Finite Group Databasebeta

← #10729162

Subgroups — #10729162

Order 768.

1802 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#383C211yesmaximal, characteristic, complemented
2C2×#4940C211yesmaximal, characteristic, complemented
3C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C2×#4665C211yesmaximal, characteristic
5#69429C211yesmaximal, characteristic, complemented
6#69428C211yesmaximal, characteristic, complemented
7#69427C211yesmaximal, characteristic, complemented
8#69427C211yesmaximal, characteristic, complemented
9#69426C211yesmaximal, characteristic
10#69426C211yesmaximal, characteristic
11(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
12#69418C211yesmaximal, characteristic, complemented
13#69413C211yesmaximal, characteristic, complemented
14#69408C211yesmaximal, characteristic, complemented
15#69407C211yesmaximal, characteristic, complemented
16#14924—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C22×C3×C42C2211yescharacteristic
20C22×(C2×D3)⋊C4C2211yescharacteristic
21C22×(C2×D3)⋊C4C2211yescharacteristic
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
34C3×#383—24no—
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
52C2×C3⋊#95C2211yescharacteristic
53#4940—24no—
54C4×(C2×D3)⋊C4—24no—
55#4665—24no—
56C2×#388—31no—
57C2×#386—31no—
58C2×#383D311yescharacteristic, complemented
59C2×C4×C22⋊C4—31no—
60#1443—31no—
61#1442—31no—
62#1440—31no—
63#1439—31no—
64#1439—31no—
65#1439—31no—
66#1438—31no—
67#1438—31no—
68#1437—31no—
69#1436—31no—
70C22⋊#95—31no—
71C24×D3C2311yescharacteristic
72C24×D3C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C22×D12—22no—
87C22×D12—22no—
88C22×D12—22no—
89C22×D12—22no—
90C22×D12—22no—
91C22×D12—41no—
92C22×D12—41no—
93C22×C4×D3—22no—
94C22×C4×D3—22no—
95C22×C4×D3—22no—
96C22×C4×D3—22no—
97C22×C4×D3—22no—
98C22×C4×D3—41no—
99C22×C4×D3—41no—
100C2×C3×C42—22no—
101C2×C3×C42—22no—
102C2×C3×C42D414yescomplemented
103C2×(C2×D3)⋊C4—22no—
104C2×(C2×D3)⋊C4—22no—
105C2×(C2×D3)⋊C4—22no—
106C2×(C2×D3)⋊C4—22no—
107C2×(C2×D3)⋊C4—22no—
108C2×(C2×D3)⋊C4—22no—
109C2×(C2×D3)⋊C4—22no—
110C2×(C2×D3)⋊C4—22no—
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×C4⋊Dic3—22no—
137C2×C4⋊Dic3—41no—
138C2×C4⋊Dic3—41no—
139C2×Dic3⋊C4—22no—
140C2×Dic3⋊C4—41no—
141C2×Dic3⋊C4—41no—
142C2×C4×Dic3—22no—
143C2×C4×Dic3—41no—
144C2×C4×Dic3—41no—
145C3×#95—22no—
146C3×#95—22no—
147C3×#95—22no—
148C3×#95—22no—
149C3×#95—22no—
150C3×#95D414yes—
151C3⋊#95—22no—
152C3⋊#95—22no—
153C3⋊#95—22no—
154C3⋊#95—22no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C3⋊#95—22no—
159C3⋊#95—41no—
160C3⋊#95—41no—
161C3⋊#95—41no—
162C3⋊#95—41no—
163C23×D4—31no—
164C24×C4—31no—
165C22×C4⋊C4—31no—
166C22×C4⋊C4—31no—
167C22×C22⋊C4—31no—
168C22×C22⋊C4—31no—
169C22×C22⋊C4—31no—
170C22×C22⋊C4—31no—
171C22×C22⋊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×C42—31no—
179C22×C42C2×D311yescharacteristic
180#388—64no—
181#386—64no—
182#383—24no—
183C4×C22⋊C4—64no—
184C2×#95—31no—
185C2×#95—31no—
