Finite Group Databasebeta

← #11773310

Subgroups — #11773310

Order 1152.

1897 conjugacy classes of subgroups.

The subgroup lattice has 799 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3752C211yesmaximal, characteristic
2C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C22×#3722C212yesmaximal
4C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
5C2×#63579C212yesmaximal, complemented
6#71570—31nomaximal
7#69427—31nomaximal
8C24×C3⋊D3C2211yescharacteristic
9C23×C32×C4C2211yescharacteristic
10C23×C3⋊Dic3C2211yescharacteristic
11C23×C3×Dic3C2212yes—
12C23×C3×Dic3C2212yes—
13C2×#3752—22no—
14C2×#3752—22no—
15C2×#3752C414yescomplemented
16C2×C3×C4⋊Dic3—22no—
17C2×C3×C4⋊Dic3—24no—
18C2×#3722—24no—
19C2×#3722—24no—
20C2×#3722—24no—
21C3×C3⋊#95—22no—
22#63579—24no—
23C22×C3×C4⋊C4—31no—
24C22×(C2×D3)⋊C4—31no—
25C22×(C2×D3)⋊C4—31no—
26C22×(C2×D3)⋊C4—32no—
27C22×(C2×D3)⋊C4—32no—
28C22×(C2×D3)⋊C4—61no—
29C22×C4⋊Dic3D311yescharacteristic, complemented
30C2×C3×#95—31no—
31C2×C3⋊#95—32no—
32C2×C3⋊#95—32no—
33C2×C3⋊#95D311yescharacteristic, complemented
34C24×C32C2311yescharacteristic
35C23×C3⋊D3—21no—
36C23×C3⋊D3—21no—
37C23×C3⋊D3—22no—
38C23×C3⋊D3—22no—
39C23×C3⋊D3—21no—
40C23×C3⋊D3—21no—
41C23×C3⋊D3—22no—
42C23×C3⋊D3—22no—
43C23×C3⋊D3C2×C412yes—
44C23×C3⋊D3D412yes—
45C23×C3⋊D3Q812yes—
46C22×C32×C4—22no—
47C22×C32×C4—22no—
48C22×C32×C4C2×C412yes—
49C22×C32×C4D412yes—
50C22×C32×C4D412yes—
51C22×C3⋊Dic3—21no—
52C22×C3⋊Dic3—21no—
53C22×C3⋊Dic3—22no—
54C22×C3⋊Dic3—22no—
55C22×C3⋊Dic3C2×C412yes—
56C22×C3×Dic3—22no—
57C22×C3×Dic3—22no—
58C22×C3×Dic3—22no—
59C22×C3×Dic3—22no—
60C22×C3×Dic3—22no—
61C22×C3×Dic3—22no—
62C22×C3×Dic3—22no—
63C22×C3×Dic3—22no—
64C22×C3×Dic3—22no—
65C22×C3×Dic3—22no—
66C22×C3×Dic3—22no—
67C22×C3×Dic3—22no—
68C22×C3×Dic3D414yes—
69C22×C3×Dic3D414yes—
70#3752—28no—
71C3×C4⋊Dic3—28no—
72#3722—216no—
73#1439—91noSylow
74C24×D3—31no—
75C24×D3—31no—
76C24×D3—61no—
77C23×C3×C4—21no—
78C23×C3×C4—32no—
79C23×C3×C4—32no—
80C23×C3×C4C2×D311yescharacteristic
81C23×C3×C4C2×D311yescharacteristic
82C23×Dic3—31no—
83C23×Dic3—31no—
84C23×Dic3—61no—
85C23×Dic3C2×D312yes—
86C23×Dic3C2×D312yes—
87C2×C3×C4⋊C4—64no—
88C2×C3×C4⋊C4—62no—
89C2×(C2×D3)⋊C4—34no—
90C2×(C2×D3)⋊C4—34no—
91C2×(C2×D3)⋊C4—64no—
92C2×(C2×D3)⋊C4—64no—
93C2×(C2×D3)⋊C4—64no—
94C2×(C2×D3)⋊C4—64no—
95C2×(C2×D3)⋊C4—64no—
96C2×(C2×D3)⋊C4—64no—
97C2×(C2×D3)⋊C4—64no—
98C2×(C2×D3)⋊C4—62no—
99C2×(C2×D3)⋊C4—62no—
100C2×(C2×D3)⋊C4—62no—
