Finite Group Databasebeta

← #10718599

Subgroups — #10718599

Order 768.

2178 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4956C211yesmaximal, characteristic
2C2×#4956C211yesmaximal, characteristic
3C2×#4956C211yesmaximal, characteristic
4C2×D3×#95C211yesmaximal, characteristic, complemented
5C2×#4666C211yesmaximal, characteristic, complemented
6C3×#1440C211yesmaximal, characteristic, complemented
7#71549C211yesmaximal, characteristic, complemented
8#71545C211yesmaximal, characteristic, complemented
9#71545C211yesmaximal, characteristic, complemented
10(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
11(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
12#69418C211yesmaximal, characteristic, complemented
13#69417C211yesmaximal, characteristic, complemented
14#69402C211yesmaximal, characteristic, complemented
15#69401C211yesmaximal, characteristic, complemented
16#14020—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×C4×Dic3C2211yescharacteristic
31C22×C4×Dic3C2211yescharacteristic
32C2×C3×#95C2211yescharacteristic
33C2×C3×#95C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3⋊#95C2211yescharacteristic
37C2×C3⋊#95C2211yescharacteristic
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2211yescharacteristic
40C2×C3⋊#95C2211yescharacteristic
41C2×C3⋊#95C2211yescharacteristic
42C2×C3⋊#95C2211yescharacteristic
43C2×C3⋊#95C2211yescharacteristic
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52#4956—24no—
53#4956—24no—
54#4956C418yescomplemented
55#4666—24no—
56D3×#95—24no—
57C2×#386—31no—
58C2×#386—31no—
59C2×#386—31no—
60C2×C4×C22⋊C4—31no—
61C22×#95—31no—
62#1443—31no—
63#1443—31no—
64#1440—31no—
65#1440D311yescharacteristic, complemented
66#1437—31no—
67#1437—31no—
68#1434—31no—
69#1434—31no—
70C22⋊#95—31no—
71C22⋊#95—31no—
72C25×C3C2311yescharacteristic
73C24×D3C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C22×#67—22no—
81C22×#67—22no—
82C22×#67—22no—
83C22×#67—22no—
84C22×#67—22no—
85C22×#67—22no—
86C22×#67C2×C414yes—
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C22×C4×D3—22no—
95C22×C4×D3—22no—
96C22×C4×D3—22no—
97C22×C4×D3—22no—
98C22×C4×D3—22no—
99C22×C4×D3—22no—
100C22×C4×D3—22no—
101C22×C4×D3—22no—
102C22×C4×D3—22no—
103C22×C4×D3—22no—
104C22×C4×D3—22no—
105C22×C4×D3—41no—
106C22×C4×D3—41no—
107C22×C4×D3—41no—
108C22×C4×D3—41no—
109C22×C4×D3—41no—
110C22×C4×D3—41no—
111C22×C4×D3—41no—
112C22×C4×D3—41no—
113C22×C4×D3C2×C414yes—
114C22×C4×D3D414yes—
115C2×C3×C22⋊C4—22no—
116C2×C3×C22⋊C4—22no—
117C2×C3×C22⋊C4—22no—
118C2×C3×C22⋊C4—41no—
119C2×C3×C22⋊C4—41no—
120C2×C3×C22⋊C4—41no—
121C2×C3×C22⋊C4—41no—
122C2×C3×C22⋊C4—41no—
123C2×C3×C22⋊C4C2×C414yescomplemented
124C2×#217—22no—
125C2×#217—22no—
126C2×#217—22no—
