Finite Group Databasebeta

← #10724479

Subgroups — #10724479

Order 768.

1666 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4956C211yesmaximal, characteristic
2C3×#1437C211yesmaximal, characteristic, complemented
3#71550C211yesmaximal, characteristic
4#71550C211yesmaximal, characteristic
5#71549C211yesmaximal, characteristic, complemented
6#71548C211yesmaximal, characteristic, complemented
7#71545C211yesmaximal, characteristic, complemented
8#71537C211yesmaximal, characteristic, complemented
9#71534C211yesmaximal, characteristic, complemented
10(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
11(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
12#69417C211yesmaximal, characteristic, complemented
13#69417C211yesmaximal, characteristic, complemented
14#69408C211yesmaximal, characteristic, complemented
15#69402C211yesmaximal, characteristic, complemented
16#14516—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C42C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×C4×Dic3C2211yescharacteristic
32C2×C3×#95C2211yescharacteristic
33C2×C3×#95C2211yescharacteristic
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#4956C418yescomplemented
53C2×#386—31no—
54#1443—31no—
55#1443—31no—
56#1440—31no—
57#1440—31no—
58#1438—31no—
59#1438—31no—
60#1437—31no—
61#1437—31no—
62#1437—31no—
63#1437D311yescharacteristic, complemented
64#1434—31no—
65#1434—31no—
66C22⋊#95—31no—
67C22⋊#95—31no—
68C25×C3C2311yescharacteristic
69C24×D3C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C22×#67—22no—
77C22×#67—22no—
78C22×#67—41no—
79C22×#67—41no—
80C22×#67—41no—
81C22×#67—41no—
82C22×#67C2×C414yes—
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C22×C4×D3—41no—
91C22×C4×D3—41no—
92C22×C4×D3—41no—
93C22×C4×D3—41no—
94C22×C4×D3—41no—
95C22×C4×D3—41no—
96C22×C4×D3C2×C414yes—
97C2×C3×C22⋊C4—22no—
98C2×C3×C22⋊C4—22no—
99C2×C3×C22⋊C4—22no—
100C2×C3×C22⋊C4—41no—
101C2×C3×C22⋊C4—41no—
102C2×C3×C22⋊C4—41no—
103C2×C3×C22⋊C4—41no—
104C2×C3×C22⋊C4—41no—
105C2×C3×C22⋊C4C2×C414yes—
106C2×C3×C42—22no—
107C2×C3×C42—41no—
108C2×C3×C42—41no—
109C2×#217—22no—
110C2×#217—41no—
111C2×#217—41no—
112C2×#217—41no—
113C2×#217—41no—
114C2×#217—41no—
115C2×#217—41no—
116C2×#217—41no—
117C2×#217C2×C414yes—
118C2×(C2×D3)⋊C4—22no—
119C2×(C2×D3)⋊C4—22no—
120C2×(C2×D3)⋊C4—22no—
121C2×(C2×D3)⋊C4—22no—
122C2×(C2×D3)⋊C4—22no—
123C2×(C2×D3)⋊C4—22no—
124C2×(C2×D3)⋊C4—22no—
125C2×(C2×D3)⋊C4—22no—
126C2×(C2×D3)⋊C4—41no—
127C2×(C2×D3)⋊C4—41no—
128C2×(C2×D3)⋊C4—41no—
129C2×(C2×D3)⋊C4—41no—
130C2×(C2×D3)⋊C4—41no—
131C2×(C2×D3)⋊C4—41no—
132C2×(C2×D3)⋊C4C2×C414yes—
133C2×C4×Dic3—22no—
134C2×C4×Dic3—41no—
135C2×C4×Dic3—41no—
136C3×#95—41no—
137C3×#95—41no—
138C3×#95—41no—
139C3⋊#95—22no—
140C3⋊#95—22no—
141C3⋊#95—41no—
142C3⋊#95—41no—
143C3⋊#95—41no—
144C3⋊#95—41no—
145C3⋊#95—41no—
