Finite Group Databasebeta

← #10733081

Subgroups — #10733081

Order 768.

2098 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#878C211yesmaximal, characteristic, complemented
2C2×C3×#394C211yesmaximal, characteristic
3C2×#5220C211yesmaximal, characteristic
4C2×#4973C211yesmaximal, characteristic, complemented
5C2×#4947C211yesmaximal, characteristic, complemented
6C2×#4945C211yesmaximal, characteristic, complemented
7#72131C211yesmaximal, characteristic
8#71566C211yesmaximal, characteristic, complemented
9#71548C211yesmaximal, characteristic, complemented
10#71547C211yesmaximal, characteristic, complemented
11#71546C211yesmaximal, characteristic, complemented
12#71545C211yesmaximal, characteristic, complemented
13#71544C211yesmaximal, characteristic, complemented
14#69415C211yesmaximal, characteristic, complemented
15#69414C211yesmaximal, characteristic, complemented
16#15275—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×Dic3C2211yescharacteristic
19C23×Dic6C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
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×#217C2211yescharacteristic
32C22×C4⋊Dic3C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×C4×Dic3C2211yescharacteristic
36C2×#878—24no—
37C2×#878—24no—
38C2×#878—24no—
39C3×#394—24no—
40C2×C3×#95C2211yescharacteristic
41#5220—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
56C2×C3⋊#95C2211yescharacteristic
57#4973—24no—
58#4947—24no—
59#4945—24no—
60C22×C22⋊Q8—31no—
61C2×#394D311yescharacteristic
62C2×#393—31no—
63C2×#391—31no—
64C2×#388—31no—
65C2×#386—31no—
66#1442—31no—
67#1442—31no—
68#1441—31no—
69#1440—31no—
70#1439—31no—
71#1439—31no—
72#1438—31no—
73#1437—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—41no—
83C22×C3×D4—41no—
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×Dic3—22no—
90C23×Dic3—22no—
91C23×Dic3—22no—
92C23×Dic3—22no—
93C23×Dic3—22no—
94C23×Dic3—41no—
95C23×Dic3—41no—
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
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—41no—
114C2×C3×C22⋊C4—22no—
115C2×C3×C22⋊C4—22no—
116C2×C3×C22⋊C4—22no—
117C2×C3×C22⋊C4—22no—
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⋊C4D414yes—
126C2×#217—22no—
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—22no—
136C2×#217—22no—
137C2×#217—22no—
138C2×#217—22no—
139C2×#217—22no—
140C2×#217—22no—
141C2×#217—22no—
142C2×#217—41no—
143C2×#217—41no—
144C2×#217—41no—
145C2×#217—41no—
146C2×#217—41no—
147C2×C4⋊Dic3—22no—
148C2×C4⋊Dic3—22no—
149C2×C4⋊Dic3—22no—
150C2×Dic3⋊C4—22no—
151C2×Dic3⋊C4—22no—
152C2×Dic3⋊C4—22no—
153C2×Dic3⋊C4—22no—
154C2×Dic3⋊C4—22no—
155C2×Dic3⋊C4D414yescomplemented
156C2×C4×Dic3—22no—
157C2×C4×Dic3—22no—
158C2×C4×Dic3—41no—
159#878—232no—
160C3×#95—22no—
161C3⋊#95—22no—
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—41no—
172C3⋊#95—41no—
173C3⋊#95—41no—
174C3⋊#95—41no—
175C3⋊#95D414yes—
176C23×Q8—31no—
177C23×D4C2×D311yescharacteristic
178C24×C4—31no—
179C2×C22⋊Q8—64no—
180C2×C22⋊Q8—64no—
181C2×C22⋊Q8—64no—
182C22×C4⋊C4—31no—
183C22×C4⋊C4—31no—
184C22×C4⋊C4—31no—
185C22×C4⋊C4C2×D311yescharacteristic
186C22×C22⋊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
196C22×C22⋊C4C2×D311yescharacteristic