127C2×#217—22no—
128C2×#217—22no—
129C2×#217—41no—
130C2×#217—41no—
131C2×#217—41no—
132C2×#217C2×C414yescomplemented
133C2×(C2×D3)⋊C4—22no—
134C2×(C2×D3)⋊C4—22no—
135C2×(C2×D3)⋊C4—22no—
136C2×(C2×D3)⋊C4—22no—
137C2×(C2×D3)⋊C4—22no—
138C2×(C2×D3)⋊C4—22no—
139C2×(C2×D3)⋊C4—22no—
140C2×(C2×D3)⋊C4C2×C414yes—
141C2×(C2×D3)⋊C4D414yes—
142C2×C4×Dic3—22no—
143C2×C4×Dic3—22no—
144C2×C4×Dic3—22no—
145C2×C4×Dic3—22no—
146C2×C4×Dic3—41no—
147C2×C4×Dic3—41no—
148C3×#95—22no—
149C3×#95—22no—
150C3×#95—22no—
151C3×#95—41no—
152C3⋊#95—22no—
153C3⋊#95—22no—
154C3⋊#95—22no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C3⋊#95—22no—
159C3⋊#95—22no—
160C3⋊#95—22no—
161C3⋊#95—41no—
162C3⋊#95—41no—
163C3⋊#95—41no—
164C3⋊#95—41no—
165C3⋊#95—41no—
166C3⋊#95C2×C414yescomplemented
167C3⋊#95C2×C414yescomplemented
168C23×D4—31no—
169C24×C4—31no—
170C24×C4—31no—
171C24×C4—31no—
172C22×C22⋊C4—31no—
173C22×C22⋊C4—31no—
174C22×C22⋊C4—31no—
175C22×C22⋊C4—31no—
176C22×C22⋊C4—31no—
177C22×C22⋊C4—31no—
178C22×C22⋊C4C2×D311yescharacteristic
179C22×C22⋊C4C2×D311yescharacteristic
180C22×C22⋊C4C2×D311yescharacteristic
181C22×C42—31no—
182C22×C42—31no—
183#386—38no—
184#386—64no—
185#386—64no—
186C4×C22⋊C4—64no—
187C2×#95—31no—
188C2×#95—31no—
189C2×#95—31no—
190C2×#95—31no—
191C2×#95—31no—
192C2×#95—31no—
193C2×#95—31no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95—31no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95—31no—
201C2×#95—31no—
202C2×#95—31no—
203C2×#95—64no—
204C2×#95C2×D311yescharacteristic
205C2×#95C2×D311yescharacteristic
206C2×#95C2×D311yescharacteristic
207C2×#95C2×D311yescharacteristic
208C24×C3—21no—
209C24×C3—21no—
210C24×C3—21no—
211C24×C3—21no—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3—21no—
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—21no—
220C24×C3—21no—
221C24×C3—21no—
222C24×C3C22×C412yes—
223C24×C3C2411yescharacteristic
224C23×D3—21no—
225C23×D3—21no—
226C23×D3—21no—
227C23×D3—21no—
228C23×D3—21no—
229C23×D3—21no—
230C23×D3—21no—
231C23×D3—21no—
232C23×D3C22×C412yes—
233C23×D3C2×D412yes—
234C23×D3C2×D412yes—
235C23×D3#4112yes—
236C23×D3#4112yes—
237C23×D3#4112yes—
238C23×D3#4112yes—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4C22×C412yes—
277C22×C3×C4C22×C412yes—
278C22×C3×C4C2×D412yes—
279C22×C3×C4C2×D412yes—
280C22×C3×C4#4112yes—
281C2×#67—28no—
282C2×#67—28no—
283C2×#67—28no—
284C2×#67—44no—
285C2×#67—44no—
286C2×#67—44no—
287C2×#67—44no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3C22×C412yes—
330C22×Dic3C22×C412yes—
331C22×Dic3C22×C412yes—
332C22×Dic3C2×D412yes—
333C22×Dic3C2×D412yes—
334C22×Dic3#4112yes—
335C22×Dic3#4112yes—
336C22×Dic3#4112yes—
337C2×C4×D3—28no—
338C2×C4×D3—28no—
339C2×C4×D3—28no—
340C2×C4×D3—28no—
