Finite Group Databasebeta

← #10733150

Subgroups — #10733150

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×#896C211yesmaximal, characteristic, complemented
2C2×C3×#396C211yesmaximal, characteristic, complemented
3C2×#4973C211yesmaximal, characteristic, complemented
4C2×#4956C211yesmaximal, characteristic
5C2×#4947C211yesmaximal, characteristic, complemented
6C2×#4957C211yesmaximal, characteristic
7#71570C211yesmaximal, characteristic, complemented
8#71570C211yesmaximal, characteristic, complemented
9#71568C211yesmaximal, characteristic, complemented
10#71564C211yesmaximal, characteristic, complemented
11#71550C211yesmaximal, characteristic
12#71547C211yesmaximal, characteristic, complemented
13#71547C211yesmaximal, characteristic, complemented
14(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
15#69409C211yesmaximal, characteristic, complemented
16#15280—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×Dic6C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C2×#896—24no—
39C2×#896—24no—
40C2×#896—24no—
41C3×#396—24no—
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
55C2×C3⋊#95C2211yescharacteristic
56#4973—24no—
57#4957—24no—
58#4956—24no—
59#4947—24no—
60C22×C22⋊Q8—31no—
61C2×#396D311yescharacteristic, complemented
62C2×#393—31no—
63C2×#391—31no—
64C2×#390—31no—
65C2×#386—31no—
66#1444—31no—
67#1441—31no—
68#1439—31no—
69#1439—31no—
70#1439—31no—
71#1439—31no—
72#1438—31no—
73#1436—31no—
74C22⋊#95—31no—
75C25×C3C2311yescharacteristic
76C24×D3C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67—22no—
84C22×#67—22no—
85C22×#67—22no—
86C22×#67—22no—
87C22×#67—41no—
88C22×#67—41no—
89C22×#67Q814yescomplemented
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
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—41no—
117C2×C3×C4⋊C4—41no—
118C2×C3×C4⋊C4—41no—
119C2×C3×C4⋊C4D414yescomplemented
120C2×C3×C22⋊C4—22no—
121C2×C3×C22⋊C4—22no—
122C2×C3×C22⋊C4—22no—
123C2×C3×C22⋊C4—22no—
124C2×C3×C22⋊C4—22no—
125C2×C3×C22⋊C4—22no—
126C2×C3×C22⋊C4—41no—
127C2×C3×C22⋊C4—41no—
128C2×C3×C22⋊C4—41no—
129C2×#217—22no—
130C2×#217—22no—
131C2×#217—22no—
132C2×#217—22no—
133C2×#217—22no—
134C2×#217—22no—
135C2×#217—41no—
136C2×#217—41no—
137C2×#217—41no—
138C2×(C2×D3)⋊C4—22no—
139C2×(C2×D3)⋊C4—22no—
140C2×(C2×D3)⋊C4—22no—
141C2×(C2×D3)⋊C4—22no—
142C2×(C2×D3)⋊C4—22no—
143C2×(C2×D3)⋊C4—22no—
144C2×(C2×D3)⋊C4—22no—
145C2×(C2×D3)⋊C4—22no—
146C2×(C2×D3)⋊C4—22no—
147C2×(C2×D3)⋊C4—22no—
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×Dic3⋊C4—22no—
154C2×Dic3⋊C4—22no—
155C2×Dic3⋊C4—22no—
156C2×Dic3⋊C4—22no—
157C2×Dic3⋊C4—22no—
158C2×Dic3⋊C4—22no—
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#896—232no—
166C3×#95—22no—
167C3⋊#95—22no—
168C3⋊#95—22no—
169C3⋊#95—22no—
170C3⋊#95—22no—
171C3⋊#95—22no—
172C3⋊#95—22no—
173C3⋊#95—22no—
174C3⋊#95—22no—
175C3⋊#95—22no—
176C3⋊#95—41no—
177C3⋊#95—41no—
178C3⋊#95—41no—
179C3⋊#95D414yes—
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⋊C4C2×D311yescharacteristic
201C22×C22⋊C4C2×D311yescharacteristic
202C22×C22⋊C4C2×D311yescharacteristic
203C22×C42—31no—
204#396—24no—
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×#95—31no—
220C2×#95—31no—
221C2×#95—31no—
222C2×#95C2×D311yescharacteristic
223C24×C3—21no—
224C24×C3—21no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3—21no—
228C24×C3—21no—
229C24×C3—21no—
230C24×C3—21no—
231C24×C3—21no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—21no—
236C24×C3—21no—
237C24×C3C2×Q812yes—
238C24×C3C2411yescharacteristic
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×D3—21no—
251C23×D3C2×D412yes—
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×C4C2×D412yes—
291C22×C3×C4C2×D412yes—
292C22×C3×C4C2×D412yes—
293C22×C3×C4C2×D412yes—