197C22×C42—31no—
198#394—24no—
199#393—64no—
200#391—64no—
201#388—64no—
202#386—64no—
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—31no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95—31no—
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×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×C3#4112yes—
247C24×C3#4112yes—
248C24×C3#4112yes—
249C24×C3C2411yescharacteristic
250C2×C3×D4—28no—
251C2×C3×D4—44no—
252C2×C3×D4—44no—
253C2×C3×D4—44no—
254C2×C3×D4—44no—
255C2×C3×D4—44no—
256C2×C3×D4—44no—
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×C4C2×D412yes—
288C22×C3×C4C2×D412yes—
289C22×C3×C4C2×D412yes—
290C22×C3×C4C2×D412yes—
291C22×C3×C4C2×D412yes—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—28no—
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—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—44no—
342C22×Dic3—44no—
343C22×Dic3—44no—
344C22×Dic3—44no—
345C22×Dic3—44no—
346C22×Dic3—44no—
347C22×Dic3C2×D412yes—
348C22×Dic3C2×D412yes—
349C22×Dic3C2×D412yes—
350C22×Dic3C2×D412yes—
351C22×Dic3C2×D412yes—
352C22×Dic3C2×D412yes—
353C22×Dic3#4112yes—
354C22×Dic3#4112yes—
355C2×Dic6—28no—
356C2×Dic6—28no—
357C2×Dic6—44no—
358C2×Dic6—44no—
359C2×Dic6—44no—
360C2×Dic6—44no—
361C2×Dic6—44no—
362C3×C4⋊C4—44no—
363C3×C22⋊C4—28no—
364C3×C22⋊C4—44no—
365C3×C22⋊C4—44no—
366C3×C22⋊C4—44no—
367#217—28no—
368#217—28no—
369#217—44no—
370#217—44no—
371#217—44no—
372#217—44no—
373#217—44no—
374C4⋊Dic3—28no—
375Dic3⋊C4—28no—
376Dic3⋊C4—28no—
377C4×Dic3—44no—
378C25C22×D311yescharacteristic
379C25C22×D311yescharacteristic
380C22×Q8—34no—
381C22×Q8—62no—
382C22×Q8—62no—
383C22×Q8—62no—
384C22×Q8—62no—
385C22×Q8—121no—
386C22×Q8—121no—
387C22×D4—22no—
388C22×D4—22no—
389C22×D4—22no—
390C22×D4—22no—
391C22×D4—22no—
392C22×D4—41no—
393C22×D4—41no—
394C23×C4—31no—
395C23×C4—31no—
396C23×C4—31no—
397C23×C4—31no—
398C23×C4—31no—
399C23×C4—31no—
400C23×C4—31no—
401C23×C4—31no—
402C23×C4—62no—
403C23×C4—62no—
404C23×C4—62no—
405C23×C4—62no—
406C23×C4—62no—
407C23×C4—121no—
408C23×C4—121no—
409C23×C4C22×D311yescharacteristic
410C23×C4C22×D311yescharacteristic
411C23×C4C22×D311yescharacteristic
412C23×C4C22×D311yescharacteristic
413C23×C4C22×D311yescharacteristic
414C22⋊Q8—632no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—34no—
418C2×C4⋊C4—41no—
419C2×C4⋊C4—62no—
420C2×C4⋊C4—62no—
421C2×C4⋊C4—62no—
422C2×C4⋊C4—62no—
423C2×C4⋊C4—62no—
424C2×C4⋊C4—62no—
425C2×C4⋊C4—62no—
426C2×C4⋊C4—62no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—41no—
438C2×C22⋊C4—62no—
439C2×C22⋊C4—62no—
440C2×C22⋊C4—62no—
441C2×C22⋊C4—62no—
442C2×C22⋊C4—62no—
443C2×C22⋊C4—62no—
444C2×C22⋊C4—62no—
445C2×C22⋊C4—62no—
446C2×C22⋊C4—62no—
447C2×C22⋊C4—62no—
448C2×C22⋊C4—62no—
449C2×C22⋊C4—62no—
450C2×C22⋊C4—62no—
451C2×C22⋊C4—62no—
452C2×C22⋊C4—62no—
453C2×C22⋊C4—62no—
454C2×C22⋊C4—121no—
455C2×C22⋊C4—121no—
456C2×C22⋊C4—121no—
457C2×C22⋊C4—121no—
458C2×C22⋊C4—121no—
459C2×C22⋊C4#6714yes—
460C2×C42—62no—
461C2×C42—62no—
462C2×C42—121no—
463#95—22no—
464#95—34no—
465#95—62no—
466#95—62no—
467#95—62no—
468#95—62no—
469#95—62no—
470#95—62no—
471#95—62no—
472#95—62no—
473#95—62no—
474#95—62no—
475#95—121no—
476#95—121no—
477#95—121no—
