Finite Group Databasebeta

← #10733210

Subgroups — #10733210

Order 768.

1746 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#390C211yesmaximal, characteristic
2C2×#5220C211yesmaximal, characteristic
3C2×#4952C211yesmaximal, characteristic, complemented
4C2×#4943C211yesmaximal, characteristic, complemented
5#72131C211yesmaximal, characteristic
6#71568C211yesmaximal, characteristic, complemented
7#71567C211yesmaximal, characteristic, complemented
8#71549C211yesmaximal, characteristic, complemented
9#71548C211yesmaximal, characteristic, complemented
10#71547C211yesmaximal, characteristic, complemented
11#71547C211yesmaximal, characteristic, complemented
12#71547C211yesmaximal, characteristic, complemented
13#71544C211yesmaximal, characteristic, complemented
14#71534C211yesmaximal, characteristic, complemented
15#71534C211yesmaximal, characteristic, complemented
16#15285—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×Dic3C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C42C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C3×#390—24no—
35#5220—24no—
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
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54#4952—24no—
55#4943—24no—
56C2×#397—31no—
57C2×#390D311yescharacteristic
58C2×#386—31no—
59C2×#381—31no—
60#1444—31no—
61#1442—31no—
62#1440—31no—
63#1440—31no—
64#1439—31no—
65#1439—31no—
66#1439—31no—
67#1438—31no—
68#1434—31no—
69#1434—31no—
70C22⋊#95—31no—
71C25×C3C2311yescharacteristic
72C25×C3C2311yescharacteristic
73C22×C3×D4—22no—
74C22×C3×D4—22no—
75C22×C3×D4—22no—
76C22×C3×D4—22no—
77C22×C3×D4—41no—
78C22×C3×D4—41no—
79C22×C3×D4D414yes—
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×Dic3—22no—
86C23×Dic3—22no—
87C23×Dic3—22no—
88C23×Dic3—22no—
89C23×Dic3—22no—
90C23×Dic3—41no—
91C23×Dic3—41no—
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C2×C3×C4⋊C4—22no—
101C2×C3×C4⋊C4—41no—
102C2×C3×C4⋊C4—41no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—22no—
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4—22no—
110C2×C3×C22⋊C4—22no—
111C2×C3×C22⋊C4—41no—
112C2×C3×C22⋊C4—41no—
113C2×C3×C22⋊C4—41no—
114C2×C3×C22⋊C4—41no—
115C2×C3×C42—22no—
116C2×C3×C42—22no—
117C2×C3×C42—22no—
118C2×#217—22no—
119C2×#217—22no—
120C2×#217—22no—
121C2×#217—22no—
122C2×#217—22no—
123C2×#217—22no—
124C2×#217—22no—
125C2×#217—22no—
126C2×#217—22no—
127C2×#217—22no—
128C2×#217—22no—
129C2×#217—41no—
130C2×#217—41no—
131C2×#217—41no—
132C2×#217—41no—
133C2×#217—41no—
134C2×#217—41no—
135C2×#217—41no—
136C2×#217—41no—
137C2×#217—41no—
138C2×#217—41no—
139C2×Dic3⋊C4—22no—
140C2×Dic3⋊C4—41no—
141C2×Dic3⋊C4—41no—
142C2×Dic3⋊C4—41no—
143C2×Dic3⋊C4—41no—
144C2×Dic3⋊C4—41no—
145C3⋊#95—22no—
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—41no—
158C3⋊#95—41no—
159C3⋊#95—41no—
160C3⋊#95—41no—
161C3⋊#95—41no—
162C3⋊#95D414yescomplemented
163C23×D4C2×D311yescharacteristic
164C24×C4—31no—
165C22×C4⋊C4—31no—
166C22×C4⋊C4—31no—
167C22×C4⋊C4C2×D311yescharacteristic
168C22×C22⋊C4—31no—
169C22×C22⋊C4—31no—
170C22×C22⋊C4—31no—
171C22×C22⋊C4—31no—
172C22×C22⋊C4—31no—
173C22×C22⋊C4—31no—
174C22×C22⋊C4—31no—
175C22×C22⋊C4C2×D311yescharacteristic
176C22×C22⋊C4C2×D311yescharacteristic
177C22×C22⋊C4C2×D311yescharacteristic
