Finite Group Databasebeta

← #11824439

Subgroups — #11824439

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×#67⋊C4C211yesmaximal, characteristic, complemented
2C2×#63979C212yesmaximal, complemented
3C2×#63978C212yesmaximal, complemented
4C2×#63911C211yesmaximal, characteristic, complemented
5C2×#63906C212yesmaximal, complemented
6#10592659C211yesmaximal, characteristic, complemented
7C3×#4960C211yesmaximal, characteristic, complemented
8#10591395C211yesmaximal, characteristic, complemented
9#10591389C211yesmaximal, characteristic, complemented
10#10591384C212yesmaximal, complemented
11#10591242C211yesmaximal, characteristic, complemented
12#82378—31nomaximal
13#76688—31nomaximal
14C22×#638C2212yes—
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×C3×#67C2212yes—
17C22×C3×#67C2211yescharacteristic
18C23×C3×Dic3C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×#626C2212yes—
22C22×#626C2212yes—
23C22×#626C2212yes—
24C22×#625C2212yes—
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3752C2212yes—
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C3×#67⋊C4—24no—
32#63979—28no—
33#63978—28no—
34C2×Dic3⋊Dic3C2212yes—
35C2×#3722C2212yes—
36C2×(C2×D3)⋊Dic3C2212yes—
37C2×Dic32C2212yes—
38#63911—24no—
39#63906—28no—
40#63658C2211yescharacteristic
41C3×C3⋊#95C2211yescharacteristic
42C2×C3×C4×D4—31no—
43C2×#940—32no—
44C2×#940—32no—
45C2×#940—31no—
46C2×#939—32no—
47C2×#930—32no—
48C2×#930—32no—
49C2×#884—32no—
50C2×#67⋊C4D311yescharacteristic, complemented
51C2×#874—31no—
52C3×#392—31no—
53#5223—31no—
54#4988—32no—
55#4960—31no—
56#4960—31no—
57#4960—31no—
58#4960—31no—
59#4960—61no—
60#4960D311yescharacteristic, complemented
61#4957—32no—
62C4×C4⋊Dic3—31no—
63#4671—31no—
64#4649—31no—
65C24×C32C2311yescharacteristic
66C23×C3⋊D3C2312yes—
67C23×C3×D3C2312yes—
68C23×C3×D3C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C2×#638—24no—
72C2×#638—24no—
73C2×#638—42no—
74C22×C3⋊Dic3C2312yes—
75C2×C4⋊(C3⋊D3)—22no—
76C2×C4⋊(C3⋊D3)—42no—
77C2×C3×#67—24no—
78C2×C3×#67—22no—
79C2×C3×#67—24no—
80C2×C3×#67—22no—
81C2×C3×#67—42no—
82C2×C3×#67D414yescomplemented
83C22×C3×Dic3—22no—
84C22×C3×Dic3—24no—
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2311yescharacteristic
89C2×C3×D12—22no—
90C2×C3×D12—42no—
91C2×C3×C4×D3—22no—
92C2×C3×C4×D3—24no—
93C2×#626—24no—
94C2×#626—24no—
95C2×#626—24no—
96C2×#626—24no—
97C2×#626—24no—
98C2×#626—24no—
99C2×#626—24no—
100C2×#626—24no—
101C2×#626—42no—
102C2×#625—24no—
103C2×#625—24no—
104C2×#625—42no—
105C32×C22⋊C4—22no—
106#3752—24no—
107C3×(C2×D3)⋊C4—22no—
108C3×(C2×D3)⋊C4—24no—
109C3×Dic3⋊C4—22no—
110C3×C4×Dic3D414yescomplemented
111Dic3⋊Dic3D418yescomplemented
112#3722—24no—
