Finite Group Databasebeta

← #10725790

Subgroups — #10725790

Order 768.

1550 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4959C211yesmaximal, characteristic
2C3×#1437C211yesmaximal, characteristic, complemented
3#71550C211yesmaximal, characteristic
4#71550C211yesmaximal, characteristic
5#71549C211yesmaximal, characteristic, complemented
6#71545C211yesmaximal, characteristic, complemented
7#71545C211yesmaximal, characteristic, complemented
8#71537C211yesmaximal, characteristic, complemented
9#71536C211yesmaximal, characteristic, complemented
10#69429C211yesmaximal, characteristic, complemented
11#69421C211yesmaximal, characteristic, complemented
12#69408C211yesmaximal, characteristic, complemented
13#69408C211yesmaximal, characteristic, complemented
14#69402C211yesmaximal, characteristic, complemented
15#69401C211yesmaximal, characteristic, complemented
16#14617—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C42C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×C4×Dic3C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3⋊#95C2211yescharacteristic
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2211yescharacteristic
40C2×C3⋊#95C2211yescharacteristic
41C2×C3⋊#95C2211yescharacteristic
42C2×C3⋊#95C2211yescharacteristic
43C2×C3⋊#95C2211yescharacteristic
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52#4959C418yescomplemented
53C2×#394—31no—
54#1445—31no—
55#1440—31no—
56#1440—31no—
57#1438—31no—
58#1438—31no—
59#1437—31no—
60#1437—31no—
61#1437—31no—
62#1437—31no—
63#1437—31no—
64#1437D311yescharacteristic, complemented
65#1436—31no—
66#1434—31no—
67#1434—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—41no—
77C22×#67—41no—
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
90C2×C3×C22⋊C4—22no—
91C2×C3×C22⋊C4—22no—
92C2×C3×C22⋊C4—22no—
93C2×C3×C22⋊C4—41no—
94C2×C3×C22⋊C4—41no—
95C2×C3×C22⋊C4—41no—
96C2×C3×C22⋊C4—41no—
97C2×C3×C22⋊C4—41no—
98C2×C3×C22⋊C4C2×C414yes—
99C2×C3×C42—41no—
100C2×C3×C42—41no—
101C2×C3×C42—41no—
102C2×#217—22no—
103C2×#217—22no—
104C2×#217—22no—
105C2×#217—41no—
106C2×#217—41no—
107C2×#217—41no—
108C2×#217—41no—
109C2×#217—41no—
110C2×#217C2×C414yes—
111C2×(C2×D3)⋊C4—22no—
112C2×(C2×D3)⋊C4—22no—
113C2×(C2×D3)⋊C4—22no—
114C2×(C2×D3)⋊C4—22no—
115C2×(C2×D3)⋊C4—22no—
116C2×(C2×D3)⋊C4—22no—
117C2×(C2×D3)⋊C4—41no—
118C2×(C2×D3)⋊C4—41no—
119C2×(C2×D3)⋊C4—41no—
120C2×(C2×D3)⋊C4—41no—
121C2×(C2×D3)⋊C4—41no—
122C2×(C2×D3)⋊C4—41no—
123C2×(C2×D3)⋊C4—41no—
124C2×(C2×D3)⋊C4—41no—
125C2×(C2×D3)⋊C4—41no—
126C2×(C2×D3)⋊C4—41no—
127C2×(C2×D3)⋊C4C2×C414yes—
128C2×(C2×D3)⋊C4C2×C414yes—
129C2×Dic3⋊C4—41no—
130C2×Dic3⋊C4—41no—
131C2×Dic3⋊C4C2×C414yes—
132C2×C4×Dic3—22no—
133C2×C4×Dic3—22no—
134C2×C4×Dic3—41no—
135C2×C4×Dic3—41no—
136C2×C4×Dic3—41no—
137C2×C4×Dic3—41no—
138C3×#95—22no—
139C3×#95—41no—
140C3×#95—41no—
141C3⋊#95—22no—
142C3⋊#95—22no—
143C3⋊#95—22no—
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⋊#95—41no—
155C3⋊#95C2×C414yes—
