Finite Group Databasebeta

← #10719217

Subgroups — #10719217

Order 768.

2070 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4940C211yesmaximal, characteristic, complemented
2C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
3C2×#4665C211yesmaximal, characteristic
4C2×#4665C211yesmaximal, characteristic
5C2×#4666C211yesmaximal, characteristic, complemented
6C3×#1434C211yesmaximal, characteristic, complemented
7#69429C211yesmaximal, characteristic, complemented
8#69428C211yesmaximal, characteristic, complemented
9#69426C211yesmaximal, characteristic
10(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
11(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
12#69416C211yesmaximal, characteristic, complemented
13#69408C211yesmaximal, characteristic, complemented
14#69406C211yesmaximal, characteristic, complemented
15#69403C211yesmaximal, characteristic, complemented
16#14068—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C22×C3×C42C2211yescharacteristic
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×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#4940—24no—
53C4×(C2×D3)⋊C4—24no—
54#4666—24no—
55#4665—24no—
56#4665C418yescomplemented
57C2×#388—31no—
58C2×#386—31no—
59C2×#386—31no—
60C2×C4×C22⋊C4—31no—
61C2×C4×C22⋊C4—31no—
62#1443—31no—
63#1440—31no—
64#1439—31no—
65#1438—31no—
66#1437—31no—
67#1436—31no—
68#1434—31no—
69#1434D311yescharacteristic, complemented
70C22⋊#95—31no—
71C22⋊#95—31no—
72C24×D3C2311yescharacteristic
73C24×D3C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C22×D12—22no—
88C22×D12—22no—
89C22×D12—22no—
90C22×D12—22no—
91C22×D12—41no—
92C22×D12—41no—
93C22×D12C2×C414yes—
94C22×C4×D3—22no—
95C22×C4×D3—22no—
96C22×C4×D3—22no—
97C22×C4×D3—22no—
98C22×C4×D3—22no—
99C22×C4×D3—22no—
100C22×C4×D3—22no—
101C22×C4×D3—41no—
102C22×C4×D3—41no—
103C22×C4×D3—41no—
104C22×C4×D3—41no—
105C22×C4×D3—41no—
106C22×C4×D3—41no—
107C22×C4×D3C2×C414yescomplemented
108C2×C3×C42—22no—
109C2×C3×C42—22no—
110C2×C3×C42—22no—
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—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—22no—
123C2×(C2×D3)⋊C4—22no—
124C2×(C2×D3)⋊C4—22no—
125C2×(C2×D3)⋊C4—22no—
126C2×(C2×D3)⋊C4—22no—
127C2×(C2×D3)⋊C4—22no—
128C2×(C2×D3)⋊C4—22no—
129C2×(C2×D3)⋊C4—22no—
130C2×(C2×D3)⋊C4—22no—
131C2×(C2×D3)⋊C4—41no—
132C2×(C2×D3)⋊C4—41no—
133C2×(C2×D3)⋊C4—41no—
134C2×(C2×D3)⋊C4—41no—
135C2×(C2×D3)⋊C4—41no—
136C2×(C2×D3)⋊C4—41no—
137C2×(C2×D3)⋊C4C2×C414yes—
138C2×(C2×D3)⋊C4C2×C414yes—
139C2×(C2×D3)⋊C4C2×C414yescomplemented
140C2×(C2×D3)⋊C4D414yes—
141C2×Dic3⋊C4—22no—
142C2×Dic3⋊C4—22no—
143C2×Dic3⋊C4—41no—
144C2×C4×Dic3—22no—
145C2×C4×Dic3—41no—
146C2×C4×Dic3—41no—
