Finite Group Databasebeta

← #11808268

Subgroups — #11808268

Order 1152.

2153 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic
2C2×#63974C211yesmaximal, characteristic
3C2×#63974C211yesmaximal, characteristic
4C2×#63900C211yesmaximal, characteristic, complemented
5C2×#63883C211yesmaximal, characteristic, complemented
6C2×#63883C211yesmaximal, characteristic, complemented
7C3×#4948C212yesmaximal, complemented
8#10591691C212yesmaximal, complemented
9#10591370C211yesmaximal, characteristic, complemented
10#10591347C212yesmaximal, complemented
11#10591311C212yesmaximal, complemented
12D3×#396—32nomaximal
13C24×C3⋊D3C2211yescharacteristic
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×#624C2211yescharacteristic
17C22×#624C2211yescharacteristic
18C22×#624C2211yescharacteristic
19C22×#624C2211yescharacteristic
20C2×C32×C22⋊C4C2211yescharacteristic
21C2×#3757C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C22⋊C4×C3⋊D3—24no—
25C2×C3×#217C2212yes—
26C2×C3×#217C2212yes—
27C2×C3×C4⋊Dic3C2212yescomplemented
28C2×C3×Dic3⋊C4C2212yescomplemented
29C2×C3×Dic3⋊C4C2212yescomplemented
30#63974—24no—
31#63974—24no—
32C2×#3724C2212yescomplemented
33C2×Dic3⋊Dic3C2212yescomplemented
34C2×Dic3⋊Dic3C2212yescomplemented
35C2×#3722C2212yes—
36C2×#3722C2212yes—
37#63900—24no—
38#63883—24no—
39#63883—24no—
40C3×C3⋊#95C2212yescomplemented
41#63579C2212yescomplemented
42C2×D3×C4⋊C4—32no—
43C2×D3×C4⋊C4—32no—
44C2×D3×C4⋊C4—32no—
45C2×D3×C22⋊C4—32no—
46C2×D3×C22⋊C4—32no—
47C2×D3×C22⋊C4—32no—
48C2×D3×C22⋊C4—61no—
49C3×#396—32no—
50#4994—32no—
51#4994—32no—
52#4994—32no—
53#4948—32no—
54#4948—32no—
55#4948D312yescomplemented
56#4676—32no—
57D3×#95—32no—
58C24×C32C2311yescharacteristic
59C23×C3⋊D3—22no—
60C23×C3⋊D3—22no—
61C23×C3⋊D3—22no—
62C23×C3⋊D3—22no—
63C23×C3⋊D3—22no—
64C23×C3⋊D3—22no—
65C23×C3⋊D3Q814yes—
66C23×C3⋊D3C2311yescharacteristic
67C23×C3⋊D3C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2311yescharacteristic
72C2×C4×C3⋊D3—22no—
73C2×C4×C3⋊D3—22no—
74C2×C4×C3⋊D3—22no—
75C2×C4×C3⋊D3—22no—
76C2×C4×C3⋊D3—22no—
77C2×C4×C3⋊D3D414yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82C2×#624—22no—
83C2×#624—22no—
84C2×#624—22no—
85C2×#624—22no—
86C2×#624—22no—
87C2×#624—22no—
88C2×#624—22no—
89C2×#624—22no—
90C2×#624—22no—
91C2×#624—22no—
92C2×#624D414yes—
93C2×#624D414yes—
94C32×C22⋊C4—22no—
95#3757—22no—
96#3752—22no—
97#3752—22no—
98C3×#217—24no—
99C3×#217—24no—
100C3×C4⋊Dic3—24no—
101C3×Dic3⋊C4—24no—
102C3×Dic3⋊C4—24no—
