Finite Group Databasebeta

← #10733155

Subgroups — #10733155

Order 768.

2142 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#897C211yesmaximal, characteristic, complemented
2C2×#4994C211yesmaximal, characteristic, complemented
3C2×#4988C211yesmaximal, characteristic
4C2×#4673C211yesmaximal, characteristic, complemented
5C2×#4665C211yesmaximal, characteristic
6C2×#4646C211yesmaximal, characteristic, complemented
7C3×#1444C211yesmaximal, characteristic, complemented
8#71570C211yesmaximal, characteristic, complemented
9#71570C211yesmaximal, characteristic, complemented
10#71565C211yesmaximal, characteristic, complemented
11#69428C211yesmaximal, characteristic, complemented
12#69427C211yesmaximal, characteristic, complemented
13#69426C211yesmaximal, characteristic
14(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
15#69407C211yesmaximal, characteristic, complemented
16#15280—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×Dic6C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊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×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×C4⋊Dic3C2211yescharacteristic
35C22×C4⋊Dic3C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C2×#897—24no—
39C2×#897—24no—
40C2×#897—24no—
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
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55#4994—24no—
56#4988—24no—
57#4673—24no—
58#4665—24no—
59#4646—24no—
60C22×C22⋊Q8—31no—
61C2×#396—31no—
62C2×#393—31no—
63C2×#391—31no—
64C2×#390—31no—
65C2×#386—31no—
66#1444D311yescharacteristic, complemented
67#1441—31no—
68#1439—31no—
69#1439—31no—
70#1439—31no—
71#1439—31no—
72#1438—31no—
73#1436—31no—
74C22⋊#95—31no—
75C24×D3C2311yescharacteristic
76C24×D3C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C22×D12—22no—
91C22×D12—22no—
92C22×D12—22no—
93C22×D12—22no—
94C22×D12—41no—
95C22×D12—41no—
96C22×D12Q814yescomplemented
97C22×C4×D3—22no—
98C22×C4×D3—22no—
99C22×C4×D3—22no—
100C22×C4×D3—22no—
101C22×C4×D3—22no—
102C22×C4×D3—41no—
103C22×C4×D3—41no—
104C22×Dic6—22no—
105C22×Dic6—22no—
106C22×Dic6—22no—
107C22×Dic6—22no—
108C22×Dic6—41no—
109C22×Dic6—41no—
110C22×Dic6D414yescomplemented
111C2×C3×C4⋊C4—22no—
112C2×C3×C4⋊C4—22no—
113C2×C3×C4⋊C4—22no—
114C2×C3×C4⋊C4—22no—
115C2×C3×C4⋊C4—22no—
116C2×C3×C4⋊C4—22no—
117C2×C3×C4⋊C4—41no—
118C2×C3×C4⋊C4—41no—
119C2×C3×C4⋊C4—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—22no—
137C2×(C2×D3)⋊C4—22no—
138C2×(C2×D3)⋊C4—22no—
139C2×(C2×D3)⋊C4—22no—
140C2×(C2×D3)⋊C4—22no—
141C2×(C2×D3)⋊C4—22no—
142C2×(C2×D3)⋊C4—41no—
143C2×(C2×D3)⋊C4—41no—
144C2×(C2×D3)⋊C4—41no—
145C2×(C2×D3)⋊C4—41no—
146C2×(C2×D3)⋊C4—41no—
147C2×(C2×D3)⋊C4—41no—
148C2×(C2×D3)⋊C4—41no—
149C2×(C2×D3)⋊C4—41no—
150C2×(C2×D3)⋊C4—41no—
151C2×(C2×D3)⋊C4—41no—
152C2×(C2×D3)⋊C4D414yes—
153C2×C4⋊Dic3—22no—
154C2×C4⋊Dic3—22no—
155C2×C4⋊Dic3—22no—
