Finite Group Databasebeta

← C3×#80166 #11883770

Subgroups — C3×#80166 #11883770

Order 1152.

1230 conjugacy classes of subgroups.

The subgroup lattice has 971 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×#67C211yesmaximal, characteristic, complemented
2C22×C3×#213C211yesmaximal, characteristic, complemented
3C2×C3×#914C211yesmaximal, characteristic, complemented
4C3×#5630C211yesmaximal, characteristic, complemented
5C32×#450C211yesmaximal, characteristic, complemented
6C3×#5176C211yesmaximal, characteristic, complemented
7C3×#5172C211yesmaximal, characteristic, complemented
8C3×#5165C211yesmaximal, characteristic, complemented
9C3×#5048C211yesmaximal, characteristic, complemented
10C3×#4786C211yesmaximal, characteristic, complemented
11C3×#4785C211yesmaximal, characteristic, complemented
12C3×#4782C211yesmaximal, characteristic, complemented
13C3×#4773C211yesmaximal, characteristic, complemented
14C3×#4732C211yesmaximal, characteristic, complemented
15C3×#4730C211yesmaximal, characteristic, complemented
16C3×#3264—31nomaximal
17#80166C311yesmaximal, characteristic, direct product factor
18C22×C32×D4C2211yescharacteristic
19C22×C3×#67—21no—
20C2×C3×#239C2211yescharacteristic, complemented
21C2×C3×D3×D4C2211yescharacteristic, complemented
22C22×C3×D12C2211yescharacteristic, complemented
23C2×C32×SD16C2211yescharacteristic, complemented
24C2×C32×SD16C2211yescharacteristic, complemented
25C32×C22⋊Q8C2211yescharacteristic, complemented
26C3×#953—21no—
27C3×#947C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic, complemented
29C3×#940C2211yescharacteristic, complemented
30C3×#939—21no—
31C3×#938C2211yescharacteristic, complemented
32C3×#937—21no—
33C3×D4×Dic3C2211yescharacteristic, complemented
34C2×C3×#213—24no—
35C2×C3×#213C2211yescharacteristic
36C2×C3×#213C2211yescharacteristic
37C2×C3×#213C2211yescharacteristic, complemented
38C2×C3×#213C2211yescharacteristic, complemented
39C3×#930C2211yescharacteristic
40C3×C4×#67C2211yescharacteristic
41C22×C3×C3⋊C8C2211yescharacteristic, complemented
42C3×#914—24no—
43C2×C3×D24C2211yescharacteristic, complemented
44C2×C3×D24C2211yescharacteristic, complemented
45C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
46C3×#895—21no—
47C3×#895C2211yescharacteristic, complemented
48C3×#894—21no—
49C3×#893C2211yescharacteristic, complemented
50C3×#882—21no—
51C3×D3×C22⋊C4—21no—
52C32×#102C2211yescharacteristic, complemented
53C32×#102C2211yescharacteristic, complemented
54C32×C22⋊C8C2211yescharacteristic, complemented
55C3×#835C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#815C2211yescharacteristic, complemented
60C3×Dic3⋊C8C2211yescharacteristic, complemented
61C3×#809C2211yescharacteristic, complemented
62C3×#808C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64C22×C3×D8—31no—
65C3×#546—31no—
66C3×D42—31no—
67D4×#67C2×C311yescharacteristic, complemented
68C22×#213C2×C311yescharacteristic, complemented
69C2×#914C2×C311yescharacteristic, complemented
70#5630C2×C311yescharacteristic, complemented
71C3×#496—31no—
72C3×#469—31no—
73C3×#465—31no—
74C3×#463—31no—
75C3×#459—31no—