103#3724—24no—
104Dic3⋊Dic3—24no—
105Dic3⋊Dic3—24no—
106#3722—24no—
107#3722—24no—
108C2×#396—91noSylow
109C24×D3—32no—
110C24×D3—61no—
111C22×C4×D3—32no—
112C22×C4×D3—32no—
113C22×C4×D3—32no—
114C22×C4×D3—32no—
115C22×C4×D3—32no—
116C22×C4×D3—32no—
117C22×C4×D3—61no—
118C22×C4×D3—61no—
119C2×C3×C4⋊C4—32no—
120C2×C3×C4⋊C4—32no—
121C2×C3×C4⋊C4—32no—
122C2×C3×C22⋊C4—21no—
123C2×C3×C22⋊C4—32no—
124C2×C3×C22⋊C4—32no—
125C2×C3×C22⋊C4C2×D312yes—
126C2×#217—32no—
127C2×#217—61no—
128C2×#217C2×D312yes—
129C2×#217C2×D312yes—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4—32no—
135C2×(C2×D3)⋊C4—32no—
136C2×(C2×D3)⋊C4—61no—
137C2×(C2×D3)⋊C4—61no—
138C2×C4⋊Dic3—32no—
139C2×C4⋊Dic3—32no—
140C2×C4⋊Dic3C2×D312yescomplemented
141C2×Dic3⋊C4—32no—
142C2×Dic3⋊C4—32no—
143C2×Dic3⋊C4—32no—
144C2×Dic3⋊C4—32no—
145C2×Dic3⋊C4C2×D312yescomplemented
146C2×Dic3⋊C4C2×D312yescomplemented
147D3×C4⋊C4—68no—
148D3×C4⋊C4—68no—
149D3×C4⋊C4—68no—
150D3×C22⋊C4—68no—
151D3×C22⋊C4—68no—
152D3×C22⋊C4—68no—
153D3×C22⋊C4—68no—
154C3×#95—32no—
155C3⋊#95—32no—
156C3⋊#95—32no—
157C3⋊#95C2×D312yescomplemented
158C23×C32—21no—
159C23×C32—21no—
160C23×C32—21no—
161C23×C32—21no—
162C23×C32—21no—
163C23×C32—21no—
164C23×C32C2×Q812yes—
165C23×C32C2411yescharacteristic
166C22×C3⋊D3—21no—
167C22×C3⋊D3—21no—
168C22×C3⋊D3—28no—
169C22×C3⋊D3—21no—
170C22×C3⋊D3—21no—
171C22×C3⋊D3—21no—
172C22×C3⋊D3—21no—
173C22×C3⋊D3—28no—
174C22×C3⋊D3—28no—
175C22×C3⋊D3—44no—
176C22×C3⋊D3—44no—
177C22×C3⋊D3—44no—
178C22×C3⋊D3—44no—
179C22×C3⋊D3C2×D412yes—
180C22×C3⋊D3C2×D412yes—
181C22×C3⋊D3C2×D412yes—
182C22×C3⋊D3C2×Q812yes—
183C22×C3⋊D3C2×Q812yes—
184C22×C3⋊D3#4112yes—
185C22×C3⋊D3#4112yes—
186C22×C3⋊D3#4112yes—
187C2×C32×C4—21no—
188C2×C32×C4—21no—
189C2×C32×C4—21no—
190C2×C32×C4—21no—
191C2×C32×C4—21no—
192C2×C32×C4C2×D412yes—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—21no—
198C2×C3⋊Dic3C2×D412yes—
199C4×C3⋊D3—28no—
200C4×C3⋊D3—44no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3C2×D414yes—
212C2×C3×Dic3C2×D414yes—
213#624—28no—
214#624—28no—
215#624—44no—
216#624—44no—
217C22×C4⋊C4—91no—
218C22×C4⋊C4—91no—
219C22×C4⋊C4—91no—
220C22×C22⋊C4—91no—
221C22×C22⋊C4—91no—
222C22×C22⋊C4—91no—
223#396—32no—
224#396—92no—
225#396—92no—
226#396—92no—
227C2×#95—91no—
228C24×C3—21no—
229C24×C3C22×D312yes—
230C23×D3—32no—
231C23×D3—38no—
232C23×D3—32no—
233C23×D3—61no—
234C23×D3—64no—
235C23×D3—61no—
236C23×D3—64no—
237C23×D3—64no—
238C23×D3—64no—
239C23×D3—64no—
240C23×D3—64no—