147C2×C4×Dic3—41no—
148C2×C4×Dic3—41no—
149C2×C4×Dic3D414yescomplemented
150C3×#95—22no—
151C3×#95—22no—
152C3×#95—22no—
153C3×#95—41no—
154C3×#95—41no—
155C3×#95C2×C414yescomplemented
156C3⋊#95—22no—
157C3⋊#95—22no—
158C3⋊#95—22no—
159C3⋊#95—22no—
160C3⋊#95—22no—
161C3⋊#95—22no—
162C3⋊#95—22no—
163C3⋊#95—22no—
164C3⋊#95—41no—
165C3⋊#95—41no—
166C3⋊#95—41no—
167C3⋊#95C2×C414yescomplemented
168C23×D4—31no—
169C24×C4—31no—
170C24×C4—31no—
171C22×C4⋊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—
179C22×C22⋊C4—31no—
180C22×C22⋊C4—31no—
181C22×C22⋊C4—31no—
182C22×C42—31no—
183C22×C42—31no—
184C22×C42C2×D311yescharacteristic
185#388—64no—
186#386—38no—
187#386—64no—
188C4×C22⋊C4—64no—
189C4×C22⋊C4—64no—
190C2×#95—31no—
191C2×#95—31no—
192C2×#95—31no—
193C2×#95—31no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95—31no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95—31no—
201C2×#95—31no—
202C2×#95C2×D311yescharacteristic
203C2×#95C2×D311yescharacteristic
204C2×#95C2×D311yescharacteristic
205C2×#95C2×D311yescharacteristic
206C2×#95C2×D311yescharacteristic
207C2×#95C2×D311yescharacteristic
208C24×C3C2411yescharacteristic
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×D3—21no—
228C23×D3—21no—
229C23×D3—21no—
230C23×D3—21no—
231C23×D3—21no—
232C23×D3—21no—
233C23×D3C22×C412yes—
234C23×D3C22×C412yes—
235C23×D3C2×D412yes—
236C23×D3#4112yes—
237C23×D3#4112yes—
238C23×D3#4112yes—
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×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4C22×C412yes—
281C22×C3×C4C22×C412yes—
282C22×C3×C4C22×C412yes—
283C22×C3×C4C2×D412yes—
284C22×C3×C4C2×D412yes—
285C22×C3×C4#4112yes—
286C22×C3×C4#4112yes—
287C22×C3×C4#4112yes—
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×Dic3C2×D412yes—
326C22×Dic3C2×D412yes—
327C22×Dic3C2×D412yes—
328C22×Dic3#4112yes—
329C22×Dic3#4112yes—
330C2×D12—28no—
331C2×D12—28no—
332C2×D12—44no—
333C2×D12—44no—
334C2×D12—44no—
335C2×D12—44no—
336C2×D12—44no—
337C2×C4×D3—28no—
338C2×C4×D3—28no—
339C2×C4×D3—44no—
340C2×C4×D3—44no—
341C2×C4×D3—44no—
342C2×C4×D3—44no—
343C2×C4×D3—44no—
344C2×C4×D3—44no—
345C2×C4×D3—44no—
346C2×C4×D3—44no—
347C2×C4×D3—44no—
348C2×C4×D3—44no—
349C2×C4×D3—44no—
350C2×C4×D3—44no—
351C3×C42—44no—
352(C2×D3)⋊C4—28no—
353(C2×D3)⋊C4—28no—
354(C2×D3)⋊C4—28no—
355(C2×D3)⋊C4—28no—
356(C2×D3)⋊C4—28no—
357(C2×D3)⋊C4—44no—
358(C2×D3)⋊C4—44no—
359(C2×D3)⋊C4—44no—
360(C2×D3)⋊C4—44no—
361(C2×D3)⋊C4—44no—
362Dic3⋊C4—44no—
363C4×Dic3—44no—
364C4×Dic3—44no—
365C25—31no—
366C25—31no—
367C22×D4—34no—
368C22×D4—62no—
369C22×D4—62no—
370C22×D4—62no—
371C22×D4—62no—
372C22×D4—121no—
373C22×D4—121no—
374C23×C4—31no—
375C23×C4—31no—
