Finite Group Databasebeta

← #10729044

Subgroups — #10729044

Order 768.

2150 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#896C211yesmaximal, characteristic
2C2×#4989C211yesmaximal, characteristic
3C2×#4668C211yesmaximal, characteristic
4C2×D3×#95C211yesmaximal, characteristic
5C3×#1441C211yesmaximal, characteristic, complemented
6#71568C211yesmaximal, characteristic, complemented
7#71566C211yesmaximal, characteristic, complemented
8(C2×D3)⋊#95C211yesmaximal, characteristic
9(C2×D3)⋊#95C211yesmaximal, characteristic
10(C2×D3)⋊#95C211yesmaximal, characteristic
11#69424C211yesmaximal, characteristic, complemented
12#69424C211yesmaximal, characteristic, complemented
13#69420C211yesmaximal, characteristic, complemented
14#69411C211yesmaximal, characteristic, complemented
15#69409C211yesmaximal, characteristic, complemented
16#14914—31nomaximal, Sylow
17C23×C4×D3C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C23×Dic6C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×C4⋊Dic3C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×Dic3⋊C4C2211yescharacteristic
30C22×Dic3⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C2×#896—24no—
33C2×#896—24no—
34C2×#896—24no—
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
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55#4989—24no—
56#4668—24no—
57D3×#95—24no—
58C22×C22⋊Q8—31no—
59C2×#385—31no—
60C2×#385—31no—
61C22×#95—31no—
62#1446—31no—
63#1446—31no—
64#1444—31no—
65#1444—31no—
66#1441—31no—
67#1441—31no—
68#1441—31no—
69#1441D311yescharacteristic, complemented
70C22⋊#95—31no—
71C22⋊#95—31no—
72C22⋊#95—31no—
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
87C23×Dic3C2311yescharacteristic
88C22×C4×D3—22no—
89C22×C4×D3—22no—
90C22×C4×D3—22no—
91C22×C4×D3—22no—
92C22×C4×D3—22no—
93C22×C4×D3—22no—
94C22×C4×D3—22no—
95C22×C4×D3—22no—
96C22×C4×D3—22no—
97C22×C4×D3—22no—
98C22×C4×D3—22no—
99C22×C4×D3—41no—
100C22×C4×D3—41no—
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×D3D414yes—
108C22×C4×D3Q814yescomplemented
109C22×Dic6—22no—
110C22×Dic6—22no—
111C22×Dic6—22no—
112C22×Dic6—22no—
113C22×Dic6—22no—
114C22×Dic6—41no—
115C22×Dic6—41no—
116C2×C3×C4⋊C4—22no—
117C2×C3×C4⋊C4—22no—
118C2×C3×C4⋊C4—22no—
119C2×C3×C4⋊C4—22no—
120C2×C3×C4⋊C4—22no—
121C2×C3×C4⋊C4—41no—
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)⋊C4D414yes—
131C2×(C2×D3)⋊C4D414yes—
132C2×(C2×D3)⋊C4Q814yescomplemented
133C2×(C2×D3)⋊C4Q814yescomplemented
134C2×C4⋊Dic3—22no—
135C2×C4⋊Dic3—22no—
136C2×C4⋊Dic3—41no—
137C2×Dic3⋊C4—22no—
138C2×Dic3⋊C4—22no—
139C2×Dic3⋊C4—22no—
140C2×Dic3⋊C4—22no—
141C2×Dic3⋊C4—22no—
142C2×Dic3⋊C4—22no—
143C2×Dic3⋊C4—22no—
144C2×Dic3⋊C4—22no—
145C2×Dic3⋊C4—22no—
146C2×Dic3⋊C4—22no—
147C2×Dic3⋊C4—41no—
148C2×Dic3⋊C4—41no—
149#896—232no—
150C3×#95—22no—
