#117—21no—
377C3×#117—41no—
378C3×#117—42no—
379C3×#117C2×D411yescharacteristic
380C2×C3×C4⋊C4—21no—
381C2×C3×C22⋊C4—41no—
382C2×C3×C42—21no—
383C2×C3×C42—41no—
384C2×C3×C42C2×D411yescharacteristic
385C3×Q32—22no—
386C3×SD32—24no—
387C3×SD32—22no—
388C3×SD32—22no—
389C3×D16—24no—
390C3×D16—22no—
391C3×M32—21no—
392C3×M32—21no—
393C3×M32—21no—
394C3×M32—21no—
395C3×M32—21no—
396C3×M32—21no—
397C3×M32—21no—
398C3×M32#4112yescomplemented
399C2×C3×C16—21no—
400C2×C3×C16—21no—
401C2×C3×C16—21no—
402C2×C3×C16#4112yescomplemented
403C3×#108—21no—
404C3×#108—21no—
405C3×#108—21no—
406C3×#108—42no—
407C3×#108#4112yescomplemented
408C3×#107—22no—
409C3×#107—21no—
410C3×#107—21no—
411C3×#106—22no—
412C3×#106—21no—
413C3×#106—21no—
414C3×#106C2×D412yes—
415C3×#106C2×D411yescharacteristic
416C3×#106C2×D411yescharacteristic
417C3×#104—42no—
418C3×#104—42no—
419C3×#104—41no—
420C3×#104—41no—
421C3×#103—22no—
422C3×#103—21no—
423C3×#103—21no—
424C3×#102—22no—
425C3×#102—22no—
426C3×#102—22no—
427C3×#102—22no—
428C3×#102—22no—
429C3×#102—21no—
430C3×#102—21no—
431C3×#101—22no—
432C3×#100—22no—
433C3×#99—42no—
434C3×#97—21no—
435C3×#97—21no—
436C3×#97—21no—
437C3×#97—41no—
438C3×#97C2×D411yescharacteristic
439C3×#97C2×D411yescharacteristic
440C3×#97C2×D411yescharacteristic
441C3×#97C2×D411yescharacteristic
442C3×C4×C8—21no—
443C3×C4×C8—21no—
444C3×C4×C8—21no—
445C3×C4×C8—41no—
446#575—21no—
447C2×AGL(1,ℤ/8)—21no—
448C2×#135C23×C311yescharacteristic
449C2×#135C23×C311yescharacteristic
450C22×D8C23×C311yescharacteristic
451C2×#131—21no—
452C2×#131C3×D411yescharacteristic
453C2×#131C23×C311yescharacteristic
454#544—21no—
455#542—22no—
456#542—41no—
457#540—22no—
458#540—41no—
459#538—42no—
460#537—21no—
461#535—21no—
462#535—21no—
463#532—22no—
464#532—41no—
465#529—22no—
466#529—41no—
467#525—42no—
468C4×#41—21no—
469C4×#41C3×D411yescharacteristic
470C2×C4×D4—21no—
471#510—21no—
472#510—21no—
473#509—22no—
474#509—21no—
475#509—21no—
476#509—22no—
477#508—22no—
478C2×SD32—21no—
479C2×D16—21no—
480C2×M32C23×C311yescharacteristic
481C2×M32C23×C311yescharacteristic
482C2×M32C23×C311yescharacteristic
483C2×M32C23×C311yescharacteristic
484#501—22no—
485#499—21no—
486#498—21no—
487#496—22no—
488#495—21no—
489#493—21no—
490#490—22no—
491#489—22no—
492#488—22no—
493#486—22no—
494#473—21no—
495#472—21no—
496#471—22no—
497#470—21no—
498#469—22no—
499#469—21no—
500#469—21no—
501#469—21no—
502#468—22no—
503#466—22no—
504#466—22no—
505#465—22no—
506#465—22no—
507#444—21no—
508#444—21no—
509#444—21no—
