Finite Group Databasebeta

← C3×#80680 #11887082

Subgroups — C3×#80680 #11887082

Order 1152.

986 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5635C211yesmaximal, characteristic, complemented
2C3×#5609C211yesmaximal, characteristic
3C32×#465C211yesmaximal, characteristic, complemented
4C3×#5169C211yesmaximal, characteristic, complemented
5C3×#5163C211yesmaximal, characteristic, complemented
6C2×C3×#821C211yesmaximal, characteristic, complemented
7C3×C8×#67C211yesmaximal, characteristic, complemented
8C3×#5046C211yesmaximal, characteristic, complemented
9C3×#5034C211yesmaximal, characteristic, complemented
10C3×#4870C211yesmaximal, characteristic, complemented
11C3×#4863C211yesmaximal, characteristic, complemented
12C3×#4807C211yesmaximal, characteristic, complemented
13C3×#4788C211yesmaximal, characteristic, complemented
14C3×D3×#102C211yesmaximal, characteristic, complemented
15C3×#4760C211yesmaximal, characteristic, complemented
16C3×#3295—31nomaximal
17#80680C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×D4—21no—
19C2×C3×D3×D4C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic, complemented
22C22×C32×C8C2211yescharacteristic, complemented
23C32×C22⋊Q8C2211yescharacteristic, complemented
24C32×#121C2211yescharacteristic
25C3×#946C2211yescharacteristic, complemented
26C3×Q8×Dic3C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C2×C3×#215C2211yescharacteristic, complemented
29C3×#940C2211yescharacteristic
30C3×#937—21no—
31C3×C4×#67C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
33C2×C3×D3×C8C2211yescharacteristic, complemented
34C3×#897—21no—
35C3×#895C2211yescharacteristic
36C3×#893C2211yescharacteristic
37C3×D3×C4⋊C4C2211yescharacteristic, complemented
38C3×#889—21no—
39C3×#888C2211yescharacteristic, complemented
40C3×#884—21no—
41C3×#882—21no—
42C3×#67⋊C4—21no—
43C3×#878—21no—
44C32×#106C2211yescharacteristic, complemented
45C32×#103C2211yescharacteristic, complemented
46C32×#102C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic, complemented
49C3×#830C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#821C2211yescharacteristic, complemented
53C3×#821C2211yescharacteristic, complemented
54C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
55C3×Dic3⋊C8C2211yescharacteristic, complemented
56C3×C8×Dic3C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic, complemented
59C3×#808C2211yescharacteristic, complemented
60C3×#808C2211yescharacteristic, complemented
61C3×#554—31no—
62C3×D42—31no—
63#5635C2×C311yescharacteristic, complemented
64#5609C2×C311yescharacteristic
65C3×#486—31no—
66C3×#481—31no—
67C3×#481—31no—
68C3×#476—31no—
69C3×#465—21no—
70C3×#465—31no—
71C3×#465D311yescharacteristic, complemented
72C3×#465C2×C311yescharacteristic, complemented
73C3×#460—31no—
74C3×#450—31no—
75C3×#450—31no—
76C3×C4×SD16—31no—
77C3×C8×D4—31no—
78C2×C3×#102—31no—
79C2×C3×#102—31no—
80#5169C2×C311yescharacteristic, complemented
81#5163C2×C311yescharacteristic, complemented
82C2×#821C2×C311yescharacteristic, complemented
83C8×#67C2×C311yescharacteristic, complemented