76C3×#450—21no—
77C3×#450D311yescharacteristic, complemented
78C3×#450C2×C311yescharacteristic, complemented
79C3×#449—31no—
80C3×#447—31no—
81C3×#447—31no—
82C3×#442—31no—
83C3×#435—31no—
84#5176C2×C311yescharacteristic, complemented
85#5172C2×C311yescharacteristic, complemented
86#5165C2×C311yescharacteristic, complemented
87#5048C2×C311yescharacteristic, complemented
88#4786C2×C311yescharacteristic, complemented
89#4785C2×C311yescharacteristic, complemented
90#4782C2×C311yescharacteristic, complemented
91#4773C2×C311yescharacteristic, complemented
92#4732C2×C311yescharacteristic, complemented
93#4730C2×C311yescharacteristic, complemented
94C24×C32—21no—
95C23×C3×D3—21no—
96C23×C3×D3—21no—
97C2×C32×Q8C2311yescharacteristic
98C2×C32×D4—22no—
99C2×C32×D4—21no—
100C2×C32×D4—41no—
101C2×C32×D4C2311yescharacteristic
102C2×C32×D4C2311yescharacteristic
103C22×C32×C4C2311yescharacteristic
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C2×C3×#67—44no—
110C2×C3×#67D411yescharacteristic
111C22×C3×Dic3—21no—
112C3×#239—22no—
113C3×#239—41no—
114C3×D3×D4—22no—
115C3×D3×D4—41no—
116C2×C3×D12—22no—
117C2×C3×D12—21no—
118C2×C3×D12—21no—
119C2×C3×D12—21no—
120C2×C3×D12—41no—
121C2×C3×D12C2311yescharacteristic
122C2×C3×D12C2311yescharacteristic
123C2×C3×D12C2311yescharacteristic
124C2×C3×C4×D3—21no—
125C2×C3×C4×D3—21no—
126C2×C3×C4×D3C2311yescharacteristic
127C32×SD16—22no—
128C32×SD16—41no—
129C2×C32×C8C2311yescharacteristic
130C2×C32×C8C2311yescharacteristic
131C32×C4⋊C4—21no—
132C32×C4⋊C4C2311yescharacteristic
133C32×C22⋊C4—21no—
134C3×#217—21no—
135C3×#217—21no—
136C3×#217D411yescharacteristic
137C3×#215—22no—
138C3×#213—22no—
139C3×#213—22no—
140C3×#213—22no—
141C3×#213D414yescomplemented
142C3×(C2×D3)⋊C4—21no—
143C3×(C2×D3)⋊C4—21no—
144C3×(C2×D3)⋊C4—21no—
145C3×(C2×D3)⋊C4—21no—
146C3×(C2×D3)⋊C4—21no—
147C3×(C2×D3)⋊C4D411yescharacteristic
148C3×C4⋊Dic3C2311yescharacteristic
149C3×Dic3⋊C4D411yescharacteristic
150C3×C4×Dic3C2311yescharacteristic
151C2×C3×C3⋊C8—22no—
152C2×C3×C3⋊C8C2311yescharacteristic
153C2×C3×C3⋊C8C2311yescharacteristic
154C3×D24—22no—
155C3×D24—41no—
156C3×ΓL(1,𝔽25)—22no—
157#3264—31noSylow
158C2×C3×#41—31no—
159C22×C3×D4—21no—
160C22×C3×D4—31no—
161C22×C3×D4—31no—
162C22×C3×D4—61no—
163C22×C3×D4C2×D311yescharacteristic
164C22×C3×D4C22×C311yescharacteristic
165C22×#67—21no—
166C2×#239C22×C311yescharacteristic, complemented
167C2×D3×D4C22×C311yescharacteristic, complemented
168C22×D12C22×C311yescharacteristic, complemented
169C3×AGL(1,ℤ/8)—64no—
170C2×C3×SD16—21no—
171C2×C3×SD16—21no—
172C2×C3×SD16—31no—
173C2×C3×SD16C2×D311yescharacteristic, complemented
174C2×C3×SD16C2×D311yescharacteristic, complemented
175C2×C3×SD16C22×C311yescharacteristic, complemented
176C2×C3×SD16C22×C311yescharacteristic, complemented
177C2×C3×D8—31no—
178C2×C3×D8—31no—
179C2×C3×D8—31no—
180C2×C3×D8—31no—
181C2×C3×D8—31no—
182C2×C3×D8—31no—
183C2×C3×D8—64no—
184C2×C3×M16—31no—
185C22×C3×C8—31no—
186C3×#127—31no—
187C3×#124—31no—
188C3×#123—61no—
189C3×C22⋊Q8—21no—
190C3×C22⋊Q8C2×D311yescharacteristic, complemented
191C3×C22⋊Q8C22×C311yescharacteristic, complemented
