Finite Group Databasebeta

← #11806902

Subgroups — #11806902

Order 1152.

1761 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×D12C211yesmaximal, characteristic, complemented
2C2×#63914C211yesmaximal, characteristic
3C2×#63898C211yesmaximal, characteristic, complemented
4C2×#63879C212yesmaximal, complemented
5C4×#3750C211yesmaximal, characteristic, complemented
6C3×#4939C211yesmaximal, characteristic, complemented
7#10591386C212yesmaximal, complemented
8#10591381C212yesmaximal, complemented
9#10591363C212yesmaximal, complemented
10#10591323C211yesmaximal, characteristic, complemented
11#10591274C211yesmaximal, characteristic, complemented
12#82343—31nomaximal
13#76306—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×C3×C4×D3C2212yes—
17C22×#625C2212yes—
18C22×#625C2212yes—
19C22×D3×Dic3C2212yes—
20C2×C32×C42C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C3×C4×D12—24no—
31C2×(C2×D3)⋊Dic3C2212yes—
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×Dic32C2212yes—
35#63914C418yescomplemented
36#63898—24no—
37#63879—28no—
38#63658C2211yescharacteristic
39#63658C2211yescharacteristic
40#63579C2212yes—
41C2×C3×C4×D4—31no—
42C2×#940—31no—
43C2×#940—31no—
44C2×D4×Dic3—31no—
45C2×C4×#67—32no—
46C2×#893—31no—
47C2×#67⋊C4—32no—
48C2×C4×D12D311yescharacteristic, complemented
49C3×#390—31no—
50#5221—31no—
51#5213—32no—
52#4988—31no—
53Dic3×C4⋊C4—31no—
54Dic3×C4⋊C4—31no—
55#4958—32no—
56#4957—32no—
57#4957—32no—
58#4956—32no—
59#4956—32no—
60#4939D311yescharacteristic, complemented
61C4×Dic3⋊C4—31no—
62C4×Dic3⋊C4—31no—
63C4×Dic3⋊C4—61no—
64C23×C3×D3C2312yes—
65C23×C3×D3C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2311yescharacteristic
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C2×C3×D12—22no—
76C2×C3×D12—22no—
77C2×C3×D12—22no—
78C2×C3×D12—22no—
79C2×C3×D12C2×C414yescomplemented
80C2×C3×D12C2×C414yescomplemented
81C2×C3×C4×D3—24no—
82C2×C3×C4×D3—24no—
83C2×C3×C4×D3—42no—
84C2×#625—24no—
85C2×#625—24no—
86C2×#625—42no—
87C2×#625—42no—
88C2×#625C2×C418yescomplemented
89C2×#625C2×C418yescomplemented
90C2×D3×Dic3—24no—
91C2×D3×Dic3—24no—
92C2×D3×Dic3—42no—
93C32×C42—22no—
94#3750—22no—
95#3750D414yescomplemented
96C4×C3⋊Dic3—22no—
97C4×C3⋊Dic3C2×C414yescomplemented
98C3×(C2×D3)⋊C4—24no—
99C3×(C2×D3)⋊C4—24no—
100C3×(C2×D3)⋊C4—42no—
101C3×C4⋊Dic3—22no—
102C3×C4⋊Dic3D414yescomplemented
103(C2×D3)⋊Dic3—24no—
104(C2×D3)⋊Dic3—24no—
105(C2×D3)⋊Dic3—42no—
106Dic32—24no—
107#2366—91noSylow
108C22×C3×D4—31no—
109C22×C3×D4—31no—
110C23×C3×C4—32no—
111C22×#67—32no—
112C22×#67—32no—
113C22×#67—32no—
