Finite Group Databasebeta

← #10751696

Subgroups — #10751696

Order 768.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#896C211yesmaximal, characteristic
2C2×#4668C211yesmaximal, characteristic
3C2×#4660C211yesmaximal, characteristic, complemented
4C2×#4656C211yesmaximal, characteristic, complemented
5C3×#1442C211yesmaximal, characteristic, complemented
6#71568C211yesmaximal, characteristic, complemented
7#69429C211yesmaximal, characteristic
8#69429C211yesmaximal, characteristic
9#69428C211yesmaximal, characteristic
10#69427C211yesmaximal, characteristic
11(C2×D3)⋊#95C211yesmaximal, characteristic
12#69424C211yesmaximal, characteristic, complemented
13#69421C211yesmaximal, characteristic, complemented
14#69420C211yesmaximal, characteristic, complemented
15#69414C211yesmaximal, characteristic, complemented
16#16601—31nomaximal, Sylow
17C23×C4×D3C2211yescharacteristic
18C23×Dic6C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
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#4668—24no—
56#4660—24no—
57#4656—24no—
58C22×C22⋊Q8—31no—
59C2×#400—31no—
60C2×#395—31no—
61C2×#385—31no—
62#1446—31no—
63#1445—31no—
64#1444—31no—
65#1444—31no—
66#1442—31no—
67#1442D311yescharacteristic, complemented
68#1440—31no—
69#1440—31no—
70#1439—31no—
71#1439—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—41no—
91C22×C4×D3—41no—
92C22×C4×D3—41no—
93C22×C4×D3—41no—
94C22×C4×D3D414yes—
95C22×Dic6—22no—
96C22×Dic6—22no—
97C22×Dic6—41no—
98C22×Dic6—41no—
99C22×Dic6—41no—
100C22×Dic6—41no—
101C22×Dic6D414yes—
102C2×C3×C4⋊C4—22no—
103C2×C3×C4⋊C4—22no—
104C2×C3×C4⋊C4—22no—
105C2×(C2×D3)⋊C4—22no—
106C2×(C2×D3)⋊C4—22no—
107C2×(C2×D3)⋊C4—22no—
108C2×(C2×D3)⋊C4—22no—
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—41no—
119C2×(C2×D3)⋊C4—41no—
120C2×(C2×D3)⋊C4—41no—
121C2×(C2×D3)⋊C4—41no—
122C2×(C2×D3)⋊C4Q814yescomplemented
123C2×C4⋊Dic3—22no—
124C2×C4⋊Dic3—22no—
125C2×C4⋊Dic3—22no—
126C2×C4⋊Dic3—22no—
127C2×C4⋊Dic3—41no—
128C2×C4⋊Dic3—41no—
129C2×Dic3⋊C4—22no—
130C2×Dic3⋊C4—22no—
131C2×Dic3⋊C4—22no—
132C2×Dic3⋊C4—22no—
133C2×Dic3⋊C4—22no—
134C2×Dic3⋊C4—22no—
135C2×Dic3⋊C4—22no—
136C2×Dic3⋊C4—41no—
137C2×Dic3⋊C4—41no—
138C2×Dic3⋊C4—41no—
139C2×Dic3⋊C4—41no—
140C2×Dic3⋊C4D414yes—
141#896—232no—
142C3×#95—22no—
143C3×#95—22no—
144C3×#95—22no—
145C3×#95—22no—
146C3×#95—41no—
147C3×#95—41no—
148C3⋊#95—22no—
149C3⋊#95—22no—
150C3⋊#95—22no—
151C3⋊#95—22no—
152C3⋊#95—22no—
153C3⋊#95—22no—
154C3⋊#95—22no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C3⋊#95—41no—
159C3⋊#95—41no—
160C3⋊#95—41no—
161C3⋊#95—41no—
162C23×Q8—31no—
163C24×C4—31no—
164C2×C22⋊Q8—64no—
165C2×C22⋊Q8—64no—
166C2×C22⋊Q8—64no—
167C22×C4⋊C4—31no—
168C22×C4⋊C4—31no—
169C22×C4⋊C4—31no—
170C22×C4⋊C4—31no—