478#95—121no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—22no—
489C23×C3—22no—
490C23×C3—22no—
491C23×C3—22no—
492C23×C3—22no—
493C23×C3—22no—
494C23×C3—22no—
495C23×C3—22no—
496C23×C3—22no—
497C23×C3—22no—
498C23×C3—22no—
499C23×C3—22no—
500C23×C3—22no—
501C23×C3—22no—
502C23×C3—22no—
503C23×C3—22no—
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×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
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#12414yes—
549C23×C3C22×D411yescharacteristic
550C23×C3C22×D411yescharacteristic
551C23×C3C22×D411yescharacteristic
552C23×C3C22×D411yescharacteristic
553C23×C3C2×#4111yescharacteristic
554C23×C3C2×#4111yescharacteristic
555C23×C3C2×#4111yescharacteristic
556C23×C3C2×#4111yescharacteristic
557C23×C3C2×#4111yescharacteristic
558C23×C3H(5,𝔽2)11yescharacteristic
559C23×C3H(5,𝔽2)11yescharacteristic
560C23×C3H(5,𝔽2)11yescharacteristic
561C23×C32−1+411yescharacteristic
562C23×C32−1+411yescharacteristic
563C23×C32−1+411yescharacteristic
564C3×D4—416no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
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—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
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#12014yes—
600C2×Dic3—22no—
601C2×Dic3—22no—
602C2×Dic3—22no—
603C2×Dic3—22no—
604C2×Dic3—22no—
605C2×Dic3—22no—
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3—22no—
610C2×Dic3—22no—
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—416no—
622C2×Dic3—41no—
623C2×Dic3—41no—
624C2×Dic3—41no—
625C2×Dic3—41no—
626C2×Dic3—41no—
627C2×Dic3—41no—
628C2×Dic3—41no—
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#12114yes—
657Dic6—416no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
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—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24#23712yes—
685C24#23712yes—
686C24#23712yes—
687C24C2×#6712yes—
688C24C23×D311yescharacteristic
689C2×Q8—68no—
690C2×Q8—68no—
691C2×Q8—124no—
692C2×Q8—124no—
693C2×Q8—124no—
694C2×Q8—124no—
695C2×Q8—124no—
696C2×D4—28no—
697C2×D4—44no—
698C2×D4—44no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
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—32no—
734C22×C4—32no—
735C22×C4—32no—
736C22×C4—32no—
737C22×C4—32no—
738C22×C4—32no—
739C22×C4—32no—
740C22×C4—32no—
741C22×C4—61no—
742C22×C4—61no—
743C22×C4—61no—
744C22×C4—61no—
745C22×C4—68no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—61no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—61no—
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—124no—
791C22×C4—124no—
792C22×C4—124no—
793C22×C4—124no—
794C22×C4—124no—
795C22×C4—124no—
796C22×C4D3×D412yes—
797C22×C4D3×D412yes—
798C22×C4D3×D412yes—
799C22×C4C2×#6712yes—
800C22×C4C2×#6712yes—
801C4⋊C4—44no—
802C4⋊C4—68no—
803C4⋊C4—68no—
804C4⋊C4—68no—
805C22⋊C4—28no—
806C22⋊C4—44no—
807C22⋊C4—44no—
808C22⋊C4—44no—
809C22⋊C4—68no—
810C22⋊C4—68no—
811C22⋊C4—124no—
812C22⋊C4—124no—
813C22⋊C4—124no—
814C22⋊C4—124no—
815C22⋊C4—124no—
816C42—124no—
817C22×C3—24no—
818C22×C3—24no—
819C22×C3—24no—
820C22×C3—42no—
821C22×C3—42no—
822C22×C3—42no—
823C22×C3—42no—
824C22×C3—42no—
825C22×C3—42no—
826C22×C3—42no—
827C22×C3—42no—
828C22×C3—42no—