114C22×#67—32no—
115C23×Dic3—32no—
116C22×D12C2×D311yescharacteristic
117C22×D12C2×D311yescharacteristic
118C22×C4×D3—32no—
119C22×C4×D3C2×D312yes—
120C3×C4×D4—64no—
121C2×C3×C4⋊C4—31no—
122C2×C3×C4⋊C4—31no—
123C2×C3×C22⋊C4—32no—
124C2×C3×C22⋊C4—32no—
125C2×C3×C22⋊C4—32no—
126C2×C3×C42—21no—
127C2×C3×C42C2×D311yescharacteristic
128C2×C3×C42C2×D311yescharacteristic
129C2×#217—32no—
130C2×#217—32no—
131C2×#217—32no—
132#940—38no—
133#940—38no—
134D4×Dic3—64no—
135C4×#67—68no—
136C2×(C2×D3)⋊C4—32no—
137C2×(C2×D3)⋊C4—32no—
138C2×(C2×D3)⋊C4—32no—
139C2×(C2×D3)⋊C4C2×D312yes—
140C2×(C2×D3)⋊C4C2×D312yes—
141C2×(C2×D3)⋊C4C2×D312yes—
142C2×C4⋊Dic3C2×D311yescharacteristic
143C2×C4⋊Dic3C2×D311yescharacteristic
144C2×Dic3⋊C4—31no—
145C2×Dic3⋊C4—31no—
146C2×Dic3⋊C4—31no—
147C2×Dic3⋊C4—31no—
148C2×Dic3⋊C4—61no—
149C2×Dic3⋊C4—61no—
150C2×C4×Dic3—31no—
151C2×C4×Dic3—31no—
152C2×C4×Dic3—31no—
153C2×C4×Dic3—31no—
154C2×C4×Dic3—32no—
155C2×C4×Dic3—32no—
156C2×C4×Dic3—61no—
157C2×C4×Dic3—61no—
158#893—64no—
159#67⋊C4—68no—
160C4×D12—24no—
161C3⋊#95—31no—
162C3⋊#95—31no—
163C3⋊#95—31no—
164C3⋊#95—31no—
165C3⋊#95—32no—
166C3⋊#95—32no—
167C3⋊#95—61no—
168C3⋊#95—61no—
169C23×C32C2411yescharacteristic
170C22×C3×D3—22no—
171C22×C3×D3—22no—
172C22×C3×D3—22no—
173C22×C3×D3—22no—
174C22×C3×D3—22no—
175C22×C3×D3—22no—
176C22×C3×D3—22no—
177C22×C3×D3—22no—
178C22×C3×D3—22no—
179C22×C3×D3—22no—
180C22×C3×D3—22no—
181C22×C3×D3—22no—
182C22×C3×D3C22×C414yes—
183C22×C3×D3C22×C414yes—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4—21no—
188C2×C32×C4—21no—
189C2×C32×C4C22×C412yes—
190C2×C32×C4C2×D412yes—
191C2×C32×C4C2×D412yes—
192C2×C32×C4#4112yes—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—21no—
198C2×C3⋊Dic3—21no—
199C2×C3⋊Dic3—21no—
200C2×C3⋊Dic3C22×C412yes—
201C2×C3⋊Dic3C22×C412yes—
202C2×C3⋊Dic3C2×D412yes—
203C2×C3⋊Dic3C2×D412yes—
204C2×C3⋊Dic3#4112yes—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3C2×D414yes—
211C3×D12—28no—
212C3×D12—28no—
213C3×C4×D3—48no—
214#625—216no—
215#625—48no—
216D3×Dic3—48no—
217C2×#127—91no—
218C2×C4×D4—31no—
219C2×C4×D4—92no—
220C2×C4×D4—91no—
221#390—31no—
222#390—92no—
223#390—91no—
224#386—92no—
225#386—92no—
226C4×C4⋊C4—91no—
227C4×C4⋊C4—91no—
228C24×C3—32no—
229C24×C3—32no—
230C23×D3C22×D312yes—
231C23×D3C22×D312yes—
232C2×C3×D4—34no—
233C2×C3×D4—34no—
234C2×C3×D4—62no—
235C2×C3×D4—62no—
236C2×C3×D4—62no—
237C2×C3×D4—62no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—32no—
242C22×C3×C4—32no—
243C22×C3×C4—64no—
244C22×C3×C4—64no—
245C22×C3×C4—122no—
