Finite Group Databasebeta

← #10726624

Subgroups — #10726624

Order 768.

2774 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#894C211yesmaximal, characteristic, complemented
2C22×#893C211yesmaximal, characteristic, complemented
3C2×#4991C211yesmaximal, characteristic, complemented
4C2×#4989C211yesmaximal, characteristic, complemented
5C2×#4671C211yesmaximal, characteristic
6C2×#4665C211yesmaximal, characteristic, complemented
7C3×#1444C211yesmaximal, characteristic, complemented
8#71570C211yesmaximal, characteristic, complemented
9#71570C211yesmaximal, characteristic, complemented
10#69429C211yesmaximal, characteristic, complemented
11#69426C211yesmaximal, characteristic, complemented
12#69426C211yesmaximal, characteristic, complemented
13(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
14#69408C211yesmaximal, characteristic, complemented
15#69406C211yesmaximal, characteristic, complemented
16#14721—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×D12C2211yescharacteristic
19C23×D12C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C23×C4×D3C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C4⋊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×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×(C2×D3)⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×C4×Dic3C2211yescharacteristic
40C2×#894—24no—
41C2×#894—24no—
42C2×#894—24no—
43C2×#893—24no—
44C2×#893—24no—
45C2×#893—24no—
46C2×C3×#95C2211yescharacteristic
47C2×C3×#95C2211yescharacteristic
48C2×C3×#95C2211yescharacteristic
49C2×C3×#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58#4991—24no—
59#4989—24no—
60#4671—24no—
61#4665—24no—
62C22×#123—31no—
63C22×C4×D4—31no—
64C2×#394—31no—
65C2×#392—31no—
66C2×#386—31no—
67C2×#385—31no—
68#1444D311yescharacteristic, complemented
69#1440—31no—
70#1439—31no—
71#1439—31no—
72#1438—31no—
73#1438—31no—
74#1437—31no—
75#1436—31no—
76C22⋊#95—31no—
77C24×D3C2311yescharacteristic
78C24×D3C2311yescharacteristic
79C24×D3C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C22×D12—22no—
93C22×D12—22no—
94C22×D12—22no—
95C22×D12—22no—
96C22×D12—22no—
97C22×D12—22no—
98C22×D12—22no—
99C22×D12—22no—
100C22×D12—22no—
101C22×D12—22no—
102C22×D12—22no—
103C22×D12—22no—
104C22×D12—22no—
105C22×D12—22no—
106C22×D12—22no—
107C22×D12—22no—
108C22×D12—41no—
109C22×D12—41no—
110C22×D12—41no—
111C22×D12—41no—
112C22×D12D414yes—
113C22×C4×D3—22no—
114C22×C4×D3—22no—
115C22×C4×D3—22no—
116C22×C4×D3—22no—
117C22×C4×D3—22no—
118C22×C4×D3—22no—
119C22×C4×D3—22no—
120C22×C4×D3—22no—
121C22×C4×D3—22no—
122C22×C4×D3—41no—
123C22×C4×D3—41no—
124C22×C4×D3—41no—
125C22×C4×D3—41no—
126C22×C4×D3D414yescomplemented
127C2×C3×C4⋊C4—22no—
128C2×C3×C4⋊C4—22no—
129C2×C3×C4⋊C4—22no—
130C2×C3×C4⋊C4—22no—
131C2×C3×C4⋊C4—22no—
132C2×C3×C4⋊C4—22no—
133C2×C3×C4⋊C4—22no—
134C2×C3×C4⋊C4—22no—
135C2×C3×C4⋊C4—41no—
136C2×(C2×D3)⋊C4—22no—
137C2×(C2×D3)⋊C4—22no—
138C2×(C2×D3)⋊C4—22no—
139C2×(C2×D3)⋊C4—22no—
140C2×(C2×D3)⋊C4—22no—
141C2×(C2×D3)⋊C4—22no—
142C2×(C2×D3)⋊C4—22no—
143C2×(C2×D3)⋊C4—22no—
144C2×(C2×D3)⋊C4—22no—
145C2×(C2×D3)⋊C4—22no—