151C3×#95—22no—
152C3×#95—41no—
153C3×#95—41no—
154C3×#95—41no—
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—41no—
164C3⋊#95—41no—
165C3⋊#95—41no—
166C3⋊#95—41no—
167C3⋊#95—41no—
168C3⋊#95—41no—
169C3⋊#95—41no—
170C23×Q8—31no—
171C24×C4—31no—
172C24×C4—31no—
173C24×C4—31no—
174C2×C22⋊Q8—64no—
175C2×C22⋊Q8—64no—
176C2×C22⋊Q8—64no—
177C22×C4⋊C4—31no—
178C22×C4⋊C4—31no—
179C22×C4⋊C4—31no—
180C22×C4⋊C4—31no—
181C22×C4⋊C4—31no—
182C22×C4⋊C4C2×D311yescharacteristic
183C22×C4⋊C4C2×D311yescharacteristic
184C22×C22⋊C4—31no—
185C22×C22⋊C4—31no—
186C22×C22⋊C4—31no—
187C22×C22⋊C4—31no—
188#385—64no—
189#385—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×#95—31no—
203C2×#95—31no—
204C2×#95—31no—
205C2×#95—64no—
206C2×#95C2×D311yescharacteristic
207C2×#95C2×D311yescharacteristic
208C2×#95C2×D311yescharacteristic
209C2×#95C2×D311yescharacteristic
210C2×#95C2×D311yescharacteristic
211C24×C3C2411yescharacteristic
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×D3C2×D412yes—
221C23×D3C2×D412yes—
222C23×D3C2×D412yes—
223C23×D3C2×Q812yes—
224C23×D3C2×Q812yes—
225C23×D3C2×Q812yes—
226C23×D3#4112yes—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4C2×D412yes—
270C22×C3×C4C2×D412yes—
271C22×C3×C4C2×D412yes—
272C22×C3×C4C2×Q812yes—
273C22×C3×C4C2×Q812yes—
274C22×C3×C4C2×Q812yes—
275C22×C3×C4#4112yes—
276C22×Dic3—21no—
277C22×Dic3—21no—
278C22×Dic3—21no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—21no—
282C22×Dic3—21no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3C2×D412yes—
317C22×Dic3C2×D412yes—
318C22×Dic3C2×D412yes—
319C22×Dic3C2×Q812yes—
320C22×Dic3C2×Q812yes—
321C22×Dic3C2×Q812yes—
322C22×Dic3#4112yes—
323C22×Dic3#4112yes—
324C22×Dic3#4112yes—
325C2×C4×D3—28no—
326C2×C4×D3—28no—
327C2×C4×D3—28no—
328C2×C4×D3—28no—
329C2×C4×D3—44no—
330C2×C4×D3—44no—
331C2×C4×D3—44no—
332C2×C4×D3—44no—
333C2×C4×D3—44no—
334C2×C4×D3—44no—
335C2×C4×D3—44no—
336C2×C4×D3—44no—
337C2×C4×D3—44no—
338C2×C4×D3—44no—
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×Dic6—28no—
347C2×Dic6—44no—
348C2×Dic6—44no—
349C2×Dic6—44no—
350C2×Dic6—44no—
351C2×Dic6—44no—
352C2×Dic6—44no—
353C3×C4⋊C4—28no—
354C3×C4⋊C4—44no—
355(C2×D3)⋊C4—28no—
356(C2×D3)⋊C4—28no—
357(C2×D3)⋊C4—28no—
358(C2×D3)⋊C4—28no—
359C4⋊Dic3—44no—
360Dic3⋊C4—28no—
361Dic3⋊C4—28no—
362Dic3⋊C4—44no—
363Dic3⋊C4—44no—
364C25—31no—
365C22×Q8—62no—
366C22×Q8—62no—
367C22×Q8—62no—
368C22×Q8—62no—
369C22×Q8—62no—
370C22×Q8—121no—
371C22×Q8—121no—
372C23×C4—31no—
373C23×C4—31no—
374C23×C4—31no—
375C23×C4—31no—
376C23×C4—31no—
377C23×C4—31no—
378C23×C4—31no—
379C23×C4—34no—
380C23×C4—34no—
381C23×C4—62no—
382C23×C4—62no—
383C23×C4—62no—
384C23×C4—62no—
385C23×C4—62no—
386C23×C4—62no—
387C23×C4—62no—
388C23×C4—62no—
389C23×C4—62no—
390C23×C4—62no—
391C23×C4—62no—
392C23×C4—121no—