294C22×C3×C4C2×D412yes—
295C22×C3×C4C2×D412yes—
296C2×#67—28no—
297C2×#67—28no—
298C2×#67—44no—
299C2×#67—44no—
300C2×#67—44no—
301C2×#67—44no—
302C2×#67—44no—
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×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3—21no—
342C22×Dic3—21no—
343C22×Dic3C2×D412yes—
344C22×Dic3C2×D412yes—
345C22×Dic3C2×D412yes—
346C22×Dic3C2×D412yes—
347C22×Dic3C2×D412yes—
348C22×Dic3C2×Q812yes—
349C22×Dic3#4112yes—
350C22×Dic3#4112yes—
351C22×Dic3#4112yes—
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—
369C3×C22⋊C4—44no—
370C3×C22⋊C4—44no—
371C3×C22⋊C4—44no—
372#217—44no—
373#217—44no—
374#217—44no—
375(C2×D3)⋊C4—28no—
376(C2×D3)⋊C4—28no—
377(C2×D3)⋊C4—44no—
378(C2×D3)⋊C4—44no—
379(C2×D3)⋊C4—44no—
380Dic3⋊C4—28no—
381Dic3⋊C4—28no—
382Dic3⋊C4—44no—
383C4×Dic3—44no—
384C25—31no—
385C25C22×D311yescharacteristic
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—31no—
407C23×C4—62no—
408C23×C4—62no—
409C23×C4—62no—
410C23×C4—62no—
411C23×C4—62no—
412C23×C4—121no—
413C23×C4—121no—
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—41no—
427C2×C4⋊C4—41no—
428C2×C4⋊C4—41no—
429C2×C4⋊C4—62no—
430C2×C4⋊C4—62no—
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—121no—
438C2×C4⋊C4#6714yescomplemented
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—34no—
446C2×C22⋊C4—41no—
447C2×C22⋊C4—41no—
448C2×C22⋊C4—41no—
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—62no—
463C2×C22⋊C4—62no—
464C2×C22⋊C4—62no—
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—34no—
477#95—62no—
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#95—121no—
489C23×C3—22no—
490C23×C3—22no—
491C23×C3—22no—
492C23×C3—22no—
493C23×C3—22no—
494C23×C3—22no—
495C23×C3—22no—
496C23×C3—41no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—41no—
500C23×C3—41no—
501C23×C3—41no—
502C23×C3—41no—
503C23×C3—41no—
504C23×C3—41no—
505C23×C3—41no—
506C23×C3—41no—
507C23×C3—41no—
508C23×C3—41no—
509C23×C3—41no—
510C23×C3—41no—
511C23×C3—41no—
512C23×C3—41no—
513C23×C3—41no—
514C23×C3—41no—
515C23×C3—41no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3C22×D411yescharacteristic
525C23×C3C22×D411yescharacteristic
526C23×C3C22×D411yescharacteristic
527C23×C3C22×D411yescharacteristic
528C23×C3C22×Q811yescharacteristic
529C23×C3C2×#4111yescharacteristic
530C23×C3C2×#4111yescharacteristic
531C23×C3C2×#4111yescharacteristic
532C23×C3C2×#4111yescharacteristic
533C23×C3H(5,𝔽2)11yescharacteristic
534C23×C3H(5,𝔽2)11yescharacteristic
535C23×C3H(5,𝔽2)11yescharacteristic
536C23×C3H(5,𝔽2)11yescharacteristic
537C23×C32−1+411yescharacteristic
538C23×C32−1+411yescharacteristic
539C22×D3—22no—
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—22no—
543C22×D3—22no—
544C22×D3—22no—
545C22×D3—22no—
546C22×D3—22no—
547C22×D3—22no—
548C22×D3—22no—
549C22×D3—22no—
550C22×D3—22no—
551C22×D3—22no—
552C22×D3—22no—
553C22×D3—22no—
554C22×D3—22no—
555C22×D3—22no—
556C22×D3—22no—
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—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×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4#12014yes—
616#67—416no—
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—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#12114yes—
665C2×Dic3C22⋊Q814yescomplemented
666C4×D3—416no—
667Dic6—416no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—32no—
683C24—32no—
684C24—32no—
685C24—61no—
686C24—61no—
687C24—61no—
688C24—61no—
689C24—61no—
690C24—61no—
691C24—61no—
692C24—61no—
693C24—61no—
694C24—61no—
695C24—61no—
696C24—61no—
697C24D3×Q812yes—
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—32no—
750C22×C4—32no—
751C22×C4—32no—
752C22×C4—32no—
753C22×C4—32no—
754C22×C4—32no—