171C22×C4⋊C4—31no—
172C22×C4⋊C4—31no—
173C22×C4⋊C4C2×D311yescharacteristic
174C22×C22⋊C4—31no—
175C22×C22⋊C4—31no—
176C22×C22⋊C4—31no—
177C22×C22⋊C4—31no—
178C22×C22⋊C4—31no—
179C22×C22⋊C4—31no—
180#400—64no—
181#395—64no—
182#385—64no—
183C2×#95—31no—
184C2×#95—31no—
185C2×#95—31no—
186C2×#95—31no—
187C2×#95—31no—
188C2×#95—31no—
189C2×#95—31no—
190C2×#95—31no—
191C2×#95—31no—
192C2×#95—31no—
193C2×#95—31no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95—31no—
197C2×#95C2×D311yescharacteristic
198C2×#95C2×D311yescharacteristic
199C2×#95C2×D311yescharacteristic
200C2×#95C2×D311yescharacteristic
201C2×#95C2×D311yescharacteristic
202C2×#95C2×D311yescharacteristic
203C24×C3C2411yescharacteristic
204C23×D3—21no—
205C23×D3—21no—
206C23×D3—21no—
207C23×D3—21no—
208C23×D3—21no—
209C23×D3—21no—
210C23×D3—21no—
211C23×D3—21no—
212C23×D3—21no—
213C23×D3—21no—
214C23×D3—21no—
215C23×D3—21no—
216C23×D3C2×D412yes—
217C23×D3C2×Q812yes—
218C23×D3#4112yes—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
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×C4C2×D412yes—
264C22×C3×C4C2×D412yes—
265C22×C3×C4C2×D412yes—
266C22×C3×C4C2×Q812yes—
267C22×C3×C4#4112yes—
268C22×Dic3—21no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—21no—
274C22×Dic3—21no—
275C22×Dic3—21no—
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×Dic3C2×D412yes—
311C22×Dic3C2×D412yes—
312C22×Dic3C2×D412yes—
313C22×Dic3C2×D412yes—
314C22×Dic3C2×D412yes—
315C22×Dic3C2×Q812yes—
316C22×Dic3#4112yes—
317C2×C4×D3—28no—
318C2×C4×D3—44no—
319C2×C4×D3—44no—
320C2×C4×D3—44no—
321C2×C4×D3—44no—
322C2×C4×D3—44no—
323C2×C4×D3—44no—
324C2×Dic6—28no—
325C2×Dic6—44no—
326C2×Dic6—44no—
327C2×Dic6—44no—
328C2×Dic6—44no—
329C2×Dic6—44no—
330C2×Dic6—44no—
331C3×C4⋊C4—28no—
332(C2×D3)⋊C4—28no—
333(C2×D3)⋊C4—28no—
334(C2×D3)⋊C4—28no—
335(C2×D3)⋊C4—44no—
336(C2×D3)⋊C4—44no—
337(C2×D3)⋊C4—44no—
338C4⋊Dic3—44no—
339C4⋊Dic3—44no—
340Dic3⋊C4—28no—
341Dic3⋊C4—28no—
342Dic3⋊C4—44no—
343Dic3⋊C4—44no—
344C25—31no—
345C22×Q8—34no—
346C22×Q8—62no—
347C22×Q8—62no—
348C22×Q8—121no—
349C22×Q8—121no—
350C22×Q8—121no—
351C22×Q8—121no—
352C23×C4—31no—
353C23×C4—31no—
354C23×C4—31no—
355C23×C4—31no—
356C23×C4—31no—
357C23×C4—34no—
358C23×C4—31no—
359C23×C4—31no—
360C23×C4—62no—
361C23×C4—62no—
362C23×C4—121no—
363C23×C4—121no—
364C23×C4—121no—
365C23×C4—121no—
366C23×C4C22×D311yescharacteristic
367C23×C4C22×D311yescharacteristic
368C23×C4C22×D311yescharacteristic
369C23×C4C22×D311yescharacteristic
370C23×C4C22×D311yescharacteristic
371C23×C4C22×D311yescharacteristic
372C23×C4C22×D311yescharacteristic
373C22⋊Q8—632no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—34no—
378C2×C4⋊C4—62no—
379C2×C4⋊C4—62no—
