Finite Group Databasebeta

← #10732579

Subgroups — #10732579

Order 768.

1686 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4976C211yesmaximal, characteristic, complemented
2C2×#4942C211yesmaximal, characteristic
3C2×#4942C211yesmaximal, characteristic
4C2×Dic3×C22⋊C4C211yesmaximal, characteristic
5C2×#4647C211yesmaximal, characteristic, complemented
6C2×#4650C211yesmaximal, characteristic, complemented
7C3×#1439C211yesmaximal, characteristic
8#71569C211yesmaximal, characteristic, complemented
9#71547C211yesmaximal, characteristic
10#71547C211yesmaximal, characteristic
11#71546C211yesmaximal, characteristic
12#69422C211yesmaximal, characteristic, complemented
13#69421C211yesmaximal, characteristic, complemented
14#69421C211yesmaximal, characteristic, complemented
15Dic3⋊#95C211yesmaximal, characteristic, complemented
16#15223—31nomaximal, Sylow
17C24×Dic3C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×C4⋊Dic3C2211yescharacteristic
26C22×Dic3⋊C4C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×Dic3⋊C4C2211yescharacteristic
30C22×Dic3⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×C4×Dic3C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
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
52#4976—24no—
53#4942—24no—
54#4942—24no—
55Dic3×C22⋊C4—24no—
56#4650—24no—
57#4647—24no—
58C2×#389—31no—
59C2×#389—31no—
60C2×#382—31no—
61C2×#380—31no—
62C2×#380—31no—
63C2×C4×C22⋊C4—31no—
64#1445—31no—
65#1445—31no—
66#1445—31no—
67#1445—31no—
68#1439—31no—
69#1439—31no—
70#1439—31no—
71#1439D311yescharacteristic
72C4⋊#95—31no—
73C25×C3C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×Dic3—22no—
81C23×Dic3—22no—
82C23×Dic3—22no—
83C23×Dic3—22no—
84C23×Dic3—22no—
85C23×Dic3—22no—
86C23×Dic3Q814yes—
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C2×C3×C4⋊C4—22no—
96C2×C3×C4⋊C4—22no—
97C2×C3×C4⋊C4—41no—
98C2×C3×C22⋊C4—22no—
99C2×C3×C22⋊C4—22no—
100C2×C3×C22⋊C4—22no—
101C2×C3×C22⋊C4—22no—
102C2×C3×C22⋊C4—22no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—41no—
106C2×C3×C22⋊C4—41no—
107C2×#217—22no—
108C2×#217—22no—
109C2×#217—22no—
110C2×#217—22no—
111C2×#217—22no—
112C2×#217—22no—
113C2×#217—22no—
114C2×#217—41no—
115C2×#217—41no—
116C2×C4⋊Dic3—22no—
117C2×C4⋊Dic3—22no—
118C2×C4⋊Dic3—41no—
119C2×Dic3⋊C4—22no—
120C2×Dic3⋊C4—22no—
121C2×Dic3⋊C4—22no—
122C2×Dic3⋊C4—22no—
123C2×Dic3⋊C4—22no—
124C2×Dic3⋊C4—22no—
125C2×Dic3⋊C4—22no—
126C2×Dic3⋊C4—22no—
127C2×Dic3⋊C4—22no—
128C2×Dic3⋊C4—22no—
129C2×Dic3⋊C4—22no—
130C2×Dic3⋊C4—22no—
131C2×Dic3⋊C4—22no—
132C2×Dic3⋊C4—22no—
133C2×Dic3⋊C4—41no—
134C2×Dic3⋊C4—41no—
135C2×Dic3⋊C4D414yes—
136C2×Dic3⋊C4D414yes—
137C2×C4×Dic3—22no—
138C2×C4×Dic3—22no—
139C2×C4×Dic3—22no—
140C2×C4×Dic3—22no—
141C2×C4×Dic3—22no—
142C2×C4×Dic3D414yes—
143C3×#95—22no—
144C3×#95—22no—
145C3×#95—41no—
146C3⋊#95—22no—
147C3⋊#95—22no—
148C3⋊#95—22no—
149C3⋊#95—22no—
150C3⋊#95—22no—
151C3⋊#95—22no—
152C3⋊#95—22no—
153C3⋊#95—22no—
154C3⋊#95—22no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C3⋊#95—41no—
159C3⋊#95—41no—
160C3⋊#95—41no—
161C24×C4—31no—
162C22×C4⋊C4—31no—
163C22×C4⋊C4—31no—
164C22×C4⋊C4—31no—
165C22×C4⋊C4—31no—
166C22×C4⋊C4—31no—
167C22×C4⋊C4—31no—
168C22×C4⋊C4—31no—
169C22×C4⋊C4C2×D311yescharacteristic
