Finite Group Databasebeta

← C3×#81166 #11868646

Subgroups — C3×#81166 #11868646

Order 1152.

931 conjugacy classes of subgroups.

The subgroup lattice has 751 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5688C211yesmaximal, characteristic, complemented
2C3×C4×D3×D4C211yesmaximal, characteristic
3C32×#478C211yesmaximal, characteristic, complemented
4C3×#5066C211yesmaximal, characteristic, complemented
5C3×#5009C211yesmaximal, characteristic, complemented
6C3×#4890C211yesmaximal, characteristic, complemented
7C3×#4881C211yesmaximal, characteristic, complemented
8C3×#4870C211yesmaximal, characteristic, complemented
9C3×#4861C211yesmaximal, characteristic, complemented
10C3×#4847C211yesmaximal, characteristic, complemented
11C3×#4837C211yesmaximal, characteristic, complemented
12C3×#4770C211yesmaximal, characteristic
13C3×#4770C211yesmaximal, characteristic
14C3×#4761C211yesmaximal, characteristic, complemented
15C3×#4759C211yesmaximal, characteristic, complemented
16C3×#3077—31nomaximal
17#81166C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×D4C2211yescharacteristic
19C22×C3×C4×D3—21no—
20C32×#125C2211yescharacteristic, complemented
21C32×C4×D4C2211yescharacteristic
22C3×D4×Dic3C2211yescharacteristic
23C3×C4×#67—21no—
24C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
25C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
26C3×#896—21no—
27C3×#896—21no—
28C3×#893C2211yescharacteristic
29C3×#892C2211yescharacteristic
30C3×#892C2211yescharacteristic
31C3×D3×C4⋊C4C2211yescharacteristic
32C3×#888C2211yescharacteristic, complemented
33C3×#888C2211yescharacteristic, complemented
34C3×#887—21no—
35C3×#887—21no—
36C3×#67⋊C4—21no—
37C3×D3×C22⋊C4—21no—
38C3×C4×D12C2211yescharacteristic
39C3×C42×D3C2211yescharacteristic
40C3×#870C2211yescharacteristic, complemented
41C32×#107C2211yescharacteristic, complemented
42C32×#106C2211yescharacteristic, complemented
43C32×C4⋊C8C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#818C2211yescharacteristic, complemented
51C3×#817C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×#809C2211yescharacteristic
55C3×#809C2211yescharacteristic
56C3×#808C2211yescharacteristic, complemented
57C3×#808C2211yescharacteristic, complemented
58C3×#807C2211yescharacteristic, complemented
59C3×#807C2211yescharacteristic, complemented
60C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#533—31no—
62C2×C3×C4×D4—31no—
63#5688C2×C311yescharacteristic, complemented
64C4×D3×D4C2×C311yescharacteristic
65C3×#478—21no—
66C3×#478—31no—
67C3×#478—31no—
68C3×#478—31no—
69C3×#478D311yescharacteristic, complemented
70C3×#478C2×C311yescharacteristic, complemented
71C3×#476—31no—
72C3×#476—31no—
73C3×#474—31no—
74C3×#474—31no—
75C3×#428—31no—
76C3×#428—31no—
77C3×#423—31no—
78C3×#418—31no—
79C3×#418—31no—
80#5066C2×C311yescharacteristic, complemented
81#5009C2×C311yescharacteristic, complemented
82#4890C2×C311yescharacteristic, complemented
83#4881C2×C311yescharacteristic, complemented
84#4870C2×C311yescharacteristic, complemented
85#4861C2×C311yescharacteristic, complemented
86#4847C2×C311yescharacteristic, complemented
87#4837C2×C311yescharacteristic, complemented
88#4770C2×C311yescharacteristic
89#4770C2×C311yescharacteristic