113(C2×D3)⋊Dic3—24no—
114Dic32—24no—
115#2541—91noSylow
116C22×C3×D4—31no—
117C22×C3×D4—32no—
118C22×C3×D4—31no—
119C23×C3×C4—31no—
120C23×C3×C4—31no—
121C22×#67—32no—
122C22×#67—32no—
123C22×#67—32no—
124C22×#67—32no—
125C22×#67—32no—
126C22×#67—32no—
127C22×#67—32no—
128C22×#67—62no—
129C22×#67C2×D312yes—
130C22×#67C2×D311yescharacteristic
131C23×Dic3C2×D311yescharacteristic
132C22×D12—32no—
133C22×D12—32no—
134C22×D12—32no—
135C22×D12—31no—
136C22×D12—31no—
137C22×D12—61no—
138C22×D12C2×D311yescharacteristic
139C22×C4×D3C2×D311yescharacteristic
140C3×C4×D4—64no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C22⋊C4—21no—
143C2×C3×C22⋊C4—32no—
144C2×C3×C22⋊C4—31no—
145C2×C3×C22⋊C4C2×D311yescharacteristic
146C2×C3×C22⋊C4C2×D311yescharacteristic
147C2×C3×C42—31no—
148C2×#217—32no—
149#940—68no—
150#940—68no—
151#940—64no—
152#939—68no—
153#930—68no—
154#930—68no—
155C2×(C2×D3)⋊C4—32no—
156C2×(C2×D3)⋊C4—32no—
157C2×(C2×D3)⋊C4—32no—
158C2×(C2×D3)⋊C4—32no—
159C2×(C2×D3)⋊C4—32no—
160C2×(C2×D3)⋊C4—62no—
161C2×(C2×D3)⋊C4C2×D311yescharacteristic
162C2×(C2×D3)⋊C4C2×D312yes—
163C2×C4⋊Dic3—32no—
164C2×Dic3⋊C4—32no—
165C2×Dic3⋊C4C2×D311yescharacteristic
166C2×C4×Dic3—32no—
167C2×C4×Dic3—32no—
168C2×C4×Dic3C2×D311yescharacteristic
169#884—68no—
170#67⋊C4—24no—
171#874—64no—
172C3×#95—31no—
173C3⋊#95—31no—
174C3⋊#95—31no—
175C3⋊#95—61no—
176C3⋊#95C2×D311yescharacteristic
177C23×C32—21no—
178C23×C32—22no—
179C23×C32—21no—
180C23×C32—22no—
181C23×C32C2×D412yes—
182C23×C32C2411yescharacteristic
183C22×C3⋊D3—22no—
184C22×C3⋊D3—22no—
185C22×C3⋊D3—22no—
186C22×C3⋊D3—22no—
187C22×C3⋊D3—22no—
188C22×C3⋊D3—22no—
189C22×C3⋊D3—22no—
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—
202C2×C32×C4—22no—
203C2×C32×C4—21no—
204C2×C32×C4—22no—
205C2×C32×C4C2×D412yes—
206#638—48no—
207C2×C3⋊Dic3—22no—
208C2×C3⋊Dic3—22no—
209C2×C3⋊Dic3C2×D414yes—
210C4⋊(C3⋊D3)—44no—
211C3×#67—28no—
212C3×#67—48no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3—22no—
215C2×C3×Dic3—22no—
216C2×C3×Dic3—21no—
217C2×C3×Dic3—44no—
218C2×C3×Dic3C2×D412yes—
219C2×C3×Dic3C2×D414yes—
220C2×C3×Dic3C2×D414yes—
221C2×C3×Dic3C2×D412yes—
222C2×C3×Dic3C2×D412yes—
223C2×C3×Dic3#4112yes—
224C3×D12—44no—
225C3×C4×D3—44no—
226#626—48no—
227#626—48no—
228#626—48no—
229#625—48no—
230C2×#127—91no—
231C2×#127—92no—
232C2×#121—92no—
233C2×#121—92no—
234C2×C4×D4—31no—
235#392—31no—
236#392—91no—
237#392—91no—
238#392—91no—
239#390—92no—
240C4×C4⋊C4—91no—
241C24×C3—21no—
242C24×C3—31no—
243C24×C3—32no—
244C24×C3C22×D311yescharacteristic
245C24×C3C22×D311yescharacteristic
246C23×D3—32no—
247C23×D3—32no—
248C23×D3—62no—
249C23×D3C22×D312yes—
250C23×D3C22×D311yescharacteristic