170C22×C22⋊C4—31no—
171C22×C22⋊C4—31no—
172C22×C22⋊C4—31no—
173C22×C22⋊C4C2×D311yescharacteristic
174C22×C22⋊C4C2×D311yescharacteristic
175C22×C22⋊C4C2×D311yescharacteristic
176C22×C42—31no—
177C22×C42—31no—
178#389—64no—
179#389—64no—
180#382—64no—
181#380—64no—
182#380—64no—
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×#95—31no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95C2×D311yescharacteristic
200C2×#95C2×D311yescharacteristic
201C2×#95C2×D311yescharacteristic
202C24×C3—21no—
203C24×C3—21no—
204C24×C3—21no—
205C24×C3—21no—
206C24×C3—21no—
207C24×C3—21no—
208C24×C3—21no—
209C24×C3—21no—
210C24×C3—21no—
211C24×C3—21no—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3C2×Q812yes—
215C24×C3#4112yes—
216C24×C3#4112yes—
217C24×C3C2411yescharacteristic
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
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×C4C2×D412yes—
257C22×C3×C4C2×D412yes—
258C22×C3×C4C2×D412yes—
259C22×C3×C4#4112yes—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—21no—
274C22×Dic3—21no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—21no—
278C22×Dic3—21no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—21no—
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—28no—
291C22×Dic3—28no—
292C22×Dic3—28no—
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—44no—
308C22×Dic3—44no—
309C22×Dic3—44no—
310C22×Dic3—44no—
311C22×Dic3C2×D412yes—
312C22×Dic3C2×D412yes—
313C22×Dic3C2×D412yes—
314C22×Dic3C2×D412yes—
315C22×Dic3C2×D412yes—
316C22×Dic3C2×D412yes—
317C22×Dic3C2×Q812yes—
318C22×Dic3C2×Q812yes—
319C22×Dic3#4112yes—
320C22×Dic3#4112yes—
321C22×Dic3#4112yes—
322C22×Dic3#4112yes—
323C3×C4⋊C4—44no—
324C3×C22⋊C4—28no—
325C3×C22⋊C4—44no—
326C3×C22⋊C4—44no—
327#217—28no—
328#217—44no—
329#217—44no—
330C4⋊Dic3—44no—
331Dic3⋊C4—28no—
332Dic3⋊C4—28no—
333Dic3⋊C4—44no—
334Dic3⋊C4—44no—
335Dic3⋊C4—44no—
336Dic3⋊C4—44no—
337C4×Dic3—28no—
338C4×Dic3—44no—
339C25C22×D311yescharacteristic
340C23×C4—31no—
341C23×C4—34no—
342C23×C4—31no—
343C23×C4—31no—
344C23×C4—31no—
345C23×C4—31no—
346C23×C4—31no—
347C23×C4—31no—
348C23×C4—31no—
349C23×C4—62no—
350C23×C4—62no—
351C23×C4—62no—
352C23×C4—62no—
353C23×C4—62no—
354C23×C4—62no—
355C23×C4C22×D311yescharacteristic
356C23×C4C22×D311yescharacteristic
357C23×C4C22×D311yescharacteristic
358C23×C4C22×D311yescharacteristic
359C23×C4C22×D311yescharacteristic
360C23×C4C22×D311yescharacteristic
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—34no—
364C2×C4⋊C4—34no—
365C2×C4⋊C4—41no—
366C2×C4⋊C4—62no—
367C2×C4⋊C4—62no—
368C2×C4⋊C4—62no—
369C2×C4⋊C4—62no—
370C2×C4⋊C4—62no—
371C2×C4⋊C4—62no—
372C2×C4⋊C4—62no—
373C2×C4⋊C4—62no—
374C2×C4⋊C4—62no—
375C2×C4⋊C4—62no—
376C2×C4⋊C4—62no—
377C2×C4⋊C4—62no—
378C2×C4⋊C4—62no—
379C2×C4⋊C4—62no—
380C2×C4⋊C4—62no—
381C2×C4⋊C4—62no—
382C2×C4⋊C4—121no—
383C2×C4⋊C4—121no—
384C2×C4⋊C4—121no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—41no—
393C2×C22⋊C4—41no—
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—121no—
402C2×C22⋊C4—121no—
403C2×C42—34no—
404C2×C42—62no—
405C2×C42—62no—
406C2×C42—62no—
407C2×C42—62no—
408C2×C42—62no—
409#95—22no—
410#95—22no—
411#95—41no—
412#95—62no—
413#95—62no—
414#95—62no—
415#95—62no—
416#95—62no—
