Finite Group Databasebeta

← #10725839

Subgroups — #10725839

Order 768.

1694 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4991C211yesmaximal, characteristic
2C2×#4665C211yesmaximal, characteristic
3C2×#4668C211yesmaximal, characteristic, complemented
4C3×#1445C211yesmaximal, characteristic, complemented
5#71565C211yesmaximal, characteristic, complemented
6#69429C211yesmaximal, characteristic, complemented
7#69429C211yesmaximal, characteristic, complemented
8#69428C211yesmaximal, characteristic, complemented
9#69428C211yesmaximal, characteristic, complemented
10#69428C211yesmaximal, characteristic, complemented
11#69427C211yesmaximal, characteristic, complemented
12#69426C211yesmaximal, characteristic
13(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
14#69414C211yesmaximal, characteristic, complemented
15#69414C211yesmaximal, characteristic, complemented
16#14622—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×(C2×D3)⋊C4C2211yescharacteristic
21C22×(C2×D3)⋊C4C2211yescharacteristic
22C22×(C2×D3)⋊C4C2211yescharacteristic
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
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#4991C418yescomplemented
53#4668—24no—
54#4665—24no—
55C2×#394—31no—
56C2×#386—31no—
57C2×#385—31no—
58#1445D311yescharacteristic, complemented
59#1442—31no—
60#1442—31no—
61#1441—31no—
62#1440—31no—
63#1440—31no—
64#1439—31no—
65#1439—31no—
66#1439—31no—
67#1439—31no—
68#1438—31no—
69C22⋊#95—31no—
70C24×D3C2311yescharacteristic
71C24×D3C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×Dic3C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C22×D12—22no—
86C22×D12—22no—
87C22×D12—41no—
88C22×D12—41no—
89C22×D12—41no—
90C22×D12—41no—
91C22×D12C2×C414yes—
92C22×C4×D3—41no—
93C22×C4×D3—41no—
94C22×C4×D3—41no—
95C22×C4×D3—41no—
96C22×C4×D3—41no—
97C22×C4×D3—41no—
98C22×C4×D3D414yes—
99C2×C3×C4⋊C4—41no—
100C2×C3×C4⋊C4—41no—
101C2×C3×C4⋊C4C2×C414yescomplemented
102C2×(C2×D3)⋊C4—22no—
103C2×(C2×D3)⋊C4—22no—
104C2×(C2×D3)⋊C4—22no—
105C2×(C2×D3)⋊C4—22no—
106C2×(C2×D3)⋊C4—22no—
107C2×(C2×D3)⋊C4—22no—
108C2×(C2×D3)⋊C4—22no—
109C2×(C2×D3)⋊C4—41no—
110C2×(C2×D3)⋊C4—41no—
111C2×(C2×D3)⋊C4—41no—
112C2×(C2×D3)⋊C4—41no—
113C2×(C2×D3)⋊C4—41no—
114C2×(C2×D3)⋊C4—41no—
115C2×(C2×D3)⋊C4—41no—
116C2×(C2×D3)⋊C4—41no—
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)⋊C4—41no—
128C2×(C2×D3)⋊C4—41no—
129C2×(C2×D3)⋊C4—41no—
130C2×(C2×D3)⋊C4—41no—
131C2×(C2×D3)⋊C4C2×C414yes—
132C2×(C2×D3)⋊C4C2×C414yes—
133C2×(C2×D3)⋊C4C2×C414yescomplemented
134C2×(C2×D3)⋊C4C2×C414yescomplemented
135C2×C4⋊Dic3—22no—
136C2×C4⋊Dic3—41no—
137C2×C4⋊Dic3—41no—
138C2×Dic3⋊C4—22no—
139C2×Dic3⋊C4—41no—
140C2×Dic3⋊C4—41no—
141C2×Dic3⋊C4—41no—
142C2×Dic3⋊C4—41no—
143C2×Dic3⋊C4—41no—
144C3×#95—22no—
145C3×#95—22no—
146C3×#95—41no—
147C3×#95—41no—
148C3×#95—41no—
149C3×#95—41no—
150C3⋊#95—22no—
151C3⋊#95—22no—
152C3⋊#95—41no—
153C3⋊#95—41no—
154C3⋊#95—41no—
155C3⋊#95—41no—
156C3⋊#95—41no—
157C3⋊#95—41no—
158C3⋊#95—41no—
159C3⋊#95—41no—
160C3⋊#95—41no—
161C3⋊#95C2×C414yescomplemented
162C23×D4—31no—
163C24×C4—31no—