376C23×C4—31no—
377C23×C4—31no—
378C23×C4—31no—
379C23×C4—34no—
380C23×C4—31no—
381C23×C4—62no—
382C23×C4—62no—
383C23×C4—62no—
384C23×C4—62no—
385C23×C4—62no—
386C23×C4—62no—
387C23×C4—62no—
388C23×C4—121no—
389C23×C4—121no—
390C23×C4—121no—
391C23×C4—121no—
392C23×C4—121no—
393C23×C4—121no—
394C23×C4C22×D311yescharacteristic
395C23×C4C22×D311yescharacteristic
396C23×C4C22×D311yescharacteristic
397C23×C4C22×D311yescharacteristic
398C23×C4C22×D311yescharacteristic
399C23×C4C22×D311yescharacteristic
400C23×C4C22×D311yescharacteristic
401C2×C4⋊C4—62no—
402C2×C4⋊C4—62no—
403C2×C4⋊C4—121no—
404C2×C22⋊C4—34no—
405C2×C22⋊C4—34no—
406C2×C22⋊C4—34no—
407C2×C22⋊C4—34no—
408C2×C22⋊C4—62no—
409C2×C22⋊C4—62no—
410C2×C22⋊C4—62no—
411C2×C22⋊C4—62no—
412C2×C22⋊C4—62no—
413C2×C22⋊C4—62no—
414C2×C22⋊C4—62no—
415C2×C22⋊C4—62no—
416C2×C22⋊C4—62no—
417C2×C22⋊C4—62no—
418C2×C22⋊C4—62no—
419C2×C22⋊C4—62no—
420C2×C22⋊C4—62no—
421C2×C22⋊C4—62no—
422C2×C22⋊C4—62no—
423C2×C22⋊C4—62no—
424C2×C22⋊C4—62no—
425C2×C22⋊C4—62no—
426C2×C22⋊C4—62no—
427C2×C22⋊C4—62no—
428C2×C22⋊C4—121no—
429C2×C22⋊C4—121no—
430C2×C22⋊C4—121no—
431C2×C22⋊C4—121no—
432C2×C22⋊C4—121no—
433C2×C22⋊C4—121no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—34no—
438C2×C42—62no—
439C2×C42—121no—
440C2×C42—121no—
441C2×C42—121no—
442C2×C42—121no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—34no—
447#95—41no—
448#95—41no—
449#95—62no—
450#95—62no—
451#95—62no—
452#95—62no—
453#95—62no—
454#95—62no—
455#95—62no—
456#95—62no—
457#95—121no—
458#95—121no—
459#95—121no—
460#95C4×D314yescomplemented
461C23×C3C23×C411yescharacteristic
462C23×C3C22×D411yescharacteristic
463C23×C3C22×D411yescharacteristic
464C23×C3C2×#4111yescharacteristic
465C23×C3C2×#4111yescharacteristic
466C23×C3C2×#4111yescharacteristic
467C23×C3C2×#4111yescharacteristic
468C23×C3C2×#4111yescharacteristic
469C23×C3C2×#4111yescharacteristic
470C23×C3C2×#4111yescharacteristic
471C23×C3C2×#4111yescharacteristic
472C23×C3H(5,𝔽2)11yescharacteristic
473C23×C3H(5,𝔽2)11yescharacteristic
474C23×C3H(5,𝔽2)11yescharacteristic
475C23×C3H(5,𝔽2)11yescharacteristic
476C22×D3—22no—
477C22×D3—22no—
478C22×D3—22no—
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—22no—
498C22×D3—22no—
499C22×D3—22no—
500C22×D3—22no—
501C22×D3—22no—
502C22×D3—22no—
503C22×D3—22no—
504C22×D3—22no—
505C22×D3—22no—
506C22×D3—22no—
507C22×D3—22no—
508C22×D3—22no—
509C22×D3—22no—
510C22×D3—22no—
511C22×D3—22no—
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×D3—41no—
528C22×D3—41no—
529C22×D3—41no—
530C22×D3—41no—
531C22×D3—41no—
532C22×D3—41no—
533C22×D3—41no—
534C22×D3—41no—
535C22×D3—41no—
536C22×D3—41no—
537C22×D3—41no—
