Finite Group Databasebeta

← C3×#76665 #11808202

Subgroups — C3×#76665 #11808202

Order 1152.

2049 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic, complemented
2C2×C3×D4×Dic3C212yesmaximal, complemented
3C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
4C32×#392C211yesmaximal, characteristic, complemented
5C3×#5223C212yesmaximal, complemented
6C3×#5222C211yesmaximal, characteristic, complemented
7C3×#4961C212yesmaximal, complemented
8C3×#4947C211yesmaximal, characteristic, complemented
9C3×Dic3×C22⋊C4C212yesmaximal, complemented
10C3×#4666C211yesmaximal, characteristic, complemented
11C3×#4656C211yesmaximal, characteristic, complemented
12C3×#2388—31nomaximal
13#76665C311yesmaximal, characteristic, direct product factor
14C22×C32×D4C2212yes—
15C22×C32×D4C2211yescharacteristic
16C22×C3×#67C2212yes—
17C22×C3×#67C2211yescharacteristic
18C23×C3×Dic3C2211yescharacteristic
19C23×C3×Dic3C2212yes—
20C2×C3×#237—28no—
21C2×C3×#237—24no—
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×Dic6C2211yescharacteristic
24C2×C32×C22⋊C4C2212yes—
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×C3×#217C2212yes—
27C2×C3×#217C2212yes—
28C2×C3×#217C2212yes—
29C3×D4×Dic3—28no—
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×C4⋊Dic3C2212yes—
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×C4×Dic3C2212yes—
35C2×C3×C4×Dic3C2211yescharacteristic
36C3×#67⋊C4—24no—
37C32×#95C2211yescharacteristic
38C3×C3⋊#95C2212yes—
39C3×C3⋊#95C2211yescharacteristic
40C3×C3⋊#95C2212yes—
41C22×C3×#41—31no—
42C22×#237C2×C311yescharacteristic, complemented
43C2×C3×C4×D4—32no—
44C2×C3×C4×D4—31no—
45C2×D4×Dic3C2×C312yescomplemented
46C2×#67⋊C4C2×C311yescharacteristic, complemented
47C3×#395—31no—
48C3×#394—31no—
49C3×#394—32no—
50C3×#393—31no—
51C3×#392—21no—
52C3×#392—32no—
53C3×#392D311yescharacteristic, complemented
54C3×#392C2×C311yescharacteristic, complemented
55C3×C4×C22⋊C4—32no—
56C3×C4×C22⋊C4—31no—
57#5223C2×C312yescomplemented
58#5222C2×C311yescharacteristic, complemented
59#4961C2×C312yescomplemented
60#4947C2×C311yescharacteristic, complemented
61Dic3×C22⋊C4C2×C312yescomplemented
62#4666C2×C311yescharacteristic, complemented
63#4656C2×C311yescharacteristic, complemented
64C24×C32C2312yes—
65C24×C32C2311yescharacteristic
66C23×C3×D3C2311yescharacteristic
67C2×C32×D4—24no—
68C2×C32×D4—24no—
69C2×C32×D4—24no—
70C2×C32×D4—22no—
71C2×C32×D4—24no—
72C22×C32×C4C2311yescharacteristic
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2312yes—
75C2×C3×#67—24no—
76C2×C3×#67—22no—
77C2×C3×#67—22no—
78C2×C3×#67—24no—
79C2×C3×#67—24no—
80C2×C3×#67—22no—
81C22×C3×Dic3—24no—
82C22×C3×Dic3—24no—
83C22×C3×Dic3—22no—
84C22×C3×Dic3—24no—
85C22×C3×Dic3D418yescomplemented
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2312yes—
