Finite Group Databasebeta

← C3×#76673 #11811934

Subgroups — C3×#76673 #11811934

Order 1152.

2857 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×D4C211yesmaximal, characteristic, complemented
2C2×C3×#940C212yesmaximal, complemented
3C2×C3×#937C212yesmaximal, complemented
4C2×C3×#884C211yesmaximal, characteristic, complemented
5C2×C3×#882C212yesmaximal, complemented
6C32×#392C211yesmaximal, characteristic, complemented
7C3×#5223C211yesmaximal, characteristic, complemented
8C3×#4960C211yesmaximal, characteristic, complemented
9C3×#4957C212yesmaximal, complemented
10C3×#4671C211yesmaximal, characteristic, complemented
11C3×#4666C211yesmaximal, characteristic, complemented
12C3×#2433—31nomaximal
13#76673C311yesmaximal, characteristic, direct product factor
14C24×C3×D3C2212yes—
15C22×C32×D4C2211yescharacteristic
16C22×C32×D4C2212yescomplemented
17C22×C3×#67C2211yescharacteristic
18C22×C3×#67C2212yes—
19C22×C3×#67C2211yescharacteristic, complemented
20C22×C3×#67C2212yescomplemented
21C22×C3×#67C2212yescomplemented
22C2×C3×D3×D4—28no—
23C2×C3×D3×D4—24no—
24C22×C3×D12C2211yescharacteristic
25C22×C3×D12C2211yescharacteristic
26C22×C3×D12C2212yescomplemented
27C22×C3×C4×D3C2211yescharacteristic
28C2×C32×C22⋊C4C2212yescomplemented
29C2×C32×C22⋊C4C2211yescharacteristic, complemented
30C2×C3×#217C2212yescomplemented
31C3×#940—28no—
32C3×#937—28no—
33C2×C3×(C2×D3)⋊C4C2212yes—
34C2×C3×(C2×D3)⋊C4C2212yescomplemented
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
36C2×C3×(C2×D3)⋊C4C2212yescomplemented
37C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
38C2×C3×C4×Dic3C2212yescomplemented
39C3×#884—24no—
40C3×#882—28no—
41C32×#95C2211yescharacteristic, complemented
42C3×C3⋊#95C2211yescharacteristic, complemented
43C23×C3×D4—31no—
44C22×D3×D4C2×C311yescharacteristic, complemented
45C2×C3×#127—32no—
46C2×C3×#121—31no—
47C2×C3×#120—32no—
48C2×C3×#120—32no—
49C2×#940C2×C312yescomplemented
50C2×#937C2×C312yescomplemented
51C2×#884C2×C311yescharacteristic, complemented
52C2×#882C2×C312yescomplemented
53C3×#392—21no—
54C3×#392—31no—
55C3×#392—31no—
56C3×#392—31no—
57C3×#392D311yescharacteristic, complemented
58C3×#392C2×C311yescharacteristic, complemented
59C3×#390—32no—
60C3×C4×C22⋊C4—31no—
61#5223C2×C311yescharacteristic, complemented
62#4960C2×C311yescharacteristic, complemented
63#4957C2×C312yescomplemented
64#4671C2×C311yescharacteristic, complemented
65#4666C2×C311yescharacteristic, complemented
66C24×C32C2311yescharacteristic
67C24×C32C2312yes—
68C23×C3×D3—24no—
69C23×C3×D3—24no—
70C23×C3×D3—24no—
71C23×C3×D3—24no—
72C23×C3×D3—24no—
73C23×C3×D3—42no—