156C23×D4—31no—
157C22×C4⋊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⋊C4—31no—
167C22×C22⋊C4C2×D311yescharacteristic
168C22×C22⋊C4C2×D311yescharacteristic
169C22×C22⋊C4C2×D311yescharacteristic
170C22×C42—31no—
171C22×C42—31no—
172C22×C42C2×D311yescharacteristic
173#394—38no—
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×D3—21no—
221C23×D3—21no—
222C23×D3C22×C412yes—
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—44no—
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×Dic3C22×C412yes—
316C22×Dic3C22×C412yes—
317C22×Dic3C22×C412yes—
318C22×Dic3#4112yes—
319C22×Dic3#4112yes—
320C22×Dic3#4112yes—
321C3×C22⋊C4—44no—
322C3×C22⋊C4—44no—
323C3×C22⋊C4—44no—
324C3×C42—44no—
325#217—44no—
326#217—44no—
327#217—44no—
328(C2×D3)⋊C4—44no—
329(C2×D3)⋊C4—44no—
330(C2×D3)⋊C4—44no—
331(C2×D3)⋊C4—44no—
332(C2×D3)⋊C4—44no—
333(C2×D3)⋊C4—44no—
334Dic3⋊C4—44no—
335C4×Dic3—44no—
336C4×Dic3—44no—
337C25—31no—
338C25C22×D311yescharacteristic
339C22×D4—34no—
340C22×D4—121no—
341C22×D4—121no—
342C22×D4—121no—
343C22×D4—121no—
344C22×D4—121no—
345C22×D4—121no—
346C23×C4—31no—
347C23×C4—31no—
348C23×C4—31no—
349C23×C4—31no—
350C23×C4—31no—
351C23×C4—31no—
352C23×C4—31no—
353C23×C4C22×D311yescharacteristic
354C23×C4C22×D311yescharacteristic
355C23×C4C22×D311yescharacteristic
356C23×C4C22×D311yescharacteristic
357C23×C4C22×D311yescharacteristic
358C23×C4C22×D311yescharacteristic
359C2×C4⋊C4—34no—
360C2×C4⋊C4—121no—
361C2×C4⋊C4—121no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—34no—
366C2×C22⋊C4—34no—
367C2×C22⋊C4—34no—
368C2×C22⋊C4—41no—
369C2×C22⋊C4—41no—
370C2×C22⋊C4—41no—
371C2×C22⋊C4—41no—
372C2×C22⋊C4—41no—
373C2×C22⋊C4—62no—
374C2×C22⋊C4—62no—
375C2×C22⋊C4—62no—
376C2×C22⋊C4—62no—
377C2×C22⋊C4—62no—
378C2×C22⋊C4—62no—
379C2×C22⋊C4—62no—
380C2×C22⋊C4—62no—
381C2×C22⋊C4—62no—
382C2×C22⋊C4—121no—
383C2×C22⋊C4—121no—
384C2×C22⋊C4—121no—
385C2×C22⋊C4—121no—
386C2×C22⋊C4—121no—
387C2×C22⋊C4—121no—
388C2×C22⋊C4—121no—
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⋊C4C4×D314yes—
398C2×C42—41no—
399C2×C42—41no—
400C2×C42—41no—
401C2×C42—62no—
402C2×C42—62no—
403C2×C42—121no—
404C2×C42—121no—
405C2×C42—121no—
406C2×C42—121no—
407#95—22no—
408#95—34no—
409#95—41no—
410#95—41no—
411#95—62no—
412#95—62no—
413#95—62no—
414#95—121no—
415#95—121no—
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—
425C23×C3—22no—
426C23×C3—22no—
427C23×C3—22no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3—41no—
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×C3C23×C411yescharacteristic
461C23×C3C2×#4111yescharacteristic
462C23×C3C2×#4111yescharacteristic
463C23×C3C2×#4111yescharacteristic
464C23×C3C2×#4111yescharacteristic
465C23×C3C2×#4111yescharacteristic
466C23×C3C2×#4111yescharacteristic
467C23×C3H(5,𝔽2)11yescharacteristic
468C23×C3H(5,𝔽2)11yescharacteristic
469C23×C3H(5,𝔽2)11yescharacteristic
470C23×C3H(5,𝔽2)11yescharacteristic
471C23×C3H(5,𝔽2)11yescharacteristic