251C2×C3×D4—34no—
252C2×C3×D4—62no—
253C2×C3×D4—62no—
254C2×C3×D4—64no—
255C2×C3×D4—64no—
256C2×C3×D4—62no—
257C2×C3×D4—122no—
258C2×C3×D4—122no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—31no—
262C22×C3×C4—31no—
263C22×C3×C4—32no—
264C22×C3×C4—31no—
265C22×C3×C4—64no—
266C22×C3×C4—62no—
267C22×C3×C4—64no—
268C22×C3×C4—62no—
269C22×C3×C4C22×D311yescharacteristic
270C22×C3×C4C22×D311yescharacteristic
271C22×C3×C4C22×D311yescharacteristic
272C22×C3×C4C22×D311yescharacteristic
273C2×#67—24no—
274C2×#67—22no—
275C2×#67—24no—
276C2×#67—22no—
277C2×#67—42no—
278C2×#67—64no—
279C2×#67—64no—
280C2×#67—64no—
281C2×#67—64no—
282C2×#67—64no—
283C2×#67—64no—
284C2×#67—64no—
285C2×#67—64no—
286C2×#67—64no—
287C2×#67—64no—
288C2×#67—64no—
289C2×#67—64no—
290C2×#67—64no—
291C2×#67—64no—
292C2×#67—64no—
293C2×#67—64no—
294C2×#67—124no—
295C2×#67—124no—
296C2×#67—122no—
297C2×#67—122no—
298C2×#67—122no—
299C2×#67—122no—
300C2×#67—122no—
301C2×#67—124no—
302C2×#67D1214yescomplemented
303C22×Dic3—24no—
304C22×Dic3—22no—
305C22×Dic3—32no—
306C22×Dic3—32no—
307C22×Dic3—62no—
308C22×Dic3C22×D311yescharacteristic
309C22×Dic3C22×D312yes—
310C22×Dic3C22×D311yescharacteristic
311C22×Dic3C22×D311yescharacteristic
312C2×D12—22no—
313C2×D12—42no—
314C2×D12—64no—
315C2×D12—64no—
316C2×D12—64no—
317C2×D12—64no—
318C2×D12—64no—
319C2×D12—64no—
320C2×D12—64no—
321C2×D12—64no—
322C2×D12—62no—
323C2×D12—62no—
324C2×D12—122no—
325C2×D12—122no—
326C2×D12—122no—
327C2×D12—124no—
328C2×D12—122no—
329C2×C4×D3—24no—
330C2×C4×D3—22no—
331C3×C4⋊C4—62no—
332C3×C22⋊C4—22no—
333C3×C22⋊C4—22no—
334C3×C22⋊C4—42no—
335C3×C22⋊C4—64no—
336C3×C22⋊C4—62no—
337C3×C42—34no—
338#217—64no—
339(C2×D3)⋊C4—22no—
340(C2×D3)⋊C4—24no—
341(C2×D3)⋊C4—64no—
342(C2×D3)⋊C4—64no—
343(C2×D3)⋊C4—64no—
344(C2×D3)⋊C4—64no—
345(C2×D3)⋊C4—64no—
346(C2×D3)⋊C4—124no—
347C4⋊Dic3—38no—
348Dic3⋊C4—22no—
349Dic3⋊C4—38no—
350C4×Dic3—64no—
351C4×Dic3—64no—
352C4×Dic3#6714yescomplemented
353C22×C32—22no—
354C22×C32—24no—
355C22×C32—41no—
356C22×C32—41no—
357C22×C32—42no—
358C22×C32C22×D411yescharacteristic
359C22×C32C22×D412yes—
360C22×C32C22×D411yescharacteristic
361C22×C32C2×#4111yescharacteristic
362C22×C32H(5,𝔽2)12yes—
363C2×C3⋊D3—42no—
364C2×C3⋊D3—42no—
365C2×C3⋊D3—42no—
366C2×C3⋊D3—42no—
367C2×C3⋊D3—42no—
368C2×C3⋊D3—42no—
369C2×C3⋊D3—42no—
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—41no—
384C3⋊Dic3—24no—
385C3×Dic3—24no—
386C3×Dic3—41no—
387C3×Dic3#12114yescomplemented
388C3×Dic3#12714yescomplemented
389C22×D4—31no—
390C22×D4—32no—
391C22×D4—31no—
392C22×D4—92no—
393C22×D4—92no—
394C22×D4—92no—
395C22×D4—92no—
396C22×D4—92no—
397C22×D4—91no—
398C23×C4—31no—
399C23×C4—31no—
400#127—184no—