186C2×#95—31no—
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×#95C2×D311yescharacteristic
197C2×#95C2×D311yescharacteristic
198C2×#95C2×D311yescharacteristic
199C2×#95C2×D311yescharacteristic
200C2×#95C2×D311yescharacteristic
201C2×#95C2×D311yescharacteristic
202C24×C3C2411yescharacteristic
203C23×D3—21no—
204C23×D3—21no—
205C23×D3—21no—
206C23×D3—21no—
207C23×D3—21no—
208C23×D3—21no—
209C23×D3—21no—
210C23×D3—21no—
211C23×D3—21no—
212C23×D3—21no—
213C23×D3—21no—
214C23×D3—21no—
215C23×D3—21no—
216C23×D3—21no—
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#4112yes—
230C23×D3#4112yes—
231C23×D3#4112yes—
232C23×D3#4112yes—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
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×C4C2×D412yes—
276C22×C3×C4C2×D412yes—
277C22×C3×C4C2×D412yes—
278C22×C3×C4C2×D412yes—
279C22×C3×C4C2×D412yes—
280C22×C3×C4C2×D412yes—
281C22×C3×C4#4112yes—
282C22×Dic3—21no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—21no—
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#4112yes—
321C22×Dic3#4112yes—
322C22×Dic3#4112yes—
323C22×Dic3#4112yes—
324C2×D12—28no—
325C2×D12—44no—
326C2×D12—44no—
327C2×D12—44no—
328C2×D12—44no—
329C2×D12—44no—
330C2×D12—44no—
331C2×C4×D3—28no—
332C2×C4×D3—44no—
333C2×C4×D3—44no—
334C2×C4×D3—44no—
335C2×C4×D3—44no—
336C2×C4×D3—44no—
337C2×C4×D3—44no—
338C3×C42—28no—
339(C2×D3)⋊C4—28no—
340(C2×D3)⋊C4—28no—
341(C2×D3)⋊C4—28no—
342(C2×D3)⋊C4—44no—
343(C2×D3)⋊C4—44no—
344(C2×D3)⋊C4—44no—
345(C2×D3)⋊C4—44no—
346(C2×D3)⋊C4—44no—
347(C2×D3)⋊C4—44no—
348(C2×D3)⋊C4—44no—
349(C2×D3)⋊C4—44no—
350C4⋊Dic3—44no—
351Dic3⋊C4—44no—
352C4×Dic3—44no—
353C25—31no—
354C25—31no—
355C22×D4—62no—
356C22×D4—62no—
357C22×D4—62no—
358C22×D4—62no—
359C22×D4—62no—
360C22×D4—121no—
361C22×D4—121no—
362C23×C4—31no—
363C23×C4—31no—
364C23×C4—31no—
365C23×C4—31no—
366C23×C4—31no—
367C23×C4—31no—
368C23×C4—62no—
369C23×C4—62no—
370C23×C4—62no—
371C23×C4—62no—
372C23×C4—62no—
373C23×C4—121no—
374C23×C4—121no—
375C23×C4C22×D311yescharacteristic
376C23×C4C22×D311yescharacteristic
377C23×C4C22×D311yescharacteristic
378C23×C4C22×D311yescharacteristic
379C23×C4C22×D311yescharacteristic
380C23×C4C22×D311yescharacteristic
381C23×C4C22×D311yescharacteristic
382C2×C4⋊C4—62no—
383C2×C4⋊C4—62no—
384C2×C4⋊C4—121no—
385C2×C4⋊C4—121no—
386C2×C4⋊C4—121no—
387C2×C4⋊C4—121no—
388C2×C22⋊C4—62no—
389C2×C22⋊C4—62no—
390C2×C22⋊C4—62no—
391C2×C22⋊C4—62no—
392C2×C22⋊C4—62no—
393C2×C22⋊C4—62no—
394C2×C22⋊C4—62no—
395C2×C22⋊C4—62no—
396C2×C22⋊C4—62no—
397C2×C22⋊C4—62no—
398C2×C22⋊C4—62no—
399C2×C22⋊C4—62no—
400C2×C22⋊C4—62no—
401C2×C22⋊C4—62no—
402C2×C22⋊C4—62no—
403C2×C22⋊C4—62no—
404C2×C22⋊C4—62no—
405C2×C22⋊C4—62no—
406C2×C22⋊C4—62no—
407C2×C22⋊C4—62no—
408C2×C22⋊C4—62no—
409C2×C22⋊C4—62no—
410C2×C22⋊C4—62no—
411C2×C22⋊C4—121no—
412C2×C22⋊C4—121no—
413C2×C22⋊C4—121no—
414C2×C22⋊C4—121no—
415C2×C22⋊C4—121no—
416C2×C22⋊C4—121no—
417C2×C22⋊C4—121no—
418C2×C22⋊C4—121no—
419C2×C22⋊C4—121no—