538C22×D3—41no—
539C22×D3—41no—
540C22×D3—41no—
541C22×D3—41no—
542C22×D3—41no—
543C22×D3—41no—
544C22×D3#11714yes—
545C22×D3C4×D414yes—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
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×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4#12114yes—
595C2×Dic3—22no—
596C2×Dic3—22no—
597C2×Dic3—22no—
598C2×Dic3—22no—
599C2×Dic3—22no—
600C2×Dic3—22no—
601C2×Dic3—22no—
602C2×Dic3—22no—
603C2×Dic3—22no—
604C2×Dic3—22no—
605C2×Dic3—22no—
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3—22no—
610C2×Dic3—22no—
611C2×Dic3—22no—
612C2×Dic3—22no—
613C2×Dic3—41no—
614C2×Dic3—41no—
615C2×Dic3—41no—
616C2×Dic3—41no—
617C2×Dic3—41no—
618C2×Dic3—41no—
619C2×Dic3—41no—
620C2×Dic3—41no—
621C2×Dic3—41no—
622C2×Dic3—41no—
623C2×Dic3—41no—
624C2×Dic3—41no—
625C2×Dic3—41no—
626C2×Dic3—41no—
627C2×Dic3—41no—
628C2×Dic3—41no—
629C2×Dic3—41no—
630C2×Dic3—41no—
631C2×Dic3—41no—
632C2×Dic3—41no—
633C2×Dic3—41no—
634C2×Dic3—41no—
635C2×Dic3—41no—
636C2×Dic3C4×D414yes—
637D12—416no—
638C4×D3—416no—
639C4×D3—416no—
640C24—32no—
641C24—32no—
642C24—32no—
643C24—32no—
644C24—32no—
645C24—32no—
646C24—61no—
647C24—61no—
648C24—61no—
649C24—61no—
650C24—61no—
651C24—61no—
652C24—61no—
653C24—61no—
654C24—61no—
655C24—61no—
656C24—61no—
657C24—61no—
658C24—61no—
659C24—61no—
660C24—61no—
661C24—61no—
662C24—61no—
663C24—61no—
664C24—61no—
665C24—61no—
666C24—61no—
667C24—61no—
668C24—61no—
669C24—61no—
670C24C23×D311yescharacteristic
671C2×D4—68no—
672C2×D4—68no—
673C2×D4—124no—
674C2×D4—124no—
675C2×D4—124no—
676C2×D4—124no—
677C2×D4—124no—
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—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—32no—
720C22×C4—32no—
721C22×C4—32no—
722C22×C4—32no—
723C22×C4—32no—
724C22×C4—32no—
725C22×C4—32no—
726C22×C4—68no—
727C22×C4—68no—
728C22×C4—61no—
729C22×C4—61no—
730C22×C4—61no—
731C22×C4—61no—
732C22×C4—61no—
733C22×C4—61no—
734C22×C4—61no—
735C22×C4—61no—
736C22×C4—61no—
737C22×C4—61no—
738C22×C4—61no—
739C22×C4—61no—
740C22×C4—61no—
741C22×C4—61no—
742C22×C4—61no—
743C22×C4—61no—
744C22×C4—61no—
745C22×C4—61no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—61no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—61no—
761C22×C4—61no—
762C22×C4—61no—
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×C4—124no—
773C22×C4—124no—
774C22×C4—124no—
775C22×C4C2×C4×D312yes—
776C22×C4C2×C4×D312yes—
777C22×C4C2×C4×D312yes—
778C22×C4#23512yes—
779C22×C4#23512yes—
780C22×C4D3×D412yes—
781C22×C4D3×D412yes—
782C22×C4#23912yes—
783C4⋊C4—124no—
784C22⋊C4—68no—
785C22⋊C4—68no—
786C22⋊C4—68no—
787C22⋊C4—68no—
788C22⋊C4—68no—
789C22⋊C4—124no—