241C23×D3—64no—
242C23×D3—64no—
243C23×D3—64no—
244C23×D3—122no—
245C23×D3—122no—
246C23×D3—122no—
247C23×D3—122no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—32no—
251C22×C3×C4—32no—
252C22×C3×C4—32no—
253C22×C3×C4—32no—
254C22×C3×C4C22×D312yes—
255C22×C3×C4C22×D312yes—
256C22×Dic3—32no—
257C22×Dic3—32no—
258C22×Dic3—61no—
259C22×Dic3—61no—
260C22×Dic3C22×D312yes—
261C22×Dic3C22×D312yes—
262C22×Dic3C22×D312yes—
263C22×Dic3C22×D312yes—
264C2×C4×D3—38no—
265C2×C4×D3—38no—
266C2×C4×D3—38no—
267C2×C4×D3—64no—
268C2×C4×D3—64no—
269C2×C4×D3—64no—
270C2×C4×D3—64no—
271C2×C4×D3—64no—
272C2×C4×D3—64no—
273C2×C4×D3—64no—
274C2×C4×D3—64no—
275C2×C4×D3—64no—
276C2×C4×D3—64no—
277C2×C4×D3—64no—
278C2×C4×D3—64no—
279C2×C4×D3—64no—
280C2×C4×D3—64no—
281C2×C4×D3—64no—
282C2×C4×D3—64no—
283C2×C4×D3—64no—
284C2×C4×D3—122no—
285C2×C4×D3—122no—
286C2×C4×D3—122no—
287C2×C4×D3—122no—
288C3×C4⋊C4—64no—
289C3×C4⋊C4—64no—
290C3×C4⋊C4—64no—
291C3×C22⋊C4—24no—
292C3×C22⋊C4—24no—
293C3×C22⋊C4—64no—
294C3×C22⋊C4—64no—
295#217—24no—
296#217—24no—
297#217—64no—
298#217—64no—
299(C2×D3)⋊C4—64no—
300(C2×D3)⋊C4—64no—
301(C2×D3)⋊C4—64no—
302(C2×D3)⋊C4—64no—
303(C2×D3)⋊C4—64no—
304(C2×D3)⋊C4—64no—
305(C2×D3)⋊C4—64no—
306(C2×D3)⋊C4—64no—
307C4⋊Dic3—24no—
308C4⋊Dic3—64no—
309C4⋊Dic3—64no—
310Dic3⋊C4—24no—
311Dic3⋊C4—24no—
312Dic3⋊C4—64no—
313Dic3⋊C4—64no—
314Dic3⋊C4—64no—
315Dic3⋊C4—64no—
316C22×C32—22no—
317C22×C32—22no—
318C22×C32—22no—
319C22×C32—41no—
320C22×C32—41no—
321C22×C32—41no—
322C22×C32—41no—
323C22×C32C22×D411yescharacteristic
324C22×C32C22×D411yescharacteristic
325C22×C32C22×D411yescharacteristic
326C22×C32C22×Q811yescharacteristic
327C22×C32C2×#4111yescharacteristic
328C22×C32C2×#4111yescharacteristic
329C22×C32C2×#4111yescharacteristic
330C2×C3⋊D3—22no—
331C2×C3⋊D3—22no—
332C2×C3⋊D3—22no—
333C2×C3⋊D3—41no—
334C2×C3⋊D3—41no—
335C2×C3⋊D3—41no—
336C2×C3⋊D3—41no—
337C2×C3⋊D3—416no—
338C2×C3⋊D3#12114yes—
339C2×C3⋊D3#12114yes—
340C2×C3⋊D3#12114yes—
341C2×C3⋊D3C22⋊Q814yes—
342C2×C3⋊D3C22⋊Q814yes—
343C2×C3⋊D3C22⋊Q814yes—
344C2×C3⋊D3#12614yes—
345C32×C4—22no—
346C32×C4—41no—
347C3⋊Dic3—22no—
348C3⋊Dic3—41no—
349C3×Dic3—24no—
350C3×Dic3—24no—
351C3×Dic3—42no—
352C3×Dic3—42no—
353C25—91no—
354C23×C4—91no—
355C23×C4—91no—
356C23×C4—91no—
357C23×C4—91no—
358C23×C4—91no—
359C23×C4—91no—
360C2×C4⋊C4—32no—
361C2×C4⋊C4—32no—
362C2×C4⋊C4—32no—
363C2×C4⋊C4—92no—
364C2×C4⋊C4—92no—
365C2×C4⋊C4—92no—
366C2×C4⋊C4—184no—
367C2×C4⋊C4—184no—
368C2×C4⋊C4—184no—
