Finite Group Databasebeta

← C3×#83953 #11883895

Subgroups — C3×#83953 #11883895

Order 1152.

1241 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C3×#5831C211yesmaximal, characteristic, complemented
3C3×D4×#67C211yesmaximal, characteristic, complemented
4C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
5C3×#5238C211yesmaximal, characteristic, complemented
6C3×#5218C211yesmaximal, characteristic, complemented
7C3×#5170C211yesmaximal, characteristic, complemented
8C3×#5164C211yesmaximal, characteristic, complemented
9C3×#5163C211yesmaximal, characteristic, complemented
10C3×#5157C211yesmaximal, characteristic, complemented
11C3×#5156C211yesmaximal, characteristic, complemented
12C3×#5154C211yesmaximal, characteristic, complemented
13C3×#5153C211yesmaximal, characteristic, complemented
14C3×#5134C211yesmaximal, characteristic, complemented
15C3×#5127C211yesmaximal, characteristic, complemented
16C3×#3265—31nomaximal
17#83953C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic, complemented
19C22×C32×D4C2211yescharacteristic
20C22×C3×#67—21no—
21C2×C3×D3×Q8C2211yescharacteristic, complemented
22C2×C3×D3×D4C2211yescharacteristic
23C32×AGL(1,ℤ/8)—24no—
24C2×C32×SD16C2211yescharacteristic
25C2×C32×SD16C2211yescharacteristic, complemented
26C2×C32×D8C2211yescharacteristic
27C2×C32×D8C2211yescharacteristic, complemented
28C2×C32×M16C2211yescharacteristic, complemented
29C3×#953—21no—
30C3×Q8×Dic3C2211yescharacteristic, complemented
31C2×C3×#215C2211yescharacteristic, complemented
32C3×#940C2211yescharacteristic
33C3×#939—21no—
34C3×#938—21no—
35C3×#938C2211yescharacteristic
36C3×#938C2211yescharacteristic, complemented
37C3×#937—21no—
38C3×#936—21no—
39C3×#936C2211yescharacteristic, complemented
40C3×D4×Dic3C2211yescharacteristic
41C2×C3×#214C2211yescharacteristic
42C2×C3×#214C2211yescharacteristic, complemented
43C2×C3×#213C2211yescharacteristic, complemented
44C3×#930C2211yescharacteristic
45C3×C4×#67—21no—
46C3×C4×#67C2211yescharacteristic
47C3×#924—21no—
48C3×#924C2211yescharacteristic, complemented
49C3×D3×SD16—24no—
50C2×C3×#204C2211yescharacteristic, complemented
51C2×C3×D3×C8C2211yescharacteristic, complemented
52C3×#835C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic
54C3×#832C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×#830C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#818C2211yescharacteristic, complemented
60C3×#816C2211yescharacteristic, complemented
61C3×#815C2211yescharacteristic, complemented
62C3×Dic3⋊C8C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—21no—
64C2×C3×AGL(1,ℤ/8)D311yescharacteristic, complemented
65C2×C3×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
66C22×C3×SD16—31no—
67C3×#548—31no—
68C3×D42—31no—
69#5831C2×C311yescharacteristic, complemented
70D4×#67C2×C311yescharacteristic, complemented
71C2×D3×SD16C2×C311yescharacteristic, complemented
72C3×#496—31no—
73C3×#468—31no—
74C3×#466—31no—
75C3×#463—31no—
76C3×#460—31no—
77C3×#450—31no—
78C3×#449—31no—
79C3×#448—31no—
80C3×#447—31no—
81C3×#440—31no—