146C3⋊#95—41no—
147C3⋊#95—41no—
148C3⋊#95—41no—
149C3⋊#95—41no—
150C3⋊#95—41no—
151C3⋊#95—41no—
152C3⋊#95—41no—
153C3⋊#95—41no—
154C3⋊#95C2×C414yes—
155C3⋊#95C2×C414yes—
156C23×D4—31no—
157C24×C4—31no—
158C22×C22⋊C4—31no—
159C22×C22⋊C4—31no—
160C22×C22⋊C4—31no—
161C22×C22⋊C4—31no—
162C22×C22⋊C4—31no—
163C22×C22⋊C4—31no—
164C22×C22⋊C4—31no—
165C22×C22⋊C4—31no—
166C22×C22⋊C4C2×D311yescharacteristic
167C22×C22⋊C4C2×D311yescharacteristic
168C22×C22⋊C4C2×D311yescharacteristic
169C22×C42—31no—
170C22×C42C2×D311yescharacteristic
171#386—38no—
172C2×#95—31no—
173C2×#95—31no—
174C2×#95—31no—
175C2×#95—31no—
176C2×#95—31no—
177C2×#95—31no—
178C2×#95—31no—
179C2×#95—31no—
180C2×#95—31no—
181C2×#95—31no—
182C2×#95—31no—
183C2×#95—31no—
184C2×#95—31no—
185C2×#95—31no—
186C2×#95—31no—
187C2×#95—31no—
188C2×#95—31no—
189C2×#95C2×D311yescharacteristic
190C2×#95C2×D311yescharacteristic
191C2×#95C2×D311yescharacteristic
192C24×C3—21no—
193C24×C3—21no—
194C24×C3—21no—
195C24×C3—21no—
196C24×C3—21no—
197C24×C3—21no—
198C24×C3—21no—
199C24×C3—21no—
200C24×C3—21no—
201C24×C3—21no—
202C24×C3—21no—
203C24×C3—21no—
204C24×C3—21no—
205C24×C3—21no—
206C24×C3C22×C412yes—
207C24×C3C2411yescharacteristic
208C23×D3—21no—
209C23×D3—21no—
210C23×D3—21no—
211C23×D3—21no—
212C23×D3—21no—
213C23×D3—21no—
214C23×D3—21no—
215C23×D3—21no—
216C23×D3—21no—
217C23×D3—21no—
218C23×D3—21no—
219C23×D3—21no—
220C23×D3C22×C412yes—
221C23×D3#4112yes—
222C23×D3#4112yes—
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×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4C22×C412yes—
261C22×C3×C4C22×C412yes—
262C22×C3×C4#4112yes—
263C22×C3×C4#4112yes—
264C22×C3×C4#4112yes—
265C2×#67—28no—
266C2×#67—44no—
267C2×#67—44no—
268C2×#67—44no—
269C2×#67—44no—
270C2×#67—44no—
271C2×#67—44no—
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—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×Dic3C22×C412yes—
318C22×Dic3C22×C412yes—
319C22×Dic3C22×C412yes—
320C22×Dic3#4112yes—
321C2×C4×D3—44no—
322C2×C4×D3—44no—
323C2×C4×D3—44no—
324C2×C4×D3—44no—
325C2×C4×D3—44no—
326C2×C4×D3—44no—
327C2×C4×D3—44no—
328C3×C22⋊C4—44no—
329C3×C22⋊C4—44no—
330C3×C22⋊C4—44no—
331C3×C42—44no—
332#217—44no—
333#217—44no—
334#217—44no—
335(C2×D3)⋊C4—44no—
336(C2×D3)⋊C4—44no—
337(C2×D3)⋊C4—44no—
338(C2×D3)⋊C4—44no—
339(C2×D3)⋊C4—44no—
340C4×Dic3—44no—
341C25—31no—
342C25C22×D311yescharacteristic
343C22×D4—34no—
344C22×D4—62no—
345C22×D4—62no—
346C22×D4—121no—
347C22×D4—121no—
348C22×D4—121no—
349C22×D4—121no—
350C23×C4—31no—
351C23×C4—31no—
352C23×C4—31no—
353C23×C4—31no—
354C23×C4—34no—
355C23×C4—31no—
356C23×C4—31no—
357C23×C4—31no—
358C23×C4—121no—
359C23×C4—121no—
360C23×C4—121no—
361C23×C4—121no—
362C23×C4—121no—
363C23×C4—121no—
364C23×C4C22×D311yescharacteristic
365C23×C4C22×D311yescharacteristic