369C2×C22⋊C4—32no—
370C2×C22⋊C4—32no—
371C2×C22⋊C4—92no—
372C2×C22⋊C4—92no—
373C2×C22⋊C4—91no—
374C2×C22⋊C4—91no—
375C2×C22⋊C4—91no—
376C2×C22⋊C4—184no—
377C2×C22⋊C4—184no—
378C2×C22⋊C4—184no—
379C2×C22⋊C4D3211yescharacteristic
380#95—32no—
381#95—92no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—21no—
391C23×C3—22no—
392C23×C3—41no—
393C23×C3—41no—
394C23×C3—41no—
395C23×C3—41no—
396C23×C3D3×Q814yes—
397C23×C3C23×D312yes—
398C22×D3—34no—
399C22×D3—34no—
400C22×D3—34no—
401C22×D3—34no—
402C22×D3—34no—
403C22×D3—34no—
404C22×D3—34no—
405C22×D3—34no—
406C22×D3—62no—
407C22×D3—62no—
408C22×D3—62no—
409C22×D3—62no—
410C22×D3—62no—
411C22×D3—62no—
412C22×D3—62no—
413C22×D3—62no—
414C22×D3—616no—
415C22×D3—616no—
416C22×D3—616no—
417C22×D3—62no—
418C22×D3—616no—
419C22×D3—62no—
420C22×D3—62no—
421C22×D3—62no—
422C22×D3—62no—
423C22×D3—62no—
424C22×D3—62no—
425C22×D3—62no—
426C22×D3—128no—
427C22×D3—128no—
428C22×D3—121no—
429C22×D3—121no—
430C22×D3—121no—
431C22×D3—121no—
432C22×D3—128no—
433C22×D3—128no—
434C22×D3—128no—
435C22×D3—128no—
436C22×D3—128no—
437C22×D3—128no—
438C22×D3—128no—
439C22×D3—128no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—34no—
448C2×C3×C4—34no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—62no—
454C2×C3×C4—62no—
455C2×C3×C4—62no—
456C2×C3×C4—62no—
457C2×C3×C4—62no—
458C2×C3×C4—62no—
459C2×C3×C4—62no—
460C2×C3×C4—62no—
461C2×C3×C4—62no—
462C2×C3×C4—62no—
463C2×C3×C4D3×D414yes—
464C2×Dic3—22no—
465C2×Dic3—22no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—22no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—22no—
473C2×Dic3—22no—
474C2×Dic3—34no—
475C2×Dic3—62no—
476C2×Dic3—62no—
477C2×Dic3—62no—
478C2×Dic3—62no—
479C2×Dic3—62no—
480C2×Dic3—62no—
481C2×Dic3—62no—
482C2×Dic3—121no—
483C2×Dic3—121no—
484C2×Dic3—121no—
485C2×Dic3—121no—
486C2×Dic3D3×D414yes—
487C2×Dic3D3×D414yes—
488C4×D3—616no—
489C4×D3—616no—
490C4×D3—616no—
491C4×D3—128no—
492C4×D3—128no—
493C4×D3—128no—
494C4×D3—128no—
495C4×D3—128no—
496C2×C32—42no—
497C2×C32C2×#12111yescharacteristic
498C2×C32C2×#12111yescharacteristic
499C2×C32C2×#12111yescharacteristic
500C2×C32C2×C22⋊Q811yescharacteristic
501C2×C32C2×C22⋊Q811yescharacteristic
502C2×C32C2×C22⋊Q811yescharacteristic
503C2×C32C2×#12611yescharacteristic
504C3⋊D3—42no—
505C3⋊D3#39618yescomplemented
506C24—91no—
507C24—91no—
508C24—94no—
509C24—182no—
510C24—182no—
511C24—182no—
512C24—182no—
513C24—182no—
514C24—182no—
515C24C2×D3211yescharacteristic
516C22×C4—32no—
