Finite Group Databasebeta

← #11803295

Subgroups — #11803295

Order 1152.

1953 conjugacy classes of subgroups.

The subgroup lattice has 751 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3752C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C211yesmaximal, characteristic, complemented
3C2×#63981C211yesmaximal, characteristic
4C3×C4×#217C211yesmaximal, characteristic, complemented
5#10591719C211yesmaximal, characteristic, complemented
6#10591714C211yesmaximal, characteristic, complemented
7#10591713C211yesmaximal, characteristic, complemented
8#10591383C212yesmaximal, complemented
9#10591382C212yesmaximal, complemented
10#10591289C212yesmaximal, complemented
11#10591194C212yesmaximal, complemented
12#82395—31nomaximal
13#73569—31nomaximal
14C24×C3⋊D3C2211yescharacteristic
15C23×C32×C4C2211yescharacteristic
16C23×C3⋊Dic3C2211yescharacteristic
17C22×C3×#67C2211yescharacteristic
18C22×C3×C4×D3C2211yescharacteristic, complemented
19C22×#626C2212yes—
20C2×#3752—24no—
21C2×#3752C2212yes—
22C2×#3752C2212yes—
23C2×C3×#217C2211yescharacteristic
24C2×C3×#217C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C3×C4×#67—24no—
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
28C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
29C2×C3×C4×Dic3C2211yescharacteristic, complemented
30C2×C3×C4×Dic3C2212yescomplemented
31#63981C418yescomplemented
32C2×Dic3⋊Dic3C2212yescomplemented
33C2×#3722C2212yes—
34C2×#3722C2212yes—
35C2×#3722C2212yes—
36C2×(C2×D3)⋊Dic3C2212yescomplemented
37C3×C3⋊#95C2212yescomplemented
38#63579C2212yescomplemented
39#63579C2212yescomplemented
40C2×C3×C4×D4—31no—
41C2×#937—31no—
42C2×C4×#67D311yescharacteristic, complemented
43C22×(C2×D3)⋊C4—31no—
44C22×(C2×D3)⋊C4—31no—
45C22×(C2×D3)⋊C4—61no—
46C2×#882—31no—
47C3×C4×C22⋊C4—31no—
48#5220—31no—
49#5213—32no—
50C4×#217D311yescharacteristic, complemented
51#4990—32no—
52#4958—31no—
53#4957—32no—
54#4955—31no—
55#4955—31no—
56#4950—31no—
57#4946—31no—
58#4940—32no—
59#4940—32no—
60#4939—32no—
61#4670—32no—
62#4665—32no—
63C24×C32C2311yescharacteristic
64C23×C3⋊D3—22no—
65C23×C3⋊D3—22no—
66C23×C3⋊D3—42no—
67C23×C3⋊D3—42no—
68C23×C3⋊D3C2×C414yescomplemented
69C23×C3⋊D3C2312yes—
70C23×C3×D3C2311yescharacteristic
71C22×C32×C4—42no—
72C22×C32×C4D414yescomplemented
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2311yescharacteristic
75C22×C3⋊Dic3—22no—
76C22×C3⋊Dic3—42no—
77C22×C3⋊Dic3C2312yes—
78C2×C3×#67—22no—
79C2×C3×#67—22no—
80C2×C3×#67C2×C414yes—
81C22×C3×Dic3C2311yescharacteristic
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2312yes—
86C2×C3×C4×D3—22no—
87C2×C3×C4×D3—42no—
88C2×#626—42no—
89C2×#626—42no—
90C2×#626C2×C418yescomplemented
91#3752—24no—
92#3752—24no—
93C3×#217—22no—