790C22⋊C4—124no—
791C22⋊C4—124no—
792C22⋊C4—124no—
793C22⋊C4—124no—
794C42—44no—
795C42—124no—
796C42—124no—
797C22×C3C2×#11711yescharacteristic
798C22×C3C2×C4×D411yescharacteristic
799C22×C3C2×C4×D411yescharacteristic
800C22×C3C4×#4111yescharacteristic
801C22×C3C4×#4111yescharacteristic
802C22×C3#51811yescharacteristic
803C22×C3#51811yescharacteristic
804C22×C3C2×#12111yescharacteristic
805C22×C3#52511yescharacteristic
806C22×C3#52511yescharacteristic
807C22×C3#52511yescharacteristic
808C22×C3#52911yescharacteristic
809C22×C3#52911yescharacteristic
810C22×C3#52911yescharacteristic
811C22×C3#53211yescharacteristic
812C22×C3#53411yescharacteristic
813C22×C3#53511yescharacteristic
814C22×C3#53811yescharacteristic
815C22×C3#53811yescharacteristic
816C22×C3#54611yescharacteristic
817C22×C3#54611yescharacteristic
818C22×C3#54611yescharacteristic
819C22×C3#54611yescharacteristic
820C22×C3#55111yescharacteristic
821C22×C3#55111yescharacteristic
822C22×C3#55111yescharacteristic
823C22×C3#55111yescharacteristic
824C22×C3#55111yescharacteristic
825C22×C3#55311yescharacteristic
826C22×C3#55311yescharacteristic
827C22×C3#55311yescharacteristic
828C22×C3#55311yescharacteristic
829C22×C3#55311yescharacteristic
830C22×C3#55311yescharacteristic
831C22×C3#55911yescharacteristic
832C2×D3—24no—
833C2×D3—24no—
834C2×D3—24no—
835C2×D3—24no—
836C2×D3—24no—
837C2×D3—24no—
838C2×D3—42no—
839C2×D3—42no—
840C2×D3—42no—
841C2×D3—42no—
842C2×D3—42no—
843C2×D3—42no—
844C2×D3—42no—
845C2×D3—42no—
846C2×D3—42no—
847C2×D3—42no—
848C2×D3—42no—
849C2×D3—42no—
850C2×D3—42no—
851C2×D3—42no—
852C2×D3—42no—
853C2×D3—42no—
854C2×D3—42no—
855C2×D3—42no—
856C2×D3—42no—
857C2×D3—42no—
858C2×D3—42no—
859C2×D3—42no—
860C2×D3—42no—
861C2×D3—42no—
862C3×C4—24no—
863C3×C4—42no—
864C3×C4—42no—
865C3×C4—42no—
866C3×C4—42no—
867C3×C4—42no—
868C3×C4—81no—
869Dic3—24no—
870Dic3—42no—
871Dic3—42no—
872Dic3—42no—
873Dic3—42no—
874Dic3—81no—
875C23—34no—
876C23—34no—
877C23—62no—
878C23—62no—
879C23—62no—
880C23—62no—
881C23—62no—
882C23—62no—
883C23—62no—
884C23—62no—
885C23—62no—
886C23—62no—
887C23—62no—
888C23—62no—
889C23—62no—
890C23—62no—
891C23—62no—
892C23—62no—
893C23—62no—
894C23—62no—
895C23—62no—
896C23—62no—
897C23—62no—
898C23—62no—
899C23—62no—
900C23—62no—
901C23—62no—
902C23—62no—
903C23—62no—
904C23—62no—
905C23—62no—
906C23—62no—
907C23—62no—
908C23—62no—
909C23—62no—
910C23—62no—
911C23—62no—
912C23—62no—
913C23—121no—
914C23—121no—
915C23—121no—
916C23—121no—
917C23—121no—
918C23—121no—
919C23—121no—
920C23—121no—
921C23—121no—
922C23—121no—
923C23—121no—
924C23—121no—
925C23—121no—
926C23—121no—
927C23—121no—
928C23—121no—
929C23—121no—
930C23—121no—