82C3×#435—31no—
83#5238C2×C311yescharacteristic, complemented
84#5218C2×C311yescharacteristic, complemented
85#5170C2×C311yescharacteristic, complemented
86#5164C2×C311yescharacteristic, complemented
87#5163C2×C311yescharacteristic, complemented
88#5157C2×C311yescharacteristic, complemented
89#5156C2×C311yescharacteristic, complemented
90#5154C2×C311yescharacteristic, complemented
91#5153C2×C311yescharacteristic, complemented
92#5134C2×C311yescharacteristic, complemented
93#5127C2×C311yescharacteristic, complemented
94C24×C32—21no—
95C23×C3×D3—21no—
96C32×#41—22no—
97C32×#41—41no—
98C2×C32×Q8C2311yescharacteristic
99C2×C32×D4—22no—
100C2×C32×D4—21no—
101C2×C32×D4—21no—
102C2×C32×D4—41no—
103C2×C32×D4C2311yescharacteristic
104C2×C32×D4C2311yescharacteristic
105C2×C32×D4C2311yescharacteristic
106C22×C32×C4—21no—
107C22×C32×C4C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67—21no—
111C2×C3×#67—21no—
112C2×C3×#67—21no—
113C2×C3×#67—21no—
114C2×C3×#67—44no—
115C2×C3×#67D411yescharacteristic
116C22×C3×Dic3—21no—
117C3×D3×Q8—22no—
118C3×D3×Q8—41no—
119C3×D3×D4—22no—
120C3×D3×D4—41no—
121C2×C3×D12C2311yescharacteristic
122C2×C3×C4×D3—21no—
123C2×C3×C4×D3C2311yescharacteristic
124C2×C3×Dic6—21no—
125C2×C3×Dic6C2311yescharacteristic
126C32×SD16—22no—
127C32×SD16D414yescomplemented
128C32×D8—22no—
129C32×D8—22no—
130C32×M16—22no—
131C2×C32×C8C2311yescharacteristic
132C2×C32×C8C2311yescharacteristic
133C3×#217—21no—
134C3×#217—21no—
135C3×#217—21no—
136C3×#217—21no—
137C3×#217—21no—
138C3×#217—21no—
139C3×#217D411yescharacteristic
140C3×#215—22no—
141C3×#214—22no—
142C3×#214—41no—
143C3×#213—41no—
144C3×(C2×D3)⋊C4—21no—
145C3×(C2×D3)⋊C4D411yescharacteristic
146C3×C4⋊Dic3—21no—
147C3×C4⋊Dic3C2311yescharacteristic
148C3×C4⋊Dic3C2311yescharacteristic
149C3×Dic3⋊C4—21no—
150C3×Dic3⋊C4D411yescharacteristic
151C3×C4×Dic3—21no—
152C3×C4×Dic3C2311yescharacteristic
153C2×C3×C3⋊C8C2311yescharacteristic
154C2×C3×C3⋊C8C2311yescharacteristic
155C3×#204—22no—
156C3×D3×C8—22no—
157#3265—31noSylow
158C2×C3×#41—21no—
159C2×C3×#41C2×D311yescharacteristic, complemented
160C2×C3×#41C22×C311yescharacteristic, complemented
161C22×C3×Q8—31no—
162C22×C3×D4—21no—
163C22×C3×D4—31no—
164C22×C3×D4—61no—
165C22×C3×D4C2×D311yescharacteristic
166C22×C3×D4C22×C311yescharacteristic
167C22×#67—21no—
168C2×D3×Q8C22×C311yescharacteristic, complemented
169C2×D3×D4C22×C311yescharacteristic
170C3×AGL(1,ℤ/8)—28no—
171C3×AGL(1,ℤ/8)—24no—
172C3×AGL(1,ℤ/8)—24no—
173C2×C3×SD16—21no—
174C2×C3×SD16—21no—
175C2×C3×SD16—31no—
176C2×C3×SD16—31no—
177C2×C3×SD16—31no—
178C2×C3×SD16—31no—
179C2×C3×SD16—64no—
180C2×C3×SD16C2×D311yescharacteristic
181C2×C3×SD16C2×D311yescharacteristic, complemented
182C2×C3×SD16C22×C311yescharacteristic
183C2×C3×SD16C22×C311yescharacteristic, complemented
184C2×C3×D8—21no—
185C2×C3×D8—21no—
186C2×C3×D8—31no—
187C2×C3×D8C2×D311yescharacteristic
188C2×C3×D8C2×D311yescharacteristic, complemented
189C2×C3×D8C22×C311yescharacteristic
190C2×C3×D8C22×C311yescharacteristic, complemented
191C2×C3×M16—21no—