401#127—188no—
402#121—188no—
403#121—188no—
404C4×D4—64no—
405C2×C4⋊C4—31no—
406C2×C4⋊C4—92no—
407C2×C22⋊C4—31no—
408C2×C22⋊C4—32no—
409C2×C22⋊C4—92no—
410C2×C22⋊C4—92no—
411C2×C22⋊C4—92no—
412C2×C22⋊C4D3211yescharacteristic
413C2×C42—31no—
414C2×C42—92no—
415#95—31no—
416#95—91no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—22no—
422C23×C3—21no—
423C23×C3—22no—
424C23×C3—21no—
425C23×C3—21no—
426C23×C3—22no—
427C23×C3—32no—
428C23×C3—41no—
429C23×C3—42no—
430C23×C3—42no—
431C23×C3—41no—
432C23×C3—61no—
433C23×C3—62no—
434C23×C3—62no—
435C23×C3—61no—
436C23×C3—62no—
437C23×C3—62no—
438C23×C3—62no—
439C23×C3—62no—
440C23×C3—62no—
441C23×C3—62no—
442C23×C3—62no—
443C23×C3C2×D1212yes—
444C23×C3D3×D412yes—
445C23×C3C23×D311yescharacteristic
446C23×C3C23×D311yescharacteristic
447C22×D3—21no—
448C22×D3—22no—
449C22×D3—22no—
450C22×D3—21no—
451C22×D3—22no—
452C22×D3—22no—
453C22×D3—22no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—64no—
459C22×D3—62no—
460C22×D3—62no—
461C22×D3—62no—
462C22×D3—62no—
463C22×D3—62no—
464C22×D3—62no—
465C22×D3—62no—
466C22×D3—62no—
467C22×D3—62no—
468C22×D3—62no—
469C22×D3—62no—
470C22×D3—62no—
471C22×D3—62no—
472C22×D3—62no—
473C22×D3—122no—
474C22×D3—122no—
475C22×D3—122no—
476C22×D3—122no—
477C22×D3—122no—
478C22×D3—122no—
479C22×D3C2×D1212yes—
480C3×D4—68no—
481C3×D4—124no—
482C3×D4—128no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—22no—
490C2×C3×C4—32no—
491C2×C3×C4—34no—
492C2×C3×C4—32no—
493C2×C3×C4—32no—
494C2×C3×C4—32no—
495C2×C3×C4—34no—
496C2×C3×C4—42no—
497C2×C3×C4—42no—
498C2×C3×C4—41no—
499C2×C3×C4—62no—
500C2×C3×C4—62no—
501C2×C3×C4—62no—
502C2×C3×C4—61no—
503C2×C3×C4—124no—
504C2×C3×C4—124no—
505C2×C3×C4D3×D412yes—
506C2×C3×C4C2×#6712yes—
507#67—28no—
508#67—48no—
509#67—128no—
510#67—128no—
511#67—128no—
512#67—128no—
513#67—128no—
514#67—1216no—
515#67—128no—
516#67—128no—
517C2×Dic3—22no—
518C2×Dic3—22no—
519C2×Dic3—22no—
520C2×Dic3—21no—
521C2×Dic3—34no—
522C2×Dic3—34no—
523C2×Dic3—44no—
524C2×Dic3—64no—
525C2×Dic3—62no—
526C2×Dic3—62no—
527C2×Dic3—62no—
528C2×Dic3—62no—
529C2×Dic3—122no—
530C2×Dic3—122no—
531C2×Dic3C2×D1212yes—
532C2×Dic3#23512yes—
533C2×Dic3D3×D414yes—
534C2×Dic3D3×D414yes—
535C2×Dic3C2×#6712yes—
536C2×Dic3C2×#6712yes—
537D12—44no—
538D12—124no—
539D12—124no—
540D12—128no—
541D12—128no—
542D12—128no—
543D12—128no—
544C4×D3—44no—
545C2×C32—42no—
546C2×C32C2×#12111yescharacteristic
547C2×C32C2×#12711yescharacteristic
548C2×C32#53511yescharacteristic
549C2×C32D4212yes—
550C2×C32#55012yes—
551C3⋊D3—82no—
552C3×D3—42no—
553C3×D3—82no—
554C24—31no—
555C24—32no—
556C24—92no—
557C24C2×D3211yescharacteristic
558C2×D4—34no—
559C2×D4—62no—