417#95—62no—
418#95—62no—
419#95—62no—
420#95—62no—
421#95—62no—
422#95—62no—
423#95—62no—
424#95—121no—
425#95—121no—
426#95—121no—
427C23×C3—22no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3—41no—
449C23×C3—41no—
450C23×C3—41no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3—41no—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3—41no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3#12514yes—
462C23×C3C22×D411yescharacteristic
463C23×C3C22×D411yescharacteristic
464C23×C3C22×D411yescharacteristic
465C23×C3C22×Q811yescharacteristic
466C23×C3C2×#4111yescharacteristic
467C23×C3C2×#4111yescharacteristic
468C23×C3C2×#4111yescharacteristic
469C23×C3C2×#4111yescharacteristic
470C23×C3C2×#4111yescharacteristic
471C23×C3C2×#4111yescharacteristic
472C23×C3C2×#4111yescharacteristic
473C23×C3H(5,𝔽2)11yescharacteristic
474C23×C3H(5,𝔽2)11yescharacteristic
475C23×C32−1+411yescharacteristic
476C23×C32−1+411yescharacteristic
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—22no—
524C2×Dic3—22no—
525C2×Dic3—22no—
526C2×Dic3—22no—
527C2×Dic3—22no—
528C2×Dic3—22no—
529C2×Dic3—22no—
530C2×Dic3—22no—
531C2×Dic3—22no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—41no—
535C2×Dic3—41no—
536C2×Dic3—41no—
537C2×Dic3—41no—
538C2×Dic3—41no—
539C2×Dic3—41no—
540C2×Dic3—41no—
541C2×Dic3—41no—
542C2×Dic3—41no—
543C2×Dic3—41no—
544C2×Dic3—41no—
545C2×Dic3—41no—
546C2×Dic3—41no—
547C2×Dic3—41no—
548C2×Dic3—41no—
549C2×Dic3—41no—
550C2×Dic3—41no—
551C2×Dic3—41no—
552C2×Dic3—41no—
553C2×Dic3—41no—
554C2×Dic3—416no—
555C2×Dic3—41no—
556C2×Dic3—41no—
557C2×Dic3—41no—
558C2×Dic3—41no—
559C2×Dic3—41no—
560C2×Dic3—41no—
561C2×Dic3—41no—
562C2×Dic3—41no—
563C2×Dic3—41no—
564C2×Dic3—41no—
565C2×Dic3—41no—
566C2×Dic3—41no—
567C2×Dic3—41no—
568C2×Dic3—41no—
569C2×Dic3C22⋊Q814yes—
570C2×Dic3C22⋊Q814yes—
571C2×Dic3C22⋊Q814yes—
572C2×Dic3#12314yes—
573C2×Dic3#12314yes—
574C2×Dic3#12314yes—
575C2×Dic3#12714yes—
576C24—21no—
577C24—21no—
578C24—21no—
579C24—21no—
580C24—21no—
581C24—21no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—21no—
586C24—21no—
587C24—21no—
588C24#23512yes—
589C24#23712yes—
590C24D3×Q812yes—
591C24C23×D311yescharacteristic
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—32no—
631C22×C4—32no—
632C22×C4—32no—
633C22×C4—32no—
634C22×C4—32no—
635C22×C4—32no—
636C22×C4—32no—
637C22×C4—32no—
638C22×C4—32no—
639C22×C4—32no—
640C22×C4—32no—
641C22×C4—32no—
642C22×C4—68no—
643C22×C4—68no—
644C22×C4—68no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—61no—
651C22×C4—61no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—61no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—61no—
662C22×C4—61no—
663C22×C4—61no—
664C22×C4—61no—
665C22×C4—61no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—61no—
669C22×C4—61no—
670C22×C4—61no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4—61no—
677C22×C4—61no—
678C22×C4—61no—
679C22×C4—61no—
680C22×C4—61no—
681C22×C4—61no—
682C22×C4—61no—
683C22×C4—61no—
684C22×C4—61no—
685C22×C4—61no—
686C22×C4—61no—
687C22×C4—61no—
688C22×C4—61no—
689C22×C4—124no—
690C22×C4—124no—
691C22×C4—124no—
692C22×C4—124no—
693C22×C4D3×D412yes—
694C22×C4D3×D412yes—
695C22×C4D3×D412yes—
696C22×C4#23712yes—