192C2×C3×M16C2×D311yescharacteristic, complemented
193C2×C3×M16C22×C311yescharacteristic, complemented
194C22×C3×C8—31no—
195C3×#127—31no—
196C3×#124—31no—
197C3×#124—61no—
198C3×C22⋊Q8—31no—
199C3×C22⋊Q8—61no—
200C3×#121—31no—
201C3×#121—31no—
202C3×#121—31no—
203C3×#121—61no—
204C3×#121—61no—
205C3×#120—61no—
206C3×#120—61no—
207C3×C4×Q8—31no—
208C3×C4×D4—31no—
209C3×C4×D4—31no—
210C3×C4×D4—61no—
211#953—21no—
212Q8×Dic3C22×C311yescharacteristic, complemented
213C2×#215C22×C311yescharacteristic, complemented
214#940C22×C311yescharacteristic
215#939—21no—
216#938—21no—
217#938C22×C311yescharacteristic
218#938C22×C311yescharacteristic, complemented
219#937—21no—
220#936—21no—
221#936C22×C311yescharacteristic, complemented
222D4×Dic3C22×C311yescharacteristic
223C2×#214C22×C311yescharacteristic
224C2×#214C22×C311yescharacteristic, complemented
225C2×#213C22×C311yescharacteristic, complemented
226#930C22×C311yescharacteristic
227C4×#67—21no—
228C4×#67C22×C311yescharacteristic
229#924—21no—
230#924C22×C311yescharacteristic, complemented
231D3×SD16—24no—
232C2×#204C22×C311yescharacteristic, complemented
233C2×D3×C8C22×C311yescharacteristic, complemented
234C3×#107—31no—
235C3×C4⋊C8—31no—
236C3×#103—31no—
237C3×#103—31no—
238C3×#102—31no—
239C3×#102—31no—
240C3×#102—31no—
241C3×#102—31no—
242C3×C22⋊C8—31no—
243C3×C22⋊C8—31no—
244C3×#97—31no—
245#835C22×C311yescharacteristic, complemented
246#832C22×C311yescharacteristic
247#832C22×C311yescharacteristic, complemented
248#832C22×C311yescharacteristic, complemented
249#830C22×C311yescharacteristic, complemented
250#821C22×C311yescharacteristic, complemented
251(C2×D3)⋊C8C22×C311yescharacteristic, complemented
252#818C22×C311yescharacteristic, complemented
253#816C22×C311yescharacteristic, complemented
254#815C22×C311yescharacteristic, complemented
255Dic3⋊C8C22×C311yescharacteristic, complemented
256C23×C32—21no—
257C23×C32—21no—
258C23×C32—21no—
259C23×C32—42no—
260C23×C32—42no—
261C23×C32—81no—
262C23×C32C2×D411yescharacteristic
263C22×C3×D3—21no—
264C22×C3×D3—42no—
265C22×C3×D3—42no—
266C22×C3×D3—81no—
267C22×C3×D3C2×D411yescharacteristic
268C32×Q8—21no—
269C32×Q8C2×D412yescomplemented
270C32×D4—21no—
271C32×D4—21no—
272C32×D4—21no—
273C32×D4—21no—
274C32×D4—21no—
275C32×D4—42no—
276C32×D4—42no—
277C32×D4C2×D412yes—
278C2×C32×C4—21no—
279C2×C32×C4—21no—
280C2×C32×C4—21no—
281C2×C32×C4—42no—
282C2×C32×C4C2×D411yescharacteristic
283C2×C32×C4C2411yescharacteristic
284C3×#67—22no—
285C3×#67—42no—
286C3×#67—42no—
287C3×#67—42no—
288C3×#67—42no—
289C3×#67—42no—
290C3×#67—81no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—42no—
295C2×C3×Dic3C2×D411yescharacteristic
296C2×C3×Dic3C2×D411yescharacteristic
297C2×C3×Dic3C2×D411yescharacteristic
298C3×D12—21no—
299C3×D12—21no—
300C3×C4×D3—21no—
301C3×C4×D3—21no—
302C3×C4×D3—42no—
303C3×Dic6—21no—
304C3×Dic6—21no—
305C3×Dic6—42no—
306C32×C8—21no—
307C32×C8C2×D412yescomplemented
308C3×C3⋊C8—21no—
309C3×C3⋊C8—21no—
310C2×AGL(1,ℤ/8)C3×D311yescharacteristic, complemented
311C22×SD16—31no—
312#548—31no—
