Finite Group Databasebeta

← #10727112

Subgroups — #10727112

Order 768.

2414 conjugacy classes of subgroups.

The subgroup lattice has 1220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#878C211yesmaximal, characteristic, complemented
2C2×C3×#386C211yesmaximal, characteristic
3C2×#5220C211yesmaximal, characteristic
4C2×#5220C211yesmaximal, characteristic
5C22×C3⋊#95C211yesmaximal, characteristic, complemented
6C2×#4947C211yesmaximal, characteristic, complemented
7#72127C211yesmaximal, characteristic, complemented
8#71547C211yesmaximal, characteristic, complemented
9#71547C211yesmaximal, characteristic, complemented
10#71546C211yesmaximal, characteristic, complemented
11#71544C211yesmaximal, characteristic, complemented
12#69424C211yesmaximal, characteristic, complemented
13#69415C211yesmaximal, characteristic, complemented
14#69414C211yesmaximal, characteristic, complemented
15#69414C211yesmaximal, characteristic, complemented
16#14759—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C24×Dic3C2211yescharacteristic
20C24×Dic3C2211yescharacteristic
21C23×Dic6C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×C4⋊Dic3C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C2×#878—24no—
35C2×#878—24no—
36C2×#878—24no—
37C3×#386—24no—
38C2×C3×#95C2211yescharacteristic
39C2×C3×#95C2211yescharacteristic
40#5220—24no—
41#5220—24no—
42C2×C3⋊#95—24no—
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
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59#4947—24no—
60C22×C22⋊Q8—31no—
61C2×#393—31no—
62C2×#386—31no—
63C2×#386—31no—
64C2×#386D311yescharacteristic
65C22×#95—31no—
66#1446—31no—
67#1442—31no—
68#1442—31no—
69#1442—31no—
70#1439—31no—
71#1439—31no—
72#1439—31no—
73C22⋊#95—31no—
74C22⋊#95—31no—
75C25×C3C2311yescharacteristic
76C25×C3C2311yescharacteristic
77C22×C3×D4—22no—
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—22no—
81C22×C3×D4—22no—
82C22×C3×D4—22no—
83C22×C3×D4Q814yescomplemented
84C23×C3×C4—22no—
85C23×C3×C4—22no—
86C23×C3×C4—22no—
87C23×C3×C4—22no—
88C23×C3×C4—22no—
89C23×C3×C4—41no—
90C23×C3×C4—41no—
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×Dic3—22no—
97C23×Dic3—22no—
98C23×Dic3—22no—
99C23×Dic3—22no—
100C23×Dic3—22no—
101C23×Dic3—22no—
102C23×Dic3—22no—
103C23×Dic3—22no—
104C23×Dic3—22no—
105C23×Dic3—41no—
106C23×Dic3—41no—
107C23×Dic3—41no—
108C23×Dic3—41no—
109C23×Dic3D414yes—
110C23×Dic3C2311yescharacteristic
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C23×Dic3C2311yescharacteristic
114C23×Dic3C2311yescharacteristic
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2311yescharacteristic
117C23×Dic3C2311yescharacteristic
118C22×Dic6—22no—
119C22×Dic6—22no—
120C22×Dic6—22no—
121C22×Dic6—22no—
122C22×Dic6—22no—
123C22×Dic6—41no—
124C22×Dic6—41no—
125C2×C3×C22⋊C4—22no—
126C2×C3×C22⋊C4—22no—
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4—22no—
129C2×C3×C22⋊C4—22no—
130C2×C3×C22⋊C4—22no—
131C2×C3×C22⋊C4—41no—
132C2×C3×C22⋊C4—41no—
133C2×C3×C22⋊C4D414yes—
134C2×#217—22no—
135C2×#217—22no—
136C2×#217—22no—
137C2×#217—22no—
138C2×#217—22no—
139C2×#217—22no—
140C2×#217—22no—
141C2×#217—22no—
142C2×#217—22no—