472C23×C3H(5,𝔽2)11yescharacteristic
473C23×C3H(5,𝔽2)11yescharacteristic
474C23×C3H(5,𝔽2)11yescharacteristic
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—22no—
478C22×D3—22no—
479C22×D3—22no—
480C22×D3—22no—
481C22×D3—22no—
482C22×D3—41no—
483C22×D3—41no—
484C22×D3—41no—
485C22×D3—41no—
486C22×D3—41no—
487C22×D3—41no—
488C22×D3—41no—
489C22×D3—41no—
490C22×D3—41no—
491C22×D3—41no—
492C22×D3—41no—
493C22×D3—41no—
494C22×D3—41no—
495C22×D3—41no—
496C22×D3—41no—
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—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
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—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
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—
552#67—416no—
553C2×Dic3—22no—
554C2×Dic3—22no—
555C2×Dic3—22no—
556C2×Dic3—22no—
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—22no—
570C2×Dic3—22no—
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—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—32no—
617C24—61no—
618C24—61no—
619C24—61no—
620C24—61no—
621C24—61no—
622C24—61no—
623C24—61no—
624C24—61no—
625C24—61no—
626C24—61no—
627C24—61no—
628C24—61no—
629C24—61no—
630C24—61no—
631C24C2×C4×D312yes—
632C24C23×D311yescharacteristic
633C2×D4—124no—
634C2×D4—124no—
635C2×D4—124no—
636C2×D4—124no—
637C2×D4—124no—
638C2×D4—124no—
639C2×D4—124no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
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—32no—
678C22×C4—32no—
679C22×C4—32no—
680C22×C4—32no—
681C22×C4—32no—
682C22×C4—32no—
683C22×C4—61no—
684C22×C4—61no—
685C22×C4—61no—
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×C4C2×C4×D312yes—
727C22×C4C2×C4×D312yes—
728C22×C4#23512yes—
729C22×C4#23512yes—
730C22×C4#23712yes—
731C4⋊C4—124no—
732C22⋊C4—44no—
733C22⋊C4—44no—
734C22⋊C4—44no—
735C22⋊C4—124no—
736C22⋊C4—124no—
737C22⋊C4—124no—
738C22⋊C4—124no—
739C22⋊C4—124no—
740C22⋊C4—124no—
741C22⋊C4—124no—
742C22⋊C4—124no—
743C22⋊C4—124no—
744C42—44no—
745C42—124no—
746C42—124no—
747C22×C3—42no—
748C22×C3—42no—
749C22×C3—42no—
750C22×C3—42no—
751C22×C3—42no—
752C22×C3—42no—
753C22×C3—42no—
754C22×C3—81no—
755C22×C3—81no—
756C22×C3—81no—
757C22×C3—81no—
758C22×C3—81no—
759C22×C3—81no—
760C22×C3—81no—
761C22×C3—81no—
762C22×C3C4×#4111yescharacteristic
763C22×C3C4×#4111yescharacteristic
764C22×C3C4×#4111yescharacteristic
765C22×C3#51811yescharacteristic
766C22×C3#51811yescharacteristic
767C22×C3#51811yescharacteristic
768C22×C3#51811yescharacteristic
769C22×C3#53811yescharacteristic
770C22×C3#53811yescharacteristic
771C22×C3#53811yescharacteristic
772C22×C3#53811yescharacteristic
773C22×C3#53811yescharacteristic
774C22×C3#53811yescharacteristic
775C22×C3#54011yescharacteristic
776C22×C3#54011yescharacteristic
777C22×C3#54011yescharacteristic
778C22×C3#54011yescharacteristic
779C22×C3#54011yescharacteristic
780C22×C3#54011yescharacteristic
781C22×C3#55111yescharacteristic
782C22×C3#55111yescharacteristic