156C2×C4⋊Dic3—22no—
157C2×C4⋊Dic3—22no—
158C2×C4⋊Dic3D414yescomplemented
159C2×Dic3⋊C4—22no—
160C2×Dic3⋊C4—22no—
161C2×Dic3⋊C4—41no—
162C2×C4×Dic3—22no—
163C2×C4×Dic3—22no—
164C2×C4×Dic3—41no—
165#897—232no—
166C3×#95—22no—
167C3×#95—22no—
168C3×#95—41no—
169C3×#95D414yes—
170C3⋊#95—22no—
171C3⋊#95—22no—
172C3⋊#95—22no—
173C3⋊#95—22no—
174C3⋊#95—22no—
175C3⋊#95—22no—
176C3⋊#95—22no—
177C3⋊#95—22no—
178C3⋊#95—41no—
179C3⋊#95—41no—
180C23×Q8—31no—
181C23×D4—31no—
182C24×C4—31no—
183C2×C22⋊Q8—64no—
184C2×C22⋊Q8—64no—
185C2×C22⋊Q8—64no—
186C22×C4⋊C4—31no—
187C22×C4⋊C4—31no—
188C22×C4⋊C4—31no—
189C22×C4⋊C4C2×D311yescharacteristic
190C22×C4⋊C4C2×D311yescharacteristic
191C22×C4⋊C4C2×D311yescharacteristic
192C22×C22⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4—31no—
200C22×C22⋊C4—31no—
201C22×C22⋊C4—31no—
202C22×C22⋊C4—31no—
203C22×C42—31no—
204#396—64no—
205#393—64no—
206#391—64no—
207#390—64no—
208#386—64no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95—31no—
218C2×#95—31no—
219C2×#95C2×D311yescharacteristic
220C2×#95C2×D311yescharacteristic
221C2×#95C2×D311yescharacteristic
222C2×#95C2×D311yescharacteristic
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×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×D3—21no—
245C23×D3—21no—
246C23×D3—21no—
247C23×D3—21no—
248C23×D3—21no—
249C23×D3—21no—
250C23×D3C2×D412yes—
251C23×D3C2×Q812yes—
252C23×D3C2×Q812yes—
253C23×D3#4112yes—
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×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×C4C2×D412yes—
295C22×C3×C4C2×D412yes—
296C22×C3×C4C2×D412yes—
297C22×C3×C4C2×D412yes—
298C22×C3×C4C2×D412yes—
299C22×C3×C4C2×D412yes—
300C22×C3×C4C2×Q812yes—
301C22×C3×C4#4112yes—
302C22×C3×C4#4112yes—
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×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3C2×D412yes—
340C22×Dic3C2×D412yes—
341C22×Dic3C2×D412yes—
342C22×Dic3C2×D412yes—
343C22×Dic3C2×D412yes—
344C22×Dic3#4112yes—
345C2×D12—28no—
346C2×D12—28no—
347C2×D12—44no—
348C2×D12—44no—
349C2×D12—44no—
350C2×D12—44no—
351C2×D12—44no—
352C2×C4×D3—28no—
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×Dic6—28no—
360C2×Dic6—28no—
361C2×Dic6—44no—
362C2×Dic6—44no—
363C2×Dic6—44no—
364C2×Dic6—44no—
365C2×Dic6—44no—
366C3×C4⋊C4—28no—
367C3×C4⋊C4—44no—
368C3×C4⋊C4—44no—
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—
376(C2×D3)⋊C4—44no—
377(C2×D3)⋊C4—44no—
378(C2×D3)⋊C4—44no—
379(C2×D3)⋊C4—44no—
380C4⋊Dic3—28no—
381C4⋊Dic3—28no—
382Dic3⋊C4—44no—
383C4×Dic3—44no—
384C25—31no—
385C25—31no—
386C22×Q8—34no—
387C22×Q8—62no—
388C22×Q8—62no—
389C22×Q8—62no—
390C22×Q8—62no—
391C22×Q8—121no—
392C22×Q8—121no—
393C22×D4—34no—
394C22×D4—62no—
395C22×D4—62no—
396C22×D4—62no—
397C22×D4—62no—
398C22×D4—121no—
399C22×D4—121no—
400C23×C4—31no—
401C23×C4—31no—
402C23×C4—31no—
403C23×C4—31no—
404C23×C4—31no—
