Finite Group Databasebeta

← #10727892

Subgroups — #10727892

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×C3×#391C211yesmaximal, characteristic, complemented
2C2×#5231C211yesmaximal, characteristic, complemented
3C2×#5231C211yesmaximal, characteristic, complemented
4C2×#4991C211yesmaximal, characteristic
5C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C2×#4665C211yesmaximal, characteristic
7#71567C211yesmaximal, characteristic, complemented
8#71537C211yesmaximal, characteristic, complemented
9#69429C211yesmaximal, characteristic, complemented
10#69429C211yesmaximal, characteristic, complemented
11#69426C211yesmaximal, characteristic
12(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
13#69417C211yesmaximal, characteristic, complemented
14#69408C211yesmaximal, characteristic, complemented
15#69401C211yesmaximal, characteristic, complemented
16#14817—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic
18C23×D12C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C42C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C3×#391—24no—
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2211yescharacteristic
39#5231—24no—
40#5231—24no—
41C2×C3⋊#95C2211yescharacteristic
42C2×C3⋊#95C2211yescharacteristic
43C2×C3⋊#95C2211yescharacteristic
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55#4991—24no—
56C4×(C2×D3)⋊C4—24no—
57#4665—24no—
58C2×#394—31no—
59C2×#393—31no—
60C2×#393—31no—
61C2×#391D311yescharacteristic, complemented
62C2×#386—31no—
63C2×C4×C22⋊C4—31no—
64#1443—31no—
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
75C22×C3×Q8—22no—
76C22×C3×Q8—22no—
77C22×C3×Q8—22no—
78C22×C3×Q8—22no—
79C22×C3×Q8—22no—
80C22×C3×Q8—41no—
81C22×C3×Q8—41no—
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C22×D12—22no—
96C22×D12—22no—
97C22×D12—22no—
98C22×D12—22no—
99C22×D12—22no—
100C22×D12—41no—
101C22×D12—41no—
102C22×C4×D3—22no—
103C22×C4×D3—22no—
104C22×C4×D3—22no—
105C22×C4×D3—22no—
106C22×C4×D3—22no—
107C22×C4×D3—41no—
108C22×C4×D3—41no—
109C2×C3×C4⋊C4—22no—
110C2×C3×C4⋊C4—22no—
111C2×C3×C4⋊C4—41no—
112C2×C3×C42—22no—
113C2×C3×C42—22no—
114C2×C3×C42—41no—
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—22no—
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—41no—
142C2×(C2×D3)⋊C4—41no—
143C2×(C2×D3)⋊C4—41no—
144C2×(C2×D3)⋊C4—41no—
145C2×(C2×D3)⋊C4—41no—
146C2×(C2×D3)⋊C4—41no—
147C2×(C2×D3)⋊C4D414yes—
148C2×C4×Dic3—22no—
149C2×C4×Dic3—22no—
150C2×C4×Dic3—41no—
151C3×#95—22no—
152C3×#95—22no—
153C3×#95—22no—
154C3×#95D414yes—
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—22no—
165C3⋊#95—41no—
166C3⋊#95—41no—
167C3⋊#95—41no—
168C3⋊#95D414yescomplemented
169C23×Q8C2×D311yescharacteristic
170C23×D4—31no—
171C24×C4—31no—
172C22×C4⋊C4C2×D311yescharacteristic
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×C42C2×D311yescharacteristic
186#394—64no—
187#393—64no—
188#393—64no—
189#391—24no—
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×#95—31no—
204C2×#95—31no—
205C2×#95—31no—
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—
241C2×C3×Q8—28no—
242C2×C3×Q8—44no—
243C2×C3×Q8—44no—
244C2×C3×Q8—44no—
245C2×C3×Q8—44no—
246C2×C3×Q8—44no—
247C2×C3×Q8—44no—
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×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4C2×D412yes—
288C22×C3×C4C2×D412yes—
289C22×C3×C4C2×D412yes—
290C22×C3×C4C2×D412yes—
291C22×C3×C4C2×D412yes—
292C22×C3×C4#4112yes—
293C22×C3×C4#4112yes—
294C22×C3×C4#4112yes—
295C22×C3×C4#4112yes—
296C22×C3×C4#4112yes—
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×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3C2×D412yes—
337C22×Dic3C2×D412yes—
338C22×Dic3C2×D412yes—
339C2×D12—28no—
340C2×D12—44no—
341C2×D12—44no—
342C2×D12—44no—
343C2×D12—44no—
344C2×D12—44no—
345C2×D12—44no—
346C2×C4×D3—28no—
347C2×C4×D3—44no—
348C2×C4×D3—44no—
349C2×C4×D3—44no—
350C2×C4×D3—44no—
351C2×C4×D3—44no—
352C2×C4×D3—44no—
353C3×C4⋊C4—44no—
354C3×C42—44no—
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—
362(C2×D3)⋊C4—44no—
363(C2×D3)⋊C4—44no—
364(C2×D3)⋊C4—44no—
365(C2×D3)⋊C4—44no—
366C4×Dic3—44no—
367C25—31no—
368C25—31no—
369C22×Q8—22no—
370C22×Q8—22no—
371C22×Q8—22no—
372C22×Q8—22no—
373C22×Q8—22no—
374C22×Q8—41no—
375C22×Q8—41no—
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—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—41no—
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—22no—
440C2×C42—22no—
441C2×C42—41no—
442C2×C42—62no—
443C2×C42—62no—
444C2×C42—121no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—34no—
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—62no—
458#95—62no—
459#95—121no—
460#95—121no—
461#95—121no—
462#95#6714yes—
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—
548C3×Q8—416no—
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—22no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