94C3×#217—22no—
95C3×#217C2×C414yescomplemented
96C3×(C2×D3)⋊C4—22no—
97C3×Dic3⋊C4—22no—
98C3×C4×Dic3—22no—
99C3×C4×Dic3—42no—
100Dic3⋊Dic3—42no—
101#3722—42no—
102#3722—42no—
103#3722C2×C418yescomplemented
104(C2×D3)⋊Dic3—42no—
105#2321—91noSylow
106C24×D3—31no—
107C24×D3—31no—
108C24×D3—61no—
109C22×C3×D4—31no—
110C23×C3×C4—21no—
111C23×C3×C4—31no—
112C23×C3×C4C2×D311yescharacteristic
113C23×C3×C4C2×D311yescharacteristic
114C22×#67—32no—
115C22×#67C2×D311yescharacteristic
116C23×Dic3—31no—
117C23×Dic3—31no—
118C23×Dic3—61no—
119C22×D12—32no—
120C22×C4×D3C2×D311yescharacteristic, complemented
121C3×C4×D4—64no—
122C2×C3×C4⋊C4—31no—
123C2×C3×C22⋊C4—31no—
124C2×C3×C22⋊C4—31no—
125C2×C3×C22⋊C4—31no—
126C2×C3×C22⋊C4—31no—
127C2×C3×C42—31no—
128C2×C3×C42—32no—
129C2×#217—32no—
130C2×#217C2×D311yescharacteristic
131C2×#217C2×D311yescharacteristic
132C2×#217C2×D311yescharacteristic
133#937—38no—
134C4×#67—24no—
135C2×(C2×D3)⋊C4—32no—
136C2×(C2×D3)⋊C4—32no—
137C2×(C2×D3)⋊C4—32no—
138C2×(C2×D3)⋊C4—32no—
139C2×(C2×D3)⋊C4—32no—
140C2×(C2×D3)⋊C4—32no—
141C2×(C2×D3)⋊C4—32no—
142C2×(C2×D3)⋊C4—32no—
143C2×(C2×D3)⋊C4—32no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4—32no—
146C2×(C2×D3)⋊C4—62no—
147C2×(C2×D3)⋊C4—62no—
148C2×(C2×D3)⋊C4—68no—
149C2×(C2×D3)⋊C4—64no—
150C2×(C2×D3)⋊C4—64no—
151C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
152C2×C4⋊Dic3—32no—
153C2×Dic3⋊C4—32no—
154C2×Dic3⋊C4C2×D311yescharacteristic, complemented
155C2×C4×Dic3C2×D311yescharacteristic, complemented
156C2×C4×Dic3C2×D312yescomplemented
157#882—38no—
158C3×#95—32no—
159C3⋊#95—32no—
160C3⋊#95—32no—
161C3⋊#95—32no—
162C3⋊#95—32no—
163C3⋊#95C2×D312yescomplemented
164C23×C32—22no—
165C23×C32—22no—
166C23×C32C22×C412yes—
167C23×C32C2×D412yes—
168C23×C32#4112yes—
169C23×C32C2411yescharacteristic
170C22×C3⋊D3—28no—
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—48no—
178C22×C3⋊D3—44no—
179C22×C3⋊D3—44no—
180C22×C3⋊D3—48no—
181C22×C3⋊D3C22×C414yes—
182C22×C3×D3—21no—
183C22×C3×D3—21no—
184C22×C3×D3—22no—
185C22×C3×D3—22no—
186C22×C3×D3C22×C412yes—
187C2×C32×C4—22no—
188C2×C32×C4—22no—
189C2×C32×C4—44no—
190C2×C32×C4C2×D412yes—
191C2×C32×C4C2×D412yes—
192C2×C3⋊Dic3—22no—
193C2×C3⋊Dic3—22no—
194C2×C3⋊Dic3—22no—
195C2×C3⋊Dic3—44no—
196C3×#67—28no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3C22×C412yes—
209C2×C3×Dic3C22×C414yes—
210C3×C4×D3—44no—
211#626—48no—
212C2×#120—91no—
213C2×C4×D4—31no—
214C22×C22⋊C4—91no—
215#390—92no—
216#388—92no—
217#388—92no—
218#386—92no—
219#386—91no—
220#385—91no—
221#379—91no—
222C4×C22⋊C4—31no—
223C24×C3—21no—
224C24×C3—31no—
225C24×C3C22×D311yescharacteristic
226C24×C3C22×D311yescharacteristic
227C23×D3—32no—
228C23×D3—32no—
229C23×D3—34no—
230C23×D3—34no—