829C22×C3—42no—
830C22×C3—42no—
831C22×C3—42no—
832C22×C3—42no—
833C22×C3—42no—
834C22×C3—42no—
835C22×C3—42no—
836C22×C3—42no—
837C22×C3—42no—
838C22×C3—42no—
839C22×C3—81no—
840C22×C3—81no—
841C22×C3—81no—
842C22×C3—81no—
843C22×C3—81no—
844C22×C3—81no—
845C22×C3—81no—
846C22×C3—81no—
847C22×C3C2×#12011yescharacteristic
848C22×C3C2×#12111yescharacteristic
849C22×C3#52511yescharacteristic
850C22×C3#52511yescharacteristic
851C22×C3C2×#12411yescharacteristic
852C22×C3#52911yescharacteristic
853C22×C3#53411yescharacteristic
854C22×C3#53611yescharacteristic
855C22×C3#53611yescharacteristic
856C22×C3#53711yescharacteristic
857C22×C3#53811yescharacteristic
858C22×C3#53911yescharacteristic
859C22×C3#53911yescharacteristic
860C22×C3#54211yescharacteristic
861C22×C3#54211yescharacteristic
862C22×C3D4211yescharacteristic
863C22×C3D4211yescharacteristic
864C22×C3#54611yescharacteristic
865C22×C3#54611yescharacteristic
866C22×C3#54611yescharacteristic
867C22×C3#54611yescharacteristic
868C22×C3#54711yescharacteristic
869C22×C3#54811yescharacteristic
870C22×C3#54811yescharacteristic
871C22×C3#54811yescharacteristic
872C22×C3#54811yescharacteristic
873C22×C3#54811yescharacteristic
874C22×C3#54811yescharacteristic
875C22×C3#55011yescharacteristic
876C22×C3#55111yescharacteristic
877C22×C3#55111yescharacteristic
878C22×C3#55211yescharacteristic
879C22×C3#55211yescharacteristic
880C22×C3#56211yescharacteristic
881C22×C3#56311yescharacteristic
882C3×C4—24no—
883C3×C4—42no—
884C3×C4—42no—
885C3×C4—81no—
886C3×C4—81no—
887Dic3—24no—
888Dic3—42no—
889Dic3—42no—
890Dic3—42no—
891Dic3—42no—
892Dic3—42no—
893Dic3—81no—
894Dic3—81no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
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—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23#93614yes—
965C23C2×D3×D411yescharacteristic
966C23C2×D3×D411yescharacteristic
967C23C2×D3×D411yescharacteristic
968C23C2×#23711yescharacteristic
969C23C2×#23711yescharacteristic
970C23C2×#23711yescharacteristic
971C23#100411yescharacteristic
972C23#100411yescharacteristic
973C23D3×#4111yescharacteristic
974C23D3×#4111yescharacteristic
975C23#100911yescharacteristic
976C23#101011yescharacteristic
977C23#101011yescharacteristic
978C23#101011yescharacteristic
979C23C22×#6711yescharacteristic
980Q8—1216no—
981D4—416no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—34no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
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—62no—
1018C2×C4—62no—
1019C2×C4—62no—
1020C2×C4—62no—
1021C2×C4—62no—
1022C2×C4—62no—
1023C2×C4—62no—
1024C2×C4—62no—
1025C2×C4—62no—
1026C2×C4—62no—
1027C2×C4—62no—
1028C2×C4—62no—
1029C2×C4—62no—
1030C2×C4—62no—
1031C2×C4—62no—
1032C2×C4—62no—
1033C2×C4—62no—
1034C2×C4—62no—
1035C2×C4—62no—
1036C2×C4—62no—
1037C2×C4—62no—
1038C2×C4—1216no—
1039C2×C4—121no—
1040C2×C4—121no—
1041C2×C4—121no—
1042C2×C4—121no—
1043C2×C4—121no—
1044C2×C4—121no—
1045C2×C4—121no—
1046C2×C4—121no—
1047C2×C4—121no—
1048C2×C4—121no—
1049C2×C4—121no—
1050C2×C4—121no—
1051C2×C4—121no—
1052C2×C4—121no—
1053C2×C4—121no—
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#93714yes—
1074C2×C3—44no—
1075C2×C3—82no—
1076C2×C3#240711yescharacteristic