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2311yescharacteristic
91C3×#237—232no—
92C2×C3×C4×D3—24no—
93C2×C3×C4×D3D414yescomplemented
94C2×C3×Dic6—22no—
95C2×C3×Dic6—24no—
96C32×C22⋊C4—22no—
97C32×C22⋊C4—24no—
98C3×#217—24no—
99C3×#217—24no—
100C3×#217—24no—
101C3×(C2×D3)⋊C4—22no—
102C3×(C2×D3)⋊C4—24no—
103C3×C4⋊Dic3—24no—
104C3×Dic3⋊C4—22no—
105C3×C4×Dic3—22no—
106C3×C4×Dic3—24no—
107#2388—31noSylow
108C2×C3×#41—68no—
109C2×C3×#41—64no—
110C22×C3×Q8—31no—
111C22×C3×D4—22no—
112C22×C3×D4—21no—
113C22×C3×D4—32no—
114C22×C3×D4—31no—
115C22×C3×D4C2×D311yescharacteristic
116C22×C3×D4C2×D312yes—
117C22×C3×D4C22×C311yescharacteristic
118C22×C3×D4C22×C312yes—
119C23×C3×C4—32no—
120C23×C3×C4—31no—
121C23×C3×C4—31no—
122C22×#67C22×C312yes—
123C22×#67C22×C311yescharacteristic
124C23×Dic3C22×C311yescharacteristic
125C23×Dic3C22×C312yes—
126C2×#237—28no—
127C2×#237—24no—
128C22×C4×D3C22×C311yescharacteristic
129C22×Dic6C22×C311yescharacteristic
130C3×C4×D4—64no—
131C3×C4×D4—68no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C4⋊C4—32no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C22⋊C4—22no—
136C2×C3×C22⋊C4—32no—
137C2×C3×C22⋊C4—32no—
138C2×C3×C22⋊C4—32no—
139C2×C3×C22⋊C4—32no—
140C2×C3×C22⋊C4—31no—
141C2×C3×C22⋊C4C2×D312yes—
142C2×C3×C22⋊C4C2×D311yescharacteristic
143C2×C3×C22⋊C4C22×C312yes—
144C2×C3×C22⋊C4C22×C311yescharacteristic
145C2×C3×C42—31no—
146C2×C3×C42—32no—
147C2×#217C22×C312yes—
148C2×#217C22×C312yes—
149C2×#217C22×C312yes—
150D4×Dic3—28no—
151C2×(C2×D3)⋊C4C22×C312yes—
152C2×(C2×D3)⋊C4C22×C311yescharacteristic
153C2×C4⋊Dic3C22×C312yes—
154C2×Dic3⋊C4C22×C311yescharacteristic
155C2×C4×Dic3C22×C312yes—
156C2×C4×Dic3C22×C311yescharacteristic
157#67⋊C4—24no—
158C3×#95—21no—
159C3×#95—32no—
160C3×#95—32no—
161C3×#95—31no—
162C3×#95C2×D311yescharacteristic
163C3×#95C22×C311yescharacteristic
164C3⋊#95C22×C312yes—
165C3⋊#95C22×C311yescharacteristic
166C3⋊#95C22×C312yes—
167C23×C32—22no—
168C23×C32—21no—
169C23×C32—22no—
170C23×C32—22no—
171C23×C32—22no—
172C23×C32—22no—
173C23×C32—21no—
174C23×C32—22no—
175C23×C32—22no—
176C23×C32—22no—
177C23×C32C2×D414yes—
178C23×C32#4112yescomplemented
179C23×C32C2411yescharacteristic
180C22×C3×D3—22no—
181C22×C3×D3—22no—
182C22×C3×D3—21no—
183C22×C3×D3—21no—
184C22×C3×D3C2×D412yes—
185C32×D4—28no—
186C32×D4—216no—
187C2×C32×C4—22no—
188C2×C32×C4—22no—
189C2×C32×C4—22no—
190C2×C32×C4—21no—
191C2×C32×C4—22no—
192C2×C32×C4C2×D412yes—
193C2×C32×C4#4114yescomplemented
194C3×#67—216no—
195C3×#67—28no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—216no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—44no—
207C2×C3×Dic3C2×D414yes—
208C2×C3×Dic3C2×D414yes—
209C2×C3×Dic3C2×D412yes—
210C2×C3×Dic3#4112yescomplemented
211C3×C4×D3—28no—
212C3×Dic6—28no—
