Finite Group Databasebeta

← #10733804

Subgroups — #10733804

Order 768.

2226 conjugacy classes of subgroups.

The subgroup lattice has 1216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#878C211yesmaximal, characteristic, complemented
2C2×#4994C211yesmaximal, characteristic, complemented
3C2×#4957C211yesmaximal, characteristic
4C2×#4958C211yesmaximal, characteristic
5C2×#4950C211yesmaximal, characteristic, complemented
6C2×#4677C211yesmaximal, characteristic, complemented
7C2×#4673C211yesmaximal, characteristic, complemented
8C2×#4656C211yesmaximal, characteristic, complemented
9C3×#1439C211yesmaximal, characteristic, complemented
10#71563C211yesmaximal, characteristic, complemented
11#71550C211yesmaximal, characteristic
12#71546C211yesmaximal, characteristic, complemented
13#69428C211yesmaximal, characteristic, complemented
14#69420C211yesmaximal, characteristic, complemented
15#69405C211yesmaximal, characteristic, complemented
16#15325—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C24×Dic3C2211yescharacteristic
19C23×Dic6C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
33C22×C4⋊Dic3C2211yescharacteristic
34C22×C4⋊Dic3C2211yescharacteristic
35C22×C4⋊Dic3C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×C4×Dic3C2211yescharacteristic
40C2×#878—24no—
41C2×#878—24no—
42C2×#878—24no—
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#4994—24no—
56#4958—24no—
57#4957—24no—
58#4950—24no—
59#4677—24no—
60#4673—24no—
61#4656—24no—
62C22×C22⋊Q8—31no—
63C2×#399—31no—
64C2×#396—31no—
65C2×#395—31no—
66C2×#393—31no—
67C2×#390—31no—
68C2×#386—31no—
69C2×#385—31no—
70#1444—31no—
71#1439—31no—
72#1439—31no—
73#1439D311yescharacteristic, complemented
74#1438—31no—
75#1436—31no—
76C4⋊#95—31no—
77C25×C3C2311yescharacteristic
78C24×D3C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C22×#67—22no—
86C22×#67—22no—
87C22×#67—22no—
88C22×#67—22no—
89C22×#67—41no—
90C22×#67—41no—
91C22×#67Q814yescomplemented
92C23×Dic3—22no—
93C23×Dic3—22no—
94C23×Dic3—22no—
95C23×Dic3—22no—
96C23×Dic3—22no—
97C23×Dic3—41no—
98C23×Dic3—41no—
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C22×Dic6—22no—
107C22×Dic6—22no—
108C22×Dic6—22no—
109C22×Dic6—22no—
110C22×Dic6—22no—
111C22×Dic6—41no—
112C22×Dic6—41no—
113C2×C3×C4⋊C4—22no—
114C2×C3×C4⋊C4—22no—
115C2×C3×C4⋊C4—41no—
116C2×C3×C22⋊C4—22no—
117C2×C3×C22⋊C4—22no—
118C2×C3×C22⋊C4—22no—
119C2×C3×C22⋊C4—22no—
120C2×C3×C22⋊C4—22no—
121C2×C3×C22⋊C4—22no—
122C2×C3×C22⋊C4—22no—
123C2×C3×C22⋊C4—41no—
124C2×C3×C22⋊C4D414yes—
125C2×#217—22no—
126C2×#217—22no—
127C2×#217—22no—
128C2×#217—22no—
129C2×#217—22no—
130C2×#217—41no—
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—22no—
142C2×(C2×D3)⋊C4—22no—
143C2×(C2×D3)⋊C4—22no—
144C2×(C2×D3)⋊C4—22no—
145C2×(C2×D3)⋊C4—41no—
146C2×(C2×D3)⋊C4—41no—
147C2×(C2×D3)⋊C4—41no—
148C2×(C2×D3)⋊C4—41no—
149C2×C4⋊Dic3—22no—
150C2×C4⋊Dic3—22no—
151C2×C4⋊Dic3—22no—