380C2×C4⋊C4—62no—
381C2×C4⋊C4—62no—
382C2×C4⋊C4—62no—
383C2×C4⋊C4—62no—
384C2×C4⋊C4—62no—
385C2×C4⋊C4—62no—
386C2×C4⋊C4—62no—
387C2×C4⋊C4—62no—
388C2×C4⋊C4—62no—
389C2×C4⋊C4—121no—
390C2×C4⋊C4—121no—
391C2×C4⋊C4—121no—
392C2×C4⋊C4—121no—
393C2×C4⋊C4—121no—
394C2×C4⋊C4—121no—
395C2×C22⋊C4—34no—
396C2×C22⋊C4—62no—
397C2×C22⋊C4—62no—
398C2×C22⋊C4—62no—
399C2×C22⋊C4—62no—
400C2×C22⋊C4—62no—
401C2×C22⋊C4—62no—
402C2×C22⋊C4—62no—
403C2×C22⋊C4—62no—
404C2×C22⋊C4—62no—
405C2×C22⋊C4—62no—
406C2×C22⋊C4—62no—
407C2×C22⋊C4—62no—
408C2×C22⋊C4—62no—
409C2×C22⋊C4—121no—
410C2×C22⋊C4—121no—
411C2×C22⋊C4—121no—
412C2×C22⋊C4—121no—
413#95—22no—
414#95—22no—
415#95—22no—
416#95—22no—
417#95—41no—
418#95—41no—
419#95—62no—
420#95—62no—
421#95—62no—
422#95—62no—
423#95—62no—
424#95—62no—
425#95—62no—
426#95—62no—
427#95—62no—
428#95—62no—
429#95—121no—
430#95—121no—
431#95—121no—
432#95—121no—
433C23×C3C22×D411yescharacteristic
434C23×C3C22×D411yescharacteristic
435C23×C3C22×D411yescharacteristic
436C23×C3C22×Q811yescharacteristic
437C23×C3C2×#4111yescharacteristic
438C23×C3C2×#4111yescharacteristic
439C23×C3C2×#4111yescharacteristic
440C23×C3H(5,𝔽2)11yescharacteristic
441C23×C3H(5,𝔽2)11yescharacteristic
442C23×C3H(5,𝔽2)11yescharacteristic
443C23×C3H(5,𝔽2)11yescharacteristic
444C23×C32−1+411yescharacteristic
445C23×C32−1+411yescharacteristic
446C23×C32−1+411yescharacteristic
447C23×C32−1+411yescharacteristic
448C22×D3—22no—
449C22×D3—22no—
450C22×D3—22no—
451C22×D3—22no—
452C22×D3—22no—
453C22×D3—22no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—41no—
467C22×D3—41no—
468C22×D3—41no—
469C22×D3—41no—
470C22×D3—41no—
471C22×D3—41no—
472C22×D3—41no—
473C22×D3—41no—
474C22×D3—41no—
475C22×D3—41no—
476C22×D3—41no—
477C22×D3—41no—
478C22×D3—41no—
479C22×D3—41no—
480C22×D3—41no—
481C22×D3—41no—
482C22×D3C22⋊Q814yes—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—22no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3—22no—
540C2×Dic3—22no—
541C2×Dic3—22no—
542C2×Dic3—22no—
543C2×Dic3—22no—
544C2×Dic3—22no—
545C2×Dic3—22no—
546C2×Dic3—22no—
547C2×Dic3—22no—
548C2×Dic3—22no—
549C2×Dic3—22no—
550C2×Dic3—41no—
551C2×Dic3—41no—
552C2×Dic3—41no—
553C2×Dic3—41no—
554C2×Dic3—41no—
555C2×Dic3—41no—
556C2×Dic3—41no—
557C2×Dic3—41no—
558C2×Dic3—41no—
559C2×Dic3—41no—
560C2×Dic3—41no—
561C2×Dic3—41no—
562C2×Dic3—41no—
563C2×Dic3—41no—
564C2×Dic3—41no—
565C2×Dic3—41no—
566C2×Dic3—41no—
567C2×Dic3—41no—
568C2×Dic3—41no—
569C2×Dic3—41no—
570C2×Dic3—41no—
571C2×Dic3—41no—
572C2×Dic3—41no—
573C2×Dic3—41no—
574C2×Dic3—41no—
575C2×Dic3—41no—
576C2×Dic3—41no—
577C2×Dic3—41no—
578C2×Dic3—41no—
579C2×Dic3—41no—
580C2×Dic3#12014yes—
581C4×D3—416no—
582Dic6—416no—
583C24—32no—
584C24—32no—