74C23×C3×D3—42no—
75C23×C3×D3C2311yescharacteristic
76C23×C3×D3C2312yes—
77C23×C3×D3C2311yescharacteristic
78C2×C32×D4—24no—
79C2×C32×D4—24no—
80C2×C32×D4—22no—
81C2×C32×D4—24no—
82C2×C32×D4—42no—
83C22×C32×C4C2311yescharacteristic
84C22×C32×C4C2311yescharacteristic
85C22×C32×C4C2312yes—
86C2×C3×#67—24no—
87C2×C3×#67—22no—
88C2×C3×#67—24no—
89C2×C3×#67—24no—
90C2×C3×#67—24no—
91C2×C3×#67—24no—
92C2×C3×#67—22no—
93C2×C3×#67—24no—
94C2×C3×#67—24no—
95C2×C3×#67—24no—
96C2×C3×#67—42no—
97C2×C3×#67—42no—
98C2×C3×#67D418yescomplemented
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2312yes—
101C22×C3×Dic3C2311yescharacteristic
102C3×D3×D4—232no—
103C2×C3×D12—24no—
104C2×C3×D12—22no—
105C2×C3×D12—24no—
106C2×C3×D12—22no—
107C2×C3×D12—24no—
108C2×C3×D12—24no—
109C2×C3×D12—42no—
110C2×C3×C4×D3—24no—
111C2×C3×C4×D3D414yescomplemented
112C32×C22⋊C4—22no—
113C32×C22⋊C4—24no—
114C3×#217—24no—
115C3×(C2×D3)⋊C4—22no—
116C3×(C2×D3)⋊C4—24no—
117C3×(C2×D3)⋊C4—24no—
118C3×(C2×D3)⋊C4D418yescomplemented
119C3×Dic3⋊C4—22no—
120C3×C4×Dic3—24no—
121#2433—31noSylow
122C25×C3—32no—
123C24×D3C22×C312yes—
124C22×C3×D4—21no—
125C22×C3×D4—22no—
126C22×C3×D4—32no—
127C22×C3×D4—31no—
128C22×C3×D4—31no—
129C22×C3×D4—32no—
130C22×C3×D4—32no—
131C22×C3×D4—31no—
132C22×C3×D4—31no—
133C22×C3×D4—32no—
134C22×C3×D4—64no—
135C22×C3×D4—68no—
136C22×C3×D4C2×D311yescharacteristic
137C22×C3×D4C2×D312yescomplemented
138C22×C3×D4C22×C311yescharacteristic
139C22×C3×D4C22×C312yescomplemented
140C23×C3×C4—31no—
141C22×#67C22×C311yescharacteristic
142C22×#67C22×C312yes—
143C22×#67C22×C311yescharacteristic, complemented
144C22×#67C22×C312yescomplemented
145C22×#67C22×C312yescomplemented
146C2×D3×D4—28no—
147C2×D3×D4—24no—
148C22×D12C22×C311yescharacteristic
149C22×D12C22×C311yescharacteristic
150C22×D12C22×C312yescomplemented
151C22×C4×D3C22×C311yescharacteristic
152C3×#127—68no—
153C3×#121—64no—
154C3×#120—68no—
155C3×#120—68no—
156C2×C3×C4⋊C4—31no—
157C2×C3×C22⋊C4—22no—
158C2×C3×C22⋊C4—21no—
159C2×C3×C22⋊C4—32no—
160C2×C3×C22⋊C4—32no—
161C2×C3×C22⋊C4—32no—
162C2×C3×C22⋊C4—32no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4C2×D312yescomplemented
165C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
166C2×C3×C22⋊C4C22×C312yescomplemented
167C2×C3×C22⋊C4C22×C311yescharacteristic, complemented
168C2×C3×C42—32no—
169C2×#217C22×C312yescomplemented
170#940—28no—
171#937—28no—
172C2×(C2×D3)⋊C4C22×C312yes—
173C2×(C2×D3)⋊C4C22×C312yescomplemented
174C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
175C2×(C2×D3)⋊C4C22×C312yescomplemented
176C2×Dic3⋊C4C22×C311yescharacteristic, complemented