755C22×C4—32no—
756C22×C4—32no—
757C22×C4—32no—
758C22×C4—68no—
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—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—61no—
797C22×C4—61no—
798C22×C4—61no—
799C22×C4—124no—
800C22×C4—124no—
801C22×C4—124no—
802C22×C4—124no—
803C22×C4—124no—
804C22×C4—124no—
805C22×C4D3×D412yes—
806C22×C4D3×D412yes—
807C22×C4D3×D412yes—
808C22×C4C2×#6712yes—
809C22×C4C2×#6712yes—
810C22×C4C2×#6712yes—
811C4⋊C4—28no—
812C4⋊C4—44no—
813C4⋊C4—44no—
814C4⋊C4—68no—
815C4⋊C4—68no—
816C4⋊C4—124no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—44no—
820C22⋊C4—68no—
821C22⋊C4—68no—
822C22⋊C4—124no—
823C22⋊C4—124no—
824C22⋊C4—124no—
825C22⋊C4—124no—
826C22⋊C4—124no—
827C22⋊C4—124no—
828C42—124no—
829C22×C3—42no—
830C22×C3—42no—
831C22×C3—42no—
832C22×C3—42no—
833C22×C3—42no—
834C22×C3—42no—
835C22×C3—42no—
836C22×C3—81no—
837C22×C3—81no—
838C22×C3—81no—
839C22×C3—81no—
840C22×C3—81no—
841C22×C3—81no—
842C22×C3—81no—
843C22×C3—81no—
844C22×C3C2×#12011yescharacteristic
845C22×C3C2×#12111yescharacteristic
846C22×C3C2×C22⋊Q811yescharacteristic
847C22×C3C2×C22⋊Q811yescharacteristic
848C22×C3#52911yescharacteristic
849C22×C3#53211yescharacteristic
850C22×C3#53411yescharacteristic
851C22×C3#53511yescharacteristic
852C22×C3#53611yescharacteristic
853C22×C3#53711yescharacteristic
854C22×C3#53811yescharacteristic
855C22×C3#53911yescharacteristic
856C22×C3#54211yescharacteristic
857C22×C3#54211yescharacteristic
858C22×C3#54311yescharacteristic
859C22×C3D4211yescharacteristic
860C22×C3D4211yescharacteristic
861C22×C3#54611yescharacteristic
862C22×C3#54611yescharacteristic
863C22×C3#54611yescharacteristic
864C22×C3#54611yescharacteristic
865C22×C3#54611yescharacteristic
866C22×C3#54811yescharacteristic
867C22×C3#54811yescharacteristic
868C22×C3#54811yescharacteristic
869C22×C3D4×Q811yescharacteristic
870C22×C3D4×Q811yescharacteristic
871C22×C3#55011yescharacteristic
872C22×C3#55011yescharacteristic
873C22×C3#55111yescharacteristic
874C22×C3#55411yescharacteristic
875C22×C3#55411yescharacteristic
876C22×C3#55611yescharacteristic
877C22×C3#56211yescharacteristic
878C22×C3#56211yescharacteristic
879C2×D3—24no—
880C2×D3—24no—
881C2×D3—24no—
882C2×D3—42no—
883C2×D3—42no—
884C2×D3—42no—
885C2×D3—42no—
886C2×D3—42no—
887C2×D3—42no—
888C2×D3—42no—
889C2×D3—42no—
890C2×D3—42no—
891C2×D3—42no—
892C2×D3—42no—
893C2×D3—42no—
894C3×C4—24no—
895C3×C4—42no—
896C3×C4—42no—
897C3×C4—42no—
898C3×C4—81no—
899C3×C4—81no—
900Dic3—24no—
901Dic3—24no—
902Dic3—42no—
903Dic3—42no—
904Dic3—42no—
905Dic3—81no—
906Dic3—81no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—34no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—62no—
944C23—62no—
945C23—62no—
946C23—62no—
947C23—62no—
948C23—62no—
949C23—62no—
950C23—62no—
951C23—62no—
952C23—62no—
953C23—62no—
954C23—62no—
955C23—62no—
956C23—62no—
957C23—62no—
958C23—62no—
959C23—62no—
960C23—62no—
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—
977C23C2×D3×D411yescharacteristic
978C23C2×D3×D411yescharacteristic
979C23C2×D3×D411yescharacteristic
980C23#100411yescharacteristic
981C23#100411yescharacteristic
982C23#100411yescharacteristic
983C23C2×D3×Q811yescharacteristic
984C23#100711yescharacteristic
985C23D3×#4111yescharacteristic
986C23D3×#4111yescharacteristic
987C23D3×#4111yescharacteristic
988C23D3×#4111yescharacteristic
989C23#100911yescharacteristic
990C23#101011yescharacteristic
991C23C22×#6711yescharacteristic
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—34no—
1010C2×C4—34no—
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—41no—
1035C2×C4—41no—
1036C2×C4—41no—
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—62no—
1053C2×C4—62no—
1054C2×C4—62no—
1055C2×C4—62no—