341C2×C4×D3—44no—
342C2×C4×D3—44no—
343C2×C4×D3—44no—
344C2×C4×D3—44no—
345C2×C4×D3—44no—
346C2×C4×D3—44no—
347C2×C4×D3—44no—
348C2×C4×D3—44no—
349C2×C4×D3—44no—
350C2×C4×D3—44no—
351C2×C4×D3—44no—
352C2×C4×D3—44no—
353C2×C4×D3—44no—
354C2×C4×D3—44no—
355C2×C4×D3—44no—
356C2×C4×D3—44no—
357C2×C4×D3—44no—
358C3×C22⋊C4—44no—
359C3×C22⋊C4—44no—
360C3×C22⋊C4—44no—
361#217—44no—
362#217—44no—
363#217—44no—
364(C2×D3)⋊C4—28no—
365(C2×D3)⋊C4—28no—
366(C2×D3)⋊C4—44no—
367C4×Dic3—44no—
368C4×Dic3—44no—
369C25—31no—
370C25C22×D311yescharacteristic
371C22×D4—34no—
372C22×D4—62no—
373C22×D4—62no—
374C22×D4—62no—
375C22×D4—62no—
376C22×D4—62no—
377C22×D4—62no—
378C23×C4—31no—
379C23×C4—31no—
380C23×C4—31no—
381C23×C4—31no—
382C23×C4—31no—
383C23×C4—31no—
384C23×C4—34no—
385C23×C4—34no—
386C23×C4—31no—
387C23×C4—62no—
388C23×C4—62no—
389C23×C4—62no—
390C23×C4—62no—
391C23×C4—62no—
392C23×C4—62no—
393C23×C4—62no—
394C23×C4—62no—
395C23×C4—62no—
396C23×C4—62no—
397C23×C4—62no—
398C23×C4—121no—
399C23×C4—121no—
400C23×C4—121no—
401C23×C4—121no—
402C23×C4—121no—
403C23×C4—121no—
404C23×C4—121no—
405C23×C4—121no—
406C23×C4C22×D311yescharacteristic
407C23×C4C22×D311yescharacteristic
408C23×C4C22×D311yescharacteristic
409C23×C4C22×D311yescharacteristic
410C23×C4C22×D311yescharacteristic
411C23×C4C22×D311yescharacteristic
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—34no—
416C2×C22⋊C4—34no—
417C2×C22⋊C4—34no—
418C2×C22⋊C4—41no—
419C2×C22⋊C4—41no—
420C2×C22⋊C4—41no—
421C2×C22⋊C4—41no—
422C2×C22⋊C4—41no—
423C2×C22⋊C4—62no—
424C2×C22⋊C4—62no—
425C2×C22⋊C4—62no—
426C2×C22⋊C4—62no—
427C2×C22⋊C4—62no—
428C2×C22⋊C4—62no—
429C2×C22⋊C4—62no—
430C2×C22⋊C4—62no—
431C2×C22⋊C4—62no—
432C2×C22⋊C4—62no—
433C2×C22⋊C4—62no—
434C2×C22⋊C4—62no—
435C2×C22⋊C4—121no—
436C2×C22⋊C4—121no—
437C2×C22⋊C4—121no—
438C2×C22⋊C4C4×D314yescomplemented
439C2×C42—62no—
440C2×C42—62no—
441C2×C42—62no—
442C2×C42—62no—
443C2×C42—121no—
444C2×C42—121no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—34no—
449#95—34no—
450#95—41no—
451#95—62no—
452#95—62no—
453#95—62no—
454#95—62no—
455#95—62no—
456#95—62no—
457#95—62no—
458#95—62no—
459#95—62no—
460#95—121no—
461#95—121no—
462#95—121no—
463#95—121no—
464#95—121no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3—41no—
493C23×C3—41no—
494C23×C3—41no—
495C23×C3—41no—
496C23×C3—41no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—41no—
500C23×C3C23×C411yescharacteristic
501C23×C3C22×D411yescharacteristic
502C23×C3C22×D411yescharacteristic
503C23×C3C2×#4111yescharacteristic
504C23×C3C2×#4111yescharacteristic
505C23×C3C2×#4111yescharacteristic
506C23×C3C2×#4111yescharacteristic
507C23×C3C2×#4111yescharacteristic
508C23×C3C2×#4111yescharacteristic