177C2×C4×Dic3C22×C312yescomplemented
178#884—24no—
179#882—28no—
180C3×#95—21no—
181C3×#95—31no—
182C3×#95C2×D311yescharacteristic, complemented
183C3×#95C22×C311yescharacteristic, complemented
184C3⋊#95C22×C311yescharacteristic, complemented
185C23×C32—21no—
186C23×C32—22no—
187C23×C32—22no—
188C23×C32—22no—
189C23×C32—22no—
190C23×C32—22no—
191C23×C32—22no—
192C23×C32—21no—
193C23×C32—22no—
194C23×C32—22no—
195C23×C32—21no—
196C23×C32C2×D414yes—
197C23×C32C2411yescharacteristic
198C22×C3×D3—22no—
199C22×C3×D3—21no—
200C22×C3×D3—21no—
201C22×C3×D3—216no—
202C22×C3×D3—22no—
203C22×C3×D3—22no—
204C22×C3×D3—22no—
205C22×C3×D3—22no—
206C22×C3×D3—22no—
207C22×C3×D3—22no—
208C22×C3×D3—21no—
209C22×C3×D3—22no—
210C22×C3×D3—22no—
211C22×C3×D3—21no—
212C22×C3×D3—21no—
213C22×C3×D3—48no—
214C22×C3×D3—48no—
215C22×C3×D3—48no—
216C22×C3×D3—48no—
217C22×C3×D3—48no—
218C22×C3×D3—48no—
219C22×C3×D3C2×D414yes—
220C22×C3×D3C2×D414yes—
221C22×C3×D3C2×D412yes—
222C32×D4—28no—
223C32×D4—48no—
224C2×C32×C4—22no—
225C2×C32×C4—22no—
226C2×C32×C4—22no—
227C2×C32×C4—21no—
228C2×C32×C4—22no—
229C2×C32×C4C2×D412yes—
230C2×C32×C4C2×D414yescomplemented
231C3×#67—216no—
232C3×#67—48no—
233C3×#67—48no—
234C3×#67—44no—
235C3×#67—44no—
236C2×C3×Dic3—22no—
237C2×C3×Dic3—22no—
238C2×C3×Dic3—21no—
239C2×C3×Dic3—22no—
240C2×C3×Dic3C2×D414yes—
241C2×C3×Dic3C2×D412yes—
242C2×C3×Dic3C2×D414yescomplemented
243C3×D12—28no—
244C3×D12—48no—
245C3×D12—44no—
246C3×C4×D3—28no—
247C23×D4—31no—
248C2×#127—32no—
249C2×#121—31no—
250C2×#120—32no—
251C2×#120—32no—
252#392—31no—
253#392—31no—
254#392—31no—
255#392C3×D311yescharacteristic, complemented
256#390—32no—
257C4×C22⋊C4—31no—
258C24×C3—21no—
259C24×C3—22no—
260C24×C3—31no—
261C24×C3—32no—
262C24×C3—31no—
263C24×C3—64no—
264C24×C3—64no—
265C24×C3—64no—
266C24×C3—64no—
267C24×C3—64no—
268C24×C3—122no—
269C24×C3—122no—
270C24×C3C22×D311yescharacteristic
271C24×C3C22×D312yes—
272C24×C3C23×C311yescharacteristic
273C24×C3C23×C312yes—
274C23×D3—24no—
275C23×D3—24no—
276C23×D3—24no—
277C23×D3—24no—
278C23×D3—24no—
279C23×D3—42no—
280C23×D3—42no—
281C23×D3C23×C311yescharacteristic
282C23×D3C23×C312yes—
283C23×D3C23×C311yescharacteristic
284C2×C3×D4—24no—
285C2×C3×D4—24no—
286C2×C3×D4—24no—
287C2×C3×D4—24no—
288C2×C3×D4—22no—
289C2×C3×D4—24no—
290C2×C3×D4—22no—
291C2×C3×D4—24no—
292C2×C3×D4—38no—
293C2×C3×D4—42no—
294C2×C3×D4—44no—
295C2×C3×D4—44no—
296C2×C3×D4—44no—
297C2×C3×D4—42no—
298C2×C3×D4—42no—
299C2×C3×D4—44no—
300C2×C3×D4—64no—
301C2×C3×D4—64no—
302C2×C3×D4—62no—
303C2×C3×D4—64no—
304C2×C3×D4—64no—
305C2×C3×D4—64no—
306C2×C3×D4—64no—
307C2×C3×D4—64no—