931C23—121no—
932C23—121no—
933C23—121no—
934C23—121no—
935C23—121no—
936C23—121no—
937C23—121no—
938C23—121no—
939C23—121no—
940C23—121no—
941C23—121no—
942C23—121no—
943C23—121no—
944C23—121no—
945C23C22×C4×D311yescharacteristic
946C23C2×#23511yescharacteristic
947C23C2×#23511yescharacteristic
948C23C2×D3×D411yescharacteristic
949C23C2×D3×D411yescharacteristic
950C23#100411yescharacteristic
951C23C2×#23911yescharacteristic
952C23D3×#4111yescharacteristic
953C23D3×#4111yescharacteristic
954C23D3×#4111yescharacteristic
955C23D3×#4111yescharacteristic
956C23D3×#4111yescharacteristic
957C23#100911yescharacteristic
958C23#100911yescharacteristic
959C23#100911yescharacteristic
960D4—1216no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—34no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—62no—
1011C2×C4—62no—
1012C2×C4—62no—
1013C2×C4—62no—
1014C2×C4—62no—
1015C2×C4—62no—
1016C2×C4—62no—
1017C2×C4—62no—
1018C2×C4—62no—
1019C2×C4—62no—
1020C2×C4—62no—
1021C2×C4—62no—
1022C2×C4—62no—
1023C2×C4—62no—
1024C2×C4—62no—
1025C2×C4—62no—
1026C2×C4—62no—
1027C2×C4—62no—
1028C2×C4—1216no—
1029C2×C4—1216no—
1030C2×C4—121no—
1031C2×C4—121no—
1032C2×C4—121no—
1033C2×C4—121no—
1034C2×C4—121no—
1035C2×C4—121no—
1036C2×C4—121no—
1037C2×C4—121no—
1038C2×C4—121no—
1039C2×C4—121no—
1040C2×C4—121no—
1041C2×C4—121no—
1042C2×C4—121no—
1043C2×C4—121no—
1044C2×C4—121no—
1045C2×C4—121no—
1046C2×C4—121no—
1047C2×C4—121no—
1048C2×C4—121no—
1049C2×C4—121no—
1050C2×C4—121no—
1051C2×C4—121no—
1052C2×C4—121no—
1053C2×C4#88414yes—
1054C2×C3#229011yescharacteristic
1055C2×C3C4×#12111yescharacteristic
1056C2×C3#232111yescharacteristic
1057C2×C3#234211yescharacteristic
1058C2×C3#235311yescharacteristic
1059C2×C3#236411yescharacteristic
1060C2×C3#237411yescharacteristic
1061C2×C3#253411yescharacteristic
1062C2×C3#253511yescharacteristic
1063C2×C3#255711yescharacteristic
1064C2×C3#255911yescharacteristic
1065C2×C3#257611yescharacteristic
1066C2×C3#257811yescharacteristic
1067C2×C3#259811yescharacteristic
1068C2×C3#260011yescharacteristic
1069D3—44no—
1070D3—44no—
1071C22—64no—
1072C22—64no—
1073C22—64no—
1074C22—64no—
1075C22—64no—
1076C22—64no—
1077C22—122no—
1078C22—122no—
1079C22—122no—
1080C22—122no—
1081C22—122no—
1082C22—122no—
1083C22—122no—
1084C22—122no—
1085C22—122no—
1086C22—122no—
1087C22—122no—
1088C22—122no—
1089C22—122no—
1090C22—122no—
1091C22—122no—
1092C22—122no—
1093C22—122no—
1094C22—122no—
1095C22—122no—
1096C22—122no—
1097C22—122no—
1098C22—122no—
1099C22—122no—
1100C22—122no—
1101C22C4×#23511yescharacteristic
1102C22C2×#88411yescharacteristic
1103C22#551411yescharacteristic
1104C22D3×#11711yescharacteristic