146C2×(C2×D3)⋊C4—22no—
147C2×(C2×D3)⋊C4—22no—
148C2×(C2×D3)⋊C4—22no—
149C2×(C2×D3)⋊C4—22no—
150C2×(C2×D3)⋊C4—22no—
151C2×(C2×D3)⋊C4—22no—
152C2×(C2×D3)⋊C4—22no—
153C2×(C2×D3)⋊C4—22no—
154C2×(C2×D3)⋊C4—22no—
155C2×(C2×D3)⋊C4—22no—
156C2×(C2×D3)⋊C4—22no—
157C2×(C2×D3)⋊C4—22no—
158C2×(C2×D3)⋊C4—22no—
159C2×(C2×D3)⋊C4—22no—
160C2×(C2×D3)⋊C4—22no—
161C2×(C2×D3)⋊C4—22no—
162C2×(C2×D3)⋊C4—22no—
163C2×(C2×D3)⋊C4—22no—
164C2×(C2×D3)⋊C4—22no—
165C2×(C2×D3)⋊C4—22no—
166C2×(C2×D3)⋊C4—22no—
167C2×(C2×D3)⋊C4—41no—
168C2×(C2×D3)⋊C4—41no—
169C2×(C2×D3)⋊C4—41no—
170C2×(C2×D3)⋊C4—41no—
171C2×(C2×D3)⋊C4—41no—
172C2×(C2×D3)⋊C4—41no—
173C2×(C2×D3)⋊C4D414yescomplemented
174C2×(C2×D3)⋊C4D414yescomplemented
175C2×Dic3⋊C4—22no—
176C2×Dic3⋊C4—22no—
177C2×Dic3⋊C4D414yescomplemented
178C2×C4×Dic3—22no—
179C2×C4×Dic3—22no—
180C2×C4×Dic3—22no—
181#894—232no—
182#893—232no—
183C3×#95—22no—
184C3×#95—22no—
185C3×#95—22no—
186C3×#95—41no—
187C3⋊#95—22no—
188C3⋊#95—22no—
189C3⋊#95—22no—
190C3⋊#95—22no—
191C3⋊#95—22no—
192C3⋊#95—22no—
193C3⋊#95—41no—
194C3⋊#95—41no—
195C23×D4—31no—
196C23×D4—31no—
197C23×D4—31no—
198C24×C4—31no—
199C24×C4—31no—
200C2×#123—64no—
201C2×#123—64no—
202C2×#123—64no—
203C2×C4×D4—64no—
204C2×C4×D4—64no—
205C2×C4×D4—64no—
206C22×C4⋊C4—31no—
207C22×C4⋊C4C2×D311yescharacteristic
208C22×C4⋊C4C2×D311yescharacteristic
209C22×C4⋊C4C2×D311yescharacteristic
210C22×C22⋊C4—31no—
211C22×C22⋊C4—31no—
212C22×C22⋊C4—31no—
213C22×C22⋊C4—31no—
214C22×C22⋊C4—31no—
215C22×C22⋊C4—31no—
216C22×C22⋊C4—31no—
217C22×C22⋊C4—31no—
218C22×C22⋊C4—31no—
219C22×C22⋊C4—31no—
220C22×C22⋊C4—31no—
221C22×C22⋊C4—31no—
222C22×C22⋊C4—31no—
223C22×C42—31no—
224#394—64no—
225#392—64no—
226#386—64no—
227#385—64no—
228C2×#95—31no—
229C2×#95—31no—
230C2×#95—31no—
231C2×#95—31no—
232C2×#95—31no—
233C2×#95—31no—
234C2×#95—31no—
235C2×#95—31no—
236C2×#95C2×D311yescharacteristic
237C2×#95C2×D311yescharacteristic
238C2×#95C2×D311yescharacteristic
239C2×#95C2×D311yescharacteristic
240C24×C3C2411yescharacteristic
241C23×D3—21no—
242C23×D3—21no—
243C23×D3—21no—
244C23×D3—21no—
245C23×D3—21no—
246C23×D3—21no—
247C23×D3—21no—
248C23×D3—21no—
249C23×D3—21no—
250C23×D3—21no—
251C23×D3—21no—
252C23×D3—21no—
253C23×D3—21no—
254C23×D3—21no—
255C23×D3—21no—
256C23×D3—21no—
257C23×D3—21no—
258C23×D3—21no—
259C23×D3—21no—
260C23×D3—21no—
261C23×D3—21no—
262C23×D3—21no—
263C23×D3—21no—
264C23×D3—21no—
265C23×D3—21no—
266C23×D3—21no—
267C23×D3—21no—
268C23×D3—21no—
269C23×D3—21no—
270C23×D3—21no—
271C23×D3—21no—
272C23×D3—21no—
273C23×D3—21no—
274C23×D3—21no—
275C23×D3—21no—
276C23×D3—21no—
277C23×D3—21no—
278C23×D3—21no—
279C23×D3C2×D412yes—
280C23×D3C2×D412yes—
281C23×D3C2×D412yes—
282C23×D3C2×D412yes—
283C23×D3C2×D412yes—
284C23×D3#4112yes—
285C23×D3#4112yes—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4C2×D412yes—
327C22×C3×C4C2×D412yes—
328C22×C3×C4C2×D412yes—
329C22×C3×C4C2×D412yes—
330C22×C3×C4C2×D412yes—
331C22×C3×C4#4112yes—
332C22×C3×C4#4112yes—
333C22×C3×C4#4112yes—
334C22×C3×C4#4112yes—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3—21no—