308C2×C3×D4—62no—
309C2×C3×D4—64no—
310C2×C3×D4—632no—
311C2×C3×D4—64no—
312C2×C3×D4—62no—
313C2×C3×D4—64no—
314C2×C3×D4—64no—
315C2×C3×D4—62no—
316C2×C3×D4—64no—
317C2×C3×D4—122no—
318C2×C3×D4—122no—
319C2×C3×D4—122no—
320C22×C3×C4—21no—
321C22×C3×C4—22no—
322C22×C3×C4—21no—
323C22×C3×C4—31no—
324C22×C3×C4—32no—
325C22×C3×C4—34no—
326C22×C3×C4—31no—
327C22×C3×C4—64no—
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C22×D311yescharacteristic
330C22×C3×C4C22×D312yes—
331C22×C3×C4C23×C311yescharacteristic
332C22×C3×C4C23×C311yescharacteristic
333C22×C3×C4C23×C312yes—
334C2×#67—24no—
335C2×#67—22no—
336C2×#67—24no—
337C2×#67—24no—
338C2×#67—24no—
339C2×#67—24no—
340C2×#67—22no—
341C2×#67—24no—
342C2×#67—24no—
343C2×#67—24no—
344C2×#67—42no—
345C2×#67—42no—
346C2×#67C3×D418yescomplemented
347C22×Dic3C23×C311yescharacteristic
348C22×Dic3C23×C312yes—
349C22×Dic3C23×C311yescharacteristic
350D3×D4—232no—
351C2×D12—24no—
352C2×D12—22no—
353C2×D12—24no—
354C2×D12—22no—
355C2×D12—24no—
356C2×D12—24no—
357C2×D12—42no—
358C2×C4×D3—24no—
359C2×C4×D3C3×D414yescomplemented
360C3×C4⋊C4—62no—
361C3×C22⋊C4—22no—
362C3×C22⋊C4—24no—
363C3×C22⋊C4—22no—
364C3×C22⋊C4—24no—
365C3×C22⋊C4—38no—
366C3×C22⋊C4—42no—
367C3×C22⋊C4—44no—
368C3×C22⋊C4—64no—
369C3×C22⋊C4—64no—
370C3×C22⋊C4—62no—
371C3×C22⋊C4—64no—
372C3×C42—64no—
373#217—24no—
374(C2×D3)⋊C4—22no—
375(C2×D3)⋊C4—24no—
376(C2×D3)⋊C4—24no—
377(C2×D3)⋊C4C3×D418yescomplemented
378Dic3⋊C4—22no—
379C4×Dic3—24no—
380C22×C32—24no—
381C22×C32—24no—
382C22×C32—24no—
383C22×C32—41no—
384C22×C32—42no—
385C22×C32—42no—
386C22×C32—42no—
387C22×C32—42no—
388C22×C32—42no—
389C22×C32—41no—
390C22×C32—41no—
391C22×C32—42no—
392C22×C32C22×D411yescharacteristic
393C22×C32C22×D412yes—
394C22×C32C22×D412yes—
395C22×C32H(5,𝔽2)11yescharacteristic
396C22×C32H(5,𝔽2)11yescharacteristic
397C2×C3×D3—22no—
398C2×C3×D3—22no—
399C2×C3×D3—24no—
400C2×C3×D3—24no—
401C2×C3×D3—24no—
402C2×C3×D3—24no—
403C2×C3×D3—24no—
404C2×C3×D3—432no—
405C2×C3×D3—42no—
406C2×C3×D3—42no—
407C2×C3×D3—42no—
408C2×C3×D3—42no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—42no—
413C2×C3×D3—42no—
414C2×C3×D3#12714yescomplemented
415C32×C4—22no—
416C32×C4—24no—
417C32×C4—41no—
418C3×Dic3—24no—
419C3×Dic3—41no—
420C3×Dic3#12014yescomplemented
421C25—32no—
422C22×D4—32no—
423C22×D4—31no—
424C22×D4—31no—
425C22×D4—32no—
426C22×D4—32no—
427C22×D4—31no—
428C22×D4—31no—
429C22×D4—32no—
430C22×D4—64no—
431C22×D4—68no—
432C22×D4C2×C3×D311yescharacteristic
433C22×D4C2×C3×D312yescomplemented
434C23×C4—31no—
435#127—68no—
436#121—64no—
437#120—68no—
438#120—68no—
439C2×C4⋊C4—31no—
440C2×C22⋊C4—32no—