213C22×#41—31no—
214C2×C4×D4—32no—
215C2×C4×D4—31no—
216#395—31no—
217#394—31no—
218#394—32no—
219#393—31no—
220#392—32no—
221#392C3×D311yescharacteristic, complemented
222C4×C22⋊C4—32no—
223C4×C22⋊C4—31no—
224C24×C3—22no—
225C24×C3—21no—
226C24×C3—31no—
227C24×C3C22×D312yes—
228C24×C3C22×D311yescharacteristic
229C24×C3C23×C312yes—
230C24×C3C23×C311yescharacteristic
231C23×D3C23×C311yescharacteristic
232C3×#41—632no—
233C2×C3×Q8—64no—
234C2×C3×Q8—62no—
235C2×C3×D4—24no—
236C2×C3×D4—24no—
237C2×C3×D4—24no—
238C2×C3×D4—24no—
239C2×C3×D4—24no—
240C2×C3×D4—24no—
241C2×C3×D4—22no—
242C2×C3×D4—24no—
243C2×C3×D4—22no—
244C2×C3×D4—24no—
245C2×C3×D4—42no—
246C2×C3×D4—44no—
247C2×C3×D4—44no—
248C2×C3×D4—44no—
249C2×C3×D4—44no—
250C2×C3×D4—62no—
251C2×C3×D4—64no—
252C2×C3×D4—62no—
253C2×C3×D4—64no—
254C2×C3×D4—64no—
255C2×C3×D4—62no—
256C22×C3×C4—21no—
257C22×C3×C4—22no—
258C22×C3×C4—21no—
259C22×C3×C4—31no—
260C22×C3×C4—38no—
261C22×C3×C4—31no—
262C22×C3×C4—32no—
263C22×C3×C4—34no—
264C22×C3×C4—32no—
265C22×C3×C4—31no—
266C22×C3×C4—64no—
267C22×C3×C4—64no—
268C22×C3×C4—64no—
269C22×C3×C4—62no—
270C22×C3×C4—64no—
271C22×C3×C4C22×D311yescharacteristic
272C22×C3×C4C22×D311yescharacteristic
273C22×C3×C4C22×D312yes—
274C22×C3×C4C23×C311yescharacteristic
275C22×C3×C4C23×C311yescharacteristic
276C22×C3×C4C23×C312yes—
277C2×#67—24no—
278C2×#67—22no—
279C2×#67—22no—
280C2×#67—24no—
281C2×#67—24no—
282C2×#67—22no—
283C22×Dic3—24no—
284C22×Dic3—24no—
285C22×Dic3—22no—
286C22×Dic3—24no—
287C22×Dic3C3×D418yescomplemented
288C22×Dic3C23×C312yes—
289C22×Dic3C23×C311yescharacteristic
290C22×Dic3C23×C312yes—
291C22×Dic3C23×C311yescharacteristic
292C22×Dic3C23×C311yescharacteristic
293#237—232no—
294C2×C4×D3—24no—
295C2×C4×D3C3×D414yescomplemented
296C2×Dic6—22no—
297C2×Dic6—24no—
298C3×C4⋊C4—64no—
299C3×C4⋊C4—62no—
300C3×C22⋊C4—22no—
301C3×C22⋊C4—24no—
302C3×C22⋊C4—22no—
303C3×C22⋊C4—24no—
304C3×C22⋊C4—42no—
305C3×C22⋊C4—44no—
306C3×C22⋊C4—62no—
307C3×C22⋊C4—64no—
308C3×C22⋊C4—64no—
309C3×C22⋊C4—64no—
310C3×C22⋊C4—64no—
311C3×C42—64no—
312C3×C42—62no—
313#217—24no—
314#217—24no—
315#217—24no—
316(C2×D3)⋊C4—22no—
317(C2×D3)⋊C4—24no—
318C4⋊Dic3—24no—
319Dic3⋊C4—22no—
320C4×Dic3—22no—
321C4×Dic3—24no—
322C22×C32—24no—
323C22×C32—22no—
324C22×C32—24no—
325C22×C32—24no—
326C22×C32—24no—
327C22×C32—41no—
328C22×C32—42no—
329C22×C32—42no—
330C22×C32—41no—
331C22×C32—42no—
332C22×C32—42no—
333C22×C32—42no—
334C22×C32C22×D411yescharacteristic
335C22×C32C22×D412yes—
336C22×C32C2×#4111yescharacteristic
337C22×C32C2×#4112yes—
338C22×C32C2×#4111yescharacteristic
339C2×C3×D3—22no—
340C2×C3×D3—22no—
341C2×C3×D3—22no—
342C2×C3×D3—42no—
343C2×C3×D3—42no—
344C32×C4—22no—
345C32×C4—24no—
346C32×C4—41no—
347C3×Dic3—24no—
348C3×Dic3—22no—
349C3×Dic3—41no—