164C22×C4⋊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⋊C4—31no—
176C22×C22⋊C4—31no—
177C22×C22⋊C4—31no—
178C22×C22⋊C4—31no—
179#394—38no—
180#386—64no—
181#385—64no—
182C2×#95—31no—
183C2×#95—31no—
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×#95C2×D311yescharacteristic
195C2×#95C2×D311yescharacteristic
196C2×#95C2×D311yescharacteristic
197C2×#95C2×D311yescharacteristic
198C2×#95C2×D311yescharacteristic
199C2×#95C2×D311yescharacteristic
200C24×C3C2411yescharacteristic
201C23×D3—21no—
202C23×D3—21no—
203C23×D3—21no—
204C23×D3—21no—
205C23×D3—21no—
206C23×D3—21no—
207C23×D3—21no—
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×D3—21no—
223C23×D3—21no—
224C23×D3—21no—
225C23×D3—21no—
226C23×D3—21no—
227C23×D3C22×C412yes—
228C23×D3C22×C412yes—
229C23×D3C2×D412yes—
230C23×D3#4112yes—
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×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4C22×C412yes—
277C22×C3×C4C22×C412yes—
278C22×C3×C4C22×C412yes—
279C22×C3×C4C2×D412yes—
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×Dic3C22×C412yes—
320C22×Dic3C22×C412yes—
321C22×Dic3C2×D412yes—
322C2×D12—28no—
323C2×D12—44no—
324C2×D12—44no—
325C2×D12—44no—
326C2×D12—44no—
327C2×D12—44no—
328C2×D12—44no—
329C2×C4×D3—44no—
330C2×C4×D3—44no—
331C2×C4×D3—44no—
332C2×C4×D3—44no—
333C2×C4×D3—44no—
334C2×C4×D3—44no—
335C2×C4×D3—44no—
336C3×C4⋊C4—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—
343(C2×D3)⋊C4—44no—
344(C2×D3)⋊C4—44no—
345(C2×D3)⋊C4—44no—
346(C2×D3)⋊C4—44no—
347(C2×D3)⋊C4—44no—
348C4⋊Dic3—44no—
349Dic3⋊C4—44no—
350Dic3⋊C4—44no—
351C25—31no—
352C25—31no—
353C22×D4—34no—
354C22×D4—62no—
355C22×D4—62no—
356C22×D4—121no—
357C22×D4—121no—
358C22×D4—121no—
359C22×D4—121no—
360C23×C4—31no—
361C23×C4—31no—
362C23×C4—31no—
363C23×C4—34no—
364C23×C4—31no—
365C23×C4—31no—
366C23×C4—31no—
367C23×C4—121no—
368C23×C4—121no—
369C23×C4—121no—
370C23×C4—121no—
371C23×C4—121no—
372C23×C4—121no—
373C23×C4C22×D311yescharacteristic
374C23×C4C22×D311yescharacteristic
375C23×C4C22×D311yescharacteristic
376C23×C4C22×D311yescharacteristic
377C23×C4C22×D311yescharacteristic
378C23×C4C22×D311yescharacteristic
379C23×C4C22×D311yescharacteristic
380C2×C4⋊C4—41no—
381C2×C4⋊C4—41no—
382C2×C4⋊C4—62no—
383C2×C4⋊C4—62no—
384C2×C4⋊C4—121no—
385C2×C4⋊C4—121no—
386C2×C4⋊C4—121no—
387C2×C4⋊C4—121no—
388C2×C4⋊C4—121no—
389C2×C4⋊C4—121no—
390C2×C4⋊C4—121no—
391C2×C4⋊C4C4×D314yescomplemented
392C2×C22⋊C4—34no—
393C2×C22⋊C4—34no—
394C2×C22⋊C4—34no—
395C2×C22⋊C4—34no—
396C2×C22⋊C4—62no—
397C2×C22⋊C4—62no—
398C2×C22⋊C4—62no—
399C2×C22⋊C4—62no—
400C2×C22⋊C4—62no—
401C2×C22⋊C4—62no—
402C2×C22⋊C4—62no—
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⋊C4—121no—
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×C22⋊C4—121no—
425#95—22no—
426#95—22no—
427#95—34no—
428#95—41no—
429#95—41no—
430#95—41no—
431#95—41no—
432#95—62no—
433#95—62no—
434#95—121no—
435#95—121no—
436#95—121no—
437#95—121no—
438#95—121no—
439#95—121no—
440#95—121no—
441#95—121no—
442#95—121no—
443C23×C3C23×C411yescharacteristic
444C23×C3C22×D411yescharacteristic