366C23×C4C22×D311yescharacteristic
367C23×C4C22×D311yescharacteristic
368C23×C4C22×D311yescharacteristic
369C23×C4C22×D311yescharacteristic
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—34no—
374C2×C22⋊C4—34no—
375C2×C22⋊C4—41no—
376C2×C22⋊C4—41no—
377C2×C22⋊C4—41no—
378C2×C22⋊C4—41no—
379C2×C22⋊C4—41no—
380C2×C22⋊C4—62no—
381C2×C22⋊C4—62no—
382C2×C22⋊C4—62no—
383C2×C22⋊C4—62no—
384C2×C22⋊C4—62no—
385C2×C22⋊C4—62no—
386C2×C22⋊C4—62no—
387C2×C22⋊C4—62no—
388C2×C22⋊C4—62no—
389C2×C22⋊C4—121no—
390C2×C22⋊C4—121no—
391C2×C22⋊C4—121no—
392C2×C22⋊C4—121no—
393C2×C22⋊C4—121no—
394C2×C22⋊C4—121no—
395C2×C22⋊C4—121no—
396C2×C22⋊C4—121no—
397C2×C22⋊C4—121no—
398C2×C22⋊C4—121no—
399C2×C22⋊C4—121no—
400C2×C22⋊C4—121no—
401C2×C22⋊C4—121no—
402C2×C22⋊C4C4×D314yes—
403C2×C42—22no—
404C2×C42—41no—
405C2×C42—41no—
406C2×C42—62no—
407C2×C42—121no—
408C2×C42—121no—
409#95—34no—
410#95—34no—
411#95—41no—
412#95—41no—
413#95—41no—
414#95—62no—
415#95—62no—
416#95—121no—
417#95—121no—
418#95—121no—
419#95—121no—
420#95—121no—
421#95—121no—
422#95—121no—
423#95—121no—
424#95—121no—
425#95—121no—
426#95—121no—
427#95—121no—
428#95—121no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—41no—
437C23×C3—41no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3—41no—
443C23×C3—41no—
444C23×C3—41no—
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—41no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3C23×C411yescharacteristic
465C23×C3C2×#4111yescharacteristic
466C23×C3C2×#4111yescharacteristic
467C23×C3C2×#4111yescharacteristic
468C23×C3C2×#4111yescharacteristic
469C23×C3C2×#4111yescharacteristic
470C23×C3C2×#4111yescharacteristic
471C23×C3H(5,𝔽2)11yescharacteristic
472C23×C3H(5,𝔽2)11yescharacteristic
473C23×C3H(5,𝔽2)11yescharacteristic
474C23×C3H(5,𝔽2)11yescharacteristic
475C23×C3H(5,𝔽2)11yescharacteristic
476C23×C3H(5,𝔽2)11yescharacteristic
477C23×C3H(5,𝔽2)11yescharacteristic
478C23×C3H(5,𝔽2)11yescharacteristic
479C22×D3—22no—
480C22×D3—22no—
481C22×D3—22no—
482C22×D3—22no—
483C22×D3—22no—
484C22×D3—22no—
485C22×D3—22no—
486C22×D3—22no—
487C22×D3—22no—
488C22×D3—22no—
489C22×D3—22no—
490C22×D3—22no—
491C22×D3—22no—
492C22×D3—22no—
493C22×D3—22no—
494C22×D3—22no—
495C22×D3—22no—
496C22×D3—22no—
497C22×D3—41no—
498C22×D3—41no—
499C22×D3—41no—
500C22×D3—41no—
501C22×D3—41no—
502C22×D3—41no—
503C22×D3—41no—
504C22×D3—41no—
505C22×D3—41no—
506C22×D3—41no—
507C22×D3—41no—
508C22×D3—41no—
509C22×D3—41no—
510C22×D3—41no—
511C22×D3—41no—
512C22×D3—41no—
513C22×D3#11714yes—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
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—
556#67—416no—
557C2×Dic3—22no—
558C2×Dic3—22no—
559C2×Dic3—22no—
560C2×Dic3—22no—
561C2×Dic3—22no—
562C2×Dic3—22no—
563C2×Dic3—22no—
564C2×Dic3—22no—
565C2×Dic3—22no—
566C2×Dic3—22no—
567C2×Dic3—22no—