313D42—31no—
314#496—31no—
315#468—31no—
316#466—31no—
317#463—31no—
318#460—31no—
319#450—31no—
320#449—31no—
321#448—31no—
322#447—31no—
323#440—31no—
324#435—31no—
325C24×C3—21no—
326C24×C3—21no—
327C24×C3—41no—
328C24×C3—61no—
329C23×D3—21no—
330C3×#41—24no—
331C3×#41—22no—
332C3×#41—22no—
333C3×#41—41no—
334C3×#41—41no—
335C3×#41—42no—
336C2×C3×Q8—21no—
337C2×C3×Q8—31no—
338C2×C3×Q8—61no—
339C2×C3×Q8—62no—
340C2×C3×Q8—121no—
341C2×C3×Q8C22×D311yescharacteristic
342C2×C3×Q8C23×C311yescharacteristic
343C2×C3×D4—24no—
344C2×C3×D4—22no—
345C2×C3×D4—22no—
346C2×C3×D4—21no—
347C2×C3×D4—21no—
348C2×C3×D4—21no—
349C2×C3×D4—21no—
350C2×C3×D4—21no—
351C2×C3×D4—21no—
352C2×C3×D4—21no—
353C2×C3×D4—31no—
354C2×C3×D4—31no—
355C2×C3×D4—41no—
356C2×C3×D4—41no—
357C2×C3×D4—41no—
358C2×C3×D4—41no—
359C2×C3×D4—42no—
360C2×C3×D4—61no—
361C2×C3×D4—61no—
362C2×C3×D4—61no—
363C2×C3×D4—62no—
364C2×C3×D4—61no—
365C2×C3×D4—61no—
366C2×C3×D4—61no—
367C2×C3×D4—121no—
368C2×C3×D4—124no—
369C2×C3×D4C22×D311yescharacteristic
370C2×C3×D4C22×D311yescharacteristic
371C2×C3×D4C22×D311yescharacteristic
372C2×C3×D4C23×C311yescharacteristic
373C2×C3×D4C23×C311yescharacteristic
374C2×C3×D4C23×C311yescharacteristic
375C22×C3×C4—21no—
376C22×C3×C4—21no—
377C22×C3×C4—21no—
378C22×C3×C4—31no—
379C22×C3×C4—41no—
380C22×C3×C4—61no—
381C22×C3×C4—61no—
382C22×C3×C4C22×D311yescharacteristic
383C22×C3×C4C23×C311yescharacteristic
384C2×#67—21no—
385C2×#67—21no—
386C2×#67—21no—
387C2×#67—21no—
388C2×#67—21no—
389C2×#67—21no—
390C2×#67—44no—
391C2×#67C3×D411yescharacteristic
392C22×Dic3—21no—
393D3×Q8—22no—
394D3×Q8—41no—
395D3×D4—22no—
396D3×D4—41no—
397C2×D12C23×C311yescharacteristic
398C2×C4×D3—21no—
399C2×C4×D3C23×C311yescharacteristic
400C2×Dic6—21no—
401C2×Dic6C23×C311yescharacteristic
402C3×SD16—24no—
403C3×SD16—22no—
404C3×SD16—22no—
405C3×SD16—24no—
406C3×SD16—62no—
407C3×SD16—62no—
408C3×SD16—62no—
409C3×SD16—121no—
410C3×SD16#6714yescomplemented
411C3×SD16C3×D414yescomplemented
412C3×D8—24no—
413C3×D8—24no—
414C3×D8—22no—
415C3×D8—22no—
416C3×D8—22no—
417C3×D8—22no—
418C3×D8—121no—
419C3×M16—24no—
420C3×M16—22no—
421C3×M16—22no—
422C2×C3×C8—21no—
423C2×C3×C8—21no—
424C2×C3×C8—31no—
425C2×C3×C8—31no—
426C2×C3×C8—62no—
427C2×C3×C8C22×D311yescharacteristic
428C2×C3×C8C22×D311yescharacteristic
429C2×C3×C8C23×C311yescharacteristic
430C2×C3×C8C23×C311yescharacteristic
431C3×C4⋊C4—31no—
432C3×C4⋊C4—31no—
433C3×C4⋊C4—31no—
434C3×C4⋊C4—61no—
435C3×C4⋊C4—61no—
436C3×C22⋊C4—31no—
437C3×C22⋊C4—31no—
438C3×C22⋊C4—61no—
439C3×C22⋊C4—61no—
440C3×C22⋊C4—61no—
441C3×C22⋊C4—61no—
442C3×C22⋊C4—61no—
443C3×C22⋊C4—61no—
444C3×C22⋊C4—61no—
445C3×C42—31no—
446C3×C42—61no—
447#217—21no—
448#217—21no—
449#217—21no—
450#217—21no—
451#217—21no—
452#217—21no—
453#217C3×D411yescharacteristic
454#215—22no—
455#214—22no—
456#214—41no—
457#213—41no—
458(C2×D3)⋊C4—21no—
459(C2×D3)⋊C4C3×D411yescharacteristic
460C4⋊Dic3—21no—
461C4⋊Dic3C23×C311yescharacteristic
462C4⋊Dic3C23×C311yescharacteristic
463Dic3⋊C4—21no—
464Dic3⋊C4C3×D411yescharacteristic