420C2×C22⋊C4—121no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—62no—
424C2×C42—121no—
425C2×C42—121no—
426C2×C42D1214yescomplemented
427#95—22no—
428#95—22no—
429#95—22no—
430#95—22no—
431#95—22no—
432#95—62no—
433#95—62no—
434#95—62no—
435#95—62no—
436#95—62no—
437#95—62no—
438#95—62no—
439#95—62no—
440#95—121no—
441#95—121no—
442#95—121no—
443#95—121no—
444#95#6714yes—
445C23×C3C22×D411yescharacteristic
446C23×C3C22×D411yescharacteristic
447C23×C3C2×#4111yescharacteristic
448C23×C3C2×#4111yescharacteristic
449C23×C3C2×#4111yescharacteristic
450C23×C3C2×#4111yescharacteristic
451C23×C3C2×#4111yescharacteristic
452C23×C3C2×#4111yescharacteristic
453C23×C3C2×#4111yescharacteristic
454C23×C3C2×#4111yescharacteristic
455C23×C3C2×#4111yescharacteristic
456C23×C3H(5,𝔽2)11yescharacteristic
457C23×C3H(5,𝔽2)11yescharacteristic
458C23×C3H(5,𝔽2)11yescharacteristic
459C23×C3H(5,𝔽2)11yescharacteristic
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—22no—
468C22×D3—22no—
469C22×D3—22no—
470C22×D3—22no—
471C22×D3—22no—
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—22no—
478C22×D3—22no—
479C22×D3—22no—
480C22×D3—22no—
481C22×D3—22no—
482C22×D3—22no—
483C22×D3—22no—
484C22×D3—22no—
485C22×D3—41no—
486C22×D3—41no—
487C22×D3—41no—
488C22×D3—41no—
489C22×D3—41no—
490C22×D3—41no—
491C22×D3—41no—
492C22×D3—41no—
493C22×D3—41no—
494C22×D3—41no—
495C22×D3—41no—
496C22×D3—41no—
497C22×D3—41no—
498C22×D3—41no—
499C22×D3—41no—
500C22×D3—41no—
501C22×D3—41no—
502C22×D3—41no—
503C22×D3—41no—
504C22×D3—41no—
505C22×D3—41no—
506C22×D3—41no—
507C22×D3—41no—
508C22×D3—41no—
509C22×D3—41no—
510C22×D3—41no—
511C22×D3—41no—
512C22×D3—41no—
513C22×D3—41no—
514C22×D3—41no—
515C22×D3—41no—
516C22×D3—41no—
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#12614yes—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—22no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
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#12114yes—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3—22no—
585C2×Dic3—22no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—41no—
592C2×Dic3—41no—
593C2×Dic3—41no—
594C2×Dic3—41no—
595C2×Dic3—41no—
596C2×Dic3—41no—
597C2×Dic3—41no—
598C2×Dic3—41no—
599C2×Dic3—41no—
600C2×Dic3—41no—
601C2×Dic3—41no—
602C2×Dic3—41no—
603C2×Dic3—41no—
604C2×Dic3—41no—
605C2×Dic3—41no—
606C2×Dic3—41no—
607C2×Dic3—41no—
608C2×Dic3—41no—
609C2×Dic3—41no—
610C2×Dic3—41no—
611C2×Dic3—41no—
612C2×Dic3—41no—
613C2×Dic3—41no—
614C2×Dic3—41no—
615C2×Dic3—41no—
616C2×Dic3—41no—
617C2×Dic3—41no—
618C2×Dic3—41no—
619C2×Dic3—41no—
620C2×Dic3—41no—
621D12—416no—
622C4×D3—416no—
623C24—32no—
624C24—32no—
625C24—32no—
626C24—32no—
627C24—61no—
628C24—61no—
629C24—61no—
630C24—61no—
631C24—61no—
632C24—61no—
633C24—61no—
634C24—61no—
635C24—61no—
636C24—61no—
637C24—61no—
638C24—61no—
639C24—61no—
640C24—61no—
641C24—61no—
642C24—61no—
643C24—61no—
644C24—61no—
645C24—61no—
646C24—61no—
647C24—61no—
648C24—61no—
649C24—61no—
650C24—61no—
651C24—61no—
