Finite Group Databasebeta

← C3×#76688 #11824413

Subgroups — C3×#76688 #11824413

Order 1152.

2057 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#940C212yesmaximal, complemented
2C2×C3×#940C211yesmaximal, characteristic, complemented
3C2×C3×#939C212yesmaximal, complemented
4C2×C3×#884C212yesmaximal, complemented
5C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
6C32×#392C211yesmaximal, characteristic, complemented
7C3×#5223C211yesmaximal, characteristic, complemented
8C3×#4960C211yesmaximal, characteristic, complemented
9C3×#4957C212yesmaximal, complemented
10C3×#4671C211yesmaximal, characteristic, complemented
11C3×#4649C211yesmaximal, characteristic, complemented
12C3×#2541—31nomaximal
13#76688C311yesmaximal, characteristic, direct product factor
14C22×C32×D4C2212yes—
15C22×C32×D4C2211yescharacteristic
16C22×C3×#67C2212yes—
17C22×C3×#67C2212yes—
18C22×C3×#67C2212yes—
19C22×C3×#67C2212yes—
20C22×C3×#67C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C22×C3×D12C2212yes—
23C22×C3×D12C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C2×C32×C22⋊C4C2212yes—
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×C3×#217C2212yes—
28C3×#940—28no—
29C3×#940—24no—
30C3×#939—28no—
31C2×C3×(C2×D3)⋊C4C2212yes—
32C2×C3×(C2×D3)⋊C4C2212yes—
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2212yes—
36C2×C3×C4×Dic3C2212yes—
37C2×C3×C4×Dic3C2211yescharacteristic
38C3×#884—28no—
39C3×#67⋊C4—24no—
40C32×#95C2211yescharacteristic
41C3×C3⋊#95C2211yescharacteristic
42C2×C3×#127—31no—
43C2×C3×#127—32no—
44C2×C3×#121—32no—
45C2×C3×#121—32no—
46C2×C3×C4×D4—31no—
47C2×#940C2×C312yescomplemented
48C2×#940C2×C311yescharacteristic, complemented
49C2×#939C2×C312yescomplemented
50C2×#884C2×C312yescomplemented
51C2×#67⋊C4C2×C311yescharacteristic, complemented
52C3×#392—21no—
53C3×#392—31no—
54C3×#392—31no—
55C3×#392—31no—
56C3×#392D311yescharacteristic, complemented
57C3×#392C2×C311yescharacteristic, complemented
58C3×#390—32no—
59C3×C4×C4⋊C4—31no—
60#5223C2×C311yescharacteristic, complemented
61#4960C2×C311yescharacteristic, complemented
62#4957C2×C312yescomplemented
63#4671C2×C311yescharacteristic, complemented
64#4649C2×C311yescharacteristic, complemented
65C24×C32C2312yes—
66C24×C32C2311yescharacteristic
67C23×C3×D3C2312yes—
68C23×C3×D3C2311yescharacteristic
69C2×C32×D4—24no—
70C2×C32×D4—24no—
71C2×C32×D4—22no—
72C2×C32×D4—42no—
73C2×C32×D4—42no—
74C22×C32×C4C2311yescharacteristic
75C22×C32×C4C2312yes—
76C22×C32×C4C2311yescharacteristic
77C2×C3×#67—24no—
78C2×C3×#67—24no—
