Finite Group Databasebeta

← #10720217

Subgroups — #10720217

Order 768.

2278 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
2C2×#4665C211yesmaximal, characteristic
3C2×#4665C211yesmaximal, characteristic
4C2×#4665C211yesmaximal, characteristic
5C2×#4668C211yesmaximal, characteristic, complemented
6C2×D3×#95C211yesmaximal, characteristic, complemented
7C2×#4669C211yesmaximal, characteristic, complemented
8C3×#1434C211yesmaximal, characteristic, complemented
9#71537C211yesmaximal, characteristic, complemented
10#69429C211yesmaximal, characteristic, complemented
11#69427C211yesmaximal, characteristic, complemented
12(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
13#69418C211yesmaximal, characteristic, complemented
14#69413C211yesmaximal, characteristic, complemented
15#69407C211yesmaximal, characteristic, complemented
16#14140—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C22×C3×C42C2211yescharacteristic
22C22×(C2×D3)⋊C4C2211yescharacteristic
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×C4⋊Dic3C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
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
52C4×(C2×D3)⋊C4—24no—
53#4669—24no—
54#4668—24no—
55#4665—24no—
56#4665—24no—
57#4665C418yescomplemented
58D3×#95—24no—
59C2×#388—31no—
60C2×#386—31no—
61C2×#386—31no—
62C2×#386—31no—
63C2×#385—31no—
64C2×C4×C22⋊C4—31no—
65C22×#95—31no—
66#1443—31no—
67#1442—31no—
68#1440—31no—
69#1439—31no—
70#1437—31no—
71#1436—31no—
72#1434D311yescharacteristic, complemented
73C22⋊#95—31no—
74C24×D3C2311yescharacteristic
75C24×D3C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C22×D12—22no—
90C22×D12—22no—
91C22×D12—22no—
92C22×D12—22no—
93C22×D12—22no—
94C22×D12—22no—
95C22×D12C2×C414yes—
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—22no—
106C22×C4×D3—22no—
107C22×C4×D3—22no—
108C22×C4×D3—22no—
109C22×C4×D3—22no—
110C22×C4×D3—41no—
111C22×C4×D3—41no—
112C22×C4×D3—41no—
113C22×C4×D3—41no—
114C22×C4×D3—41no—
115C22×C4×D3—41no—
116C22×C4×D3C2×C414yes—
117C2×C3×C42—22no—
118C2×C3×C42—22no—
119C2×C3×C42—41no—
120C2×(C2×D3)⋊C4—22no—
121C2×(C2×D3)⋊C4—22no—
122C2×(C2×D3)⋊C4—22no—
123C2×(C2×D3)⋊C4—22no—
124C2×(C2×D3)⋊C4—22no—
125C2×(C2×D3)⋊C4—22no—
126C2×(C2×D3)⋊C4—22no—
127C2×(C2×D3)⋊C4—22no—
128C2×(C2×D3)⋊C4—22no—
129C2×(C2×D3)⋊C4—22no—
130C2×(C2×D3)⋊C4—22no—
131C2×(C2×D3)⋊C4—22no—
132C2×(C2×D3)⋊C4—22no—
133C2×(C2×D3)⋊C4—22no—
134C2×(C2×D3)⋊C4—22no—
135C2×(C2×D3)⋊C4—22no—
136C2×(C2×D3)⋊C4—41no—
137C2×(C2×D3)⋊C4—41no—
138C2×(C2×D3)⋊C4—41no—
139C2×(C2×D3)⋊C4—41no—
140C2×(C2×D3)⋊C4—41no—
141C2×(C2×D3)⋊C4—41no—
142C2×(C2×D3)⋊C4C2×C414yes—
143C2×(C2×D3)⋊C4C2×C414yescomplemented
144C2×(C2×D3)⋊C4C2×C414yescomplemented
145C2×(C2×D3)⋊C4D414yes—