652C24—61no—
653C24C23×D311yescharacteristic
654C2×D4—68no—
655C2×D4—124no—
656C2×D4—124no—
657C2×D4—124no—
658C2×D4—124no—
659C2×D4—124no—
660C2×D4—124no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
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—32no—
704C22×C4—32no—
705C22×C4—32no—
706C22×C4—32no—
707C22×C4—68no—
708C22×C4—61no—
709C22×C4—61no—
710C22×C4—61no—
711C22×C4—61no—
712C22×C4—61no—
713C22×C4—61no—
714C22×C4—61no—
715C22×C4—61no—
716C22×C4—61no—
717C22×C4—61no—
718C22×C4—61no—
719C22×C4—61no—
720C22×C4—61no—
721C22×C4—61no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4—61no—
725C22×C4—61no—
726C22×C4—61no—
727C22×C4—61no—
728C22×C4—61no—
729C22×C4—61no—
730C22×C4—61no—
731C22×C4—61no—
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—124no—
747C22×C4—124no—
748C22×C4—124no—
749C22×C4—124no—
750C22×C4—124no—
751C22×C4—124no—
752C22×C4C2×D1212yes—
753C22×C4C2×D1212yes—
754C22×C4C2×D1212yes—
755C22×C4#23512yes—
756C22×C4C2×#6712yes—
757C22×C4C2×#6712yes—
758C22×C4C2×#6712yes—
759C4⋊C4—124no—
760C4⋊C4—124no—
761C22⋊C4—68no—
762C22⋊C4—68no—
763C22⋊C4—68no—
764C22⋊C4—124no—
765C22⋊C4—124no—
766C22⋊C4—124no—
767C22⋊C4—124no—
768C22⋊C4—124no—
769C22⋊C4—124no—
770C22⋊C4—124no—
771C22⋊C4—124no—
772C42—28no—
773C42—124no—
774C22×C3C2×#12111yescharacteristic
775C22×C3#52511yescharacteristic
776C22×C3#52511yescharacteristic
777C22×C3#52511yescharacteristic
778C22×C3#52511yescharacteristic
779C22×C3#52511yescharacteristic
780C22×C3C2×#12611yescharacteristic
781C22×C3#52911yescharacteristic
782C22×C3#52911yescharacteristic
783C22×C3#52911yescharacteristic
784C22×C3#52911yescharacteristic
785C22×C3#52911yescharacteristic
786C22×C3#53211yescharacteristic
787C22×C3#53511yescharacteristic
788C22×C3#53511yescharacteristic
789C22×C3#53811yescharacteristic
790C22×C3#53811yescharacteristic
791C22×C3#53811yescharacteristic
792C22×C3#53811yescharacteristic
793C22×C3#54611yescharacteristic
794C22×C3#54611yescharacteristic
795C22×C3#54611yescharacteristic
796C22×C3#55011yescharacteristic
797C22×C3#55111yescharacteristic
798C22×C3#55111yescharacteristic
799C22×C3#55111yescharacteristic
800C22×C3#55111yescharacteristic
801C22×C3#55111yescharacteristic
802C22×C3#55111yescharacteristic
803C22×C3#55311yescharacteristic
804C22×C3#55311yescharacteristic
805C22×C3#55311yescharacteristic
806C22×C3#55311yescharacteristic
807C22×C3#55311yescharacteristic
808C22×C3#55511yescharacteristic
809C2×D3—24no—
810C2×D3—24no—
811C2×D3—24no—
812C2×D3—42no—
813C2×D3—42no—
814C2×D3—42no—
815C2×D3—42no—
816C2×D3—42no—
817C2×D3—42no—
818C2×D3—42no—
819C2×D3—42no—
820C2×D3—42no—
821C2×D3—42no—
822C2×D3—42no—
823C2×D3—42no—
824C2×D3—42no—
825C2×D3—42no—
826C2×D3—42no—
827C2×D3—42no—
828C2×D3—42no—
829C2×D3—42no—
830C2×D3—42no—
831C2×D3—81no—
832C2×D3—81no—
833C2×D3—81no—
834C2×D3—81no—
835C2×D3—81no—
836C2×D3—81no—
837C2×D3—81no—
838C2×D3—81no—
839C3×C4—24no—
840C3×C4—42no—
841C3×C4—42no—
842C3×C4—42no—
843C3×C4—42no—
844C3×C4—81no—
845C3×C4—81no—