192C3×#121—31no—
193C3×#121—31no—
194C3×#121—31no—
195C3×#121—61no—
196C3×#121—61no—
197C3×#120—61no—
198C3×#120—61no—
199C3×#120—61no—
200C3×C4×D4—31no—
201C3×C4×D4—31no—
202C3×C4×D4—31no—
203C2×C3×C22⋊C4—61no—
204#953—21no—
205#947C22×C311yescharacteristic, complemented
206C2×#215C22×C311yescharacteristic, complemented
207#940C22×C311yescharacteristic, complemented
208#939—21no—
209#938C22×C311yescharacteristic, complemented
210#937—21no—
211D4×Dic3C22×C311yescharacteristic, complemented
212C2×#213—24no—
213C2×#213C22×C311yescharacteristic
214C2×#213C22×C311yescharacteristic
215C2×#213C22×C311yescharacteristic, complemented
216C2×#213C22×C311yescharacteristic, complemented
217#930C22×C311yescharacteristic
218C4×#67C22×C311yescharacteristic
219C22×C3⋊C8C22×C311yescharacteristic, complemented
220#914—24no—
221C2×D24C22×C311yescharacteristic, complemented
222C2×D24C22×C311yescharacteristic, complemented
223C2×ΓL(1,𝔽25)C22×C311yescharacteristic, complemented
224#895—21no—
225#895C22×C311yescharacteristic, complemented
226#894—21no—
227#893C22×C311yescharacteristic, complemented
228#882—21no—
229D3×C22⋊C4—21no—
230C3×#106—31no—
231C3×C4⋊C8—31no—
232C3×#103—31no—
233C3×#102—21no—
234C3×#102—21no—
235C3×#102—31no—
236C3×#102—31no—
237C3×#102—31no—
238C3×#102C2×D311yescharacteristic, complemented
239C3×#102C2×D311yescharacteristic, complemented
240C3×#102C22×C311yescharacteristic, complemented
241C3×#102C22×C311yescharacteristic, complemented
242C3×C22⋊C8—21no—
243C3×C22⋊C8—31no—
244C3×C22⋊C8C2×D311yescharacteristic, complemented
245C3×C22⋊C8C22×C311yescharacteristic, complemented
246C3×#97—31no—
247#835C22×C311yescharacteristic, complemented
248#821C22×C311yescharacteristic, complemented
249#821C22×C311yescharacteristic, complemented
250(C2×D3)⋊C8C22×C311yescharacteristic, complemented
251#815C22×C311yescharacteristic, complemented
252Dic3⋊C8C22×C311yescharacteristic, complemented
253#809C22×C311yescharacteristic, complemented
254#808C22×C311yescharacteristic, complemented
255C23×C32—21no—
256C23×C32—21no—
257C23×C32—42no—
258C23×C32—42no—
259C23×C32—81no—
260C23×C32C2×D411yescharacteristic
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—21no—
264C22×C3×D3—42no—
265C22×C3×D3—42no—
266C22×C3×D3—42no—
267C22×C3×D3—42no—
268C22×C3×D3—81no—
269C22×C3×D3—81no—
270C22×C3×D3C2×D411yescharacteristic
271C32×Q8—21no—
272C32×Q8—21no—
273C32×D4—21no—
274C32×D4—21no—
275C32×D4—21no—
276C32×D4—42no—
277C32×D4C2×D412yes—
278C2×C32×C4—21no—
279C2×C32×C4—21no—
280C2×C32×C4—21no—
281C2×C32×C4—21no—
282C2×C32×C4C2×D411yescharacteristic
283C2×C32×C4C2411yescharacteristic
284C3×#67—22no—
285C3×#67—42no—
286C3×#67—42no—
287C3×#67—42no—
288C3×#67—42no—
289C3×#67—81no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—42no—
292C2×C3×Dic3C2×D411yescharacteristic
293C2×C3×Dic3C2×D411yescharacteristic
294C2×C3×Dic3C2×D411yescharacteristic
295C3×D12—21no—
296C3×D12—21no—
297C3×D12—21no—
298C3×D12—21no—
299C3×D12—21no—
300C3×D12—42no—
301C3×D12—42no—
302C3×D12—81no—
303C3×D12C2×D412yescomplemented
304C3×C4×D3—21no—
305C3×C4×D3—21no—
306C3×C4×D3—42no—
307C3×C4×D3—81no—