146C2×(C2×D3)⋊C4D414yes—
147C2×C4⋊Dic3—22no—
148C2×C4⋊Dic3—22no—
149C2×C4⋊Dic3—41no—
150C2×Dic3⋊C4—22no—
151C2×Dic3⋊C4—22no—
152C2×Dic3⋊C4—41no—
153C2×C4×Dic3—22no—
154C2×C4×Dic3—22no—
155C2×C4×Dic3—41no—
156C3×#95—22no—
157C3×#95—22no—
158C3×#95—22no—
159C3×#95—41no—
160C3×#95C2×C414yescomplemented
161C3×#95D414yescomplemented
162C3⋊#95—22no—
163C3⋊#95—22no—
164C3⋊#95—22no—
165C3⋊#95—22no—
166C3⋊#95—22no—
167C3⋊#95—22no—
168C3⋊#95—22no—
169C3⋊#95—22no—
170C3⋊#95—22no—
171C3⋊#95—22no—
172C3⋊#95—41no—
173C3⋊#95C2×C414yescomplemented
174C23×D4—31no—
175C24×C4—31no—
176C24×C4—31no—
177C24×C4—31no—
178C22×C4⋊C4—31no—
179C22×C4⋊C4—31no—
180C22×C22⋊C4—31no—
181C22×C22⋊C4—31no—
182C22×C22⋊C4—31no—
183C22×C22⋊C4—31no—
184C22×C22⋊C4—31no—
185C22×C22⋊C4—31no—
186C22×C22⋊C4—31no—
187C22×C22⋊C4—31no—
188C22×C22⋊C4—31no—
189C22×C42—31no—
190C22×C42C2×D311yescharacteristic
191#388—64no—
192#386—38no—
193#386—64no—
194#386—64no—
195#385—64no—
196C4×C22⋊C4—64no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95—31no—
201C2×#95—31no—
202C2×#95—31no—
203C2×#95—31no—
204C2×#95—31no—
205C2×#95—31no—
206C2×#95—31no—
207C2×#95—31no—
208C2×#95—31no—
209C2×#95—64no—
210C2×#95C2×D311yescharacteristic
211C2×#95C2×D311yescharacteristic
212C2×#95C2×D311yescharacteristic
213C2×#95C2×D311yescharacteristic
214C2×#95C2×D311yescharacteristic
215C2×#95C2×D311yescharacteristic
216C24×C3C2411yescharacteristic
217C23×D3—21no—
218C23×D3—21no—
219C23×D3—21no—
220C23×D3—21no—
221C23×D3—21no—
222C23×D3—21no—
223C23×D3—21no—
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×D3—21no—
233C23×D3—21no—
234C23×D3—21no—
235C23×D3—21no—
236C23×D3—21no—
237C23×D3—21no—
238C23×D3—21no—
239C23×D3C22×C412yes—
240C23×D3C22×C412yes—
241C23×D3C2×D412yes—
242C23×D3C2×D412yes—
243C23×D3#4112yes—
244C23×D3#4112yes—
245C23×D3#4112yes—
246C23×D3#4112yes—
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×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4C22×C412yes—
288C22×C3×C4C22×C412yes—
289C22×C3×C4C22×C412yes—
290C22×C3×C4C2×D412yes—
291C22×C3×C4C2×D412yes—
292C22×C3×C4C2×D412yes—
293C22×C3×C4C2×D412yes—
294C22×C3×C4C2×D412yes—
295C22×C3×C4#4112yes—
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×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3C22×C412yes—
333C22×Dic3C22×C412yes—
334C22×Dic3C2×D412yes—
335C22×Dic3C2×D412yes—
336C22×Dic3#4112yes—
337C22×Dic3#4112yes—
338C2×D12—28no—
339C2×D12—28no—
340C2×D12—28no—
341C2×D12—44no—
342C2×D12—44no—
343C2×D12—44no—
344C2×D12—44no—
345C2×C4×D3—28no—
346C2×C4×D3—28no—
347C2×C4×D3—28no—
348C2×C4×D3—28no—
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—
358C2×C4×D3—44no—
359C2×C4×D3—44no—
360C2×C4×D3—44no—
361C2×C4×D3—44no—
362C2×C4×D3—44no—