510#444—21no—
511#444—42no—
512#443—42no—
513#442—22no—
514#442—21no—
515#442—21no—
516#442C3×D411yescharacteristic
517#442C3×D412yes—
518#442C3×D412yes—
519#442C3×D411yescharacteristic
520#441C3×D411yescharacteristic
521#441C3×D411yescharacteristic
522#440—22no—
523#440—21no—
524#440—21no—
525C4×SD16—22no—
526C4×D8—22no—
527#430—21no—
528C2×#108C23×C311yescharacteristic
529C2×#108C23×C311yescharacteristic
530#428—21no—
531#427C23×C311yescharacteristic
532#427C23×C311yescharacteristic
533C2×#106C23×C311yescharacteristic
534#421—21no—
535#421—21no—
536C2×#104—21no—
537#418—21no—
538#417—21no—
539#416—21no—
540C2×#102—21no—
541#413—21no—
542#410—21no—
543#405—21no—
544#405—21no—
545#405—21no—
546#405C3×D411yescharacteristic
547#405C23×C311yescharacteristic
548C4×M16—21no—
549C4×M16C3×D411yescharacteristic
550C2×#97—21no—
551C2×#97C23×C311yescharacteristic
552#365—22no—
553#365—21no—
554#365—21no—
555#362—21no—
556#361—22no—
557#361—21no—
558#361—22no—
559#360—22no—
560#360—22no—
561#360—21no—
562#360—21no—
563#359—22no—
564#357—22no—
565#350—22no—
566#350—22no—
567#347—21no—
568#347—21no—
569#347—21no—
570#347—21no—
571#344—21no—
572#344—21no—
573#339—21no—
574C24×C3—41no—
575C3×#41—21no—
576C3×#41—21no—
577C3×#41—21no—
578C3×#41—21no—
579C3×#41—41no—
580C3×#41—41no—
581C3×#41—41no—
582C3×#41—41no—
583C3×#41—41no—
584C3×#41—41no—
585C3×#41—41no—
586C3×#41—41no—
587C3×#41—164no—
588C2×C3×Q8—21no—
589C2×C3×Q8—21no—
590C2×C3×Q8—42no—
591C2×C3×Q8AGL(1,ℤ/8)11yescharacteristic
592C2×C3×D4—21no—
593C2×C3×D4—22no—
594C2×C3×D4—21no—
595C2×C3×D4—21no—
596C2×C3×D4—42no—
597C2×C3×D4—42no—
598C2×C3×D4—41no—
599C2×C3×D4—41no—
600C2×C3×D4—42no—
601C2×C3×D4—42no—
602C2×C3×D4—42no—
603C2×C3×D4—41no—
604C2×C3×D4—41no—
605C2×C3×D4—41no—
606C2×C3×D4—41no—
607C2×C3×D4—41no—
608C2×C3×D4AGL(1,ℤ/8)11yescharacteristic
609C22×C3×C4—22no—
610C22×C3×C4—21no—
611C22×C3×C4—21no—
612C22×C3×C4—41no—
613C22×C3×C4—42no—
614C22×C3×C4—41no—
615C22×C3×C4—42no—
616C22×C3×C4—41no—
617C22×C3×C4—41no—
618C22×C3×C4—41no—
619C22×C3×C4—162no—
620C22×C3×C4C22×D411yescharacteristic
621C3×Q16—21no—
622C3×Q16—21no—
623C3×Q16—21no—
624C3×Q16—21no—
625C3×Q16—42no—
626C3×SD16—44no—
627C3×SD16—42no—
628C3×SD16—42no—
629C3×SD16—41no—
630C3×SD16—41no—
631C3×SD16—41no—
632C3×SD16—41no—
633C3×D8—21no—
634C3×D8—22no—
635C3×D8—21no—
636C3×D8—21no—
637C3×D8—22no—
638C3×D8—21no—
639C3×D8—44no—
640C3×D8—42no—
641C3×D8—41no—
642C3×D8—41no—
643C3×M16—21no—
644C3×M16—21no—
645C3×M16—22no—
646C3×M16—21no—
647C3×M16—42no—
648C3×M16—41no—
