Finite Group Databasebeta

← #10723639

Subgroups — #10723639

Order 768.

1658 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#388C211yesmaximal, characteristic, complemented
2C2×#4957C211yesmaximal, characteristic
3C2×#4670C211yesmaximal, characteristic, complemented
4#71570C211yesmaximal, characteristic, complemented
5#71563C211yesmaximal, characteristic, complemented
6#71550C211yesmaximal, characteristic
7#71550C211yesmaximal, characteristic
8#71549C211yesmaximal, characteristic, complemented
9#71546C211yesmaximal, characteristic, complemented
10#71545C211yesmaximal, characteristic, complemented
11#71537C211yesmaximal, characteristic, complemented
12#71536C211yesmaximal, characteristic, complemented
13#69429C211yesmaximal, characteristic, complemented
14#69406C211yesmaximal, characteristic, complemented
15#69401C211yesmaximal, characteristic, complemented
16#14444—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
32C22×C4⋊Dic3C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×C4×Dic3C2211yescharacteristic
35C22×C4×Dic3C2211yescharacteristic
36C3×#388—24no—
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2211yescharacteristic
39C2×C3⋊#95C2211yescharacteristic
40C2×C3⋊#95C2211yescharacteristic
41C2×C3⋊#95C2211yescharacteristic
42C2×C3⋊#95C2211yescharacteristic
43C2×C3⋊#95C2211yescharacteristic
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53#4957C418yescomplemented
54#4670—24no—
55C2×#390—31no—
56C2×#388—31no—
57C2×#388D311yescharacteristic, complemented
58#1440—31no—
59#1440—31no—
60#1439—31no—
61#1439—31no—
62#1438—31no—
63#1438—31no—
64#1437—31no—
65#1437—31no—
66#1436—31no—
67#1436—31no—
68C4⋊#95—31no—
69#1434—31no—
70C25×C3C2311yescharacteristic
71C24×D3C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C22×#67—22no—
79C22×#67—22no—
80C22×#67—41no—
81C22×#67—41no—
82C22×#67—41no—
83C22×#67—41no—
84C22×#67C2×C414yes—
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C2×C3×C4⋊C4—22no—
93C2×C3×C4⋊C4—22no—
94C2×C3×C4⋊C4—41no—
95C2×C3×C22⋊C4—22no—
96C2×C3×C22⋊C4—22no—
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⋊C4C2×C414yes—
104C2×C3×C42—22no—
105C2×C3×C42—41no—
106C2×C3×C42—41no—
107C2×#217—22no—
108C2×#217—41no—
109C2×#217—41no—
110C2×#217—41no—
111C2×#217—41no—
112C2×#217—41no—
113C2×#217—41no—
114C2×#217—41no—
115C2×#217C2×C414yes—
116C2×(C2×D3)⋊C4—22no—
117C2×(C2×D3)⋊C4—22no—
118C2×(C2×D3)⋊C4—22no—
119C2×(C2×D3)⋊C4—22no—
120C2×(C2×D3)⋊C4—22no—
121C2×(C2×D3)⋊C4—22no—
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)⋊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×(C2×D3)⋊C4C2×C414yes—
134C2×C4⋊Dic3—22no—
135C2×C4⋊Dic3—22no—
136C2×C4⋊Dic3—41no—
137C2×Dic3⋊C4—41no—
138C2×Dic3⋊C4—41no—
139C2×Dic3⋊C4C2×C414yes—
140C2×C4×Dic3—22no—
141C2×C4×Dic3—41no—
142C2×C4×Dic3—41no—
143C2×C4×Dic3—41no—
144C2×C4×Dic3—41no—
145C2×C4×Dic3C2×C414yes—
146C3×#95—22no—
147C3×#95D414yescomplemented
148C3⋊#95—22no—
149C3⋊#95—22no—
150C3⋊#95—22no—
151C3⋊#95—22no—
152C3⋊#95—22no—
153C3⋊#95—22no—
154C3⋊#95—41no—
155C3⋊#95—41no—
156C3⋊#95—41no—
157C3⋊#95—41no—
158C3⋊#95—41no—
159C3⋊#95—41no—
160C3⋊#95—41no—
161C3⋊#95—41no—
162C23×D4—31no—
163C22×C4⋊C4—31no—
164C22×C4⋊C4—31no—