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C22×C3×C4C22×D311yescharacteristic
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C2×#67—38no—
253C2×#67—38no—
254C2×#67—38no—
255C2×#67—38no—
256C2×#67—64no—
257C2×#67—64no—
258C2×#67—64no—
259C2×#67—64no—
260C2×#67—122no—
261C2×#67—122no—
262C2×#67—122no—
263C2×#67—122no—
264C22×Dic3—31no—
265C22×Dic3—31no—
266C22×Dic3—31no—
267C22×Dic3—31no—
268C22×Dic3—31no—
269C22×Dic3—31no—
270C22×Dic3—31no—
271C22×Dic3—31no—
272C22×Dic3—61no—
273C22×Dic3—61no—
274C22×Dic3—61no—
275C22×Dic3—61no—
276C22×Dic3—64no—
277C22×Dic3—64no—
278C22×Dic3—122no—
279C22×Dic3C22×D312yes—
280C22×Dic3C22×D312yes—
281C2×D12—22no—
282C2×D12—22no—
283C2×D12—22no—
284C2×D12—22no—
285C2×D12C4×D314yescomplemented
286C2×D12C4×D314yescomplemented
287C2×C4×D3—24no—
288C2×C4×D3—24no—
289C2×C4×D3—42no—
290C2×C4×D3—64no—
291C2×C4×D3—64no—
292C2×C4×D3—122no—
293C3×C4⋊C4—34no—
294C3×C4⋊C4—62no—
295C3×C22⋊C4—64no—
296C3×C22⋊C4—64no—
297C3×C22⋊C4—122no—
298C3×C42—22no—
299C3×C42—22no—
300C3×C42—42no—
301#217—64no—
302#217—64no—
303#217—122no—
304(C2×D3)⋊C4—24no—
305(C2×D3)⋊C4—24no—
306(C2×D3)⋊C4—42no—
307(C2×D3)⋊C4—64no—
308(C2×D3)⋊C4—64no—
309(C2×D3)⋊C4—122no—
310C4⋊Dic3—22no—
311C4⋊Dic3#6714yescomplemented
312Dic3⋊C4—34no—
313Dic3⋊C4—34no—
314Dic3⋊C4—64no—
315Dic3⋊C4—62no—
316Dic3⋊C4—62no—
317Dic3⋊C4—64no—
318C4×Dic3—34no—
319C4×Dic3—34no—
320C4×Dic3—64no—
321C4×Dic3—64no—
322C4×Dic3—64no—
323C4×Dic3—62no—
324C4×Dic3—62no—
325C4×Dic3—122no—
326C22×C32C23×C411yescharacteristic
327C22×C32C22×D411yescharacteristic
328C22×C32C22×D411yescharacteristic
329C22×C32C2×#4111yescharacteristic
330C22×C32C2×#4111yescharacteristic
331C22×C32H(5,𝔽2)11yescharacteristic
332C22×C32H(5,𝔽2)11yescharacteristic
333C2×C3×D3—24no—
334C2×C3×D3—24no—
335C2×C3×D3—24no—
336C2×C3×D3—24no—
337C2×C3×D3—24no—
338C2×C3×D3—24no—
339C2×C3×D3—42no—
340C2×C3×D3—42no—
341C2×C3×D3—42no—
342C2×C3×D3—42no—
343C2×C3×D3—42no—
344C2×C3×D3—42no—
345C2×C3×D3—42no—
346C2×C3×D3—42no—
347C32×C4—22no—
348C32×C4—41no—
349C32×C4C4×D414yescomplemented
350C3⋊Dic3—22no—
351C3⋊Dic3—22no—
352C3⋊Dic3—41no—
353C3⋊Dic3C4×D414yescomplemented
354C3×Dic3—24no—
355C3×Dic3—42no—
356C22×D4—31no—
357C22×D4—31no—
358C22×D4—92no—
359C22×D4—92no—
360C23×C4—32no—
361C23×C4—92no—
362#127—98no—
363C4×D4—64no—
364C4×D4—188no—
365C4×D4—184no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—91no—
369C2×C4⋊C4—91no—
370C2×C22⋊C4—32no—
371C2×C22⋊C4—32no—
372C2×C22⋊C4—32no—
373C2×C22⋊C4—92no—
374C2×C22⋊C4—92no—
375C2×C22⋊C4—92no—
376C2×C42—91no—
377C2×C42—92no—
378C2×C42—91no—
379C2×C42D3211yescharacteristic