350C3×Dic3—42no—
351C3×Dic3#12014yes—
352C2×#41—68no—
353C2×#41—64no—
354C22×Q8—31no—
355C22×D4—31no—
356C22×D4—32no—
357C22×D4C2×C3×D312yes—
358C22×D4C2×C3×D311yescharacteristic
359C23×C4—32no—
360C23×C4—31no—
361C23×C4—31no—
362C4×D4—64no—
363C4×D4—68no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—32no—
366C2×C22⋊C4—32no—
367C2×C22⋊C4—32no—
368C2×C22⋊C4—32no—
369C2×C22⋊C4—31no—
370C2×C22⋊C4—32no—
371C2×C22⋊C4C2×C3×D311yescharacteristic
372C2×C22⋊C4C2×C3×D312yes—
373C2×C42—31no—
374C2×C42—32no—
375#95—32no—
376#95—32no—
377#95—31no—
378#95C2×C3×D311yescharacteristic
379C23×C3—21no—
380C23×C3—22no—
381C23×C3—22no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—21no—
389C23×C3—22no—
390C23×C3—21no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—22no—
394C23×C3—22no—
395C23×C3—21no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—21no—
400C23×C3—24no—
401C23×C3—22no—
402C23×C3—32no—
403C23×C3—41no—
404C23×C3—42no—
405C23×C3—42no—
406C23×C3—42no—
407C23×C3—42no—
408C23×C3—42no—
409C23×C3—42no—
410C23×C3—42no—
411C23×C3—42no—
412C23×C3—41no—
413C23×C3—62no—
414C23×C3—62no—
415C23×C3—61no—
416C23×C3—61no—
417C23×C3D3×D414yes—
418C23×C3#23712yescomplemented
419C23×C3C2×C3×D414yes—
420C23×C3C3×#4112yescomplemented
421C23×C3C23×D311yescharacteristic
422C23×C3C24×C311yescharacteristic
423C22×D3—22no—
424C22×D3—22no—
425C22×D3—21no—
426C22×D3—21no—
427C22×D3C2×C3×D412yes—
428C3×Q8—68no—
429C3×D4—28no—
430C3×D4—216no—
431C3×D4—216no—
432C3×D4—28no—
433C3×D4—48no—
434C3×D4—416no—
435C3×D4—68no—
436C3×D4—616no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—21no—
444C2×C3×C4—22no—
445C2×C3×C4—21no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—24no—
449C2×C3×C4—32no—
450C2×C3×C4—34no—
451C2×C3×C4—34no—
452C2×C3×C4—32no—
453C2×C3×C4—42no—
454C2×C3×C4—42no—
455C2×C3×C4—42no—
456C2×C3×C4—41no—
457C2×C3×C4—42no—
458C2×C3×C4—68no—
459C2×C3×C4—616no—
460C2×C3×C4—61no—
461C2×C3×C4—62no—
462C2×C3×C4—62no—
463C2×C3×C4—61no—
464C2×C3×C4—62no—
465C2×C3×C4—61no—
466C2×C3×C4—62no—
467C2×C3×C4—62no—
468C2×C3×C4—62no—
469C2×C3×C4—124no—
470C2×C3×C4D3×D412yes—
471C2×C3×C4#23714yescomplemented
472C2×C3×C4C2×C3×D412yes—
473C2×C3×C4C3×#4114yescomplemented
474#67—216no—
475#67—28no—
476C2×Dic3—21no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—21no—
480C2×Dic3—216no—
481C2×Dic3—22no—
482C2×Dic3—21no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—44no—
487C2×Dic3C2×C3×D414yes—
488C2×Dic3C2×C3×D414yes—
489C2×Dic3C2×C3×D412yes—
490C2×Dic3C3×#4112yescomplemented
491C4×D3—28no—
492Dic6—28no—
493C2×C32—44no—
494C2×C32—42no—
495C2×C32C2×#12011yescharacteristic
496C2×C32#52512yes—
497C2×C32#52511yescharacteristic
498C2×C32#53211yescharacteristic
499C2×C32#53212yes—
500C3×D3—42no—
501C24—31no—
502C24C22×C3×D312yes—