465C4×Dic3—21no—
466C4×Dic3C23×C311yescharacteristic
467C2×C3⋊C8C23×C311yescharacteristic
468C2×C3⋊C8C23×C311yescharacteristic
469#204—22no—
470D3×C8—22no—
471C22×C32—21no—
472C22×C32—22no—
473C22×C32—21no—
474C22×C32—21no—
475C22×C32—41no—
476C22×C32—41no—
477C22×C32—41no—
478C22×C32—41no—
479C22×C32—41no—
480C22×C32—41no—
481C22×C32—41no—
482C22×C32—41no—
483C22×C32—84no—
484C22×C32C22×D411yescharacteristic
485C2×C3×D3—21no—
486C2×C3×D3—21no—
487C2×C3×D3—41no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C2×C3×D3—84no—
491C2×C3×D3AGL(1,ℤ/8)12yescomplemented
492C32×C4—21no—
493C32×C4—22no—
494C32×C4C22×D411yescharacteristic
495C32×C4H(5,𝔽2)11yescharacteristic
496C3×Dic3—21no—
497C3×Dic3—21no—
498C3×Dic3—21no—
499C3×Dic3—41no—
500C3×Dic3—41no—
501C3×Dic3—41no—
502C2×#41C2×C3×D311yescharacteristic, complemented
503C22×Q8—31no—
504C22×D4—31no—
505C22×D4—61no—
506C22×D4C2×C3×D311yescharacteristic
507AGL(1,ℤ/8)—24no—
508C2×SD16—31no—
509C2×SD16—31no—
510C2×SD16—31no—
511C2×SD16—31no—
512C2×SD16—64no—
513C2×SD16C2×C3×D311yescharacteristic
514C2×SD16C2×C3×D311yescharacteristic, complemented
515C2×D8—31no—
516C2×D8C2×C3×D311yescharacteristic
517C2×D8C2×C3×D311yescharacteristic, complemented
518C2×M16C2×C3×D311yescharacteristic, complemented
519C22×C8—31no—
520#127—31no—
521#124—31no—
522#124—61no—
523C22⋊Q8—31no—
524C22⋊Q8—61no—
525#121—31no—
526#121—31no—
527#121—31no—
528#121—61no—
529#121—61no—
530#120—61no—
531#120—61no—
532C4×Q8—31no—
533C4×D4—31no—
534C4×D4—31no—
535C4×D4—61no—
536#107—31no—
537C4⋊C8—31no—
538#103—31no—
539#103—31no—
540#102—31no—
541#102—31no—
542#102—31no—
543#102—31no—
544C22⋊C8—31no—
545C22⋊C8—31no—
546#97—31no—
547C23×C3—21no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—31no—
555C23×C3—41no—
556C23×C3—41no—
557C23×C3—41no—
558C23×C3—42no—
559C23×C3—42no—
560C23×C3—42no—
561C23×C3—44no—
562C23×C3—42no—
563C23×C3—61no—
564C23×C3—82no—
565C23×C3—81no—
566C23×C3—81no—
567C23×C3—82no—
568C23×C3—122no—
569C23×C3—122no—
570C23×C3—241no—
571C23×C3D3×D411yescharacteristic
572C23×C3C2×C3×D411yescharacteristic
573C22×D3—21no—
574C22×D3—42no—
575C22×D3—42no—
576C22×D3—81no—
577C22×D3C2×C3×D411yescharacteristic
578C3×Q8—21no—
579C3×Q8—21no—
580C3×Q8—22no—
581C3×Q8—41no—
582C3×Q8—61no—
583C3×Q8—61no—
584C3×Q8—122no—
585C3×Q8C2×#6712yescomplemented
586C3×Q8C2×C3×D412yescomplemented
587C3×D4—22no—
588C3×D4—22no—
589C3×D4—21no—
590C3×D4—21no—
591C3×D4—21no—
592C3×D4—21no—
593C3×D4—21no—
594C3×D4—21no—
595C3×D4—21no—
596C3×D4—21no—
597C3×D4—21no—
598C3×D4—21no—
599C3×D4—22no—
600C3×D4—41no—
601C3×D4—41no—
602C3×D4—41no—
603C3×D4—42no—
604C3×D4—42no—
605C3×D4—42no—
606C3×D4—42no—
607C3×D4—44no—
608C3×D4—44no—
609C3×D4—62no—
610C3×D4—61no—
611C3×D4—61no—
612C3×D4—122no—
613C3×D4—122no—
614C3×D4—122no—
615C3×D4—122no—
616C3×D4—122no—
617C3×D4—241no—
618C3×D4C2×#6712yes—
619C3×D4C2×C3×D412yes—
620C2×C3×C4—22no—
621C2×C3×C4—22no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—31no—
631C2×C3×C4—31no—
632C2×C3×C4—31no—
633C2×C3×C4—41no—
634C2×C3×C4—42no—