79C2×C3×#67—22no—
80C2×C3×#67—24no—
81C2×C3×#67—24no—
82C2×C3×#67—24no—
83C2×C3×#67—24no—
84C2×C3×#67—24no—
85C2×C3×#67—24no—
86C2×C3×#67—24no—
87C2×C3×#67—22no—
88C2×C3×#67—24no—
89C2×C3×#67—42no—
90C2×C3×#67—42no—
91C2×C3×#67D414yescomplemented
92C22×C3×Dic3—22no—
93C22×C3×Dic3—24no—
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2312yes—
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C2×C3×D12—24no—
99C2×C3×D12—24no—
100C2×C3×D12—22no—
101C2×C3×D12—42no—
102C2×C3×D12—42no—
103C2×C3×C4×D3—22no—
104C2×C3×C4×D3—24no—
105C32×C22⋊C4—22no—
106C32×C22⋊C4—24no—
107C3×#217—24no—
108C3×(C2×D3)⋊C4—22no—
109C3×(C2×D3)⋊C4—24no—
110C3×(C2×D3)⋊C4—24no—
111C3×Dic3⋊C4—22no—
112C3×Dic3⋊C4D418yescomplemented
113C3×C4×Dic3—24no—
114C3×C4×Dic3D414yescomplemented
115#2541—31noSylow
116C22×C3×D4—22no—
117C22×C3×D4—21no—
118C22×C3×D4—31no—
119C22×C3×D4—32no—
120C22×C3×D4—32no—
121C22×C3×D4—32no—
122C22×C3×D4—32no—
123C22×C3×D4—32no—
124C22×C3×D4—31no—
125C22×C3×D4C2×D312yes—
126C22×C3×D4C2×D311yescharacteristic
127C22×C3×D4C22×C312yes—
128C22×C3×D4C22×C311yescharacteristic
129C23×C3×C4—31no—
130C23×C3×C4—31no—
131C22×#67C22×C312yes—
132C22×#67C22×C312yes—
133C22×#67C22×C312yes—
134C22×#67C22×C312yes—
135C22×#67C22×C311yescharacteristic
136C23×Dic3C22×C311yescharacteristic
137C22×D12C22×C312yes—
138C22×D12C22×C311yescharacteristic
139C22×C4×D3C22×C311yescharacteristic
140C3×#127—64no—
141C3×#127—68no—
142C3×#121—68no—
143C3×#121—68no—
144C3×C4×D4—64no—
145C2×C3×C4⋊C4—32no—
146C2×C3×C4⋊C4—31no—
147C2×C3×C22⋊C4—21no—
148C2×C3×C22⋊C4—22no—
149C2×C3×C22⋊C4—32no—
150C2×C3×C22⋊C4—32no—
151C2×C3×C22⋊C4—32no—
152C2×C3×C22⋊C4—31no—
153C2×C3×C22⋊C4C2×D312yes—
154C2×C3×C22⋊C4C2×D311yescharacteristic
155C2×C3×C22⋊C4C22×C312yes—
156C2×C3×C22⋊C4C22×C311yescharacteristic
157C2×C3×C42—31no—
158C2×C3×C42—32no—
159C2×#217C22×C312yes—
160#940—28no—
161#940—24no—
162#939—28no—
163C2×(C2×D3)⋊C4C22×C312yes—
164C2×(C2×D3)⋊C4C22×C311yescharacteristic
165C2×(C2×D3)⋊C4C22×C312yes—
166C2×Dic3⋊C4C22×C311yescharacteristic
167C2×Dic3⋊C4C22×C312yes—
168C2×C4×Dic3C22×C312yes—
169C2×C4×Dic3C22×C311yescharacteristic
170#884—28no—
171#67⋊C4—24no—
172C3×#95—21no—
173C3×#95—31no—
174C3×#95C2×D311yescharacteristic
175C3×#95C22×C311yescharacteristic
176C3⋊#95C22×C311yescharacteristic
177C23×C32—22no—
178C23×C32—21no—
179C23×C32—22no—
180C23×C32—21no—
181C23×C32—22no—
182C23×C32—22no—
183C23×C32—22no—
184C23×C32—22no—
185C23×C32—22no—
186C23×C32—22no—
187C23×C32—22no—
188C23×C32C2×D412yes—
189C23×C32C2411yescharacteristic