308C32×C8—21no—
309C32×C8—21no—
310C3×C3⋊C8—21no—
311C3×C3⋊C8C2×D412yescomplemented
312C2×AGL(1,ℤ/8)—31no—
313C22×D8—31no—
314#546—31no—
315D42—31no—
316#496—31no—
317#469—31no—
318#465—31no—
319#463—31no—
320#459—31no—
321#450C3×D311yescharacteristic, complemented
322#449—31no—
323#447—31no—
324#447—31no—
325#442—31no—
326#435—31no—
327C24×C3—21no—
328C24×C3—21no—
329C24×C3—41no—
330C24×C3—61no—
331C24×C3—61no—
332C23×D3—21no—
333C23×D3—21no—
334C3×#41—62no—
335C3×#41—121no—
336C2×C3×Q8—21no—
337C2×C3×Q8C22×D311yescharacteristic
338C2×C3×Q8C23×C311yescharacteristic
339C2×C3×D4—22no—
340C2×C3×D4—22no—
341C2×C3×D4—21no—
342C2×C3×D4—21no—
343C2×C3×D4—21no—
344C2×C3×D4—21no—
345C2×C3×D4—31no—
346C2×C3×D4—31no—
347C2×C3×D4—31no—
348C2×C3×D4—31no—
349C2×C3×D4—41no—
350C2×C3×D4—42no—
351C2×C3×D4—41no—
352C2×C3×D4—41no—
353C2×C3×D4—42no—
354C2×C3×D4—62no—
355C2×C3×D4—61no—
356C2×C3×D4—61no—
357C2×C3×D4—61no—
358C2×C3×D4—61no—
359C2×C3×D4—61no—
360C2×C3×D4—62no—
361C2×C3×D4—61no—
362C2×C3×D4—61no—
363C2×C3×D4—61no—
364C2×C3×D4—121no—
365C2×C3×D4—121no—
366C2×C3×D4—124no—
367C2×C3×D4C22×D311yescharacteristic
368C2×C3×D4C22×D311yescharacteristic
369C2×C3×D4C23×C311yescharacteristic
370C2×C3×D4C23×C311yescharacteristic
371C22×C3×C4—21no—
372C22×C3×C4—31no—
373C22×C3×C4—61no—
374C22×C3×C4—61no—
375C22×C3×C4—61no—
376C22×C3×C4C22×D311yescharacteristic
377C22×C3×C4C23×C311yescharacteristic
378C2×#67—21no—
379C2×#67—21no—
380C2×#67—21no—
381C2×#67—21no—
382C2×#67—21no—
383C2×#67—44no—
384C2×#67C3×D411yescharacteristic
385C22×Dic3—21no—
386#239—22no—
387#239—41no—
388D3×D4—22no—
389D3×D4—41no—
390C2×D12—22no—
391C2×D12—21no—
392C2×D12—21no—
393C2×D12—21no—
394C2×D12—41no—
395C2×D12C23×C311yescharacteristic
396C2×D12C23×C311yescharacteristic
397C2×D12C23×C311yescharacteristic
398C2×C4×D3—21no—
399C2×C4×D3—21no—
400C2×C4×D3C23×C311yescharacteristic
401C3×SD16—22no—
402C3×SD16—22no—
403C3×SD16—42no—
404C3×SD16—41no—
405C3×SD16—41no—
406C3×SD16—42no—
407C3×SD16—62no—
408C3×D8—34no—
409C3×D8—62no—
410C3×D8—62no—
411C3×D8—62no—
412C3×D8—62no—
413C3×D8—121no—
414C3×M16—62no—
415C2×C3×C8—21no—
416C2×C3×C8—21no—
417C2×C3×C8—31no—
418C2×C3×C8—31no—
419C2×C3×C8—62no—
420C2×C3×C8C22×D311yescharacteristic
421C2×C3×C8C22×D311yescharacteristic
422C2×C3×C8C23×C311yescharacteristic
423C2×C3×C8C23×C311yescharacteristic
424C3×C4⋊C4—21no—
425C3×C4⋊C4—21no—
426C3×C4⋊C4—21no—
427C3×C4⋊C4—31no—
428C3×C4⋊C4—31no—
429C3×C4⋊C4—41no—
430C3×C4⋊C4C22×D311yescharacteristic
431C3×C4⋊C4C23×C311yescharacteristic
432C3×C22⋊C4—21no—
433C3×C22⋊C4—21no—
434C3×C22⋊C4—31no—
435C3×C22⋊C4—31no—
436C3×C22⋊C4—41no—
437C3×C22⋊C4—61no—
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×C42—31no—
445#217—21no—
446#217—21no—
447#217C3×D411yescharacteristic
448#215—22no—
449#213—22no—
450#213—22no—
451#213—22no—
452#213C3×D414yescomplemented
453(C2×D3)⋊C4—21no—
454(C2×D3)⋊C4—21no—
455(C2×D3)⋊C4—21no—
456(C2×D3)⋊C4—21no—
457(C2×D3)⋊C4—21no—
458(C2×D3)⋊C4C3×D411yescharacteristic
459C4⋊Dic3C23×C311yescharacteristic
460Dic3⋊C4C3×D411yescharacteristic
461C4×Dic3C23×C311yescharacteristic
462C2×C3⋊C8—22no—