393C23×C4—121no—
394C23×C4—121no—
395C23×C4—121no—
396C23×C4—121no—
397C23×C4—121no—
398C23×C4—121no—
399C23×C4—121no—
400C23×C4C22×D311yescharacteristic
401C23×C4C22×D311yescharacteristic
402C23×C4C22×D311yescharacteristic
403C23×C4C22×D311yescharacteristic
404C23×C4C22×D311yescharacteristic
405C23×C4C22×D311yescharacteristic
406C23×C4C22×D311yescharacteristic
407C22⋊Q8—632no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—41no—
414C2×C4⋊C4—62no—
415C2×C4⋊C4—62no—
416C2×C4⋊C4—62no—
417C2×C4⋊C4—62no—
418C2×C4⋊C4—62no—
419C2×C4⋊C4—62no—
420C2×C4⋊C4—62no—
421C2×C4⋊C4—62no—
422C2×C4⋊C4—62no—
423C2×C4⋊C4—62no—
424C2×C4⋊C4—62no—
425C2×C4⋊C4—62no—
426C2×C4⋊C4—121no—
427C2×C4⋊C4—121no—
428C2×C4⋊C4—121no—
429C2×C22⋊C4—34no—
430C2×C22⋊C4—34no—
431C2×C22⋊C4—34no—
432C2×C22⋊C4—34no—
433C2×C22⋊C4—62no—
434C2×C22⋊C4—62no—
435C2×C22⋊C4—62no—
436C2×C22⋊C4—62no—
437C2×C22⋊C4—62no—
438C2×C22⋊C4—62no—
439C2×C22⋊C4—62no—
440C2×C22⋊C4—62no—
441#95—22no—
442#95—22no—
443#95—41no—
444#95—41no—
445#95—41no—
446#95—62no—
447#95—62no—
448#95—62no—
449#95—62no—
450#95—62no—
451#95—62no—
452#95—62no—
453#95—62no—
454#95—121no—
455#95—121no—
456#95—121no—
457#95—121no—
458#95—121no—
459#95—121no—
460#95—121no—
461C23×C3C22×D411yescharacteristic
462C23×C3C22×D411yescharacteristic
463C23×C3C22×D411yescharacteristic
464C23×C3C22×Q811yescharacteristic
465C23×C3C22×Q811yescharacteristic
466C23×C3C22×Q811yescharacteristic
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#12014yes—
505C22×D3C22⋊Q814yes—
506C22×D3C22⋊Q814yes—
507C22×D3C22⋊Q814yes—
508C22×D3C4⋊Q814yes—
509C22×D3C4⋊Q814yes—
510C22×D3C4⋊Q814yes—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×Dic3—22no—
561C2×Dic3—22no—
562C2×Dic3—22no—
563C2×Dic3—22no—
564C2×Dic3—22no—
565C2×Dic3—22no—
566C2×Dic3—22no—
567C2×Dic3—22no—
568C2×Dic3—22no—
569C2×Dic3—22no—
570C2×Dic3—22no—
571C2×Dic3—22no—
572C2×Dic3—22no—
573C2×Dic3—22no—
574C2×Dic3—22no—
575C2×Dic3—22no—
576C2×Dic3—22no—
577C2×Dic3—22no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3—41no—
585C2×Dic3—41no—
586C2×Dic3—41no—
587C2×Dic3—41no—
588C2×Dic3—41no—
589C2×Dic3—41no—
590C2×Dic3—41no—
591C2×Dic3—41no—
592C2×Dic3—41no—
593C2×Dic3—41no—
594C2×Dic3—41no—
595C2×Dic3—41no—
596C2×Dic3—41no—
597C2×Dic3—41no—
598C2×Dic3—41no—
599C2×Dic3—41no—
600C2×Dic3—41no—
601C2×Dic3—41no—
602C2×Dic3—41no—
603C2×Dic3—41no—
604C2×Dic3—41no—
605C2×Dic3—41no—
606C2×Dic3—41no—
607C2×Dic3—41no—
608C2×Dic3#12314yes—
609C4×D3—416no—
610C4×D3—416no—
611C4×D3—416no—
612Dic6—416no—
613C24—32no—
614C24—32no—
615C24—32no—
616C24—32no—
617C24—32no—
618C24—32no—
619C24—32no—
620C24—61no—
621C24—61no—
622C24—61no—
623C24—61no—
624C24—61no—
625C24—61no—
626C24—61no—
627C24—61no—
628C24C23×D311yescharacteristic
629C2×Q8—68no—
630C2×Q8—124no—
631C2×Q8—124no—