380#95—92no—
381#95—91no—
382#95—91no—
383C23×C3—21no—
384C23×C3—34no—
385C23×C3—34no—
386C23×C3—62no—
387C23×C3—62no—
388C23×C3—62no—
389C23×C3—62no—
390C23×C3—62no—
391C23×C3—62no—
392C23×C3—62no—
393C23×C3—62no—
394C23×C3—62no—
395C23×C3—62no—
396C23×C3—62no—
397C23×C3—62no—
398C23×C3C23×D311yescharacteristic
399C23×C3C23×D311yescharacteristic
400C22×D3—22no—
401C22×D3—22no—
402C22×D3—22no—
403C22×D3—22no—
404C22×D3—22no—
405C22×D3—22no—
406C22×D3—22no—
407C22×D3—22no—
408C22×D3—22no—
409C22×D3—22no—
410C22×D3—22no—
411C22×D3—22no—
412C22×D3C2×C4×D314yes—
413C22×D3C2×C4×D314yes—
414C3×D4—68no—
415C3×D4—68no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—22no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—34no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—62no—
437C2×C3×C4—62no—
438C2×C3×C4—62no—
439C2×C3×C4—62no—
440C2×C3×C4—62no—
441C2×C3×C4—128no—
442C2×C3×C4C2×C4×D312yes—
443C2×C3×C4C2×C4×D312yes—
444C2×C3×C4#23512yes—
445C2×C3×C4D3×D412yes—
446C2×C3×C4D3×D412yes—
447C2×C3×C4D3×D412yes—
448C2×C3×C4#23712yes—
449C2×C3×C4C2×#6712yes—
450#67—616no—
451#67—616no—
452#67—128no—
453#67—128no—
454C2×Dic3—22no—
455C2×Dic3—22no—
456C2×Dic3—22no—
457C2×Dic3—22no—
458C2×Dic3—22no—
459C2×Dic3—32no—
460C2×Dic3—32no—
461C2×Dic3—32no—
462C2×Dic3—32no—
463C2×Dic3—32no—
464C2×Dic3—32no—
465C2×Dic3—32no—
466C2×Dic3—32no—
467C2×Dic3—32no—
468C2×Dic3—32no—
469C2×Dic3—62no—
470C2×Dic3—62no—
471C2×Dic3—62no—
472C2×Dic3—62no—
473C2×Dic3—62no—
474C2×Dic3—61no—
475C2×Dic3—61no—
476C2×Dic3—61no—
477C2×Dic3—61no—
478C2×Dic3—61no—
479C2×Dic3—61no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—62no—
483C2×Dic3—61no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—121no—
490C2×Dic3—121no—
491C2×Dic3—121no—
492C2×Dic3—121no—
493C2×Dic3—121no—
494C2×Dic3—121no—
495C2×Dic3—128no—
496C2×Dic3C2×#6714yes—
497D12—28no—
498D12—28no—
499C4×D3—48no—
500C4×D3—128no—
501C2×C32C2×C4×D411yescharacteristic
502C2×C32C2×C4×D411yescharacteristic
503C2×C32#51811yescharacteristic
504C2×C32D4211yescharacteristic
505C2×C32#55011yescharacteristic
506C2×C32#55011yescharacteristic
507C2×C32#55911yescharacteristic
508C3×D3—44no—
509C3×D3—44no—
510C24—32no—
511C24—32no—
512C2×D4—34no—
513C2×D4—34no—
514C2×D4—62no—
515C2×D4—62no—
516C2×D4—62no—
517C2×D4—62no—
518C2×D4—98no—
519C2×D4—98no—
520C2×D4—184no—
521C2×D4—184no—
522C2×D4—362no—
523C2×D4—362no—
524C22×C4—32no—
525C22×C4—32no—
526C22×C4—64no—
527C22×C4—64no—
528C22×C4—91no—
529C22×C4—91no—
530C22×C4—91no—
531C22×C4—91no—
532C22×C4—122no—
533C22×C4—184no—
534C22×C4—184no—
535C22×C4—362no—