509C23×C3C2×#4111yescharacteristic
510C23×C3C2×#4111yescharacteristic
511C23×C3H(5,𝔽2)11yescharacteristic
512C23×C3H(5,𝔽2)11yescharacteristic
513C23×C3H(5,𝔽2)11yescharacteristic
514C23×C3H(5,𝔽2)11yescharacteristic
515C22×D3—22no—
516C22×D3—22no—
517C22×D3—22no—
518C22×D3—22no—
519C22×D3—22no—
520C22×D3—22no—
521C22×D3—22no—
522C22×D3—22no—
523C22×D3—22no—
524C22×D3—22no—
525C22×D3—22no—
526C22×D3—22no—
527C22×D3—22no—
528C22×D3—22no—
529C22×D3—22no—
530C22×D3—22no—
531C22×D3—22no—
532C22×D3—22no—
533C22×D3—22no—
534C22×D3—22no—
535C22×D3—22no—
536C22×D3—22no—
537C22×D3—22no—
538C22×D3—22no—
539C22×D3—22no—
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—22no—
543C22×D3#11714yes—
544C22×D3C4×D414yes—
545C22×D3C4×D414yes—
546C22×D3#12114yes—
547C22×D3#12314yes—
548C22×D3#12414yes—
549C22×D3#12614yes—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592#67—416no—
593C2×Dic3—22no—
594C2×Dic3—22no—
595C2×Dic3—22no—
596C2×Dic3—22no—
597C2×Dic3—22no—
598C2×Dic3—22no—
599C2×Dic3—22no—
600C2×Dic3—22no—
601C2×Dic3—22no—
602C2×Dic3—22no—
603C2×Dic3—22no—
604C2×Dic3—22no—
605C2×Dic3—22no—
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3—22no—
610C2×Dic3—22no—
611C2×Dic3—22no—
612C2×Dic3—22no—
613C2×Dic3—22no—
614C2×Dic3—41no—
615C2×Dic3—41no—
616C2×Dic3—41no—
617C2×Dic3—41no—
618C2×Dic3—41no—
619C2×Dic3—41no—
620C2×Dic3—41no—
621C2×Dic3—41no—
622C2×Dic3—41no—
623C2×Dic3—41no—
624C2×Dic3—41no—
625C2×Dic3—41no—
626C2×Dic3—41no—
627C2×Dic3—41no—
628C2×Dic3—41no—
629C2×Dic3—41no—
630C2×Dic3—41no—
631C2×Dic3—41no—
632C2×Dic3—41no—
633C2×Dic3—41no—
634C2×Dic3—41no—
635C2×Dic3—41no—
636C2×Dic3—41no—
637C2×Dic3—41no—
638C2×Dic3—41no—
639C2×Dic3—41no—
640C2×Dic3—41no—
641C2×Dic3#12314yes—
642C4×D3—416no—
643C4×D3—416no—
644C4×D3—416no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—32no—
660C24—32no—
661C24—32no—
662C24—32no—
663C24—32no—
664C24—32no—
665C24—32no—
666C24—61no—
667C24—61no—
668C24—61no—
669C24—61no—
670C24—61no—
671C24—61no—
672C24—61no—
673C24—61no—
674C24C2×C4×D312yes—
675C24C23×D311yescharacteristic
676C2×D4—68no—
677C2×D4—68no—
678C2×D4—68no—
679C2×D4—124no—
680C2×D4—124no—
681C2×D4—124no—
682C2×D4—124no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—32no—
721C22×C4—32no—
722C22×C4—32no—
723C22×C4—32no—
724C22×C4—32no—
725C22×C4—32no—
726C22×C4—32no—
727C22×C4—32no—
728C22×C4—68no—
729C22×C4—68no—
730C22×C4—68no—
731C22×C4—68no—
732C22×C4—61no—
733C22×C4—61no—
734C22×C4—61no—
735C22×C4—61no—
736C22×C4—61no—
737C22×C4—61no—
738C22×C4—61no—
739C22×C4—61no—
740C22×C4—61no—
741C22×C4—61no—
742C22×C4—61no—
743C22×C4—61no—
744C22×C4—61no—
745C22×C4—61no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—61no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—61no—
