Finite Group Databasebeta

← #11773329

Subgroups — #11773329

Order 1152.

2208 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3752C211yesmaximal, characteristic
2C22×#3752C211yesmaximal, characteristic
3C22×#3752C211yesmaximal, characteristic
4C2×C32×#95C211yesmaximal, characteristic, complemented
5C2×#63658C211yesmaximal, characteristic, complemented
6C2×#63658C211yesmaximal, characteristic, complemented
7C2×#63658C211yesmaximal, characteristic, complemented
8#69429—34nomaximal
9C24×C3⋊D3C2211yescharacteristic
10C23×C32×C4C2211yescharacteristic
11C23×C32×C4C2211yescharacteristic
12C23×C32×C4C2211yescharacteristic
13C23×C3⋊Dic3C2211yescharacteristic
14C23×C3⋊Dic3C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C2×#3752—22no—
17C2×#3752—22no—
18C2×#3752—22no—
19C2×#3752—22no—
20C2×#3752—22no—
21C2×#3752—22no—
22C2×#3752—22no—
23C2×#3752—22no—
24C2×#3752C414yescomplemented
25C32×#95—22no—
26#63658—22no—
27#63658—22no—
28#63658—22no—
29C22×(C2×D3)⋊C4—34no—
30C22×(C2×D3)⋊C4—34no—
31C22×(C2×D3)⋊C4—34no—
32C2×C3×#95D314yescomplemented
33C2×C3⋊#95—34no—
34C2×C3⋊#95—34no—
35C2×C3⋊#95—34no—
36C24×C32C2311yescharacteristic
37C23×C3⋊D3—21no—
38C23×C3⋊D3—21no—
39C23×C3⋊D3—21no—
40C23×C3⋊D3—21no—
41C23×C3⋊D3—21no—
42C23×C3⋊D3—21no—
43C23×C3⋊D3—21no—
44C23×C3⋊D3—21no—
45C23×C3⋊D3—21no—
46C23×C3⋊D3—21no—
47C23×C3⋊D3—21no—
48C23×C3⋊D3—21no—
49C23×C3⋊D3C2×C412yes—
50C23×C3⋊D3D412yes—
51C23×C3⋊D3D412yes—
52C22×C32×C4—21no—
53C22×C32×C4—21no—
54C22×C32×C4—21no—
55C22×C32×C4—21no—
56C22×C32×C4—21no—
57C22×C32×C4—21no—
58C22×C32×C4—21no—
59C22×C32×C4—21no—
60C22×C32×C4—21no—
61C22×C32×C4—21no—
62C22×C32×C4—21no—
63C22×C32×C4—21no—
64C22×C32×C4—21no—
65C22×C32×C4—21no—
66C22×C32×C4—21no—
67C22×C32×C4—21no—
68C22×C32×C4—21no—
69C22×C32×C4—21no—
70C22×C32×C4C2×C412yes—
71C22×C32×C4D412yes—
72C22×C32×C4D412yes—
73C22×C3⋊Dic3—21no—
74C22×C3⋊Dic3—21no—
75C22×C3⋊Dic3—21no—
76C22×C3⋊Dic3—21no—
77C22×C3⋊Dic3—21no—
78C22×C3⋊Dic3—21no—
79C22×C3⋊Dic3—21no—
80C22×C3⋊Dic3—21no—
81C22×C3⋊Dic3—21no—
82C22×C3⋊Dic3—21no—
83C22×C3⋊Dic3—21no—
84C22×C3⋊Dic3—21no—
85C22×C3⋊Dic3—21no—
86C22×C3⋊Dic3—21no—
87C22×C3⋊Dic3—21no—
88C22×C3⋊Dic3—21no—
89C22×C3⋊Dic3—21no—
90C22×C3⋊Dic3—21no—
91C22×C3⋊Dic3C2×C412yes—
92C22×C3⋊Dic3D412yes—
93C22×C3⋊Dic3D412yes—
94#3752—28no—
95#3752—28no—
96#3752—28no—
97#1440—91noSylow
98C24×D3—34no—
99C23×C3×C4C2×D314yes—
100C23×C3×C4C2×D314yes—
101C23×C3×C4C2×D314yes—
102C23×Dic3—34no—
103C23×Dic3—34no—
104C23×Dic3—34no—
105C2×(C2×D3)⋊C4—316no—
106C2×(C2×D3)⋊C4—68no—
107C2×(C2×D3)⋊C4—68no—
108C2×(C2×D3)⋊C4—68no—
109C2×(C2×D3)⋊C4—68no—
110C2×(C2×D3)⋊C4—68no—
111C2×(C2×D3)⋊C4—68no—
112C2×(C2×D3)⋊C4—68no—
113C2×(C2×D3)⋊C4—68no—
114C3×#95—28no—
115C3⋊#95—68no—
