Finite Group Databasebeta

← #10723366

Subgroups — #10723366

Order 768.

2126 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#947C211yesmaximal, characteristic
2C2×#5229C211yesmaximal, characteristic, complemented
3C2×#4665C211yesmaximal, characteristic
4C2×#4668C211yesmaximal, characteristic, complemented
5C2×#4669C211yesmaximal, characteristic, complemented
6C3×#1446C211yesmaximal, characteristic, complemented
7#69429C211yesmaximal, characteristic, complemented
8#69428C211yesmaximal, characteristic, complemented
9#69428C211yesmaximal, characteristic, complemented
10#69427C211yesmaximal, characteristic, complemented
11#69426C211yesmaximal, characteristic
12(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
13#69408C211yesmaximal, characteristic, complemented
14Dic3⋊#95C211yesmaximal, characteristic, complemented
15#69401C211yesmaximal, characteristic, complemented
16#14421—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic
18C23×D12C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C2×#947—24no—
21C2×#947—24no—
22C2×#947C418yescomplemented
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×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×C4⋊Dic3C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C22×C4×Dic3C2211yescharacteristic
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42C2×C3×#95C2211yescharacteristic
43C2×C3×#95C2211yescharacteristic
44C2×C3×#95C2211yescharacteristic
45#5229—24no—
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56#4669—24no—
57#4668—24no—
58#4665—24no—
59C22×#124—31no—
60C2×#391—31no—
61C2×#388—31no—
62C2×#386—31no—
63C2×#385—31no—
64#1446D311yescharacteristic, complemented
65#1440—31no—
66#1439—31no—
67#1439—31no—
68#1439—31no—
69#1438—31no—
70#1437—31no—
71C4⋊#95—31no—
72#1434—31no—
73C22⋊#95—31no—
74C24×D3C2311yescharacteristic
75C24×D3C2311yescharacteristic
76C22×C3×Q8—22no—
77C22×C3×Q8—22no—
78C22×C3×Q8—22no—
79C22×C3×Q8—22no—
80C22×C3×Q8—41no—
81C22×C3×Q8—41no—
82C22×C3×Q8C2×C414yescomplemented
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C22×D12—22no—
97C22×D12—22no—
98C22×D12—22no—
99C22×D12—22no—
100C22×D12—41no—
101C22×D12—41no—
102C22×D12C2×C414yes—
103C22×C4×D3—22no—
104C22×C4×D3—22no—
105C22×C4×D3—22no—
106C22×C4×D3—41no—
107C22×C4×D3—41no—
108C22×C4×D3—41no—
109C22×C4×D3—41no—
110#947—232no—
111C2×(C2×D3)⋊C4—22no—
112C2×(C2×D3)⋊C4—22no—
113C2×(C2×D3)⋊C4—22no—
114C2×(C2×D3)⋊C4—22no—
115C2×(C2×D3)⋊C4—22no—
116C2×(C2×D3)⋊C4—22no—
117C2×(C2×D3)⋊C4—22no—
118C2×(C2×D3)⋊C4—22no—
119C2×(C2×D3)⋊C4—22no—
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—41no—
127C2×(C2×D3)⋊C4—41no—
128C2×(C2×D3)⋊C4—41no—
129C2×(C2×D3)⋊C4—41no—
130C2×(C2×D3)⋊C4—41no—
131C2×(C2×D3)⋊C4—41no—
132C2×(C2×D3)⋊C4—41no—
133C2×(C2×D3)⋊C4—41no—
134C2×(C2×D3)⋊C4—41no—
135C2×(C2×D3)⋊C4—41no—
136C2×(C2×D3)⋊C4—41no—
137C2×(C2×D3)⋊C4—41no—
138C2×(C2×D3)⋊C4C2×C414yes—
139C2×(C2×D3)⋊C4C2×C414yes—