1105C22#552111yescharacteristic
1106C22#552711yescharacteristic
1107C22#552711yescharacteristic
1108C22#552711yescharacteristic
1109C22#552811yescharacteristic
1110C22#553011yescharacteristic
1111C22#553011yescharacteristic
1112C22#554011yescharacteristic
1113C22C4×D3×D411yescharacteristic
1114C22C4×D3×D411yescharacteristic
1115C22#554511yescharacteristic
1116C22#554711yescharacteristic
1117C22#554811yescharacteristic
1118C22C4×#23911yescharacteristic
1119C22#558511yescharacteristic
1120C22#560711yescharacteristic
1121C22#561211yescharacteristic
1122C22#562711yescharacteristic
1123C22#563011yescharacteristic
1124C22#565311yescharacteristic
1125C22#565411yescharacteristic
1126C22#565411yescharacteristic
1127C22#565611yescharacteristic
1128C22#567811yescharacteristic
1129C22#567911yescharacteristic
1130C22#569111yescharacteristic
1131C22#569511yescharacteristic
1132C22#570411yescharacteristic
1133C22#570511yescharacteristic
1134C22#570611yescharacteristic
1135C22#570911yescharacteristic
1136C4—24no—
1137C4—42no—
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—64no—
1143C4—81no—
1144C4—122no—
1145C4—122no—
1146C4—122no—
1147C4—122no—
1148C4—241no—
1149C3#1406811yescharacteristic, complemented, Sylow
1150C2—124no—
1151C2—124no—
1152C2#7341711yescharacteristic
1153C2C4×#88411yescharacteristic
1154C2#7366711yescharacteristic
1155C2#7393311yescharacteristic
1156C2#7413111yescharacteristic
1157C2#7424211yescharacteristic
1158C2#7430611yescharacteristic
1159C2#7493711yescharacteristic
1160C2#7530911yescharacteristic
1161C2#7535811yescharacteristic
1162C2#7537211yescharacteristic
1163C2#7582711yescharacteristic
1164C2#7583211yescharacteristic
1165C2#7588811yescharacteristic
1166C2#7589511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1434C2
socle, cosocleC24×C3C24
prime radicalC23×D12C22
hypercenter#1434D3
hypocenterC3#14068
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
1. C2×#4940C2semidirect
2. C2×C4×(C2×D3)⋊C4C2semidirect
5. C2×#4666C2semidirect
6. C3×#1434C2semidirect
7. #69429C2semidirect
8. #69428C2semidirect
10. (C2×D3)⋊#95C2semidirect
11. (C2×D3)⋊#95C2semidirect
12. #69416C2semidirect
13. #69408C2semidirect
14. #69406C2semidirect
15. #69403C2semidirect
56. #4665C4semidirect
69. #1434D3semidirect
107. C22×C4×D3C2×C4semidirect
139. C2×(C2×D3)⋊C4C2×C4semidirect
149. C2×C4×Dic3D4semidirect
155. C3×#95C2×C4semidirect
167. C3⋊#95C2×C4semidirect
460. #95C4×D3semidirect
1149. C3#14068semidirect

Maximal subgroups

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

subgroupindex
C2×#49402
C2×C4×(C2×D3)⋊C42
C2×#46652
C2×#46662
C3×#14342
#694292
#694282
#694262
(C2×D3)⋊#952
#694162
#694082
#694062
#694032
#140683