342C22×Dic3—21no—
343C22×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—21no—
346C22×Dic3—21no—
347C22×Dic3—21no—
348C22×Dic3—21no—
349C22×Dic3—21no—
350C22×Dic3—21no—
351C22×Dic3—21no—
352C22×Dic3—21no—
353C22×Dic3—21no—
354C22×Dic3—21no—
355C22×Dic3—21no—
356C22×Dic3—21no—
357C22×Dic3—21no—
358C22×Dic3—21no—
359C22×Dic3—21no—
360C22×Dic3—21no—
361C22×Dic3—21no—
362C22×Dic3—21no—
363C22×Dic3—21no—
364C22×Dic3—21no—
365C22×Dic3C2×D412yes—
366C22×Dic3C2×D412yes—
367C22×Dic3C2×D412yes—
368C22×Dic3C2×D412yes—
369C22×Dic3C2×D412yes—
370C2×D12—28no—
371C2×D12—28no—
372C2×D12—28no—
373C2×D12—28no—
374C2×D12—28no—
375C2×D12—28no—
376C2×D12—28no—
377C2×D12—28no—
378C2×D12—28no—
379C2×D12—44no—
380C2×D12—44no—
381C2×D12—44no—
382C2×D12—44no—
383C2×D12—44no—
384C2×D12—44no—
385C2×D12—44no—
386C2×D12—44no—
387C2×D12—44no—
388C2×D12—44no—
389C2×D12—44no—
390C2×D12—44no—
391C2×C4×D3—28no—
392C2×C4×D3—28no—
393C2×C4×D3—28no—
394C2×C4×D3—44no—
395C2×C4×D3—44no—
396C2×C4×D3—44no—
397C2×C4×D3—44no—
398C2×C4×D3—44no—
399C2×C4×D3—44no—
400C2×C4×D3—44no—
401C2×C4×D3—44no—
402C2×C4×D3—44no—
403C2×C4×D3—44no—
404C2×C4×D3—44no—
405C3×C4⋊C4—28no—
406C3×C4⋊C4—28no—
407C3×C4⋊C4—44no—
408(C2×D3)⋊C4—28no—
409(C2×D3)⋊C4—28no—
410(C2×D3)⋊C4—28no—
411(C2×D3)⋊C4—28no—
412(C2×D3)⋊C4—28no—
413(C2×D3)⋊C4—28no—
414(C2×D3)⋊C4—44no—
415(C2×D3)⋊C4—44no—
416(C2×D3)⋊C4—44no—
417(C2×D3)⋊C4—44no—
418(C2×D3)⋊C4—44no—
419(C2×D3)⋊C4—44no—
420(C2×D3)⋊C4—44no—
421Dic3⋊C4—28no—
422C4×Dic3—28no—
423C25—31no—
424C25—31no—
425C25—31no—
426C22×D4—34no—
427C22×D4—62no—
428C22×D4—62no—
429C22×D4—62no—
430C22×D4—62no—
431C22×D4—62no—
432C22×D4—62no—
433C22×D4—62no—
434C22×D4—62no—
435C22×D4—62no—
436C22×D4—62no—
437C22×D4—62no—
438C22×D4—62no—
439C22×D4—62no—
440C22×D4—62no—
441C22×D4—62no—
442C22×D4—62no—
443C22×D4—121no—
444C22×D4—121no—
445C22×D4—121no—
446C22×D4—121no—
447C23×C4—31no—
448C23×C4—31no—
449C23×C4—31no—
450C23×C4—34no—
451C23×C4—31no—
452C23×C4—31no—
453C23×C4—62no—
454C23×C4—62no—
455C23×C4—62no—
456C23×C4—62no—
457C23×C4—62no—
458C23×C4—62no—
459C23×C4—62no—
460C23×C4—62no—
461C23×C4—62no—
462C23×C4—121no—
463C23×C4—121no—
464C23×C4—121no—
465C23×C4—121no—
466C23×C4C22×D311yescharacteristic
467C23×C4C22×D311yescharacteristic
468C23×C4C22×D311yescharacteristic
469C23×C4C22×D311yescharacteristic
470C23×C4C22×D311yescharacteristic
471C23×C4C22×D311yescharacteristic
472C23×C4C22×D311yescharacteristic
473#123—632no—
474C4×D4—632no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—34no—
484C2×C4⋊C4—41no—
485C2×C4⋊C4—62no—
486C2×C4⋊C4—62no—
487C2×C22⋊C4—34no—
488C2×C22⋊C4—34no—
489C2×C22⋊C4—62no—
490C2×C22⋊C4—62no—
491C2×C22⋊C4—62no—
492C2×C22⋊C4—62no—
493C2×C22⋊C4—62no—
494C2×C22⋊C4—62no—
495C2×C22⋊C4—62no—
496C2×C22⋊C4—62no—
497C2×C22⋊C4—62no—
498C2×C22⋊C4—62no—
499C2×C22⋊C4—62no—
500C2×C22⋊C4—62no—
501C2×C22⋊C4—62no—
502C2×C22⋊C4—62no—
503C2×C22⋊C4—62no—
504C2×C22⋊C4—62no—
505C2×C22⋊C4—62no—
506C2×C22⋊C4—62no—
507C2×C22⋊C4—62no—
508C2×C22⋊C4—62no—
509C2×C22⋊C4—62no—
510C2×C22⋊C4—62no—
511C2×C22⋊C4—62no—
512C2×C22⋊C4—62no—
513C2×C22⋊C4—62no—