441C2×C22⋊C4—32no—
442C2×C22⋊C4—32no—
443C2×C22⋊C4—32no—
444C2×C22⋊C4—31no—
445C2×C22⋊C4C2×C3×D312yescomplemented
446C2×C22⋊C4C2×C3×D311yescharacteristic, complemented
447C2×C42—32no—
448#95—31no—
449#95C2×C3×D311yescharacteristic, complemented
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—21no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—24no—
475C23×C3—34no—
476C23×C3—32no—
477C23×C3—34no—
478C23×C3—42no—
479C23×C3—41no—
480C23×C3—42no—
481C23×C3—42no—
482C23×C3—42no—
483C23×C3—42no—
484C23×C3—42no—
485C23×C3—42no—
486C23×C3—42no—
487C23×C3—41no—
488C23×C3—616no—
489C23×C3—62no—
490C23×C3—61no—
491C23×C3—61no—
492C23×C3—62no—
493C23×C3—62no—
494C23×C3—62no—
495C23×C3—62no—
496C23×C3—62no—
497C23×C3—62no—
498C23×C3—61no—
499C23×C3—62no—
500C23×C3—62no—
501C23×C3—61no—
502C23×C3—61no—
503C23×C3—128no—
504C23×C3—128no—
505C23×C3—128no—
506C23×C3—128no—
507C23×C3—128no—
508C23×C3—128no—
509C23×C3D3×D414yes—
510C23×C3C2×C3×D414yes—
511C23×C3C23×D311yescharacteristic
512C23×C3C24×C311yescharacteristic
513C22×D3—22no—
514C22×D3—21no—
515C22×D3—21no—
516C22×D3—216no—
517C22×D3—22no—
518C22×D3—22no—
519C22×D3—22no—
520C22×D3—22no—
521C22×D3—22no—
522C22×D3—22no—
523C22×D3—21no—
524C22×D3—22no—
525C22×D3—22no—
526C22×D3—21no—
527C22×D3—21no—
528C22×D3—48no—
529C22×D3—48no—
530C22×D3—48no—
531C22×D3—48no—
532C22×D3—48no—
533C22×D3—48no—
534C22×D3C2×C3×D414yes—
535C22×D3C2×C3×D414yes—
536C22×D3C2×C3×D412yes—
537C3×D4—28no—
538C3×D4—28no—
539C3×D4—48no—
540C3×D4—48no—
541C3×D4—48no—
542C3×D4—416no—
543C3×D4—68no—
544C3×D4—616no—
545C3×D4—128no—
546C3×D4—124no—
547C3×D4—124no—
548C3×D4—128no—
549C3×D4—128no—
550C3×D4—124no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—24no—
563C2×C3×C4—34no—
564C2×C3×C4—32no—
565C2×C3×C4—34no—
566C2×C3×C4—42no—
567C2×C3×C4—42no—
568C2×C3×C4—42no—
569C2×C3×C4—42no—
570C2×C3×C4—41no—
571C2×C3×C4—68no—
572C2×C3×C4—62no—
573C2×C3×C4—62no—
574C2×C3×C4—62no—
575C2×C3×C4—61no—
576C2×C3×C4D3×D412yes—
577C2×C3×C4D3×D414yescomplemented
578C2×C3×C4C2×C3×D412yes—
579C2×C3×C4C2×C3×D414yescomplemented
580#67—216no—
581#67—48no—
582#67—48no—
583#67—44no—
584#67—44no—
585C2×Dic3—22no—
586C2×Dic3—22no—
587C2×Dic3—21no—
588C2×Dic3—22no—
589C2×Dic3C2×C3×D414yes—
590C2×Dic3C2×C3×D412yes—
591C2×Dic3C2×C3×D414yescomplemented
592D12—28no—
593D12—48no—
594D12—44no—
595C4×D3—28no—
596C2×C32—44no—
597C2×C32—81no—
598C2×C32C2×#12011yescharacteristic
599C2×C32C2×#12711yescharacteristic
600C2×C32#53511yescharacteristic
601C2×C32D4212yes—
602C2×C32D4212yes—
603C3×D3—24no—
604C3×D3—44no—
605C3×D3—81no—
606C24—31no—
607C24—32no—
608C24—31no—
