Finite Group Databasebeta

← #10727903

Subgroups — #10727903

Order 768.

1942 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4673C211yesmaximal, characteristic, complemented
2C2×#4673C211yesmaximal, characteristic, complemented
3C2×#4665C211yesmaximal, characteristic
4C2×#4672C211yesmaximal, characteristic
5C2×#4646C211yesmaximal, characteristic, complemented
6C2×#4666C211yesmaximal, characteristic, complemented
7C3×#1443C211yesmaximal, characteristic, complemented
8#69429C211yesmaximal, characteristic, complemented
9#69429C211yesmaximal, characteristic, complemented
10#69426C211yesmaximal, characteristic
11(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
12#69414C211yesmaximal, characteristic, complemented
13#69408C211yesmaximal, characteristic, complemented
14#69408C211yesmaximal, characteristic, complemented
15#69403C211yesmaximal, characteristic, complemented
16#14817—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×Dic6C2211yescharacteristic
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×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#4673—24no—
53#4673—24no—
54#4672—24no—
55#4666—24no—
56#4665—24no—
57#4646—24no—
58C2×#394—31no—
59C2×#393—31no—
60C2×#393—31no—
61C2×#391—31no—
62C2×#386—31no—
63C2×C4×C22⋊C4—31no—
64#1443D311yescharacteristic, complemented
65#1442—31no—
66#1440—31no—
67#1440—31no—
68#1438—31no—
69#1437—31no—
70#1437—31no—
71#1434—31no—
72C22⋊#95—31no—
73C24×D3C2311yescharacteristic
74C24×D3C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C22×D12—22no—
89C22×D12—22no—
90C22×D12—22no—
91C22×D12—22no—
92C22×D12—22no—
93C22×D12—41no—
94C22×D12—41no—
95C22×C4×D3—22no—
96C22×C4×D3—22no—
97C22×C4×D3—22no—
98C22×C4×D3—22no—
99C22×C4×D3—22no—
100C22×C4×D3—41no—
101C22×C4×D3—41no—
102C22×Dic6—22no—
103C22×Dic6—22no—
104C22×Dic6—22no—
105C22×Dic6—22no—
106C22×Dic6—22no—
107C22×Dic6—41no—
108C22×Dic6—41no—
109C2×(C2×D3)⋊C4—22no—
110C2×(C2×D3)⋊C4—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—22no—
132C2×(C2×D3)⋊C4—22no—
133C2×(C2×D3)⋊C4—22no—
134C2×(C2×D3)⋊C4—22no—
135C2×(C2×D3)⋊C4—41no—
136C2×(C2×D3)⋊C4—41no—
137C2×(C2×D3)⋊C4—41no—
138C2×(C2×D3)⋊C4—41no—
139C2×(C2×D3)⋊C4—41no—
140C2×(C2×D3)⋊C4—41no—
141C2×(C2×D3)⋊C4D414yes—
142C2×Dic3⋊C4—22no—
143C2×Dic3⋊C4—22no—
144C2×Dic3⋊C4—41no—
145C2×C4×Dic3—22no—
146C2×C4×Dic3—22no—
147C2×C4×Dic3—22no—
148C2×C4×Dic3—22no—
149C2×C4×Dic3—41no—
150C2×C4×Dic3—41no—
151C3×#95—22no—
152C3×#95—22no—
153C3×#95—22no—
154C3×#95—22no—
155C3×#95—22no—
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⋊#95D414yes—
168C3⋊#95D414yescomplemented
169C23×Q8—31no—
170C23×D4—31no—
171C24×C4—31no—
172C22×C4⋊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×C22⋊C4—31no—
183C22×C22⋊C4—31no—
184C22×C42—31no—
185C22×C42—31no—
186#394—64no—
187#393—64no—
188#393—64no—
189#391—64no—
190#386—64no—
191C4×C22⋊C4—64no—
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×#95—31no—
203C2×#95C2×D311yescharacteristic
204C2×#95C2×D311yescharacteristic
205C2×#95C2×D311yescharacteristic
206C2×#95C2×D311yescharacteristic
207C2×#95C2×D311yescharacteristic
208C2×#95C2×D311yescharacteristic
209C2×#95C2×D311yescharacteristic
210C24×C3C2411yescharacteristic
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×D3—21no—
234C23×D3—21no—
235C23×D3—21no—
236C23×D3—21no—
237C23×D3C2×D412yes—
238C23×D3#4112yes—
239C23×D3#4112yes—
240C23×D3#4112yes—
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×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4C2×D412yes—
286C22×C3×C4C2×D412yes—
287C22×C3×C4C2×D412yes—