1077C2×C3#241011yescharacteristic
1078C2×C3#242611yescharacteristic
1079C2×C3#243611yescharacteristic
1080C2×C3#246311yescharacteristic
1081C2×C3#247211yescharacteristic
1082C2×C3#247711yescharacteristic
1083C2×C3#248811yescharacteristic
1084C2×C3#253611yescharacteristic
1085C2×C3#267411yescharacteristic
1086C2×C3#268111yescharacteristic
1087C2×C3#268711yescharacteristic
1088C2×C3#270211yescharacteristic
1089C2×C3#272811yescharacteristic
1090C2×C3#273011yescharacteristic
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—81no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22—81no—
1121C22#558611yescharacteristic
1122C22#558711yescharacteristic
1123C22#559111yescharacteristic
1124C22#559311yescharacteristic
1125C22#559811yescharacteristic
1126C22#559811yescharacteristic
1127C22#559811yescharacteristic
1128C22#559811yescharacteristic
1129C22#559811yescharacteristic
1130C22#559911yescharacteristic
1131C22D3×#12111yescharacteristic
1132C22#560511yescharacteristic
1133C22#560611yescharacteristic
1134C22#560811yescharacteristic
1135C22#560911yescharacteristic
1136C22#561011yescharacteristic
1137C22#564911yescharacteristic
1138C22#565011yescharacteristic
1139C22#565011yescharacteristic
1140C22#565811yescharacteristic
1141C22#566211yescharacteristic
1142C22#566511yescharacteristic
1143C22#566511yescharacteristic
1144C22#566711yescharacteristic
1145C22#566911yescharacteristic
1146C22#567211yescharacteristic
1147C22#567511yescharacteristic
1148C22#567711yescharacteristic
1149C22C2×#93611yescharacteristic
1150C22C2×#93711yescharacteristic
1151C22D4×#6711yescharacteristic
1152C22#580611yescharacteristic
1153C22#582411yescharacteristic
1154C22#582511yescharacteristic
1155C22#582911yescharacteristic
1156C4—24no—
1157C4—42no—
1158C4—42no—
1159C4—64no—
1160C4—81no—
1161C4—81no—
1162C4—122no—
1163C4—122no—
1164C4—122no—
1165C4—122no—
1166C4—122no—
1167C4—241no—
1168C4—241no—
1169C3#1527511yescharacteristic, complemented, Sylow
1170C2—44no—
1171C2—82no—
1172C2#7690111yescharacteristic
1173C2#7691611yescharacteristic
1174C2#7693111yescharacteristic
1175C2#7694311yescharacteristic
1176C2#7702311yescharacteristic
1177C2#7704311yescharacteristic
1178C2#7704511yescharacteristic
1179C2#7713911yescharacteristic
1180C2#8258911yescharacteristic
1181C2#8265411yescharacteristic
1182C2#8270111yescharacteristic
1183C2#8270211yescharacteristic
1184C2#8285711yescharacteristic
1185C2#8287411yescharacteristic
1186C2#8298211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#394C2
prime radicalC23×C3×D4C22
hypercenterC2×#394D3
hypocenterC3#15275
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#878C2semidirect
4. C2×#4973C2semidirect
5. C2×#4947C2semidirect
6. C2×#4945C2semidirect
8. #71566C2semidirect
9. #71548C2semidirect
10. #71547C2semidirect
11. #71546C2semidirect
12. #71545C2semidirect
13. #71544C2semidirect
14. #69415C2semidirect
15. #69414C2semidirect
110. C22×Dic6D4semidirect
155. C2×Dic3⋊C4D4semidirect
1169. C3#15275semidirect

Maximal subgroups

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

subgroupindex
C22×#8782
C2×C3×#3942
C2×#52202
C2×#49732
C2×#49472
C2×#49452
#721312
#715662
#715482
#715472
#715462
#715452
#715442
#694152
#694142
#152753