585C24—32no—
586C24—61no—
587C24—61no—
588C24—61no—
589C24—61no—
590C24—61no—
591C24—61no—
592C24—61no—
593C24—61no—
594C24—61no—
595C24—61no—
596C24—61no—
597C24—61no—
598C24C23×D311yescharacteristic
599C2×Q8—68no—
600C2×Q8—124no—
601C2×Q8—124no—
602C2×Q8—124no—
603C2×Q8—124no—
604C2×Q8—124no—
605C2×Q8—124no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
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—32no—
651C22×C4—32no—
652C22×C4—32no—
653C22×C4—32no—
654C22×C4—32no—
655C22×C4—32no—
656C22×C4—32no—
657C22×C4—68no—
658C22×C4—61no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—61no—
662C22×C4—61no—
663C22×C4—61no—
664C22×C4—61no—
665C22×C4—61no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—61no—
669C22×C4—61no—
670C22×C4—61no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4—61no—
677C22×C4—61no—
678C22×C4—61no—
679C22×C4—61no—
680C22×C4—61no—
681C22×C4—61no—
682C22×C4—61no—
683C22×C4—61no—
684C22×C4—61no—
685C22×C4—61no—
686C22×C4—61no—
687C22×C4—61no—
688C22×C4—61no—
689C22×C4—61no—
690C22×C4—61no—
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—124no—
701C22×C4—124no—
702C22×C4—124no—
703C22×C4—124no—
704C22×C4—124no—
705C22×C4—124no—
706C22×C4#23512yes—
707C22×C4D3×D412yes—
708C22×C4D3×D412yes—
709C22×C4D3×D412yes—
710C22×C4D3×Q812yes—
711C4⋊C4—28no—
712C4⋊C4—68no—
713C4⋊C4—68no—
714C4⋊C4—124no—
715C4⋊C4—124no—
716C4⋊C4—124no—
717C4⋊C4—124no—
718C22⋊C4—68no—
719C22⋊C4—68no—
720C22⋊C4—68no—
721C22⋊C4—124no—
722C22⋊C4—124no—
723C22⋊C4—124no—
724C22×C3C2×#12011yescharacteristic
725C22×C3C2×C22⋊Q811yescharacteristic
726C22×C3#53211yescharacteristic
727C22×C3#53411yescharacteristic
728C22×C3#53411yescharacteristic
729C22×C3#53411yescharacteristic
730C22×C3#53411yescharacteristic
731C22×C3#53511yescharacteristic
732C22×C3#53511yescharacteristic
733C22×C3#53611yescharacteristic
734C22×C3#53611yescharacteristic
735C22×C3#53911yescharacteristic
736C22×C3#53911yescharacteristic
737C22×C3#53911yescharacteristic
738C22×C3#53911yescharacteristic
739C22×C3#54211yescharacteristic
740C22×C3#54211yescharacteristic
741C22×C3#54411yescharacteristic
742C22×C3#54411yescharacteristic
743C22×C3#54711yescharacteristic
744C22×C3#54711yescharacteristic
745C22×C3#54811yescharacteristic
746C22×C3#54811yescharacteristic
747C22×C3#54811yescharacteristic
748C22×C3#54811yescharacteristic
749C22×C3D4×Q811yescharacteristic
750C22×C3D4×Q811yescharacteristic
751C22×C3#55111yescharacteristic
752C22×C3#55111yescharacteristic
753C22×C3#55411yescharacteristic
754C22×C3#55411yescharacteristic
755C22×C3#56311yescharacteristic
756C22×C3#56311yescharacteristic
757C22×C3#56311yescharacteristic
758C22×C3#56311yescharacteristic
759C2×D3—24no—
760C2×D3—24no—
761C2×D3—24no—