90#4761C2×C311yescharacteristic, complemented
91#4759C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×C3×#67—21no—
96C22×C3×Dic3—21no—
97C3×D3×D4—22no—
98C3×D3×D4Q814yescomplemented
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—44no—
104C2×C3×C4×D3D411yescharacteristic
105C2×C3×C4×D3D411yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6—21no—
108C2×C3×Dic6—21no—
109C2×C32×C8C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4—21no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C22⋊C4—21no—
117C32×C42C2311yescharacteristic
118C3×#217—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3D411yescharacteristic
134C3×C4×Dic3D411yescharacteristic
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×ΓL(1,𝔽25)—22no—
139C3×ΓL(1,𝔽25)—22no—
140#3077—31noSylow
141C22×C3×D4—31no—
142C23×C3×C4—61no—
143C2×D3×D4C22×C311yescharacteristic
144C22×C4×D3—21no—
145C2×C3×M16—31no—
146C2×C3×M16—31no—
147C3×C4⋊Q8—31no—
148C3×C4⋊Q8—31no—
149C3×#125—21no—
150C3×#125—31no—
151C3×#125C2×D311yescharacteristic, complemented
152C3×#125C22×C311yescharacteristic, complemented
153C3×C22⋊Q8—61no—
154C3×C22⋊Q8—61no—
155C3×C4×Q8—61no—
156C3×C4×Q8—61no—
157C3×C4×D4—21no—
158C3×C4×D4—31no—
159C3×C4×D4—31no—
160C3×C4×D4—31no—
161C3×C4×D4—61no—
162C3×C4×D4—61no—
163C3×C4×D4C2×D311yescharacteristic
164C3×C4×D4C22×C311yescharacteristic
165C3×#117—31no—
166C3×#117—31no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C22⋊C4—61no—
169C2×C3×C42—31no—
170D4×Dic3C22×C311yescharacteristic
171C4×#67—21no—
172C2×ΓL(1,𝔽25)C22×C311yescharacteristic
173C2×ΓL(1,𝔽25)C22×C311yescharacteristic
174#896—21no—
175#896—21no—
176#893C22×C311yescharacteristic
177#892C22×C311yescharacteristic
178#892C22×C311yescharacteristic
179D3×C4⋊C4C22×C311yescharacteristic
180#888C22×C311yescharacteristic, complemented
181#888C22×C311yescharacteristic, complemented
182#887—21no—
183#887—21no—
184#67⋊C4—21no—
185D3×C22⋊C4—21no—
186C4×D12C22×C311yescharacteristic
187C42×D3C22×C311yescharacteristic
188#870C22×C311yescharacteristic, complemented
189C3×#107—21no—
190C3×#107—31no—
191C3×#107—31no—
192C3×#107—31no—
193C3×#107C2×D311yescharacteristic, complemented
194C3×#107C22×C311yescharacteristic, complemented
195C3×#106—21no—
196C3×#106—31no—
197C3×#106—31no—
198C3×#106—31no—
199C3×#106C2×D311yescharacteristic, complemented
200C3×#106C22×C311yescharacteristic, complemented
201C3×C4⋊C8—21no—
202C3×C4⋊C8—31no—
203C3×C4⋊C8—31no—
204C3×C4⋊C8—31no—
205C3×C4⋊C8C2×D311yescharacteristic, complemented
206C3×C4⋊C8C22×C311yescharacteristic, complemented
207C3×#102—21no—
208C3×#102—21no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102C2×D311yescharacteristic
216C3×#102C2×D311yescharacteristic
217C3×#102C22×C311yescharacteristic
218C3×#102C22×C311yescharacteristic
219#832C22×C311yescharacteristic
220#832C22×C311yescharacteristic
221#821C22×C311yescharacteristic
222#821C22×C311yescharacteristic
223#818C22×C311yescharacteristic, complemented
224#817C22×C311yescharacteristic, complemented
225Dic3⋊C8C22×C311yescharacteristic, complemented
226Dic3⋊C8C22×C311yescharacteristic, complemented
227#809C22×C311yescharacteristic
228#809C22×C311yescharacteristic
229#808C22×C311yescharacteristic, complemented