363C2×C4×D3—44no—
364C2×C4×D3—44no—
365C2×C4×D3—44no—
366C3×C42—44no—
367(C2×D3)⋊C4—28no—
368(C2×D3)⋊C4—28no—
369(C2×D3)⋊C4—28no—
370(C2×D3)⋊C4—28no—
371(C2×D3)⋊C4—44no—
372(C2×D3)⋊C4—44no—
373(C2×D3)⋊C4—44no—
374(C2×D3)⋊C4—44no—
375(C2×D3)⋊C4—44no—
376C4⋊Dic3—44no—
377Dic3⋊C4—44no—
378C4×Dic3—44no—
379C25—31no—
380C25—31no—
381C22×D4—34no—
382C22×D4—62no—
383C22×D4—62no—
384C22×D4—62no—
385C22×D4—62no—
386C22×D4—62no—
387C22×D4—62no—
388C23×C4—31no—
389C23×C4—31no—
390C23×C4—31no—
391C23×C4—31no—
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—34no—
395C23×C4—62no—
396C23×C4—62no—
397C23×C4—62no—
398C23×C4—62no—
399C23×C4—62no—
400C23×C4—62no—
401C23×C4—62no—
402C23×C4—62no—
403C23×C4—62no—
404C23×C4—62no—
405C23×C4—62no—
406C23×C4—62no—
407C23×C4—62no—
408C23×C4—62no—
409C23×C4—121no—
410C23×C4—121no—
411C23×C4—121no—
412C23×C4—121no—
413C23×C4—121no—
414C23×C4—121no—
415C23×C4C22×D311yescharacteristic
416C23×C4C22×D311yescharacteristic
417C23×C4C22×D311yescharacteristic
418C23×C4C22×D311yescharacteristic
419C23×C4C22×D311yescharacteristic
420C23×C4C22×D311yescharacteristic
421C23×C4C22×D311yescharacteristic
422C2×C4⋊C4—62no—
423C2×C4⋊C4—62no—
424C2×C4⋊C4—62no—
425C2×C4⋊C4—62no—
426C2×C4⋊C4—121no—
427C2×C4⋊C4—121no—
428C2×C22⋊C4—34no—
429C2×C22⋊C4—34no—
430C2×C22⋊C4—34no—
431C2×C22⋊C4—34no—
432C2×C22⋊C4—34no—
433C2×C22⋊C4—62no—
434C2×C22⋊C4—62no—
435C2×C22⋊C4—62no—
436C2×C22⋊C4—62no—
437C2×C22⋊C4—62no—
438C2×C22⋊C4—62no—
439C2×C22⋊C4—62no—
440C2×C22⋊C4—62no—
441C2×C22⋊C4—62no—
442C2×C22⋊C4—62no—
443C2×C22⋊C4—62no—
444C2×C22⋊C4—62no—
445C2×C22⋊C4—62no—
446C2×C22⋊C4—62no—
447C2×C22⋊C4—62no—
448C2×C22⋊C4—62no—
449C2×C22⋊C4—121no—
450C2×C22⋊C4—121no—
451C2×C22⋊C4—121no—
452C2×C22⋊C4—121no—
453C2×C22⋊C4—121no—
454C2×C22⋊C4—121no—
455C2×C42—22no—
456C2×C42—22no—
457C2×C42—41no—
458C2×C42—62no—
459C2×C42—62no—
460C2×C42—121no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—34no—
465#95—41no—
466#95—62no—
467#95—62no—
468#95—62no—
469#95—62no—
470#95—62no—
471#95—62no—
472#95—62no—
473#95—62no—
474#95—62no—
475#95—62no—
476#95—121no—
477#95C4×D314yescomplemented
478#95D1214yescomplemented
479C23×C3C23×C411yescharacteristic
480C23×C3C22×D411yescharacteristic
481C23×C3C22×D411yescharacteristic
482C23×C3C22×D411yescharacteristic
483C23×C3C2×#4111yescharacteristic
484C23×C3C2×#4111yescharacteristic
485C23×C3C2×#4111yescharacteristic
486C23×C3C2×#4111yescharacteristic
487C23×C3C2×#4111yescharacteristic
488C23×C3C2×#4111yescharacteristic
489C23×C3C2×#4111yescharacteristic
490C23×C3H(5,𝔽2)11yescharacteristic
491C23×C3H(5,𝔽2)11yescharacteristic
492C23×C3H(5,𝔽2)11yescharacteristic
493C23×C32−1+411yescharacteristic
494C22×D3—22no—
495C22×D3—22no—
496C22×D3—22no—