143C2×#217—22no—
144C2×#217—22no—
145C2×#217—22no—
146C2×#217—22no—
147C2×#217—41no—
148C2×#217—41no—
149C2×#217—41no—
150C2×#217—41no—
151C2×#217D414yes—
152C2×C4⋊Dic3—22no—
153C2×C4⋊Dic3—22no—
154C2×C4⋊Dic3—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—
161#878—232no—
162C3×#95—22no—
163C3×#95—22no—
164C3⋊#95—22no—
165C3⋊#95—22no—
166C3⋊#95—22no—
167C3⋊#95—22no—
168C3⋊#95—22no—
169C3⋊#95—22no—
170C3⋊#95—22no—
171C3⋊#95—22no—
172C3⋊#95—22no—
173C3⋊#95—22no—
174C3⋊#95—22no—
175C3⋊#95—41no—
176C3⋊#95—41no—
177C3⋊#95—41no—
178C3⋊#95—41no—
179C3⋊#95D414yescomplemented
180C23×Q8—31no—
181C23×D4C2×D311yescharacteristic
182C24×C4—31no—
183C24×C4—31no—
184C24×C4C2×D311yescharacteristic
185C2×C22⋊Q8—64no—
186C2×C22⋊Q8—64no—
187C2×C22⋊Q8—64no—
188C22×C4⋊C4—31no—
189C22×C4⋊C4—31no—
190C22×C4⋊C4—31no—
191C22×C22⋊C4—31no—
192C22×C22⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4—31no—
197C22×C22⋊C4C2×D311yescharacteristic
198C22×C22⋊C4C2×D311yescharacteristic
199C22×C22⋊C4C2×D311yescharacteristic
200#393—64no—
201#386—24no—
202#386—64no—
203#386—64no—
204C2×#95—31no—
205C2×#95—31no—
206C2×#95—31no—
207C2×#95—31no—
208C2×#95—31no—
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—64no—
221C2×#95C2×D311yescharacteristic
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×C3—21no—
238C24×C3—21no—
239C24×C3—21no—
240C24×C3—21no—
241C24×C3—21no—
242C24×C3—21no—
243C24×C3—21no—
244C24×C3—21no—
245C24×C3C2×D412yes—
246C24×C3C2×D412yes—
247C24×C3C2×D412yes—
248C24×C3C2×Q812yes—
249C24×C3C2×Q812yes—
250C24×C3#4112yes—
251C24×C3#4112yes—
252C24×C3#4112yes—
253C24×C3C2411yescharacteristic
254C2×C3×D4—28no—
255C2×C3×D4—28no—
256C2×C3×D4—28no—
257C2×C3×D4—44no—
258C2×C3×D4—44no—
259C2×C3×D4—44no—
260C2×C3×D4—44no—
261C22×C3×C4—28no—
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—44no—
293C22×C3×C4—44no—
294C22×C3×C4—44no—
295C22×C3×C4—44no—
296C22×C3×C4—44no—
297C22×C3×C4—44no—
298C22×C3×C4C2×D412yes—
299C22×C3×C4C2×D412yes—
300C22×C3×C4C2×D412yes—
301C22×C3×C4C2×Q812yes—
302C22×C3×C4#4112yes—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—28no—
308C22×Dic3—28no—
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—28no—
340C22×Dic3—21no—
341C22×Dic3—21no—
342C22×Dic3—21no—
343C22×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—21no—
346C22×Dic3—21no—
347C22×Dic3—21no—
348C22×Dic3—21no—
349C22×Dic3—21no—
350C22×Dic3—21no—
351C22×Dic3—21no—
352C22×Dic3—21no—
353C22×Dic3—21no—
354C22×Dic3—44no—
355C22×Dic3—44no—
356C22×Dic3—44no—
357C22×Dic3—44no—
358C22×Dic3—44no—
359C22×Dic3—44no—
360C22×Dic3—44no—
361C22×Dic3—44no—
362C22×Dic3—44no—
363C22×Dic3—44no—
364C22×Dic3—44no—
365C22×Dic3C2×D412yes—
366C22×Dic3C2×D412yes—
367C22×Dic3C2×D412yes—
368C22×Dic3C2×D412yes—
369C22×Dic3C2×D412yes—
370C22×Dic3C2×D412yes—
371C22×Dic3#4112yes—
372C22×Dic3#4112yes—
373C2×Dic6—28no—
374C2×Dic6—44no—
375C2×Dic6—44no—
376C2×Dic6—44no—
377C2×Dic6—44no—
378C2×Dic6—44no—
379C2×Dic6—44no—
380C3×C22⋊C4—28no—
381C3×C22⋊C4—44no—
382C3×C22⋊C4—44no—
383#217—28no—
384#217—44no—
385#217—44no—
386#217—44no—
387#217—44no—
388#217—44no—
389C4⋊Dic3—28no—
390Dic3⋊C4—28no—
391Dic3⋊C4—28no—