230#808C22×C311yescharacteristic, complemented
231#807C22×C311yescharacteristic, complemented
232#807C22×C311yescharacteristic, complemented
233C4⋊(C3⋊C8)C22×C311yescharacteristic, complemented
234C23×C32—21no—
235C22×C3×D3—21no—
236C22×C3×D3—24no—
237C22×C3×D3—42no—
238C22×C3×D3—42no—
239C22×C3×D3C2×D411yescharacteristic
240C32×D4—21no—
241C32×D4C2×Q812yes—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—42no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C3×#67—24no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—42no—
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C3×D12—21no—
258C3×D12C2×Q812yes—
259C3×C4×D3—22no—
260C3×C4×D3—41no—
261C3×C4×D3—42no—
262C3×C4×D3—42no—
263C3×C4×D3—42no—
264C3×C4×D3C2×Q812yes—
265C3×C4×D3#4112yes—
266C3×Dic6—42no—
267C3×Dic6—42no—
268C32×C8—21no—
269C32×C8—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#533—31no—
273C2×C4×D4—31no—
274#478—31no—
275#478—31no—
276#478—31no—
277#478C3×D311yescharacteristic, complemented
278#476—31no—
279#476—31no—
280#474—31no—
281#474—31no—
282#428—31no—
283#428—31no—
284#423—31no—
285#418—31no—
286#418—31no—
287C24×C3—61no—
288C23×D3—21no—
289C2×C3×Q8—61no—
290C2×C3×Q8—61no—
291C2×C3×D4—21no—
292C2×C3×D4—34no—
293C2×C3×D4—31no—
294C2×C3×D4—62no—
295C2×C3×D4—61no—
296C2×C3×D4C22×D311yescharacteristic
297C2×C3×D4C23×C311yescharacteristic
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—41no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×C3×C4—124no—
309C2×#67—21no—
310C22×Dic3—21no—
311D3×D4—22no—
312D3×D4C3×Q814yescomplemented
313C2×D12C23×C311yescharacteristic
314C2×C4×D3—21no—
315C2×C4×D3—21no—
316C2×C4×D3—21no—
317C2×C4×D3—44no—
318C2×C4×D3C3×D411yescharacteristic
319C2×C4×D3C3×D411yescharacteristic
320C2×C4×D3C23×C311yescharacteristic
321C2×Dic6—21no—
322C2×Dic6—21no—
323C3×M16—62no—
324C3×M16—62no—
325C2×C3×C8—21no—
326C2×C3×C8—21no—
327C2×C3×C8—31no—
328C2×C3×C8—31no—
329C2×C3×C8C22×D311yescharacteristic
330C2×C3×C8C22×D311yescharacteristic
331C2×C3×C8C23×C311yescharacteristic
332C2×C3×C8C23×C311yescharacteristic
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—41no—
344C3×C4⋊C4—41no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C23×C311yescharacteristic
354C3×C4⋊C4C23×C311yescharacteristic
355C3×C4⋊C4C23×C311yescharacteristic
356C3×C22⋊C4—21no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—41no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C42—21no—
365C3×C42—31no—
366C3×C42—31no—
367C3×C42—31no—
368C3×C42—61no—
369C3×C42—61no—
370C3×C42C22×D311yescharacteristic
371C3×C42C23×C311yescharacteristic
372#217—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377C4⋊Dic3C23×C311yescharacteristic
378C4⋊Dic3C23×C311yescharacteristic
379C4⋊Dic3C23×C311yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385C4×Dic3—21no—
386C4×Dic3—21no—
387C4×Dic3C3×D411yescharacteristic
388C4×Dic3C3×D411yescharacteristic
389C4×Dic3C23×C311yescharacteristic
390C2×C3⋊C8C23×C311yescharacteristic
391C2×C3⋊C8C23×C311yescharacteristic
392ΓL(1,𝔽25)—22no—
393ΓL(1,𝔽25)—22no—
394C22×C32—22no—
395C22×C32—41no—
396C22×C32—41no—
397C22×C32C22×D411yescharacteristic
398C2×C3×D3—21no—
399C2×C3×D3—21no—
400C2×C3×D3—22no—
401C2×C3×D3—48no—
402C2×C3×D3—41no—
403C2×C3×D3—41no—