761C22×C4—61no—
762C22×C4—61no—
763C22×C4—61no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—61no—
772C22×C4—61no—
773C22×C4—124no—
774C22×C4—124no—
775C22×C4—124no—
776C22×C4—124no—
777C22×C4—124no—
778C22×C4—124no—
779C22×C4—124no—
780C22×C4—124no—
781C22×C4—124no—
782C22×C4—124no—
783C22×C4—124no—
784C22×C4—124no—
785C22×C4—124no—
786C22×C4—124no—
787C22×C4—124no—
788C22×C4—124no—
789C22×C4—124no—
790C22×C4C2×C4×D312yes—
791C22×C4C2×C4×D312yes—
792C22×C4D3×D412yes—
793C22×C4D3×D412yes—
794C22×C4#23712yes—
795C22⋊C4—44no—
796C22⋊C4—44no—
797C22⋊C4—44no—
798C22⋊C4—68no—
799C22⋊C4—68no—
800C22⋊C4—124no—
801C22⋊C4—124no—
802C22⋊C4—124no—
803C22⋊C4—124no—
804C42—124no—
805C42—124no—
806C22×C3—42no—
807C22×C3—42no—
808C22×C3—42no—
809C22×C3—42no—
810C22×C3—42no—
811C22×C3—42no—
812C22×C3—42no—
813C22×C3—81no—
814C22×C3—81no—
815C22×C3—81no—
816C22×C3—81no—
817C22×C3—81no—
818C22×C3—81no—
819C22×C3—81no—
820C22×C3—81no—
821C22×C3C2×#11711yescharacteristic
822C22×C3C2×C4×D411yescharacteristic
823C22×C3C2×C4×D411yescharacteristic
824C22×C3C4×#4111yescharacteristic
825C22×C3C4×#4111yescharacteristic
826C22×C3#51811yescharacteristic
827C22×C3#51811yescharacteristic
828C22×C3C2×#12111yescharacteristic
829C22×C3C2×#12311yescharacteristic
830C22×C3C2×#12311yescharacteristic
831C22×C3#52511yescharacteristic
832C22×C3C2×#12411yescharacteristic
833C22×C3C2×#12611yescharacteristic
834C22×C3#52911yescharacteristic
835C22×C3#52911yescharacteristic
836C22×C3#53411yescharacteristic
837C22×C3#53511yescharacteristic
838C22×C3#53811yescharacteristic
839C22×C3#53811yescharacteristic
840C22×C3#54611yescharacteristic
841C22×C3#54611yescharacteristic
842C22×C3#54611yescharacteristic
843C22×C3#54611yescharacteristic
844C22×C3#55111yescharacteristic
845C22×C3#55111yescharacteristic
846C22×C3#55111yescharacteristic
847C22×C3#55111yescharacteristic
848C22×C3#55311yescharacteristic
849C22×C3#55311yescharacteristic
850C22×C3#55311yescharacteristic
851C22×C3#55311yescharacteristic
852C22×C3#55311yescharacteristic
853C22×C3#55311yescharacteristic
854C22×C3#55311yescharacteristic
855C22×C3#55311yescharacteristic
856C2×D3—24no—
857C2×D3—24no—
858C2×D3—24no—
859C2×D3—24no—
860C2×D3—24no—
861C2×D3—24no—
862C2×D3—24no—
863C2×D3—24no—
864C2×D3—24no—
865C2×D3—24no—
866C2×D3—24no—
867C2×D3—24no—
868C2×D3—24no—
869C2×D3—24no—
870C2×D3#38818yes—
871C3×C4—42no—
872C3×C4—42no—
873C3×C4—42no—
874C3×C4—42no—
875C3×C4—42no—
876C3×C4—81no—
877Dic3—24no—
878Dic3—42no—
879Dic3—42no—
880Dic3—42no—
881Dic3—42no—
882Dic3—42no—
883Dic3—81no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—34no—
892C23—34no—
893C23—34no—
894C23—34no—
895C23—34no—
896C23—34no—
897C23—34no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—62no—