101C2×(C2×D3)⋊C4—62no—
102C2×(C2×D3)⋊C4—64no—
103C2×(C2×D3)⋊C4—64no—
104C2×C4⋊Dic3—22no—
105C2×C4⋊Dic3—24no—
106C3×#95—62no—
107C3⋊#95—22no—
108C3⋊#95—64no—
109C3⋊#95—64no—
110C23×C32C22×C411yescharacteristic
111C23×C32C2×D412yes—
112C23×C32C2×D411yescharacteristic
113C23×C32C2×D411yescharacteristic
114C23×C32C2×D411yescharacteristic
115C23×C32C2×D412yes—
116C23×C32C2×Q811yescharacteristic
117C23×C32#4112yes—
118C23×C32#4112yes—
119C23×C32#4111yescharacteristic
120C23×C32#4111yescharacteristic
121C22×C3⋊D3—22no—
122C22×C3⋊D3—22no—
123C22×C3⋊D3—22no—
124C22×C3⋊D3—22no—
125C22×C3⋊D3—22no—
126C22×C3⋊D3—22no—
127C22×C3⋊D3—24no—
128C22×C3⋊D3—24no—
129C22×C3⋊D3—24no—
130C22×C3⋊D3—24no—
131C22×C3⋊D3—24no—
132C22×C3⋊D3—24no—
133C22×C3⋊D3—41no—
134C22×C3⋊D3—42no—
135C22×C3⋊D3—42no—
136C22×C3⋊D3—42no—
137C22×C3⋊D3—42no—
138C22×C3⋊D3—41no—
139C22×C3⋊D3—41no—
140C22×C3⋊D3—42no—
141C22×C3⋊D3—42no—
142C22×C3⋊D3—41no—
143C22×C3⋊D3C4⋊C414yescomplemented
144C2×C32×C4—24no—
145C2×C32×C4—22no—
146C2×C32×C4—24no—
147C2×C32×C4—22no—
148C2×C32×C4C22⋊C414yescomplemented
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—24no—
151C2×C3⋊Dic3—42no—
152C2×C3⋊Dic3—41no—
153C2×C3⋊Dic3—41no—
154C2×C3×Dic3—24no—
155C2×C3×Dic3—24no—
156C2×C3×Dic3—24no—
157C2×C3×Dic3—24no—
158C2×C3×Dic3—24no—
159C2×C3×Dic3—24no—
160C2×C3×Dic3—42no—
161C2×C3×Dic3—42no—
162C2×C3×Dic3—42no—
163C2×C3×Dic3—42no—
164C2×C3×Dic3—42no—
165C2×C3×Dic3—42no—
166C2×C3×Dic3—42no—
167C2×C3×Dic3—42no—
168C22×C4⋊C4—31no—
169C22×C22⋊C4—91no—
170C22×C22⋊C4—92no—
171C2×#95—31no—
172C2×#95—92no—
173C24×C3—21no—
174C24×C3C22×D311yescharacteristic
175C24×C3C22×D311yescharacteristic
176C23×D3—32no—
177C23×D3—32no—
178C23×D3—32no—
179C23×D3—32no—
180C23×D3—32no—
181C23×D3—32no—
182C23×D3—62no—
183C23×D3—62no—
184C23×D3—62no—
185C23×D3—62no—
186C23×D3—62no—
187C23×D3—62no—
188C23×D3—62no—
189C23×D3—62no—
190C23×D3—61no—
191C23×D3—61no—
192C23×D3—62no—
193C23×D3—62no—
194C23×D3—62no—
195C23×D3—62no—
196C23×D3—61no—
197C23×D3—61no—
198C23×D3—62no—
199C23×D3—61no—
200C23×D3—61no—
201C23×D3—62no—
202C23×D3—61no—
203C23×D3—61no—
204C23×D3—62no—
205C23×D3—122no—
206C23×D3—122no—
207C23×D3—122no—
208C23×D3—122no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—34no—
217C22×C3×C4—34no—
218C22×C3×C4—42no—
219C22×C3×C4—42no—
220C22×C3×C4—62no—
221C22×C3×C4—62no—
222C22×C3×C4—62no—
223C22×C3×C4—62no—
224C22×C3×C4—62no—
225C22×C3×C4—62no—
226C22×C3×C4—62no—
227C22×C3×C4—62no—