536C22×C4C2×D3211yescharacteristic
537C22×C4C2×D3211yescharacteristic
538C22×C4C2×D3211yescharacteristic
539C4⋊C4—34no—
540C4⋊C4—62no—
541C4⋊C4—94no—
542C4⋊C4—182no—
543C22⋊C4—64no—
544C22⋊C4—64no—
545C22⋊C4—122no—
546C22⋊C4—184no—
547C22⋊C4—184no—
548C22⋊C4—362no—
549C42—22no—
550C42—94no—
551C42—184no—
552C42—182no—
553C22×C3—21no—
554C22×C3—21no—
555C22×C3—21no—
556C22×C3—21no—
557C22×C3—21no—
558C22×C3—21no—
559C22×C3—21no—
560C22×C3—64no—
561C22×C3—64no—
562C22×C3—64no—
563C22×C3—64no—
564C22×C3—64no—
565C22×C3—64no—
566C22×C3—122no—
567C22×C3—122no—
568C22×C3—122no—
569C22×C3—122no—
570C22×C3—122no—
571C22×C3—122no—
572C22×C3—122no—
573C22×C3—122no—
574C22×C3C22×C4×D311yescharacteristic
575C22×C3C22×C4×D311yescharacteristic
576C22×C3C2×#23511yescharacteristic
577C22×C3C2×D3×D411yescharacteristic
578C22×C3C2×D3×D411yescharacteristic
579C22×C3C2×D3×D411yescharacteristic
580C22×C3C2×#23711yescharacteristic
581C22×C3#100411yescharacteristic
582C22×C3#100411yescharacteristic
583C22×C3D3×#4111yescharacteristic
584C22×C3D3×#4111yescharacteristic
585C22×C3#100911yescharacteristic
586C22×C3#100911yescharacteristic
587C22×C3C22×#6711yescharacteristic
588C2×D3—24no—
589C2×D3—24no—
590C2×D3—24no—
591C2×D3—24no—
592C2×D3—24no—
593C2×D3—24no—
594C2×D3—42no—
595C2×D3—42no—
596C2×D3—42no—
597C2×D3—42no—
598C2×D3—42no—
599C2×D3—42no—
600C2×D3—42no—
601C2×D3—42no—
602C3×C4—22no—
603C3×C4—22no—
604C3×C4—24no—
605C3×C4—42no—
606C3×C4—42no—
607C3×C4—41no—
608C3×C4—41no—
609C3×C4—64no—
610C3×C4—122no—
611C3×C4#67⋊C414yescomplemented
612C3×C4C4×#6714yescomplemented
613Dic3—24no—
614Dic3—34no—
615Dic3—34no—
616Dic3—42no—
617Dic3—64no—
618Dic3—62no—
619Dic3—62no—
620Dic3—62no—
621Dic3—62no—
622Dic3—122no—
623Dic3—122no—
624Dic3—122no—
625Dic3—121no—
626Dic3—121no—
627C32#236611yescharacteristic, complemented, Sylow
628C23—34no—
629C23—34no—
630C23—62no—
631C23—62no—
632C23—62no—
633C23—62no—
634C23—62no—
635C23—62no—
636C23—62no—
637C23—62no—
638C23—62no—
639C23—62no—
640C23—62no—
641C23—62no—
642C23C22×D3211yescharacteristic
643D4—68no—
644D4—68no—
645D4—1816no—
646D4—368no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—34no—
653C2×C4—62no—
654C2×C4—62no—
655C2×C4—62no—
656C2×C4—62no—
657C2×C4—62no—
658C2×C4—92no—
659C2×C4—92no—
660C2×C4—92no—
661C2×C4—92no—
662C2×C4—92no—
663C2×C4—128no—
664C2×C4—181no—
665C2×C4—181no—
666C2×C4—181no—
667C2×C4—181no—
668C2×C4—181no—
669C2×C4—181no—
670C2×C4—181no—
671C2×C4—368no—
672C2×C4#379512yes—
673C2×C4C4×D3212yes—
674C2×C4#380212yes—
675C2×C4D3×#6712yes—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—124no—