404C2×C3×D3C22⋊Q812yes—
405C32×C4—21no—
406C32×C4—21no—
407C32×C4—41no—
408C32×C4—41no—
409C32×C4—41no—
410C32×C4C22×Q811yescharacteristic
411C32×C4C2×#4111yescharacteristic
412C3×Dic3—21no—
413C3×Dic3—41no—
414C3×Dic3—41no—
415C3×Dic3—41no—
416C3×Dic3C22⋊Q812yes—
417C3×Dic3AGL(1,ℤ/8)12yes—
418C22×D4—31no—
419C23×C4—61no—
420C2×M16—31no—
421C2×M16—31no—
422C4⋊Q8—31no—
423C4⋊Q8—31no—
424#125—31no—
425#125C2×C3×D311yescharacteristic, complemented
426C22⋊Q8—61no—
427C22⋊Q8—61no—
428C4×Q8—61no—
429C4×Q8—61no—
430C4×D4—31no—
431C4×D4—31no—
432C4×D4—31no—
433C4×D4—61no—
434C4×D4—61no—
435C4×D4C2×C3×D311yescharacteristic
436#117—31no—
437#117—31no—
438C2×C4⋊C4—31no—
439C2×C22⋊C4—61no—
440C2×C42—31no—
441#107—31no—
442#107—31no—
443#107—31no—
444#107C2×C3×D311yescharacteristic, complemented
445#106—31no—
446#106—31no—
447#106—31no—
448#106C2×C3×D311yescharacteristic, complemented
449C4⋊C8—31no—
450C4⋊C8—31no—
451C4⋊C8—31no—
452C4⋊C8C2×C3×D311yescharacteristic, complemented
453#102—31no—
454#102—31no—
455#102—31no—
456#102—31no—
457#102—31no—
458#102—31no—
459#102C2×C3×D311yescharacteristic
460#102C2×C3×D311yescharacteristic
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—31no—
464C23×C3—41no—
465C23×C3—64no—
466C23×C3—61no—
467C23×C3—122no—
468C23×C3—122no—
469C22×D3—21no—
470C22×D3—24no—
471C22×D3—42no—
472C22×D3—42no—
473C22×D3C2×C3×D411yescharacteristic
474C3×Q8—122no—
475C3×Q8—122no—
476C3×D4—21no—
477C3×D4—21no—
478C3×D4—22no—
479C3×D4—32no—
480C3×D4—41no—
481C3×D4—64no—
482C3×D4—61no—
483C3×D4D3×Q812yes—
484C3×D4C2×C3×Q812yes—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—32no—
497C2×C3×C4—32no—
498C2×C3×C4—31no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—42no—
503C2×C3×C4—42no—
504C2×C3×C4—62no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—82no—
509C2×C3×C4—121no—
510C2×C3×C4—122no—
511C2×C3×C4—122no—
512C2×C3×C4—122no—
513C2×C3×C4—122no—
514C2×C3×C4D3×D411yescharacteristic
515C2×C3×C4D3×D411yescharacteristic
516C2×C3×C4C2×C3×D411yescharacteristic
517C2×C3×C4C2×C3×D411yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519C2×C3×C4C24×C311yescharacteristic
520#67—24no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—42no—
525C2×Dic3C2×C3×D411yescharacteristic
526C2×Dic3C2×C3×D411yescharacteristic
527C2×Dic3C2×C3×D411yescharacteristic
528D12—21no—
529D12C2×C3×Q812yes—
530C4×D3—22no—
531C4×D3—41no—
532C4×D3—42no—
533C4×D3—42no—
534C4×D3—42no—
535C4×D3C2×C3×Q812yes—
536C4×D3C3×#4112yes—
537Dic6—42no—
538Dic6—42no—
539C3×C8—21no—
540C3×C8—21no—
541C3×C8—21no—
542C3×C8—21no—
543C3×C8—41no—
544C3×C8—41no—
545C3×C8—61no—
546C3×C8—61no—
547C3⋊C8—21no—
548C3⋊C8—21no—
549C2×C32—42no—
550C2×C32C2×C22⋊Q811yescharacteristic
551C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
552C2×C32#57511yescharacteristic
553C3×D3—22no—
554C3×D3—42no—
555C24—61no—
556C2×Q8—61no—
557C2×Q8—61no—
558C2×D4—34no—
559C2×D4—31no—
560C2×D4—62no—
561C2×D4—61no—
562C2×D4C22×C3×D311yescharacteristic
563C22×C4—21no—
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4—124no—
572M16—62no—
573M16—62no—
574C2×C8—31no—
575C2×C8—31no—
576C2×C8C22×C3×D311yescharacteristic
577C2×C8C22×C3×D311yescharacteristic
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—31no—