190C22×C3×D3—21no—
191C22×C3×D3—22no—
192C22×C3×D3—21no—
193C22×C3×D3—22no—
194C22×C3×D3—22no—
195C22×C3×D3—22no—
196C22×C3×D3—22no—
197C22×C3×D3—22no—
198C22×C3×D3—22no—
199C22×C3×D3—22no—
200C22×C3×D3—22no—
201C22×C3×D3C2×D412yes—
202C32×D4—48no—
203C32×D4—44no—
204C2×C32×C4—22no—
205C2×C32×C4—22no—
206C2×C32×C4—22no—
207C2×C32×C4—21no—
208C2×C32×C4—22no—
209C2×C32×C4C2×D412yes—
210C2×C32×C4C2×D414yes—
211C3×#67—28no—
212C3×#67—48no—
213C3×#67—48no—
214C3×#67—48no—
215C3×#67—48no—
216C2×C3×Dic3—22no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3—21no—
219C2×C3×Dic3—22no—
220C2×C3×Dic3—44no—
221C2×C3×Dic3C2×D414yes—
222C2×C3×Dic3C2×D412yes—
223C2×C3×Dic3C2×D412yes—
224C2×C3×Dic3C2×D412yes—
225C2×C3×Dic3C2×D414yes—
226C2×C3×Dic3#4112yes—
227C3×D12—48no—
228C3×D12—44no—
229C3×C4×D3—44no—
230C2×#127—31no—
231C2×#127—32no—
232C2×#121—32no—
233C2×#121—32no—
234C2×C4×D4—31no—
235#392—31no—
236#392—31no—
237#392—31no—
238#392C3×D311yescharacteristic, complemented
239#390—32no—
240C4×C4⋊C4—31no—
241C24×C3—22no—
242C24×C3—21no—
243C24×C3—31no—
244C24×C3—32no—
245C24×C3C22×D312yes—
246C24×C3C22×D311yescharacteristic
247C24×C3C23×C312yes—
248C24×C3C23×C311yescharacteristic
249C23×D3C23×C312yes—
250C23×D3C23×C311yescharacteristic
251C2×C3×D4—24no—
252C2×C3×D4—24no—
253C2×C3×D4—24no—
254C2×C3×D4—22no—
255C2×C3×D4—24no—
256C2×C3×D4—22no—
257C2×C3×D4—34no—
258C2×C3×D4—44no—
259C2×C3×D4—42no—
260C2×C3×D4—44no—
261C2×C3×D4—42no—
262C2×C3×D4—42no—
263C2×C3×D4—42no—
264C2×C3×D4—42no—
265C2×C3×D4—44no—
266C2×C3×D4—44no—
267C2×C3×D4—64no—
268C2×C3×D4—62no—
269C2×C3×D4—62no—
270C2×C3×D4—64no—
271C2×C3×D4—64no—
272C2×C3×D4—64no—
273C2×C3×D4—64no—
274C2×C3×D4—64no—
275C2×C3×D4—64no—
276C2×C3×D4—64no—
277C2×C3×D4—64no—
278C2×C3×D4—64no—
279C2×C3×D4—64no—
280C2×C3×D4—64no—
281C2×C3×D4—62no—
282C2×C3×D4—122no—
283C2×C3×D4—122no—
284C2×C3×D4—122no—
285C2×C3×D4—122no—
286C22×C3×C4—21no—
287C22×C3×C4—22no—
288C22×C3×C4—21no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—32no—
292C22×C3×C4—31no—
293C22×C3×C4—62no—
294C22×C3×C4—64no—
295C22×C3×C4—62no—
296C22×C3×C4—64no—
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D312yes—
300C22×C3×C4C23×C311yescharacteristic
301C22×C3×C4C23×C311yescharacteristic
302C22×C3×C4C23×C312yes—
303C2×#67—24no—
304C2×#67—24no—
305C2×#67—22no—
306C2×#67—24no—
307C2×#67—24no—
308C2×#67—24no—
309C2×#67—24no—
310C2×#67—24no—
311C2×#67—24no—
312C2×#67—24no—
313C2×#67—22no—
314C2×#67—24no—
315C2×#67—42no—
316C2×#67—42no—
317C2×#67C3×D414yescomplemented
318C22×Dic3—22no—