463C2×C3⋊C8C23×C311yescharacteristic
464C2×C3⋊C8C23×C311yescharacteristic
465D24—22no—
466D24—41no—
467ΓL(1,𝔽25)—22no—
468C22×C32—21no—
469C22×C32—21no—
470C22×C32—22no—
471C22×C32—41no—
472C22×C32—41no—
473C22×C32—41no—
474C22×C32—41no—
475C22×C32—41no—
476C22×C32—84no—
477C22×C32AGL(1,ℤ/8)12yescomplemented
478C22×C32C22×D411yescharacteristic
479C2×C3×D3—21no—
480C2×C3×D3—22no—
481C2×C3×D3—21no—
482C2×C3×D3—21no—
483C2×C3×D3—41no—
484C2×C3×D3—41no—
485C2×C3×D3—41no—
486C2×C3×D3—41no—
487C2×C3×D3—41no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C2×C3×D3—41no—
491C2×C3×D3—84no—
492C2×C3×D3—84no—
493C32×C4—21no—
494C32×C4—41no—
495C32×C4—41no—
496C32×C4C22×D411yescharacteristic
497C32×C4H(5,𝔽2)11yescharacteristic
498C3×Dic3—21no—
499C3×Dic3—21no—
500C3×Dic3—21no—
501C3×Dic3—41no—
502C2×#41—31no—
503C22×D4—31no—
504C22×D4—31no—
505C22×D4—61no—
506C22×D4C2×C3×D311yescharacteristic
507AGL(1,ℤ/8)—64no—
508C2×SD16—31no—
509C2×SD16C2×C3×D311yescharacteristic, complemented
510C2×SD16C2×C3×D311yescharacteristic, complemented
511C2×D8—31no—
512C2×D8—31no—
513C2×D8—31no—
514C2×D8—31no—
515C2×D8—31no—
516C2×D8—31no—
517C2×D8—64no—
518C2×M16—31no—
519C22×C8—31no—
520#127—31no—
521#124—31no—
522#123—61no—
523C22⋊Q8C2×C3×D311yescharacteristic, complemented
524#121—31no—
525#121—31no—
526#121—31no—
527#121—61no—
528#121—61no—
529#120—61no—
530#120—61no—
531#120—61no—
532C4×D4—31no—
533C4×D4—31no—
534C4×D4—31no—
535C2×C22⋊C4—61no—
536#106—31no—
537C4⋊C8—31no—
538#103—31no—
539#102—31no—
540#102—31no—
541#102—31no—
542#102C2×C3×D311yescharacteristic, complemented
543#102C2×C3×D311yescharacteristic, complemented
544C22⋊C8—31no—
545C22⋊C8C2×C3×D311yescharacteristic, complemented
546#97—31no—
547C23×C3—21no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—31no—
553C23×C3—41no—
554C23×C3—41no—
555C23×C3—42no—
556C23×C3—42no—
557C23×C3—44no—
558C23×C3—42no—
559C23×C3—42no—
560C23×C3—61no—
561C23×C3—61no—
562C23×C3—61no—
563C23×C3—82no—
564C23×C3—81no—
565C23×C3—81no—
566C23×C3—82no—
567C23×C3—122no—
568C23×C3—122no—
569C23×C3—122no—
570C23×C3—122no—
571C23×C3—241no—
572C23×C3—241no—
573C23×C3D3×D411yescharacteristic
574C23×C3C2×C3×D411yescharacteristic
575C22×D3—21no—
576C22×D3—21no—
577C22×D3—21no—
578C22×D3—42no—
579C22×D3—42no—
580C22×D3—42no—
581C22×D3—42no—
582C22×D3—81no—
583C22×D3—81no—
584C22×D3C2×C3×D411yescharacteristic
585C3×Q8—21no—
586C3×Q8—21no—
587C3×Q8—21no—
588C3×Q8—21no—
589C3×Q8—41no—
590C3×Q8—41no—
591C3×D4—22no—
592C3×D4—21no—
593C3×D4—21no—
594C3×D4—21no—
595C3×D4—21no—
596C3×D4—21no—
597C3×D4—21no—
598C3×D4—22no—
599C3×D4—32no—
600C3×D4—41no—
601C3×D4—41no—
602C3×D4—42no—
603C3×D4—42no—
604C3×D4—44no—
605C3×D4—62no—
606C3×D4—61no—
607C3×D4—61no—
608C3×D4—61no—
609C3×D4—61no—
610C3×D4—61no—
611C3×D4—122no—
612C3×D4—122no—
613C3×D4—122no—
614C3×D4—122no—
615C3×D4—122no—
616C3×D4—122no—
617C3×D4—241no—
618C3×D4—241no—
619C3×D4D3×D412yes—
620C3×D4C2×C3×D412yes—
621C2×C3×C4—21no—
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—21no—
631C2×C3×C4—31no—
632C2×C3×C4—31no—
633C2×C3×C4—31no—
634C2×C3×C4—41no—
635C2×C3×C4—41no—
636C2×C3×C4—41no—