560C2×D4—62no—
561C2×D4—64no—
562C2×D4—64no—
563C2×D4—62no—
564C2×D4—122no—
565C2×D4—122no—
566C2×D4—184no—
567C2×D4—184no—
568C2×D4—184no—
569C2×D4—184no—
570C2×D4—184no—
571C2×D4—184no—
572C2×D4—184no—
573C2×D4—184no—
574C2×D4—184no—
575C2×D4—184no—
576C2×D4—184no—
577C2×D4—184no—
578C2×D4—182no—
579C2×D4—362no—
580C2×D4—362no—
581C2×D4—362no—
582C2×D4—362no—
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×C4—92no—
592C22×C4C2×D3211yescharacteristic
593C22×C4C2×D3211yescharacteristic
594C4⋊C4—62no—
595C4⋊C4—98no—
596C22⋊C4—22no—
597C22⋊C4—64no—
598C22⋊C4—62no—
599C22⋊C4—184no—
600C22⋊C4—184no—
601C22⋊C4—184no—
602C42—34no—
603C42—184no—
604C22×C3—22no—
605C22×C3—24no—
606C22×C3—24no—
607C22×C3—22no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—21no—
613C22×C3—44no—
614C22×C3—42no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—42no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—42no—
621C22×C3—64no—
622C22×C3—62no—
623C22×C3—81no—
624C22×C3—82no—
625C22×C3—81no—
626C22×C3—121no—
627C22×C3—121no—
628C22×C3—122no—
629C22×C3—122no—
630C22×C3—122no—
631C22×C3—122no—
632C22×C3—122no—
633C22×C3—122no—
634C22×C3—122no—
635C22×C3—122no—
636C22×C3C22×D1211yescharacteristic
637C22×C3C2×#23511yescharacteristic
638C22×C3C2×D3×D411yescharacteristic
639C22×C3C2×D3×D412yes—
640C22×C3C2×D3×D412yes—
641C22×C3C2×D3×D411yescharacteristic
642C22×C3#100412yes—
643C22×C3D3×#4111yescharacteristic
644C22×C3#100912yes—
645C22×C3C22×#6711yescharacteristic
646C2×D3—22no—
647C2×D3—24no—
648C2×D3—41no—
649C2×D3—42no—
650C2×D3—41no—
651C2×D3—42no—
652C2×D3—42no—
653C2×D3—42no—
654C2×D3—42no—
655C2×D3—42no—
656C2×D3—42no—
657C2×D3—42no—
658C2×D3—124no—
659C2×D3—124no—
660C2×D3—124no—
661C2×D3—122no—
662C2×D3—122no—
663C2×D3—122no—
664C2×D3—122no—
665C2×D3—122no—
666C2×D3—122no—
667C2×D3—122no—
668C2×D3—122no—
669C2×D3—122no—
670C2×D3—122no—
671C2×D3—122no—
672C2×D3—122no—
673C2×D3—122no—
674C2×D3—122no—
675C2×D3—242no—
676C2×D3—242no—
677C2×D3—242no—
678C2×D3—242no—
679C3×C4—22no—
680C3×C4—22no—
681C3×C4—34no—
682C3×C4—34no—
683C3×C4—42no—
684C3×C4—41no—
685C3×C4—41no—
686C3×C4—64no—
687C3×C4—81no—
688C3×C4—121no—
689Dic3—24no—
690Dic3—41no—
691Dic3—64no—
692Dic3—64no—
693Dic3—124no—
694Dic3#93014yescomplemented
695Dic3#94014yescomplemented
696C32#254111yescharacteristic, complemented, Sylow
697C23—21no—
698C23—22no—
699C23—22no—
700C23—21no—
701C23—32no—
702C23—61no—
703C23—62no—
704C23—62no—
705C23—61no—
706C23—62no—
707C23—62no—
708C23—62no—
709C23—62no—
710C23—62no—
711C23—62no—
712C23—62no—
713C23—182no—
714C23—182no—
715C23—182no—
716C23—182no—
717C23—182no—
718C23—182no—
719C23—182no—
720C23D3×D1212yes—
721C23C22×D3211yescharacteristic
