Finite Group Databasebeta

← #10729205

Subgroups — #10729205

Order 768.

2314 conjugacy classes of subgroups.

The subgroup lattice has 1198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#883C211yesmaximal, characteristic
2C2×#4956C211yesmaximal, characteristic
3C2×#4956C211yesmaximal, characteristic
4C2×#4664C211yesmaximal, characteristic, complemented
5C2×#4667C211yesmaximal, characteristic, complemented
6C2×D3×#95C211yesmaximal, characteristic, complemented
7C3×#1440C211yesmaximal, characteristic, complemented
8#71549C211yesmaximal, characteristic, complemented
9#71547C211yesmaximal, characteristic, complemented
10#71547C211yesmaximal, characteristic, complemented
11(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
12#69415C211yesmaximal, characteristic, complemented
13#69413C211yesmaximal, characteristic, complemented
14#69410C211yesmaximal, characteristic, complemented
15#69409C211yesmaximal, characteristic, complemented
16#14927—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×C4⋊Dic3C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C2×#883—24no—
35C2×#883—24no—
36C2×#883—24no—
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2211yescharacteristic
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41C2×C3⋊#95C2211yescharacteristic
42C2×C3⋊#95C2211yescharacteristic
43C2×C3⋊#95C2211yescharacteristic
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55#4956—24no—
56#4956—24no—
57#4667—24no—
58#4664—24no—
59D3×#95—24no—
60C22×#123—31no—
61C2×#386—31no—
62C2×#386—31no—
63C2×#381—31no—
64C2×#380—31no—
65C22×#95—31no—
66#1442—31no—
67#1442—31no—
68#1441—31no—
69#1441—31no—
70#1440—31no—
71#1440D311yescharacteristic, complemented
72#1439—31no—
73#1439—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—22no—
88C22×#67—22no—
89C22×#67D414yes—
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—22no—
103C22×C4×D3—22no—
104C22×C4×D3—22no—
105C22×C4×D3—22no—
106C22×C4×D3—22no—
107C22×C4×D3—22no—
108C22×C4×D3—22no—
109C22×C4×D3—22no—
110C22×C4×D3—22no—
111C22×C4×D3—22no—
112C22×C4×D3—41no—
113C22×C4×D3—41no—
114C22×C4×D3—41no—
115C22×C4×D3—41no—
116C22×C4×D3D414yes—
117C22×C4×D3D414yes—
118C2×C3×C22⋊C4—22no—
119C2×C3×C22⋊C4—22no—
120C2×C3×C22⋊C4—22no—
121C2×C3×C22⋊C4—22no—
122C2×C3×C22⋊C4—22no—
123C2×C3×C22⋊C4—22no—
124C2×C3×C22⋊C4—41no—
125C2×C3×C22⋊C4—41no—
126C2×C3×C22⋊C4—41no—
127C2×#217—22no—
128C2×#217—22no—
129C2×#217—22no—
130C2×#217—22no—
131C2×#217—22no—
132C2×#217—22no—
133C2×#217—22no—
134C2×#217—22no—
135C2×#217—41no—
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—22no—
143C2×(C2×D3)⋊C4—22no—
144C2×(C2×D3)⋊C4D414yes—
145C2×C4⋊Dic3—22no—
146C2×C4⋊Dic3—22no—
147C2×C4⋊Dic3—22no—
148C2×Dic3⋊C4—22no—
149C2×Dic3⋊C4—22no—
150C2×Dic3⋊C4—22no—
151C2×Dic3⋊C4—22no—
152C2×Dic3⋊C4—22no—
153C2×Dic3⋊C4—22no—
154C2×Dic3⋊C4—22no—
155C2×Dic3⋊C4—41no—
156C2×Dic3⋊C4—41no—
157#883—232no—
158C3×#95—22no—
159C3×#95—22no—
160C3×#95—22no—
161C3×#95—41no—
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—
176C23×D4—31no—
177C24×C4—31no—
178C24×C4—31no—
179C24×C4—31no—
180C2×#123—64no—
181C2×#123—64no—
182C2×#123—64no—
183C22×C4⋊C4—31no—
184C22×C4⋊C4—31no—
185C22×C4⋊C4—31no—
186C22×C4⋊C4—31no—
187C22×C22⋊C4—31no—
188C22×C22⋊C4—31no—
189C22×C22⋊C4—31no—
190C22×C22⋊C4—31no—
191C22×C22⋊C4—31no—
192C22×C22⋊C4—31no—