392C25C22×D311yescharacteristic
393C25C22×D311yescharacteristic
394C22×Q8—62no—
395C22×Q8—62no—
396C22×Q8—62no—
397C22×Q8—62no—
398C22×Q8—62no—
399C22×Q8—121no—
400C22×Q8—121no—
401C22×D4—22no—
402C22×D4—22no—
403C22×D4—22no—
404C22×D4—22no—
405C22×D4—22no—
406C22×D4—22no—
407C22×D4Dic614yescomplemented
408C23×C4—22no—
409C23×C4—22no—
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—22no—
413C23×C4—31no—
414C23×C4—31no—
415C23×C4—31no—
416C23×C4—31no—
417C23×C4—31no—
418C23×C4—31no—
419C23×C4—34no—
420C23×C4—31no—
421C23×C4—31no—
422C23×C4—41no—
423C23×C4—41no—
424C23×C4—62no—
425C23×C4—62no—
426C23×C4—62no—
427C23×C4—62no—
428C23×C4—62no—
429C23×C4—62no—
430C23×C4—62no—
431C23×C4—62no—
432C23×C4—62no—
433C23×C4—121no—
434C23×C4—121no—
435C23×C4—121no—
436C23×C4—121no—
437C23×C4C22×D311yescharacteristic
438C23×C4C22×D311yescharacteristic
439C23×C4C22×D311yescharacteristic
440C23×C4C22×D311yescharacteristic
441C23×C4C22×D311yescharacteristic
442C22⋊Q8—632no—
443C2×C4⋊C4—62no—
444C2×C4⋊C4—62no—
445C2×C4⋊C4—62no—
446C2×C4⋊C4—62no—
447C2×C4⋊C4—62no—
448C2×C4⋊C4—62no—
449C2×C4⋊C4—62no—
450C2×C4⋊C4—62no—
451C2×C4⋊C4—62no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—34no—
459C2×C22⋊C4—41no—
460C2×C22⋊C4—41no—
461C2×C22⋊C4—62no—
462C2×C22⋊C4—62no—
463C2×C22⋊C4—62no—
464C2×C22⋊C4—62no—
465C2×C22⋊C4—62no—
466C2×C22⋊C4—62no—
467C2×C22⋊C4—62no—
468C2×C22⋊C4—62no—
469C2×C22⋊C4—62no—
470C2×C22⋊C4—62no—
471C2×C22⋊C4—62no—
472C2×C22⋊C4—62no—
473C2×C22⋊C4—62no—
474C2×C22⋊C4—121no—
475C2×C22⋊C4—121no—
476C2×C22⋊C4—121no—
477C2×C22⋊C4—121no—
478C2×C22⋊C4#6714yes—
479#95—22no—
480#95—22no—
481#95—34no—
482#95—62no—
483#95—62no—
484#95—62no—
485#95—62no—
486#95—62no—
487#95—62no—
488#95—62no—
489#95—62no—
490#95—62no—
491#95—62no—
492#95—62no—
493#95—121no—
494#95—121no—
495#95—121no—
496#95—121no—
497C23×C3—22no—
498C23×C3—22no—
499C23×C3—22no—
500C23×C3—22no—
501C23×C3—22no—
502C23×C3—22no—
503C23×C3—22no—
504C23×C3—22no—
505C23×C3—22no—
506C23×C3—22no—
507C23×C3—22no—
508C23×C3—22no—
509C23×C3—22no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—22no—
514C23×C3—22no—
515C23×C3—22no—
516C23×C3—22no—
517C23×C3—22no—
518C23×C3—22no—
519C23×C3—22no—
520C23×C3—22no—
521C23×C3—22no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—22no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—41no—
539C23×C3—41no—
540C23×C3—41no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—41no—
546C23×C3—41no—
547C23×C3—41no—
548C23×C3—41no—
549C23×C3—41no—
550C23×C3—41no—
551C23×C3—41no—
552C23×C3—41no—
553C23×C3—41no—
554C23×C3—41no—
555C23×C3—41no—
556C23×C3—41no—
557C23×C3—41no—
558C23×C3—41no—
559C23×C3—41no—
560C23×C3#12014yes—
561C23×C3C22⋊Q814yes—
562C23×C3C22⋊Q814yes—
563C23×C3C22⋊Q814yes—
564C23×C3#12414yes—
565C23×C3#12414yes—
566C23×C3#12414yes—
567C23×C3C22×D411yescharacteristic
568C23×C3C22×D411yescharacteristic
569C23×C3C22×D411yescharacteristic
570C23×C3C22×D411yescharacteristic
571C23×C3C22×Q811yescharacteristic
572C23×C3C2×#4111yescharacteristic
573C23×C3C2×#4111yescharacteristic
574C23×C3C2×#4111yescharacteristic
575C23×C3C2×#4111yescharacteristic
576C23×C3C2×#4111yescharacteristic