762C2×D3—42no—
763C2×D3—42no—
764C2×D3—42no—
765C2×D3—42no—
766C2×D3—42no—
767C2×D3—42no—
768C2×D3—42no—
769C2×D3—42no—
770C2×D3—42no—
771C2×D3—42no—
772C2×D3—42no—
773C2×D3—42no—
774C3×C4—42no—
775C3×C4—42no—
776C3×C4—42no—
777C3×C4—42no—
778C3×C4—42no—
779C3×C4—81no—
780C3×C4—81no—
781Dic3—24no—
782Dic3—42no—
783Dic3—42no—
784Dic3—42no—
785Dic3—42no—
786Dic3—81no—
787Dic3—81no—
788C23—34no—
789C23—62no—
790C23—62no—
791C23—62no—
792C23—62no—
793C23—62no—
794C23—62no—
795C23—62no—
796C23—62no—
797C23—62no—
798C23—62no—
799C23—62no—
800C23—62no—
801C23—62no—
802C23—62no—
803C23—62no—
804C23—62no—
805C23—62no—
806C23—62no—
807C23—121no—
808C23—121no—
809C23—121no—
810C23—121no—
811C23—121no—
812C23—121no—
813C23—121no—
814C23—121no—
815C23—121no—
816C23—121no—
817C23—121no—
818C23—121no—
819C23—121no—
820C23—121no—
821C23—121no—
822C23—121no—
823C23C2×#23511yescharacteristic
824C23C2×D3×D411yescharacteristic
825C23C2×D3×D411yescharacteristic
826C23C2×D3×D411yescharacteristic
827C23#100411yescharacteristic
828C23C2×D3×Q811yescharacteristic
829C23#100711yescharacteristic
830C23D3×#4111yescharacteristic
831C23D3×#4111yescharacteristic
832C23#100911yescharacteristic
833C23#100911yescharacteristic
834C23#100911yescharacteristic
835C23#101011yescharacteristic
836C23#101011yescharacteristic
837C23#101011yescharacteristic
838Q8—1216no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—34no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—62no—
890C2×C4—62no—
891C2×C4—62no—
892C2×C4—62no—
893C2×C4—62no—
894C2×C4—62no—
895C2×C4—62no—
896C2×C4—62no—
897C2×C4—62no—
898C2×C4—62no—
899C2×C4—62no—
900C2×C4—62no—
901C2×C4—62no—
902C2×C4—62no—
903C2×C4—62no—
904C2×C4—62no—
905C2×C4—62no—
906C2×C4—62no—
907C2×C4—1216no—
908C2×C4—121no—
909C2×C4—121no—
910C2×C4—121no—
911C2×C4—121no—
912C2×C4—121no—
913C2×C4—121no—
914C2×C4—121no—
915C2×C4—121no—
916C2×C4—121no—
917C2×C4—121no—
918C2×C4—121no—
919C2×C4—121no—
920C2×C4—121no—
921C2×C4—121no—
922C2×C4—121no—
923C2×C4—121no—
924C2×C4—121no—
925C2×C4—121no—
926C2×C4—121no—
927C2×C4—121no—
928C2×C4—121no—
929C2×C4—121no—
930C2×C4—121no—
931C2×C4—121no—
932C2×C4—121no—
933C2×C4—121no—
934C2×C4—121no—
935C2×C4—121no—
936C2×C4—121no—
937C2×C4—121no—
938C2×C3#240911yescharacteristic
939C2×C3#243211yescharacteristic
940C2×C3#256411yescharacteristic
941C2×C3#261311yescharacteristic
942C2×C3#262711yescharacteristic
943C2×C3#266311yescharacteristic
944C2×C3#272011yescharacteristic
945C2×C3#272011yescharacteristic
946C2×C3#272311yescharacteristic
947C2×C3#272311yescharacteristic
948C2×C3#272811yescharacteristic
949C2×C3#272811yescharacteristic
950C2×C3#272911yescharacteristic
951C2×C3#272911yescharacteristic
952C2×C3#281711yescharacteristic