783C22×C3#55111yescharacteristic
784C22×C3#55111yescharacteristic
785C22×C3#55311yescharacteristic
786C22×C3#55311yescharacteristic
787C22×C3#55311yescharacteristic
788C22×C3#55311yescharacteristic
789C22×C3#55511yescharacteristic
790C22×C3#55511yescharacteristic
791C22×C3#55911yescharacteristic
792C22×C3#55911yescharacteristic
793C22×C3#56011yescharacteristic
794C22×C3#56011yescharacteristic
795C22×C3#56011yescharacteristic
796C22×C3H(3,𝔽4)11yescharacteristic
797C2×D3—42no—
798C2×D3—42no—
799C2×D3—42no—
800C2×D3—42no—
801C2×D3—42no—
802C2×D3—42no—
803C2×D3—42no—
804C2×D3—81no—
805C2×D3—81no—
806C2×D3—81no—
807C2×D3—81no—
808C2×D3—81no—
809C2×D3—81no—
810C2×D3—81no—
811C2×D3—81no—
812C3×C4—42no—
813C3×C4—42no—
814C3×C4—42no—
815C3×C4—42no—
816C3×C4—42no—
817C3×C4—81no—
818Dic3—42no—
819Dic3—42no—
820Dic3—42no—
821Dic3—42no—
822Dic3—42no—
823Dic3—42no—
824Dic3—81no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
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—62no—
861C23—62no—
862C23—62no—
863C23—62no—
864C23—62no—
865C23—62no—
866C23—62no—
867C23—121no—
868C23—121no—
869C23—121no—
870C23—121no—
871C23—121no—
872C23—121no—
873C23—121no—
874C23—121no—
875C23—121no—
876C23—121no—
877C23—121no—
878C23—121no—
879C23—121no—
880C23—121no—
881C23—121no—
882C23—121no—
883C23—121no—
884C23—121no—
885C23—121no—
886C23—121no—
887C23—121no—
888C23—121no—
889C23—121no—
890C23—121no—
891C23—121no—
892C23—121no—
893C23—121no—
894C23—121no—
895C23C22×C4×D311yescharacteristic
896C23C2×#23511yescharacteristic
897C23C2×#23511yescharacteristic
898C23C2×#23711yescharacteristic
899C23#100411yescharacteristic
900C23#100411yescharacteristic
901C23#100411yescharacteristic
902C23#100411yescharacteristic
903C23#100411yescharacteristic
904C23D3×#4111yescharacteristic
905C23D3×#4111yescharacteristic
906C23D3×#4111yescharacteristic
907C23#100911yescharacteristic
908C23#100911yescharacteristic
909C23#100911yescharacteristic
910D4—1216no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
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—62no—
954C2×C4—62no—
955C2×C4—62no—
956C2×C4—62no—
957C2×C4—62no—
958C2×C4—62no—
959C2×C4—62no—
960C2×C4—62no—
961C2×C4—62no—
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—121no—
972C2×C4—121no—
973C2×C4—121no—
974C2×C4—121no—
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×C3—82no—
1003C2×C3#233311yescharacteristic
1004C2×C3#233311yescharacteristic
1005C2×C3#233311yescharacteristic
1006C2×C3#237211yescharacteristic
1007C2×C3#237411yescharacteristic
1008C2×C3#237411yescharacteristic
1009C2×C3#237511yescharacteristic
1010C2×C3#275211yescharacteristic
1011C2×C3#275211yescharacteristic
1012C2×C3#275311yescharacteristic
1013C2×C3#275311yescharacteristic
1014C2×C3#275611yescharacteristic
1015C2×C3#275611yescharacteristic
1016C2×C3#280311yescharacteristic
1017C2×C3#280311yescharacteristic
1018D3—82no—
1019C22—42no—
1020C22—42no—
1021C22—42no—