927C23—62no—
928C23—62no—
929C23—62no—
930C23—62no—
931C23—62no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—62no—
936C23—62no—
937C23—62no—
938C23—62no—
939C23—62no—
940C23—62no—
941C23—62no—
942C23—62no—
943C23—62no—
944C23—62no—
945C23—62no—
946C23—62no—
947C23—62no—
948C23—62no—
949C23—62no—
950C23—62no—
951C23—62no—
952C23—62no—
953C23—62no—
954C23C22×C4×D311yescharacteristic
955C23C2×D3×D411yescharacteristic
956C23C2×D3×D411yescharacteristic
957C23C2×#23711yescharacteristic
958C23#100411yescharacteristic
959C23#100411yescharacteristic
960C23#100411yescharacteristic
961C23D3×#4111yescharacteristic
962C23D3×#4111yescharacteristic
963C23D3×#4111yescharacteristic
964C23D3×#4111yescharacteristic
965C23D3×#4111yescharacteristic
966C23D3×#4111yescharacteristic
967C23D3×#4111yescharacteristic
968C23#100911yescharacteristic
969D4—1216no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—34no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—62no—
1014C2×C4—62no—
1015C2×C4—62no—
1016C2×C4—62no—
1017C2×C4—62no—
1018C2×C4—62no—
1019C2×C4—62no—
1020C2×C4—62no—
1021C2×C4—62no—
1022C2×C4—62no—
1023C2×C4—62no—
1024C2×C4—62no—
1025C2×C4—62no—
1026C2×C4—62no—
1027C2×C4—62no—
1028C2×C4—62no—
1029C2×C4—62no—
1030C2×C4—62no—
1031C2×C4—62no—
1032C2×C4—62no—
1033C2×C4—62no—
1034C2×C4—1216no—
1035C2×C4—1216no—
1036C2×C4—1216no—
1037C2×C4—121no—
1038C2×C4—121no—
1039C2×C4—121no—
1040C2×C4—121no—
1041C2×C4—121no—
1042C2×C4—121no—
1043C2×C4—121no—
1044C2×C4—121no—
1045C2×C4—121no—
1046C2×C4—121no—
1047C2×C4—121no—
1048C2×C4—121no—
1049C2×C4—121no—
1050C2×C4—121no—
1051C2×C4—121no—
1052C2×C4—121no—
1053C2×C4—121no—
1054C2×C4—121no—
1055C2×C4—121no—
1056C2×C4—121no—
1057C2×C4—121no—
1058C2×C4—121no—
1059C2×C4—121no—
1060C2×C4—121no—
1061C2×C4—121no—
1062C2×C4—121no—
1063C2×C4—121no—
1064C2×C3—82no—
1065C2×C3C2×#38811yescharacteristic
1066C2×C3C4×#12311yescharacteristic
1067C2×C3#232111yescharacteristic
1068C2×C3#235311yescharacteristic
1069C2×C3#235311yescharacteristic
1070C2×C3#236411yescharacteristic
1071C2×C3#236411yescharacteristic
1072C2×C3#241111yescharacteristic
1073C2×C3#241211yescharacteristic
1074C2×C3#244411yescharacteristic
1075C2×C3#244411yescharacteristic
1076C2×C3#250411yescharacteristic
1077C2×C3#251011yescharacteristic
1078C2×C3#251011yescharacteristic
1079C2×C3#259111yescharacteristic
1080D3—28no—
1081C22—38no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—64no—
1090C22—64no—
1091C22—64no—
1092C22—64no—
1093C22—64no—
1094C22—64no—
1095C22—64no—
1096C22—64no—
1097C22—64no—
1098C22—64no—
1099C22—64no—
1100C22—64no—
1101C22—64no—
1102C22—64no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22#548611yescharacteristic