140C2×(C2×D3)⋊C4C2×C414yescomplemented
141C2×(C2×D3)⋊C4C2×C414yescomplemented
142C2×(C2×D3)⋊C4D414yes—
143C2×(C2×D3)⋊C4D414yes—
144C2×C4⋊Dic3—22no—
145C2×C4⋊Dic3—22no—
146C2×C4⋊Dic3—41no—
147C2×Dic3⋊C4—22no—
148C2×Dic3⋊C4—22no—
149C2×Dic3⋊C4—22no—
150C2×Dic3⋊C4—22no—
151C2×Dic3⋊C4—41no—
152C2×Dic3⋊C4—41no—
153C2×C4×Dic3—22no—
154C2×C4×Dic3—22no—
155C2×C4×Dic3—22no—
156C2×C4×Dic3—22no—
157C2×C4×Dic3—41no—
158C2×C4×Dic3C2×C414yescomplemented
159C3×#95—22no—
160C3×#95—22no—
161C3×#95—22no—
162C3×#95—22no—
163C3×#95—41no—
164C3×#95—41no—
165C3⋊#95—22no—
166C3⋊#95—22no—
167C3⋊#95—22no—
168C3⋊#95—22no—
169C3⋊#95—22no—
170C3⋊#95—41no—
171C3⋊#95—41no—
172C3⋊#95—41no—
173C3⋊#95—41no—
174C3⋊#95D414yes—
175C23×Q8C2×D311yescharacteristic
176C23×D4—31no—
177C24×C4—31no—
178C2×#124—38no—
179C2×#124—64no—
180C2×#124—64no—
181C22×C4⋊C4—31no—
182C22×C4⋊C4—31no—
183C22×C4⋊C4—31no—
184C22×C22⋊C4—31no—
185C22×C22⋊C4—31no—
186C22×C22⋊C4—31no—
187C22×C22⋊C4—31no—
188C22×C22⋊C4—31no—
189C22×C22⋊C4—31no—
190C22×C22⋊C4—31no—
191C22×C22⋊C4—31no—
192C22×C22⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C42—31no—
196C22×C42—31no—
197#391—64no—
198#388—64no—
199#386—64no—
200#385—64no—
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—31no—
210C2×#95—31no—
211C2×#95C2×D311yescharacteristic
212C2×#95C2×D311yescharacteristic
213C2×#95C2×D311yescharacteristic
214C2×#95C2×D311yescharacteristic
215C2×#95C2×D311yescharacteristic
216C2×#95C2×D311yescharacteristic
217C24×C3C2411yescharacteristic
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×D3—21no—
240C23×D3—21no—
241C23×D3—21no—
242C23×D3—21no—
243C23×D3—21no—
244C23×D3C22×C412yes—
245C23×D3C22×C412yes—
246C23×D3C2×D412yes—
247C23×D3C2×D412yes—
248C2×C3×Q8—28no—
249C2×C3×Q8—28no—
250C2×C3×Q8—44no—
251C2×C3×Q8—44no—
252C2×C3×Q8—44no—
253C2×C3×Q8—44no—
254C2×C3×Q8—44no—
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×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4C22×C412yes—
297C22×C3×C4C22×C412yes—
298C22×C3×C4C22×C412yes—
299C22×C3×C4C2×D412yes—
300C22×C3×C4C2×D412yes—
301C22×C3×C4C2×D412yes—
302C22×C3×C4#4112yes—
303C22×C3×C4#4112yes—
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×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3C22×C412yes—
340C22×Dic3C22×C412yes—
341C22×Dic3C2×D412yes—
342C22×Dic3C2×D412yes—
343C22×Dic3C2×D412yes—
344C22×Dic3C2×D412yes—
345C22×Dic3#4112yes—
346C2×D12—28no—
347C2×D12—28no—
348C2×D12—44no—
349C2×D12—44no—
350C2×D12—44no—
351C2×D12—44no—
352C2×D12—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—
360(C2×D3)⋊C4—28no—
361(C2×D3)⋊C4—28no—
362(C2×D3)⋊C4—28no—
363(C2×D3)⋊C4—44no—
364(C2×D3)⋊C4—44no—
365(C2×D3)⋊C4—44no—
366(C2×D3)⋊C4—44no—
367(C2×D3)⋊C4—44no—
368(C2×D3)⋊C4—44no—
369(C2×D3)⋊C4—44no—
370(C2×D3)⋊C4C22⋊C4116yescomplemented
371C4⋊Dic3—44no—
372Dic3⋊C4—44no—
373Dic3⋊C4—44no—
374C4×Dic3—28no—
375C4×Dic3—44no—
376C25—31no—
377C25—31no—
378C22×Q8—22no—