632C2×Q8—124no—
633C2×Q8—124no—
634C2×Q8—124no—
635C2×Q8—124no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—32no—
679C22×C4—32no—
680C22×C4—32no—
681C22×C4—32no—
682C22×C4—32no—
683C22×C4—32no—
684C22×C4—32no—
685C22×C4—32no—
686C22×C4—32no—
687C22×C4—68no—
688C22×C4—68no—
689C22×C4—68no—
690C22×C4—68no—
691C22×C4—61no—
692C22×C4—61no—
693C22×C4—61no—
694C22×C4—61no—
695C22×C4—61no—
696C22×C4—61no—
697C22×C4—61no—
698C22×C4—61no—
699C22×C4—61no—
700C22×C4—61no—
701C22×C4—61no—
702C22×C4—61no—
703C22×C4—61no—
704C22×C4—61no—
705C22×C4—61no—
706C22×C4—61no—
707C22×C4—61no—
708C22×C4—61no—
709C22×C4—61no—
710C22×C4—61no—
711C22×C4—61no—
712C22×C4—61no—
713C22×C4—61no—
714C22×C4—61no—
715C22×C4—61no—
716C22×C4—61no—
717C22×C4—61no—
718C22×C4—61no—
719C22×C4—61no—
720C22×C4—61no—
721C22×C4—61no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4—61no—
725C22×C4—61no—
726C22×C4—61no—
727C22×C4—61no—
728C22×C4—61no—
729C22×C4—61no—
730C22×C4—61no—
731C22×C4—124no—
732C22×C4—124no—
733C22×C4—124no—
734C22×C4—124no—
735C22×C4—124no—
736C22×C4—124no—
737C22×C4—124no—
738C22×C4—124no—
739C22×C4—124no—
740C22×C4—124no—
741C22×C4—124no—
742C22×C4—124no—
743C22×C4—124no—
744C22×C4—124no—
745C22×C4—124no—
746C22×C4—124no—
747C22×C4—124no—
748C22×C4#23512yes—
749C22×C4D3×D412yes—
750C22×C4D3×D412yes—
751C22×C4D3×D412yes—
752C22×C4D3×Q812yes—
753C22×C4D3×Q812yes—
754C22×C4D3×Q812yes—
755C4⋊C4—28no—
756C4⋊C4—44no—
757C4⋊C4—68no—
758C4⋊C4—68no—
759C4⋊C4—124no—
760C4⋊C4—124no—
761C4⋊C4—124no—
762C22⋊C4—68no—
763C22⋊C4—68no—
764C22⋊C4—68no—
765C22⋊C4—68no—
766C22×C3C2×#12011yescharacteristic
767C22×C3C2×C22⋊Q811yescharacteristic
768C22×C3C2×C22⋊Q811yescharacteristic
769C22×C3C2×C22⋊Q811yescharacteristic
770C22×C3C2×#12311yescharacteristic
771C22×C3#52511yescharacteristic
772C22×C3#52911yescharacteristic
773C22×C3#52911yescharacteristic
774C22×C3C2×C4⋊Q811yescharacteristic
775C22×C3C2×C4⋊Q811yescharacteristic
776C22×C3C2×C4⋊Q811yescharacteristic
777C22×C3#53311yescharacteristic
778C22×C3#53311yescharacteristic
779C22×C3#53411yescharacteristic
780C22×C3#53511yescharacteristic
781C22×C3#53811yescharacteristic
782C22×C3#53811yescharacteristic
783C22×C3#54311yescharacteristic
784C22×C3#54311yescharacteristic
785C22×C3#54611yescharacteristic
786C22×C3#54611yescharacteristic
787C22×C3#54611yescharacteristic
788C22×C3#54611yescharacteristic
789C22×C3#54611yescharacteristic
790C22×C3#54611yescharacteristic
791C22×C3#54611yescharacteristic
792C22×C3#54611yescharacteristic
793C22×C3#55411yescharacteristic
794C22×C3#55411yescharacteristic
795C22×C3#55411yescharacteristic
796C22×C3#55411yescharacteristic
797C22×C3#55411yescharacteristic
798C22×C3#55411yescharacteristic
799C22×C3#55411yescharacteristic
800C22×C3#55411yescharacteristic
801C2×D3—24no—