178C22×C22⋊C4C2×D311yescharacteristic
179C22×C42C2×D311yescharacteristic
180#397—64no—
181#390—24no—
182#386—64no—
183#381—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×#95—31no—
200C2×#95—31no—
201C2×#95—31no—
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×C3—21no—
215C24×C3—21no—
216C24×C3—21no—
217C24×C3—21no—
218C24×C3—21no—
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×C3C2×D412yes—
229C24×C3C2×D412yes—
230C24×C3#4112yes—
231C24×C3#4112yes—
232C24×C3C2411yescharacteristic
233C2×C3×D4—28no—
234C2×C3×D4—28no—
235C2×C3×D4—44no—
236C2×C3×D4—44no—
237C2×C3×D4—44no—
238C2×C3×D4—44no—
239C2×C3×D4—44no—
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×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×C4C2×D412yes—
271C22×C3×C4C2×D412yes—
272C22×C3×C4#4112yes—
273C22×C3×C4#4112yes—
274C22×C3×C4#4112yes—
275C22×Dic3—28no—
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—21no—
291C22×Dic3—21no—
292C22×Dic3—21no—
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—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—44no—
329C22×Dic3—44no—
330C22×Dic3—44no—
331C22×Dic3—44no—
332C22×Dic3—44no—
333C22×Dic3—44no—
334C22×Dic3C2×D412yes—
335C22×Dic3C2×D412yes—
336C22×Dic3#4112yes—
337C22×Dic3#4112yes—
338C3×C4⋊C4—44no—
339C3×C22⋊C4—44no—
340C3×C22⋊C4—44no—
341C3×C22⋊C4—44no—
342C3×C22⋊C4—44no—
343C3×C42—44no—
344#217—44no—
345#217—44no—
346#217—44no—
347#217—44no—
348#217—44no—
349#217—44no—
350#217—44no—
351Dic3⋊C4—44no—
352Dic3⋊C4—44no—
353C25C22×D311yescharacteristic
354C25C22×D311yescharacteristic
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—41no—
360C22×D4—41no—
361C22×D4#6714yes—
362C23×C4—31no—
363C23×C4—31no—
364C23×C4—31no—
365C23×C4—31no—
366C23×C4—31no—
367C23×C4—31no—
368C23×C4—31no—
369C23×C4—31no—
370C23×C4—62no—
371C23×C4—62no—
372C23×C4—62no—
373C23×C4—62no—
374C23×C4—62no—
375C23×C4—121no—
376C23×C4—121no—
377C23×C4C22×D311yescharacteristic
378C23×C4C22×D311yescharacteristic
379C23×C4C22×D311yescharacteristic
380C23×C4C22×D311yescharacteristic
381C23×C4C22×D311yescharacteristic
382C2×C4⋊C4—22no—
383C2×C4⋊C4—41no—
384C2×C4⋊C4—41no—
385C2×C4⋊C4—62no—
386C2×C4⋊C4—121no—
387C2×C4⋊C4—121no—
388C2×C4⋊C4—121no—
389C2×C4⋊C4—121no—
390C2×C4⋊C4—121no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—41no—
400C2×C22⋊C4—41no—
401C2×C22⋊C4—41no—
402C2×C22⋊C4—41no—
403C2×C22⋊C4—62no—
404C2×C22⋊C4—62no—
405C2×C22⋊C4—62no—
406C2×C22⋊C4—62no—
407C2×C22⋊C4—62no—
408C2×C22⋊C4—62no—
409C2×C22⋊C4—62no—
410C2×C22⋊C4—62no—
411C2×C22⋊C4—62no—
412C2×C22⋊C4—62no—
413C2×C22⋊C4—62no—
414C2×C22⋊C4—121no—
415C2×C22⋊C4—121no—
416C2×C22⋊C4—121no—
417C2×C22⋊C4—121no—
418C2×C22⋊C4—121no—
419C2×C22⋊C4—121no—
420C2×C22⋊C4—121no—
421C2×C22⋊C4—121no—
422C2×C22⋊C4—121no—
423C2×C22⋊C4—121no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427#95—34no—
428#95—62no—
429#95—62no—
430#95—62no—
431#95—62no—
432#95—62no—
433#95—62no—
434#95—62no—
435#95—62no—
436#95—62no—
437#95—62no—
438#95—62no—
439#95—62no—
440#95—121no—
441#95—121no—
442#95—121no—
443#95—121no—
444#95—121no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—41no—
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#12314yes—
515C23×C3C22×D411yescharacteristic
516C23×C3C22×D411yescharacteristic
517C23×C3C2×#4111yescharacteristic