635C2×C3×C4—42no—
636C2×C3×C4—44no—
637C2×C3×C4—61no—
638C2×C3×C4—61no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4—61no—
642C2×C3×C4—122no—
643C2×C3×C4—122no—
644C2×C3×C4D3×D411yescharacteristic
645C2×C3×C4C2×C3×D411yescharacteristic
646C2×C3×C4C23×D311yescharacteristic
647C2×C3×C4C24×C311yescharacteristic
648#67—22no—
649#67—42no—
650#67—42no—
651#67—42no—
652#67—42no—
653#67—42no—
654#67—81no—
655C2×Dic3—21no—
656C2×Dic3—21no—
657C2×Dic3—21no—
658C2×Dic3—42no—
659C2×Dic3C2×C3×D411yescharacteristic
660C2×Dic3C2×C3×D411yescharacteristic
661C2×Dic3C2×C3×D411yescharacteristic
662D12—21no—
663D12—21no—
664C4×D3—21no—
665C4×D3—21no—
666C4×D3—42no—
667Dic6—21no—
668Dic6—21no—
669Dic6—42no—
670C3×C8—22no—
671C3×C8—21no—
672C3×C8—21no—
673C3×C8—22no—
674C3×C8—61no—
675C3×C8—61no—
676C3×C8C2×#6712yescomplemented
677C3×C8C2×C3×D412yescomplemented
678C3⋊C8—21no—
679C3⋊C8—21no—
680C2×C32—41no—
681C2×C32—42no—
682C2×C32—81no—
683C2×C32—81no—
684C2×C32D4211yescharacteristic
685C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
686C2×C32#57711yescharacteristic
687C3×D3—22no—
688C3×D3—81no—
689C24—21no—
690C24—61no—
691#41—22no—
692#41—41no—
693C2×Q8—31no—
694C2×Q8—61no—
695C2×Q8—62no—
696C2×Q8—121no—
697C2×Q8C22×C3×D311yescharacteristic
698C2×D4—22no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—31no—
702C2×D4—31no—
703C2×D4—41no—
704C2×D4—61no—
705C2×D4—61no—
706C2×D4—61no—
707C2×D4—62no—
708C2×D4—61no—
709C2×D4—61no—
710C2×D4—61no—
711C2×D4—121no—
712C2×D4—124no—
713C2×D4C22×C3×D311yescharacteristic
714C2×D4C22×C3×D311yescharacteristic
715C2×D4C22×C3×D311yescharacteristic
716C22×C4—21no—
717C22×C4—31no—
718C22×C4—61no—
719C22×C4—61no—
720C22×C4C22×C3×D311yescharacteristic
721SD16—22no—
722SD16—62no—
723SD16—62no—
724SD16—62no—
725SD16—121no—
726SD16C3×#6714yescomplemented
727D8—22no—
728D8—22no—
729D8—121no—
730M16—22no—
731C2×C8—31no—
732C2×C8—31no—
733C2×C8—62no—
734C2×C8C22×C3×D311yescharacteristic
735C2×C8C22×C3×D311yescharacteristic
736C4⋊C4—31no—
737C4⋊C4—31no—
738C4⋊C4—31no—
739C4⋊C4—61no—
740C4⋊C4—61no—
741C22⋊C4—31no—
742C22⋊C4—31no—
743C22⋊C4—61no—
744C22⋊C4—61no—
745C22⋊C4—61no—
746C22⋊C4—61no—
747C22⋊C4—61no—
748C22⋊C4—61no—
749C22⋊C4—61no—
750C42—31no—
751C42—61no—
752C22×C3—22no—
753C22×C3—21no—
754C22×C3—21no—
755C22×C3—21no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—22no—
759C22×C3—22no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—32no—
763C22×C3—41no—
764C22×C3—41no—
765C22×C3—42no—
766C22×C3—42no—
767C22×C3—42no—
768C22×C3—41no—
769C22×C3—41no—
770C22×C3—41no—
771C22×C3—41no—
772C22×C3—41no—
773C22×C3—41no—
774C22×C3—41no—
775C22×C3—41no—
776C22×C3—41no—
777C22×C3—41no—
778C22×C3—41no—
779C22×C3—41no—
780C22×C3—41no—
781C22×C3—41no—
782C22×C3—41no—
783C22×C3—41no—
784C22×C3—61no—
785C22×C3—61no—
786C22×C3—81no—
787C22×C3—81no—
788C22×C3—81no—
789C22×C3—81no—
790C22×C3—81no—
791C22×C3—81no—
792C22×C3—84no—
793C22×C3—84no—
794C22×C3—88no—
795C22×C3—121no—
796C22×C3—121no—
797C22×C3—121no—
798C22×C3—244no—
799C22×C3C2×D3×D411yescharacteristic