405C23×C4—31no—
406C23×C4—62no—
407C23×C4—62no—
408C23×C4—62no—
409C23×C4—62no—
410C23×C4—62no—
411C23×C4—121no—
412C23×C4—121no—
413C23×C4C22×D311yescharacteristic
414C23×C4C22×D311yescharacteristic
415C23×C4C22×D311yescharacteristic
416C23×C4C22×D311yescharacteristic
417C23×C4C22×D311yescharacteristic
418C23×C4C22×D311yescharacteristic
419C23×C4C22×D311yescharacteristic
420C22⋊Q8—632no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—34no—
428C2×C4⋊C4—41no—
429C2×C4⋊C4—41no—
430C2×C4⋊C4—41no—
431C2×C4⋊C4—62no—
432C2×C4⋊C4—62no—
433C2×C4⋊C4—62no—
434C2×C4⋊C4—62no—
435C2×C4⋊C4—62no—
436C2×C4⋊C4—62no—
437C2×C4⋊C4—62no—
438C2×C4⋊C4—121no—
439C2×C22⋊C4—34no—
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—62no—
450C2×C22⋊C4—62no—
451C2×C22⋊C4—62no—
452C2×C22⋊C4—62no—
453C2×C22⋊C4—62no—
454C2×C22⋊C4—62no—
455C2×C22⋊C4—62no—
456C2×C22⋊C4—62no—
457C2×C22⋊C4—62no—
458C2×C22⋊C4—62no—
459C2×C22⋊C4—62no—
460C2×C22⋊C4—62no—
461C2×C22⋊C4—62no—
462C2×C22⋊C4—121no—
463C2×C22⋊C4—121no—
464C2×C22⋊C4—121no—
465C2×C22⋊C4—121no—
466C2×C22⋊C4—121no—
467C2×C22⋊C4—121no—
468C2×C22⋊C4—121no—
469C2×C22⋊C4—121no—
470C2×C22⋊C4—121no—
471C2×C22⋊C4—121no—
472C2×C42—62no—
473C2×C42—62no—
474C2×C42—121no—
475#95—22no—
476#95—22no—
477#95—41no—
478#95—62no—
479#95—62no—
480#95—62no—
481#95—62no—
482#95—62no—
483#95—62no—
484#95—62no—
485#95—62no—
486#95—121no—
487#95—121no—
488#95D1214yes—
489C23×C3C22×D411yescharacteristic
490C23×C3C22×D411yescharacteristic
491C23×C3C22×D411yescharacteristic
492C23×C3C22×D411yescharacteristic
493C23×C3C22×Q811yescharacteristic
494C23×C3C2×#4111yescharacteristic
495C23×C3C2×#4111yescharacteristic
496C23×C3C2×#4111yescharacteristic
497C23×C3C2×#4111yescharacteristic
498C23×C3H(5,𝔽2)11yescharacteristic
499C23×C3H(5,𝔽2)11yescharacteristic
500C23×C3H(5,𝔽2)11yescharacteristic
501C23×C3H(5,𝔽2)11yescharacteristic
502C23×C32−1+411yescharacteristic
503C23×C32−1+411yescharacteristic
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—41no—
558C22×D3—41no—
559C22×D3—41no—
560C22×D3—41no—
561C22×D3—41no—
562C22×D3—41no—
563C22×D3—41no—
564C22×D3—41no—
565C22×D3—41no—
566C22×D3—41no—
567C22×D3—41no—
568C22×D3—41no—
569C22×D3—41no—
570C22×D3—41no—
571C22×D3—41no—
572C22×D3—41no—
573C22×D3C22⋊Q814yes—
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—22no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
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×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—41no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4#12114yes—
622C2×C3×C4C22⋊Q814yescomplemented
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—22no—
632C2×Dic3—22no—
633C2×Dic3—22no—
634C2×Dic3—22no—
635C2×Dic3—22no—
636C2×Dic3—22no—
637C2×Dic3—22no—
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—
655C2×Dic3—41no—
656C2×Dic3—41no—
657C2×Dic3—41no—
658C2×Dic3—41no—