193C22×C22⋊C4C2×D311yescharacteristic
194C22×C22⋊C4C2×D311yescharacteristic
195C22×C22⋊C4C2×D311yescharacteristic
196#386—64no—
197#386—64no—
198#381—64no—
199#380—64no—
200C2×#95—31no—
201C2×#95—31no—
202C2×#95—31no—
203C2×#95—31no—
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—64no—
215C2×#95C2×D311yescharacteristic
216C2×#95C2×D311yescharacteristic
217C2×#95C2×D311yescharacteristic
218C2×#95C2×D311yescharacteristic
219C24×C3—21no—
220C24×C3—21no—
221C24×C3—21no—
222C24×C3—21no—
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×C3C2×D412yes—
234C24×C3C2411yescharacteristic
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×D3C2×D412yes—
244C23×D3C2×D412yes—
245C23×D3C2×D412yes—
246C23×D3C2×D412yes—
247C23×D3#4112yes—
248C23×D3#4112yes—
249C23×D3#4112yes—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×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×C4C2×D412yes—
289C22×C3×C4C2×D412yes—
290C22×C3×C4C2×D412yes—
291C22×C3×C4#4112yes—
292C2×#67—28no—
293C2×#67—28no—
294C2×#67—28no—
295C2×#67—44no—
296C2×#67—44no—
297C2×#67—44no—
298C2×#67—44no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—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×Dic3C2×D412yes—
342C22×Dic3C2×D412yes—
343C22×Dic3C2×D412yes—
344C22×Dic3C2×D412yes—
345C22×Dic3#4112yes—
346C22×Dic3#4112yes—
347C22×Dic3#4112yes—
348C2×C4×D3—28no—
349C2×C4×D3—28no—
350C2×C4×D3—28no—
351C2×C4×D3—28no—
352C2×C4×D3—28no—
353C2×C4×D3—28no—
354C2×C4×D3—44no—
355C2×C4×D3—44no—
356C2×C4×D3—44no—
357C2×C4×D3—44no—
358C2×C4×D3—44no—
359C2×C4×D3—44no—
360C2×C4×D3—44no—
361C2×C4×D3—44no—
362C2×C4×D3—44no—
363C2×C4×D3—44no—
364C2×C4×D3—44no—
365C2×C4×D3—44no—
366C2×C4×D3—44no—
367C2×C4×D3—44no—
368C2×C4×D3—44no—
369C3×C22⋊C4—28no—
370C3×C22⋊C4—44no—
371C3×C22⋊C4—44no—
372#217—28no—
373#217—44no—
374#217—44no—
375(C2×D3)⋊C4—28no—
376(C2×D3)⋊C4—44no—
377(C2×D3)⋊C4—44no—
378C4⋊Dic3—28no—
379Dic3⋊C4—28no—
380Dic3⋊C4—44no—
381Dic3⋊C4—44no—
382C25—31no—
383C25C22×D311yescharacteristic
384C22×D4—34no—
385C22×D4—62no—
386C22×D4—62no—
387C22×D4—62no—
388C22×D4—62no—
389C22×D4—62no—
390C22×D4—62no—
391C23×C4—31no—
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—31no—
395C23×C4—31no—
396C23×C4—34no—
397C23×C4—34no—
398C23×C4—31no—
399C23×C4—31no—
400C23×C4—62no—
401C23×C4—62no—
402C23×C4—62no—
403C23×C4—62no—
404C23×C4—62no—
405C23×C4—62no—
406C23×C4—62no—
407C23×C4—62no—
408C23×C4—62no—
409C23×C4—62no—
410C23×C4—62no—
411C23×C4—62no—
412C23×C4—62no—
413C23×C4—62no—
414C23×C4—62no—
415C23×C4—121no—
416C23×C4—121no—
417C23×C4—121no—
418C23×C4—121no—
419C23×C4C22×D311yescharacteristic
420C23×C4C22×D311yescharacteristic
421C23×C4C22×D311yescharacteristic
422C23×C4C22×D311yescharacteristic
423C23×C4C22×D311yescharacteristic
424C23×C4C22×D311yescharacteristic
425#123—632no—
426C2×C4⋊C4—62no—
427C2×C4⋊C4—62no—
428C2×C4⋊C4—62no—
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—121no—
437C2×C4⋊C4—121no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—34no—
445C2×C22⋊C4—41no—
446C2×C22⋊C4—41no—
447C2×C22⋊C4—41no—
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—62no—
463C2×C22⋊C4—62no—
464C2×C22⋊C4—121no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—41no—
469#95—62no—
470#95—62no—
471#95—62no—
472#95—62no—
473#95—62no—
474#95—62no—
475#95—62no—
476#95—62no—
477#95—62no—