231C23×D3—64no—
232C23×D3—62no—
233C23×D3—64no—
234C23×D3—64no—
235C23×D3—62no—
236C23×D3—62no—
237C23×D3—62no—
238C23×D3—62no—
239C23×D3—122no—
240C23×D3—122no—
241C23×D3—122no—
242C23×D3—122no—
243C23×D3—124no—
244C23×D3—124no—
245C23×D3C22×D311yescharacteristic
246C2×C3×D4—34no—
247C2×C3×D4—62no—
248C2×C3×D4—62no—
249C22×C3×C4—24no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—31no—
253C22×C3×C4—32no—
254C22×C3×C4—31no—
255C22×C3×C4—32no—
256C22×C3×C4—31no—
257C22×C3×C4—42no—
258C22×C3×C4—42no—
259C22×C3×C4—44no—
260C22×C3×C4—62no—
261C22×C3×C4—122no—
262C22×C3×C4D1214yescomplemented
263C22×C3×C4#6714yescomplemented
264C22×C3×C4C22×D311yescharacteristic
265C22×C3×C4C22×D311yescharacteristic
266C22×C3×C4C22×D311yescharacteristic
267C22×C3×C4C22×D311yescharacteristic
268C2×#67—22no—
269C2×#67—22no—
270C2×#67—38no—
271C2×#67—122no—
272C2×#67—122no—
273C2×#67C4×D314yes—
274C22×Dic3—32no—
275C22×Dic3—32no—
276C22×Dic3—62no—
277C22×Dic3—64no—
278C22×Dic3—62no—
279C22×Dic3—62no—
280C22×Dic3—122no—
281C22×Dic3—122no—
282C22×Dic3—124no—
283C22×Dic3C22×D311yescharacteristic
284C22×Dic3C22×D312yes—
285C22×Dic3C22×D311yescharacteristic
286C22×Dic3C22×D311yescharacteristic
287C22×Dic3C22×D312yes—
288C2×D12—38no—
289C2×D12—122no—
290C2×D12—122no—
291C2×C4×D3—22no—
292C2×C4×D3—42no—
293C3×C4⋊C4—62no—
294C3×C22⋊C4—34no—
295C3×C22⋊C4—62no—
296C3×C22⋊C4—62no—
297C3×C22⋊C4—62no—
298C3×C42—62no—
299C3×C42—122no—
300#217—22no—
301#217—22no—
302#217—122no—
303#217C4×D314yescomplemented
304(C2×D3)⋊C4—22no—
305(C2×D3)⋊C4—38no—
306(C2×D3)⋊C4—38no—
307(C2×D3)⋊C4—68no—
308(C2×D3)⋊C4—68no—
309(C2×D3)⋊C4—64no—
310(C2×D3)⋊C4—64no—
311(C2×D3)⋊C4—64no—
312(C2×D3)⋊C4—64no—
313(C2×D3)⋊C4—122no—
314(C2×D3)⋊C4—122no—
315(C2×D3)⋊C4—122no—
316(C2×D3)⋊C4—122no—
317(C2×D3)⋊C4—122no—
318C4⋊Dic3—122no—
319Dic3⋊C4—22no—
320Dic3⋊C4—122no—
321C4×Dic3—22no—
322C4×Dic3—42no—
323C22×C32—24no—
324C22×C32—22no—
325C22×C32—22no—
326C22×C32—24no—
327C22×C32C4×D414yes—
328C22×C32C23×C411yescharacteristic
329C22×C32C22×D411yescharacteristic
330C22×C32C2×#4111yescharacteristic
331C22×C32H(5,𝔽2)12yes—
332C22×C32H(5,𝔽2)12yes—
333C2×C3⋊D3—24no—
334C2×C3⋊D3—24no—
335C2×C3⋊D3—24no—
336C2×C3⋊D3—416no—
337C2×C3⋊D3—42no—
338C2×C3⋊D3—42no—
339C2×C3⋊D3—42no—
340C2×C3⋊D3—42no—
341C2×C3×D3—22no—
342C2×C3×D3—24no—
343C2×C3×D3—41no—
344C2×C3×D3—41no—
345C2×C3×D3—42no—
346C32×C4—22no—
347C32×C4—22no—
348C3⋊Dic3—42no—
349C3×Dic3—22no—
350C3×Dic3—24no—
351C3×Dic3—41no—
352C3×Dic3—41no—
353C3×Dic3—42no—
354C25—91no—
355C22×D4—31no—
356C22×D4—92no—
357C23×C4—31no—
358C23×C4—91no—
359C23×C4D3211yescharacteristic
360#120—98no—
361C4×D4—64no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—92no—
364C2×C22⋊C4—31no—
365C2×C22⋊C4—31no—