84#5046C2×C311yescharacteristic, complemented
85#5034C2×C311yescharacteristic, complemented
86#4870C2×C311yescharacteristic, complemented
87#4863C2×C311yescharacteristic, complemented
88#4807C2×C311yescharacteristic, complemented
89#4788C2×C311yescharacteristic, complemented
90D3×#102C2×C311yescharacteristic, complemented
91#4760C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C23×C3×D3—21no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67D411yescharacteristic
102C22×C3×Dic3—21no—
103C3×D3×D4—22no—
104C3×D3×D4—41no—
105C3×D3×D4—44no—
106C2×C3×D12—22no—
107C2×C3×D12—21no—
108C2×C3×D12—21no—
109C2×C3×D12—41no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6—21no—
116C32×SD16—41no—
117C2×C32×C8—41no—
118C2×C32×C8C2311yescharacteristic
119C2×C32×C8C2311yescharacteristic
120C32×C4⋊C4—21no—
121C32×C4⋊C4C2311yescharacteristic
122C32×C4⋊C4C2311yescharacteristic
123C32×C22⋊C4—21no—
124C32×C22⋊C4—21no—
125C3×#217D411yescharacteristic
126C3×#215—22no—
127C3×#215—41no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4D411yescharacteristic
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3—21no—
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4D411yescharacteristic
140C3×C4×Dic3—21no—
141C3×C4×Dic3C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C3×D3×C8—41no—
145#3295—31noSylow
146C22×C3×D4—31no—
147C22×C3×D4—31no—
148C22×C3×D4—61no—
149C2×D3×D4—21no—
150C2×D3×D4C22×C311yescharacteristic
151C22×D12C22×C311yescharacteristic
152C2×C3×SD16—21no—
153C2×C3×SD16—31no—
154C2×C3×SD16—31no—
155C2×C3×SD16C2×D311yescharacteristic, complemented
156C2×C3×SD16C22×C311yescharacteristic, complemented
157C22×C3×C8—21no—
158C22×C3×C8—31no—
159C22×C3×C8C2×D311yescharacteristic, complemented
160C22×C3×C8C22×C311yescharacteristic, complemented
161C3×C4⋊Q8—31no—
162C3×#127—31no—
163C3×#125—61no—
164C3×C22⋊Q8—21no—
165C3×C22⋊Q8—31no—
166C3×C22⋊Q8—61no—
167C3×C22⋊Q8—61no—
168C3×C22⋊Q8C2×D311yescharacteristic, complemented
169C3×C22⋊Q8C22×C311yescharacteristic, complemented
170C3×#121—21no—
171C3×#121—31no—
172C3×#121—61no—
173C3×#121C2×D311yescharacteristic
174C3×#121C22×C311yescharacteristic
175C3×#120—61no—
176C3×#120—61no—
177C3×C4×Q8—31no—
178C3×C4×D4—31no—
179C3×C4×D4—31no—
180C3×C4×D4—61no—
181C2×C3×C4⋊C4—31no—
182C2×C3×C4⋊C4—31no—
183#946C22×C311yescharacteristic, complemented
184Q8×Dic3C22×C311yescharacteristic, complemented
185C2×#215C22×C311yescharacteristic
186C2×#215C22×C311yescharacteristic, complemented
187#940C22×C311yescharacteristic
188#937—21no—
189C4×#67C22×C311yescharacteristic
190C2×C4⋊Dic3C22×C311yescharacteristic, complemented
191C2×D3×C8C22×C311yescharacteristic, complemented
192#897—21no—
193#895C22×C311yescharacteristic
194#893C22×C311yescharacteristic
195D3×C4⋊C4C22×C311yescharacteristic, complemented
196#889—21no—
197#888C22×C311yescharacteristic, complemented
198#884—21no—
199#882—21no—
200#67⋊C4—21no—
201#878—21no—
202C3×#106—21no—
203C3×#106—31no—
204C3×#106—31no—
205C3×#106C2×D311yescharacteristic, complemented
206C3×#106C22×C311yescharacteristic, complemented
207C3×C4⋊C8—31no—