517C22×C4—32no—
518C22×C4—32no—
519C22×C4—32no—
520C22×C4—94no—
521C22×C4—94no—
522C22×C4—91no—
523C22×C4—94no—
524C22×C4—91no—
525C22×C4—182no—
526C22×C4—182no—
527C22×C4—182no—
528C22×C4—182no—
529C22×C4—182no—
530C22×C4—182no—
531C22×C4—182no—
532C22×C4—182no—
533C22×C4—182no—
534C22×C4—182no—
535C22×C4—182no—
536C22×C4—182no—
537C22×C4—182no—
538C22×C4—182no—
539C22×C4—182no—
540C22×C4C2×D3211yescharacteristic
541C22×C4C2×D3211yescharacteristic
542C4⋊C4—64no—
543C4⋊C4—64no—
544C4⋊C4—64no—
545C4⋊C4—184no—
546C4⋊C4—184no—
547C4⋊C4—184no—
548C22⋊C4—22no—
549C22⋊C4—64no—
550C22⋊C4—64no—
551C22⋊C4—182no—
552C22⋊C4—184no—
553C22⋊C4—184no—
554C22⋊C4—182no—
555C22⋊C4—182no—
556C22×C3—24no—
557C22×C3—24no—
558C22×C3—24no—
559C22×C3—24no—
560C22×C3—21no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—21no—
566C22×C3—21no—
567C22×C3—42no—
568C22×C3—42no—
569C22×C3—42no—
570C22×C3—42no—
571C22×C3—42no—
572C22×C3—42no—
573C22×C3—42no—
574C22×C3—42no—
575C22×C3—42no—
576C22×C3—42no—
577C22×C3C2×D3×D412yes—
578C22×C3C2×D3×D412yes—
579C22×C3C2×D3×D412yes—
580C22×C3C2×D3×Q812yes—
581C22×C3D3×#4112yes—
582C22×C3D3×#4112yes—
583C22×C3D3×#4112yes—
584C2×D3—38no—
585C2×D3—38no—
586C2×D3—38no—
587C2×D3—38no—
588C2×D3—38no—
589C2×D3—38no—
590C2×D3—38no—
591C2×D3—64no—
592C2×D3—64no—
593C2×D3—64no—
594C2×D3—64no—
595C2×D3—64no—
596C2×D3—64no—
597C2×D3—64no—
598C2×D3—64no—
599C2×D3—64no—
600C2×D3—64no—
601C2×D3—64no—
602C2×D3—122no—
603C2×D3—122no—
604C2×D3—1232no—
605C2×D3—1232no—
606C2×D3—122no—
607C2×D3—122no—
608C2×D3—122no—
609C2×D3—122no—
610C2×D3—122no—
611C2×D3—122no—
612C2×D3—122no—
613C2×D3—122no—
614C3×C4—24no—
615C3×C4—42no—
616C3×C4—42no—
617C3×C4—42no—
618C3×C4—64no—
619C3×C4—64no—
620C3×C4—122no—
621C3×C4—122no—
622Dic3—24no—
623Dic3—24no—
624Dic3—42no—
625Dic3—42no—
626Dic3—64no—
627Dic3—122no—
628Dic3—122no—
629Dic3—122no—
630C32C2×#39611yescharacteristic, complemented, Sylow
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—92no—
638C23—92no—
639C23—92no—
640C23—92no—
641C23—92no—
642C23—92no—
643C23—92no—
644C23—92no—
645C23—188no—
646C23—188no—
647C23—188no—
648C23—181no—
649C23—181no—
650C23—181no—
651C23—181no—
652C23—181no—
653C23—181no—
654C23—364no—
655C23—364no—
656C23—364no—
657C23—364no—
658C23#379712yes—
659C23C22×D3211yescharacteristic
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—34no—
666C2×C4—34no—
667C2×C4—62no—
668C2×C4—62no—
669C2×C4—62no—
670C2×C4—62no—