514C2×C22⋊C4—62no—
515C2×C22⋊C4—62no—
516C2×C22⋊C4—62no—
517C2×C22⋊C4—62no—
518C2×C22⋊C4—62no—
519C2×C22⋊C4—62no—
520C2×C22⋊C4—121no—
521C2×C22⋊C4—121no—
522C2×C22⋊C4—121no—
523C2×C22⋊C4—121no—
524C2×C22⋊C4—121no—
525C2×C22⋊C4—121no—
526C2×C42—62no—
527C2×C42—62no—
528C2×C42—62no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—41no—
533#95—62no—
534#95—62no—
535#95—62no—
536#95—62no—
537#95—62no—
538#95—62no—
539#95—121no—
540#95—121no—
541C23×C3C22×D411yescharacteristic
542C23×C3C22×D411yescharacteristic
543C23×C3C22×D411yescharacteristic
544C23×C3C22×D411yescharacteristic
545C23×C3C22×D411yescharacteristic
546C23×C3C2×#4111yescharacteristic
547C23×C3C2×#4111yescharacteristic
548C23×C3C2×#4111yescharacteristic
549C23×C3C2×#4111yescharacteristic
550C23×C3C2×#4111yescharacteristic
551C23×C3C2×#4111yescharacteristic
552C23×C3H(5,𝔽2)11yescharacteristic
553C23×C3H(5,𝔽2)11yescharacteristic
554C23×C3H(5,𝔽2)11yescharacteristic
555C23×C32−1+411yescharacteristic
556C22×D3—22no—
557C22×D3—22no—
558C22×D3—22no—
559C22×D3—22no—
560C22×D3—22no—
561C22×D3—22no—
562C22×D3—22no—
563C22×D3—22no—
564C22×D3—22no—
565C22×D3—22no—
566C22×D3—22no—
567C22×D3—22no—
568C22×D3—22no—
569C22×D3—22no—
570C22×D3—22no—
571C22×D3—22no—
572C22×D3—22no—
573C22×D3—22no—
574C22×D3—22no—
575C22×D3—22no—
576C22×D3—22no—
577C22×D3—22no—
578C22×D3—22no—
579C22×D3—22no—
580C22×D3—22no—
581C22×D3—22no—
582C22×D3—22no—
583C22×D3—22no—
584C22×D3—22no—
585C22×D3—22no—
586C22×D3—22no—
587C22×D3—22no—
588C22×D3—22no—
589C22×D3—22no—
590C22×D3—22no—
591C22×D3—22no—
592C22×D3—22no—
593C22×D3—22no—
594C22×D3—22no—
595C22×D3—22no—
596C22×D3—22no—
597C22×D3—22no—
598C22×D3—22no—
599C22×D3—41no—
600C22×D3—41no—
601C22×D3—41no—
602C22×D3—41no—
603C22×D3—41no—
604C22×D3—41no—
605C22×D3—41no—
606C22×D3—41no—
607C22×D3—41no—
608C22×D3—41no—
609C22×D3—41no—
610C22×D3—41no—
611C22×D3—41no—
612C22×D3—41no—
613C22×D3—41no—
614C22×D3—41no—
615C22×D3—41no—
616C22×D3—41no—
617C22×D3—41no—
618C22×D3—41no—
619C22×D3—41no—
620C22×D3—41no—
621C22×D3—41no—
622C22×D3—41no—
623C22×D3—41no—
624C22×D3—41no—
625C22×D3—41no—
626C22×D3—41no—
627C22×D3—41no—
628C22×D3—41no—
629C22×D3—41no—
630C22×D3—41no—
631C22×D3—41no—
632C22×D3—41no—
633C22×D3—41no—
634C22×D3—41no—
635C22×D3—41no—
636C22×D3—41no—
637C22×D3—41no—
638C22×D3—41no—
639C22×D3—41no—
640C22×D3—41no—
641C22×D3—41no—
642C22×D3—41no—
643C22×D3—41no—
644C22×D3—41no—
645C22×D3—41no—
646C22×D3—41no—
647C22×D3—41no—
648C22×D3—41no—
649C22×D3—41no—
650C22×D3—41no—
651C22×D3—41no—
652C22×D3—41no—
653C22×D3—41no—
654C22×D3—41no—
655C22×D3—41no—
656C22×D3—41no—
657C22×D3—41no—
658C22×D3—41no—
659C22×D3#12014yes—
660C22×D3#12314yescomplemented
661C2×C3×C4—22no—
662C2×C3×C4—22no—
663C2×C3×C4—22no—
664C2×C3×C4—22no—
665C2×C3×C4—22no—
666C2×C3×C4—22no—
667C2×C3×C4—22no—
668C2×C3×C4—22no—
669C2×C3×C4—22no—
670C2×C3×C4—22no—
671C2×C3×C4—22no—
672C2×C3×C4—22no—
673C2×C3×C4—22no—
674C2×C3×C4—22no—
675C2×C3×C4—22no—
676C2×C3×C4—22no—
677C2×C3×C4—22no—
678C2×C3×C4—22no—
679C2×C3×C4—22no—
680C2×C3×C4—22no—
681C2×C3×C4—22no—
682C2×C3×C4—22no—