684C2×C3—124no—
685C2×C3C2×#67⋊C411yescharacteristic
686C2×C3C4×D3×D411yescharacteristic
687C2×C3C4×D3×D411yescharacteristic
688C2×C3#554511yescharacteristic
689C2×C3#554511yescharacteristic
690C2×C3#555311yescharacteristic
691C2×C3#555911yescharacteristic
692C2×C3#559911yescharacteristic
693C2×C3#560911yescharacteristic
694C2×C3#568111yescharacteristic
695C2×C3#571811yescharacteristic
696C2×C3C2×C4×#6711yescharacteristic
697C2×C3D4×#6711yescharacteristic
698C2×C3#583411yescharacteristic
699D3—44no—
700D3—44no—
701C22—64no—
702C22—64no—
703C22—64no—
704C22—64no—
705C22—64no—
706C22—64no—
707C22—122no—
708C22—122no—
709C22—122no—
710C22—122no—
711C22—122no—
712C22—122no—
713C22—122no—
714C22—122no—
715C22C2×#379511yescharacteristic
716C22C2×C4×D3211yescharacteristic
717C22C2×#380211yescharacteristic
718C22#6430611yescharacteristic
719C22#6430711yescharacteristic
720C22#6430711yescharacteristic
721C22C2×D3×#6711yescharacteristic
722C4—22no—
723C4—41no—
724C4—64no—
725C4—94no—
726C4—122no—
727C4—182no—
728C4—182no—
729C4—361no—
730C4#6387914yescomplemented
731C3—21no—
732C3#7630611yescharacteristic, complemented
733C3#8234311yescharacteristic, complemented
734C2—124no—
735C2—124no—
736C2#1059390611yescharacteristic
737C2#1059398111yescharacteristic
738C2C4×#380211yescharacteristic
739C2#1059399611yescharacteristic
740C2C2×#6387911yescharacteristic
741C2#1059500611yescharacteristic
742C2#1059506911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC2×#63914C2
hypercenterC2×C42D32
hypocenterC32#2366
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×D12C2semidirect
3. C2×#63898C2semidirect
4. C2×#63879C2semidirect
5. C4×#3750C2semidirect
6. C3×#4939C2semidirect
7. #10591386C2semidirect
8. #10591381C2semidirect
9. #10591363C2semidirect
10. #10591323C2semidirect
11. #10591274C2semidirect
35. #63914C4semidirect
48. C2×C4×D12D3semidirect
60. #4939D3semidirect
79. C2×C3×D12C2×C4semidirect
80. C2×C3×D12C2×C4semidirect
88. C2×#625C2×C4semidirect
89. C2×#625C2×C4semidirect
95. #3750D4semidirect
97. C4×C3⋊Dic3C2×C4semidirect
102. C3×C4⋊Dic3D4semidirect
285. C2×D12C4×D3semidirect
286. C2×D12C4×D3semidirect
311. C4⋊Dic3#67semidirect
349. C32×C4C4×D4semidirect
353. C3⋊Dic3C4×D4semidirect
611. C3×C4#67⋊C4semidirect
612. C3×C4C4×#67semidirect
627. C32#2366semidirect
730. C4#63879semidirect
732. C3#76306semidirect
733. C3#82343semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D122
C2×#639142
C2×#638982
C2×#638792
C4×#37502
C3×#49392
#105913862
#105913812
#105913632
#105913232
#105912742
#823433
#763063