497C22×D3—22no—
498C22×D3—22no—
499C22×D3—22no—
500C22×D3—22no—
501C22×D3—22no—
502C22×D3—22no—
503C22×D3—22no—
504C22×D3—22no—
505C22×D3—22no—
506C22×D3—22no—
507C22×D3—22no—
508C22×D3—22no—
509C22×D3—22no—
510C22×D3—22no—
511C22×D3—22no—
512C22×D3—22no—
513C22×D3—22no—
514C22×D3—22no—
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—41no—
530C22×D3—41no—
531C22×D3—41no—
532C22×D3—41no—
533C22×D3—41no—
534C22×D3—41no—
535C22×D3—41no—
536C22×D3—41no—
537C22×D3—41no—
538C22×D3—41no—
539C22×D3—41no—
540C22×D3—41no—
541C22×D3—41no—
542C22×D3—41no—
543C22×D3—41no—
544C22×D3—41no—
545C22×D3—41no—
546C22×D3—41no—
547C22×D3—41no—
548C22×D3—41no—
549C22×D3—41no—
550C22×D3—41no—
551C22×D3—41no—
552C22×D3—41no—
553C22×D3—41no—
554C22×D3—41no—
555C22×D3—41no—
556C22×D3—41no—
557C22×D3#11714yes—
558C22×D3C4×D414yes—
559C22×D3C4×D414yes—
560C22×D3#12114yes—
561C22×D3#12314yes—
562C22×D3#12414yes—
563C22×D3#12614yes—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4C4×D414yes—
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—22no—
616C2×Dic3—22no—
617C2×Dic3—22no—
618C2×Dic3—22no—
619C2×Dic3—22no—
620C2×Dic3—22no—
621C2×Dic3—22no—
622C2×Dic3—22no—
623C2×Dic3—22no—
624C2×Dic3—22no—
625C2×Dic3—22no—
626C2×Dic3—22no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—22no—
630C2×Dic3—22no—
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—41no—
642C2×Dic3—41no—
643C2×Dic3—41no—
644C2×Dic3—41no—
645C2×Dic3—41no—
646C2×Dic3—41no—
647C2×Dic3—41no—
648C2×Dic3—41no—
649C2×Dic3—41no—
650C2×Dic3—41no—
651C2×Dic3—41no—
652C2×Dic3—41no—
653C2×Dic3—41no—
654C2×Dic3—41no—
655D12—416no—
656C4×D3—416no—
657C4×D3—416no—
658C4×D3—416no—
659C24—32no—
660C24—32no—
661C24—32no—
662C24—32no—
663C24—32no—
664C24—32no—
665C24—32no—
666C24—32no—
667C24—61no—
668C24—61no—
669C24—61no—
670C24—61no—
671C24—61no—
672C24—61no—
673C24—61no—
674C24—61no—
675C24—61no—
676C24—61no—
677C24—61no—
678C24—61no—
679C24—61no—
680C24—61no—
681C24—61no—
682C24—61no—
683C24—61no—
684C24—61no—
685C24—61no—
686C24—61no—
687C24—61no—
688C24—61no—
689C24C23×D311yescharacteristic
690C2×D4—68no—
691C2×D4—68no—
692C2×D4—68no—
693C2×D4—124no—
694C2×D4—124no—
695C2×D4—124no—
696C2×D4—124no—
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—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—32no—
738C22×C4—32no—
739C22×C4—32no—
740C22×C4—32no—
741C22×C4—32no—
742C22×C4—32no—
743C22×C4—68no—
744C22×C4—68no—
745C22×C4—68no—
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—61no—
774C22×C4—61no—
775C22×C4—61no—
776C22×C4—61no—
777C22×C4—61no—
778C22×C4—61no—
779C22×C4—61no—
780C22×C4—61no—
781C22×C4—61no—
782C22×C4—68no—
783C22×C4—124no—
784C22×C4—124no—
785C22×C4—124no—
786C22×C4—124no—