609C24—64no—
610C24—64no—
611C24—64no—
612C24—64no—
613C24—64no—
614C24—122no—
615C24—122no—
616C24C22×C3×D311yescharacteristic
617C24C22×C3×D312yes—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—22no—
621C2×D4—24no—
622C2×D4—38no—
623C2×D4—42no—
624C2×D4—64no—
625C2×D4—64no—
626C2×D4—62no—
627C2×D4—64no—
628C2×D4—64no—
629C2×D4—64no—
630C2×D4—64no—
631C2×D4—64no—
632C2×D4—62no—
633C2×D4—64no—
634C2×D4—632no—
635C2×D4—64no—
636C2×D4—62no—
637C2×D4—64no—
638C2×D4—64no—
639C2×D4—62no—
640C2×D4—64no—
641C2×D4—122no—
642C2×D4—122no—
643C2×D4—122no—
644C22×C4—31no—
645C22×C4—32no—
646C22×C4—34no—
647C22×C4—31no—
648C22×C4—64no—
649C22×C4C22×C3×D311yescharacteristic
650C22×C4C22×C3×D311yescharacteristic
651C22×C4C22×C3×D312yes—
652C4⋊C4—62no—
653C22⋊C4—22no—
654C22⋊C4—24no—
655C22⋊C4—38no—
656C22⋊C4—64no—
657C22⋊C4—64no—
658C22⋊C4—62no—
659C22⋊C4—64no—
660C42—64no—
661C22×C3—24no—
662C22×C3—24no—
663C22×C3—24no—
664C22×C3—24no—
665C22×C3—24no—
666C22×C3—24no—
667C22×C3—21no—
668C22×C3—22no—
669C22×C3—22no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—34no—
673C22×C3—44no—
674C22×C3—44no—
675C22×C3—44no—
676C22×C3—44no—
677C22×C3—42no—
678C22×C3—42no—
679C22×C3—42no—
680C22×C3—42no—
681C22×C3—42no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3—42no—
685C22×C3—42no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—42no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—42no—
693C22×C3—41no—
694C22×C3—42no—
695C22×C3—42no—
696C22×C3—62no—
697C22×C3—64no—
698C22×C3—62no—
699C22×C3—64no—
700C22×C3—64no—
701C22×C3—64no—
702C22×C3—64no—
703C22×C3—82no—
704C22×C3—82no—
705C22×C3—82no—
706C22×C3—82no—
707C22×C3—81no—
708C22×C3—82no—
709C22×C3—81no—
710C22×C3—1232no—
711C22×C3—122no—
712C22×C3—122no—
713C22×C3—122no—
714C22×C3—122no—
715C22×C3—121no—
716C22×C3—121no—
717C22×C3—122no—
718C22×C3—121no—
719C22×C3—122no—
720C22×C3C2×D3×D411yescharacteristic
721C22×C3C2×D3×D412yes—
722C22×C3C2×D3×D412yes—
723C22×C3#100411yescharacteristic
724C22×C3#100911yescharacteristic
725C22×C3C22×C3×D411yescharacteristic
726C22×C3C22×C3×D412yes—
727C22×C3C22×C3×D412yes—
728C22×C3C3×H(5,𝔽2)11yescharacteristic
729C22×C3C3×H(5,𝔽2)11yescharacteristic
730C2×D3—22no—
731C2×D3—22no—
732C2×D3—24no—
733C2×D3—24no—
734C2×D3—24no—
735C2×D3—24no—
736C2×D3—24no—
737C2×D3—432no—
738C2×D3—42no—
739C2×D3—42no—
740C2×D3—42no—
741C2×D3—42no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—41no—
745C2×D3—42no—
746C2×D3—42no—
747C2×D3C3×#12714yescomplemented
748C3×C4—22no—
749C3×C4—24no—
750C3×C4—22no—
751C3×C4—24no—
752C3×C4—34no—
753C3×C4—42no—
754C3×C4—44no—
755C3×C4—41no—