208C3×#103—21no—
209C3×#103C2×D311yescharacteristic, complemented
210C3×#103C22×C311yescharacteristic, complemented
211C3×#102—21no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×#102—31no—
217C3×#102—31no—
218C3×#102—31no—
219C3×#102—31no—
220C3×#102C2×D311yescharacteristic, complemented
221C3×#102C22×C311yescharacteristic, complemented
222C3×C22⋊C8—31no—
223C3×C22⋊C8—31no—
224C3×C4×C8—31no—
225#832C22×C311yescharacteristic, complemented
226#832C22×C311yescharacteristic, complemented
227#830C22×C311yescharacteristic, complemented
228#821C22×C311yescharacteristic
229#821C22×C311yescharacteristic
230#821C22×C311yescharacteristic, complemented
231#821C22×C311yescharacteristic, complemented
232(C2×D3)⋊C8C22×C311yescharacteristic, complemented
233Dic3⋊C8C22×C311yescharacteristic, complemented
234C8×Dic3C22×C311yescharacteristic, complemented
235#809C22×C311yescharacteristic
236#809C22×C311yescharacteristic, complemented
237#808C22×C311yescharacteristic, complemented
238#808C22×C311yescharacteristic, complemented
239C23×C32—21no—
240C23×C32C2×D411yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—42no—
244C22×C3×D3—42no—
245C22×C3×D3—42no—
246C22×C3×D3—42no—
247C22×C3×D3—81no—
248C22×C3×D3—81no—
249C22×C3×D3C2×D411yescharacteristic
250C32×Q8—21no—
251C32×Q8—21no—
252C32×D4—21no—
253C32×D4—21no—
254C32×D4—42no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4C2×D411yescharacteristic
261C2×C32×C4C2411yescharacteristic
262C3×#67—42no—
263C3×#67—42no—
264C3×#67—81no—
265C3×#67SD1614yescomplemented
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—81no—
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C2×C3×Dic3C2×D411yescharacteristic
272C3×D12—21no—
273C3×D12—21no—
274C3×D12—21no—
275C3×D12—42no—
276C3×D12—42no—
277C3×D12#4112yes—
278C3×C4×D3—21no—
279C3×C4×D3—21no—
280C3×C4×D3—42no—
281C3×C4×D3—81no—
282C3×Dic6—81no—
283C32×C8—21no—
284C32×C8—21no—
285C3×C3⋊C8—21no—
286C3×C3⋊C8—21no—
287#554—31no—
288D42—31no—
289#486—31no—
290#481—31no—
291#481—31no—
292#476—31no—
293#465—31no—
294#465C3×D311yescharacteristic, complemented
295#460—31no—
296#450—31no—
297#450—31no—
298C4×SD16—31no—
299C8×D4—31no—
300C2×#102—31no—
301C2×#102—31no—
302C24×C3—61no—
303C24×C3—61no—
304C23×D3—21no—
305C23×D3—21no—
306C2×C3×Q8—21no—
307C2×C3×Q8—61no—
308C2×C3×Q8C22×D311yescharacteristic
309C2×C3×Q8C23×C311yescharacteristic
310C2×C3×D4—21no—
311C2×C3×D4—21no—
312C2×C3×D4—21no—
313C2×C3×D4—31no—
314C2×C3×D4—31no—
315C2×C3×D4—31no—
316C2×C3×D4—41no—
317C2×C3×D4—62no—
318C2×C3×D4—61no—
319C2×C3×D4—61no—
320C2×C3×D4—61no—
321C2×C3×D4—61no—
322C2×C3×D4—62no—
323C2×C3×D4—61no—
324C2×C3×D4—121no—
325C2×C3×D4—121no—
326C2×C3×D4—124no—
327C2×C3×D4C22×D311yescharacteristic
328C2×C3×D4C23×C311yescharacteristic
329C22×C3×C4—21no—
330C22×C3×C4—31no—
331C22×C3×C4—61no—
332C22×C3×C4—61no—
333C22×C3×C4—61no—
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C23×C311yescharacteristic
336C2×#67—21no—
337C2×#67—21no—
338C2×#67—21no—
339C2×#67C3×D411yescharacteristic
340C22×Dic3—21no—
341D3×D4—22no—
342D3×D4—41no—
343D3×D4—44no—