379C22×Q8—22no—
380C22×Q8—22no—
381C22×Q8—22no—
382C22×Q8—41no—
383C22×Q8—41no—
384C22×Q8C4×D314yescomplemented
385C22×D4—34no—
386C22×D4—62no—
387C22×D4—62no—
388C22×D4—62no—
389C22×D4—62no—
390C22×D4—121no—
391C22×D4—121no—
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—31no—
395C23×C4—31no—
396C23×C4—31no—
397C23×C4—31no—
398C23×C4—62no—
399C23×C4—62no—
400C23×C4—62no—
401C23×C4—121no—
402C23×C4—121no—
403C23×C4—121no—
404C23×C4—121no—
405C23×C4C22×D311yescharacteristic
406C23×C4C22×D311yescharacteristic
407C23×C4C22×D311yescharacteristic
408C23×C4C22×D311yescharacteristic
409C23×C4C22×D311yescharacteristic
410C23×C4C22×D311yescharacteristic
411C23×C4C22×D311yescharacteristic
412#124—632no—
413C2×C4⋊C4—62no—
414C2×C4⋊C4—62no—
415C2×C4⋊C4—62no—
416C2×C4⋊C4—62no—
417C2×C4⋊C4—62no—
418C2×C4⋊C4—62no—
419C2×C4⋊C4—121no—
420C2×C4⋊C4—121no—
421C2×C4⋊C4—121no—
422C2×C22⋊C4—34no—
423C2×C22⋊C4—34no—
424C2×C22⋊C4—34no—
425C2×C22⋊C4—34no—
426C2×C22⋊C4—34no—
427C2×C22⋊C4—34no—
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—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—121no—
444C2×C22⋊C4—121no—
445C2×C22⋊C4—121no—
446C2×C22⋊C4—121no—
447C2×C22⋊C4—121no—
448C2×C22⋊C4—121no—
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—34no—
456C2×C42—62no—
457C2×C42—62no—
458C2×C42—62no—
459C2×C42—62no—
460C2×C42—121no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—34no—
466#95—41no—
467#95—41no—
468#95—62no—
469#95—62no—
470#95—62no—
471#95—62no—
472#95—62no—
473#95—121no—
474#95—121no—
475#95—121no—
476#95—121no—
477C23×C3C23×C411yescharacteristic
478C23×C3C22×D411yescharacteristic
479C23×C3C22×D411yescharacteristic
480C23×C3C22×D411yescharacteristic
481C23×C3C2×#4111yescharacteristic
482C23×C3C2×#4111yescharacteristic
483C23×C3C2×#4111yescharacteristic
484C23×C3H(5,𝔽2)11yescharacteristic
485C23×C3H(5,𝔽2)11yescharacteristic
486C23×C3H(5,𝔽2)11yescharacteristic
487C23×C3H(5,𝔽2)11yescharacteristic
488C23×C3H(5,𝔽2)11yescharacteristic
489C23×C32−1+411yescharacteristic
490C23×C32−1+411yescharacteristic
491C23×C32−1+411yescharacteristic
492C22×D3—22no—
493C22×D3—22no—
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—41no—
518C22×D3—41no—
519C22×D3—41no—
520C22×D3—41no—
521C22×D3—41no—
522C22×D3—41no—
523C22×D3—41no—
524C22×D3—41no—
525C22×D3—41no—
526C22×D3—41no—
527C22×D3—41no—
528C22×D3—41no—
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—41no—
558C22×D3—41no—
559C22×D3—41no—
560C22×D3—41no—
561C22×D3C2×C22⋊C414yes—
562C3×Q8—416no—
563C2×C3×C4—22no—
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—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—
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×C4C2×C22⋊C414yes—
611C2×C3×C4C4×D414yes—
612C2×Dic3—22no—
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—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—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×Dic3C2×C22⋊C414yes—