649C3×M16—41no—
650C3×M16—41no—
651C3×M16—41no—
652C3×M16—41no—
653C3×M16—81no—
654C3×M16—81no—
655C3×M16AGL(1,ℤ/8)12yes—
656C2×C3×C8—21no—
657C2×C3×C8—21no—
658C2×C3×C8—21no—
659C2×C3×C8—21no—
660C2×C3×C8—42no—
661C2×C3×C8—41no—
662C2×C3×C8—41no—
663C2×C3×C8—41no—
664C2×C3×C8—41no—
665C2×C3×C8—81no—
666C2×C3×C8—81no—
667C2×C3×C8#12011yescharacteristic
668C2×C3×C8#12011yescharacteristic
669C2×C3×C8C22×D411yescharacteristic
670C2×C3×C8C22×D411yescharacteristic
671C2×C3×C8C2×#4111yescharacteristic
672C2×C3×C8C2×#4111yescharacteristic
673C2×C3×C8C2×#4111yescharacteristic
674C2×C3×C8C2×#4111yescharacteristic
675C3×C4⋊C4—22no—
676C3×C4⋊C4—21no—
677C3×C4⋊C4—22no—
678C3×C4⋊C4—21no—
679C3×C4⋊C4—21no—
680C3×C4⋊C4—41no—
681C3×C4⋊C4—41no—
682C3×C4⋊C4—42no—
683C3×C4⋊C4—42no—
684C3×C4⋊C4—42no—
685C3×C4⋊C4—42no—
686C3×C4⋊C4—41no—
687C3×C4⋊C4—41no—
688C3×C22⋊C4—22no—
689C3×C22⋊C4—42no—
690C3×C22⋊C4—42no—
691C3×C22⋊C4—41no—
692C3×C22⋊C4—41no—
693C3×C22⋊C4—42no—
694C3×C22⋊C4—42no—
695C3×C22⋊C4—42no—
696C3×C22⋊C4—42no—
697C3×C22⋊C4—42no—
698C3×C22⋊C4—42no—
699C3×C22⋊C4—41no—
700C3×C22⋊C4—41no—
701C3×C22⋊C4AGL(1,ℤ/8)12yes—
702C3×C42—22no—
703C3×C42—21no—
704C3×C42—21no—
705C3×C42—41no—
706C3×C42—41no—
707C3×C42—41no—
708C3×C42—41no—
709C3×C42#12011yescharacteristic
710C3×C42#12011yescharacteristic
711C3×C16—22no—
712C3×C16—22no—
713C3×C16—41no—
714C3×C16—41no—
715C2×#41—21no—
716C2×#41—21no—
717C2×#41—42no—
718C2×#41C2×C3×D411yescharacteristic
719C22×D4—21no—
720C23×C4—41no—
721#137—22no—
722#137—41no—
723AGL(1,ℤ/8)—22no—
724AGL(1,ℤ/8)—42no—
725AGL(1,ℤ/8)—41no—
726AGL(1,ℤ/8)—42no—
727#135—21no—
728#135—21no—
729#135—21no—
730#135—21no—
731#135—21no—
732#135—21no—
733#135—21no—
734#135—21no—
735#135—42no—
736C2×Q16C2×C3×D411yescharacteristic
737C2×Q16C3×#4111yescharacteristic, complemented
738C2×SD16—22no—
739C2×SD16—21no—
740C2×SD16—21no—
741C2×D8—22no—
742C2×D8—21no—
743C2×D8—21no—
744C2×D8—21no—
745C2×D8—21no—
746C2×D8—21no—
747C2×D8C2×C3×D412yes—
748C2×D8C2×C3×D411yescharacteristic
749C2×D8C3×#4111yescharacteristic, complemented
750#131—22no—
751#131—21no—
752#131—21no—
753#131—21no—
754#131—21no—
755#131—41no—
756#131—41no—
757#131—41no—
758#131—41no—
759#131—41no—
760C2×M16—21no—
761C2×M16—21no—
762C2×M16—21no—
763C2×M16—21no—
764C2×M16—41no—
765C2×M16C2×C3×D411yescharacteristic
766C2×M16C2×C3×D411yescharacteristic
767C22×C8—21no—
768C22×C8—21no—
769C22×C8—41no—
770C22×C8C2×C3×D411yescharacteristic
771C22×C8C24×C311yescharacteristic
772C4⋊Q8—22no—
773C4⋊Q8—41no—
774#127—22no—