1022C22—42no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—81no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—81no—
1031C22—81no—
1032C22—81no—
1033C22—81no—
1034C22—122no—
1035C22—122no—
1036C22—122no—
1037C22—122no—
1038C22—122no—
1039C22—122no—
1040C22—122no—
1041C22—241no—
1042C22—241no—
1043C22—241no—
1044C22—241no—
1045C22—241no—
1046C22—241no—
1047C22—241no—
1048C22—241no—
1049C22C4×#23511yescharacteristic
1050C22#548611yescharacteristic
1051C22#549411yescharacteristic
1052C22#549511yescharacteristic
1053C22#552211yescharacteristic
1054C22#553211yescharacteristic
1055C22#553511yescharacteristic
1056C22C4×#23711yescharacteristic
1057C22#554011yescharacteristic
1058C22#554511yescharacteristic
1059C22#554511yescharacteristic
1060C22#554511yescharacteristic
1061C22#555611yescharacteristic
1062C22#555611yescharacteristic
1063C22#555811yescharacteristic
1064C22#555911yescharacteristic
1065C22#556011yescharacteristic
1066C22#556211yescharacteristic
1067C22#556311yescharacteristic
1068C22#559411yescharacteristic
1069C22#560111yescharacteristic
1070C22#561511yescharacteristic
1071C22#561511yescharacteristic
1072C22#561711yescharacteristic
1073C22#562011yescharacteristic
1074C22#562011yescharacteristic
1075C22#566111yescharacteristic
1076C22#566311yescharacteristic
1077C22#566611yescharacteristic
1078C22#567811yescharacteristic
1079C22#567811yescharacteristic
1080C22#568111yescharacteristic
1081C22#570411yescharacteristic
1082C22#570511yescharacteristic
1083C22#571911yescharacteristic
1084C4—42no—
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—42no—
1089C4—81no—
1090C4—122no—
1091C4—122no—
1092C4—122no—
1093C4—122no—
1094C4—122no—
1095C4—122no—
1096C4—241no—
1097C3#1461711yescharacteristic, complemented, Sylow
1098C2—82no—
1099C2—242no—
1100C2#7347511yescharacteristic
1101C2#7347811yescharacteristic
1102C2#7357011yescharacteristic
1103C2#7484611yescharacteristic
1104C2#7484711yescharacteristic
1105C2#7488211yescharacteristic
1106C2#7548711yescharacteristic
1107C2#7573911yescharacteristic
1108C2#7574011yescharacteristic
1109C2#7581011yescharacteristic
1110C2#7583011yescharacteristic
1111C2#7594511yescharacteristic
1112C2#7629911yescharacteristic
1113C2#7640811yescharacteristic
1114C2#7642011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1437C2
socle, cosocleC24×C3C24
prime radicalC23×#67C22
hypercenter#1437D3
hypocenterC3#14617
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. #71545C2semidirect
7. #71545C2semidirect
8. #71537C2semidirect
9. #71536C2semidirect
10. #69429C2semidirect
11. #69421C2semidirect
12. #69408C2semidirect
13. #69408C2semidirect
14. #69402C2semidirect
15. #69401C2semidirect
52. #4959C4semidirect
64. #1437D3semidirect
1097. C3#14617semidirect

Maximal subgroups

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

subgroupindex
C2×#49592
C3×#14372
#715502
#715492
#715452
#715372
#715362
#694292
#694212
#694082
#694022
#694012
#146173