503C24C22×C3×D311yescharacteristic
504#41—632no—
505C2×Q8—64no—
506C2×Q8—62no—
507C2×D4—24no—
508C2×D4—24no—
509C2×D4—24no—
510C2×D4—22no—
511C2×D4—24no—
512C2×D4—64no—
513C2×D4—62no—
514C2×D4—62no—
515C2×D4—64no—
516C2×D4—64no—
517C2×D4—62no—
518C22×C4—31no—
519C22×C4—31no—
520C22×C4—32no—
521C22×C4—38no—
522C22×C4—34no—
523C22×C4—32no—
524C22×C4—31no—
525C22×C4—64no—
526C22×C4—64no—
527C22×C4—64no—
528C22×C4—62no—
529C22×C4—64no—
530C22×C4C22×C3×D311yescharacteristic
531C22×C4C22×C3×D311yescharacteristic
532C22×C4C22×C3×D312yes—
533C4⋊C4—64no—
534C4⋊C4—62no—
535C22⋊C4—22no—
536C22⋊C4—24no—
537C22⋊C4—62no—
538C22⋊C4—64no—
539C22⋊C4—64no—
540C22⋊C4—64no—
541C22⋊C4—64no—
542C42—64no—
543C42—62no—
544C22×C3—24no—
545C22×C3—24no—
546C22×C3—24no—
547C22×C3—24no—
548C22×C3—24no—
549C22×C3—22no—
550C22×C3—24no—
551C22×C3—24no—
552C22×C3—22no—
553C22×C3—24no—
554C22×C3—21no—
555C22×C3—22no—
556C22×C3—22no—
557C22×C3—21no—
558C22×C3—21no—
559C22×C3—44no—
560C22×C3—44no—
561C22×C3—44no—
562C22×C3—44no—
563C22×C3—42no—
564C22×C3—41no—
565C22×C3—42no—
566C22×C3—42no—
567C22×C3—41no—
568C22×C3—41no—
569C22×C3—42no—
570C22×C3—42no—
571C22×C3—42no—
572C22×C3—42no—
573C22×C3—42no—
574C22×C3—42no—
575C22×C3—42no—
576C22×C3—41no—
577C22×C3—42no—
578C22×C3—62no—
579C22×C3—62no—
580C22×C3—62no—
581C22×C3—82no—
582C22×C3—81no—
583C22×C3—82no—
584C22×C3—82no—
585C22×C3—82no—
586C22×C3—81no—
587C22×C3—82no—
588C22×C3—122no—
589C22×C3—122no—
590C22×C3C2×D3×D411yescharacteristic
591C22×C3C2×D3×D412yes—
592C22×C3C2×#23712yes—
593C22×C3C2×#23711yescharacteristic
594C22×C3D3×#4111yescharacteristic
595C22×C3C22×C3×D411yescharacteristic
596C22×C3C22×C3×D412yes—
597C22×C3C2×C3×#4111yescharacteristic
598C22×C3C2×C3×#4112yes—
599C22×C3C2×C3×#4111yescharacteristic
600C2×D3—22no—
601C2×D3—22no—
602C2×D3—22no—
603C2×D3—42no—
604C2×D3—42no—
605C3×C4—24no—
606C3×C4—22no—
607C3×C4—22no—
608C3×C4—24no—
609C3×C4—34no—
610C3×C4—44no—
611C3×C4—42no—
612C3×C4—41no—
613C3×C4—41no—
614C3×C4—64no—
615C3×C4—62no—
616C3×C4—81no—
617C3×C4—121no—
618C3×C4—122no—
619Dic3—24no—
620Dic3—22no—
621Dic3—41no—
622Dic3—42no—
623Dic3C3×#12014yes—
624C32#238811yescharacteristic, complemented, Sylow
625C23—21no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—21no—
635C23—32no—
636C23—62no—
637C23—62no—
638C23—61no—
639C23—61no—
640C23C3×D3×D414yes—
641C23C3×#23712yescomplemented
642C23C23×C3×D311yescharacteristic
643Q8—68no—
644D4—28no—
645D4—216no—
646D4—616no—
647D4—68no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—34no—
654C2×C4—32no—
655C2×C4—34no—
656C2×C4—32no—
657C2×C4—68no—
658C2×C4—616no—
659C2×C4—61no—
660C2×C4—62no—
661C2×C4—62no—
662C2×C4—61no—
663C2×C4—62no—
664C2×C4—62no—
665C2×C4—61no—
666C2×C4—62no—
667C2×C4—62no—
668C2×C4—124no—
669C2×C4C3×D3×D412yes—