577C23×C3C2×#4111yescharacteristic
578C23×C3H(5,𝔽2)11yescharacteristic
579C23×C3H(5,𝔽2)11yescharacteristic
580C23×C3H(5,𝔽2)11yescharacteristic
581C23×C32−1+411yescharacteristic
582C3×D4—416no—
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—22no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—416no—
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×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—22no—
639C2×Dic3—22no—
640C2×Dic3—416no—
641C2×Dic3—416no—
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—41no—
665C2×Dic3—41no—
666C2×Dic3—41no—
667C2×Dic3—41no—
668C2×Dic3—41no—
669C2×Dic3—41no—
670C2×Dic3—41no—
671C2×Dic3—41no—
672C2×Dic3—41no—
673C2×Dic3—41no—
674C2×Dic3—41no—
675C2×Dic3—41no—
676C2×Dic3#12114yes—
677Dic6—416no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—21no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24C2×Dic612yes—
701C24C2×Dic612yes—
702C24#23512yes—
703C24D3×D412yes—
704C24D3×D412yes—
705C24#23712yes—
706C24#23712yes—
707C24C2×#6712yes—
708C24C23×D311yescharacteristic
709C2×Q8—68no—
710C2×Q8—124no—
711C2×Q8—124no—
712C2×Q8—124no—
713C2×Q8—124no—
714C2×Q8—124no—
715C2×Q8—124no—
716C2×D4—28no—
717C2×D4—28no—
718C2×D4—28no—
719C2×D4—44no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4—44no—
723C22×C4—28no—
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—21no—
754C22×C4—32no—
755C22×C4—32no—
756C22×C4—32no—
757C22×C4—32no—
758C22×C4—32no—
759C22×C4—32no—
760C22×C4—32no—
761C22×C4—32no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—68no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—61no—
772C22×C4—61no—
773C22×C4—68no—
774C22×C4—68no—
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—61no—
800C22×C4—61no—
801C22×C4—61no—
802C22×C4—61no—
803C22×C4—61no—
804C22×C4—61no—
805C22×C4—61no—
806C22×C4—61no—
807C22×C4—61no—
808C22×C4—61no—
809C22×C4—61no—
810C22×C4—61no—
811C22×C4—61no—
812C22×C4—61no—
813C22×C4—61no—
814C22×C4—61no—
815C22×C4—61no—
816C22×C4—61no—
817C22×C4—61no—
818C22×C4—61no—
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—
828C22×C4—124no—
829C22×C4—124no—
830C22×C4C2×Dic612yes—
831C22×C4D3×D412yes—
832C22×C4#23712yes—
833C22×C4C2×#6712yes—
834C22×C4C2×#6712yes—
835C4⋊C4—68no—
836C4⋊C4—68no—
837C4⋊C4—68no—
838C22⋊C4—28no—
839C22⋊C4—44no—
840C22⋊C4—44no—
841C22⋊C4—68no—
842C22⋊C4—124no—
843C22⋊C4—124no—
844C22⋊C4—124no—
845C22⋊C4—124no—
846C22⋊C4—124no—
847C22×C3—24no—
848C22×C3—24no—
849C22×C3—24no—
850C22×C3—24no—
851C22×C3—24no—
852C22×C3—24no—
853C22×C3—24no—
854C22×C3—24no—
855C22×C3—24no—
856C22×C3—24no—
857C22×C3—24no—
858C22×C3—24no—
859C22×C3—24no—
860C22×C3—24no—
861C22×C3—42no—
862C22×C3—42no—
863C22×C3—42no—
864C22×C3—42no—
865C22×C3—42no—
866C22×C3—42no—
867C22×C3—42no—
868C22×C3—81no—
869C22×C3—81no—
870C22×C3—81no—
871C22×C3—81no—
872C22×C3—81no—
873C22×C3—81no—
874C22×C3—81no—
875C22×C3—81no—
876C22×C3#39318yescomplemented
877C22×C3C2×#12011yescharacteristic
878C22×C3C2×#12111yescharacteristic
879C22×C3C2×C22⋊Q811yescharacteristic
880C22×C3C2×C22⋊Q811yescharacteristic
881C22×C3C2×C22⋊Q811yescharacteristic
882C22×C3#52511yescharacteristic
883C22×C3#52511yescharacteristic