319C22×Dic3—24no—
320C22×Dic3C23×C311yescharacteristic
321C22×Dic3C23×C312yes—
322C22×Dic3C23×C311yescharacteristic
323C22×Dic3C23×C311yescharacteristic
324C2×D12—24no—
325C2×D12—24no—
326C2×D12—22no—
327C2×D12—42no—
328C2×D12—42no—
329C2×C4×D3—22no—
330C2×C4×D3—24no—
331C3×C4⋊C4—38no—
332C3×C4⋊C4—62no—
333C3×C22⋊C4—22no—
334C3×C22⋊C4—24no—
335C3×C22⋊C4—22no—
336C3×C22⋊C4—24no—
337C3×C22⋊C4—42no—
338C3×C22⋊C4—44no—
339C3×C22⋊C4—64no—
340C3×C22⋊C4—64no—
341C3×C22⋊C4—62no—
342C3×C22⋊C4—64no—
343C3×C42—34no—
344C3×C42—64no—
345#217—24no—
346(C2×D3)⋊C4—22no—
347(C2×D3)⋊C4—24no—
348(C2×D3)⋊C4—24no—
349Dic3⋊C4—22no—
350Dic3⋊C4C3×D418yescomplemented
351C4×Dic3—24no—
352C4×Dic3C3×D414yescomplemented
353C22×C32—22no—
354C22×C32—24no—
355C22×C32—42no—
356C22×C32—42no—
357C22×C32—42no—
358C22×C32—41no—
359C22×C32—41no—
360C22×C32—42no—
361C22×C32—42no—
362C22×C32—42no—
363C22×C32—42no—
364C22×C32—42no—
365C22×C32C22×D411yescharacteristic
366C22×C32C22×D411yescharacteristic
367C22×C32C22×D412yes—
368C22×C32C2×#4111yescharacteristic
369C22×C32H(5,𝔽2)12yes—
370C2×C3×D3—22no—
371C2×C3×D3—24no—
372C2×C3×D3—41no—
373C2×C3×D3—41no—
374C2×C3×D3—42no—
375C2×C3×D3—42no—
376C2×C3×D3—42no—
377C2×C3×D3—42no—
378C2×C3×D3—42no—
379C2×C3×D3—42no—
380C2×C3×D3—42no—
381C2×C3×D3—42no—
382C32×C4—22no—
383C32×C4—24no—
384C32×C4—41no—
385C3×Dic3—24no—
386C3×Dic3—41no—
387C3×Dic3#12114yescomplemented
388C3×Dic3#12714yescomplemented
389C22×D4—31no—
390C22×D4—32no—
391C22×D4—32no—
392C22×D4—32no—
393C22×D4—32no—
394C22×D4—32no—
395C22×D4—31no—
396C22×D4C2×C3×D312yes—
397C22×D4C2×C3×D311yescharacteristic
398C23×C4—31no—
399C23×C4—31no—
400#127—64no—
401#127—68no—
402#121—68no—
403#121—68no—
404C4×D4—64no—
405C2×C4⋊C4—32no—
406C2×C4⋊C4—31no—
407C2×C22⋊C4—32no—
408C2×C22⋊C4—31no—
409C2×C22⋊C4—32no—
410C2×C22⋊C4—32no—
411C2×C22⋊C4C2×C3×D311yescharacteristic
412C2×C22⋊C4C2×C3×D312yes—
413C2×C42—31no—
414C2×C42—32no—
415#95—31no—
416#95C2×C3×D311yescharacteristic
417C23×C3—21no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—22no—
423C23×C3—21no—
424C23×C3—22no—
425C23×C3—24no—
426C23×C3—22no—
427C23×C3—22no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—22no—
440C23×C3—21no—
441C23×C3—22no—
442C23×C3—32no—
443C23×C3—41no—
444C23×C3—42no—
445C23×C3—42no—
446C23×C3—42no—
447C23×C3—42no—
448C23×C3—42no—
449C23×C3—42no—
450C23×C3—42no—
451C23×C3—41no—
452C23×C3—42no—
453C23×C3—61no—
454C23×C3—62no—
455C23×C3—62no—
456C23×C3—61no—
457C23×C3—62no—
458C23×C3—62no—
459C23×C3—62no—
460C23×C3—62no—
461C23×C3—62no—