366C2×C22⋊C4—31no—
367C2×C22⋊C4—31no—
368C2×C22⋊C4—92no—
369C2×C22⋊C4—92no—
370C2×C22⋊C4—92no—
371C2×C22⋊C4—92no—
372C2×C22⋊C4—92no—
373C2×C22⋊C4—92no—
374C2×C22⋊C4—184no—
375C2×C42—31no—
376C2×C42—32no—
377#95—32no—
378#95—92no—
379#95—92no—
380C23×C3—24no—
381C23×C3—24no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—21no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—32no—
391C23×C3—61no—
392C23×C3—61no—
393C23×C3—62no—
394C23×C3—62no—
395C23×C3C2×C4×D312yes—
396C23×C3C2×C4×D312yes—
397C23×C3C2×D1212yes—
398C23×C3#23512yes—
399C23×C3#23512yes—
400C23×C3C2×#6712yes—
401C23×C3C23×D311yescharacteristic
402C23×C3C23×D311yescharacteristic
403C22×D3—21no—
404C22×D3—22no—
405C22×D3—22no—
406C22×D3—21no—
407C22×D3—34no—
408C22×D3—34no—
409C22×D3—64no—
410C22×D3—64no—
411C22×D3—64no—
412C22×D3—616no—
413C22×D3—68no—
414C22×D3—68no—
415C22×D3—62no—
416C22×D3—62no—
417C22×D3—62no—
418C22×D3—62no—
419C22×D3—62no—
420C22×D3—62no—
421C22×D3—62no—
422C22×D3—62no—
423C22×D3—62no—
424C22×D3—62no—
425C22×D3—62no—
426C22×D3—62no—
427C22×D3—122no—
428C22×D3—122no—
429C22×D3—122no—
430C22×D3—122no—
431C22×D3—128no—
432C22×D3—128no—
433C22×D3—1216no—
434C22×D3—128no—
435C22×D3—128no—
436C22×D3—1216no—
437C22×D3—124no—
438C22×D3—124no—
439C22×D3—124no—
440C22×D3—128no—
441C22×D3—128no—
442C22×D3—124no—
443C22×D3C2×C4×D312yes—
444C3×D4—68no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—32no—
452C2×C3×C4—34no—
453C2×C3×C4—42no—
454C2×C3×C4—42no—
455C2×C3×C4—44no—
456C2×C3×C4—44no—
457C2×C3×C4—48no—
458C2×C3×C4—61no—
459C2×C3×C4—61no—
460C2×C3×C4—62no—
461C2×C3×C4—62no—
462C2×C3×C4—61no—
463C2×C3×C4—61no—
464C2×C3×C4—62no—
465C2×C3×C4—62no—
466C2×C3×C4—62no—
467C2×C3×C4—62no—
468C2×C3×C4—62no—
469C2×C3×C4—124no—
470C2×C3×C4C2×D1212yes—
471C2×C3×C4C2×D1212yes—
472C2×C3×C4C2×#6712yes—
473C2×C3×C4C2×#6712yes—
474#67—28no—
475#67—128no—
476C2×Dic3—21no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—21no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—64no—
488C2×Dic3—62no—
489C2×Dic3—62no—
490C2×Dic3—62no—
491C2×Dic3—62no—
492C2×Dic3—62no—
493C2×Dic3—62no—
494C2×Dic3—122no—
495C2×Dic3—122no—
496C2×Dic3—128no—
497C2×Dic3—124no—
498C2×Dic3—124no—
499C2×Dic3C2×C4×D312yes—
500C2×Dic3C2×C4×D314yes—
501D12—128no—
502C4×D3—44no—
503C2×C32—24no—
504C2×C32C2×C4×D411yescharacteristic
505C2×C32#51812yes—
506C2×C32#53411yescharacteristic
507C2×C32#53511yescharacteristic
508C2×C32#53812yes—
509C3⋊D3—44no—
510C3×D3—42no—
511C24—31no—
512C24—92no—
513C24—94no—
514C24—182no—
515C24—182no—
516C24—362no—
517C24—362no—
518C24C2×D3211yescharacteristic
519C2×D4—34no—
520C2×D4—62no—
521C2×D4—62no—
522C2×D4—98no—
523C2×D4—362no—
524C2×D4—362no—
525C22×C4—32no—
526C22×C4—31no—
527C22×C4—32no—