802C2×D3—24no—
803C2×D3—24no—
804C2×D3—24no—
805C2×D3—24no—
806C2×D3—24no—
807C2×D3—24no—
808C2×D3—24no—
809C2×D3—24no—
810C2×D3—24no—
811C2×D3—24no—
812C2×D3—24no—
813C2×D3—24no—
814C2×D3—24no—
815C2×D3#39518yes—
816C3×C4—42no—
817C3×C4—42no—
818C3×C4—42no—
819C3×C4—42no—
820C3×C4—42no—
821C3×C4—42no—
822C3×C4—42no—
823Dic3—24no—
824Dic3—42no—
825Dic3—42no—
826Dic3—42no—
827Dic3—42no—
828Dic3—42no—
829Dic3—42no—
830C23—34no—
831C23—34no—
832C23—34no—
833C23—34no—
834C23—34no—
835C23—34no—
836C23—34no—
837C23—62no—
838C23—62no—
839C23—62no—
840C23—62no—
841C23—62no—
842C23—62no—
843C23—62no—
844C23—62no—
845C23—62no—
846C23—62no—
847C23—62no—
848C23—62no—
849C23—62no—
850C23—62no—
851C23—62no—
852C23—62no—
853C23—62no—
854C23—62no—
855C23—62no—
856C23—62no—
857C23—62no—
858C23—62no—
859C23—62no—
860C23—62no—
861C23—62no—
862C23—62no—
863C23—62no—
864C23—62no—
865C23C2×#23511yescharacteristic
866C23C2×D3×D411yescharacteristic
867C23C2×D3×D411yescharacteristic
868C23C2×D3×D411yescharacteristic
869C23#100411yescharacteristic
870C23#100411yescharacteristic
871C23C2×D3×Q811yescharacteristic
872C23C2×D3×Q811yescharacteristic
873C23C2×D3×Q811yescharacteristic
874C23D3×#4111yescharacteristic
875C23D3×#4111yescharacteristic
876C23D3×#4111yescharacteristic
877C23D3×#4111yescharacteristic
878C23#100911yescharacteristic
879C23#100911yescharacteristic
880Q8—1216no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—34no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—62no—
932C2×C4—62no—
933C2×C4—62no—
934C2×C4—62no—
935C2×C4—62no—
936C2×C4—62no—
937C2×C4—62no—
938C2×C4—62no—
939C2×C4—62no—
940C2×C4—62no—
941C2×C4—62no—
942C2×C4—62no—
943C2×C4—62no—
944C2×C4—62no—
945C2×C4—62no—
946C2×C4—62no—
947C2×C4—62no—
948C2×C4—62no—
949C2×C4—62no—
950C2×C4—62no—
951C2×C4—62no—
952C2×C4—62no—
953C2×C4—62no—
954C2×C4—62no—
955C2×C4—1216no—
956C2×C4—1216no—
957C2×C4—1216no—
958C2×C4—121no—
959C2×C4—121no—
960C2×C4—121no—
961C2×C4—121no—
962C2×C4—121no—
963C2×C4—121no—
964C2×C4—121no—
965C2×C4—121no—
966C2×C4—121no—
967C2×C4—121no—
968C2×C4—121no—
969C2×C4—121no—
970C2×C4—121no—
971C2×C4—121no—
972C2×C4—121no—
973C2×C4—121no—
974C2×C4—121no—
975C2×C4—121no—
976C2×C4—121no—
977C2×C4—121no—
978C2×C4—121no—
979C2×C4—121no—
980C2×C4—121no—
981C2×C4—121no—
982C2×C3C2×#39511yescharacteristic
983C2×C3#240411yescharacteristic
984C2×C3#240511yescharacteristic
985C2×C3#245011yescharacteristic
986C2×C3#245011yescharacteristic
987C2×C3#245011yescharacteristic
988C2×C3#245011yescharacteristic
989C2×C3#250211yescharacteristic
990C2×C3#254911yescharacteristic
991C2×C3#254911yescharacteristic
992C2×C3#254911yescharacteristic
993C2×C3#254911yescharacteristic
994C2×C3#258311yescharacteristic
995C2×C3#262611yescharacteristic
996C2×C3#285511yescharacteristic
997D3—28no—