462C23×C3—62no—
463C23×C3—62no—
464C23×C3D3×D412yes—
465C23×C3C2×C3×D412yes—
466C23×C3C23×D311yescharacteristic
467C23×C3C24×C311yescharacteristic
468C22×D3—21no—
469C22×D3—22no—
470C22×D3—21no—
471C22×D3—22no—
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—22no—
478C22×D3—22no—
479C22×D3C2×C3×D412yes—
480C3×D4—48no—
481C3×D4—48no—
482C3×D4—44no—
483C3×D4—44no—
484C3×D4—416no—
485C3×D4—48no—
486C3×D4—68no—
487C3×D4—128no—
488C3×D4—124no—
489C3×D4—128no—
490C3×D4—128no—
491C3×D4—128no—
492C3×D4—128no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—24no—
505C2×C3×C4—32no—
506C2×C3×C4—32no—
507C2×C3×C4—32no—
508C2×C3×C4—34no—
509C2×C3×C4—32no—
510C2×C3×C4—34no—
511C2×C3×C4—42no—
512C2×C3×C4—42no—
513C2×C3×C4—42no—
514C2×C3×C4—42no—
515C2×C3×C4—41no—
516C2×C3×C4—62no—
517C2×C3×C4—62no—
518C2×C3×C4—62no—
519C2×C3×C4—61no—
520C2×C3×C4—124no—
521C2×C3×C4—124no—
522C2×C3×C4D3×D412yes—
523C2×C3×C4D3×D414yes—
524C2×C3×C4C2×C3×D412yes—
525C2×C3×C4C2×C3×D414yes—
526#67—28no—
527#67—48no—
528#67—48no—
529#67—48no—
530#67—48no—
531C2×Dic3—22no—
532C2×Dic3—22no—
533C2×Dic3—21no—
534C2×Dic3—22no—
535C2×Dic3—44no—
536C2×Dic3C2×C3×D414yes—
537C2×Dic3C2×C3×D412yes—
538C2×Dic3C2×C3×D412yes—
539C2×Dic3C2×C3×D412yes—
540C2×Dic3C2×C3×D414yes—
541C2×Dic3C3×#4112yes—
542D12—48no—
543D12—44no—
544C4×D3—44no—
545C2×C32—42no—
546C2×C32—82no—
547C2×C32C2×#12111yescharacteristic
548C2×C32C2×#12711yescharacteristic
549C2×C32#53511yescharacteristic
550C2×C32D4212yes—
551C2×C32#55012yes—
552C3×D3—42no—
553C3×D3—82no—
554C24—31no—
555C24—32no—
556C24C22×C3×D312yes—
557C24C22×C3×D311yescharacteristic
558C2×D4—24no—
559C2×D4—24no—
560C2×D4—22no—
561C2×D4—34no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—64no—
565C2×D4—62no—
566C2×D4—62no—
567C2×D4—64no—
568C2×D4—64no—
569C2×D4—64no—
570C2×D4—64no—
571C2×D4—64no—
572C2×D4—64no—
573C2×D4—64no—
574C2×D4—64no—
575C2×D4—64no—
576C2×D4—64no—
577C2×D4—64no—
578C2×D4—62no—
579C2×D4—122no—
580C2×D4—122no—
581C2×D4—122no—
582C2×D4—122no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—32no—
586C22×C4—31no—
587C22×C4—62no—
588C22×C4—64no—
589C22×C4—62no—
590C22×C4—64no—
591C22×C4C22×C3×D311yescharacteristic
592C22×C4C22×C3×D311yescharacteristic
593C22×C4C22×C3×D312yes—
594C4⋊C4—38no—
595C4⋊C4—62no—
596C22⋊C4—22no—
597C22⋊C4—24no—
598C22⋊C4—64no—
599C22⋊C4—64no—
600C22⋊C4—62no—
601C22⋊C4—64no—
602C42—34no—
603C42—64no—
604C22×C3—24no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—24no—
608C22×C3—22no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—22no—