1056C2×C4—62no—
1057C2×C4—62no—
1058C2×C4—1216no—
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—121no—
1085C2×C4#93714yes—
1086C2×C3—82no—
1087C2×C3#240911yescharacteristic
1088C2×C3#241011yescharacteristic
1089C2×C3#242611yescharacteristic
1090C2×C3#243111yescharacteristic
1091C2×C3#243711yescharacteristic
1092C2×C3#245011yescharacteristic
1093C2×C3#245211yescharacteristic
1094C2×C3#253811yescharacteristic
1095C2×C3#256011yescharacteristic
1096C2×C3#267611yescharacteristic
1097C2×C3#268111yescharacteristic
1098C2×C3#269211yescharacteristic
1099C2×C3#270011yescharacteristic
1100C2×C3#273011yescharacteristic
1101C2×C3#273211yescharacteristic
1102D3—44no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—64no—
1111C22—64no—
1112C22—64no—
1113C22—81no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22—81no—
1121C22—122no—
1122C22—122no—
1123C22—122no—
1124C22—122no—
1125C22—122no—
1126C22—122no—
1127C22—122no—
1128C22—122no—
1129C22—122no—
1130C22—122no—
1131C22—122no—
1132C22—122no—
1133C22#559711yescharacteristic
1134C22#559911yescharacteristic
1135C22#559911yescharacteristic
1136C22D3×#12111yescharacteristic
1137C22#560511yescharacteristic
1138C22#560911yescharacteristic
1139C22#561011yescharacteristic
1140C22#561011yescharacteristic
1141C22#561211yescharacteristic
1142C22#561211yescharacteristic
1143C22#561311yescharacteristic
1144C22#562111yescharacteristic
1145C22D3×C22⋊Q811yescharacteristic
1146C22D3×C22⋊Q811yescharacteristic
1147C22#562811yescharacteristic
1148C22#563211yescharacteristic
1149C22#563311yescharacteristic
1150C22#563311yescharacteristic
1151C22#563411yescharacteristic
1152C22#563611yescharacteristic
1153C22#563611yescharacteristic
1154C22#564011yescharacteristic
1155C22#564011yescharacteristic
1156C22#564711yescharacteristic
1157C22#570211yescharacteristic
1158C22#570511yescharacteristic
1159C22#570611yescharacteristic
1160C22#570711yescharacteristic
1161C22C2×#93711yescharacteristic
1162C22D4×#6711yescharacteristic
1163C22#580511yescharacteristic
1164C22Q8×#6711yescharacteristic
1165C22#582911yescharacteristic
1166C22#583111yescharacteristic
1167C22#583211yescharacteristic
1168C4—24no—
1169C4—42no—
1170C4—42no—
1171C4—42no—
1172C4—64no—
1173C4—64no—
1174C4—81no—
1175C4—81no—
1176C4—122no—
1177C4—122no—
1178C4—122no—
1179C4—241no—
1180C4—241no—
1181C3#1528011yescharacteristic, complemented, Sylow
1182C2—82no—
1183C2—124no—
1184C2#7728611yescharacteristic
1185C2#7731411yescharacteristic
1186C2#7737011yescharacteristic
1187C2#7737211yescharacteristic
1188C2#7741811yescharacteristic
1189C2#7742011yescharacteristic
1190C2#7743111yescharacteristic
1191C2#7743811yescharacteristic
1192C2#8265211yescharacteristic
1193C2#8270211yescharacteristic
1194C2#8271911yescharacteristic
1195C2#8275111yescharacteristic
1196C2#8276611yescharacteristic
1197C2#8283011yescharacteristic
1198C2#8311011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#396C2
prime radicalC23×#67C22
hypercenterC2×#396D3
hypocenterC3#15280
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#896C2semidirect
2. C2×C3×#396C2semidirect
3. C2×#4973C2semidirect
5. C2×#4947C2semidirect
7. #71570C2semidirect
8. #71570C2semidirect
9. #71568C2semidirect
10. #71564C2semidirect
12. #71547C2semidirect
13. #71547C2semidirect
14. (C2×D3)⋊#95C2semidirect
15. #69409C2semidirect
61. C2×#396D3semidirect
89. C22×#67Q8semidirect
110. C22×Dic6D4semidirect
119. C2×C3×C4⋊C4D4semidirect
438. C2×C4⋊C4#67semidirect
665. C2×Dic3C22⋊Q8semidirect
1181. C3#15280semidirect

Maximal subgroups

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

subgroupindex
C22×#8962
C2×C3×#3962
C2×#49732
C2×#49562
C2×#49472
C2×#49572
#715702
#715682
#715642
#715502
#715472
(C2×D3)⋊#952
#694092
#152803