288C22×C3×C4#4112yes—
289C22×C3×C4#4112yes—
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×Dic3—21no—
324C22×Dic3C2×D412yes—
325C22×Dic3C2×D412yes—
326C22×Dic3C2×D412yes—
327C22×Dic3C2×D412yes—
328C22×Dic3C2×D412yes—
329C22×Dic3#4112yes—
330C22×Dic3#4112yes—
331C22×Dic3#4112yes—
332C2×D12—28no—
333C2×D12—44no—
334C2×D12—44no—
335C2×D12—44no—
336C2×D12—44no—
337C2×D12—44no—
338C2×D12—44no—
339C2×C4×D3—28no—
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×Dic6—28no—
347C2×Dic6—44no—
348C2×Dic6—44no—
349C2×Dic6—44no—
350C2×Dic6—44no—
351C2×Dic6—44no—
352C2×Dic6—44no—
353(C2×D3)⋊C4—28no—
354(C2×D3)⋊C4—28no—
355(C2×D3)⋊C4—44no—
356(C2×D3)⋊C4—44no—
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—
362(C2×D3)⋊C4—44no—
363(C2×D3)⋊C4—44no—
364Dic3⋊C4—44no—
365C4×Dic3—44no—
366C4×Dic3—44no—
367C25—31no—
368C25—31no—
369C22×Q8—62no—
370C22×Q8—62no—
371C22×Q8—62no—
372C22×Q8—62no—
373C22×Q8—62no—
374C22×Q8—121no—
375C22×Q8—121no—
376C22×D4—62no—
377C22×D4—62no—
378C22×D4—62no—
379C22×D4—62no—
380C22×D4—62no—
381C22×D4—121no—
382C22×D4—121no—
383C23×C4—31no—
384C23×C4—31no—
385C23×C4—31no—
386C23×C4—31no—
387C23×C4—31no—
388C23×C4—31no—
389C23×C4—62no—
390C23×C4—62no—
391C23×C4—62no—
392C23×C4—62no—
393C23×C4—62no—
394C23×C4—121no—
395C23×C4—121no—
396C23×C4C22×D311yescharacteristic
397C23×C4C22×D311yescharacteristic
398C23×C4C22×D311yescharacteristic
399C23×C4C22×D311yescharacteristic
400C23×C4C22×D311yescharacteristic
401C23×C4C22×D311yescharacteristic
402C23×C4C22×D311yescharacteristic
403C2×C4⋊C4—62no—
404C2×C4⋊C4—62no—
405C2×C4⋊C4—121no—
406C2×C22⋊C4—34no—
407C2×C22⋊C4—62no—
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—62no—
429C2×C22⋊C4—62no—
430C2×C22⋊C4—62no—
431C2×C22⋊C4—62no—
432C2×C22⋊C4—62no—
433C2×C22⋊C4—121no—
434C2×C22⋊C4—121no—
435C2×C22⋊C4—121no—
436C2×C22⋊C4—121no—
437C2×C22⋊C4—121no—
438C2×C22⋊C4—121no—
439C2×C42—62no—
440C2×C42—62no—
441C2×C42—62no—
442C2×C42—62no—
443C2×C42—121no—
444C2×C42—121no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—34no—
453#95—34no—
454#95—62no—
455#95—62no—
456#95—62no—
457#95—62no—
458#95—62no—
459#95—62no—
460#95—121no—
461#95—121no—
462#95—121no—
463C23×C3C22×D411yescharacteristic
464C23×C3C22×D411yescharacteristic
465C23×C3C22×D411yescharacteristic
466C23×C3C2×#4111yescharacteristic
467C23×C3C2×#4111yescharacteristic
468C23×C3C2×#4111yescharacteristic
469C23×C3C2×#4111yescharacteristic
470C23×C3C2×#4111yescharacteristic
471C23×C3C2×#4111yescharacteristic
472C23×C3C2×#4111yescharacteristic
473C23×C3C2×#4111yescharacteristic
474C23×C3H(5,𝔽2)11yescharacteristic
475C23×C3H(5,𝔽2)11yescharacteristic
476C23×C3H(5,𝔽2)11yescharacteristic
477C23×C32−1+411yescharacteristic
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—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×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—41no—
545C22×D3—41no—
546C22×D3—41no—
547C22×D3#12414yes—
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—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×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—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
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—22no—
614C2×Dic3—22no—
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×Dic3—41no—
637C2×Dic3#12114yes—
638C2×Dic3#12414yes—
639D12—416no—
640C4×D3—416no—
641Dic6—416no—
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—
670C24—61no—
671C24—61no—
672C24C23×D311yescharacteristic
673C2×Q8—68no—
674C2×Q8—124no—
675C2×Q8—124no—
676C2×Q8—124no—