800C22×C3C22×C3×D411yescharacteristic
801C2×D3—21no—
802C2×D3—21no—
803C2×D3—41no—
804C2×D3—41no—
805C2×D3—41no—
806C2×D3—84no—
807C2×D3C3×AGL(1,ℤ/8)12yescomplemented
808C3×C4—22no—
809C3×C4—21no—
810C3×C4—22no—
811C3×C4—22no—
812C3×C4—21no—
813C3×C4—21no—
814C3×C4—21no—
815C3×C4—42no—
816C3×C4—61no—
817C3×C4—61no—
818C3×C4—61no—
819C3×C4—121no—
820C3×C4—121no—
821C3×C4—121no—
822C3×C4#100411yescharacteristic
823C3×C4C22×#6711yescharacteristic
824C3×C4C22×C3×D411yescharacteristic
825C3×C4C3×H(5,𝔽2)11yescharacteristic
826Dic3—21no—
827Dic3—21no—
828Dic3—21no—
829Dic3—41no—
830Dic3—41no—
831Dic3—41no—
832C32#326511yescharacteristic, complemented, Sylow
833C23—21no—
834C23—21no—
835C23—21no—
836C23—31no—
837C23—42no—
838C23—42no—
839C23—61no—
840C23—81no—
841C23—122no—
842C23—122no—
843C23—241no—
844C23C3×D3×D411yescharacteristic
845Q8—21no—
846Q8—61no—
847Q8—61no—
848Q8—122no—
849Q8C2×C3×#6712yescomplemented
850D4—21no—
851D4—21no—
852D4—21no—
853D4—21no—
854D4—21no—
855D4—42no—
856D4—42no—
857D4—62no—
858D4—61no—
859D4—61no—
860D4—122no—
861D4—122no—
862D4—122no—
863D4—122no—
864D4—122no—
865D4—241no—
866D4C2×C3×#6712yes—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—31no—
871C2×C4—31no—
872C2×C4—31no—
873C2×C4—42no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—61no—
878C2×C4—61no—
879C2×C4—122no—
880C2×C4—122no—
881C2×C4C3×D3×D411yescharacteristic
882C2×C4C23×C3×D311yescharacteristic
883C8—21no—
884C8—61no—
885C8—61no—
886C8C2×C3×#6712yescomplemented
887C2×C3—21no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—42no—
891C2×C3—42no—
892C2×C3—41no—
893C2×C3—41no—
894C2×C3—42no—
895C2×C3—62no—
896C2×C3—82no—
897C2×C3—82no—
898C2×C3—82no—
899C2×C3—81no—
900C2×C3—81no—
901C2×C3—81no—
902C2×C3—81no—
903C2×C3—241no—
904C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
905C2×C3#577511yescharacteristic
906C2×C3D4×#6711yescharacteristic
907C2×C3C3×D4211yescharacteristic
908C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
909C2×C3C3×#57711yescharacteristic
910D3—22no—
911D3—81no—
912C22—21no—
913C22—21no—
914C22—21no—
915C22—22no—
916C22—32no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—61no—
926C22—61no—
927C22—84no—
928C22—121no—
929C22—121no—
930C22—121no—
931C22—244no—
932C22C2×C3×D3×D411yescharacteristic
933C4—21no—
934C4—22no—
935C4—61no—
936C4—61no—
937C4—61no—
938C4—121no—
939C4—121no—
940C4—121no—
941C4C3×#100411yescharacteristic
942C4C22×C3×#6711yescharacteristic
943C3—21no—
944C3#8395311yescharacteristic, direct product factor
945C3C3×#326511yescharacteristic, complemented
946C2—41no—
947C2—42no—
948C2—62no—
949C2—81no—
950C2—81no—
951C2—241no—
952C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
953C2C3×#577511yescharacteristic
954C2C3×D4×#6711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×AGL(1,ℤ/8)C2
socleC22×C32C22×D4
hypercenterC2×C3×AGL(1,ℤ/8)D3
hypocenterC3C3×#3265
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×C32×AGL(1,ℤ/8)C2semidirect
2. C3×#5831C2semidirect
3. C3×D4×#67C2semidirect
4. C2×C3×D3×SD16C2semidirect