165C22×C4⋊C4C2×D311yescharacteristic
166C22×C22⋊C4—31no—
167C22×C22⋊C4—31no—
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×C42—31no—
179C22×C42—31no—
180C22×C42C2×D311yescharacteristic
181#390—38no—
182#388—24no—
183#388—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×#95C2×D311yescharacteristic
199C2×#95C2×D311yescharacteristic
200C24×C3—21no—
201C24×C3—21no—
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×C3C22×C412yes—
215C24×C3C2411yescharacteristic
216C23×D3—21no—
217C23×D3—21no—
218C23×D3—21no—
219C23×D3—21no—
220C23×D3—21no—
221C23×D3—21no—
222C23×D3—21no—
223C23×D3—21no—
224C23×D3—21no—
225C23×D3—21no—
226C23×D3—21no—
227C23×D3—21no—
228C23×D3—21no—
229C23×D3—21no—
230C23×D3C22×C412yes—
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×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4C22×C412yes—
267C22×C3×C4C22×C412yes—
268C22×C3×C4C2×D412yes—
269C22×C3×C4C2×D412yes—
270C22×C3×C4C2×D412yes—
271C22×C3×C4#4112yes—
272C22×C3×C4#4112yes—
273C2×#67—28no—
274C2×#67—44no—
275C2×#67—44no—
276C2×#67—44no—
277C2×#67—44no—
278C2×#67—44no—
279C2×#67—44no—
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×Dic3C22×C412yes—
324C22×Dic3C22×C412yes—
325C22×Dic3C22×C412yes—
326C22×Dic3#4112yes—
327C22×Dic3#4112yes—
328C22×Dic3#4112yes—
329C3×C4⋊C4—44no—
330C3×C22⋊C4—28no—
331C3×C22⋊C4—44no—
332C3×C22⋊C4—44no—
333C3×C42—44no—
334#217—44no—
335#217—44no—
336#217—44no—
337(C2×D3)⋊C4—28no—
338(C2×D3)⋊C4—44no—
339(C2×D3)⋊C4—44no—
340(C2×D3)⋊C4—44no—
341(C2×D3)⋊C4—44no—
342(C2×D3)⋊C4—44no—
343C4⋊Dic3—44no—
344Dic3⋊C4—44no—
345C4×Dic3—44no—
346C4×Dic3—44no—
347C25—31no—
348C25C22×D311yescharacteristic
349C22×D4—34no—
350C22×D4—62no—
351C22×D4—62no—
352C22×D4—121no—
353C22×D4—121no—
354C22×D4—121no—
355C22×D4—121no—
356C23×C4—31no—
357C23×C4—31no—
358C23×C4—31no—
359C23×C4—31no—
360C23×C4—31no—
361C23×C4—31no—
362C23×C4—31no—
363C23×C4C22×D311yescharacteristic
364C23×C4C22×D311yescharacteristic
365C23×C4C22×D311yescharacteristic
366C23×C4C22×D311yescharacteristic
367C23×C4C22×D311yescharacteristic
368C23×C4C22×D311yescharacteristic
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—34no—
372C2×C4⋊C4—41no—
373C2×C4⋊C4—62no—
374C2×C4⋊C4—62no—
375C2×C4⋊C4—121no—
376C2×C4⋊C4—121no—
377C2×C4⋊C4—121no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—34no—
384C2×C22⋊C4—34no—
385C2×C22⋊C4—34no—
386C2×C22⋊C4—41no—
387C2×C22⋊C4—41no—
388C2×C22⋊C4—41no—
389C2×C22⋊C4—62no—
390C2×C22⋊C4—62no—
391C2×C22⋊C4—62no—
392C2×C22⋊C4—62no—
393C2×C22⋊C4—62no—
394C2×C22⋊C4—62no—
395C2×C22⋊C4—62no—
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⋊C4—121no—
403C2×C22⋊C4—121no—
404C2×C22⋊C4—121no—
405C2×C22⋊C4—121no—
406C2×C22⋊C4—121no—
407C2×C22⋊C4—121no—
408C2×C22⋊C4—121no—
409C2×C22⋊C4—121no—
410C2×C22⋊C4—121no—
411C2×C22⋊C4—121no—
412C2×C22⋊C4—121no—
413C2×C22⋊C4C4×D314yes—
414C2×C42—22no—
415C2×C42—34no—
416C2×C42—41no—
417C2×C42—41no—
418C2×C42—62no—
419C2×C42—121no—
420C2×C42—121no—
421C2×C42—121no—
422C2×C42—121no—
423#95—22no—
424#95—62no—
425#95—62no—
426#95—62no—
427#95—62no—
428#95—62no—
429#95—62no—
430#95—121no—
431#95—121no—
432#95—121no—
433#95—121no—
434#95—121no—
435#95—121no—
436#95—121no—
437#95—121no—