756C3×C4—41no—
757C3×C4—64no—
758C3×C4—81no—
759C3×C4—121no—
760Dic3—24no—
761Dic3—41no—
762Dic3C3×#12014yescomplemented
763C32#243311yescharacteristic, complemented, Sylow
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—21no—
771C23—22no—
772C23—22no—
773C23—21no—
774C23—21no—
775C23—34no—
776C23—32no—
777C23—34no—
778C23—616no—
779C23—62no—
780C23—61no—
781C23—61no—
782C23—62no—
783C23—62no—
784C23—62no—
785C23—62no—
786C23—62no—
787C23—62no—
788C23—61no—
789C23—62no—
790C23—62no—
791C23—61no—
792C23—61no—
793C23—128no—
794C23—128no—
795C23—128no—
796C23—128no—
797C23—128no—
798C23—128no—
799C23C3×D3×D414yes—
800C23C23×C3×D311yescharacteristic
801D4—28no—
802D4—48no—
803D4—68no—
804D4—616no—
805D4—128no—
806D4—124no—
807D4—124no—
808D4—128no—
809D4—128no—
810D4—124no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—34no—
817C2×C4—32no—
818C2×C4—34no—
819C2×C4—68no—
820C2×C4—62no—
821C2×C4—62no—
822C2×C4—62no—
823C2×C4—61no—
824C2×C4C3×D3×D412yes—
825C2×C4C3×D3×D414yescomplemented
826C2×C3—21no—
827C2×C3—22no—
828C2×C3—21no—
829C2×C3—22no—
830C2×C3—21no—
831C2×C3—44no—
832C2×C3—44no—
833C2×C3—64no—
834C2×C3—84no—
835C2×C3—82no—
836C2×C3—81no—
837C2×C3—81no—
838C2×C3—124no—
839C2×C3—241no—
840C2×C3D3×#12011yescharacteristic
841C2×C3#559012yes—
842C2×C3#560711yescharacteristic
843C2×C3#560912yes—
844C2×C3D3×#12711yescharacteristic
845C2×C3C2×C3×#12011yescharacteristic
846C2×C3C2×C3×#12711yescharacteristic
847C2×C3C3×#53511yescharacteristic
848C2×C3C3×D4212yes—
849C2×C3C3×D4212yes—
850D3—24no—
851D3—44no—
852D3—81no—
853C22—24no—
854C22—24no—
855C22—24no—
856C22—34no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—41no—
862C22—42no—
863C22—41no—
864C22—42no—
865C22—41no—
866C22—62no—
867C22—64no—
868C22—62no—
869C22—64no—
870C22—64no—
871C22—64no—
872C22—64no—
873C22—1232no—
874C22—122no—
875C22—122no—
876C22—122no—
877C22—122no—
878C22—121no—
879C22—122no—
880C22—121no—
881C22—122no—
882C22—121no—
883C22C2×C3×D3×D412yes—
884C22C2×C3×D3×D411yescharacteristic
885C22C2×C3×D3×D412yes—
886C22C3×#100411yescharacteristic
887C22C3×#100911yescharacteristic
888C4—22no—
889C4—24no—
890C4—34no—
891C4—41no—
892C4—64no—
893C4—121no—
894C3—21no—
895C3#7667311yescharacteristic, direct product factor
896C3C3×#243311yescharacteristic, complemented
897C2—44no—
898C2—64no—
899C2—81no—
900C2—124no—
901C2—241no—
902C2C3×D3×#12011yescharacteristic
903C2C3×#559012yes—
904C2C3×#560711yescharacteristic
905C2C3×#560912yes—
906C2C3×D3×#12711yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#392C2
socleC23×C32C24
hypercenterC3×#392D3
hypocenterC3C3×#2433