344C2×D12—22no—
345C2×D12—21no—
346C2×D12—21no—
347C2×D12—41no—
348C2×D12C23×C311yescharacteristic
349C2×D12C23×C311yescharacteristic
350C2×C4×D3—21no—
351C2×C4×D3—21no—
352C2×C4×D3C23×C311yescharacteristic
353C2×Dic6—21no—
354C3×SD16—41no—
355C3×SD16—41no—
356C3×SD16—42no—
357C3×SD16—62no—
358C3×SD16—121no—
359C2×C3×C8—21no—
360C2×C3×C8—21no—
361C2×C3×C8—31no—
362C2×C3×C8—31no—
363C2×C3×C8—41no—
364C2×C3×C8—41no—
365C2×C3×C8—42no—
366C2×C3×C8—121no—
367C2×C3×C8C22×D311yescharacteristic
368C2×C3×C8C22×D311yescharacteristic
369C2×C3×C8C23×C311yescharacteristic
370C2×C3×C8C23×C311yescharacteristic
371C3×C4⋊C4—21no—
372C3×C4⋊C4—21no—
373C3×C4⋊C4—21no—
374C3×C4⋊C4—21no—
375C3×C4⋊C4—31no—
376C3×C4⋊C4—31no—
377C3×C4⋊C4—31no—
378C3×C4⋊C4—41no—
379C3×C4⋊C4—61no—
380C3×C4⋊C4—61no—
381C3×C4⋊C4—61no—
382C3×C4⋊C4—61no—
383C3×C4⋊C4—61no—
384C3×C4⋊C4C22×D311yescharacteristic
385C3×C4⋊C4C22×D311yescharacteristic
386C3×C4⋊C4C23×C311yescharacteristic
387C3×C4⋊C4C23×C311yescharacteristic
388C3×C22⋊C4—21no—
389C3×C22⋊C4—21no—
390C3×C22⋊C4—21no—
391C3×C22⋊C4—21no—
392C3×C22⋊C4—31no—
393C3×C22⋊C4—31no—
394C3×C22⋊C4—41no—
395C3×C22⋊C4—41no—
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399C3×C42—31no—
400C3×C42—61no—
401#217C3×D411yescharacteristic
402#215—22no—
403#215—41no—
404(C2×D3)⋊C4—21no—
405(C2×D3)⋊C4—21no—
406(C2×D3)⋊C4—21no—
407(C2×D3)⋊C4C3×D411yescharacteristic
408C4⋊Dic3—21no—
409C4⋊Dic3—21no—
410C4⋊Dic3C23×C311yescharacteristic
411C4⋊Dic3C23×C311yescharacteristic
412Dic3⋊C4—21no—
413Dic3⋊C4—21no—
414Dic3⋊C4—21no—
415Dic3⋊C4C3×D411yescharacteristic
416C4×Dic3—21no—
417C4×Dic3C23×C311yescharacteristic
418C2×C3⋊C8C23×C311yescharacteristic
419C2×C3⋊C8C23×C311yescharacteristic
420D3×C8—41no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32—41no—
424C22×C32—41no—
425C22×C32—41no—
426C22×C32C2×SD1612yes—
427C22×C32C22×D411yescharacteristic
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—22no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—41no—
436C2×C3×D3—84no—
437C2×C3×D3—84no—
438C2×C3×D3C2×SD1612yes—
439C32×C4—21no—
440C32×C4—41no—
441C32×C4—41no—
442C32×C4—41no—
443C32×C4C2×#4111yescharacteristic
444C32×C4H(5,𝔽2)11yescharacteristic
445C3×Dic3—21no—
446C3×Dic3—21no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C3×Dic3C2×SD1612yes—
450C22×D4—31no—
451C22×D4—31no—
452C22×D4—61no—
453C2×SD16—31no—
454C2×SD16—31no—
455C2×SD16C2×C3×D311yescharacteristic, complemented
456C22×C8—31no—
457C22×C8C2×C3×D311yescharacteristic, complemented
458C4⋊Q8—31no—
459#127—31no—
460#125—61no—
461C22⋊Q8—31no—
462C22⋊Q8—61no—
463C22⋊Q8—61no—
464C22⋊Q8C2×C3×D311yescharacteristic, complemented
465#121—31no—
466#121—61no—
467#121C2×C3×D311yescharacteristic
468#120—61no—
469#120—61no—
470C4×Q8—31no—
471C4×D4—31no—
472C4×D4—31no—
473C4×D4—61no—
474C2×C4⋊C4—31no—
475C2×C4⋊C4—31no—
476#106—31no—
477#106—31no—
478#106C2×C3×D311yescharacteristic, complemented
479C4⋊C8—31no—
480#103C2×C3×D311yescharacteristic, complemented
481#102—31no—
482#102—31no—
483#102—31no—
484#102—31no—
485#102—31no—
486#102—31no—
487#102—31no—