612C22×C3—21no—
613C22×C3—44no—
614C22×C3—42no—
615C22×C3—44no—
616C22×C3—44no—
617C22×C3—44no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—42no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—42no—
624C22×C3—42no—
625C22×C3—42no—
626C22×C3—42no—
627C22×C3—42no—
628C22×C3—42no—
629C22×C3—42no—
630C22×C3—42no—
631C22×C3—42no—
632C22×C3—42no—
633C22×C3—42no—
634C22×C3—42no—
635C22×C3—42no—
636C22×C3—42no—
637C22×C3—42no—
638C22×C3—64no—
639C22×C3—62no—
640C22×C3—81no—
641C22×C3—82no—
642C22×C3—81no—
643C22×C3—82no—
644C22×C3—82no—
645C22×C3—82no—
646C22×C3—82no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—122no—
650C22×C3—122no—
651C22×C3—122no—
652C22×C3—122no—
653C22×C3—122no—
654C22×C3—122no—
655C22×C3—122no—
656C22×C3—122no—
657C22×C3C2×D3×D412yes—
658C22×C3C2×D3×D411yescharacteristic
659C22×C3C2×D3×D411yescharacteristic
660C22×C3#100412yes—
661C22×C3D3×#4111yescharacteristic
662C22×C3C22×C3×D411yescharacteristic
663C22×C3C22×C3×D411yescharacteristic
664C22×C3C22×C3×D412yes—
665C22×C3C2×C3×#4111yescharacteristic
666C22×C3C3×H(5,𝔽2)12yes—
667C2×D3—22no—
668C2×D3—24no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—42no—
672C2×D3—42no—
673C2×D3—42no—
674C2×D3—42no—
675C2×D3—42no—
676C2×D3—42no—
677C2×D3—42no—
678C2×D3—42no—
679C3×C4—24no—
680C3×C4—22no—
681C3×C4—22no—
682C3×C4—24no—
683C3×C4—34no—
684C3×C4—34no—
685C3×C4—44no—
686C3×C4—42no—
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—64no—
690C3×C4—81no—
691C3×C4—121no—
692Dic3—24no—
693Dic3—41no—
694Dic3C3×#12114yescomplemented
695Dic3C3×#12714yescomplemented
696C32#254111yescharacteristic, complemented, Sylow
697C23—21no—
698C23—22no—
699C23—22no—
700C23—21no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—32no—
709C23—61no—
710C23—62no—
711C23—62no—
712C23—61no—
713C23—62no—
714C23—62no—
715C23—62no—
716C23—62no—
717C23—62no—
718C23—62no—
719C23—62no—
720C23C3×D3×D412yes—
721C23C23×C3×D311yescharacteristic
722D4—48no—
723D4—44no—
724D4—68no—
725D4—128no—
726D4—124no—
727D4—128no—
728D4—128no—
729D4—128no—
730D4—128no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—32no—
737C2×C4—32no—
738C2×C4—32no—
739C2×C4—34no—
740C2×C4—32no—
741C2×C4—34no—
742C2×C4—62no—
743C2×C4—62no—
744C2×C4—62no—
745C2×C4—61no—
746C2×C4—124no—
747C2×C4—124no—
748C2×C4C3×D3×D412yes—
749C2×C4C3×D3×D414yes—
750C2×C3—22no—
751C2×C3—21no—
752C2×C3—22no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—42no—
756C2×C3—42no—
757C2×C3—82no—
758C2×C3—84no—
759C2×C3—82no—
760C2×C3—82no—
761C2×C3—122no—