518C23×C3C2×#4111yescharacteristic
519C23×C3C2×#4111yescharacteristic
520C23×C3C2×#4111yescharacteristic
521C23×C3C2×#4111yescharacteristic
522C23×C3C2×#4111yescharacteristic
523C23×C3C2×#4111yescharacteristic
524C23×C3H(5,𝔽2)11yescharacteristic
525C23×C3H(5,𝔽2)11yescharacteristic
526C23×C3H(5,𝔽2)11yescharacteristic
527C23×C3H(5,𝔽2)11yescharacteristic
528C23×C3H(5,𝔽2)11yescharacteristic
529C23×C32−1+411yescharacteristic
530C3×D4—416no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—22no—
542C2×C3×C4—22no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4#12314yes—
566C2×Dic3—22no—
567C2×Dic3—22no—
568C2×Dic3—22no—
569C2×Dic3—22no—
570C2×Dic3—22no—
571C2×Dic3—22no—
572C2×Dic3—22no—
573C2×Dic3—22no—
574C2×Dic3—22no—
575C2×Dic3—22no—
576C2×Dic3—22no—
577C2×Dic3—22no—
578C2×Dic3—416no—
579C2×Dic3—41no—
580C2×Dic3—41no—
581C2×Dic3—41no—
582C2×Dic3—41no—
583C2×Dic3—41no—
584C2×Dic3—41no—
585C2×Dic3—41no—
586C2×Dic3—41no—
587C2×Dic3—41no—
588C2×Dic3—41no—
589C2×Dic3—41no—
590C2×Dic3—41no—
591C2×Dic3—41no—
592C2×Dic3—41no—
593C2×Dic3—41no—
594C2×Dic3—41no—
595C2×Dic3—41no—
596C2×Dic3—41no—
597C2×Dic3—41no—
598C2×Dic3—41no—
599C2×Dic3—41no—
600C2×Dic3—41no—
601C2×Dic3—41no—
602C2×Dic3—41no—
603C2×Dic3—41no—
604C2×Dic3—41no—
605C2×Dic3—41no—
606C2×Dic3—41no—
607C2×Dic3—41no—
608C2×Dic3—41no—
609C2×Dic3—41no—
610C2×Dic3—41no—
611C2×Dic3—41no—
612C2×Dic3—41no—
613C2×Dic3—41no—
614C2×Dic3—41no—
615C2×Dic3—41no—
616C2×Dic3—41no—
617C2×Dic3—41no—
618C2×Dic3—41no—
619C2×Dic3—41no—
620C2×Dic3—41no—
621C2×Dic3—41no—
622C2×Dic3—41no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24#23512yes—
650C24#23512yes—
651C24C2×#6712yes—
652C24C2×#6712yes—
653C24C23×D311yescharacteristic
654C2×D4—28no—
655C2×D4—28no—
656C2×D4—44no—
657C2×D4—44no—
658C2×D4—44no—
659C2×D4—44no—
660C2×D4—44no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—32no—
692C22×C4—32no—
693C22×C4—32no—
694C22×C4—32no—
695C22×C4—68no—
696C22×C4—61no—
697C22×C4—61no—
698C22×C4—61no—
699C22×C4—61no—
700C22×C4—61no—
701C22×C4—61no—
702C22×C4—61no—
703C22×C4—61no—
704C22×C4—61no—
705C22×C4—61no—
706C22×C4—61no—
707C22×C4—61no—
708C22×C4—61no—
709C22×C4—61no—
710C22×C4—61no—
711C22×C4—61no—
712C22×C4—61no—
713C22×C4—61no—
714C22×C4—61no—
715C22×C4—61no—
716C22×C4—61no—
717C22×C4—61no—
718C22×C4—61no—
719C22×C4—61no—
720C22×C4—61no—
721C22×C4—61no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4—61no—
725C22×C4—61no—
726C22×C4—61no—
727C22×C4—61no—
728C22×C4—61no—
729C22×C4—61no—
730C22×C4—61no—
731C22×C4—61no—
732C22×C4—61no—
733C22×C4—61no—
734C22×C4—61no—
735C22×C4—61no—
736C22×C4—61no—
737C22×C4—61no—
738C22×C4—61no—
739C22×C4—61no—
740C22×C4—61no—
741C22×C4—61no—
742C22×C4—61no—
743C22×C4—61no—
744C22×C4—61no—
745C22×C4—61no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—124no—
749C22×C4—124no—
750C22×C4—124no—
751C22×C4—124no—
752C22×C4—124no—
753C22×C4—124no—
754C22×C4D3×D412yes—
755C22×C4#23712yes—
756C22×C4#23712yes—
757C22×C4#23712yes—
758C22×C4C2×#6712yes—
759C4⋊C4—44no—
760C4⋊C4—124no—
761C4⋊C4—124no—
762C22⋊C4—44no—
763C22⋊C4—44no—
764C22⋊C4—44no—
765C22⋊C4—44no—
766C22⋊C4—124no—
767C22⋊C4—124no—
768C22⋊C4—124no—
769C22⋊C4—124no—
770C22⋊C4—124no—
771C22⋊C4—124no—
772C22⋊C4—124no—
773C42—44no—