116C3⋊#95—68no—
117C3⋊#95—68no—
118C23×C32C22×C411yescharacteristic
119C23×C32C2×D411yescharacteristic
120C23×C32C2×D411yescharacteristic
121C23×C32C2×D411yescharacteristic
122C23×C32C2×D411yescharacteristic
123C23×C32C2×D411yescharacteristic
124C23×C32C2×D411yescharacteristic
125C23×C32#4111yescharacteristic
126C23×C32#4111yescharacteristic
127C23×C32#4111yescharacteristic
128C23×C32#4111yescharacteristic
129C23×C32#4111yescharacteristic
130C23×C32#4111yescharacteristic
131C23×C32#4111yescharacteristic
132C23×C32#4111yescharacteristic
133C22×C3⋊D3—22no—
134C22×C3⋊D3—22no—
135C22×C3⋊D3—22no—
136C22×C3⋊D3—22no—
137C22×C3⋊D3—22no—
138C22×C3⋊D3—22no—
139C22×C3⋊D3—22no—
140C22×C3⋊D3—22no—
141C22×C3⋊D3—22no—
142C22×C3⋊D3—22no—
143C22×C3⋊D3—22no—
144C22×C3⋊D3—22no—
145C22×C3⋊D3—22no—
146C22×C3⋊D3—22no—
147C22×C3⋊D3—22no—
148C22×C3⋊D3—22no—
149C22×C3⋊D3—22no—
150C22×C3⋊D3—22no—
151C22×C3⋊D3—41no—
152C22×C3⋊D3—41no—
153C22×C3⋊D3—41no—
154C22×C3⋊D3—41no—
155C22×C3⋊D3—41no—
156C22×C3⋊D3—41no—
157C22×C3⋊D3—41no—
158C22×C3⋊D3—41no—
159C22×C3⋊D3—41no—
160C22×C3⋊D3—41no—
161C22×C3⋊D3—41no—
162C22×C3⋊D3—41no—
163C22×C3⋊D3—41no—
164C22×C3⋊D3—41no—
165C22×C3⋊D3—41no—
166C22×C3⋊D3—41no—
167C22×C3⋊D3C22⋊C414yes—
168C2×C32×C4—22no—
169C2×C32×C4—22no—
170C2×C32×C4—22no—
171C2×C32×C4—22no—
172C2×C32×C4—22no—
173C2×C32×C4—22no—
174C2×C32×C4—22no—
175C2×C32×C4—22no—
176C2×C32×C4—22no—
177C2×C32×C4—41no—
178C2×C32×C4—41no—
179C2×C32×C4—41no—
180C2×C32×C4—41no—
181C2×C32×C4—41no—
182C2×C32×C4—41no—
183C2×C32×C4—41no—
184C2×C32×C4—41no—
185C2×C32×C4—41no—
186C2×C32×C4—41no—
187C2×C32×C4—41no—
188C2×C32×C4—41no—
189C2×C3⋊Dic3—22no—
190C2×C3⋊Dic3—22no—
191C2×C3⋊Dic3—22no—
192C2×C3⋊Dic3—22no—
193C2×C3⋊Dic3—22no—
194C2×C3⋊Dic3—22no—
195C2×C3⋊Dic3—22no—
196C2×C3⋊Dic3—22no—
197C2×C3⋊Dic3—22no—
198C2×C3⋊Dic3—41no—
199C2×C3⋊Dic3—41no—
200C2×C3⋊Dic3—41no—
201C2×C3⋊Dic3—41no—
202C2×C3⋊Dic3—41no—
203C2×C3⋊Dic3—41no—
204C2×C3⋊Dic3—41no—
205C2×C3⋊Dic3—41no—
206C2×C3⋊Dic3—41no—
207C2×C3⋊Dic3—41no—
208C2×C3⋊Dic3—41no—
209C2×C3⋊Dic3—41no—
210C22×C22⋊C4—91no—
211C22×C22⋊C4—91no—
212C22×C22⋊C4—91no—
213C2×#95—91no—
214C2×#95—91no—
215C2×#95—91no—
216C2×#95C3⋊D311yescharacteristic, complemented
217C24×C3C22×D314yes—
218C23×D3—38no—
219C23×D3—38no—
220C23×D3—38no—
221C23×D3—64no—
222C23×D3—64no—
223C23×D3—64no—
224C23×D3—64no—
225C23×D3—64no—
226C23×D3—64no—
227C23×D3—64no—
228C23×D3—64no—
229C23×D3—64no—
230C23×D3—64no—
231C23×D3—64no—
232C23×D3—64no—
233C22×C3×C4—24no—
234C22×C3×C4—24no—
235C22×C3×C4—24no—
236C22×C3×C4—24no—
237C22×C3×C4—24no—
238C22×C3×C4—24no—
239C22×C3×C4—24no—
240C22×C3×C4—24no—
241C22×C3×C4—24no—
242C22×C3×C4—24no—
243C22×C3×C4—24no—
244C22×C3×C4—24no—
245C22×C3×C4—24no—