762C2×C3—242no—
763C2×C3#559012yes—
764C2×C3#559211yescharacteristic
765C2×C3#559912yes—
766C2×C3D3×#12111yescharacteristic
767C2×C3D3×#12711yescharacteristic
768C2×C3C2×C3×#12111yescharacteristic
769C2×C3C2×C3×#12711yescharacteristic
770C2×C3C3×#53511yescharacteristic
771C2×C3C3×D4212yes—
772C2×C3C3×#55012yes—
773D3—42no—
774D3—82no—
775C22—24no—
776C22—22no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—64no—
788C22—62no—
789C22—121no—
790C22—122no—
791C22—121no—
792C22—122no—
793C22—122no—
794C22—122no—
795C22—122no—
796C22—122no—
797C22—122no—
798C22—122no—
799C22C2×C3×D3×D411yescharacteristic
800C22C2×C3×D3×D412yes—
801C22C2×C3×D3×D411yescharacteristic
802C22C3×#100412yes—
803C22C3×D3×#4111yescharacteristic
804C4—24no—
805C4—22no—
806C4—34no—
807C4—34no—
808C4—41no—
809C4—64no—
810C4—121no—
811C3—21no—
812C3#7668811yescharacteristic, direct product factor
813C3C3×#254111yescharacteristic, complemented
814C2—42no—
815C2—82no—
816C2—122no—
817C2—242no—
818C2C3×#559012yes—
819C2C3×#559211yescharacteristic
820C2C3×#559912yes—
821C2C3×D3×#12111yescharacteristic
822C2C3×D3×#12711yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#392C2
socleC23×C32C24
hypercenterC3×#392D3
hypocenterC3C3×#2541
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#392

Complements

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

NH ≅ G/Ntype
1. C2×C3×#940C2semidirect
2. C2×C3×#940C2semidirect
3. C2×C3×#939C2semidirect
4. C2×C3×#884C2semidirect
5. C2×C3×#67⋊C4C2semidirect
6. C32×#392C2semidirect
7. C3×#5223C2semidirect
8. C3×#4960C2semidirect
9. C3×#4957C2semidirect
10. C3×#4671C2semidirect
11. C3×#4649C2semidirect
13. #76688C3direct (N × H)
47. C2×#940C2×C3semidirect
48. C2×#940C2×C3semidirect
49. C2×#939C2×C3semidirect
50. C2×#884C2×C3semidirect
51. C2×#67⋊C4C2×C3semidirect
56. C3×#392D3semidirect
57. C3×#392C2×C3semidirect
60. #5223C2×C3semidirect
61. #4960C2×C3semidirect
62. #4957C2×C3semidirect
63. #4671C2×C3semidirect
64. #4649C2×C3semidirect
91. C2×C3×#67D4semidirect
112. C3×Dic3⋊C4D4semidirect
114. C3×C4×Dic3D4semidirect
238. #392C3×D3semidirect
317. C2×#67C3×D4semidirect
350. Dic3⋊C4C3×D4semidirect
352. C4×Dic3C3×D4semidirect
387. C3×Dic3#121semidirect
388. C3×Dic3#127semidirect
694. Dic3C3×#121semidirect
695. Dic3C3×#127semidirect
696. C32#2541semidirect
812. C3#76688direct (N × H)
813. C3C3×#2541semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9402
C2×C3×#9392
C2×C3×#8842
C2×C3×#67⋊C42
C32×#3922
C3×#52232
C3×#49602
C3×#49572
C3×#46712
C3×#46492
C3×#25413
#766883