568C2×Dic3—22no—
569C2×Dic3—41no—
570C2×Dic3—41no—
571C2×Dic3—41no—
572C2×Dic3—41no—
573C2×Dic3—41no—
574C2×Dic3—41no—
575C2×Dic3—41no—
576C2×Dic3—41no—
577C2×Dic3—41no—
578C2×Dic3—41no—
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—
606C4×D3—416no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—32no—
622C24—32no—
623C24—32no—
624C24—61no—
625C24—61no—
626C24—61no—
627C24—61no—
628C24—61no—
629C24—61no—
630C24—61no—
631C24—61no—
632C24—61no—
633C24—61no—
634C24—61no—
635C24—61no—
636C24C2×C4×D312yes—
637C24C23×D311yescharacteristic
638C2×D4—68no—
639C2×D4—124no—
640C2×D4—124no—
641C2×D4—124no—
642C2×D4—124no—
643C2×D4—124no—
644C2×D4—124no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
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—32no—
683C22×C4—32no—
684C22×C4—32no—
685C22×C4—32no—
686C22×C4—61no—
687C22×C4—61no—
688C22×C4—61no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—61no—
692C22×C4—61no—
693C22×C4—61no—
694C22×C4—61no—
695C22×C4—61no—
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—124no—
732C22×C4—124no—
733C22×C4—124no—
734C22×C4—124no—
735C22×C4—124no—
736C22×C4—124no—
737C22×C4—124no—
738C22×C4C2×C4×D312yes—
739C22×C4C2×C4×D312yes—
740C22×C4#23512yes—
741C22×C4#23512yes—
742C22×C4#23712yes—
743C22⋊C4—44no—
744C22⋊C4—44no—
745C22⋊C4—44no—
746C22⋊C4—124no—
747C22⋊C4—124no—
748C22⋊C4—124no—
749C22⋊C4—124no—
750C22⋊C4—124no—
751C22⋊C4—124no—
752C22⋊C4—124no—
753C22⋊C4—124no—
754C42—44no—
755C42—124no—
756C22×C3—42no—
757C22×C3—42no—
758C22×C3—42no—
759C22×C3—42no—
760C22×C3—42no—
761C22×C3—42no—
762C22×C3—42no—
763C22×C3—81no—
764C22×C3—81no—
765C22×C3—81no—
766C22×C3—81no—
767C22×C3—81no—
768C22×C3—81no—
769C22×C3—81no—
770C22×C3—81no—
771C22×C3C2×#11711yescharacteristic
772C22×C3C4×#4111yescharacteristic
773C22×C3C4×#4111yescharacteristic
774C22×C3#51811yescharacteristic
775C22×C3#51811yescharacteristic
776C22×C3#51811yescharacteristic
777C22×C3#51811yescharacteristic
778C22×C3#53811yescharacteristic
779C22×C3#53811yescharacteristic
780C22×C3#53811yescharacteristic
781C22×C3#53811yescharacteristic
782C22×C3#53811yescharacteristic
783C22×C3#53811yescharacteristic
784C22×C3#53811yescharacteristic
785C22×C3#53811yescharacteristic
786C22×C3#54011yescharacteristic
787C22×C3#54011yescharacteristic
788C22×C3#54011yescharacteristic
789C22×C3#54011yescharacteristic
790C22×C3#55111yescharacteristic
791C22×C3#55111yescharacteristic
792C22×C3#55111yescharacteristic
793C22×C3#55111yescharacteristic
794C22×C3#55111yescharacteristic
795C22×C3#55311yescharacteristic
796C22×C3#55311yescharacteristic
797C22×C3#55311yescharacteristic
798C22×C3#55311yescharacteristic
799C22×C3#55311yescharacteristic
800C22×C3#55311yescharacteristic
801C22×C3#55911yescharacteristic
802C22×C3#56011yescharacteristic