246C22×C3×C4—24no—
247C22×C3×C4—24no—
248C22×C3×C4—24no—
249C22×C3×C4—24no—
250C22×C3×C4—24no—
251C22×C3×C4C4×D318yes—
252C22×C3×C4D1218yes—
253C22×C3×C4#6718yes—
254C22×Dic3—38no—
255C22×Dic3—38no—
256C22×Dic3—38no—
257C22×Dic3—64no—
258C22×Dic3—64no—
259C22×Dic3—64no—
260C22×Dic3—64no—
261C22×Dic3—64no—
262C22×Dic3—64no—
263C22×Dic3—64no—
264C22×Dic3—64no—
265C22×Dic3—64no—
266C22×Dic3—64no—
267C22×Dic3—64no—
268C22×Dic3—64no—
269C22×Dic3—64no—
270C22×Dic3—64no—
271C22×Dic3—64no—
272C22×Dic3—64no—
273C22×Dic3—64no—
274C22×Dic3—64no—
275(C2×D3)⋊C4—632no—
276(C2×D3)⋊C4—632no—
277(C2×D3)⋊C4—632no—
278C22×C32C2×C22⋊C411yescharacteristic
279C22×C32#11711yescharacteristic
280C22×C32#11711yescharacteristic
281C22×C32C4×D411yescharacteristic
282C22×C32C4×D411yescharacteristic
283C22×C32C4×D411yescharacteristic
284C22×C32C4×D411yescharacteristic
285C22×C32#12011yescharacteristic
286C22×C32#12011yescharacteristic
287C22×C32#12111yescharacteristic
288C22×C32#12111yescharacteristic
289C22×C32#12111yescharacteristic
290C22×C32#12111yescharacteristic
291C22×C32#12111yescharacteristic
292C22×C32#12111yescharacteristic
293C22×C32#12111yescharacteristic
294C22×C32#12111yescharacteristic
295C22×C32#12311yescharacteristic
296C22×C32#12311yescharacteristic
297C22×C32#12311yescharacteristic
298C22×C32#12311yescharacteristic
299C22×C32#12311yescharacteristic
300C22×C32#12311yescharacteristic
301C22×C32#12311yescharacteristic
302C22×C32#12311yescharacteristic
303C22×C32#12311yescharacteristic
304C22×C32#12311yescharacteristic
305C22×C32#12411yescharacteristic
306C22×C32#12411yescharacteristic
307C22×C32#12411yescharacteristic
308C22×C32#12411yescharacteristic
309C22×C32#12611yescharacteristic
310C22×C32#12611yescharacteristic
311C22×C32#12611yescharacteristic
312C22×C32#12611yescharacteristic
313C2×C3⋊D3—24no—
314C2×C3⋊D3—24no—
315C2×C3⋊D3—24no—
316C2×C3⋊D3—42no—
317C2×C3⋊D3—42no—
318C2×C3⋊D3—42no—
319C2×C3⋊D3—42no—
320C2×C3⋊D3—42no—
321C2×C3⋊D3—42no—
322C2×C3⋊D3—42no—
323C2×C3⋊D3—42no—
324C2×C3⋊D3—42no—
325C2×C3⋊D3—42no—
326C2×C3⋊D3—42no—
327C2×C3⋊D3—42no—
328C32×C4—42no—
329C32×C4—42no—
330C32×C4—42no—
331C3⋊Dic3—42no—
332C3⋊Dic3—42no—
333C3⋊Dic3—42no—
334C25—91no—
335C23×C4—91no—
336C23×C4—91no—
337C23×C4—91no—
338C23×C4C2×C3⋊D311yescharacteristic
339C23×C4C2×C3⋊D311yescharacteristic
340C23×C4C2×C3⋊D311yescharacteristic
341C2×C22⋊C4—94no—
342C2×C22⋊C4—182no—
343C2×C22⋊C4—182no—
344C2×C22⋊C4—182no—
345C2×C22⋊C4—182no—
346C2×C22⋊C4—182no—
347C2×C22⋊C4—182no—
348C2×C22⋊C4—182no—
349C2×C22⋊C4—182no—
350#95—22no—
351#95—182no—
352#95—182no—
353#95—182no—
354C23×C3C2×C4×D314yes—
355C23×C3C2×D1214yes—
356C23×C3#23514yes—
357C23×C3#23514yes—
358C23×C3#23514yes—
359C23×C3#23514yes—