683C2×C3×C4—22no—
684C2×C3×C4—22no—
685C2×C3×C4—41no—
686C2×C3×C4—41no—
687C2×C3×C4—41no—
688C2×C3×C4—41no—
689C2×C3×C4—41no—
690C2×C3×C4—41no—
691C2×C3×C4—41no—
692C2×C3×C4—41no—
693C2×C3×C4—41no—
694C2×C3×C4—41no—
695C2×C3×C4—41no—
696C2×C3×C4—41no—
697C2×C3×C4—41no—
698C2×C3×C4—41no—
699C2×C3×C4—41no—
700C2×C3×C4—41no—
701C2×C3×C4—41no—
702C2×C3×C4—41no—
703C2×C3×C4—41no—
704C2×C3×C4—41no—
705C2×C3×C4—41no—
706C2×C3×C4—41no—
707C2×C3×C4—41no—
708C2×C3×C4—41no—
709C2×C3×C4#12314yescomplemented
710C2×Dic3—22no—
711C2×Dic3—22no—
712C2×Dic3—22no—
713C2×Dic3—22no—
714C2×Dic3—22no—
715C2×Dic3—22no—
716C2×Dic3—22no—
717C2×Dic3—22no—
718C2×Dic3—22no—
719C2×Dic3—22no—
720C2×Dic3—22no—
721C2×Dic3—22no—
722C2×Dic3—41no—
723C2×Dic3—41no—
724C2×Dic3—41no—
725C2×Dic3—41no—
726C2×Dic3—41no—
727C2×Dic3—41no—
728C2×Dic3—41no—
729C2×Dic3—41no—
730C2×Dic3—41no—
731C2×Dic3—41no—
732C2×Dic3—41no—
733C2×Dic3—41no—
734C2×Dic3—41no—
735C2×Dic3—41no—
736C2×Dic3—41no—
737C2×Dic3—41no—
738C2×Dic3—41no—
739C2×Dic3—41no—
740C2×Dic3—41no—
741C2×Dic3—41no—
742C2×Dic3—41no—
743C2×Dic3—41no—
744C2×Dic3#12014yes—
745D12—232no—
746D12—416no—
747D12—416no—
748C4×D3—416no—
749C4×D3—416no—
750C24—32no—
751C24—32no—
752C24—32no—
753C24—32no—
754C24—32no—
755C24—32no—
756C24—32no—
757C24—61no—
758C24—61no—
759C24—61no—
760C24—61no—
761C24—61no—
762C24—61no—
763C24—61no—
764C24—61no—
765C24—61no—
766C24—61no—
767C24—61no—
768C24—61no—
769C24—61no—
770C24—61no—
771C24—61no—
772C24—61no—
773C24—61no—
774C24—61no—
775C24—61no—
776C24—61no—
777C24—61no—
778C24—61no—
779C24—61no—
780C24—61no—
781C24—61no—
782C24—61no—
783C24—61no—
784C24—61no—
785C24—61no—
786C24—61no—
787C24—61no—
788C24—61no—
789C24—61no—
790C24—61no—
791C24—61no—
792C24—61no—
793C24—61no—
794C24—61no—
795C24C23×D311yescharacteristic
796C2×D4—68no—
797C2×D4—68no—
798C2×D4—68no—
799C2×D4—68no—
800C2×D4—68no—
801C2×D4—68no—
802C2×D4—68no—
803C2×D4—68no—
804C2×D4—68no—
805C2×D4—124no—
806C2×D4—124no—
807C2×D4—124no—
808C2×D4—124no—
809C2×D4—124no—
810C2×D4—124no—
811C2×D4—124no—
812C2×D4—124no—
813C2×D4—124no—
814C2×D4—124no—
815C2×D4—124no—
816C2×D4—124no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—32no—
858C22×C4—32no—
859C22×C4—32no—
860C22×C4—32no—
861C22×C4—32no—
862C22×C4—68no—
863C22×C4—68no—
864C22×C4—68no—
865C22×C4—61no—
866C22×C4—61no—
867C22×C4—61no—
868C22×C4—61no—
869C22×C4—61no—
870C22×C4—61no—
871C22×C4—61no—
872C22×C4—61no—
873C22×C4—61no—
874C22×C4—61no—
875C22×C4—61no—
876C22×C4—61no—
877C22×C4—61no—
878C22×C4—61no—
879C22×C4—61no—
880C22×C4—61no—
881C22×C4—61no—
882C22×C4—61no—
883C22×C4—61no—
884C22×C4—61no—
885C22×C4—61no—
886C22×C4—61no—
887C22×C4—61no—
888C22×C4—61no—
889C22×C4—61no—
890C22×C4—61no—
891C22×C4—61no—
892C22×C4—61no—
893C22×C4—61no—
894C22×C4—61no—
895C22×C4—124no—
896C22×C4—124no—
897C22×C4—124no—
898C22×C4—124no—
899C22×C4—124no—
900C22×C4—124no—
901C22×C4—124no—
902C22×C4—124no—
903C22×C4—124no—
904C22×C4—124no—
905C22×C4—124no—
906C22×C4#23512yes—
907C22×C4D3×D412yes—
908C22×C4D3×D412yes—
909C22×C4D3×D412yes—
910C22×C4D3×D412yes—
911C22×C4D3×D412yes—