803C22×C3#56011yescharacteristic
804C22×C3#56011yescharacteristic
805C22×C3H(3,𝔽4)11yescharacteristic
806C2×D3—24no—
807C2×D3—24no—
808C2×D3—24no—
809C2×D3—42no—
810C2×D3—42no—
811C2×D3—42no—
812C2×D3—42no—
813C2×D3—42no—
814C2×D3—42no—
815C2×D3—42no—
816C2×D3—42no—
817C2×D3—42no—
818C2×D3—42no—
819C2×D3—42no—
820C2×D3—42no—
821C3×C4—42no—
822C3×C4—42no—
823C3×C4—42no—
824C3×C4—42no—
825C3×C4—42no—
826C3×C4—81no—
827Dic3—42no—
828Dic3—42no—
829Dic3—42no—
830Dic3—42no—
831Dic3—81no—
832Dic3—81no—
833Dic3—81no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—34no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—62no—
871C23—62no—
872C23—62no—
873C23—62no—
874C23—62no—
875C23—62no—
876C23—62no—
877C23—62no—
878C23—62no—
879C23—62no—
880C23—62no—
881C23—62no—
882C23—62no—
883C23—62no—
884C23—62no—
885C23—62no—
886C23—62no—
887C23—62no—
888C23—121no—
889C23—121no—
890C23—121no—
891C23—121no—
892C23—121no—
893C23—121no—
894C23—121no—
895C23—121no—
896C23—121no—
897C23—121no—
898C23—121no—
899C23—121no—
900C23—121no—
901C23—121no—
902C23—121no—
903C23—121no—
904C23C22×C4×D311yescharacteristic
905C23C2×#23511yescharacteristic
906C23C2×#23511yescharacteristic
907C23C2×#23711yescharacteristic
908C23#100411yescharacteristic
909C23#100411yescharacteristic
910C23#100411yescharacteristic
911C23#100411yescharacteristic
912C23#100411yescharacteristic
913C23D3×#4111yescharacteristic
914C23D3×#4111yescharacteristic
915C23D3×#4111yescharacteristic
916C23#100911yescharacteristic
917C23#100911yescharacteristic
918C23#100911yescharacteristic
919D4—1216no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
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—62no—
963C2×C4—62no—
964C2×C4—62no—
965C2×C4—62no—
966C2×C4—62no—
967C2×C4—62no—
968C2×C4—62no—
969C2×C4—62no—
970C2×C4—62no—
971C2×C4—62no—
972C2×C4—62no—
973C2×C4—62no—
974C2×C4—1216no—
975C2×C4—121no—
976C2×C4—121no—
977C2×C4—121no—
978C2×C4—121no—
979C2×C4—121no—
980C2×C4—121no—
981C2×C4—121no—
982C2×C4—121no—
983C2×C4—121no—
984C2×C4—121no—
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×C3—82no—
1013C2×C3#231211yescharacteristic
1014C2×C3#233311yescharacteristic
1015C2×C3#233311yescharacteristic
1016C2×C3#235311yescharacteristic
1017C2×C3#235311yescharacteristic
1018C2×C3#237411yescharacteristic
1019C2×C3#237511yescharacteristic
1020C2×C3#274911yescharacteristic
1021C2×C3#274911yescharacteristic
1022C2×C3#275311yescharacteristic
1023C2×C3#275311yescharacteristic
1024C2×C3#277811yescharacteristic
1025C2×C3#277811yescharacteristic
1026C2×C3#279711yescharacteristic
1027C2×C3#279711yescharacteristic
1028D3—44no—
1029C22—42no—
1030C22—42no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—64no—
1037C22—64no—
1038C22—64no—
1039C22—81no—
1040C22—81no—
1041C22—81no—
1042C22—81no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22—81no—