488#102—31no—
489#102C2×C3×D311yescharacteristic, complemented
490C22⋊C8—31no—
491C22⋊C8—31no—
492C4×C8—31no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—31no—
497C23×C3—41no—
498C23×C3—61no—
499C23×C3—61no—
500C23×C3—122no—
501C23×C3—122no—
502C23×C3—122no—
503C23×C3—122no—
504C23×C3—241no—
505C23×C3—241no—
506C23×C3D3×D411yescharacteristic
507C23×C3C2×C3×D411yescharacteristic
508C22×D3—21no—
509C22×D3—21no—
510C22×D3—42no—
511C22×D3—42no—
512C22×D3—42no—
513C22×D3—42no—
514C22×D3—81no—
515C22×D3—81no—
516C22×D3C2×C3×D411yescharacteristic
517C3×Q8—21no—
518C3×Q8—21no—
519C3×Q8—21no—
520C3×Q8—21no—
521C3×Q8—41no—
522C3×Q8—41no—
523C3×Q8—241no—
524C3×D4—21no—
525C3×D4—21no—
526C3×D4—21no—
527C3×D4—21no—
528C3×D4—34no—
529C3×D4—32no—
530C3×D4—41no—
531C3×D4—41no—
532C3×D4—42no—
533C3×D4—42no—
534C3×D4—61no—
535C3×D4—61no—
536C3×D4—61no—
537C3×D4—82no—
538C3×D4—122no—
539C3×D4—122no—
540C3×D4—122no—
541C3×D4—122no—
542C3×D4—241no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—31no—
556C2×C3×C4—31no—
557C2×C3×C4—31no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—122no—
568C2×C3×C4—241no—
569C2×C3×C4—241no—
570C2×C3×C4D3×D411yescharacteristic
571C2×C3×C4C2×C3×D411yescharacteristic
572C2×C3×C4C23×D311yescharacteristic
573C2×C3×C4C24×C311yescharacteristic
574#67—42no—
575#67—42no—
576#67—81no—
577#67C3×SD1614yescomplemented
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—81no—
581C2×Dic3C2×C3×D411yescharacteristic
582C2×Dic3C2×C3×D411yescharacteristic
583C2×Dic3C2×C3×D411yescharacteristic
584D12—21no—
585D12—21no—
586D12—21no—
587D12—42no—
588D12—42no—
589D12C3×#4112yes—
590C4×D3—21no—
591C4×D3—21no—
592C4×D3—42no—
593C4×D3—81no—
594Dic6—81no—
595C3×C8—22no—
596C3×C8—21no—
597C3×C8—21no—
598C3×C8—21no—
599C3×C8—21no—
600C3×C8—41no—
601C3×C8—61no—
602C3×C8—61no—
603C3⋊C8—21no—
604C3⋊C8—21no—
605C2×C32—22no—
606C2×C32—81no—
607C2×C32#54611yescharacteristic
608C2×C32C22×SD1611yescharacteristic
609C2×C32#57611yescharacteristic
610C3×D3—22no—
611C3×D3—42no—
612C3×D3—81no—
613C24—61no—
614C24—61no—
615C2×Q8—61no—
616C2×Q8C22×C3×D311yescharacteristic
617C2×D4—21no—
618C2×D4—31no—
619C2×D4—31no—
620C2×D4—31no—
621C2×D4—62no—
622C2×D4—61no—
623C2×D4—61no—
624C2×D4—61no—
625C2×D4—61no—
626C2×D4—62no—
627C2×D4—61no—
628C2×D4—121no—
629C2×D4—121no—
630C2×D4—124no—
631C2×D4C22×C3×D311yescharacteristic
632C22×C4—31no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—61no—
636C22×C4C22×C3×D311yescharacteristic
637SD16—41no—
638SD16—62no—
639SD16—121no—
640C2×C8—31no—
641C2×C8—31no—
642C2×C8—41no—
643C2×C8—121no—
644C2×C8C22×C3×D311yescharacteristic
645C2×C8C22×C3×D311yescharacteristic
646C4⋊C4—21no—
647C4⋊C4—31no—
648C4⋊C4—31no—
649C4⋊C4—31no—
650C4⋊C4—61no—
651C4⋊C4—61no—
652C4⋊C4—61no—
653C4⋊C4—61no—
654C4⋊C4—61no—
655C4⋊C4C22×C3×D311yescharacteristic
656C4⋊C4C22×C3×D311yescharacteristic
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—31no—
660C22⋊C4—31no—
661C22⋊C4—61no—
662C22⋊C4—61no—
663C22⋊C4—61no—
664C42—31no—
665C42—61no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—22no—