438#95#6714yescomplemented
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
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×C3—41no—
465C23×C3—41no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3C23×C411yescharacteristic
475C23×C3C22×D411yescharacteristic
476C23×C3C2×#4111yescharacteristic
477C23×C3C2×#4111yescharacteristic
478C23×C3C2×#4111yescharacteristic
479C23×C3C2×#4111yescharacteristic
480C23×C3C2×#4111yescharacteristic
481C23×C3H(5,𝔽2)11yescharacteristic
482C23×C3H(5,𝔽2)11yescharacteristic
483C23×C3H(5,𝔽2)11yescharacteristic
484C23×C3H(5,𝔽2)11yescharacteristic
485C23×C3H(5,𝔽2)11yescharacteristic
486C23×C3H(5,𝔽2)11yescharacteristic
487C23×C3H(5,𝔽2)11yescharacteristic
488C23×C32−1+411yescharacteristic
489C22×D3—22no—
490C22×D3—22no—
491C22×D3—22no—
492C22×D3—22no—
493C22×D3—22no—
494C22×D3—22no—
495C22×D3—22no—
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—
510C22×D3—41no—
511C22×D3—41no—
512C22×D3—41no—
513C22×D3—41no—
514C22×D3—41no—
515C22×D3—41no—
516C22×D3—41no—
517C22×D3—41no—
518C22×D3—41no—
519C22×D3—41no—
520C22×D3—41no—
521C22×D3—41no—
522C22×D3—41no—
523C22×D3—41no—
524C2×C3×C4—22no—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
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—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—
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×C4C4×D414yes—
566#67—416no—
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—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
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#11714yes—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—32no—
631C24—61no—
632C24—61no—
633C24—61no—
634C24—61no—
635C24—61no—
636C24—61no—
637C24—61no—
638C24—61no—
639C24—61no—
640C24—61no—
641C24—61no—
642C24—61no—
643C24—61no—
644C24—61no—
645C24C2×C4×D312yes—
646C24C23×D311yescharacteristic
647C2×D4—68no—
648C2×D4—124no—
649C2×D4—124no—
650C2×D4—124no—
651C2×D4—124no—
652C2×D4—124no—
653C2×D4—124no—
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—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—32no—
690C22×C4—32no—
691C22×C4—32no—
692C22×C4—32no—
693C22×C4—32no—
694C22×C4—32no—
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—61no—
732C22×C4—61no—
733C22×C4—61no—
734C22×C4—61no—
735C22×C4—61no—
736C22×C4—61no—
737C22×C4—61no—
738C22×C4C2×C4×D312yes—
739C22×C4C2×C4×D312yes—
740C22×C4#23512yes—
741C22×C4#23712yes—
742C22×C4C2×#6712yes—
743C22×C4C2×#6712yes—
744C22×C4C2×#6712yes—
745C4⋊C4—44no—
746C4⋊C4—124no—
747C4⋊C4—124no—
748C22⋊C4—28no—
749C22⋊C4—44no—
750C22⋊C4—44no—
751C22⋊C4—68no—
752C22⋊C4—124no—
753C22⋊C4—124no—
754C22⋊C4—124no—
755C22⋊C4—124no—
756C22⋊C4—124no—
757C22⋊C4—124no—
758C22⋊C4—124no—
759C22⋊C4—124no—
760C42—44no—
761C42—124no—
762C42—124no—
763C22×C3—42no—
764C22×C3—42no—
765C22×C3—42no—
766C22×C3—42no—
767C22×C3—42no—
768C22×C3—42no—
769C22×C3—42no—
770C22×C3—81no—
771C22×C3—81no—
772C22×C3—81no—
773C22×C3—81no—
774C22×C3—81no—
775C22×C3—81no—
776C22×C3—81no—
777C22×C3—81no—
778C22×C3C2×#11711yescharacteristic
779C22×C3C2×C4×D411yescharacteristic
780C22×C3C4×#4111yescharacteristic
781C22×C3#51811yescharacteristic
782C22×C3#51811yescharacteristic