1047C22—122no—
1048C22—122no—
1049C22—122no—
1050C22—122no—
1051C22—122no—
1052C22—122no—
1053C22—122no—
1054C22—122no—
1055C22—122no—
1056C22—122no—
1057C22—122no—
1058C22—122no—
1059C22C4×#23511yescharacteristic
1060C22#548611yescharacteristic
1061C22#549411yescharacteristic
1062C22#549511yescharacteristic
1063C22D3×#11711yescharacteristic
1064C22#553011yescharacteristic
1065C22#553511yescharacteristic
1066C22C4×#23711yescharacteristic
1067C22#554511yescharacteristic
1068C22#554511yescharacteristic
1069C22#554511yescharacteristic
1070C22#555611yescharacteristic
1071C22#555611yescharacteristic
1072C22#555811yescharacteristic
1073C22#555811yescharacteristic
1074C22#555911yescharacteristic
1075C22#556011yescharacteristic
1076C22#556211yescharacteristic
1077C22#556511yescharacteristic
1078C22#559311yescharacteristic
1079C22#561311yescharacteristic
1080C22#561411yescharacteristic
1081C22#561511yescharacteristic
1082C22#561911yescharacteristic
1083C22#562011yescharacteristic
1084C22#562011yescharacteristic
1085C22#565711yescharacteristic
1086C22#565711yescharacteristic
1087C22#565811yescharacteristic
1088C22#567811yescharacteristic
1089C22#567911yescharacteristic
1090C22#568311yescharacteristic
1091C22#570411yescharacteristic
1092C22#570911yescharacteristic
1093C22#572011yescharacteristic
1094C4—42no—
1095C4—42no—
1096C4—42no—
1097C4—42no—
1098C4—42no—
1099C4—81no—
1100C4—122no—
1101C4—122no—
1102C4—122no—
1103C4—122no—
1104C4—241no—
1105C4—241no—
1106C4—241no—
1107C3#1451611yescharacteristic, complemented, Sylow
1108C2—82no—
1109C2—124no—
1110C2#7347911yescharacteristic
1111C2#7357011yescharacteristic
1112C2#7357611yescharacteristic
1113C2#7466911yescharacteristic
1114C2#7493011yescharacteristic
1115C2#7493211yescharacteristic
1116C2#7573311yescharacteristic
1117C2#7582511yescharacteristic
1118C2#7583511yescharacteristic
1119C2#7594611yescharacteristic
1120C2#7594911yescharacteristic
1121C2#7595411yescharacteristic
1122C2#7640611yescharacteristic
1123C2#7643411yescharacteristic
1124C2#7647111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1437C2
socle, cosocleC24×C3C24
prime radicalC23×#67C22
hypercenter#1437D3
hypocenterC3#14516
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C3×#1437C2semidirect
5. #71549C2semidirect
6. #71548C2semidirect
7. #71545C2semidirect
8. #71537C2semidirect
9. #71534C2semidirect
10. (C2×D3)⋊#95C2semidirect
11. (C2×D3)⋊#95C2semidirect
12. #69417C2semidirect
13. #69417C2semidirect
14. #69408C2semidirect
15. #69402C2semidirect
52. #4956C4semidirect
63. #1437D3semidirect
1107. C3#14516semidirect

Maximal subgroups

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

subgroupindex
C2×#49562
C3×#14372
#715502
#715492
#715482
#715452
#715372
#715342
(C2×D3)⋊#952
#694172
#694082
#694022
#145163