912C22×C4#23912yes—
913C22×C4#23912yes—
914C22×C4#23912yes—
915C4⋊C4—28no—
916C4⋊C4—28no—
917C4⋊C4—44no—
918C4⋊C4—68no—
919C22⋊C4—68no—
920C22⋊C4—68no—
921C22⋊C4—68no—
922C22⋊C4—68no—
923C22⋊C4—68no—
924C22⋊C4—68no—
925C22⋊C4—124no—
926C22⋊C4—124no—
927C22⋊C4—124no—
928C22⋊C4—124no—
929C22⋊C4—124no—
930C22⋊C4—124no—
931C22⋊C4—124no—
932C42—68no—
933C22×C3C2×#12011yescharacteristic
934C22×C3C2×#12011yescharacteristic
935C22×C3C2×#12311yescharacteristic
936C22×C3C2×#12311yescharacteristic
937C22×C3#52511yescharacteristic
938C22×C3#52511yescharacteristic
939C22×C3#52511yescharacteristic
940C22×C3#52511yescharacteristic
941C22×C3#52511yescharacteristic
942C22×C3#52511yescharacteristic
943C22×C3#53211yescharacteristic
944C22×C3#53211yescharacteristic
945C22×C3#53211yescharacteristic
946C22×C3#53411yescharacteristic
947C22×C3#53711yescharacteristic
948C22×C3#53811yescharacteristic
949C22×C3#53911yescharacteristic
950C22×C3#54011yescharacteristic
951C22×C3#54211yescharacteristic
952C22×C3D4211yescharacteristic
953C22×C3D4211yescharacteristic
954C22×C3D4211yescharacteristic
955C22×C3D4211yescharacteristic
956C22×C3#54611yescharacteristic
957C22×C3#54611yescharacteristic
958C22×C3#54611yescharacteristic
959C22×C3#54711yescharacteristic
960C22×C3#54711yescharacteristic
961C22×C3#54711yescharacteristic
962C22×C3#54811yescharacteristic
963C22×C3#55011yescharacteristic
964C22×C3#55111yescharacteristic
965C22×C3#55311yescharacteristic
966C22×C3#55311yescharacteristic
967C22×C3#55911yescharacteristic
968C2×D3—24no—
969C2×D3—24no—
970C2×D3—24no—
971C2×D3—24no—
972C2×D3—24no—
973C2×D3—24no—
974C2×D3—42no—
975C2×D3—42no—
976C2×D3—42no—
977C2×D3—42no—
978C2×D3—42no—
979C2×D3—42no—
980C2×D3—42no—
981C2×D3—42no—
982C2×D3—42no—
983C2×D3—42no—
984C2×D3—42no—
985C2×D3—42no—
986C2×D3—42no—
987C2×D3—42no—
988C2×D3—42no—
989C2×D3—42no—
990C2×D3—42no—
991C2×D3—42no—
992C2×D3—42no—
993C2×D3—42no—
994C2×D3—42no—
995C2×D3—42no—
996C2×D3—42no—
997C2×D3—42no—
998C2×D3—42no—
999C2×D3—42no—
1000C2×D3—42no—
1001C2×D3—42no—
1002C2×D3—42no—
1003C2×D3—42no—
1004C2×D3—42no—
1005C2×D3—81no—
1006C2×D3—81no—
1007C2×D3—81no—
1008C2×D3—81no—
1009C2×D3—81no—
1010C2×D3—81no—
1011C2×D3—81no—
1012C2×D3—81no—
1013C3×C4—24no—
1014C3×C4—42no—
1015C3×C4—42no—
1016C3×C4—42no—
1017C3×C4—42no—
1018C3×C4—42no—
1019C3×C4—42no—
1020Dic3—24no—
1021Dic3—42no—
1022Dic3—42no—
1023Dic3—81no—
1024Dic3—81no—
1025C23—34no—
1026C23—34no—
1027C23—62no—
1028C23—62no—
1029C23—62no—
1030C23—62no—
1031C23—62no—
1032C23—62no—
1033C23—62no—
1034C23—62no—
1035C23—62no—
1036C23—62no—
1037C23—62no—
1038C23—62no—
1039C23—62no—
1040C23—62no—
1041C23—62no—
1042C23—62no—
1043C23—62no—
1044C23—62no—
1045C23—62no—
1046C23—62no—
1047C23—62no—
1048C23—62no—
1049C23—62no—
1050C23—62no—
1051C23—62no—
1052C23—62no—
1053C23—62no—
1054C23—62no—
1055C23—62no—
1056C23—62no—
1057C23—62no—
1058C23—62no—
1059C23—62no—
1060C23—62no—
1061C23—62no—
1062C23—62no—
1063C23—62no—
1064C23—62no—
1065C23—62no—
1066C23—62no—
1067C23—62no—
1068C23—62no—
1069C23—62no—
1070C23—121no—
1071C23—121no—
1072C23—121no—