671C2×C4—62no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—62no—
675C2×C4—62no—
676C2×C4—62no—
677C2×C4—92no—
678C2×C4—188no—
679C2×C4—188no—
680C2×C4—188no—
681C2×C4—181no—
682C2×C4—181no—
683C2×C4—181no—
684C2×C4—181no—
685C2×C4—181no—
686C2×C4—364no—
687C2×C4—364no—
688C2×C4—364no—
689C2×C4#381112yes—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—21no—
694C2×C3—21no—
695C2×C3—21no—
696C2×C3—21no—
697C2×C3—44no—
698C2×C3—44no—
699C2×C3D3×#12112yes—
700C2×C3D3×#12112yes—
701C2×C3D3×#12112yes—
702C2×C3D3×C22⋊Q812yes—
703C2×C3D3×C22⋊Q812yes—
704C2×C3D3×C22⋊Q812yes—
705C2×C3D3×#12612yes—
706D3—316no—
707D3—68no—
708D3—124no—
709D3—124no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—94no—
718C22—94no—
719C22—94no—
720C22—94no—
721C22—94no—
722C22—94no—
723C22—94no—
724C22—182no—
725C22—182no—
726C22—182no—
727C22—3616no—
728C22—361no—
729C22—361no—
730C22—361no—
731C22—361no—
732C22C2×#379711yescharacteristic
733C22#6430611yescharacteristic
734C22D32×D411yescharacteristic
735C22D32×D411yescharacteristic
736C22#6431211yescharacteristic
737C22#6431211yescharacteristic
738C22C2×#381111yescharacteristic
739C4—22no—
740C4—41no—
741C4—64no—
742C4—64no—
743C4—122no—
744C4—122no—
745C4—182no—
746C4—361no—
747C3—21no—
748C3D3×#39612yescomplemented
749C2—42no—
750C2—98no—
751C2—362no—
752C2#1059406711yescharacteristic
753C2#1059406711yescharacteristic
754C2#1059415411yescharacteristic
755C2#1059426511yescharacteristic
756C2#1059492511yescharacteristic
757C2#1059528211yescharacteristic
758C2#1059529811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC24×C3⋊D3C22
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#396
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#63900C2semidirect
5. C2×#63883C2semidirect
6. C2×#63883C2semidirect
7. C3×#4948C2semidirect
8. #10591691C2semidirect
9. #10591370C2semidirect
10. #10591347C2semidirect
11. #10591311C2semidirect
27. C2×C3×C4⋊Dic3C22semidirect
28. C2×C3×Dic3⋊C4C22semidirect
29. C2×C3×Dic3⋊C4C22semidirect
32. C2×#3724C22semidirect
33. C2×Dic3⋊Dic3C22semidirect
34. C2×Dic3⋊Dic3C22semidirect
40. C3×C3⋊#95C22semidirect
41. #63579C22semidirect
55. #4948D3semidirect
140. C2×C4⋊Dic3C2×D3semidirect
145. C2×Dic3⋊C4C2×D3semidirect
146. C2×Dic3⋊C4C2×D3semidirect
157. C3⋊#95C2×D3semidirect
505. C3⋊D3#396semidirect
630. C32C2×#396semidirect
748. C3D3×#396semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×C3⋊D32
C2×#639742
C2×#639002
C2×#638832
C3×#49482
#105916912
#105913702
#105913472
#105913112
D3×#3963