228C22×C3×C4—62no—
229C22×C3×C4—62no—
230C22×C3×C4—62no—
231C22×C3×C4—62no—
232C22×C3×C4C4×D312yes—
233C22×C3×C4C4×D312yes—
234C22×C3×C4D1212yes—
235C22×C3×C4D1212yes—
236C22×C3×C4#6712yes—
237C22×C3×C4#6712yes—
238C22×Dic3—22no—
239C22×Dic3—22no—
240C22×Dic3—22no—
241C22×Dic3—22no—
242C22×Dic3—22no—
243C22×Dic3—22no—
244C22×Dic3—22no—
245C22×Dic3—22no—
246C22×Dic3—22no—
247C22×Dic3—22no—
248C22×Dic3—22no—
249C22×Dic3—22no—
250C22×Dic3—32no—
251C22×Dic3—32no—
252C22×Dic3—62no—
253C22×Dic3—62no—
254C22×Dic3—62no—
255C22×Dic3—62no—
256C22×Dic3—61no—
257C22×Dic3—61no—
258C22×Dic3—62no—
259C22×Dic3—62no—
260C22×Dic3—62no—
261C22×Dic3—61no—
262C22×Dic3—61no—
263C22×Dic3—122no—
264C22×Dic3—122no—
265C22×Dic3D1214yes—
266C22×Dic3#6714yes—
267C3×C4⋊C4—68no—
268(C2×D3)⋊C4—616no—
269(C2×D3)⋊C4—616no—
270(C2×D3)⋊C4—616no—
271(C2×D3)⋊C4—68no—
272(C2×D3)⋊C4—68no—
273C4⋊Dic3—28no—
274C22×C32C2×C22⋊C411yescharacteristic
275C22×C32C2×C4⋊C411yescharacteristic
276C22×C32#11711yescharacteristic
277C22×C32C4×D412yes—
278C22×C32C4×D412yes—
279C22×C32#12012yes—
280C22×C32#12011yescharacteristic
281C22×C32#12112yes—
282C22×C32#12111yescharacteristic
283C22×C32#12111yescharacteristic
284C22×C32#12112yes—
285C22×C32#12112yes—
286C22×C32C22⋊Q812yes—
287C22×C32C22⋊Q812yes—
288C22×C32C22⋊Q811yescharacteristic
289C22×C32C22⋊Q811yescharacteristic
290C22×C32#12312yes—
291C22×C32#12312yes—
292C22×C32#12311yescharacteristic
293C22×C32#12411yescharacteristic
294C22×C32#12412yes—
295C22×C32#12612yes—
296C22×C32#12711yescharacteristic
297C2×C3⋊D3—24no—
298C2×C3⋊D3—28no—
299C2×C3⋊D3—42no—
300C2×C3⋊D3—44no—
301C2×C3⋊D3—42no—
302C2×C3⋊D3—42no—
303C2×C3⋊D3—42no—
304C2×C3⋊D3—44no—
305C2×C3⋊D3—44no—
306C2×C3⋊D3—42no—
307C2×C3⋊D3—42no—
308C32×C4—24no—
309C3⋊Dic3—42no—
310C3×Dic3—44no—
311C3×Dic3—44no—
312C25—91no—
313C23×C4—32no—
314C23×C4—32no—
315C23×C4—91no—
316C23×C4D3211yescharacteristic
317C2×C4⋊C4—64no—
318C2×C4⋊C4—62no—
319C2×C22⋊C4—94no—
320C2×C22⋊C4—184no—
321C2×C22⋊C4—184no—
322C2×C22⋊C4—184no—
323C2×C22⋊C4—182no—
324C2×C22⋊C4—182no—
325#95—62no—
326#95—184no—
327C23×C3—21no—
328C23×C3—21no—
329C23×C3—21no—
330C23×C3—22no—
331C23×C3—22no—
332C23×C3—21no—
333C23×C3—22no—
334C23×C3—21no—
335C23×C3—21no—
336C23×C3—21no—
337C23×C3—22no—
338C23×C3C2×C4×D311yescharacteristic
339C23×C3C2×C4×D311yescharacteristic
340C23×C3C2×D1212yes—
341C23×C3C2×D1211yescharacteristic
342C23×C3C2×D1211yescharacteristic
343C23×C3#23512yes—
344C23×C3#23512yes—