787C22×C4—124no—
788C22×C4—124no—
789C22×C4—124no—
790C22×C4—124no—
791C22×C4—124no—
792C22×C4—124no—
793C22×C4—124no—
794C22×C4—124no—
795C22×C4—124no—
796C22×C4—124no—
797C22×C4—124no—
798C22×C4—124no—
799C22×C4—124no—
800C22×C4C2×C4×D312yes—
801C22×C4C2×C4×D312yes—
802C22×C4C2×C4×D312yes—
803C22×C4C2×D1212yes—
804C22×C4C2×D1212yes—
805C22×C4C2×D1212yes—
806C22×C4#23512yes—
807C22×C4D3×D412yes—
808C22×C4D3×D412yes—
809C4⋊C4—124no—
810C4⋊C4—124no—
811C22⋊C4—68no—
812C22⋊C4—68no—
813C22⋊C4—68no—
814C22⋊C4—68no—
815C22⋊C4—124no—
816C22⋊C4—124no—
817C22⋊C4—124no—
818C22⋊C4—124no—
819C22⋊C4—124no—
820C42—44no—
821C42—124no—
822C22×C3C2×#11711yescharacteristic
823C22×C3C2×C4×D411yescharacteristic
824C22×C3C2×C4×D411yescharacteristic
825C22×C3C2×C4×D411yescharacteristic
826C22×C3C4×#4111yescharacteristic
827C22×C3#51811yescharacteristic
828C22×C3#52011yescharacteristic
829C22×C3C2×#12111yescharacteristic
830C22×C3C2×#12311yescharacteristic
831C22×C3#52511yescharacteristic
832C22×C3#52511yescharacteristic
833C22×C3C2×#12411yescharacteristic
834C22×C3C2×#12611yescharacteristic
835C22×C3#52911yescharacteristic
836C22×C3#52911yescharacteristic
837C22×C3#53811yescharacteristic
838C22×C3#53811yescharacteristic
839C22×C3#53911yescharacteristic
840C22×C3#53911yescharacteristic
841C22×C3D4211yescharacteristic
842C22×C3D4211yescharacteristic
843C22×C3#54611yescharacteristic
844C22×C3#54611yescharacteristic
845C22×C3#54611yescharacteristic
846C22×C3#54611yescharacteristic
847C22×C3#54611yescharacteristic
848C22×C3#54711yescharacteristic
849C22×C3#54711yescharacteristic
850C22×C3#54811yescharacteristic
851C22×C3#55111yescharacteristic
852C22×C3#55111yescharacteristic
853C22×C3#55211yescharacteristic
854C22×C3#55311yescharacteristic
855C22×C3#55311yescharacteristic
856C22×C3#55311yescharacteristic
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—24no—
871C2×D3—42no—
872C2×D3—42no—
873C2×D3—42no—
874C2×D3—42no—
875C2×D3—42no—
876C2×D3—42no—
877C2×D3—42no—
878C2×D3—81no—
879C2×D3—81no—
880C2×D3—81no—
881C2×D3—81no—
882C2×D3—81no—
883C2×D3—81no—
884C2×D3—81no—
885C2×D3—81no—
886C2×D3#38818yescomplemented
887C3×C4—24no—
888C3×C4—42no—
889C3×C4—42no—
890C3×C4—42no—
891C3×C4—42no—
892C3×C4—42no—
893C3×C4—42no—
894Dic3—42no—
895Dic3—42no—
896Dic3—42no—
897Dic3—42no—
898Dic3—42no—
899Dic3—42no—
900C23—34no—
901C23—34no—
902C23—34no—
903C23—34no—
904C23—34no—
905C23—34no—
906C23—34no—
907C23—62no—
908C23—62no—
909C23—62no—
910C23—62no—
911C23—62no—
912C23—62no—
913C23—62no—
914C23—62no—
915C23—62no—
916C23—62no—
917C23—62no—
918C23—62no—
919C23—62no—
920C23—62no—
921C23—62no—
922C23—62no—
923C23—62no—
924C23—62no—
925C23—62no—
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—121no—