722D4—68no—
723D4—124no—
724D4—128no—
725D4—364no—
726D4—368no—
727D4—368no—
728D4—368no—
729D4—368no—
730D4—368no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—32no—
735C2×C4—32no—
736C2×C4—34no—
737C2×C4—32no—
738C2×C4—32no—
739C2×C4—34no—
740C2×C4—62no—
741C2×C4—62no—
742C2×C4—62no—
743C2×C4—61no—
744C2×C4—94no—
745C2×C4—124no—
746C2×C4—124no—
747C2×C4—182no—
748C2×C4—182no—
749C2×C4D3×#6712yes—
750C2×C3—21no—
751C2×C3—22no—
752C2×C3—21no—
753C2×C3—22no—
754C2×C3—21no—
755C2×C3—42no—
756C2×C3—42no—
757C2×C3—82no—
758C2×C3—122no—
759C2×C3—242no—
760C2×C3D4×D1212yes—
761C2×C3#555312yes—
762C2×C3#559012yes—
763C2×C3#559211yescharacteristic
764C2×C3#559912yes—
765C2×C3D3×#12111yescharacteristic
766C2×C3D3×#12711yescharacteristic
767C2×C3C2×#93011yescharacteristic
768C2×C3C2×#94011yescharacteristic
769C2×C3#583011yescharacteristic
770D3—42no—
771D3—82no—
772D3—244no—
773D3—242no—
774D3—242no—
775C22—24no—
776C22—22no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—64no—
781C22—62no—
782C22—121no—
783C22—122no—
784C22—121no—
785C22—122no—
786C22—122no—
787C22—122no—
788C22—122no—
789C22—122no—
790C22—122no—
791C22—122no—
792C22—362no—
793C22—362no—
794C22—362no—
795C22—362no—
796C22—362no—
797C22—362no—
798C22—362no—
799C22C2×D3×D1211yescharacteristic
800C22D3×#23511yescharacteristic
801C22D32×D412yes—
802C22#6431412yes—
803C22C2×D3×#6711yescharacteristic
804C4—22no—
805C4—34no—
806C4—34no—
807C4—41no—
808C4—64no—
809C4—121no—
810C4—184no—
811C3—21no—
812C3#7668811yescharacteristic, complemented
813C3#8237811yescharacteristic, complemented
814C2—42no—
815C2—122no—
816C2—242no—
817C2—722no—
818C2#1059424612yes—
819C2#1059427712yes—
820C2D3×#93011yescharacteristic
821C2#1059523811yescharacteristic
822C2D3×#94011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2541
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#67⋊C4C2semidirect
2. C2×#63979C2semidirect
3. C2×#63978C2semidirect
4. C2×#63911C2semidirect
5. C2×#63906C2semidirect
6. #10592659C2semidirect
7. C3×#4960C2semidirect
8. #10591395C2semidirect
9. #10591389C2semidirect
10. #10591384C2semidirect
11. #10591242C2semidirect
50. C2×#67⋊C4D3semidirect
60. #4960D3semidirect
82. C2×C3×#67D4semidirect
110. C3×C4×Dic3D4semidirect
111. Dic3⋊Dic3D4semidirect
302. C2×#67D12semidirect
352. C4×Dic3#67semidirect
387. C3×Dic3#121semidirect
388. C3×Dic3#127semidirect
694. Dic3#930semidirect
695. Dic3#940semidirect
696. C32#2541semidirect
812. C3#76688semidirect
813. C3#82378semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#67⋊C42
C2×#639792
C2×#639782
C2×#639112
C2×#639062
#105926592
C3×#49602
#105913952
#105913892
#105913842
#105912422
#823783
#766883