345C23×C3D3×D412yes—
346C23×C3D3×D411yescharacteristic
347C23×C3D3×D411yescharacteristic
348C23×C3D3×D412yes—
349C23×C3#23711yescharacteristic
350C23×C3#23711yescharacteristic
351C23×C3#23712yes—
352C23×C3D3×Q811yescharacteristic
353C23×C3D3×Q811yescharacteristic
354C23×C3#23911yescharacteristic
355C23×C3#23911yescharacteristic
356C23×C3#23912yes—
357C23×C3C2×#6711yescharacteristic
358C23×C3C2×#6711yescharacteristic
359C23×C3C2×#6712yes—
360C22×D3—34no—
361C22×D3—34no—
362C22×D3—64no—
363C22×D3—64no—
364C22×D3—64no—
365C22×D3—64no—
366C22×D3—64no—
367C22×D3—64no—
368C22×D3—64no—
369C22×D3—64no—
370C22×D3—64no—
371C22×D3—64no—
372C22×D3—64no—
373C22×D3—62no—
374C22×D3—62no—
375C22×D3—64no—
376C22×D3—64no—
377C22×D3—62no—
378C22×D3—62no—
379C22×D3—64no—
380C22×D3—64no—
381C22×D3—62no—
382C22×D3—62no—
383C22×D3—64no—
384C22×D3—62no—
385C22×D3—62no—
386C22×D3—64no—
387C22×D3—64no—
388C22×D3—62no—
389C22×D3—62no—
390C22×D3—62no—
391C22×D3—62no—
392C22×D3—64no—
393C22×D3—124no—
394C22×D3—124no—
395C22×D3—124no—
396C22×D3—124no—
397C22×D3—124no—
398C22×D3—124no—
399C22×D3—124no—
400C22×D3—122no—
401C22×D3—124no—
402C22×D3—124no—
403C22×D3—124no—
404C22×D3—124no—
405C22×D3—122no—
406C22×D3—122no—
407C22×D3—122no—
408C22×D3—124no—
409C22×D3—121no—
410C22×D3—121no—
411C22×D3—121no—
412C22×D3—122no—
413C22×D3—122no—
414C22×D3—121no—
415C22×D3—122no—
416C22×D3—122no—
417C22×D3—122no—
418C22×D3—122no—
419C22×D3—122no—
420C22×D3—121no—
421C22×D3—122no—
422C22×D3—122no—
423C22×D3—122no—
424C22×D3—122no—
425C22×D3—121no—
426C22×D3—121no—
427C22×D3—122no—
428C22×D3—121no—
429C2×C3×C4—24no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—24no—
433C2×C3×C4—22no—
434C2×C3×C4—24no—
435C2×C3×C4—24no—
436C2×C3×C4—22no—
437C2×C3×C4—24no—
438C2×C3×C4—44no—
439C2×C3×C4—42no—
440C2×C3×C4—42no—
441C2×C3×C4—44no—
442C2×C3×C4—64no—
443C2×C3×C4—64no—
444C2×C3×C4—64no—
445C2×C3×C4—64no—
446C2×C3×C4—64no—
447C2×C3×C4—64no—
448C2×C3×C4—122no—
449C2×C3×C4—122no—
450C2×C3×C4—122no—
451C2×C3×C4—122no—
452C2×C3×C4—122no—
453C2×C3×C4—122no—
454C2×C3×C4—122no—
455C2×C3×C4—122no—
456C2×C3×C4(C2×D3)⋊C414yescomplemented
457C2×C3×C4(C2×D3)⋊C414yescomplemented
458C2×Dic3—24no—
459C2×Dic3—24no—
460C2×Dic3—24no—
461C2×Dic3—24no—
462C2×Dic3—24no—
463C2×Dic3—24no—
464C2×Dic3—42no—
465C2×Dic3—42no—
466C2×Dic3—42no—
467C2×Dic3—42no—
468C2×Dic3—42no—
469C2×Dic3—42no—
470C2×Dic3—42no—
471C2×Dic3—42no—
472C2×Dic3—64no—
473C2×Dic3—64no—
474C2×Dic3—64no—