846Dic3—42no—
847Dic3—42no—
848Dic3—42no—
849Dic3—42no—
850Dic3—81no—
851Dic3—81no—
852C23—34no—
853C23—62no—
854C23—62no—
855C23—62no—
856C23—62no—
857C23—62no—
858C23—62no—
859C23—62no—
860C23—62no—
861C23—62no—
862C23—62no—
863C23—62no—
864C23—62no—
865C23—62no—
866C23—62no—
867C23—62no—
868C23—62no—
869C23—62no—
870C23—62no—
871C23—62no—
872C23—62no—
873C23—62no—
874C23—62no—
875C23—62no—
876C23—62no—
877C23—62no—
878C23—121no—
879C23—121no—
880C23—121no—
881C23—121no—
882C23—121no—
883C23—121no—
884C23—121no—
885C23—121no—
886C23—121no—
887C23—121no—
888C23—121no—
889C23—121no—
890C23—121no—
891C23—121no—
892C23—121no—
893C23—121no—
894C23—121no—
895C23—121no—
896C23—121no—
897C23—121no—
898C23—121no—
899C23—121no—
900C23—121no—
901C23—121no—
902C23—121no—
903C23—121no—
904C23—121no—
905C23—121no—
906C23—121no—
907C23—121no—
908C23—121no—
909C23—121no—
910C23—121no—
911C23—121no—
912C23—121no—
913C23—121no—
914C23—121no—
915C23—121no—
916C23—121no—
917C23—121no—
918C23—121no—
919C23—121no—
920C23—121no—
921C23—121no—
922C23C22×D1211yescharacteristic
923C23C2×#23511yescharacteristic
924C23D3×#4111yescharacteristic
925C23D3×#4111yescharacteristic
926C23D3×#4111yescharacteristic
927C23D3×#4111yescharacteristic
928C23D3×#4111yescharacteristic
929C23D3×#4111yescharacteristic
930C23D3×#4111yescharacteristic
931C23D3×#4111yescharacteristic
932C23#100911yescharacteristic
933C23#100911yescharacteristic
934C23#100911yescharacteristic
935C23#100911yescharacteristic
936C23C22×#6711yescharacteristic
937D4—1216no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—62no—
987C2×C4—62no—
988C2×C4—62no—
989C2×C4—62no—
990C2×C4—62no—
991C2×C4—62no—
992C2×C4—62no—
993C2×C4—62no—
994C2×C4—62no—
995C2×C4—62no—
996C2×C4—62no—
997C2×C4—62no—
998C2×C4—1216no—
999C2×C4—121no—
1000C2×C4—121no—
1001C2×C4—121no—
1002C2×C4—121no—
1003C2×C4—121no—
1004C2×C4—121no—
1005C2×C4—121no—
1006C2×C4—121no—
1007C2×C4—121no—
1008C2×C4—121no—
1009C2×C4—121no—
1010C2×C4—121no—
1011C2×C4—121no—
1012C2×C4—121no—
1013C2×C4—121no—
1014C2×C4—121no—
1015C2×C4—121no—
1016C2×C4—121no—
1017C2×C4—121no—
1018C2×C4—121no—
1019C2×C4—121no—
1020C2×C4—121no—
1021C2×C4—121no—
1022C2×C4—121no—
1023C2×C4—121no—
1024C2×C4—121no—
1025C2×C4—121no—
1026C2×C4—121no—
1027C2×C4—121no—
1028C2×C4—121no—
1029C2×C4#93014yes—
1030C2×C3#239211yescharacteristic
1031C2×C3#241111yescharacteristic
1032C2×C3#241411yescharacteristic
1033C2×C3#246711yescharacteristic
1034C2×C3#248011yescharacteristic
1035C2×C3#251011yescharacteristic
1036C2×C3#251811yescharacteristic
1037C2×C3#255411yescharacteristic
1038C2×C3#255911yescharacteristic
1039C2×C3#257211yescharacteristic
1040C2×C3#257811yescharacteristic
1041C2×C3#259811yescharacteristic
1042C2×C3#259811yescharacteristic
1043C2×C3#263111yescharacteristic
1044C2×C3#285211yescharacteristic
1045D3—44no—
1046D3—82no—
1047C22—64no—
1048C22—64no—
1049C22—64no—
1050C22—122no—
1051C22—122no—
1052C22—122no—
1053C22—122no—
1054C22—122no—
1055C22—122no—