783C22×C3#51811yescharacteristic
784C22×C3#52011yescharacteristic
785C22×C3#53511yescharacteristic
786C22×C3#53511yescharacteristic
787C22×C3#53811yescharacteristic
788C22×C3#53811yescharacteristic
789C22×C3#53811yescharacteristic
790C22×C3#53811yescharacteristic
791C22×C3#53811yescharacteristic
792C22×C3#53811yescharacteristic
793C22×C3#54011yescharacteristic
794C22×C3#54011yescharacteristic
795C22×C3#54211yescharacteristic
796C22×C3#54211yescharacteristic
797C22×C3#54611yescharacteristic
798C22×C3#54611yescharacteristic
799C22×C3#54711yescharacteristic
800C22×C3#55011yescharacteristic
801C22×C3#55311yescharacteristic
802C22×C3#55311yescharacteristic
803C22×C3#55311yescharacteristic
804C22×C3#55311yescharacteristic
805C22×C3#55511yescharacteristic
806C22×C3#55611yescharacteristic
807C22×C3#55911yescharacteristic
808C22×C3#55911yescharacteristic
809C22×C3#56011yescharacteristic
810C22×C3#56011yescharacteristic
811C22×C3#56211yescharacteristic
812C22×C3#56211yescharacteristic
813C2×D3—42no—
814C2×D3—42no—
815C2×D3—42no—
816C2×D3—42no—
817C2×D3—42no—
818C2×D3—42no—
819C2×D3—42no—
820C2×D3—81no—
821C2×D3—81no—
822C2×D3—81no—
823C2×D3—81no—
824C2×D3—81no—
825C2×D3—81no—
826C2×D3—81no—
827C2×D3—81no—
828C3×C4—24no—
829C3×C4—42no—
830C3×C4—42no—
831C3×C4—42no—
832C3×C4—42no—
833C3×C4—81no—
834Dic3—24no—
835Dic3—42no—
836Dic3—42no—
837Dic3—42no—
838Dic3—81no—
839Dic3—81no—
840Dic3—81no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
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—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—62no—
877C23—62no—
878C23—62no—
879C23—62no—
880C23—62no—
881C23—62no—
882C23—62no—
883C23—121no—
884C23—121no—
885C23—121no—
886C23—121no—
887C23—121no—
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—
904C23—121no—
905C23—121no—
906C23—121no—
907C23—121no—
908C23—121no—
909C23—121no—
910C23—121no—
911C23C22×C4×D311yescharacteristic
912C23C2×#23511yescharacteristic
913C23C2×#23711yescharacteristic
914C23#100411yescharacteristic
915C23#100411yescharacteristic
916C23#100411yescharacteristic
917C23D3×#4111yescharacteristic
918C23D3×#4111yescharacteristic
919C23D3×#4111yescharacteristic
920C23#100911yescharacteristic
921C23#100911yescharacteristic
922C23#100911yescharacteristic
923C23#100911yescharacteristic
924C23#101011yescharacteristic
925C23C22×#6711yescharacteristic
926D4—1216no—
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—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—34no—
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—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—62no—
970C2×C4—62no—
971C2×C4—62no—
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—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×C4—121no—
1013C2×C4—121no—
1014C2×C4—121no—
1015C2×C4—121no—
1016C2×C4—121no—
1017C2×C4C4×#6714yes—
1018C2×C3—82no—
1019C2×C3#231211yescharacteristic
1020C2×C3#232811yescharacteristic
1021C2×C3#233711yescharacteristic
1022C2×C3#235411yescharacteristic
1023C2×C3#235711yescharacteristic
1024C2×C3#236411yescharacteristic
1025C2×C3#237711yescharacteristic
1026C2×C3#271011yescharacteristic
1027C2×C3#271011yescharacteristic
1028C2×C3#271411yescharacteristic