884C22×C3C2×#12411yescharacteristic
885C22×C3C2×#12411yescharacteristic
886C22×C3C2×#12411yescharacteristic
887C22×C3#52911yescharacteristic
888C22×C3#52911yescharacteristic
889C22×C3#53211yescharacteristic
890C22×C3#53411yescharacteristic
891C22×C3#53711yescharacteristic
892C22×C3#53811yescharacteristic
893C22×C3#53811yescharacteristic
894C22×C3#53911yescharacteristic
895C22×C3#53911yescharacteristic
896C22×C3D4211yescharacteristic
897C22×C3D4211yescharacteristic
898C22×C3#54611yescharacteristic
899C22×C3#54611yescharacteristic
900C22×C3#54611yescharacteristic
901C22×C3#54611yescharacteristic
902C22×C3#54611yescharacteristic
903C22×C3#54711yescharacteristic
904C22×C3#54711yescharacteristic
905C22×C3D4×Q811yescharacteristic
906C22×C3#55111yescharacteristic
907C22×C3#55111yescharacteristic
908C22×C3#55211yescharacteristic
909C22×C3#55411yescharacteristic
910C22×C3#55411yescharacteristic
911C22×C3#55411yescharacteristic
912C3×C4—42no—
913C3×C4—42no—
914C3×C4—42no—
915C3×C4—42no—
916C3×C4—42no—
917Dic3—24no—
918Dic3—42no—
919Dic3—42no—
920Dic3—42no—
921Dic3—42no—
922Dic3—42no—
923Dic3—81no—
924Dic3—81no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23#87814yes—
989C23#87814yes—
990C23#88514yes—
991C23#88514yes—
992C23#92414yes—
993C23#93614yes—
994C23#93714yes—
995C23C22×Dic611yescharacteristic
996C23C2×#23511yescharacteristic
997C23C2×D3×D411yescharacteristic
998C23C2×D3×D411yescharacteristic
999C23C2×D3×D411yescharacteristic
1000C23C2×#23711yescharacteristic
1001C23C2×#23711yescharacteristic
1002C23C2×#23711yescharacteristic
1003C23#100411yescharacteristic
1004C23#100411yescharacteristic
1005C23D3×#4111yescharacteristic
1006C23D3×#4111yescharacteristic
1007C23#100911yescharacteristic
1008C23#101011yescharacteristic
1009C23C22×#6711yescharacteristic
1010Q8—1216no—
1011D4—416no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—34no—
1028C2×C4—416no—
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—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
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—62no—
1059C2×C4—62no—
1060C2×C4—62no—
1061C2×C4—62no—
1062C2×C4—62no—
1063C2×C4—62no—
1064C2×C4—62no—
1065C2×C4—62no—
1066C2×C4—62no—
1067C2×C4—62no—
1068C2×C4—62no—
1069C2×C4—62no—
1070C2×C4—1216no—
1071C2×C4—1216no—
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—121no—
1086C2×C4—121no—
1087C2×C4—121no—
1088C2×C4—121no—
1089C2×C4—121no—
1090C2×C4—121no—
1091C2×C4—121no—
1092C2×C4—121no—
1093C2×C4—121no—
1094C2×C4—121no—
1095C2×C4—121no—
1096C2×C4—121no—
1097C2×C4—121no—
1098C2×C4—121no—
1099C2×C4—121no—
1100C2×C4—121no—
1101C2×C4—121no—
1102C2×C4—121no—
1103C2×C4—121no—
1104C2×C4—121no—
1105C2×C4—121no—
1106C2×C3—28no—
1107C2×C3—82no—
1108C2×C3C2×#39311yescharacteristic
1109C2×C3#241011yescharacteristic
1110C2×C3#241711yescharacteristic
1111C2×C3#243011yescharacteristic
1112C2×C3#244911yescharacteristic
1113C2×C3#244911yescharacteristic
1114C2×C3#245011yescharacteristic
1115C2×C3#245011yescharacteristic
1116C2×C3#247211yescharacteristic
1117C2×C3#247211yescharacteristic
1118C2×C3#248811yescharacteristic
1119C2×C3#248811yescharacteristic