775#127—41no—
776#126—42no—
777#126—42no—
778#125—22no—
779#125—41no—
780#124—22no—
781#124—42no—
782#124—42no—
783#124—41no—
784#123—42no—
785#123—42no—
786#123—42no—
787#123—42no—
788C22⋊Q8—22no—
789C22⋊Q8—42no—
790C22⋊Q8—41no—
791C22⋊Q8—42no—
792#121—22no—
793#121—22no—
794#121—22no—
795#121—42no—
796#121—42no—
797#121—41no—
798#121—41no—
799#121—42no—
800#121—42no—
801#121—41no—
802#120—42no—
803#120—42no—
804C4×Q8—21no—
805C4×Q8—21no—
806C4×Q8—21no—
807C4×D4—21no—
808C4×D4—22no—
809C4×D4—22no—
810C4×D4—22no—
811C4×D4—21no—
812C4×D4—21no—
813C4×D4—41no—
814C4×D4—41no—
815C4×D4—42no—
816C4×D4—41no—
817C4×D4—41no—
818C4×D4—42no—
819#117—21no—
820#117—21no—
821#117—21no—
822#117—41no—
823#117—42no—
824#117C2×C3×D411yescharacteristic
825C2×C4⋊C4—21no—
826C2×C22⋊C4—41no—
827C2×C42—21no—
828C2×C42—41no—
829C2×C42C2×C3×D411yescharacteristic
830Q32—22no—
831SD32—24no—
832SD32—22no—
833SD32—22no—
834D16—24no—
835D16—22no—
836M32—21no—
837M32—21no—
838M32—21no—
839M32—21no—
840M32—21no—
841M32—21no—
842M32—21no—
843M32C3×#4112yescomplemented
844C2×C16—21no—
845C2×C16—21no—
846C2×C16—21no—
847C2×C16C3×#4112yescomplemented
848#108—21no—
849#108—21no—
850#108—21no—
851#108—42no—
852#108C3×#4112yescomplemented
853#107—22no—
854#107—21no—
855#107—21no—
856#106—22no—
857#106—21no—
858#106—21no—
859#106C2×C3×D412yes—
860#106C2×C3×D411yescharacteristic
861#106C2×C3×D411yescharacteristic
862#104—42no—
863#104—42no—
864#104—41no—
865#104—41no—
866#103—22no—
867#103—21no—
868#103—21no—
869#102—22no—
870#102—22no—
871#102—22no—
872#102—22no—
873#102—22no—
874#102—21no—
875#102—21no—
876#101—22no—
877#100—22no—
878#99—42no—
879#97—21no—
880#97—21no—
881#97—21no—
882#97—41no—
883#97C2×C3×D411yescharacteristic
884#97C2×C3×D411yescharacteristic
885#97C2×C3×D411yescharacteristic
886#97C2×C3×D411yescharacteristic
887C4×C8—21no—
888C4×C8—21no—
889C4×C8—21no—
890C4×C8—41no—
891C23×C3—21no—
892C23×C3—42no—
893C23×C3—41no—
894C23×C3—41no—
895C23×C3—81no—
896C23×C3—81no—
897C23×C3—161no—
898C23×C3—161no—
899C23×C3C2×AGL(1,ℤ/8)11yescharacteristic
900C3×Q8—21no—
901C3×Q8—21no—
902C3×Q8—41no—
903C3×Q8—41no—
904C3×Q8—41no—
905C3×Q8—41no—
906C3×Q8—162no—
907C3×D4—21no—
908C3×D4—21no—
909C3×D4—41no—
910C3×D4—41no—
911C3×D4—41no—
912C3×D4—42no—
913C3×D4—41no—
914C3×D4—41no—
915C3×D4—41no—
916C3×D4—42no—
917C3×D4—81no—
918C3×D4—81no—
919C3×D4—81no—
920C3×D4—81no—
921C3×D4—81no—
922C3×D4—81no—
923C3×D4—162no—
924C3×D4—162no—
925C3×D4—162no—
926C3×D4—162no—
927C3×D4—162no—
928C2×C3×C4—21no—
929C2×C3×C4—22no—