677C2×Q8—124no—
678C2×Q8—124no—
679C2×Q8—124no—
680C2×D4—68no—
681C2×D4—124no—
682C2×D4—124no—
683C2×D4—124no—
684C2×D4—124no—
685C2×D4—124no—
686C2×D4—124no—
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—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—32no—
732C22×C4—32no—
733C22×C4—32no—
734C22×C4—32no—
735C22×C4—32no—
736C22×C4—32no—
737C22×C4—32no—
738C22×C4—32no—
739C22×C4—68no—
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—61no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—61no—
772C22×C4—61no—
773C22×C4—61no—
774C22×C4—124no—
775C22×C4—124no—
776C22×C4—124no—
777C22×C4—124no—
778C22×C4—124no—
779C22×C4—124no—
780C22×C4#23512yes—
781C22×C4D3×D412yes—
782C22×C4D3×D412yes—
783C22×C4D3×D412yes—
784C22×C4#23912yes—
785C4⋊C4—124no—
786C22⋊C4—68no—
787C22⋊C4—68no—
788C22⋊C4—124no—
789C22⋊C4—124no—
790C22⋊C4—124no—
791C22⋊C4—124no—
792C22⋊C4—124no—
793C22⋊C4—124no—
794C22⋊C4—124no—
795C22⋊C4—124no—
796C22⋊C4—124no—
797C42—124no—
798C42—124no—
799C22×C3C2×#12111yescharacteristic
800C22×C3#52511yescharacteristic
801C22×C3#52511yescharacteristic
802C22×C3#52511yescharacteristic
803C22×C3#52511yescharacteristic
804C22×C3C2×#12411yescharacteristic
805C22×C3C2×#12411yescharacteristic
806C22×C3#52911yescharacteristic
807C22×C3#52911yescharacteristic
808C22×C3#52911yescharacteristic
809C22×C3#52911yescharacteristic
810C22×C3#52911yescharacteristic
811C22×C3#53211yescharacteristic
812C22×C3#53811yescharacteristic
813C22×C3#53811yescharacteristic
814C22×C3#53811yescharacteristic
815C22×C3#53911yescharacteristic
816C22×C3#54211yescharacteristic
817C22×C3#54211yescharacteristic
818C22×C3D4211yescharacteristic
819C22×C3D4211yescharacteristic
820C22×C3#54611yescharacteristic
821C22×C3#54611yescharacteristic
822C22×C3#54611yescharacteristic
823C22×C3#54611yescharacteristic
824C22×C3#54611yescharacteristic
825C22×C3#54711yescharacteristic
826C22×C3#54811yescharacteristic
827C22×C3#54811yescharacteristic
828C22×C3#55111yescharacteristic
829C22×C3#55111yescharacteristic
830C22×C3#55111yescharacteristic
831C22×C3#55211yescharacteristic
832C22×C3#55511yescharacteristic
833C22×C3#55911yescharacteristic
834C2×D3—24no—
835C2×D3—24no—
836C2×D3—24no—
837C2×D3—42no—
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—81no—
857C2×D3—81no—
858C2×D3—81no—
859C2×D3—81no—
860C2×D3—81no—
861C2×D3—81no—
862C2×D3—81no—
863C2×D3—81no—
864C3×C4—42no—
865C3×C4—42no—
866C3×C4—42no—
867C3×C4—42no—
868C3×C4—42no—
869C3×C4—81no—
870C3×C4—81no—
871Dic3—24no—
872Dic3—24no—
873Dic3—42no—
874Dic3—42no—
875Dic3—81no—
876Dic3—81no—
877C23—34no—
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—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—
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—
945C23—121no—
946C23—121no—
947C23C2×#23511yescharacteristic
948C23C2×D3×D411yescharacteristic
949C23C2×D3×D411yescharacteristic
950C23C2×D3×D411yescharacteristic
951C23C2×#23911yescharacteristic
952C23D3×#4111yescharacteristic
953C23D3×#4111yescharacteristic
954C23D3×#4111yescharacteristic
955C23D3×#4111yescharacteristic
956C23D3×#4111yescharacteristic
957C23D3×#4111yescharacteristic
958C23#100911yescharacteristic
959C23#100911yescharacteristic
960C23#100911yescharacteristic
961C23#101011yescharacteristic
962Q8—1216no—
963D4—1216no—
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—34no—
980C2×C4—34no—
981C2×C4—41no—
982C2×C4—41no—
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—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
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—62no—