654D12—416no—
655C4×D3—416no—
656C24—32no—
657C24—32no—
658C24—32no—
659C24—32no—
660C24—61no—
661C24—61no—
662C24—61no—
663C24—61no—
664C24—61no—
665C24—61no—
666C24—61no—
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—
686C24C23×D311yescharacteristic
687C2×Q8—28no—
688C2×Q8—28no—
689C2×Q8—44no—
690C2×Q8—44no—
691C2×Q8—44no—
692C2×Q8—44no—
693C2×Q8—44no—
694C2×D4—68no—
695C2×D4—68no—
696C2×D4—124no—
697C2×D4—124no—
698C2×D4—124no—
699C2×D4—124no—
700C2×D4—124no—
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—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—32no—
743C22×C4—32no—
744C22×C4—32no—
745C22×C4—32no—
746C22×C4—32no—
747C22×C4—32no—
748C22×C4—32no—
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—61no—
783C22×C4—61no—
784C22×C4—124no—
785C22×C4—124no—
786C22×C4—124no—
787C22×C4—124no—
788C22×C4—124no—
789C22×C4—124no—
790C22×C4—124no—
791C22×C4C2×C4×D312yes—
792C22×C4C2×C4×D312yes—
793C22×C4C2×C4×D312yes—
794C22×C4D3×D412yes—
795C22×C4D3×D412yes—
796C22×C4D3×D412yes—
797C22×C4#23712yes—
798C22×C4#23912yes—
799C4⋊C4—124no—
800C4⋊C4—124no—
801C4⋊C4—124no—
802C22⋊C4—316no—
803C22⋊C4—68no—
804C22⋊C4—68no—
805C22⋊C4—68no—
806C22⋊C4—124no—
807C22⋊C4—124no—
808C22⋊C4—124no—
809C22⋊C4—124no—
810C22⋊C4—124no—
811C22⋊C4—124no—
812C22⋊C4—124no—
813C42—68no—
814C42—124no—
815C22×C3C22×C22⋊C411yescharacteristic
816C22×C3C2×C4×D411yescharacteristic
817C22×C3C4×#4111yescharacteristic
818C22×C3#51811yescharacteristic
819C22×C3#52011yescharacteristic
820C22×C3#52011yescharacteristic
821C22×C3#52011yescharacteristic
822C22×C3#53511yescharacteristic
823C22×C3#53511yescharacteristic
824C22×C3#53611yescharacteristic
825C22×C3#53611yescharacteristic
826C22×C3#53711yescharacteristic
827C22×C3#53711yescharacteristic
828C22×C3#53811yescharacteristic
829C22×C3#53811yescharacteristic
830C22×C3#54211yescharacteristic
831C22×C3#54211yescharacteristic
832C22×C3#54211yescharacteristic
833C22×C3#54211yescharacteristic
834C22×C3D4211yescharacteristic
835C22×C3D4211yescharacteristic
836C22×C3#54611yescharacteristic
837C22×C3#54611yescharacteristic
838C22×C3#54611yescharacteristic
839C22×C3#54611yescharacteristic
840C22×C3#54611yescharacteristic
841C22×C3#54711yescharacteristic
842C22×C3#54711yescharacteristic
843C22×C3#54811yescharacteristic
844C22×C3#55611yescharacteristic
845C22×C3#55911yescharacteristic
846C22×C3H(3,𝔽4)11yescharacteristic
847C22×C3#56211yescharacteristic
848C22×C3#56211yescharacteristic
849C22×C3#56311yescharacteristic
850C2×D3—24no—
851C2×D3—24no—
852C2×D3—24no—
853C2×D3—42no—
854C2×D3—42no—
855C2×D3—42no—
856C2×D3—42no—
857C2×D3—42no—
858C2×D3—42no—
859C2×D3—42no—
860C2×D3—42no—
861C2×D3—42no—
862C2×D3—42no—
863C2×D3—42no—
864C2×D3—42no—
865C2×D3—42no—
866C2×D3—42no—
867C2×D3—42no—
868C2×D3—42no—
869C2×D3—42no—
870C2×D3—42no—
871C2×D3—42no—
872C2×D3—81no—
873C2×D3—81no—
874C2×D3—81no—
875C2×D3—81no—
876C2×D3—81no—
877C2×D3—81no—