360C23×C3D3×D414yes—
361C23×C3D3×D414yes—
362C23×C3D3×D414yes—
363C23×C3D3×D414yes—
364C23×C3#23714yes—
365C23×C3#23714yes—
366C23×C3#23914yes—
367C23×C3#23914yes—
368C23×C3C2×#6714yes—
369C22×D3—316no—
370C22×D3—68no—
371C22×D3—68no—
372C22×D3—68no—
373C22×D3—68no—
374C22×D3—68no—
375C22×D3—68no—
376C22×D3—68no—
377C22×D3—68no—
378C22×D3—68no—
379C22×D3—68no—
380C22×D3—68no—
381C22×D3—68no—
382C22×D3—68no—
383C22×D3—68no—
384C22×D3—68no—
385C22×D3—68no—
386C22×D3—68no—
387C22×D3—68no—
388C22×D3—124no—
389C22×D3—124no—
390C22×D3—124no—
391C22×D3—124no—
392C22×D3—124no—
393C22×D3—124no—
394C22×D3—124no—
395C22×D3—124no—
396C22×D3—124no—
397C22×D3—124no—
398C22×D3—124no—
399C22×D3—124no—
400C22×D3—124no—
401C22×D3—124no—
402C22×D3—124no—
403C22×D3—124no—
404C2×C3×C4—28no—
405C2×C3×C4—28no—
406C2×C3×C4—28no—
407C2×C3×C4—28no—
408C2×C3×C4—28no—
409C2×C3×C4—28no—
410C2×C3×C4—28no—
411C2×C3×C4—28no—
412C2×C3×C4—28no—
413C2×C3×C4—44no—
414C2×C3×C4—44no—
415C2×C3×C4—44no—
416C2×C3×C4—44no—
417C2×C3×C4—44no—
418C2×C3×C4—44no—
419C2×C3×C4—44no—
420C2×C3×C4—44no—
421C2×C3×C4—44no—
422C2×C3×C4—44no—
423C2×C3×C4—44no—
424C2×C3×C4—44no—
425C2×Dic3—68no—
426C2×Dic3—68no—
427C2×Dic3—68no—
428C2×Dic3—68no—
429C2×Dic3—68no—
430C2×Dic3—68no—
431C2×Dic3—68no—
432C2×Dic3—68no—
433C2×Dic3—68no—
434C2×Dic3—124no—
435C2×Dic3—124no—
436C2×Dic3—124no—
437C2×Dic3—124no—
438C2×Dic3—124no—
439C2×Dic3—124no—
440C2×Dic3—124no—
441C2×Dic3—124no—
442C2×Dic3—124no—
443C2×Dic3—124no—
444C2×Dic3—124no—
445C2×Dic3—124no—
446C2×C32#38111yescharacteristic
447C2×C32#38611yescharacteristic
448C2×C32#38611yescharacteristic
449C2×C32#38811yescharacteristic
450C2×C32#38811yescharacteristic
451C2×C32#38811yescharacteristic
452C2×C32#38811yescharacteristic
453C2×C32#39411yescharacteristic
454C2×C32#39411yescharacteristic
455C2×C32#39411yescharacteristic
456C2×C32#39411yescharacteristic
457C2×C32#39711yescharacteristic
458C2×C32#39711yescharacteristic
459C2×C32#39711yescharacteristic
460C2×C32#39711yescharacteristic
461C3⋊D3—44no—
462C24—92no—
463C24—92no—
464C24—92no—
465C24—181no—
466C24—181no—
467C24—181no—
468C24—181no—
469C24—181no—
470C24—181no—
471C24—181no—
472C24—181no—
473C24—181no—
474C24—181no—
475C24—181no—
476C24—181no—
477C24C22×C3⋊D311yescharacteristic
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—92no—
497C22×C4—92no—
498C22×C4—92no—
499C22×C4—181no—
500C22×C4—181no—
501C22×C4—181no—
502C22×C4—181no—
503C22×C4—181no—
504C22×C4—181no—
505C22×C4—181no—
506C22×C4—181no—
507C22×C4—181no—
508C22×C4—181no—
509C22×C4—181no—
510C22×C4—181no—
511C22×C4—181no—
512C22×C4—181no—
513C22×C4—181no—
514C22×C4—181no—
515C22×C4—181no—
516C22×C4—181no—
517C22×C4C4×C3⋊D312yes—
518C22×C4C4⋊(C3⋊D3)12yes—