1029C2×C4—62no—
1030C2×C4—62no—
1031C2×C4—62no—
1032C2×C4—62no—
1033C2×C4—1216no—
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—121no—
1054C2×C4—121no—
1055C2×C4—121no—
1056C2×C3#239811yescharacteristic
1057C2×C3#242411yescharacteristic
1058C2×C3#242711yescharacteristic
1059C2×C3#245811yescharacteristic
1060C2×C3#245911yescharacteristic
1061C2×C3#246311yescharacteristic
1062C2×C3#247211yescharacteristic
1063C2×C3#247211yescharacteristic
1064C2×C3#247711yescharacteristic
1065C2×C3#248811yescharacteristic
1066C2×C3#249111yescharacteristic
1067C2×C3#255711yescharacteristic
1068C2×C3#257211yescharacteristic
1069C2×C3#265311yescharacteristic
1070C2×C3#285011yescharacteristic
1071D3—44no—
1072D3—82no—
1073C22—64no—
1074C22—64no—
1075C22—64no—
1076C22—122no—
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—241no—
1096C22—241no—
1097C22—241no—
1098C22—241no—
1099C22—241no—
1100C22—241no—
1101C22—241no—
1102C22—241no—
1103C22#552711yescharacteristic
1104C22#552811yescharacteristic
1105C22#553211yescharacteristic
1106C22#554711yescharacteristic
1107C22#554811yescharacteristic
1108C22#555211yescharacteristic
1109C22#558511yescharacteristic
1110C22D3×#12111yescharacteristic
1111C22#560911yescharacteristic
1112C22#560911yescharacteristic
1113C22#562711yescharacteristic
1114C22#563011yescharacteristic
1115C22#563011yescharacteristic
1116C22#565411yescharacteristic
1117C22#565411yescharacteristic
1118C22#565411yescharacteristic
1119C22#565511yescharacteristic
1120C22#565611yescharacteristic
1121C22#565611yescharacteristic
1122C22D3×#12411yescharacteristic
1123C22D3×#12411yescharacteristic
1124C22#567711yescharacteristic
1125C22#569111yescharacteristic
1126C22#569111yescharacteristic
1127C22#569411yescharacteristic
1128C22#570411yescharacteristic
1129C22#570411yescharacteristic
1130C22#570411yescharacteristic
1131C22#570511yescharacteristic
1132C22#570511yescharacteristic
1133C22#570611yescharacteristic
1134C22#570611yescharacteristic
1135C22#570711yescharacteristic
1136C22#571011yescharacteristic
1137C22#571011yescharacteristic
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—42no—
1143C4—64no—
1144C4—64no—
1145C4—81no—
1146C4—81no—
1147C4—122no—
1148C4—122no—
1149C4—241no—
1150C4—241no—
1151C3#1481711yescharacteristic, complemented, Sylow
1152C2—124no—
1153C2—242no—
1154C2#7430311yescharacteristic
1155C2#7498911yescharacteristic
1156C2#7532611yescharacteristic
1157C2#7535811yescharacteristic
1158C2#7554611yescharacteristic
1159C2#7585611yescharacteristic
1160C2#7595711yescharacteristic
1161C2#7741611yescharacteristic
1162C2#7746611yescharacteristic
1163C2#7747411yescharacteristic
1164C2#7747411yescharacteristic
1165C2#7813111yescharacteristic
1166C2#7814311yescharacteristic
1167C2#7834611yescharacteristic
1168C2#7841711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1443C2
prime radicalC23×D12C22
hypercenter#1443D3
hypocenterC3#14817
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
1. C2×#4673C2semidirect
2. C2×#4673C2semidirect
5. C2×#4646C2semidirect
6. C2×#4666C2semidirect
7. C3×#1443C2semidirect
8. #69429C2semidirect
9. #69429C2semidirect
11. (C2×D3)⋊#95C2semidirect
12. #69414C2semidirect
13. #69408C2semidirect
14. #69408C2semidirect
15. #69403C2semidirect
64. #1443D3semidirect
168. C3⋊#95D4semidirect
1151. C3#14817semidirect

Maximal subgroups

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

subgroupindex
C2×#46732
C2×#46652
C2×#46722
C2×#46462
C2×#46662
C3×#14432
#694292
#694262
(C2×D3)⋊#952
#694142
#694082
#694032
#148173