478#95—62no—
479#95—62no—
480#95—62no—
481#95—62no—
482#95—121no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—22no—
489C23×C3—22no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3—41no—
493C23×C3—41no—
494C23×C3—41no—
495C23×C3—41no—
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×C3C22×D411yescharacteristic
519C23×C3C22×D411yescharacteristic
520C23×C3C22×D411yescharacteristic
521C23×C3C22×D411yescharacteristic
522C23×C3C2×#4111yescharacteristic
523C23×C3C2×#4111yescharacteristic
524C23×C3C2×#4111yescharacteristic
525C23×C3C2×#4111yescharacteristic
526C23×C3C2×#4111yescharacteristic
527C23×C3C2×#4111yescharacteristic
528C23×C3C2×#4111yescharacteristic
529C23×C3H(5,𝔽2)11yescharacteristic
530C23×C3H(5,𝔽2)11yescharacteristic
531C23×C32−1+411yescharacteristic
532C23×C32−1+411yescharacteristic
533C22×D3—22no—
534C22×D3—22no—
535C22×D3—22no—
536C22×D3—22no—
537C22×D3—22no—
538C22×D3—22no—
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—22no—
558C22×D3—22no—
559C22×D3—22no—
560C22×D3—22no—
561C22×D3#12014yes—
562C22×D3#12114yes—
563C22×D3#12114yes—
564C22×D3#12114yes—
565C22×D3#12314yes—
566C22×D3#12314yes—
567C22×D3#12414yes—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
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—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
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—
610#67—416no—
611C2×Dic3—22no—
612C2×Dic3—22no—
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—22no—
616C2×Dic3—22no—
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—41no—
630C2×Dic3—41no—
631C2×Dic3—41no—
632C2×Dic3—41no—
633C2×Dic3—41no—
634C2×Dic3—41no—
635C2×Dic3—41no—
636C2×Dic3—41no—
637C2×Dic3—41no—
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#12314yescomplemented
660C4×D3—416no—
661C4×D3—416no—
662C4×D3—416no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—32no—
678C24—32no—
679C24—32no—
680C24—32no—
681C24—32no—
682C24—32no—
683C24—32no—
684C24—61no—
685C24—61no—
686C24—61no—
687C24—61no—
688C24—61no—
689C24—61no—
690C24—61no—
691C24—61no—
692C24D3×D412yes—
693C24C23×D311yescharacteristic
694C2×D4—68no—
695C2×D4—68no—
696C2×D4—68no—
697C2×D4—124no—
698C2×D4—124no—
699C2×D4—124no—
700C2×D4—124no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
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—32no—
740C22×C4—32no—
741C22×C4—32no—
742C22×C4—32no—
743C22×C4—32no—
744C22×C4—32no—
745C22×C4—32no—
746C22×C4—68no—
747C22×C4—68no—
748C22×C4—68no—
749C22×C4—68no—
750C22×C4—68no—
751C22×C4—68no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—61no—
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—124no—
795C22×C4—124no—
796C22×C4—124no—
797C22×C4—124no—
798C22×C4—124no—
799C22×C4—124no—
800C22×C4—124no—
801C22×C4—124no—
802C22×C4—124no—
803C22×C4—124no—
804C22×C4—124no—
805C22×C4—124no—
806C22×C4—124no—
807C22×C4—124no—
808C22×C4—124no—
809C22×C4#23512yes—
810C22×C4D3×D412yes—
811C22×C4D3×D412yes—
812C22×C4D3×D412yes—
813C4⋊C4—68no—
814C4⋊C4—68no—
815C4⋊C4—124no—
816C4⋊C4—124no—
817C22⋊C4—28no—
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×C3—42no—
827C22×C3—42no—
828C22×C3—42no—
829C22×C3—42no—
830C22×C3—42no—
831C22×C3—42no—
832C22×C3—42no—
833C22×C3—81no—
834C22×C3—81no—
835C22×C3—81no—
836C22×C3—81no—
837C22×C3—81no—
838C22×C3—81no—