930C2×C3×C4—21no—
931C2×C3×C4—21no—
932C2×C3×C4—41no—
933C2×C3×C4—41no—
934C2×C3×C4—41no—
935C2×C3×C4—41no—
936C2×C3×C4—41no—
937C2×C3×C4—41no—
938C2×C3×C4—42no—
939C2×C3×C4—81no—
940C2×C3×C4—82no—
941C2×C3×C4—84no—
942C2×C3×C4—82no—
943C2×C3×C4—81no—
944C2×C3×C4—81no—
945C2×C3×C4—81no—
946C2×C3×C4—81no—
947C2×C3×C4—81no—
948C2×C3×C4—161no—
949C2×C3×C4—162no—
950C2×C3×C4—161no—
951C2×C3×C4C2×#12011yescharacteristic
952C2×C3×C4#52511yescharacteristic
953C2×C3×C4#53211yescharacteristic
954C2×C3×C4C2×AGL(1,ℤ/8)11yescharacteristic
955C2×C3×C4C2×AGL(1,ℤ/8)11yescharacteristic
956C2×C3×C4#57511yescharacteristic
957C3×C8—21no—
958C3×C8—21no—
959C3×C8—22no—
960C3×C8—42no—
961C3×C8—41no—
962C3×C8—81no—
963C3×C8#52511yescharacteristic
964C3×C8#52511yescharacteristic
965C3×C8#53211yescharacteristic
966C3×C8#53211yescharacteristic
967C24—41no—
968#41—21no—
969#41—21no—
970#41—21no—
971#41—21no—
972#41—41no—
973#41—41no—
974#41—41no—
975#41—41no—
976#41—41no—
977#41—41no—
978#41—41no—
979#41—41no—
980#41—164no—
981C2×Q8—21no—
982C2×Q8—21no—
983C2×Q8—42no—
984C2×Q8C3×AGL(1,ℤ/8)11yescharacteristic
985C2×D4—21no—
986C2×D4—22no—
987C2×D4—21no—
988C2×D4—21no—
989C2×D4—42no—
990C2×D4—42no—
991C2×D4—41no—
992C2×D4—41no—
993C2×D4—42no—
994C2×D4—42no—
995C2×D4—42no—
996C2×D4—41no—
997C2×D4—41no—
998C2×D4—41no—
999C2×D4—41no—
1000C2×D4—41no—
1001C2×D4C3×AGL(1,ℤ/8)11yescharacteristic
1002C22×C4—22no—
1003C22×C4—21no—
1004C22×C4—21no—
1005C22×C4—41no—
1006C22×C4—42no—
1007C22×C4—41no—
1008C22×C4—42no—
1009C22×C4—41no—
1010C22×C4—41no—
1011C22×C4—41no—
1012C22×C4—162no—
1013C22×C4C22×C3×D411yescharacteristic
1014Q16—21no—
1015Q16—21no—
1016Q16—21no—
1017Q16—21no—
1018Q16—42no—
1019SD16—44no—
1020SD16—42no—
1021SD16—42no—
1022SD16—41no—
1023SD16—41no—
1024SD16—41no—
1025SD16—41no—
1026D8—21no—
1027D8—22no—
1028D8—21no—
1029D8—21no—
1030D8—22no—
1031D8—21no—
1032D8—44no—
1033D8—42no—
1034D8—41no—
1035D8—41no—
1036M16—21no—
1037M16—21no—
1038M16—22no—
1039M16—21no—
1040M16—42no—
1041M16—41no—
1042M16—41no—
1043M16—41no—
1044M16—41no—
1045M16—41no—
1046M16—81no—
1047M16—81no—
1048M16C3×AGL(1,ℤ/8)12yes—
1049C2×C8—21no—
1050C2×C8—21no—
1051C2×C8—21no—
1052C2×C8—21no—
1053C2×C8—42no—
1054C2×C8—41no—
1055C2×C8—41no—
1056C2×C8—41no—
1057C2×C8—41no—
1058C2×C8—81no—
1059C2×C8—81no—
1060C2×C8C3×#12011yescharacteristic
1061C2×C8C3×#12011yescharacteristic
1062C2×C8C22×C3×D411yescharacteristic
1063C2×C8C22×C3×D411yescharacteristic
1064C2×C8C2×C3×#4111yescharacteristic
1065C2×C8C2×C3×#4111yescharacteristic