671C22×C3—21no—
672C22×C3—32no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—61no—
682C22×C3—61no—
683C22×C3—62no—
684C22×C3—81no—
685C22×C3—81no—
686C22×C3—81no—
687C22×C3—121no—
688C22×C3—121no—
689C22×C3—121no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—244no—
693C22×C3—244no—
694C22×C3D3×SD1612yes—
695C22×C3C2×C3×SD1612yes—
696C22×C3C2×D3×D411yescharacteristic
697C22×C3C22×C3×D411yescharacteristic
698C2×D3—21no—
699C2×D3—21no—
700C2×D3—22no—
701C2×D3—41no—
702C2×D3—41no—
703C2×D3—41no—
704C2×D3—41no—
705C2×D3—41no—
706C2×D3—84no—
707C2×D3—84no—
708C2×D3C2×C3×SD1612yes—
709C3×C4—21no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—32no—
714C3×C4—41no—
715C3×C4—41no—
716C3×C4—41no—
717C3×C4—41no—
718C3×C4—41no—
719C3×C4—41no—
720C3×C4—41no—
721C3×C4—61no—
722C3×C4—61no—
723C3×C4—81no—
724C3×C4—81no—
725C3×C4—81no—
726C3×C4—121no—
727C3×C4—121no—
728C3×C4#100411yescharacteristic
729C3×C4D3×#4111yescharacteristic
730C3×C4C2×C3×#4111yescharacteristic
731C3×C4C3×H(5,𝔽2)11yescharacteristic
732Dic3—21no—
733Dic3—21no—
734Dic3—41no—
735Dic3—41no—
736Dic3C2×C3×SD1612yes—
737C32#329511yescharacteristic, complemented, Sylow
738C23—21no—
739C23—31no—
740C23—61no—
741C23—61no—
742C23—122no—
743C23—122no—
744C23—122no—
745C23—122no—
746C23—241no—
747C23—241no—
748C23C3×D3×D411yescharacteristic
749Q8—21no—
750Q8—21no—
751Q8—241no—
752D4—21no—
753D4—21no—
754D4—34no—
755D4—32no—
756D4—42no—
757D4—61no—
758D4—61no—
759D4—61no—
760D4—122no—
761D4—122no—
762D4—122no—
763D4—122no—
764D4—241no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—31no—
771C2×C4—31no—
772C2×C4—31no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—122no—
778C2×C4—241no—
779C2×C4—241no—
780C2×C4C3×D3×D411yescharacteristic
781C2×C4C23×C3×D311yescharacteristic
782C8—21no—
783C8—21no—
784C8—61no—
785C8—61no—
786C2×C3—22no—
787C2×C3—22no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—42no—
792C2×C3—62no—
793C2×C3—81no—
794C2×C3—81no—
795C2×C3—122no—
796C2×C3—161no—
797C2×C3—241no—
798C2×C3#561011yescharacteristic
799C2×C3C2×D3×SD1611yescharacteristic
800C2×C3#576911yescharacteristic
801C2×C3C3×#54611yescharacteristic
802C2×C3C22×C3×SD1611yescharacteristic
803C2×C3C3×#57611yescharacteristic
804D3—22no—
805D3—42no—
806D3—81no—
807C22—21no—
808C22—21no—
809C22—32no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—61no—
814C22—61no—
815C22—62no—
816C22—121no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22—121no—
821C22—244no—
822C22—244no—
823C22C3×D3×SD1612yes—
824C22C2×C3×D3×D411yescharacteristic
825C4—21no—
826C4—32no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—61no—
831C4—61no—
832C4—121no—
833C4—121no—
834C4C3×#100411yescharacteristic
835C4C3×D3×#4111yescharacteristic
836C3—21no—
837C3#8068011yescharacteristic, direct product factor
838C3C3×#329511yescharacteristic, complemented
839C2—22no—
840C2—62no—
841C2—81no—
842C2—122no—
843C2—241no—
844C2C3×#561011yescharacteristic
845C2C2×C3×D3×SD1611yescharacteristic
846C2C3×#576911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#465C2
socleC22×C32C22×D4