1112C22D3×#11711yescharacteristic
1113C22#552211yescharacteristic
1114C22C4×#23711yescharacteristic
1115C22C4×D3×D411yescharacteristic
1116C22C4×D3×D411yescharacteristic
1117C22#554511yescharacteristic
1118C22#558911yescharacteristic
1119C22#559111yescharacteristic
1120C22D3×#12111yescharacteristic
1121C22#560611yescharacteristic
1122C22#560711yescharacteristic
1123C22#561011yescharacteristic
1124C22#561211yescharacteristic
1125C22#561311yescharacteristic
1126C22#561411yescharacteristic
1127C22#561411yescharacteristic
1128C22D3×#12311yescharacteristic
1129C22D3×#12311yescharacteristic
1130C22#565711yescharacteristic
1131C22#565811yescharacteristic
1132C22#565911yescharacteristic
1133C22#565911yescharacteristic
1134C22#566111yescharacteristic
1135C22#566111yescharacteristic
1136C22#566111yescharacteristic
1137C22#566111yescharacteristic
1138C22D3×#12411yescharacteristic
1139C22#567611yescharacteristic
1140C22#567911yescharacteristic
1141C22#568011yescharacteristic
1142C22D3×#12611yescharacteristic
1143C22#570611yescharacteristic
1144C22#570911yescharacteristic
1145C22#570911yescharacteristic
1146C4—42no—
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—64no—
1152C4—81no—
1153C4—122no—
1154C4—122no—
1155C4—122no—
1156C4—122no—
1157C4—122no—
1158C4—241no—
1159C3#1402011yescharacteristic, complemented, Sylow
1160C2—68no—
1161C2—82no—
1162C2#7412311yescharacteristic
1163C2#7487611yescharacteristic
1164C2#7488111yescharacteristic
1165C2#7545311yescharacteristic
1166C2D3×#38811yescharacteristic
1167C2#7583511yescharacteristic
1168C2#7583911yescharacteristic
1169C2#7710911yescharacteristic
1170C2#7711011yescharacteristic
1171C2#7711811yescharacteristic
1172C2#7712111yescharacteristic
1173C2#7749211yescharacteristic
1174C2#7767511yescharacteristic
1175C2#7768011yescharacteristic
1176C2#7768111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1440C2
socle, cosocleC24×C3C24
prime radicalC23×#67C22
hypercenter#1440D3
hypocenterC3#14020
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
4. C2×D3×#95C2semidirect
5. C2×#4666C2semidirect
6. C3×#1440C2semidirect
7. #71549C2semidirect
8. #71545C2semidirect
9. #71545C2semidirect
10. (C2×D3)⋊#95C2semidirect
11. (C2×D3)⋊#95C2semidirect
12. #69418C2semidirect
13. #69417C2semidirect
14. #69402C2semidirect
15. #69401C2semidirect
54. #4956C4semidirect
65. #1440D3semidirect
123. C2×C3×C22⋊C4C2×C4semidirect
132. C2×#217C2×C4semidirect
166. C3⋊#95C2×C4semidirect
167. C3⋊#95C2×C4semidirect
438. C2×C22⋊C4C4×D3semidirect
1159. C3#14020semidirect

Maximal subgroups

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

subgroupindex
C2×#49562
C2×D3×#952
C2×#46662
C3×#14402
#715492
#715452
(C2×D3)⋊#952
#694182
#694172
#694022
#694012
#140203