445C23×C3C2×#4111yescharacteristic
446C23×C3H(5,𝔽2)11yescharacteristic
447C23×C3H(5,𝔽2)11yescharacteristic
448C23×C3H(5,𝔽2)11yescharacteristic
449C23×C3H(5,𝔽2)11yescharacteristic
450C23×C3H(5,𝔽2)11yescharacteristic
451C23×C3H(5,𝔽2)11yescharacteristic
452C23×C3H(5,𝔽2)11yescharacteristic
453C23×C3H(5,𝔽2)11yescharacteristic
454C23×C3H(5,𝔽2)11yescharacteristic
455C23×C32−1+411yescharacteristic
456C23×C32−1+411yescharacteristic
457C23×C32−1+411yescharacteristic
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—22no—
468C22×D3—22no—
469C22×D3—22no—
470C22×D3—22no—
471C22×D3—22no—
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—22no—
478C22×D3—22no—
479C22×D3—22no—
480C22×D3—22no—
481C22×D3—22no—
482C22×D3—22no—
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—
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—
524C22×D3—41no—
525C22×D3—41no—
526C22×D3—41no—
527C22×D3C4×D414yes—
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—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—
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—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×Dic3—22no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3—22no—
585C2×Dic3—22no—
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—
619D12—416no—
620C4×D3—416no—
621C24—32no—
622C24—32no—
623C24—32no—
624C24—32no—
625C24—61no—
626C24—61no—
627C24—61no—
628C24—61no—
629C24—61no—
630C24—61no—
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—
645C24—61no—
646C24—61no—
647C24—61no—
648C24—61no—
649C24—61no—
650C24—61no—
651C24C23×D311yescharacteristic
652C2×D4—68no—
653C2×D4—124no—
654C2×D4—124no—
655C2×D4—124no—
656C2×D4—124no—
657C2×D4—124no—
658C2×D4—124no—
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—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—32no—
705C22×C4—32no—
706C22×C4—32no—
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—124no—
747C22×C4—124no—
748C22×C4—124no—
749C22×C4—124no—
750C22×C4—124no—
751C22×C4—124no—
752C22×C4—124no—
753C22×C4C2×C4×D312yes—
754C22×C4C2×C4×D312yes—
755C22×C4C2×C4×D312yes—
756C22×C4D3×D412yes—
757C4⋊C4—44no—
758C4⋊C4—124no—
759C4⋊C4—124no—
760C4⋊C4—124no—
761C22⋊C4—68no—
762C22⋊C4—124no—
763C22⋊C4—124no—
764C22⋊C4—124no—
765C22⋊C4—124no—
766C22⋊C4—124no—
767C22⋊C4—124no—
768C22⋊C4—124no—
769C22⋊C4—124no—
770C22⋊C4—124no—
771C22⋊C4—124no—
772C22×C3C2×C4×D411yescharacteristic
773C22×C3#51811yescharacteristic
774C22×C3#51811yescharacteristic
775C22×C3#51811yescharacteristic
776C22×C3#52011yescharacteristic
777C22×C3#52011yescharacteristic
778C22×C3#52011yescharacteristic
779C22×C3#53411yescharacteristic
780C22×C3#53411yescharacteristic
781C22×C3#53411yescharacteristic
782C22×C3#53511yescharacteristic
783C22×C3#53611yescharacteristic
784C22×C3#53711yescharacteristic
785C22×C3#53811yescharacteristic
786C22×C3#53811yescharacteristic
787C22×C3#53811yescharacteristic
788C22×C3#53911yescharacteristic
789C22×C3#53911yescharacteristic
790C22×C3#53911yescharacteristic
791C22×C3#56011yescharacteristic
792C22×C3#56011yescharacteristic
793C22×C3#56011yescharacteristic