475C2×Dic3—62no—
476C2×Dic3—62no—
477C2×Dic3—124no—
478C2×Dic3—122no—
479C2×Dic3—124no—
480C2×Dic3—122no—
481C2×Dic3—121no—
482C2×Dic3—121no—
483C2×Dic3—122no—
484C2×Dic3—122no—
485C2×Dic3—121no—
486C2×Dic3—121no—
487C2×C32#38011yescharacteristic
488C2×C32#38512yes—
489C2×C32#38611yescharacteristic
490C2×C32#38812yes—
491C2×C32#39011yescharacteristic
492C2×C32#39211yescharacteristic
493C2×C32#39311yescharacteristic
494C2×C32#39412yes—
495C2×C32#39612yes—
496C2×C32#39711yescharacteristic
497C2×C32#39911yescharacteristic
498C3⋊D3—44no—
499C24—92no—
500C24—92no—
501C24—92no—
502C24—181no—
503C24—181no—
504C24—182no—
505C24—182no—
506C24—182no—
507C24—181no—
508C24—181no—
509C24—182no—
510C24C2×D3211yescharacteristic
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—34no—
514C22×C4—34no—
515C22×C4—62no—
516C22×C4—62no—
517C22×C4—62no—
518C22×C4—62no—
519C22×C4—62no—
520C22×C4—62no—
521C22×C4—62no—
522C22×C4—62no—
523C22×C4—62no—
524C22×C4—62no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—92no—
528C22×C4—182no—
529C22×C4—182no—
530C22×C4—181no—
531C22×C4—181no—
532C22×C4#62412yes—
533C22×C4#62612yes—
534C22×C4#62612yes—
535C4⋊C4—68no—
536C22⋊C4—1816no—
537C22⋊C4—188no—
538C22×C3—22no—
539C22×C3—21no—
540C22×C3—22no—
541C22×C3—21no—
542C22×C3—21no—
543C22×C3—21no—
544C22×C3—22no—
545C22×C3—22no—
546C22×C3—22no—
547C22×C3—22no—
548C22×C3—22no—
549C22×C3—21no—
550C22×C3—22no—
551C22×C3—22no—
552C22×C3—21no—
553C22×C3—21no—
554C22×C3—21no—
555C22×C3—22no—
556C22×C3—22no—
557C22×C3—21no—
558C22×C3—21no—
559C22×C3—21no—
560C22×C3—22no—
561C22×C3C4×D1212yes—
562C22×C3#87411yescharacteristic
563C22×C3#87511yescharacteristic
564C22×C3#67⋊C412yes—
565C22×C3#88212yes—
566C22×C3#88211yescharacteristic
567C22×C3#88312yes—
568C22×C3#88512yes—
569C22×C3#88612yes—
570C22×C3#88611yescharacteristic
571C22×C3D3×C4⋊C411yescharacteristic
572C22×C3D3×C4⋊C411yescharacteristic
573C22×C3#89211yescharacteristic
574C22×C3#89211yescharacteristic
575C22×C3#89312yes—
576C22×C3#89412yes—
577C22×C3#89412yes—
578C22×C3#89512yes—
579C22×C3#89512yes—
580C22×C3#89511yescharacteristic
581C22×C3#89511yescharacteristic
582C22×C3#89612yes—
583C22×C3#89612yes—
584C22×C3#89711yescharacteristic
585C22×C3#89711yescharacteristic
586C22×C3#89712yes—
587C22×C3#89812yes—
588C22×C3#89812yes—
589C22×C3C2×(C2×D3)⋊C411yescharacteristic
590C22×C3C2×(C2×D3)⋊C411yescharacteristic
591C22×C3C4×#6712yes—
592C22×C3#92911yescharacteristic