697C4⋊C4—44no—
698C4⋊C4—68no—
699C4⋊C4—68no—
700C4⋊C4—124no—
701C4⋊C4—124no—
702C4⋊C4—124no—
703C4⋊C4—124no—
704C4⋊C4—124no—
705C22⋊C4—28no—
706C22⋊C4—44no—
707C22⋊C4—44no—
708C22⋊C4—68no—
709C22⋊C4—124no—
710C22⋊C4—124no—
711C42—68no—
712C42—124no—
713C22×C3—24no—
714C22×C3—24no—
715C22×C3—24no—
716C22×C3—42no—
717C22×C3—42no—
718C22×C3—42no—
719C22×C3—42no—
720C22×C3—42no—
721C22×C3—42no—
722C22×C3—42no—
723C22×C3—42no—
724C22×C3—42no—
725C22×C3—42no—
726C22×C3—42no—
727C22×C3—42no—
728C22×C3C2×C22⋊Q811yescharacteristic
729C22×C3C2×C22⋊Q811yescharacteristic
730C22×C3C2×C22⋊Q811yescharacteristic
731C22×C3C2×#12311yescharacteristic
732C22×C3C2×#12311yescharacteristic
733C22×C3C2×#12311yescharacteristic
734C22×C3#52511yescharacteristic
735C22×C3#52511yescharacteristic
736C22×C3C2×#12511yescharacteristic
737C22×C3#52911yescharacteristic
738C22×C3#52911yescharacteristic
739C22×C3C2×#12711yescharacteristic
740C22×C3#53311yescharacteristic
741C22×C3#53711yescharacteristic
742C22×C3#53711yescharacteristic
743C22×C3#54011yescharacteristic
744C22×C3#54111yescharacteristic
745C22×C3#54411yescharacteristic
746C22×C3#54411yescharacteristic
747C22×C3#54611yescharacteristic
748C22×C3#54611yescharacteristic
749C22×C3#54611yescharacteristic
750C22×C3#54611yescharacteristic
751C22×C3#54811yescharacteristic
752C22×C3#54811yescharacteristic
753C22×C3#54811yescharacteristic
754C22×C3#54811yescharacteristic
755C22×C3#55211yescharacteristic
756C22×C3#55211yescharacteristic
757C22×C3#55311yescharacteristic
758C22×C3#55311yescharacteristic
759C22×C3#55511yescharacteristic
760C22×C3#55511yescharacteristic
761C22×C3#55611yescharacteristic
762C22×C3#55611yescharacteristic
763C3×C4—42no—
764C3×C4—42no—
765C3×C4—42no—
766C3×C4—42no—
767C3×C4—81no—
768C3×C4—81no—
769Dic3—42no—
770Dic3—42no—
771Dic3—42no—
772Dic3—42no—
773Dic3—42no—
774Dic3—81no—
775Dic3—81no—
776Dic3#39918yes—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23#88914yes—
812C23C2×#23511yescharacteristic
813C23C2×D3×D411yescharacteristic
814C23C2×D3×D411yescharacteristic
815C23C2×D3×D411yescharacteristic
816C23C2×#23711yescharacteristic
817C23C2×#23711yescharacteristic
818C23#100411yescharacteristic
819C23#100411yescharacteristic
820C23C2×D3×Q811yescharacteristic
821C23D3×#4111yescharacteristic
822C23D3×#4111yescharacteristic
823C23D3×#4111yescharacteristic
824C23D3×#4111yescharacteristic
825C23#101011yescharacteristic
826C23#101011yescharacteristic
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—34no—
840C2×C4—34no—
841C2×C4—34no—
842C2×C4—34no—
843C2×C4—34no—
844C2×C4—34no—
845C2×C4—34no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—62no—
877C2×C4—62no—
878C2×C4—62no—
879C2×C4—62no—
880C2×C4—62no—
881C2×C4—62no—
882C2×C4—62no—
883C2×C4—62no—
884C2×C4—62no—
885C2×C4—62no—
886C2×C4—62no—
887C2×C4—62no—
888C2×C4—62no—
889C2×C4—62no—
890C2×C4—62no—
891C2×C4—1216no—
892C2×C4—121no—
893C2×C4—121no—
894C2×C4—121no—
895C2×C4—121no—
896C2×C4—121no—
897C2×C4—121no—
898C2×C4—121no—
899C2×C4—121no—
900C2×C4—121no—
901C2×C4—121no—
902C2×C4—121no—
903C2×C4—121no—
904C2×C4—121no—
905C2×C4—121no—
906C2×C4—121no—
907C2×C4—121no—
908C2×C4—121no—
909C2×C4—121no—
910C2×C4—121no—
911C2×C4—121no—
912C2×C4—121no—
913C2×C4—121no—