878C2×D3—81no—
879C2×D3—81no—
880C3×C4—24no—
881C3×C4—24no—
882C3×C4—42no—
883C3×C4—42no—
884C3×C4—81no—
885C3×C4—81no—
886C3×C4—81no—
887Dic3—24no—
888Dic3—42no—
889Dic3—42no—
890Dic3—42no—
891Dic3—42no—
892Dic3—81no—
893C23—34no—
894C23—62no—
895C23—62no—
896C23—62no—
897C23—62no—
898C23—62no—
899C23—62no—
900C23—62no—
901C23—62no—
902C23—62no—
903C23—62no—
904C23—62no—
905C23—62no—
906C23—62no—
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—121no—
920C23—121no—
921C23—121no—
922C23—121no—
923C23—121no—
924C23—121no—
925C23—121no—
926C23—121no—
927C23—121no—
928C23—121no—
929C23—121no—
930C23—121no—
931C23—121no—
932C23—121no—
933C23—121no—
934C23—121no—
935C23—121no—
936C23—121no—
937C23—121no—
938C23—121no—
939C23—121no—
940C23—121no—
941C23—121no—
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—
963C23C22×C4×D311yescharacteristic
964C23C2×D3×D411yescharacteristic
965C23C2×D3×D411yescharacteristic
966C23C2×D3×D411yescharacteristic
967C23C2×#23711yescharacteristic
968C23#100411yescharacteristic
969C23#100411yescharacteristic
970C23C2×#23911yescharacteristic
971C23#100711yescharacteristic
972C23#100711yescharacteristic
973C23#100711yescharacteristic
974C23D3×#4111yescharacteristic
975C23#100911yescharacteristic
976C23#100911yescharacteristic
977C23#100911yescharacteristic
978Q8—416no—
979D4—1216no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
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—34no—
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—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—62no—
1029C2×C4—62no—
1030C2×C4—62no—
1031C2×C4—62no—
1032C2×C4—62no—
1033C2×C4—62no—
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—1216no—
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×C4—121no—
1065C2×C4—121no—
1066C2×C4—121no—
1067C2×C4—121no—
1068C2×C4—121no—
1069C2×C4—121no—
1070C2×C4D3×C22⋊C414yes—
1071C2×C4#67⋊C414yes—
1072C2×C3#231111yescharacteristic
1073C2×C3#232611yescharacteristic
1074C2×C3#233711yescharacteristic
1075C2×C3D4×C22⋊C411yescharacteristic
1076C2×C3#233911yescharacteristic
1077C2×C3#236711yescharacteristic
1078C2×C3#237911yescharacteristic
1079C2×C3#267011yescharacteristic
1080C2×C3#267211yescharacteristic
1081C2×C3#267411yescharacteristic
1082C2×C3#267611yescharacteristic
1083C2×C3#270011yescharacteristic
1084C2×C3#271011yescharacteristic
1085C2×C3#271211yescharacteristic
1086C2×C3#271511yescharacteristic
1087D3—44no—
1088D3—82no—
1089C22—64no—
1090C22—64no—
1091C22—64no—
1092C22—122no—
1093C22—122no—
1094C22—122no—
1095C22—122no—
1096C22—122no—
1097C22—122no—
1098C22—122no—
1099C22—122no—
1100C22—122no—
1101C22—122no—
1102C22—122no—
1103C22—122no—
1104C22—122no—
1105C22—122no—
1106C22—122no—
1107C22—122no—
1108C22—122no—
1109C22—122no—
1110C22—122no—
1111C22—241no—
1112C22—241no—
1113C22—241no—
1114C22—241no—
1115C22—241no—
1116C22—241no—
1117C22—241no—
1118C22—241no—