637C2×C3×C4—41no—
638C2×C3×C4—61no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4—122no—
642C2×C3×C4—122no—
643C2×C3×C4—241no—
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—81no—
654C2×Dic3—21no—
655C2×Dic3—42no—
656C2×Dic3C2×C3×D411yescharacteristic
657C2×Dic3C2×C3×D411yescharacteristic
658C2×Dic3C2×C3×D411yescharacteristic
659D12—21no—
660D12—21no—
661D12—21no—
662D12—21no—
663D12—21no—
664D12—42no—
665D12—42no—
666D12—81no—
667D12C2×C3×D412yescomplemented
668C4×D3—21no—
669C4×D3—21no—
670C4×D3—42no—
671C4×D3—81no—
672C3×C8—21no—
673C3×C8—21no—
674C3×C8—21no—
675C3×C8—21no—
676C3×C8—32no—
677C3×C8—41no—
678C3×C8—41no—
679C3×C8—61no—
680C3⋊C8—21no—
681C3⋊C8C2×C3×D412yescomplemented
682C2×C32—22no—
683C2×C32—42no—
684C2×C32—81no—
685C2×C32D4211yescharacteristic
686C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
687C2×C32#57611yescharacteristic
688C3×D3—41no—
689C3×D3—42no—
690C3×D3—81no—
691C3×D3—81no—
692C24—21no—
693C24—61no—
694C24—61no—
695#41—62no—
696#41—121no—
697C2×Q8C22×C3×D311yescharacteristic
698C2×D4—22no—
699C2×D4—21no—
700C2×D4—31no—
701C2×D4—31no—
702C2×D4—31no—
703C2×D4—31no—
704C2×D4—41no—
705C2×D4—62no—
706C2×D4—61no—
707C2×D4—61no—
708C2×D4—61no—
709C2×D4—61no—
710C2×D4—61no—
711C2×D4—62no—
712C2×D4—61no—
713C2×D4—61no—
714C2×D4—61no—
715C2×D4—121no—
716C2×D4—121no—
717C2×D4—124no—
718C2×D4C22×C3×D311yescharacteristic
719C2×D4C22×C3×D311yescharacteristic
720C22×C4—31no—
721C22×C4—61no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4C22×C3×D311yescharacteristic
725SD16—22no—
726SD16—41no—
727SD16—62no—
728D8—34no—
729D8—62no—
730D8—62no—
731D8—62no—
732D8—62no—
733D8—121no—
734M16—62no—
735C2×C8—31no—
736C2×C8—31no—
737C2×C8—62no—
738C2×C8C22×C3×D311yescharacteristic
739C2×C8C22×C3×D311yescharacteristic
740C4⋊C4—21no—
741C4⋊C4—31no—
742C4⋊C4—31no—
743C4⋊C4C22×C3×D311yescharacteristic
744C22⋊C4—21no—
745C22⋊C4—31no—
746C22⋊C4—31no—
747C22⋊C4—61no—
748C22⋊C4—61no—
749C22⋊C4—61no—
750C22⋊C4—61no—
751C22⋊C4—61no—
752C22⋊C4—61no—
753C22⋊C4—61no—
754C42—31no—
755C22×C3—21no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—22no—
760C22×C3—22no—
761C22×C3—22no—
762C22×C3—21no—
763C22×C3—41no—
764C22×C3—41no—
765C22×C3—42no—
766C22×C3—42no—
767C22×C3—41no—
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—61no—
778C22×C3—61no—
779C22×C3—61no—
780C22×C3—62no—
781C22×C3—81no—
782C22×C3—81no—
783C22×C3—81no—
784C22×C3—81no—
785C22×C3—84no—
786C22×C3—84no—
787C22×C3—88no—
788C22×C3—121no—
789C22×C3—121no—
790C22×C3—121no—
791C22×C3—121no—
792C22×C3—121no—
793C22×C3—121no—
794C22×C3—121no—
795C22×C3—121no—
796C22×C3—244no—
797C22×C3—244no—
798C22×C3#91412yescomplemented
799C22×C3C3×AGL(1,ℤ/8)12yescomplemented
800C22×C3C2×D3×D411yescharacteristic
801C22×C3C22×C3×D411yescharacteristic
802C2×D3—21no—
803C2×D3—21no—
804C2×D3—21no—
805C2×D3—22no—
806C2×D3—41no—
807C2×D3—41no—
808C2×D3—41no—
809C2×D3—41no—
810C2×D3—41no—
811C2×D3—41no—
812C2×D3—41no—
813C2×D3—41no—
814C2×D3—84no—
815C2×D3—84no—
816C3×C4—21no—
817C3×C4—21no—
818C3×C4—21no—
819C3×C4—21no—
820C3×C4—41no—
821C3×C4—41no—
822C3×C4—41no—
823C3×C4—41no—