774C22×C3—24no—
775C22×C3—24no—
776C22×C3—24no—
777C22×C3—42no—
778C22×C3—42no—
779C22×C3—42no—
780C22×C3—42no—
781C22×C3—42no—
782C22×C3—42no—
783C22×C3—42no—
784C22×C3—42no—
785C22×C3—42no—
786C22×C3—42no—
787C22×C3—42no—
788C22×C3—42no—
789C22×C3—42no—
790C22×C3—42no—
791C22×C3—42no—
792C22×C3—42no—
793C22×C3—42no—
794C22×C3—42no—
795C22×C3—42no—
796C22×C3—81no—
797C22×C3—81no—
798C22×C3—81no—
799C22×C3—81no—
800C22×C3—81no—
801C22×C3—81no—
802C22×C3—81no—
803C22×C3—81no—
804C22×C3C2×#12311yescharacteristic
805C22×C3C2×#12311yescharacteristic
806C22×C3#52511yescharacteristic
807C22×C3#52911yescharacteristic
808C22×C3#52911yescharacteristic
809C22×C3#53211yescharacteristic
810C22×C3#53411yescharacteristic
811C22×C3#53511yescharacteristic
812C22×C3#53811yescharacteristic
813C22×C3#53811yescharacteristic
814C22×C3#53911yescharacteristic
815C22×C3#54011yescharacteristic
816C22×C3#54011yescharacteristic
817C22×C3#54211yescharacteristic
818C22×C3#54211yescharacteristic
819C22×C3D4211yescharacteristic
820C22×C3#54611yescharacteristic
821C22×C3#54611yescharacteristic
822C22×C3#54611yescharacteristic
823C22×C3#54711yescharacteristic
824C22×C3#54711yescharacteristic
825C22×C3#55011yescharacteristic
826C22×C3#55111yescharacteristic
827C22×C3#55111yescharacteristic
828C22×C3#55111yescharacteristic
829C22×C3#55111yescharacteristic
830C22×C3#55111yescharacteristic
831C22×C3#55111yescharacteristic
832C22×C3#55211yescharacteristic
833C22×C3#55311yescharacteristic
834C22×C3#55311yescharacteristic
835C22×C3#55511yescharacteristic
836C22×C3#55511yescharacteristic
837C22×C3#56011yescharacteristic
838C22×C3#56211yescharacteristic
839C3×C4—24no—
840C3×C4—42no—
841C3×C4—42no—
842C3×C4—81no—
843C3×C4—81no—
844Dic3—42no—
845Dic3—42no—
846Dic3—42no—
847Dic3—42no—
848Dic3—81no—
849Dic3—81no—
850Dic3—81no—
851Dic3—81no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23#92914yes—
922C23C2×#23511yescharacteristic
923C23C2×#23511yescharacteristic
924C23C2×D3×D411yescharacteristic
925C23C2×#23711yescharacteristic
926C23C2×#23711yescharacteristic
927C23C2×#23711yescharacteristic
928C23#100411yescharacteristic
929C23#100411yescharacteristic
930C23#100411yescharacteristic
931C23#100411yescharacteristic
932C23D3×#4111yescharacteristic
933C23D3×#4111yescharacteristic
934C23#100911yescharacteristic
935C23#101011yescharacteristic
936C23C22×#6711yescharacteristic
937D4—416no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—62no—
973C2×C4—62no—
974C2×C4—62no—
975C2×C4—62no—
976C2×C4—62no—
977C2×C4—62no—
978C2×C4—62no—
979C2×C4—62no—
980C2×C4—62no—
981C2×C4—62no—
982C2×C4—62no—
983C2×C4—62no—
984C2×C4—1216no—
985C2×C4—121no—
986C2×C4—121no—
987C2×C4—121no—
988C2×C4—121no—
989C2×C4—121no—
990C2×C4—121no—
991C2×C4—121no—
992C2×C4—121no—
993C2×C4—121no—
994C2×C4—121no—
995C2×C4—121no—
996C2×C4—121no—
997C2×C4—121no—
998C2×C4—121no—
999C2×C4—121no—
1000C2×C4—121no—
1001C2×C4—121no—
1002C2×C4—121no—
1003C2×C4—121no—
1004C2×C4—121no—
1005C2×C4—121no—
1006C2×C4—121no—
1007C2×C4—121no—
1008C2×C4—121no—
1009C2×C4—121no—
1010C2×C4—121no—
1011C2×C4—121no—
1012C2×C4—121no—
1013C2×C4—121no—
1014C2×C4—121no—
1015C2×C4—121no—
1016C2×C4—121no—
1017C2×C4—121no—
1018C2×C4—121no—
1019C2×C4—121no—
1020C2×C4—121no—
1021C2×C4—121no—
1022C2×C4—121no—