953D3—44no—
954C22—64no—
955C22—64no—
956C22—64no—
957C22—122no—
958C22—122no—
959C22—122no—
960C22—122no—
961C22—122no—
962C22—122no—
963C22—122no—
964C22—122no—
965C22—122no—
966C22—122no—
967C22—122no—
968C22—122no—
969C22#550711yescharacteristic
970C22#552711yescharacteristic
971C22#553411yescharacteristic
972C22#554811yescharacteristic
973C22#555211yescharacteristic
974C22#556411yescharacteristic
975C22#557911yescharacteristic
976C22D3×#12011yescharacteristic
977C22#560511yescharacteristic
978C22#560511yescharacteristic
979C22#560711yescharacteristic
980C22D3×C22⋊Q811yescharacteristic
981C22#562811yescharacteristic
982C22#563211yescharacteristic
983C22#563211yescharacteristic
984C22#563311yescharacteristic
985C22#565311yescharacteristic
986C22#565311yescharacteristic
987C22#565511yescharacteristic
988C22#566011yescharacteristic
989C22#566211yescharacteristic
990C22#567411yescharacteristic
991C22#567511yescharacteristic
992C22#567711yescharacteristic
993C22#567711yescharacteristic
994C22#568911yescharacteristic
995C22#569011yescharacteristic
996C22#569211yescharacteristic
997C22#569911yescharacteristic
998C22#569911yescharacteristic
999C22#570511yescharacteristic
1000C22#570711yescharacteristic
1001C22#571211yescharacteristic
1002C22#571211yescharacteristic
1003C22#572911yescharacteristic
1004C4—42no—
1005C4—42no—
1006C4—42no—
1007C4—42no—
1008C4—42no—
1009C4—64no—
1010C4—81no—
1011C4—81no—
1012C4—122no—
1013C4—122no—
1014C4—122no—
1015C4—122no—
1016C4—241no—
1017C4—241no—
1018C3#1660111yescharacteristic, complemented, Sylow
1019C2—124no—
1020C2#7420011yescharacteristic
1021C2#7441111yescharacteristic
1022C2#7517711yescharacteristic
1023C2#7536011yescharacteristic
1024C2#7570511yescharacteristic
1025C2#7591111yescharacteristic
1026C2#7611911yescharacteristic
1027C2#7678011yescharacteristic
1028C2#7712211yescharacteristic
1029C2#7759311yescharacteristic
1030C2#7787111yescharacteristic
1031C2#7796411yescharacteristic
1032C2#7824811yescharacteristic
1033C2#7831611yescharacteristic
1034C2#7837311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1442C2
prime radicalC24×D3C23
hypercenter#1442D3
hypocenterC3#16601
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
3. C2×#4660C2semidirect
4. C2×#4656C2semidirect
5. C3×#1442C2semidirect
6. #71568C2semidirect
12. #69424C2semidirect
13. #69421C2semidirect
14. #69420C2semidirect
15. #69414C2semidirect
67. #1442D3semidirect
122. C2×(C2×D3)⋊C4Q8semidirect
1018. C3#16601semidirect

Maximal subgroups

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

subgroupindex
C22×#8962
C2×#46682
C2×#46602
C2×#46562
C3×#14422
#715682
#694292
#694282
#694272
(C2×D3)⋊#952
#694242
#694212
#694202
#694142
#166013