519C22×C4#63812yes—
520C22⋊C4—188no—
521C22⋊C4—188no—
522C22⋊C4—188no—
523C22×C3#87214yes—
524C22×C3C4×D1214yes—
525C22×C3#87514yes—
526C22×C3#87614yes—
527C22×C3D3×C22⋊C414yes—
528C22×C3#67⋊C414yes—
529C22×C3#88214yes—
530C22×C3#88314yes—
531C22×C3#88314yes—
532C22×C3#88314yes—
533C22×C3#88414yes—
534C22×C3#88414yes—
535C22×C3#88414yes—
536C22×C3#88514yes—
537C22×C3#88514yes—
538C22×C3#88614yes—
539C22×C3#89214yes—
540C22×C3#89314yes—
541C22×C3#89414yes—
542C22×C3#89414yes—
543C22×C3#89414yes—
544C22×C3#89414yes—
545C22×C3#89414yes—
546C22×C3#89514yes—
547C22×C3#89514yes—
548C22×C3#89814yes—
549C22×C3#89814yes—
550C22×C3#89814yes—
551C22×C3C4×#6714yes—
552C22×C3#92914yes—
553C22×C3#93014yes—
554C22×C3#93714yes—
555C22×C3#93814yes—
556C22×C3#93914yes—
557C22×C3#94714yes—
558C2×D3—616no—
559C2×D3—616no—
560C2×D3—616no—
561C2×D3—128no—
562C2×D3—128no—
563C2×D3—128no—
564C2×D3—128no—
565C2×D3—128no—
566C2×D3—128no—
567C2×D3—128no—
568C2×D3—128no—
569C2×D3—128no—
570C2×D3—128no—
571C2×D3—128no—
572C2×D3—128no—
573C3×C4—48no—
574C3×C4—48no—
575C3×C4—48no—
576Dic3—128no—
577Dic3—128no—
578Dic3—128no—
579C32#144011yescharacteristic, complemented, Sylow
580C23—94no—
581C23—182no—
582C23—182no—
583C23—182no—
584C23—182no—
585C23—182no—
586C23—182no—
587C23—182no—
588C23—182no—
589C23—182no—
590C23—182no—
591C23—182no—
592C23—182no—
593C23—182no—
594C23—182no—
595C23—182no—
596C23—182no—
597C23—182no—
598C23—182no—
599C23—361no—
600C23—361no—
601C23—361no—
602C23—361no—
603C23—361no—
604C23—361no—
605C23—361no—
606C23—361no—
607C23—361no—
608C23—361no—
609C23—361no—
610C23—361no—
611C23—361no—
612C23—361no—
613C23—361no—
614C23—361no—
615C23C2×C4×C3⋊D311yescharacteristic
616C23C2×C4⋊(C3⋊D3)11yescharacteristic
617C23#382811yescharacteristic
618C23#382811yescharacteristic
619C23#382811yescharacteristic
620C23#382811yescharacteristic
621C23D4×C3⋊D311yescharacteristic
622C23D4×C3⋊D311yescharacteristic
623C23D4×C3⋊D311yescharacteristic
624C23D4×C3⋊D311yescharacteristic
625C23#383011yescharacteristic
626C23#383011yescharacteristic
627C23#383211yescharacteristic
628C23#383211yescharacteristic
629C23C2×#63811yescharacteristic
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—182no—
652C2×C4—182no—
653C2×C4—182no—
654C2×C4—182no—
655C2×C4—182no—
656C2×C4—182no—
657C2×C4—182no—
658C2×C4—182no—
659C2×C4—182no—
660C2×C4—361no—
661C2×C4—361no—
662C2×C4—361no—
663C2×C4—361no—
664C2×C4—361no—
665C2×C4—361no—
666C2×C4—361no—
667C2×C4—361no—
668C2×C4—361no—
669C2×C4—361no—
670C2×C4—361no—
671C2×C4—361no—
672C2×C3#466414yes—
673C2×C3#466514yes—
674C2×C3#466914yes—
675C2×C3#467014yes—
676C2×C3#467214yes—
677C2×C3#467414yes—
678C2×C3#467514yes—
679C2×C3#467514yes—
680C2×C3#494014yes—