1066C2×C8C2×C3×#4111yescharacteristic
1067C2×C8C2×C3×#4111yescharacteristic
1068C4⋊C4—22no—
1069C4⋊C4—21no—
1070C4⋊C4—22no—
1071C4⋊C4—21no—
1072C4⋊C4—21no—
1073C4⋊C4—41no—
1074C4⋊C4—41no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—41no—
1080C4⋊C4—41no—
1081C22⋊C4—22no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—41no—
1085C22⋊C4—41no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—41no—
1093C22⋊C4—41no—
1094C22⋊C4C3×AGL(1,ℤ/8)12yes—
1095C42—22no—
1096C42—21no—
1097C42—21no—
1098C42—41no—
1099C42—41no—
1100C42—41no—
1101C42—41no—
1102C42C3×#12011yescharacteristic
1103C42C3×#12011yescharacteristic
1104C16—22no—
1105C16—22no—
1106C16—41no—
1107C16—41no—
1108C22×C3—41no—
1109C22×C3—42no—
1110C22×C3—41no—
1111C22×C3—82no—
1112C22×C3—81no—
1113C22×C3—81no—
1114C22×C3—82no—
1115C22×C3—81no—
1116C22×C3—81no—
1117C22×C3—82no—
1118C22×C3—161no—
1119C22×C3—162no—
1120C22×C3—162no—
1121C22×C3#300311yescharacteristic
1122C22×C3#311511yescharacteristic
1123C22×C3#318411yescharacteristic
1124C3×C4—41no—
1125C3×C4—41no—
1126C3×C4—42no—
1127C3×C4—41no—
1128C3×C4—82no—
1129C3×C4—81no—
1130C3×C4—81no—
1131C3×C4—81no—
1132C3×C4—81no—
1133C3×C4—161no—
1134C3×C4#238811yescharacteristic
1135C3×C4#300611yescharacteristic
1136C3×C4#310911yescharacteristic
1137C3×C4#318011yescharacteristic
1138C23—21no—
1139C23—42no—
1140C23—41no—
1141C23—41no—
1142C23—81no—
1143C23—81no—
1144C23—161no—
1145C23—161no—
1146C23C2×C3×AGL(1,ℤ/8)11yescharacteristic
1147Q8—21no—
1148Q8—21no—
1149Q8—41no—
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153Q8—162no—
1154D4—21no—
1155D4—21no—
1156D4—41no—
1157D4—41no—
1158D4—42no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—42no—
1163D4—41no—
1164D4—81no—
1165D4—81no—
1166D4—81no—
1167D4—81no—
1168D4—81no—
1169D4—81no—
1170D4—162no—
1171D4—162no—
1172D4—162no—
1173D4—162no—
1174D4—162no—
1175C2×C4—21no—
1176C2×C4—22no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—42no—
1185C2×C4—41no—
1186C2×C4—81no—
1187C2×C4—82no—
1188C2×C4—84no—
1189C2×C4—82no—
1190C2×C4—81no—
1191C2×C4—81no—
1192C2×C4—81no—
1193C2×C4—81no—
1194C2×C4—81no—
1195C2×C4—162no—
1196C2×C4—161no—
1197C2×C4—161no—
1198C2×C4C2×C3×#12011yescharacteristic
1199C2×C4C3×#52511yescharacteristic
1200C2×C4C3×#53211yescharacteristic
1201C2×C4C2×C3×AGL(1,ℤ/8)11yescharacteristic
1202C2×C4C2×C3×AGL(1,ℤ/8)11yescharacteristic
1203C2×C4C3×#57511yescharacteristic
1204C8—21no—
1205C8—21no—
1206C8—22no—
1207C8—41no—
1208C8—42no—
1209C8—81no—
1210C8C3×#52511yescharacteristic