528C22×C4—31no—
529C22×C4—31no—
530C22×C4—42no—
531C22×C4—62no—
532C22×C4—92no—
533C22×C4—122no—
534C22×C4—182no—
535C22×C4—362no—
536C22×C4#62614yescomplemented
537C22×C4C2×D3211yescharacteristic
538C22×C4C2×D3211yescharacteristic
539C4⋊C4—62no—
540C4⋊C4—362no—
541C22⋊C4—34no—
542C22⋊C4—62no—
543C22⋊C4—62no—
544C22⋊C4—62no—
545C22⋊C4—98no—
546C22⋊C4—184no—
547C22⋊C4—184no—
548C22⋊C4—362no—
549C22⋊C4—362no—
550C22⋊C4—362no—
551C42—62no—
552C42—122no—
553C22×C3—24no—
554C22×C3—24no—
555C22×C3—28no—
556C22×C3—28no—
557C22×C3—22no—
558C22×C3—22no—
559C22×C3—24no—
560C22×C3—24no—
561C22×C3—22no—
562C22×C3—24no—
563C22×C3—24no—
564C22×C3—22no—
565C22×C3—21no—
566C22×C3—21no—
567C22×C3—22no—
568C22×C3—21no—
569C22×C3—22no—
570C22×C3—24no—
571C22×C3—62no—
572C22×C3—64no—
573C22×C3—121no—
574C22×C3—121no—
575C22×C3—122no—
576C22×C3C4×D1214yes—
577C22×C3C4×#6714yes—
578C22×C3C22×C4×D311yescharacteristic
579C22×C3C22×C4×D311yescharacteristic
580C22×C3C22×D1211yescharacteristic
581C22×C3C2×#23511yescharacteristic
582C22×C3C2×#23511yescharacteristic
583C22×C3#100412yes—
584C22×C3#100412yes—
585C22×C3#100912yes—
586C22×C3#100912yes—
587C22×C3C22×#6711yescharacteristic
588C2×D3—22no—
589C2×D3—24no—
590C2×D3—41no—
591C2×D3—42no—
592C2×D3—41no—
593C2×D3—68no—
594C2×D3—64no—
595C2×D3—64no—
596C2×D3—64no—
597C2×D3—64no—
598C2×D3—64no—
599C2×D3—64no—
600C2×D3—124no—
601C2×D3—124no—
602C2×D3—1232no—
603C2×D3—1216no—
604C2×D3—1216no—
605C2×D3—124no—
606C2×D3—124no—
607C2×D3—124no—
608C2×D3—124no—
609C2×D3—122no—
610C2×D3—122no—
611C2×D3—122no—
612C2×D3—122no—
613C2×D3—122no—
614C2×D3—122no—
615C2×D3—122no—
616C2×D3—122no—
617C3×C4—22no—
618C3×C4—22no—
619C3×C4—22no—
620C3×C4—22no—
621C3×C4—42no—
622C3×C4—42no—
623C3×C4—62no—
624C3×C4—64no—
625C3×C4—121no—
626C3×C4—121no—
627C3×C4—122no—
628Dic3—22no—
629Dic3—24no—
630Dic3—41no—
631Dic3—42no—
632Dic3—41no—
633Dic3—124no—
634Dic3—122no—
635Dic3—122no—
636C32#232111yescharacteristic, complemented, Sylow
637C23—22no—
638C23—22no—
639C23—32no—
640C23—61no—
641C23—62no—
642C23—61no—
643C23—62no—
644C23—94no—
645C23—182no—
646C23—182no—
647C23—182no—
648C23—182no—
649C23—182no—
650C23—182no—
651C23—188no—
652C23—368no—
653C23—364no—
654C23—368no—
655C23—364no—
656C23#379812yes—
657C23C4×D3212yes—
658C23C2×#62612yes—
659C23C22×D3211yescharacteristic
660D4—68no—
661D4—368no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—34no—
665C2×C4—32no—
666C2×C4—44no—
667C2×C4—61no—
668C2×C4—62no—
669C2×C4—61no—
670C2×C4—62no—
671C2×C4—62no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—62no—
677C2×C4—62no—
678C2×C4—124no—
679C2×C4—182no—
680C2×C4—182no—
681C2×C4—182no—
682C2×C4—364no—
683C2×C4C2×#62612yes—
684C2×C4C2×#62612yes—
685C2×C3—28no—
686C2×C3—24no—