659C2×Dic3—41no—
660C2×Dic3—41no—
661C2×Dic3—41no—
662C2×Dic3—41no—
663C2×Dic3—41no—
664C2×Dic3#12014yes—
665D12—416no—
666C4×D3—416no—
667Dic6—416no—
668C24—32no—
669C24—32no—
670C24—32no—
671C24—32no—
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—
689C24—61no—
690C24—61no—
691C24—61no—
692C24—61no—
693C24—61no—
694C24—61no—
695C24—61no—
696C24—61no—
697C24—61no—
698C24C23×D311yescharacteristic
699C2×Q8—68no—
700C2×Q8—68no—
701C2×Q8—124no—
702C2×Q8—124no—
703C2×Q8—124no—
704C2×Q8—124no—
705C2×Q8—124no—
706C2×D4—68no—
707C2×D4—68no—
708C2×D4—124no—
709C2×D4—124no—
710C2×D4—124no—
711C2×D4—124no—
712C2×D4—124no—
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—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—32no—
754C22×C4—32no—
755C22×C4—32no—
756C22×C4—32no—
757C22×C4—32no—
758C22×C4—32no—
759C22×C4—68no—
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—61no—
785C22×C4—61no—
786C22×C4—61no—
787C22×C4—61no—
788C22×C4—61no—
789C22×C4—61no—
790C22×C4—61no—
791C22×C4—61no—
792C22×C4—61no—
793C22×C4—61no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—124no—
797C22×C4—124no—
798C22×C4—124no—
799C22×C4—124no—
800C22×C4—124no—
801C22×C4—124no—
802C22×C4C2×D1212yes—
803C22×C4C2×D1212yes—
804C22×C4C2×D1212yes—
805C22×C4D3×D412yes—
806C22×C4D3×D412yes—
807C22×C4D3×D412yes—
808C22×C4#23712yes—
809C22×C4D3×Q812yes—
810C22×C4#23912yes—
811C4⋊C4—28no—
812C4⋊C4—44no—
813C4⋊C4—44no—
814C4⋊C4—68no—
815C4⋊C4—68no—
816C4⋊C4—124no—
817C22⋊C4—68no—
818C22⋊C4—68no—
819C22⋊C4—124no—
820C22⋊C4—124no—
821C22⋊C4—124no—
822C22⋊C4—124no—
823C22⋊C4—124no—
824C22⋊C4—124no—
825C22⋊C4—124no—
826C22⋊C4—124no—
827C22⋊C4—124no—
828C42—124no—
829C22×C3C2×#12011yescharacteristic
830C22×C3C2×#12111yescharacteristic
831C22×C3C2×C22⋊Q811yescharacteristic
832C22×C3C2×C22⋊Q811yescharacteristic
833C22×C3#52911yescharacteristic
834C22×C3#53211yescharacteristic
835C22×C3#53411yescharacteristic
836C22×C3#53511yescharacteristic
837C22×C3#53611yescharacteristic
838C22×C3#53711yescharacteristic
839C22×C3#53811yescharacteristic
840C22×C3#53911yescharacteristic
841C22×C3#54211yescharacteristic
842C22×C3#54211yescharacteristic
843C22×C3#54311yescharacteristic
844C22×C3D4211yescharacteristic
845C22×C3D4211yescharacteristic
846C22×C3#54611yescharacteristic
847C22×C3#54611yescharacteristic
848C22×C3#54611yescharacteristic
849C22×C3#54611yescharacteristic
850C22×C3#54611yescharacteristic
851C22×C3#54811yescharacteristic
852C22×C3#54811yescharacteristic
853C22×C3#54811yescharacteristic
854C22×C3D4×Q811yescharacteristic
855C22×C3D4×Q811yescharacteristic
856C22×C3#55011yescharacteristic
857C22×C3#55011yescharacteristic
858C22×C3#55111yescharacteristic
859C22×C3#55411yescharacteristic
860C22×C3#55411yescharacteristic
861C22×C3#55611yescharacteristic
862C22×C3#56211yescharacteristic
863C22×C3#56211yescharacteristic
864C2×D3—24no—