839C22×C3—81no—
840C22×C3—81no—
841C22×C3C2×#12011yescharacteristic
842C22×C3C2×#12111yescharacteristic
843C22×C3C2×#12111yescharacteristic
844C22×C3C2×#12111yescharacteristic
845C22×C3C2×#12311yescharacteristic
846C22×C3C2×#12311yescharacteristic
847C22×C3C2×#12311yescharacteristic
848C22×C3#52511yescharacteristic
849C22×C3C2×#12411yescharacteristic
850C22×C3#52911yescharacteristic
851C22×C3#52911yescharacteristic
852C22×C3#53211yescharacteristic
853C22×C3#53211yescharacteristic
854C22×C3#53411yescharacteristic
855C22×C3#53611yescharacteristic
856C22×C3#53711yescharacteristic
857C22×C3#53711yescharacteristic
858C22×C3#53911yescharacteristic
859C22×C3#53911yescharacteristic
860C22×C3#54611yescharacteristic
861C22×C3#54611yescharacteristic
862C22×C3#54611yescharacteristic
863C22×C3#54611yescharacteristic
864C22×C3#54711yescharacteristic
865C22×C3#54711yescharacteristic
866C22×C3#54711yescharacteristic
867C22×C3#54711yescharacteristic
868C22×C3#55111yescharacteristic
869C22×C3#55111yescharacteristic
870C22×C3#55111yescharacteristic
871C22×C3#55111yescharacteristic
872C22×C3#55211yescharacteristic
873C22×C3#55211yescharacteristic
874C22×C3#55211yescharacteristic
875C22×C3#55211yescharacteristic
876C2×D3—24no—
877C2×D3—24no—
878C2×D3—24no—
879C2×D3—24no—
880C2×D3—24no—
881C2×D3—24no—
882C2×D3—24no—
883C2×D3—24no—
884C2×D3—24no—
885C2×D3—24no—
886C2×D3—24no—
887C2×D3—24no—
888C2×D3—24no—
889C2×D3—24no—
890C2×D3#39418yes—
891C3×C4—42no—
892C3×C4—42no—
893C3×C4—42no—
894C3×C4—42no—
895C3×C4—81no—
896C3×C4—81no—
897Dic3—24no—
898Dic3—42no—
899Dic3—42no—
900Dic3—42no—
901Dic3—42no—
902Dic3—81no—
903Dic3—81no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—34no—
912C23—34no—
913C23—34no—
914C23—34no—
915C23—34no—
916C23—34no—
917C23—34no—
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—41no—
944C23—41no—
945C23—41no—
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—62no—
962C23—62no—
963C23—62no—
964C23—62no—
965C23—62no—
966C23—62no—
967C23—62no—
968C23—62no—
969C23—62no—
970C23—62no—
971C23—62no—
972C23—62no—
973C23—62no—
974C23C2×#23511yescharacteristic
975C23C2×D3×D411yescharacteristic
976C23C2×D3×D411yescharacteristic
977C23C2×D3×D411yescharacteristic
978C23C2×D3×D411yescharacteristic
979C23#100411yescharacteristic
980C23#100411yescharacteristic
981C23D3×#4111yescharacteristic
982C23D3×#4111yescharacteristic
983C23D3×#4111yescharacteristic
984C23D3×#4111yescharacteristic
985C23D3×#4111yescharacteristic
986C23D3×#4111yescharacteristic
987C23#101011yescharacteristic
988C23#101011yescharacteristic
989D4—1216no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
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—34no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
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—62no—
1034C2×C4—62no—
1035C2×C4—62no—
1036C2×C4—62no—
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—1216no—
1052C2×C4—1216no—
1053C2×C4—1216no—
1054C2×C4—121no—
1055C2×C4—121no—
1056C2×C4—121no—
1057C2×C4—121no—
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×C3—82no—
1085C2×C3C2×#39411yescharacteristic
1086C2×C3#241211yescharacteristic
1087C2×C3#241311yescharacteristic
1088C2×C3#241911yescharacteristic
1089C2×C3#241911yescharacteristic
1090C2×C3#243011yescharacteristic
1091C2×C3#243011yescharacteristic