1120C2×C3#256411yescharacteristic
1121C2×C3#263911yescharacteristic
1122C2×C3#285011yescharacteristic
1123C22—24no—
1124C22—24no—
1125C22—24no—
1126C22—24no—
1127C22—24no—
1128C22—24no—
1129C22—24no—
1130C22—24no—
1131C22—24no—
1132C22—24no—
1133C22—24no—
1134C22—24no—
1135C22—24no—
1136C22—24no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—81no—
1145C22—81no—
1146C22—81no—
1147C22—81no—
1148C22—81no—
1149C22—81no—
1150C22—81no—
1151C22—81no—
1152C22#494718yescomplemented
1153C22C2×#87811yescharacteristic
1154C22C2×#87811yescharacteristic
1155C22C2×#88511yescharacteristic
1156C22C2×#88511yescharacteristic
1157C22D4×Dic611yescharacteristic
1158C22#553811yescharacteristic
1159C22#553911yescharacteristic
1160C22#553911yescharacteristic
1161C22#554311yescharacteristic
1162C22#554711yescharacteristic
1163C22#556011yescharacteristic
1164C22#556411yescharacteristic
1165C22#558611yescharacteristic
1166C22#558711yescharacteristic
1167C22#559111yescharacteristic
1168C22#559311yescharacteristic
1169C22#559611yescharacteristic
1170C22#559711yescharacteristic
1171C22D3×#12111yescharacteristic
1172C22#560511yescharacteristic
1173C22#560911yescharacteristic
1174C22#561011yescharacteristic
1175C22#561011yescharacteristic
1176C22#561111yescharacteristic
1177C22#564911yescharacteristic
1178C22#565011yescharacteristic
1179C22#565811yescharacteristic
1180C22#566511yescharacteristic
1181C22C2×#92411yescharacteristic
1182C22C2×#93611yescharacteristic
1183C22C2×#93711yescharacteristic
1184C22D4×#6711yescharacteristic
1185C22#580611yescharacteristic
1186C22#582411yescharacteristic
1187C22#582911yescharacteristic
1188C4—42no—
1189C4—42no—
1190C4—42no—
1191C4—42no—
1192C4—42no—
1193C4—64no—
1194C4—122no—
1195C4—122no—
1196C4—122no—
1197C4—122no—
1198C4—122no—
1199C4—241no—
1200C4—241no—
1201C3#1475911yescharacteristic, complemented, Sylow
1202C2—28no—
1203C2—82no—
1204C2#7469311yescharacteristic
1205C2#7471011yescharacteristic
1206C2#7471211yescharacteristic
1207C2#7472711yescharacteristic
1208C2#7473911yescharacteristic
1209C2#7476311yescharacteristic
1210C2#7478511yescharacteristic
1211C2#7486911yescharacteristic
1212C2C2×#494711yescharacteristic
1213C2#8236011yescharacteristic
1214C2#8236111yescharacteristic
1215C2#8258911yescharacteristic
1216C2#8265111yescharacteristic
1217C2#8270211yescharacteristic
1218C2#8285711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#386C2
prime radicalC23×C3×D4C22
hypercenterC2×#386D3
hypocenterC3#14759
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#878C2semidirect
5. C22×C3⋊#95C2semidirect
6. C2×#4947C2semidirect
7. #72127C2semidirect
8. #71547C2semidirect
9. #71547C2semidirect
10. #71546C2semidirect
11. #71544C2semidirect
12. #69424C2semidirect
13. #69415C2semidirect
14. #69414C2semidirect
15. #69414C2semidirect
83. C22×C3×D4Q8semidirect
179. C3⋊#95D4semidirect
407. C22×D4Dic6semidirect
876. C22×C3#393semidirect
1152. C22#4947semidirect
1201. C3#14759semidirect

Maximal subgroups

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

subgroupindex
C22×#8782
C2×C3×#3862
C2×#52202
C22×C3⋊#952
C2×#49472
#721272
#715472
#715462
#715442
#694242
#694152
#694142
#147593