794C22×C3#56011yescharacteristic
795C22×C3#56011yescharacteristic
796C22×C3H(3,𝔽4)11yescharacteristic
797C22×C3#56211yescharacteristic
798C22×C3#56211yescharacteristic
799C22×C3#56211yescharacteristic
800C22×C3#56211yescharacteristic
801C22×C3#56211yescharacteristic
802C22×C3#56211yescharacteristic
803C22×C3#56211yescharacteristic
804C22×C3#56211yescharacteristic
805C22×C3#56311yescharacteristic
806C22×C3#56311yescharacteristic
807C2×D3—24no—
808C2×D3—24no—
809C2×D3—24no—
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—
821C2×D3—42no—
822C2×D3—42no—
823C2×D3—42no—
824C2×D3—42no—
825C2×D3—42no—
826C2×D3—42no—
827C2×D3—42no—
828C2×D3—42no—
829C2×D3—81no—
830C2×D3—81no—
831C2×D3—81no—
832C2×D3—81no—
833C2×D3—81no—
834C2×D3—81no—
835C2×D3—81no—
836C2×D3—81no—
837C3×C4—42no—
838C3×C4—42no—
839C3×C4—42no—
840C3×C4—42no—
841C3×C4—81no—
842C3×C4—81no—
843C3×C4—81no—
844Dic3—42no—
845Dic3—42no—
846Dic3—42no—
847Dic3—81no—
848Dic3—81no—
849Dic3—81no—
850C23—34no—
851C23—62no—
852C23—62no—
853C23—62no—
854C23—62no—
855C23—62no—
856C23—62no—
857C23—62no—
858C23—62no—
859C23—62no—
860C23—62no—
861C23—62no—
862C23—62no—
863C23—62no—
864C23—62no—
865C23—62no—
866C23—62no—
867C23—62no—
868C23—62no—
869C23—62no—
870C23—62no—
871C23—62no—
872C23—62no—
873C23—62no—
874C23—62no—
875C23—62no—
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—
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—
911C23—121no—
912C23—121no—
913C23—121no—
914C23—121no—
915C23—121no—
916C23—121no—
917C23—121no—
918C23—121no—
919C23—121no—
920C23C22×C4×D311yescharacteristic
921C23C2×D3×D411yescharacteristic
922C23#100411yescharacteristic
923C23#100411yescharacteristic
924C23#100411yescharacteristic
925C23#100711yescharacteristic
926C23#100711yescharacteristic
927C23D3×#4111yescharacteristic
928C23#100911yescharacteristic
929C23#100911yescharacteristic
930C23#100911yescharacteristic
931C23#100911yescharacteristic
932C23#100911yescharacteristic
933C23#100911yescharacteristic
934C23#101011yescharacteristic
935D4—1216no—
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—22no—
946C2×C4—22no—
947C2×C4—22no—
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—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—62no—
986C2×C4—62no—
987C2×C4—62no—
988C2×C4—62no—
989C2×C4—62no—
990C2×C4—62no—
991C2×C4—62no—
992C2×C4—62no—
993C2×C4—62no—
994C2×C4—1216no—
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×C3#232111yescharacteristic
1029C2×C3#232211yescharacteristic
1030C2×C3#232511yescharacteristic
1031C2×C3#237611yescharacteristic
1032C2×C3#237711yescharacteristic
1033C2×C3#237711yescharacteristic
1034C2×C3#237911yescharacteristic
1035C2×C3#281211yescharacteristic
1036C2×C3#281311yescharacteristic
1037C2×C3#281411yescharacteristic
1038C2×C3#281611yescharacteristic
1039C2×C3#282411yescharacteristic
1040C2×C3#282611yescharacteristic
1041C2×C3#282711yescharacteristic
1042C2×C3#282711yescharacteristic
1043D3—44no—
1044D3—82no—
1045C22—64no—
1046C22—64no—
1047C22—64no—
1048C22—122no—
1049C22—122no—
1050C22—122no—
1051C22—122no—
1052C22—122no—