824C3×C4—41no—
825C3×C4—61no—
826C3×C4—61no—
827C3×C4—61no—
828C3×C4—81no—
829C3×C4—81no—
830C3×C4—121no—
831C3×C4C2×D3×D411yescharacteristic
832C3×C4#100411yescharacteristic
833C3×C4C22×C3×D411yescharacteristic
834C3×C4C3×H(5,𝔽2)11yescharacteristic
835Dic3—21no—
836Dic3—21no—
837Dic3—21no—
838Dic3—41no—
839C32#326411yescharacteristic, complemented, Sylow
840C23—21no—
841C23—21no—
842C23—31no—
843C23—42no—
844C23—42no—
845C23—61no—
846C23—61no—
847C23—61no—
848C23—81no—
849C23—122no—
850C23—122no—
851C23—122no—
852C23—122no—
853C23—241no—
854C23—241no—
855C23C3×D3×D411yescharacteristic
856Q8—21no—
857Q8—21no—
858D4—21no—
859D4—21no—
860D4—21no—
861D4—32no—
862D4—42no—
863D4—62no—
864D4—61no—
865D4—61no—
866D4—61no—
867D4—61no—
868D4—61no—
869D4—122no—
870D4—122no—
871D4—122no—
872D4—122no—
873D4—122no—
874D4—122no—
875D4—241no—
876D4—241no—
877D4C3×D3×D412yes—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—31no—
883C2×C4—31no—
884C2×C4—31no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—122no—
889C2×C4—122no—
890C2×C4—241no—
891C2×C4C3×D3×D411yescharacteristic
892C2×C4C23×C3×D311yescharacteristic
893C8—21no—
894C8—21no—
895C8—32no—
896C8—61no—
897C2×C3—22no—
898C2×C3—22no—
899C2×C3—21no—
900C2×C3—21no—
901C2×C3—21no—
902C2×C3—42no—
903C2×C3—42no—
904C2×C3—42no—
905C2×C3—82no—
906C2×C3—82no—
907C2×C3—81no—
908C2×C3—81no—
909C2×C3—121no—
910C2×C3—122no—
911C2×C3—241no—
912C2×C3—241no—
913C2×C3#559011yescharacteristic
914C2×C3C2×#91411yescharacteristic
915C2×C3#577411yescharacteristic
916C2×C3C3×D4211yescharacteristic
917C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
918C2×C3C3×#57611yescharacteristic
919D3—41no—
920D3—42no—
921D3—81no—
922D3—81no—
923C22—21no—
924C22—21no—
925C22—22no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—61no—
932C22—61no—
933C22—61no—
934C22—62no—
935C22—84no—
936C22—121no—
937C22—121no—
938C22—121no—
939C22—121no—
940C22—121no—
941C22—121no—
942C22—121no—
943C22—121no—
944C22—244no—
945C22—244no—
946C22C3×#91412yescomplemented
947C22C2×C3×D3×D411yescharacteristic
948C4—21no—
949C4—41no—
950C4—41no—
951C4—61no—
952C4—61no—
953C4—61no—
954C4—121no—
955C4C2×C3×D3×D411yescharacteristic
956C4C3×#100411yescharacteristic
957C3—21no—
958C3#8016611yescharacteristic, direct product factor
959C3C3×#326411yescharacteristic, complemented
960C2—22no—
961C2—42no—
962C2—81no—
963C2—121no—
964C2—122no—
965C2—241no—
966C2—241no—
967C2C3×#559011yescharacteristic
968C2C2×C3×#91411yescharacteristic
969C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#450C2
socleC22×C32C22×D4
hypercenterC3×#450D3
hypocenterC3C3×#3264
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#450

Complements

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

NH ≅ G/Ntype
1. C3×D4×#67C2semidirect
2. C22×C3×#213C2semidirect
3. C2×C3×#914C2semidirect
4. C3×#5630C2semidirect
5. C32×#450C2semidirect
6. C3×#5176C2semidirect
7. C3×#5172C2semidirect
8. C3×#5165C2semidirect
9. C3×#5048C2semidirect
10. C3×#4786C2semidirect
11. C3×#4785C2semidirect
12. C3×#4782C2semidirect
13. C3×#4773C2semidirect
14. C3×#4732C2semidirect