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#12114yes—
597C2×C3×C4#12414yes—
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—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—
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—41no—
638C2×Dic3—41no—
639C2×Dic3—41no—
640D12—416no—
641C4×D3—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—28no—
674C2×Q8—44no—
675C2×Q8—44no—
676C2×Q8—44no—
677C2×Q8—44no—
678C2×Q8—44no—
679C2×Q8—44no—
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—32no—
727C22×C4—32no—
728C22×C4—32no—
729C22×C4—68no—
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—61no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—124no—
770C22×C4—124no—
771C22×C4—124no—
772C22×C4—124no—
773C22×C4—124no—
774C22×C4—124no—
775C22×C4#23512yes—
776C22×C4#23512yes—
777C22×C4D3×D412yes—
778C22×C4D3×D412yes—
779C22×C4#23912yes—
780C22×C4#23912yes—
781C22×C4#23912yes—
782C22×C4C2×#6712yes—
783C22×C4C2×#6712yes—
784C22×C4C2×#6712yes—
785C4⋊C4—44no—
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—44no—
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—24no—
865C3×C4—24no—
866C3×C4—42no—
867C3×C4—42no—
868C3×C4—42no—
869C3×C4—42no—
870C3×C4—81no—
871Dic3—42no—
872Dic3—42no—
873Dic3—42no—
874Dic3—81no—
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×#23511yescharacteristic
949C23C2×D3×D411yescharacteristic
950C23C2×D3×D411yescharacteristic
951C23#100411yescharacteristic
952C23#100411yescharacteristic
953C23C2×#23911yescharacteristic
954C23C2×#23911yescharacteristic
955C23C2×#23911yescharacteristic
956C23#100711yescharacteristic
957C23D3×#4111yescharacteristic
958C23D3×#4111yescharacteristic
959C23D3×#4111yescharacteristic
960C23#100911yescharacteristic
961C23C22×#6711yescharacteristic
962Q8—416no—
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—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
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—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—1216no—
1021C2×C4—121no—
1022C2×C4—121no—
1023C2×C4—121no—
1024C2×C4—121no—
1025C2×C4—121no—
1026C2×C4—121no—
1027C2×C4—121no—
1028C2×C4—121no—
1029C2×C4—121no—
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—121no—
1054C2×C4#88414yes—
1055C2×C4#94714yes—
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—
1103C22C2×#88411yescharacteristic
1104C22#549011yescharacteristic
1105C22#549011yescharacteristic
1106C22#549411yescharacteristic
1107C22#558011yescharacteristic
1108C22#558011yescharacteristic
1109C22#558011yescharacteristic
1110C22#558011yescharacteristic
1111C22#558011yescharacteristic
1112C22#558111yescharacteristic
1113C22#558211yescharacteristic
1114C22#558511yescharacteristic
1115C22#562711yescharacteristic
1116C22#562711yescharacteristic
1117C22#563011yescharacteristic
1118C22#563311yescharacteristic
1119C22#563711yescharacteristic
1120C22#563711yescharacteristic
1121C22#563811yescharacteristic
1122C22#564411yescharacteristic
1123C22D3×#12411yescharacteristic
1124C22#567611yescharacteristic
1125C22#567811yescharacteristic
1126C22#567911yescharacteristic
1127C22#572511yescharacteristic
1128C22#572611yescharacteristic
1129C22#573311yescharacteristic
1130C22#573411yescharacteristic
1131C22#579111yescharacteristic
1132C22D4×#6711yescharacteristic
1133C22D4×#6711yescharacteristic
1134C22C2×#94711yescharacteristic
1135C22#581711yescharacteristic
1136C22#582811yescharacteristic
1137C22#582911yescharacteristic
1138C4—24no—
1139C4—24no—
1140C4—42no—
1141C4—42no—
1142C4—42no—
1143C4—42no—
1144C4—81no—
1145C4—122no—
1146C4—122no—
1147C4—122no—
1148C4—241no—
1149C4—241no—
1150C4—241no—
1151C3#1481711yescharacteristic, complemented, Sylow
1152C2—124no—
1153C2—242no—
1154C2#7651311yescharacteristic
1155C2#7651611yescharacteristic
1156C2#7653911yescharacteristic
1157C2#7656111yescharacteristic
1158C2#7662411yescharacteristic
1159C2#7662911yescharacteristic
1160C2#7663811yescharacteristic
1161C2#7666211yescharacteristic
1162C2#8210911yescharacteristic
1163C2#8249211yescharacteristic
1164C2#8249711yescharacteristic
1165C2#8276911yescharacteristic
1166C2#8281811yescharacteristic
1167C2#8296511yescharacteristic
1168C2#8325711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#391C2
prime radicalC23×D12C22
hypercenterC2×#391D3
hypocenterC3#14817
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
1. C2×C3×#391C2semidirect
2. C2×#5231C2semidirect
3. C2×#5231C2semidirect
5. C2×C4×(C2×D3)⋊C4C2semidirect
7. #71567C2semidirect
8. #71537C2semidirect
9. #69429C2semidirect
10. #69429C2semidirect
12. (C2×D3)⋊#95C2semidirect
13. #69417C2semidirect
14. #69408C2semidirect
15. #69401C2semidirect
61. C2×#391D3semidirect
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×C3×#3912
C2×#52312
C2×#49912
C2×C4×(C2×D3)⋊C42
C2×#46652
#715672
#715372
#694292
#694262
(C2×D3)⋊#952
#694172
#694082
#694012
#148173