1056C22—122no—
1057C22—122no—
1058C22—122no—
1059C22—122no—
1060C22—122no—
1061C22—122no—
1062C22—122no—
1063C22—122no—
1064C22—122no—
1065C22—122no—
1066C22—122no—
1067C22—122no—
1068C22—122no—
1069C22—241no—
1070C22—241no—
1071C22—241no—
1072C22—241no—
1073C22—241no—
1074C22—241no—
1075C22—241no—
1076C22—241no—
1077C22#552411yescharacteristic
1078C22#552411yescharacteristic
1079C22#552411yescharacteristic
1080C22#552411yescharacteristic
1081C22#552511yescharacteristic
1082C22#552511yescharacteristic
1083C22#552711yescharacteristic
1084C22#552711yescharacteristic
1085C22#552811yescharacteristic
1086C22#552811yescharacteristic
1087C22#553011yescharacteristic
1088C22#553211yescharacteristic
1089C22D3×#12611yescharacteristic
1090C22#570411yescharacteristic
1091C22#570411yescharacteristic
1092C22#570411yescharacteristic
1093C22#570411yescharacteristic
1094C22#570511yescharacteristic
1095C22#570511yescharacteristic
1096C22#570511yescharacteristic
1097C22#570511yescharacteristic
1098C22#570611yescharacteristic
1099C22#570611yescharacteristic
1100C22#570611yescharacteristic
1101C22#570911yescharacteristic
1102C22#570911yescharacteristic
1103C22#570911yescharacteristic
1104C22#570911yescharacteristic
1105C22C2×#93011yescharacteristic
1106C22#582811yescharacteristic
1107C22#582911yescharacteristic
1108C22#582911yescharacteristic
1109C22#582911yescharacteristic
1110C22#583211yescharacteristic
1111C22#583411yescharacteristic
1112C4—24no—
1113C4—42no—
1114C4—42no—
1115C4—42no—
1116C4—42no—
1117C4—81no—
1118C4—81no—
1119C4—122no—
1120C4—122no—
1121C4—122no—
1122C4—122no—
1123C4—241no—
1124C4—241no—
1125C3#1492411yescharacteristic, complemented, Sylow
1126C2—124no—
1127C2—242no—
1128C2#7426911yescharacteristic
1129C2#7430111yescharacteristic
1130C2#7430311yescharacteristic
1131C2#7430611yescharacteristic
1132C2#7430711yescharacteristic
1133C2#7430711yescharacteristic
1134C2#7430911yescharacteristic
1135C2#7431711yescharacteristic
1136C2#8227311yescharacteristic
1137C2#8227511yescharacteristic
1138C2#8227611yescharacteristic
1139C2#8308111yescharacteristic
1140C2#8310611yescharacteristic
1141C2#8310811yescharacteristic
1142C2#8310911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#383C2
prime radicalC23×D12C22
hypercenterC2×#383D3
hypocenterC3#14924
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#383

Complements

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

NH ≅ G/Ntype
1. C2×C3×#383C2semidirect
2. C2×#4940C2semidirect
3. C2×C4×(C2×D3)⋊C4C2semidirect
5. #69429C2semidirect
6. #69428C2semidirect
7. #69427C2semidirect
8. #69427C2semidirect
11. (C2×D3)⋊#95C2semidirect
12. #69418C2semidirect
13. #69413C2semidirect
14. #69408C2semidirect
15. #69407C2semidirect
58. C2×#383D3semidirect
102. C2×C3×C42D4semidirect
426. C2×C42D12semidirect
1125. C3#14924semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3832
C2×#49402
C2×C4×(C2×D3)⋊C42
C2×#46652
#694292
#694282
#694272
#694262
(C2×D3)⋊#952
#694182
#694132
#694082
#694072
#149243