15. C3×#4730C2semidirect
17. #80166C3direct (N × H)
20. C2×C3×#239C22semidirect
21. C2×C3×D3×D4C22semidirect
22. C22×C3×D12C22semidirect
23. C2×C32×SD16C22semidirect
24. C2×C32×SD16C22semidirect
25. C32×C22⋊Q8C22semidirect
27. C3×#947C22semidirect
28. C2×C3×#215C22semidirect
29. C3×#940C22semidirect
31. C3×#938C22semidirect
33. C3×D4×Dic3C22semidirect
37. C2×C3×#213C22semidirect
38. C2×C3×#213C22semidirect
41. C22×C3×C3⋊C8C22semidirect
43. C2×C3×D24C22semidirect
44. C2×C3×D24C22semidirect
45. C2×C3×ΓL(1,𝔽25)C22semidirect
47. C3×#895C22semidirect
49. C3×#893C22semidirect
52. C32×#102C22semidirect
53. C32×#102C22semidirect
54. C32×C22⋊C8C22semidirect
55. C3×#835C22semidirect
56. C3×#821C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#815C22semidirect
60. C3×Dic3⋊C8C22semidirect
61. C3×#809C22semidirect
62. C3×#808C22semidirect
67. D4×#67C2×C3semidirect
68. C22×#213C2×C3semidirect
69. C2×#914C2×C3semidirect
70. #5630C2×C3semidirect
77. C3×#450D3semidirect
78. C3×#450C2×C3semidirect
84. #5176C2×C3semidirect
85. #5172C2×C3semidirect
86. #5165C2×C3semidirect
87. #5048C2×C3semidirect
88. #4786C2×C3semidirect
89. #4785C2×C3semidirect
90. #4782C2×C3semidirect
91. #4773C2×C3semidirect
92. #4732C2×C3semidirect
93. #4730C2×C3semidirect
141. C3×#213D4semidirect
166. C2×#239C22×C3semidirect
167. C2×D3×D4C22×C3semidirect
168. C22×D12C22×C3semidirect
173. C2×C3×SD16C2×D3semidirect
174. C2×C3×SD16C2×D3semidirect
175. C2×C3×SD16C22×C3semidirect
176. C2×C3×SD16C22×C3semidirect
190. C3×C22⋊Q8C2×D3semidirect
191. C3×C22⋊Q8C22×C3semidirect
205. #947C22×C3semidirect
206. C2×#215C22×C3semidirect
207. #940C22×C3semidirect
209. #938C22×C3semidirect
211. D4×Dic3C22×C3semidirect
215. C2×#213C22×C3semidirect
216. C2×#213C22×C3semidirect
219. C22×C3⋊C8C22×C3semidirect
221. C2×D24C22×C3semidirect
222. C2×D24C22×C3semidirect
223. C2×ΓL(1,𝔽25)C22×C3semidirect
225. #895C22×C3semidirect
227. #893C22×C3semidirect
238. C3×#102C2×D3semidirect
239. C3×#102C2×D3semidirect
240. C3×#102C22×C3semidirect
241. C3×#102C22×C3semidirect
244. C3×C22⋊C8C2×D3semidirect
245. C3×C22⋊C8C22×C3semidirect
247. #835C22×C3semidirect
248. #821C22×C3semidirect
249. #821C22×C3semidirect
250. (C2×D3)⋊C8C22×C3semidirect
251. #815C22×C3semidirect
252. Dic3⋊C8C22×C3semidirect
253. #809C22×C3semidirect
254. #808C22×C3semidirect
303. C3×D12C2×D4semidirect
311. C3×C3⋊C8C2×D4semidirect
321. #450C3×D3semidirect
452. #213C3×D4semidirect
477. C22×C32AGL(1,ℤ/8)semidirect
509. C2×SD16C2×C3×D3semidirect
510. C2×SD16C2×C3×D3semidirect
523. C22⋊Q8C2×C3×D3semidirect
542. #102C2×C3×D3semidirect
543. #102C2×C3×D3semidirect
545. C22⋊C8C2×C3×D3semidirect
667. D12C2×C3×D4semidirect
681. C3⋊C8C2×C3×D4semidirect
798. C22×C3#914semidirect
799. C22×C3C3×AGL(1,ℤ/8)semidirect
839. C32#3264semidirect
946. C22C3×#914semidirect
958. C3#80166direct (N × H)
959. C3C3×#3264semidirect

Maximal subgroups

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

subgroupindex
C3×D4×#672
C22×C3×#2132
C2×C3×#9142
C3×#56302
C32×#4502
C3×#51762
C3×#51722
C3×#51652
C3×#50482
C3×#47862
C3×#47852
C3×#47822
C3×#47732
C3×#47322
C3×#47302
C3×#32643
#801663