1023C2×C4—121no—
1024C2×C4—121no—
1025C2×C4—121no—
1026C2×C4—121no—
1027C2×C4—121no—
1028C2×C4—121no—
1029C2×C4#93514yes—
1030C2×C3—44no—
1031C2×C3—82no—
1032C2×C3#241811yescharacteristic
1033C2×C3#241911yescharacteristic
1034C2×C3#242011yescharacteristic
1035C2×C3#242211yescharacteristic
1036C2×C3#247911yescharacteristic
1037C2×C3#248311yescharacteristic
1038C2×C3#252611yescharacteristic
1039C2×C3#255411yescharacteristic
1040C2×C3#261011yescharacteristic
1041C2×C3#267311yescharacteristic
1042C2×C3#268611yescharacteristic
1043C2×C3#270611yescharacteristic
1044C2×C3#273711yescharacteristic
1045C2×C3#274911yescharacteristic
1046C2×C3#276111yescharacteristic
1047C22—24no—
1048C22—24no—
1049C22—24no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22#549511yescharacteristic
1078C22#549511yescharacteristic
1079C22#549511yescharacteristic
1080C22#549511yescharacteristic
1081C22#553811yescharacteristic
1082C22#554111yescharacteristic
1083C22#554711yescharacteristic
1084C22#555011yescharacteristic
1085C22#555611yescharacteristic
1086C22#555611yescharacteristic
1087C22#556011yescharacteristic
1088C22#556411yescharacteristic
1089C22#559611yescharacteristic
1090C22#560011yescharacteristic
1091C22#560311yescharacteristic
1092C22#561111yescharacteristic
1093C22#561411yescharacteristic
1094C22#561611yescharacteristic
1095C22#561811yescharacteristic
1096C22#561911yescharacteristic
1097C22#566911yescharacteristic
1098C22#567011yescharacteristic
1099C22#567811yescharacteristic
1100C22#568411yescharacteristic
1101C22#571511yescharacteristic
1102C22#571811yescharacteristic
1103C22#571911yescharacteristic
1104C22#572011yescharacteristic
1105C22C2×#92911yescharacteristic
1106C22C2×#93511yescharacteristic
1107C22D4×#6711yescharacteristic
1108C22#580411yescharacteristic
1109C22#580611yescharacteristic
1110C22#582411yescharacteristic
1111C22#582911yescharacteristic
1112C4—24no—
1113C4—42no—
1114C4—42no—
1115C4—81no—
1116C4—81no—
1117C4—122no—
1118C4—122no—
1119C4—122no—
1120C4—122no—
1121C4—241no—
1122C4—241no—
1123C4—241no—
1124C4—241no—
1125C3#1528511yescharacteristic, complemented, Sylow
1126C2—44no—
1127C2—82no—
1128C2#7633211yescharacteristic
1129C2#7634411yescharacteristic
1130C2#7635411yescharacteristic
1131C2#7637211yescharacteristic
1132C2#7639011yescharacteristic
1133C2#7640311yescharacteristic
1134C2#7640611yescharacteristic
1135C2#7641211yescharacteristic
1136C2#8211411yescharacteristic
1137C2#8235411yescharacteristic
1138C2#8240411yescharacteristic
1139C2#8264311yescharacteristic
1140C2#8264411yescharacteristic
1141C2#8298411yescharacteristic
1142C2#8318211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#390C2
prime radicalC23×C3×D4C22
hypercenterC2×#390D3
hypocenterC3#15285
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
3. C2×#4952C2semidirect
4. C2×#4943C2semidirect
6. #71568C2semidirect
7. #71567C2semidirect
8. #71549C2semidirect
9. #71548C2semidirect
10. #71547C2semidirect
11. #71547C2semidirect
12. #71547C2semidirect
13. #71544C2semidirect
14. #71534C2semidirect
15. #71534C2semidirect
162. C3⋊#95D4semidirect
1125. C3#15285semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3902
C2×#52202
C2×#49522
C2×#49432
#721312
#715682
#715672
#715492
#715482
#715472
#715442
#715342
#152853