1211C8C3×#52511yescharacteristic
1212C8C3×#53211yescharacteristic
1213C8C3×#53211yescharacteristic
1214C2×C3—21no—
1215C2×C3—21no—
1216C2×C3—21no—
1217C2×C3—81no—
1218C2×C3—161no—
1219C2×C3—162no—
1220C2×C3—161no—
1221C2×C3#2357311yescharacteristic
1222C22—41no—
1223C22—42no—
1224C22—41no—
1225C22—82no—
1226C22—81no—
1227C22—81no—
1228C22—82no—
1229C22—81no—
1230C22—81no—
1231C22—82no—
1232C22—161no—
1233C22—162no—
1234C22—162no—
1235C22C3×#300311yescharacteristic
1236C22C3×#311511yescharacteristic
1237C22C3×#318411yescharacteristic
1238C4—41no—
1239C4—41no—
1240C4—42no—
1241C4—41no—
1242C4—82no—
1243C4—81no—
1244C4—81no—
1245C4—81no—
1246C4—81no—
1247C4—161no—
1248C4C3×#238811yescharacteristic
1249C4C3×#300611yescharacteristic
1250C4C3×#310911yescharacteristic
1251C4C3×#318011yescharacteristic
1252C3#49926911yescharacteristic, direct product factor, Sylow
1253C2—21no—
1254C2—21no—
1255C2—21no—
1256C2—81no—
1257C2—162no—
1258C2—161no—
1259C2—161no—
1260C2C3×#2357311yescharacteristic
subgroupG/H
center, socleC2×C3#23573
commutator, Frattini, cosocleC22×C8C24×C3
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#2875 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#60698C2semidirect
2. C3×#33468C2semidirect
3. C2×C3×AGL(1,ℤ/16)C2semidirect
4. C3×#21559C2semidirect
5. C3×#13460C2semidirect
6. C3×#13417C2semidirect
7. C3×#13400C2semidirect
8. C3×#13396C2semidirect
9. C3×#13374C2semidirect
10. C3×#13334C2semidirect
11. C3×#13318C2semidirect
12. C3×#13310C2semidirect
13. C3×#12649C2semidirect
14. C3×#12647C2semidirect
15. C3×#12609C2semidirect
16. #499269C3direct (N × H)
72. #60698C2×C3semidirect
73. #33468C2×C3semidirect
74. C2×AGL(1,ℤ/16)C2×C3semidirect
75. #21559C2×C3semidirect
76. #13460C2×C3semidirect
77. #13417C2×C3semidirect
78. #13400C2×C3semidirect
79. #13396C2×C3semidirect
80. #13374C2×C3semidirect
81. #13334C2×C3semidirect
82. #13318C2×C3semidirect
83. #13310C2×C3semidirect
84. #12649C2×C3semidirect
85. #12647C2×C3semidirect
86. #12609C2×C3semidirect
292. C2×C3×Q16#41semidirect
304. C2×C3×D8#41semidirect
398. C3×M32#41semidirect
402. C2×C3×C16#41semidirect
407. C3×#108#41semidirect
737. C2×Q16C3×#41semidirect
749. C2×D8C3×#41semidirect
843. M32C3×#41semidirect
847. C2×C16C3×#41semidirect
852. #108C3×#41semidirect
1252. C3#499269direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#606982
C3×#334682
C2×C3×AGL(1,ℤ/16)2
C3×#215592
C3×#134602
C3×#134172
C3×#134002
C3×#133962
C3×#133742
C3×#133342
C3×#133182
C3×#133102
C3×#126492
C3×#126472
C3×#126092
#4992693