865C2×D3—24no—
866C2×D3—24no—
867C2×D3—42no—
868C2×D3—42no—
869C2×D3—42no—
870C2×D3—42no—
871C2×D3—42no—
872C2×D3—42no—
873C2×D3—42no—
874C2×D3—42no—
875C2×D3—42no—
876C2×D3—42no—
877C2×D3—42no—
878C2×D3—42no—
879C2×D3—42no—
880C2×D3—42no—
881C2×D3—42no—
882C2×D3—42no—
883C2×D3—42no—
884C2×D3—42no—
885C2×D3—42no—
886C2×D3—81no—
887C2×D3—81no—
888C2×D3—81no—
889C2×D3—81no—
890C2×D3—81no—
891C2×D3—81no—
892C2×D3—81no—
893C2×D3—81no—
894C3×C4—24no—
895C3×C4—24no—
896C3×C4—42no—
897C3×C4—42no—
898C3×C4—42no—
899C3×C4—81no—
900C3×C4—81no—
901Dic3—24no—
902Dic3—42no—
903Dic3—42no—
904Dic3—42no—
905Dic3—81no—
906Dic3—81no—
907C23—34no—
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—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—
963C23—121no—
964C23—121no—
965C23—121no—
966C23—121no—
967C23—121no—
968C23—121no—
969C23—121no—
970C23—121no—
971C23—121no—
972C23—121no—
973C23—121no—
974C23—121no—
975C23—121no—
976C23—121no—
977C23C22×D1211yescharacteristic
978C23C2×D3×D411yescharacteristic
979C23C2×D3×D411yescharacteristic
980C23C2×D3×D411yescharacteristic
981C23C2×#23711yescharacteristic
982C23#100411yescharacteristic
983C23#100411yescharacteristic
984C23C2×D3×Q811yescharacteristic
985C23C2×#23911yescharacteristic
986C23#100711yescharacteristic
987C23#100711yescharacteristic
988C23D3×#4111yescharacteristic
989C23D3×#4111yescharacteristic
990C23#100911yescharacteristic
991C23#100911yescharacteristic
992Q8—1216no—
993D4—1216no—
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—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—34no—
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—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
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—62no—
1053C2×C4—62no—
1054C2×C4—62no—
1055C2×C4—62no—
1056C2×C4—62no—
1057C2×C4—1216no—
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×C4—121no—
1080C2×C4—121no—
1081C2×C4—121no—
1082C2×C4—121no—
1083C2×C4—121no—
1084C2×C4#89514yes—
1085C2×C4#89714yescomplemented
1086C2×C3#240911yescharacteristic
1087C2×C3#241011yescharacteristic
1088C2×C3#242611yescharacteristic
1089C2×C3#243111yescharacteristic
1090C2×C3#243711yescharacteristic
1091C2×C3#245011yescharacteristic
1092C2×C3#245211yescharacteristic
1093C2×C3#253811yescharacteristic
1094C2×C3#256011yescharacteristic
1095C2×C3#267611yescharacteristic
1096C2×C3#268111yescharacteristic
1097C2×C3#269211yescharacteristic
1098C2×C3#270011yescharacteristic
1099C2×C3#273011yescharacteristic
1100C2×C3#273211yescharacteristic
1101D3—44no—
1102D3—82no—
1103C22—64no—
1104C22—64no—
1105C22—64no—
1106C22—122no—
1107C22—122no—
1108C22—122no—
1109C22—122no—
1110C22—122no—
1111C22—122no—
1112C22—122no—
1113C22—122no—
1114C22—122no—
1115C22—122no—
1116C22—122no—
1117C22—122no—
1118C22—122no—
1119C22—122no—
1120C22—122no—
1121C22—122no—
1122C22—122no—
1123C22—122no—