1119C22C2×D3×C22⋊C411yescharacteristic
1120C22C2×#67⋊C411yescharacteristic
1121C22#548611yescharacteristic
1122C22C4×#23911yescharacteristic
1123C22#557411yescharacteristic
1124C22#557411yescharacteristic
1125C22#557411yescharacteristic
1126C22#559011yescharacteristic
1127C22#559011yescharacteristic
1128C22#559111yescharacteristic
1129C22#559111yescharacteristic
1130C22#562911yescharacteristic
1131C22#562911yescharacteristic
1132C22#563011yescharacteristic
1133C22#563011yescharacteristic
1134C22#563111yescharacteristic
1135C22#563311yescharacteristic
1136C22#564011yescharacteristic
1137C22#564311yescharacteristic
1138C22#564311yescharacteristic
1139C22#564411yescharacteristic
1140C22#564711yescharacteristic
1141C22#564711yescharacteristic
1142C22#567411yescharacteristic
1143C22#567411yescharacteristic
1144C22#567611yescharacteristic
1145C22#567811yescharacteristic
1146C22#568111yescharacteristic
1147C22#568311yescharacteristic
1148C22#572411yescharacteristic
1149C22#572411yescharacteristic
1150C22#572611yescharacteristic
1151C22#573211yescharacteristic
1152C22#573311yescharacteristic
1153C22#573511yescharacteristic
1154C4—24no—
1155C4—24no—
1156C4—42no—
1157C4—42no—
1158C4—64no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C4—122no—
1163C4—122no—
1164C4—122no—
1165C4—122no—
1166C4—241no—
1167C3#1442111yescharacteristic, complemented, Sylow
1168C2—124no—
1169C2—242no—
1170C2#7385011yescharacteristic
1171C2#7648211yescharacteristic
1172C2#7648411yescharacteristic
1173C2#7648811yescharacteristic
1174C2#7649311yescharacteristic
1175C2#7649611yescharacteristic
1176C2#7661311yescharacteristic
1177C2#7682211yescharacteristic
1178C2#7682911yescharacteristic
1179C2#7687311yescharacteristic
1180C2#7688011yescharacteristic
1181C2#7721911yescharacteristic
1182C2#7725911yescharacteristic
1183C2#7726011yescharacteristic
1184C2#7726711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1446C2
socle, cosocleC24×C3C24
prime radicalC23×D12C22
hypercenter#1446D3
hypocenterC3#14421
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1446

Complements

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

NH ≅ G/Ntype
2. C2×#5229C2semidirect
4. C2×#4668C2semidirect
5. C2×#4669C2semidirect
6. C3×#1446C2semidirect
7. #69429C2semidirect
8. #69428C2semidirect
9. #69428C2semidirect
10. #69427C2semidirect
12. (C2×D3)⋊#95C2semidirect
13. #69408C2semidirect
14. Dic3⋊#95C2semidirect
15. #69401C2semidirect
22. C2×#947C4semidirect
64. #1446D3semidirect
82. C22×C3×Q8C2×C4semidirect
140. C2×(C2×D3)⋊C4C2×C4semidirect
141. C2×(C2×D3)⋊C4C2×C4semidirect
158. C2×C4×Dic3C2×C4semidirect
370. (C2×D3)⋊C4C22⋊C4semidirect
384. C22×Q8C4×D3semidirect
1167. C3#14421semidirect

Maximal subgroups

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

subgroupindex
C22×#9472
C2×#52292
C2×#46652
C2×#46682
C2×#46692
C3×#14462
#694292
#694282
#694272
#694262
(C2×D3)⋊#952
#694082
Dic3⋊#952
#694012
#144213