1029C2×C3#271411yescharacteristic
1030C2×C3#280011yescharacteristic
1031C2×C3#280011yescharacteristic
1032C2×C3#280311yescharacteristic
1033C2×C3#280311yescharacteristic
1034D3—82no—
1035C22—42no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—81no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22—81no—
1049C22—81no—
1050C22—122no—
1051C22—122no—
1052C22—122no—
1053C22—122no—
1054C22—122no—
1055C22—122no—
1056C22—122no—
1057C22—241no—
1058C22—241no—
1059C22—241no—
1060C22—241no—
1061C22—241no—
1062C22—241no—
1063C22—241no—
1064C22—241no—
1065C22D3×#11711yescharacteristic
1066C22#552311yescharacteristic
1067C22#553211yescharacteristic
1068C22#553311yescharacteristic
1069C22C4×#23711yescharacteristic
1070C22#554011yescharacteristic
1071C22#554511yescharacteristic
1072C22#554511yescharacteristic
1073C22#554511yescharacteristic
1074C22#556211yescharacteristic
1075C22#556211yescharacteristic
1076C22#556511yescharacteristic
1077C22#560111yescharacteristic
1078C22#561311yescharacteristic
1079C22#561711yescharacteristic
1080C22#562011yescharacteristic
1081C22#565711yescharacteristic
1082C22#566211yescharacteristic
1083C22#566411yescharacteristic
1084C22#566711yescharacteristic
1085C22#567811yescharacteristic
1086C22#568111yescharacteristic
1087C22#568211yescharacteristic
1088C22#568411yescharacteristic
1089C22#570411yescharacteristic
1090C22#570411yescharacteristic
1091C22#570911yescharacteristic
1092C22#571111yescharacteristic
1093C22C2×C4×#6711yescharacteristic
1094C22#580511yescharacteristic
1095C22#580611yescharacteristic
1096C22#582411yescharacteristic
1097C22#582911yescharacteristic
1098C22#583011yescharacteristic
1099C22#583411yescharacteristic
1100C4—24no—
1101C4—42no—
1102C4—42no—
1103C4—42no—
1104C4—42no—
1105C4—64no—
1106C4—81no—
1107C4—122no—
1108C4—122no—
1109C4—122no—
1110C4—241no—
1111C4—241no—
1112C4—241no—
1113C3#1444411yescharacteristic, complemented, Sylow
1114C2—82no—
1115C2—242no—
1116C2#7547211yescharacteristic
1117C2#7547611yescharacteristic
1118C2#7549011yescharacteristic
1119C2#7580011yescharacteristic
1120C2#7580311yescharacteristic
1121C2#7580611yescharacteristic
1122C2#7580911yescharacteristic
1123C2#7582511yescharacteristic
1124C2#8224111yescharacteristic
1125C2#8232911yescharacteristic
1126C2#8234211yescharacteristic
1127C2#8269611yescharacteristic
1128C2#8288511yescharacteristic
1129C2#8298611yescharacteristic
1130C2#8311711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×#388C2
socle, cosocleC24×C3C24
prime radicalC23×#67C22
hypercenterC2×#388D3
hypocenterC3#14444
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C2×C3×#388C2semidirect
3. C2×#4670C2semidirect
4. #71570C2semidirect
5. #71563C2semidirect
8. #71549C2semidirect
9. #71546C2semidirect
10. #71545C2semidirect
11. #71537C2semidirect
12. #71536C2semidirect
13. #69429C2semidirect
14. #69406C2semidirect
15. #69401C2semidirect
53. #4957C4semidirect
57. C2×#388D3semidirect
147. C3×#95D4semidirect
438. #95#67semidirect
1113. C3#14444semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3882
C2×#49572
C2×#46702
#715702
#715632
#715502
#715492
#715462
#715452
#715372
#715362
#694292
#694062
#694012
#144443