914C2×C4—121no—
915C2×C4—121no—
916C2×C4—121no—
917C2×C4—121no—
918C2×C4—121no—
919C2×C4—121no—
920C2×C4—121no—
921C2×C4—121no—
922C2×C4—121no—
923C2×C4—121no—
924C2×C4—121no—
925C2×C4—121no—
926C2×C3—44no—
927C2×C3C2×#39911yescharacteristic
928C2×C3#242011yescharacteristic
929C2×C3#242011yescharacteristic
930C2×C3#242111yescharacteristic
931C2×C3#242111yescharacteristic
932C2×C3#243911yescharacteristic
933C2×C3#243911yescharacteristic
934C2×C3#244211yescharacteristic
935C2×C3#244211yescharacteristic
936C2×C3#248511yescharacteristic
937C2×C3#248511yescharacteristic
938C2×C3#254011yescharacteristic
939C2×C3#254011yescharacteristic
940C2×C3#262911yescharacteristic
941C2×C3#285111yescharacteristic
942C22—24no—
943C22—24no—
944C22—24no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22#549011yescharacteristic
958C22C2×#88911yescharacteristic
959C22#553111yescharacteristic
960C22#553811yescharacteristic
961C22#554011yescharacteristic
962C22#554711yescharacteristic
963C22#555211yescharacteristic
964C22#558611yescharacteristic
965C22#559111yescharacteristic
966C22#559111yescharacteristic
967C22#559711yescharacteristic
968C22#559811yescharacteristic
969C22#559811yescharacteristic
970C22#560111yescharacteristic
971C22#560811yescharacteristic
972C22#561011yescharacteristic
973C22#561511yescharacteristic
974C22#561611yescharacteristic
975C22#562211yescharacteristic
976C22#562311yescharacteristic
977C22#562311yescharacteristic
978C22D3×C22⋊Q811yescharacteristic
979C22D3×C22⋊Q811yescharacteristic
980C22D3×C22⋊Q811yescharacteristic
981C22#564911yescharacteristic
982C22#565011yescharacteristic
983C22D3×#12311yescharacteristic
984C22D3×#12311yescharacteristic
985C22D3×#12311yescharacteristic
986C22#567011yescharacteristic
987C22#567111yescharacteristic
988C22#567711yescharacteristic
989C22#570111yescharacteristic
990C22#570211yescharacteristic
991C22D3×#12711yescharacteristic
992C4—38no—
993C4—42no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—81no—
998C4—81no—
999C4—122no—
1000C4—122no—
1001C4—122no—
1002C4—122no—
1003C4—122no—
1004C4—241no—
1005C4—241no—
1006C3#1522311yescharacteristic, complemented, Sylow
1007C2—44no—
1008C2#7390211yescharacteristic
1009C2#7441711yescharacteristic
1010C2#7458611yescharacteristic
1011C2#7469511yescharacteristic
1012C2#7549711yescharacteristic
1013C2#7554311yescharacteristic
1014C2#7634711yescharacteristic
1015C2#7668711yescharacteristic
1016C2#7678211yescharacteristic
1017C2#7689911yescharacteristic
1018C2#7693311yescharacteristic
1019C2#7728811yescharacteristic
1020C2#7733211yescharacteristic
1021C2#7746411yescharacteristic
1022C2D3×#39911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1439C2
prime radicalC25×C3C23
hypercenter#1439D3
hypocenterC3#15223
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C2×#4976C2semidirect
5. C2×#4647C2semidirect
6. C2×#4650C2semidirect
8. #71569C2semidirect
12. #69422C2semidirect
13. #69421C2semidirect
14. #69421C2semidirect
15. Dic3⋊#95C2semidirect
1006. C3#15223semidirect

Maximal subgroups

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

subgroupindex
C2×#49762
C2×#49422
C2×Dic3×C22⋊C42
C2×#46472
C2×#46502
C3×#14392
#715692
#715472
#715462
#694222
#694212
Dic3⋊#952
#152233