1073C23—121no—
1074C23—121no—
1075C23—121no—
1076C23—121no—
1077C23—121no—
1078C23—121no—
1079C23—121no—
1080C23—121no—
1081C23—121no—
1082C23—121no—
1083C23—121no—
1084C23—121no—
1085C23—121no—
1086C23—121no—
1087C23—121no—
1088C23—121no—
1089C23—121no—
1090C23—121no—
1091C23—121no—
1092C23—121no—
1093C23—121no—
1094C23—121no—
1095C23—121no—
1096C23—121no—
1097C23—121no—
1098C23—121no—
1099C23—121no—
1100C23—121no—
1101C23—121no—
1102C23—121no—
1103C23—121no—
1104C23—121no—
1105C23—121no—
1106C23—121no—
1107C23—121no—
1108C23—121no—
1109C23—121no—
1110C23—121no—
1111C23—121no—
1112C23—121no—
1113C23—121no—
1114C23—121no—
1115C23—121no—
1116C23—121no—
1117C23—121no—
1118C23—121no—
1119C23—121no—
1120C23—121no—
1121C23—121no—
1122C23—121no—
1123C23—121no—
1124C23—121no—
1125C23—121no—
1126C23—121no—
1127C23—121no—
1128C23—121no—
1129C23—121no—
1130C23C2×#23511yescharacteristic
1131C23C2×D3×D411yescharacteristic
1132C23C2×D3×D411yescharacteristic
1133C23C2×D3×D411yescharacteristic
1134C23C2×D3×D411yescharacteristic
1135C23C2×D3×D411yescharacteristic
1136C23#100411yescharacteristic
1137C23C2×#23911yescharacteristic
1138C23C2×#23911yescharacteristic
1139C23C2×#23911yescharacteristic
1140C23#100711yescharacteristic
1141C23D3×#4111yescharacteristic
1142C23D3×#4111yescharacteristic
1143C23#100911yescharacteristic
1144C23#100911yescharacteristic
1145D4—632no—
1146D4—1216no—
1147D4—1216no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—34no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—62no—
1198C2×C4—62no—
1199C2×C4—62no—
1200C2×C4—62no—
1201C2×C4—62no—
1202C2×C4—62no—
1203C2×C4—62no—
1204C2×C4—62no—
1205C2×C4—62no—
1206C2×C4—62no—
1207C2×C4—62no—
1208C2×C4—62no—
1209C2×C4—1216no—
1210C2×C4—1216no—
1211C2×C4—121no—
1212C2×C4—121no—
1213C2×C4—121no—
1214C2×C4—121no—
1215C2×C4—121no—
1216C2×C4—121no—
1217C2×C4—121no—
1218C2×C4—121no—
1219C2×C4—121no—
1220C2×C4—121no—
1221C2×C4—121no—
1222C2×C4—121no—
1223C2×C4—121no—
1224C2×C4—121no—
1225C2×C4—121no—
1226C2×C4—121no—
1227C2×C4—121no—
1228C2×C4—121no—
1229C2×C4—121no—
1230C2×C4—121no—
1231C2×C4—121no—
1232C2×C4—121no—
1233C2×C4#89414yescomplemented
1234C2×C3#238811yescharacteristic
1235C2×C3#240311yescharacteristic
1236C2×C3#240711yescharacteristic
1237C2×C3#241811yescharacteristic
1238C2×C3#242211yescharacteristic
1239C2×C3#243011yescharacteristic
1240C2×C3#244311yescharacteristic
1241C2×C3#244511yescharacteristic
1242C2×C3#245511yescharacteristic
1243C2×C3#245611yescharacteristic
1244C2×C3#246111yescharacteristic
1245C2×C3#246411yescharacteristic
1246C2×C3#260211yescharacteristic
1247C2×C3#263011yescharacteristic
1248C2×C3#284911yescharacteristic
1249D3—44no—
1250D3—44no—
1251D3—82no—
1252C22—64no—
1253C22—64no—
1254C22—64no—
1255C22—64no—
1256C22—64no—
1257C22—64no—
1258C22—122no—
1259C22—122no—
1260C22—122no—
1261C22—122no—
1262C22—122no—
1263C22—122no—
1264C22—122no—
1265C22—122no—
1266C22—122no—
1267C22—122no—
1268C22—122no—
1269C22—122no—
1270C22—122no—
1271C22—122no—
1272C22—122no—
1273C22—122no—
1274C22—122no—
1275C22—122no—
1276C22—122no—
1277C22—122no—