581C4⋊C4—31no—
582C4⋊C4—31no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—61no—
588C4⋊C4C22×C3×D311yescharacteristic
589C4⋊C4C22×C3×D311yescharacteristic
590C4⋊C4C22×C3×D311yescharacteristic
591C22⋊C4—21no—
592C22⋊C4—61no—
593C22⋊C4—61no—
594C22⋊C4—61no—
595C22⋊C4—61no—
596C22⋊C4—61no—
597C42—31no—
598C42—31no—
599C42—31no—
600C42—61no—
601C42—61no—
602C42C22×C3×D311yescharacteristic
603C22×C3—22no—
604C22×C3—22no—
605C22×C3—21no—
606C22×C3—32no—
607C22×C3—42no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—61no—
613C22×C3—61no—
614C22×C3—62no—
615C22×C3—81no—
616C22×C3—81no—
617C22×C3—128no—
618C22×C3—121no—
619C22×C3—121no—
620C22×C3C2×D3×D411yescharacteristic
621C22×C3C22×C3×D411yescharacteristic
622C2×D3—21no—
623C2×D3—21no—
624C2×D3—22no—
625C2×D3—48no—
626C2×D3—41no—
627C2×D3—41no—
628C2×D3C3×C22⋊Q812yes—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—32no—
636C3×C4—32no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—61no—
646C3×C4—81no—
647C3×C4—81no—
648C3×C4—81no—
649C3×C4—121no—
650C3×C4—121no—
651C3×C4—121no—
652C3×C4C2×D3×Q811yescharacteristic
653C3×C4D3×#4111yescharacteristic
654C3×C4C22×C3×Q811yescharacteristic
655C3×C4C2×C3×#4111yescharacteristic
656Dic3—21no—
657Dic3—41no—
658Dic3—41no—
659Dic3—41no—
660Dic3C3×C22⋊Q812yes—
661Dic3C3×AGL(1,ℤ/8)12yes—
662C32#307711yescharacteristic, complemented, Sylow
663C23—21no—
664C23—31no—
665C23—64no—
666C23—61no—
667C23—122no—
668C23—122no—
669Q8—122no—
670Q8—122no—
671D4—21no—
672D4—32no—
673D4—64no—
674D4—61no—
675D4C3×D3×Q812yes—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—31no—
680C2×C4—31no—
681C2×C4—32no—
682C2×C4—32no—
683C2×C4—31no—
684C2×C4—42no—
685C2×C4—62no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—121no—
690C2×C4—122no—
691C2×C4—122no—
692C2×C4—122no—
693C2×C4—122no—
694C2×C4C3×D3×D411yescharacteristic
695C2×C4C3×D3×D411yescharacteristic
696C2×C4C23×C3×D311yescharacteristic
697C8—21no—
698C8—21no—
699C8—61no—
700C8—61no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—42no—
705C2×C3—42no—
706C2×C3—62no—
707C2×C3—82no—
708C2×C3—122no—
709C2×C3D3×C22⋊Q811yescharacteristic
710C2×C3#576811yescharacteristic
711C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
712C2×C3C2×C3×C22⋊Q811yescharacteristic
713C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
714C2×C3C3×#57511yescharacteristic
715D3—22no—
716D3—42no—
717C22—22no—
718C22—32no—
719C22—41no—
720C22—41no—
721C22—61no—
722C22—61no—
723C22—62no—
724C22—128no—
725C22—121no—
726C22—121no—
727C22C2×C3×D3×D411yescharacteristic
728C4—21no—
729C4—21no—
730C4—32no—
731C4—32no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—61no—
736C4—121no—
737C4—121no—
738C4—121no—
739C4C2×C3×D3×Q811yescharacteristic
740C4C3×D3×#4111yescharacteristic
741C3—21no—
742C3#8116611yescharacteristic, direct product factor
743C3C3×#307711yescharacteristic, complemented
744C2—42no—
745C2—62no—
746C2—122no—
747C2C3×D3×C22⋊Q811yescharacteristic
748C2C3×#576811yescharacteristic
749C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#478C2
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
hypercenterC3×#478D3
hypocenterC3C3×#3077
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#478