681C2×C3#495614yes—
682C2×C3#495914yes—
683C2×C3#496114yes—
684C2×C3#499014yes—
685C2×C3#499114yes—
686C2×C3#499214yes—
687D3—1216no—
688C22—184no—
689C22—184no—
690C22—184no—
691C22—362no—
692C22—362no—
693C22—362no—
694C22—362no—
695C22—362no—
696C22—362no—
697C22—362no—
698C22—362no—
699C22—362no—
700C22—362no—
701C22—362no—
702C22—362no—
703C22#6408111yescharacteristic
704C22C4×C4⋊(C3⋊D3)11yescharacteristic
705C22#6408411yescharacteristic
706C22#6408511yescharacteristic
707C22C22⋊C4×C3⋊D311yescharacteristic
708C22#6409011yescharacteristic
709C22#6409111yescharacteristic
710C22#6409211yescharacteristic
711C22#6409211yescharacteristic
712C22#6409211yescharacteristic
713C22#6409311yescharacteristic
714C22#6409311yescharacteristic
715C22#6409311yescharacteristic
716C22#6409411yescharacteristic
717C22#6409411yescharacteristic
718C22#6409511yescharacteristic
719C22#6410111yescharacteristic
720C22#6410211yescharacteristic
721C22#6410311yescharacteristic
722C22#6410311yescharacteristic
723C22#6410311yescharacteristic
724C22#6410311yescharacteristic
725C22#6410311yescharacteristic
726C22#6410411yescharacteristic
727C22#6410411yescharacteristic
728C22#6410711yescharacteristic
729C22#6410711yescharacteristic
730C22#6410711yescharacteristic
731C22C4×#63811yescharacteristic
732C22#6413811yescharacteristic
733C22#6413911yescharacteristic
734C22#6414611yescharacteristic
735C22#6414711yescharacteristic
736C22#6414811yescharacteristic
737C22#6415611yescharacteristic
738C4—42no—
739C4—42no—
740C4—42no—
741C4—362no—
742C4—362no—
743C4—362no—
744C3#6942914yescomplemented
745C2—364no—
746C2#1059236311yescharacteristic
747C2#1059236411yescharacteristic
748C2#1059236811yescharacteristic
749C2#1059236911yescharacteristic
750C2#1059237111yescharacteristic
751C2#1059237311yescharacteristic
752C2#1059237411yescharacteristic
753C2#1059237411yescharacteristic
754C2#1059263911yescharacteristic
755C2#1059265511yescharacteristic
756C2#1059265811yescharacteristic
757C2#1059266011yescharacteristic
758C2#1059268911yescharacteristic
759C2#1059269011yescharacteristic
760C2#1059269111yescharacteristic
subgroupG/H
center, FrattiniC24C22×C3⋊D3
commutatorC23×C32C22×C4
FittingC2×C32×#95C2
socle, cosocleC24×C32C23
prime radicalC24×C3⋊D3C22
hypercenterC2×#95C3⋊D3
hypocenterC32#1440
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
4. C2×C32×#95C2semidirect
5. C2×#63658C2semidirect
6. C2×#63658C2semidirect
7. C2×#63658C2semidirect
24. C2×#3752C4semidirect
32. C2×C3×#95D3semidirect
216. C2×#95C3⋊D3semidirect
579. C32#1440semidirect
744. C3#69429semidirect

Maximal subgroups

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

subgroupindex
C22×#37522
C2×C32×#952
C2×#636582
#694293