1278C22—122no—
1279C22—122no—
1280C22—122no—
1281C22—122no—
1282C22—122no—
1283C22—122no—
1284C22—122no—
1285C22—122no—
1286C22—122no—
1287C22—122no—
1288C22—122no—
1289C22—241no—
1290C22—241no—
1291C22—241no—
1292C22—241no—
1293C22—241no—
1294C22—241no—
1295C22—241no—
1296C22—241no—
1297C22C2×#89411yescharacteristic
1298C22#550711yescharacteristic
1299C22#551411yescharacteristic
1300C22#554711yescharacteristic
1301C22#554711yescharacteristic
1302C22#555311yescharacteristic
1303C22#558511yescharacteristic
1304C22D3×#12011yescharacteristic
1305C22D3×#12011yescharacteristic
1306C22#559011yescharacteristic
1307C22#560511yescharacteristic
1308C22#560911yescharacteristic
1309C22#560911yescharacteristic
1310C22#562711yescharacteristic
1311C22#562711yescharacteristic
1312C22#562711yescharacteristic
1313C22#562711yescharacteristic
1314C22#562911yescharacteristic
1315C22#563011yescharacteristic
1316C22#563011yescharacteristic
1317C22#563311yescharacteristic
1318C22#563711yescharacteristic
1319C22D3×#12311yescharacteristic
1320C22#565411yescharacteristic
1321C22#565711yescharacteristic
1322C22#569211yescharacteristic
1323C22#569511yescharacteristic
1324C22#569711yescharacteristic
1325C22#571711yescharacteristic
1326C22#572511yescharacteristic
1327C22#572511yescharacteristic
1328C22#572511yescharacteristic
1329C22#572611yescharacteristic
1330C22#572611yescharacteristic
1331C22#573311yescharacteristic
1332C4—24no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—64no—
1340C4—122no—
1341C4—122no—
1342C4—241no—
1343C4—241no—
1344C3#1472111yescharacteristic, complemented, Sylow
1345C2—124no—
1346C2—124no—
1347C2—242no—
1348C2#7436211yescharacteristic
1349C2#7440411yescharacteristic
1350C2#7442711yescharacteristic
1351C2#7465611yescharacteristic
1352C2#7600411yescharacteristic
1353C2#7609611yescharacteristic
1354C2#7622611yescharacteristic
1355C2#7675311yescharacteristic
1356C2#7716911yescharacteristic
1357C2#7717611yescharacteristic
1358C2#7725011yescharacteristic
1359C2#7775311yescharacteristic
1360C2#7782111yescharacteristic
1361C2#7795111yescharacteristic
1362C2#7810111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1444C2
prime radicalC2×#4671C2
hypercenter#1444D3
hypocenterC3#14721
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
1. C22×#894C2semidirect
2. C22×#893C2semidirect
3. C2×#4991C2semidirect
4. C2×#4989C2semidirect
6. C2×#4665C2semidirect
7. C3×#1444C2semidirect
8. #71570C2semidirect
9. #71570C2semidirect
10. #69429C2semidirect
11. #69426C2semidirect
12. #69426C2semidirect
13. (C2×D3)⋊#95C2semidirect
14. #69408C2semidirect
15. #69406C2semidirect
68. #1444D3semidirect
126. C22×C4×D3D4semidirect
173. C2×(C2×D3)⋊C4D4semidirect
174. C2×(C2×D3)⋊C4D4semidirect
177. C2×Dic3⋊C4D4semidirect
660. C22×D3#123semidirect
709. C2×C3×C4#123semidirect
1233. C2×C4#894semidirect
1344. C3#14721semidirect

Maximal subgroups

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

subgroupindex
C22×#8942
C22×#8932
C2×#49912
C2×#49892
C2×#46712
C2×#46652
C3×#14442
#715702
#694292
#694262
(C2×D3)⋊#952
#694082
#694062
#147213