687C2×C3—24no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—22no—
691C2×C3—21no—
692C2×C3—22no—
693C2×C3—122no—
694C2×C3C2×C4×D1211yescharacteristic
695C2×C3#549311yescharacteristic
696C2×C3#552511yescharacteristic
697C2×C3#554512yes—
698C2×C3#554512yes—
699C2×C3#556012yes—
700C2×C3#556012yes—
701C2×C3C2×C4×#6711yescharacteristic
702C2×C3#580411yescharacteristic
703C2×C3#583011yescharacteristic
704D3—42no—
705D3—128no—
706D3—124no—
707D3—124no—
708C22—22no—
709C22—24no—
710C22—22no—
711C22—24no—
712C22—62no—
713C22—64no—
714C22—121no—
715C22—122no—
716C22—121no—
717C22—184no—
718C22—184no—
719C22—184no—
720C22—3616no—
721C22—362no—
722C22—362no—
723C22—362no—
724C22—362no—
725C22C4×#62614yes—
726C22C2×#379811yescharacteristic
727C22C2×C4×D3211yescharacteristic
728C22#6430812yes—
729C22C22×#62611yescharacteristic
730C22#6433012yes—
731C4—22no—
732C4—22no—
733C4—62no—
734C4—64no—
735C4—121no—
736C4—122no—
737C4—121no—
738C4—362no—
739C3—21no—
740C3#7356911yescharacteristic, complemented
741C3#8239511yescharacteristic, complemented
742C2—24no—
743C2—122no—
744C2—364no—
745C2C2×C4×#62611yescharacteristic
746C2#1059503912yes—
747C2#1059504511yescharacteristic
748C2#1059505812yes—
749C2#1059551911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63981C2
hypercenterC23×C4D32
hypocenterC32#2321
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3752C2semidirect
2. C2×C3×C4×#67C2semidirect
4. C3×C4×#217C2semidirect
5. #10591719C2semidirect
6. #10591714C2semidirect
7. #10591713C2semidirect
8. #10591383C2semidirect
9. #10591382C2semidirect
10. #10591289C2semidirect
11. #10591194C2semidirect
18. C22×C3×C4×D3C22semidirect
27. C2×C3×(C2×D3)⋊C4C22semidirect
28. C2×C3×Dic3⋊C4C22semidirect
29. C2×C3×C4×Dic3C22semidirect
30. C2×C3×C4×Dic3C22semidirect
31. #63981C4semidirect
32. C2×Dic3⋊Dic3C22semidirect
36. C2×(C2×D3)⋊Dic3C22semidirect
37. C3×C3⋊#95C22semidirect
38. #63579C22semidirect
39. #63579C22semidirect
42. C2×C4×#67D3semidirect
50. C4×#217D3semidirect
68. C23×C3⋊D3C2×C4semidirect
72. C22×C32×C4D4semidirect
90. C2×#626C2×C4semidirect
95. C3×#217C2×C4semidirect
103. #3722C2×C4semidirect
120. C22×C4×D3C2×D3semidirect
151. C2×(C2×D3)⋊C4C2×D3semidirect
154. C2×Dic3⋊C4C2×D3semidirect
155. C2×C4×Dic3C2×D3semidirect
156. C2×C4×Dic3C2×D3semidirect
163. C3⋊#95C2×D3semidirect
262. C22×C3×C4D12semidirect
263. C22×C3×C4#67semidirect
303. #217C4×D3semidirect
536. C22×C4#626semidirect
636. C32#2321semidirect
740. C3#73569semidirect
741. C3#82395semidirect

Maximal subgroups

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

subgroupindex
C22×#37522
C2×C3×C4×#672
C2×#639812
C3×C4×#2172
#105917192
#105917142
#105917132
#105913832
#105913822
#105912892
#105911942
#823953
#735693