1124C22—122no—
1125C22—241no—
1126C22—241no—
1127C22—241no—
1128C22—241no—
1129C22—241no—
1130C22—241no—
1131C22—241no—
1132C22—241no—
1133C22C2×#89511yescharacteristic
1134C22C2×#89711yescharacteristic
1135C22#551011yescharacteristic
1136C22D4×D1211yescharacteristic
1137C22D4×D1211yescharacteristic
1138C22#555411yescharacteristic
1139C22#557611yescharacteristic
1140C22D3×#12011yescharacteristic
1141C22#559111yescharacteristic
1142C22#559211yescharacteristic
1143C22#559611yescharacteristic
1144C22#559911yescharacteristic
1145C22#561011yescharacteristic
1146C22D3×C22⋊Q811yescharacteristic
1147C22#563011yescharacteristic
1148C22#563011yescharacteristic
1149C22#563311yescharacteristic
1150C22#563311yescharacteristic
1151C22#563411yescharacteristic
1152C22#564311yescharacteristic
1153C22#564711yescharacteristic
1154C22#564711yescharacteristic
1155C22#565311yescharacteristic
1156C22#565711yescharacteristic
1157C22#565811yescharacteristic
1158C22#569011yescharacteristic
1159C22#569111yescharacteristic
1160C22#569211yescharacteristic
1161C22#571811yescharacteristic
1162C22#572411yescharacteristic
1163C22#572711yescharacteristic
1164C22#572711yescharacteristic
1165C22#573011yescharacteristic
1166C22#573211yescharacteristic
1167C22#573311yescharacteristic
1168C4—24no—
1169C4—24no—
1170C4—42no—
1171C4—42no—
1172C4—42no—
1173C4—64no—
1174C4—81no—
1175C4—81no—
1176C4—122no—
1177C4—122no—
1178C4—122no—
1179C4—241no—
1180C4—241no—
1181C3#1528011yescharacteristic, complemented, Sylow
1182C2—124no—
1183C2—242no—
1184C2#7436911yescharacteristic
1185C2#7441311yescharacteristic
1186C2#7450911yescharacteristic
1187C2#7460111yescharacteristic
1188C2#7601111yescharacteristic
1189C2#7621811yescharacteristic
1190C2#7625911yescharacteristic
1191C2#7667211yescharacteristic
1192C2#7717211yescharacteristic
1193C2#7721511yescharacteristic
1194C2#7726711yescharacteristic
1195C2#7779111yescharacteristic
1196C2#7795311yescharacteristic
1197C2#7798611yescharacteristic
1198C2#7807311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1444C2
prime radicalC23×D12C22
hypercenter#1444D3
hypocenterC3#15280
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
1. C22×#897C2semidirect
2. C2×#4994C2semidirect
4. C2×#4673C2semidirect
6. C2×#4646C2semidirect
7. C3×#1444C2semidirect
8. #71570C2semidirect
9. #71570C2semidirect
10. #71565C2semidirect
11. #69428C2semidirect
12. #69427C2semidirect
14. (C2×D3)⋊#95C2semidirect
15. #69407C2semidirect
66. #1444D3semidirect
96. C22×D12Q8semidirect
110. C22×Dic6D4semidirect
158. C2×C4⋊Dic3D4semidirect
622. C2×C3×C4C22⋊Q8semidirect
1085. C2×C4#897semidirect
1181. C3#15280semidirect

Maximal subgroups

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

subgroupindex
C22×#8972
C2×#49942
C2×#49882
C2×#46732
C2×#46652
C2×#46462
C3×#14442
#715702
#715652
#694282
#694272
#694262
(C2×D3)⋊#952
#694072
#152803