1092C2×C3#248611yescharacteristic
1093C2×C3#248811yescharacteristic
1094C2×C3#248811yescharacteristic
1095C2×C3#249811yescharacteristic
1096C2×C3#249811yescharacteristic
1097C2×C3#253411yescharacteristic
1098C2×C3#261811yescharacteristic
1099C2×C3#285411yescharacteristic
1100D3—28no—
1101C22—38no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—64no—
1110C22—64no—
1111C22—64no—
1112C22—64no—
1113C22—64no—
1114C22—64no—
1115C22—64no—
1116C22—64no—
1117C22—64no—
1118C22—64no—
1119C22—64no—
1120C22—64no—
1121C22—64no—
1122C22—64no—
1123C22—81no—
1124C22—81no—
1125C22—81no—
1126C22—81no—
1127C22—81no—
1128C22—81no—
1129C22—81no—
1130C22—81no—
1131C22#549011yescharacteristic
1132C22#552811yescharacteristic
1133C22#552911yescharacteristic
1134C22#554711yescharacteristic
1135C22#554811yescharacteristic
1136C22#555111yescharacteristic
1137C22#555611yescharacteristic
1138C22D3×#12011yescharacteristic
1139C22#558911yescharacteristic
1140C22D3×#12111yescharacteristic
1141C22D3×#12111yescharacteristic
1142C22D3×#12111yescharacteristic
1143C22#560811yescharacteristic
1144C22#560811yescharacteristic
1145C22#561011yescharacteristic
1146C22#561011yescharacteristic
1147C22#561211yescharacteristic
1148C22D3×#12311yescharacteristic
1149C22D3×#12311yescharacteristic
1150C22D3×#12311yescharacteristic
1151C22#565511yescharacteristic
1152C22#565511yescharacteristic
1153C22#565511yescharacteristic
1154C22#565911yescharacteristic
1155C22#565911yescharacteristic
1156C22#566011yescharacteristic
1157C22#566011yescharacteristic
1158C22#566811yescharacteristic
1159C22D3×#12411yescharacteristic
1160C22#567511yescharacteristic
1161C22#567911yescharacteristic
1162C22#570611yescharacteristic
1163C22#570811yescharacteristic
1164C22#570811yescharacteristic
1165C22#570811yescharacteristic
1166C4—42no—
1167C4—42no—
1168C4—42no—
1169C4—42no—
1170C4—64no—
1171C4—81no—
1172C4—81no—
1173C4—122no—
1174C4—122no—
1175C4—122no—
1176C4—122no—
1177C4—241no—
1178C4—241no—
1179C3#1492711yescharacteristic, complemented, Sylow
1180C2—68no—
1181C2—82no—
1182C2#7412711yescharacteristic
1183C2#7489611yescharacteristic
1184C2#7490111yescharacteristic
1185C2#7584311yescharacteristic
1186C2#7586711yescharacteristic
1187C2#7586911yescharacteristic
1188C2#7596011yescharacteristic
1189C2D3×#39411yescharacteristic
1190C2#7711011yescharacteristic
1191C2#7711611yescharacteristic
1192C2#7712411yescharacteristic
1193C2#7748511yescharacteristic
1194C2#7767111yescharacteristic
1195C2#7767811yescharacteristic
1196C2#7767911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1440C2
prime radicalC23×#67C22
hypercenter#1440D3
hypocenterC3#14927
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
4. C2×#4664C2semidirect
5. C2×#4667C2semidirect
6. C2×D3×#95C2semidirect
7. C3×#1440C2semidirect
8. #71549C2semidirect
9. #71547C2semidirect
10. #71547C2semidirect
11. (C2×D3)⋊#95C2semidirect
12. #69415C2semidirect
13. #69413C2semidirect
14. #69410C2semidirect
15. #69409C2semidirect
71. #1440D3semidirect
659. C2×Dic3#123semidirect
1179. C3#14927semidirect

Maximal subgroups

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

subgroupindex
C22×#8832
C2×#49562
C2×#46642
C2×#46672
C2×D3×#952
C3×#14402
#715492
#715472
(C2×D3)⋊#952
#694152
#694132
#694102
#694092
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