943C23—121no—
944C23—121no—
945C23—121no—
946C23—121no—
947C23—121no—
948C23—121no—
949C23—121no—
950C23—121no—
951C23—121no—
952C23—121no—
953C23—121no—
954C23—121no—
955C23—121no—
956C23—121no—
957C23—121no—
958C23—121no—
959C23—121no—
960C23—121no—
961C23—121no—
962C23—121no—
963C23—121no—
964C23—121no—
965C23—121no—
966C23—121no—
967C23—121no—
968C23—121no—
969C23—121no—
970C23C22×C4×D311yescharacteristic
971C23C22×D1211yescharacteristic
972C23C2×#23511yescharacteristic
973C23C2×D3×D411yescharacteristic
974C23C2×D3×D411yescharacteristic
975C23#100411yescharacteristic
976C23#100711yescharacteristic
977C23D3×#4111yescharacteristic
978C23D3×#4111yescharacteristic
979C23D3×#4111yescharacteristic
980C23D3×#4111yescharacteristic
981C23D3×#4111yescharacteristic
982C23D3×#4111yescharacteristic
983C23#100911yescharacteristic
984C23#100911yescharacteristic
985D4—1216no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—62no—
1035C2×C4—62no—
1036C2×C4—62no—
1037C2×C4—62no—
1038C2×C4—62no—
1039C2×C4—62no—
1040C2×C4—62no—
1041C2×C4—62no—
1042C2×C4—62no—
1043C2×C4—62no—
1044C2×C4—62no—
1045C2×C4—62no—
1046C2×C4—62no—
1047C2×C4—62no—
1048C2×C4—62no—
1049C2×C4—62no—
1050C2×C4—62no—
1051C2×C4—62no—
1052C2×C4—1216no—
1053C2×C4—1216no—
1054C2×C4—1216no—
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×C4—121no—
1065C2×C4—121no—
1066C2×C4—121no—
1067C2×C4—121no—
1068C2×C4—121no—
1069C2×C4—121no—
1070C2×C4—121no—
1071C2×C4—121no—
1072C2×C4—121no—
1073C2×C4—121no—
1074C2×C4—121no—
1075C2×C4—121no—
1076C2×C4—121no—
1077C2×C4—121no—
1078C2×C4—121no—
1079C2×C4C4×D1214yes—
1080C2×C3C2×#38811yescharacteristic
1081C2×C3#229011yescharacteristic
1082C2×C3#231811yescharacteristic
1083C2×C3#235811yescharacteristic
1084C2×C3#235911yescharacteristic
1085C2×C3#236111yescharacteristic
1086C2×C3#236411yescharacteristic
1087C2×C3#242411yescharacteristic
1088C2×C3#242511yescharacteristic
1089C2×C3#244311yescharacteristic
1090C2×C3#244411yescharacteristic
1091C2×C3#247211yescharacteristic
1092C2×C3#248111yescharacteristic
1093C2×C3#248811yescharacteristic
1094C2×C3#251011yescharacteristic
1095D3—28no—
1096D3—82no—
1097C22—38no—
1098C22—64no—
1099C22—64no—
1100C22—64no—
1101C22—64no—
1102C22—64no—
1103C22—64no—
1104C22—64no—
1105C22—64no—
1106C22—64no—
1107C22—64no—
1108C22—64no—
1109C22—64no—
1110C22—64no—
1111C22—64no—
1112C22—122no—
1113C22—122no—
1114C22—122no—
1115C22—122no—
1116C22—122no—
1117C22—122no—
1118C22—122no—
1119C22—241no—
1120C22—241no—
1121C22—241no—
1122C22—241no—
1123C22—241no—
1124C22—241no—
1125C22—241no—
1126C22—241no—
1127C22C2×C4×D1211yescharacteristic
1128C22#549011yescharacteristic
1129C22#550711yescharacteristic
1130C22D3×#11711yescharacteristic