593C22×C3#93012yes—
594C22×C3#93012yes—
595C22×C3#93712yes—
596C22×C3#93811yescharacteristic
597C22×C3#93811yescharacteristic
598C22×C3#93912yes—
599C22×C3#93912yes—
600C22×C3#94011yescharacteristic
601C22×C3#94611yescharacteristic
602C22×C3#94611yescharacteristic
603C22×C3#94612yes—
604C22×C3#94711yescharacteristic
605C22×C3#94712yes—
606C22×C3#95311yescharacteristic
607C2×D3—68no—
608C2×D3—68no—
609C2×D3—64no—
610C2×D3—64no—
611C2×D3—68no—
612C2×D3—128no—
613C2×D3—128no—
614C2×D3—124no—
615C2×D3—128no—
616C2×D3—124no—
617C2×D3—124no—
618C2×D3—124no—
619C2×D3—124no—
620C2×D3—128no—
621C2×D3—124no—
622C2×D3—124no—
623C2×D3—122no—
624C2×D3—122no—
625C2×D3—122no—
626C2×D3—122no—
627C2×D3—122no—
628C2×D3—122no—
629C2×D3—122no—
630C2×D3—124no—
631C2×D3—122no—
632C2×D3—122no—
633C2×D3—122no—
634C2×D3—124no—
635C2×D3—124no—
636C2×D3—122no—
637C2×D3—122no—
638C2×D3—124no—
639C2×D3—124no—
640C3×C4—24no—
641C3×C4—24no—
642C3×C4—44no—
643C3×C4—124no—
644C3×C4—124no—
645Dic3—44no—
646Dic3—44no—
647Dic3—124no—
648Dic3—122no—
649Dic3—122no—
650C32#143911yescharacteristic, complemented, Sylow
651C23—94no—
652C23—182no—
653C23—184no—
654C23—182no—
655C23—182no—
656C23—184no—
657C23—184no—
658C23—184no—
659C23—182no—
660C23—182no—
661C23—184no—
662C23—184no—
663C23—182no—
664C23—362no—
665C23—361no—
666C23—362no—
667C23—362no—
668C23—362no—
669C23—362no—
670C23—361no—
671C23—361no—
672C23—361no—
673C23—362no—
674C23#379611yescharacteristic
675C23#379611yescharacteristic
676C23#379711yescharacteristic
677C23#379912yes—
678C23D3×D1212yes—
679C23#380211yescharacteristic
680C23#380412yes—
681C23C2×#62411yescharacteristic
682C23C2×#62611yescharacteristic
683C23C2×#62611yescharacteristic
684C23D3×#6712yes—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—64no—
690C2×C4—64no—
691C2×C4—64no—
692C2×C4—64no—
693C2×C4—64no—
694C2×C4—64no—
695C2×C4—122no—
696C2×C4—122no—
697C2×C4—122no—
698C2×C4—122no—
699C2×C4—122no—
700C2×C4—122no—
701C2×C4—122no—
702C2×C4—122no—
703C2×C4—184no—
704C2×C4—182no—
705C2×C4—361no—
706C2×C4—362no—
707C2×C4—361no—
708C2×C4#372214yescomplemented
709C2×C3—22no—
710C2×C3—21no—
711C2×C3—22no—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—22no—
717C2×C3—21no—
718C2×C3—22no—
719C2×C3—21no—
720C2×C3#466812yes—
721C2×C3#467012yes—
722C2×C3#467111yescharacteristic
723C2×C3#467311yescharacteristic
724C2×C3#467411yescharacteristic
725C2×C3#467711yescharacteristic
726C2×C3#493911yescharacteristic