prime radicalC3×#5609C2
hypercenterC3×#465D3
hypocenterC3C3×#3295
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#465

Complements

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

NH ≅ G/Ntype
1. C3×#5635C2semidirect
3. C32×#465C2semidirect
4. C3×#5169C2semidirect
5. C3×#5163C2semidirect
6. C2×C3×#821C2semidirect
7. C3×C8×#67C2semidirect
8. C3×#5046C2semidirect
9. C3×#5034C2semidirect
10. C3×#4870C2semidirect
11. C3×#4863C2semidirect
12. C3×#4807C2semidirect
13. C3×#4788C2semidirect
14. C3×D3×#102C2semidirect
15. C3×#4760C2semidirect
17. #80680C3direct (N × H)
21. C2×C32×SD16C22semidirect
22. C22×C32×C8C22semidirect
23. C32×C22⋊Q8C22semidirect
25. C3×#946C22semidirect
26. C3×Q8×Dic3C22semidirect
28. C2×C3×#215C22semidirect
32. C2×C3×C4⋊Dic3C22semidirect
33. C2×C3×D3×C8C22semidirect
37. C3×D3×C4⋊C4C22semidirect
39. C3×#888C22semidirect
44. C32×#106C22semidirect
45. C32×#103C22semidirect
46. C32×#102C22semidirect
47. C3×#832C22semidirect
48. C3×#832C22semidirect
49. C3×#830C22semidirect
52. C3×#821C22semidirect
53. C3×#821C22semidirect
54. C3×(C2×D3)⋊C8C22semidirect
55. C3×Dic3⋊C8C22semidirect
56. C3×C8×Dic3C22semidirect
58. C3×#809C22semidirect
59. C3×#808C22semidirect
60. C3×#808C22semidirect
63. #5635C2×C3semidirect
71. C3×#465D3semidirect
72. C3×#465C2×C3semidirect
80. #5169C2×C3semidirect
81. #5163C2×C3semidirect
82. C2×#821C2×C3semidirect
83. C8×#67C2×C3semidirect
84. #5046C2×C3semidirect
85. #5034C2×C3semidirect
86. #4870C2×C3semidirect
87. #4863C2×C3semidirect
88. #4807C2×C3semidirect
89. #4788C2×C3semidirect
90. D3×#102C2×C3semidirect
91. #4760C2×C3semidirect
155. C2×C3×SD16C2×D3semidirect
156. C2×C3×SD16C22×C3semidirect
159. C22×C3×C8C2×D3semidirect
160. C22×C3×C8C22×C3semidirect
168. C3×C22⋊Q8C2×D3semidirect
169. C3×C22⋊Q8C22×C3semidirect
183. #946C22×C3semidirect
184. Q8×Dic3C22×C3semidirect
186. C2×#215C22×C3semidirect
190. C2×C4⋊Dic3C22×C3semidirect
191. C2×D3×C8C22×C3semidirect
195. D3×C4⋊C4C22×C3semidirect
197. #888C22×C3semidirect
205. C3×#106C2×D3semidirect
206. C3×#106C22×C3semidirect
209. C3×#103C2×D3semidirect
210. C3×#103C22×C3semidirect
220. C3×#102C2×D3semidirect
221. C3×#102C22×C3semidirect
225. #832C22×C3semidirect
226. #832C22×C3semidirect
227. #830C22×C3semidirect
230. #821C22×C3semidirect
231. #821C22×C3semidirect
232. (C2×D3)⋊C8C22×C3semidirect
233. Dic3⋊C8C22×C3semidirect
234. C8×Dic3C22×C3semidirect
236. #809C22×C3semidirect
237. #808C22×C3semidirect
238. #808C22×C3semidirect
265. C3×#67SD16semidirect
294. #465C3×D3semidirect
455. C2×SD16C2×C3×D3semidirect
457. C22×C8C2×C3×D3semidirect
464. C22⋊Q8C2×C3×D3semidirect
478. #106C2×C3×D3semidirect
480. #103C2×C3×D3semidirect
489. #102C2×C3×D3semidirect
577. #67C3×SD16semidirect
737. C32#3295semidirect
837. C3#80680direct (N × H)
838. C3C3×#3295semidirect

Maximal subgroups

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

subgroupindex
C3×#56352
C3×#56092
C32×#4652
C3×#51692
C3×#51632
C2×C3×#8212
C3×C8×#672
C3×#50462
C3×#50342
C3×#48702
C3×#48632
C3×#48072
C3×#47882
C3×D3×#1022
C3×#47602
C3×#32953
#806803