5. C3×#5238C2semidirect
6. C3×#5218C2semidirect
7. C3×#5170C2semidirect
8. C3×#5164C2semidirect
9. C3×#5163C2semidirect
10. C3×#5157C2semidirect
11. C3×#5156C2semidirect
12. C3×#5154C2semidirect
13. C3×#5153C2semidirect
14. C3×#5134C2semidirect
15. C3×#5127C2semidirect
17. #83953C3direct (N × H)
18. C2×C32×#41C22semidirect
21. C2×C3×D3×Q8C22semidirect
25. C2×C32×SD16C22semidirect
27. C2×C32×D8C22semidirect
28. C2×C32×M16C22semidirect
30. C3×Q8×Dic3C22semidirect
31. C2×C3×#215C22semidirect
36. C3×#938C22semidirect
39. C3×#936C22semidirect
42. C2×C3×#214C22semidirect
43. C2×C3×#213C22semidirect
48. C3×#924C22semidirect
50. C2×C3×#204C22semidirect
51. C2×C3×D3×C8C22semidirect
52. C3×#835C22semidirect
54. C3×#832C22semidirect
55. C3×#832C22semidirect
56. C3×#830C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#818C22semidirect
60. C3×#816C22semidirect
61. C3×#815C22semidirect
62. C3×Dic3⋊C8C22semidirect
64. C2×C3×AGL(1,ℤ/8)D3semidirect
65. C2×C3×AGL(1,ℤ/8)C2×C3semidirect
69. #5831C2×C3semidirect
70. D4×#67C2×C3semidirect
71. C2×D3×SD16C2×C3semidirect
83. #5238C2×C3semidirect
84. #5218C2×C3semidirect
85. #5170C2×C3semidirect
86. #5164C2×C3semidirect
87. #5163C2×C3semidirect
88. #5157C2×C3semidirect
89. #5156C2×C3semidirect
90. #5154C2×C3semidirect
91. #5153C2×C3semidirect
92. #5134C2×C3semidirect
93. #5127C2×C3semidirect
127. C32×SD16D4semidirect
159. C2×C3×#41C2×D3semidirect
160. C2×C3×#41C22×C3semidirect
168. C2×D3×Q8C22×C3semidirect
181. C2×C3×SD16C2×D3semidirect
183. C2×C3×SD16C22×C3semidirect
188. C2×C3×D8C2×D3semidirect
190. C2×C3×D8C22×C3semidirect
192. C2×C3×M16C2×D3semidirect
193. C2×C3×M16C22×C3semidirect
212. Q8×Dic3C22×C3semidirect
213. C2×#215C22×C3semidirect
218. #938C22×C3semidirect
221. #936C22×C3semidirect
224. C2×#214C22×C3semidirect
225. C2×#213C22×C3semidirect
230. #924C22×C3semidirect
232. C2×#204C22×C3semidirect
233. C2×D3×C8C22×C3semidirect
245. #835C22×C3semidirect
247. #832C22×C3semidirect
248. #832C22×C3semidirect
249. #830C22×C3semidirect
250. #821C22×C3semidirect
251. (C2×D3)⋊C8C22×C3semidirect
252. #818C22×C3semidirect
253. #816C22×C3semidirect
254. #815C22×C3semidirect
255. Dic3⋊C8C22×C3semidirect
269. C32×Q8C2×D4semidirect
307. C32×C8C2×D4semidirect
310. C2×AGL(1,ℤ/8)C3×D3semidirect
410. C3×SD16#67semidirect
411. C3×SD16C3×D4semidirect
491. C2×C3×D3AGL(1,ℤ/8)semidirect
502. C2×#41C2×C3×D3semidirect
514. C2×SD16C2×C3×D3semidirect
517. C2×D8C2×C3×D3semidirect
518. C2×M16C2×C3×D3semidirect
585. C3×Q8C2×#67semidirect
586. C3×Q8C2×C3×D4semidirect
676. C3×C8C2×#67semidirect
677. C3×C8C2×C3×D4semidirect
726. SD16C3×#67semidirect
807. C2×D3C3×AGL(1,ℤ/8)semidirect
832. C32#3265semidirect
849. Q8C2×C3×#67semidirect
886. C8C2×C3×#67semidirect
944. C3#83953direct (N × H)
945. C3C3×#3265semidirect

Maximal subgroups

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

subgroupindex
C2×C32×AGL(1,ℤ/8)2
C3×#58312
C3×D4×#672
C2×C3×D3×SD162
C3×#52382
C3×#52182
C3×#51702
C3×#51642
C3×#51632
C3×#51572
C3×#51562
C3×#51542
C3×#51532
C3×#51342
C3×#51272
C3×#32653
#839533