727C2×C3#495811yescharacteristic
728C2×C3#496112yes—
729C2×C3#498711yescharacteristic
730C2×C3#498711yescharacteristic
731C2×C3#498811yescharacteristic
732C2×C3#498912yes—
733C2×C3#499012yes—
734C2×C3#499112yes—
735C2×C3#499211yescharacteristic
736C2×C3#499311yescharacteristic
737C2×C3#499412yes—
738C2×C3#499412yes—
739C2×C3#521311yescharacteristic
740C2×C3#522311yescharacteristic
741C2×C3#523111yescharacteristic
742D3—128no—
743D3—124no—
744D3—124no—
745C22—184no—
746C22—188no—
747C22—364no—
748C22—362no—
749C22—364no—
750C22—362no—
751C22—362no—
752C22—362no—
753C22—362no—
754C22—364no—
755C22—362no—
756C22#6384812yes—
757C22#6384911yescharacteristic
758C22#6385412yes—
759C22#6386411yescharacteristic
760C22#6387111yescharacteristic
761C22#6387111yescharacteristic
762C22#6388612yes—
763C22#6388812yes—
764C22#6389012yes—
765C22#6389412yes—
766C22#6389512yes—
767C22#6390011yescharacteristic
768C22#6390712yes—
769C22#6390912yes—
770C22#6391111yescharacteristic
771C22#6391611yescharacteristic
772C22#6391611yescharacteristic
773C22#6392212yes—
774C22#6395212yes—
775C22C2×#372211yescharacteristic
776C22#6396611yescharacteristic
777C22#6397711yescharacteristic
778C22#6397812yes—
779C4—24no—
780C4—124no—
781C4—124no—
782C4—362no—
783C3—21no—
784C3#6942711yescharacteristic, complemented
785C3#7157011yescharacteristic, complemented
786C2—364no—
787C2#1059126612yes—
788C2#1059131011yescharacteristic
789C2#1059131112yes—
790C2#1059132011yescharacteristic
791C2#1059132511yescharacteristic
792C2#1059132611yescharacteristic
793C2#1059135011yescharacteristic
794C2#1059137812yes—
795C2#1059139111yescharacteristic
796C2#1059139212yes—
797C2#1059171111yescharacteristic
subgroupG/H
center, FrattiniC24C2×D32
commutatorC23×C32C22×C4
FittingC23×C32×C4C22
socle, cosocleC24×C32C23
prime radicalC24×C3⋊D3C22
hypercenterC23×C4D32
hypocenterC32#1439
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4⋊Dic3C2semidirect
4. C2×C3×C3⋊#95C2semidirect
5. C2×#63579C2semidirect
15. C2×#3752C4semidirect
29. C22×C4⋊Dic3D3semidirect
33. C2×C3⋊#95D3semidirect
143. C22×C3⋊D3C4⋊C4semidirect
148. C2×C32×C4C22⋊C4semidirect
456. C2×C3×C4(C2×D3)⋊C4semidirect
457. C2×C3×C4(C2×D3)⋊C4semidirect
650. C32#1439semidirect
708. C2×C4#3722semidirect
784. C3#69427semidirect
785. C3#71570semidirect

Maximal subgroups

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

subgroupindex
C22×#37522
C22×C3×C4⋊Dic32
C22×#37222
C2×C3×C3⋊#952
C2×#635792
#715703
#694273