Complements

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

NH ≅ G/Ntype
1. C3×#5688C2semidirect
3. C32×#478C2semidirect
4. C3×#5066C2semidirect
5. C3×#5009C2semidirect
6. C3×#4890C2semidirect
7. C3×#4881C2semidirect
8. C3×#4870C2semidirect
9. C3×#4861C2semidirect
10. C3×#4847C2semidirect
11. C3×#4837C2semidirect
14. C3×#4761C2semidirect
15. C3×#4759C2semidirect
17. #81166C3direct (N × H)
20. C32×#125C22semidirect
32. C3×#888C22semidirect
33. C3×#888C22semidirect
40. C3×#870C22semidirect
41. C32×#107C22semidirect
42. C32×#106C22semidirect
43. C32×C4⋊C8C22semidirect
50. C3×#818C22semidirect
51. C3×#817C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×Dic3⋊C8C22semidirect
56. C3×#808C22semidirect
57. C3×#808C22semidirect
58. C3×#807C22semidirect
59. C3×#807C22semidirect
60. C3×C4⋊(C3⋊C8)C22semidirect
63. #5688C2×C3semidirect
69. C3×#478D3semidirect
70. C3×#478C2×C3semidirect
80. #5066C2×C3semidirect
81. #5009C2×C3semidirect
82. #4890C2×C3semidirect
83. #4881C2×C3semidirect
84. #4870C2×C3semidirect
85. #4861C2×C3semidirect
86. #4847C2×C3semidirect
87. #4837C2×C3semidirect
90. #4761C2×C3semidirect
91. #4759C2×C3semidirect
98. C3×D3×D4Q8semidirect
151. C3×#125C2×D3semidirect
152. C3×#125C22×C3semidirect
180. #888C22×C3semidirect
181. #888C22×C3semidirect
188. #870C22×C3semidirect
193. C3×#107C2×D3semidirect
194. C3×#107C22×C3semidirect
199. C3×#106C2×D3semidirect
200. C3×#106C22×C3semidirect
205. C3×C4⋊C8C2×D3semidirect
206. C3×C4⋊C8C22×C3semidirect
223. #818C22×C3semidirect
224. #817C22×C3semidirect
225. Dic3⋊C8C22×C3semidirect
226. Dic3⋊C8C22×C3semidirect
229. #808C22×C3semidirect
230. #808C22×C3semidirect
231. #807C22×C3semidirect
232. #807C22×C3semidirect
233. C4⋊(C3⋊C8)C22×C3semidirect
277. #478C3×D3semidirect
312. D3×D4C3×Q8semidirect
425. #125C2×C3×D3semidirect
444. #107C2×C3×D3semidirect
448. #106C2×C3×D3semidirect
452. C4⋊C8C2×C3×D3semidirect
662. C32#3077semidirect
742. C3#81166direct (N × H)
743. C3C3×#3077semidirect

Maximal subgroups

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

subgroupindex
C3×#56882
C3×C4×D3×D42
C32×#4782
C3×#50662
C3×#50092
C3×#48902
C3×#48812
C3×#48702
C3×#48612
C3×#48472
C3×#48372
C3×#47702
C3×#47612
C3×#47592
C3×#30773
#811663