998C22—38no—
999C22—64no—
1000C22—64no—
1001C22—64no—
1002C22—64no—
1003C22—64no—
1004C22—64no—
1005C22—64no—
1006C22—64no—
1007C22—64no—
1008C22—64no—
1009C22—64no—
1010C22—64no—
1011C22—64no—
1012C22—64no—
1013C22#549011yescharacteristic
1014C22#551111yescharacteristic
1015C22#552811yescharacteristic
1016C22#554711yescharacteristic
1017C22#555011yescharacteristic
1018C22#557811yescharacteristic
1019C22#557911yescharacteristic
1020C22D3×#12011yescharacteristic
1021C22#560511yescharacteristic
1022C22#560711yescharacteristic
1023C22#561011yescharacteristic
1024C22#561211yescharacteristic
1025C22#561211yescharacteristic
1026C22#561311yescharacteristic
1027C22D3×C22⋊Q811yescharacteristic
1028C22D3×C22⋊Q811yescharacteristic
1029C22D3×C22⋊Q811yescharacteristic
1030C22#563411yescharacteristic
1031C22#563411yescharacteristic
1032C22#563611yescharacteristic
1033C22#563611yescharacteristic
1034C22#563611yescharacteristic
1035C22D3×#12311yescharacteristic
1036C22#565411yescharacteristic
1037C22#565411yescharacteristic
1038C22#567611yescharacteristic
1039C22#568811yescharacteristic
1040C22#569011yescharacteristic
1041C22#569011yescharacteristic
1042C22#569011yescharacteristic
1043C22#570411yescharacteristic
1044C22#570611yescharacteristic
1045C22D3×C4⋊Q811yescharacteristic
1046C22D3×C4⋊Q811yescharacteristic
1047C22D3×C4⋊Q811yescharacteristic
1048C4—42no—
1049C4—42no—
1050C4—42no—
1051C4—42no—
1052C4—42no—
1053C4—42no—
1054C4—42no—
1055C4—64no—
1056C4—122no—
1057C4—122no—
1058C4—122no—
1059C4—122no—
1060C4—122no—
1061C4—122no—
1062C3#1491411yescharacteristic, complemented, Sylow
1063C2—68no—
1064C2#7402311yescharacteristic
1065C2#7488611yescharacteristic
1066C2#7532211yescharacteristic
1067C2#7544811yescharacteristic
1068C2#7624411yescharacteristic
1069C2#7624711yescharacteristic
1070C2#7663711yescharacteristic
1071C2#7710611yescharacteristic
1072C2D3×#39511yescharacteristic
1073C2#7742011yescharacteristic
1074C2#7742411yescharacteristic
1075C2#7776511yescharacteristic
1076C2#7795811yescharacteristic
1077C2#7795811yescharacteristic
1078C2#7834411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1441C2
prime radicalC24×D3C23
hypercenter#1441D3
hypocenterC3#14914
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
5. C3×#1441C2semidirect
6. #71568C2semidirect
7. #71566C2semidirect
11. #69424C2semidirect
12. #69424C2semidirect
13. #69420C2semidirect
14. #69411C2semidirect
15. #69409C2semidirect
69. #1441D3semidirect
108. C22×C4×D3Q8semidirect
132. C2×(C2×D3)⋊C4Q8semidirect
133. C2×(C2×D3)⋊C4Q8semidirect
1062. C3#14914semidirect

Maximal subgroups

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

subgroupindex
C22×#8962
C2×#49892
C2×#46682
C2×D3×#952
C3×#14412
#715682
#715662
(C2×D3)⋊#952
#694242
#694202
#694112
#694092
#149143