670C2×C4C3×#23714yescomplemented
671C2×C3—22no—
672C2×C3—21no—
673C2×C3—22no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—44no—
677C2×C3—42no—
678C2×C3—44no—
679C2×C3—42no—
680C2×C3—84no—
681C2×C3—82no—
682C2×C3—122no—
683C2×C3#558612yes—
684C2×C3D3×#12011yescharacteristic
685C2×C3#559612yes—
686C2×C3#560611yescharacteristic
687C2×C3#571611yescharacteristic
688C2×C3C2×C3×#12011yescharacteristic
689C2×C3C3×#52512yes—
690C2×C3C3×#52511yescharacteristic
691C2×C3C3×#53212yes—
692C2×C3C3×#53211yescharacteristic
693D3—42no—
694C22—24no—
695C22—24no—
696C22—24no—
697C22—24no—
698C22—22no—
699C22—42no—
700C22—41no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—41no—
705C22—42no—
706C22—62no—
707C22—62no—
708C22—62no—
709C22—122no—
710C22—122no—
711C22C2×C3×D3×D412yes—
712C22C2×C3×D3×D411yescharacteristic
713C22C2×C3×#23711yescharacteristic
714C22C2×C3×#23712yes—
715C22C3×D3×#4111yescharacteristic
716C4—24no—
717C4—22no—
718C4—34no—
719C4—41no—
720C4—64no—
721C4—62no—
722C4—121no—
723C4—122no—
724C3—21no—
725C3#7666511yescharacteristic, direct product factor
726C3C3×#238811yescharacteristic, complemented
727C2—44no—
728C2—42no—
729C2—122no—
730C2C3×#558612yes—
731C2C3×D3×#12011yescharacteristic
732C2C3×#559612yes—
733C2C3×#560611yescharacteristic
734C2C3×#571611yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#392C2
socleC23×C32C24
hypercenterC3×#392D3
hypocenterC3C3×#2388
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×#237C2semidirect
2. C2×C3×D4×Dic3C2semidirect
3. C2×C3×#67⋊C4C2semidirect
4. C32×#392C2semidirect
5. C3×#5223C2semidirect
6. C3×#5222C2semidirect
7. C3×#4961C2semidirect
8. C3×#4947C2semidirect
9. C3×Dic3×C22⋊C4C2semidirect
10. C3×#4666C2semidirect
11. C3×#4656C2semidirect
13. #76665C3direct (N × H)
42. C22×#237C2×C3semidirect
45. C2×D4×Dic3C2×C3semidirect
46. C2×#67⋊C4C2×C3semidirect
53. C3×#392D3semidirect
54. C3×#392C2×C3semidirect
57. #5223C2×C3semidirect
58. #5222C2×C3semidirect
59. #4961C2×C3semidirect
60. #4947C2×C3semidirect
61. Dic3×C22⋊C4C2×C3semidirect
62. #4666C2×C3semidirect
63. #4656C2×C3semidirect
85. C22×C3×Dic3D4semidirect
93. C2×C3×C4×D3D4semidirect
178. C23×C32#41semidirect
193. C2×C32×C4#41semidirect
210. C2×C3×Dic3#41semidirect
221. #392C3×D3semidirect
287. C22×Dic3C3×D4semidirect
295. C2×C4×D3C3×D4semidirect
418. C23×C3#237semidirect
420. C23×C3C3×#41semidirect
471. C2×C3×C4#237semidirect
473. C2×C3×C4C3×#41semidirect
490. C2×Dic3C3×#41semidirect
624. C32#2388semidirect
641. C23C3×#237semidirect
670. C2×C4C3×#237semidirect
725. C3#76665direct (N × H)
726. C3C3×#2388semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C2×C3×D4×Dic32
C2×C3×#67⋊C42
C32×#3922
C3×#52232
C3×#52222
C3×#49612
C3×#49472
C3×Dic3×C22⋊C42
C3×#46662
C3×#46562
C3×#23883
#766653