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#392

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×D4C2semidirect
2. C2×C3×#940C2semidirect
3. C2×C3×#937C2semidirect
4. C2×C3×#884C2semidirect
5. C2×C3×#882C2semidirect
6. C32×#392C2semidirect
7. C3×#5223C2semidirect
8. C3×#4960C2semidirect
9. C3×#4957C2semidirect
10. C3×#4671C2semidirect
11. C3×#4666C2semidirect
13. #76673C3direct (N × H)
16. C22×C32×D4C22semidirect
19. C22×C3×#67C22semidirect
20. C22×C3×#67C22semidirect
21. C22×C3×#67C22semidirect
26. C22×C3×D12C22semidirect
28. C2×C32×C22⋊C4C22semidirect
29. C2×C32×C22⋊C4C22semidirect
30. C2×C3×#217C22semidirect
34. C2×C3×(C2×D3)⋊C4C22semidirect
35. C2×C3×(C2×D3)⋊C4C22semidirect
36. C2×C3×(C2×D3)⋊C4C22semidirect
37. C2×C3×Dic3⋊C4C22semidirect
38. C2×C3×C4×Dic3C22semidirect
41. C32×#95C22semidirect
42. C3×C3⋊#95C22semidirect
44. C22×D3×D4C2×C3semidirect
49. C2×#940C2×C3semidirect
50. C2×#937C2×C3semidirect
51. C2×#884C2×C3semidirect
52. C2×#882C2×C3semidirect
57. C3×#392D3semidirect
58. C3×#392C2×C3semidirect
61. #5223C2×C3semidirect
62. #4960C2×C3semidirect
63. #4957C2×C3semidirect
64. #4671C2×C3semidirect
65. #4666C2×C3semidirect
98. C2×C3×#67D4semidirect
111. C2×C3×C4×D3D4semidirect
118. C3×(C2×D3)⋊C4D4semidirect
137. C22×C3×D4C2×D3semidirect
139. C22×C3×D4C22×C3semidirect
143. C22×#67C22×C3semidirect
144. C22×#67C22×C3semidirect
145. C22×#67C22×C3semidirect
150. C22×D12C22×C3semidirect
164. C2×C3×C22⋊C4C2×D3semidirect
165. C2×C3×C22⋊C4C2×D3semidirect
166. C2×C3×C22⋊C4C22×C3semidirect
167. C2×C3×C22⋊C4C22×C3semidirect
169. C2×#217C22×C3semidirect
173. C2×(C2×D3)⋊C4C22×C3semidirect
174. C2×(C2×D3)⋊C4C22×C3semidirect
175. C2×(C2×D3)⋊C4C22×C3semidirect
176. C2×Dic3⋊C4C22×C3semidirect
177. C2×C4×Dic3C22×C3semidirect
182. C3×#95C2×D3semidirect
183. C3×#95C22×C3semidirect
184. C3⋊#95C22×C3semidirect
230. C2×C32×C4C2×D4semidirect
242. C2×C3×Dic3C2×D4semidirect
255. #392C3×D3semidirect
346. C2×#67C3×D4semidirect
359. C2×C4×D3C3×D4semidirect
377. (C2×D3)⋊C4C3×D4semidirect
414. C2×C3×D3#127semidirect
420. C3×Dic3#120semidirect
433. C22×D4C2×C3×D3semidirect
445. C2×C22⋊C4C2×C3×D3semidirect
446. C2×C22⋊C4C2×C3×D3semidirect
449. #95C2×C3×D3semidirect
577. C2×C3×C4D3×D4semidirect
579. C2×C3×C4C2×C3×D4semidirect
591. C2×Dic3C2×C3×D4semidirect
747. C2×D3C3×#127semidirect
762. Dic3C3×#120semidirect
763. C32#2433semidirect
825. C2×C4C3×D3×D4semidirect
895. C3#76673direct (N × H)
896. C3C3×#2433semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×D42
C2×C3×#9402
C2×C3×#9372
C2×C3×#8842
C2×C3×#8822
C32×#3922
C3×#52232
C3×#49602
C3×#49572
C3×#46712
C3×#46662
C3×#24333
#766733