1131C22#552211yescharacteristic
1132C22#552411yescharacteristic
1133C22#552411yescharacteristic
1134C22#552711yescharacteristic
1135C22#552811yescharacteristic
1136C22#552811yescharacteristic
1137C22#553011yescharacteristic
1138C22C4×D3×D411yescharacteristic
1139C22C4×D3×D411yescharacteristic
1140C22#554511yescharacteristic
1141C22D4×D1211yescharacteristic
1142C22D4×D1211yescharacteristic
1143C22#555411yescharacteristic
1144C22#557411yescharacteristic
1145C22#557611yescharacteristic
1146C22D3×#12111yescharacteristic
1147C22#561011yescharacteristic
1148C22#563111yescharacteristic
1149C22#563811yescharacteristic
1150C22D3×#12311yescharacteristic
1151C22#565411yescharacteristic
1152C22#565711yescharacteristic
1153C22#566111yescharacteristic
1154C22D3×#12411yescharacteristic
1155C22#567611yescharacteristic
1156C22#569211yescharacteristic
1157C22#569311yescharacteristic
1158C22D3×#12611yescharacteristic
1159C22#570411yescharacteristic
1160C22#570511yescharacteristic
1161C22#570911yescharacteristic
1162C4—24no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—42no—
1169C4—122no—
1170C4—122no—
1171C4—122no—
1172C4—122no—
1173C4—122no—
1174C4—122no—
1175C3#1414011yescharacteristic, complemented, Sylow
1176C2—68no—
1177C2—242no—
1178C2#7341411yescharacteristic
1179C2#7357711yescharacteristic
1180C2#7377411yescharacteristic
1181C2#7402211yescharacteristic
1182C2#7412811yescharacteristic
1183C2#7423311yescharacteristic
1184C2#7430111yescharacteristic
1185C2#7494511yescharacteristic
1186C2#7502011yescharacteristic
1187C2#7530711yescharacteristic
1188C2#7531911yescharacteristic
1189C2#7552711yescharacteristic
1190C2D3×#38811yescharacteristic
1191C2#7583911yescharacteristic
1192C2#7584611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1434C2
socle, cosocleC24×C3C24
prime radicalC23×D12C22
hypercenter#1434D3
hypocenterC3#14140
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
1. C2×C4×(C2×D3)⋊C4C2semidirect
5. C2×#4668C2semidirect
6. C2×D3×#95C2semidirect
7. C2×#4669C2semidirect
8. C3×#1434C2semidirect
9. #71537C2semidirect
10. #69429C2semidirect
11. #69427C2semidirect
12. (C2×D3)⋊#95C2semidirect
13. #69418C2semidirect
14. #69413C2semidirect
15. #69407C2semidirect
57. #4665C4semidirect
72. #1434D3semidirect
143. C2×(C2×D3)⋊C4C2×C4semidirect
144. C2×(C2×D3)⋊C4C2×C4semidirect
160. C3×#95C2×C4semidirect
161. C3×#95D4semidirect
173. C3⋊#95C2×C4semidirect
477. #95C4×D3semidirect
478. #95D12semidirect
886. C2×D3#388semidirect
1175. C3#14140semidirect

Maximal subgroups

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

subgroupindex
C2×C4×(C2×D3)⋊C42
C2×#46652
C2×#46682
C2×D3×#952
C2×#46692
C3×#14342
#715372
#694292
#694272
(C2×D3)⋊#952
#694182
#694132
#694072
#141403