1053C22—122no—
1054C22—122no—
1055C22—122no—
1056C22—122no—
1057C22—122no—
1058C22—122no—
1059C22—122no—
1060C22—122no—
1061C22—122no—
1062C22—122no—
1063C22—122no—
1064C22—122no—
1065C22—122no—
1066C22—122no—
1067C22—241no—
1068C22—241no—
1069C22—241no—
1070C22—241no—
1071C22—241no—
1072C22—241no—
1073C22—241no—
1074C22—241no—
1075C22#548611yescharacteristic
1076C22#552111yescharacteristic
1077C22#552311yescharacteristic
1078C22C4×D3×D411yescharacteristic
1079C22#554511yescharacteristic
1080C22#557411yescharacteristic
1081C22#557411yescharacteristic
1082C22#560511yescharacteristic
1083C22#561311yescharacteristic
1084C22#562811yescharacteristic
1085C22#562911yescharacteristic
1086C22#564711yescharacteristic
1087C22#564711yescharacteristic
1088C22#564711yescharacteristic
1089C22#564711yescharacteristic
1090C22#565311yescharacteristic
1091C22#565311yescharacteristic
1092C22#566611yescharacteristic
1093C22#566611yescharacteristic
1094C22#566611yescharacteristic
1095C22#566711yescharacteristic
1096C22#566711yescharacteristic
1097C22#566711yescharacteristic
1098C22#567811yescharacteristic
1099C22#568311yescharacteristic
1100C22#569211yescharacteristic
1101C22#569211yescharacteristic
1102C22#569911yescharacteristic
1103C22#570011yescharacteristic
1104C22#570411yescharacteristic
1105C22#570711yescharacteristic
1106C22#571111yescharacteristic
1107C22#571111yescharacteristic
1108C22#571511yescharacteristic
1109C22#573511yescharacteristic
1110C4—42no—
1111C4—42no—
1112C4—42no—
1113C4—42no—
1114C4—81no—
1115C4—81no—
1116C4—81no—
1117C4—122no—
1118C4—122no—
1119C4—122no—
1120C4—241no—
1121C4—241no—
1122C4—241no—
1123C3#1462211yescharacteristic, complemented, Sylow
1124C2—124no—
1125C2—242no—
1126C2#7412411yescharacteristic
1127C2#7529711yescharacteristic
1128C2#7529811yescharacteristic
1129C2#7531211yescharacteristic
1130C2#7531311yescharacteristic
1131C2#7642911yescharacteristic
1132C2#7649611yescharacteristic
1133C2#7772611yescharacteristic
1134C2#7773011yescharacteristic
1135C2#7800511yescharacteristic
1136C2#7800911yescharacteristic
1137C2#7809011yescharacteristic
1138C2#7812511yescharacteristic
1139C2#7840311yescharacteristic
1140C2#7840411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1445C2
socle, cosocleC24×C3C24
prime radicalC23×D12C22
hypercenter#1445D3
hypocenterC3#14622
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
3. C2×#4668C2semidirect
4. C3×#1445C2semidirect
5. #71565C2semidirect
6. #69429C2semidirect
7. #69429C2semidirect
8. #69428C2semidirect
9. #69428C2semidirect
10. #69428C2semidirect
11. #69427C2semidirect
13. (C2×D3)⋊#95C2semidirect
14. #69414C2semidirect
15. #69414C2semidirect
52. #4991C4semidirect
58. #1445D3semidirect
101. C2×C3×C4⋊C4C2×C4semidirect
133. C2×(C2×D3)⋊C4C2×C4semidirect
134. C2×(C2×D3)⋊C4C2×C4semidirect
161. C3⋊#95C2×C4semidirect
391. C2×C4⋊C4C4×D3semidirect
1123. C3#14622semidirect

Maximal subgroups

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

subgroupindex
C2×#49912
C2×#46652
C2×#46682
C3×#14452
#715652
#694292
#694282
#694272
#694262
(C2×D3)⋊#952
#694142
#146223