152C2×C4⋊Dic3—22no—
153C2×C4⋊Dic3—22no—
154C2×C4⋊Dic3—22no—
155C2×C4⋊Dic3—22no—
156C2×C4⋊Dic3—22no—
157C2×C4⋊Dic3—22no—
158C2×C4⋊Dic3—41no—
159C2×C4⋊Dic3—41no—
160C2×C4⋊Dic3D414yescomplemented
161C2×Dic3⋊C4—22no—
162C2×Dic3⋊C4—22no—
163C2×Dic3⋊C4—22no—
164C2×Dic3⋊C4—22no—
165C2×Dic3⋊C4—22no—
166C2×Dic3⋊C4—22no—
167C2×Dic3⋊C4—22no—
168C2×Dic3⋊C4—41no—
169C2×Dic3⋊C4D414yescomplemented
170C2×C4×Dic3—22no—
171C2×C4×Dic3—22no—
172C2×C4×Dic3—41no—
173#878—232no—
174C3×#95—22no—
175C3×#95—22no—
176C3×#95—22no—
177C3⋊#95—22no—
178C3⋊#95—22no—
179C3⋊#95—22no—
180C3⋊#95—22no—
181C3⋊#95—22no—
182C3⋊#95—22no—
183C3⋊#95—41no—
184C3⋊#95D414yes—
185C3⋊#95D414yescomplemented
186C23×Q8—31no—
187C23×D4—31no—
188C24×C4—31no—
189C2×C22⋊Q8—64no—
190C2×C22⋊Q8—64no—
191C2×C22⋊Q8—64no—
192C22×C4⋊C4—31no—
193C22×C4⋊C4—31no—
194C22×C4⋊C4—31no—
195C22×C4⋊C4—31no—
196C22×C4⋊C4—31no—
197C22×C4⋊C4—31no—
198C22×C4⋊C4—31no—
199C22×C4⋊C4C2×D311yescharacteristic
200C22×C22⋊C4—31no—
201C22×C22⋊C4—31no—
202C22×C22⋊C4—31no—
203C22×C22⋊C4—31no—
204C22×C22⋊C4—31no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4—31no—
208C22×C22⋊C4C2×D311yescharacteristic
209C22×C22⋊C4C2×D311yescharacteristic
210C22×C22⋊C4C2×D311yescharacteristic
211C22×C42—31no—
212#399—64no—
213#396—64no—
214#395—64no—
215#393—64no—
216#390—64no—
217#386—64no—
218#385—64no—
219C2×#95—31no—
220C2×#95—31no—
221C2×#95—31no—
222C2×#95—31no—
223C2×#95—31no—
224C2×#95—31no—
225C2×#95—31no—
226C2×#95—31no—
227C2×#95—31no—
228C2×#95C2×D311yescharacteristic
229C2×#95C2×D311yescharacteristic
230C2×#95C2×D311yescharacteristic
231C24×C3—21no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—21no—
236C24×C3—21no—
237C24×C3—21no—
238C24×C3—21no—
239C24×C3—21no—
240C24×C3—21no—
241C24×C3—21no—
242C24×C3—21no—
243C24×C3C2×D412yes—
244C24×C3C2×Q812yes—
245C24×C3#4112yes—
246C24×C3C2411yescharacteristic
247C23×D3—21no—
248C23×D3—21no—
249C23×D3—21no—
250C23×D3—21no—
251C23×D3—21no—
252C23×D3—21no—
253C23×D3—21no—
254C23×D3—21no—
255C23×D3—21no—
256C23×D3—21no—
257C23×D3—21no—
258C23×D3—21no—
259C23×D3—21no—
260C23×D3—21no—
261C23×D3C2×Q812yes—
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×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4C2×D412yes—
298C22×C3×C4C2×D412yes—
299C22×C3×C4C2×D412yes—
300C22×C3×C4C2×D412yes—
301C22×C3×C4C2×D412yes—
302C22×C3×C4C2×D412yes—
303C22×C3×C4#4112yes—
304C2×#67—28no—
305C2×#67—28no—
306C2×#67—44no—
307C2×#67—44no—
308C2×#67—44no—
309C2×#67—44no—
310C2×#67—44no—
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—28no—
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×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3—21no—
342C22×Dic3—21no—
343C22×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—21no—
346C22×Dic3—21no—
347C22×Dic3—21no—
348C22×Dic3—21no—
349C22×Dic3—21no—
350C22×Dic3—21no—
351C22×Dic3—44no—
352C22×Dic3—44no—
353C22×Dic3—44no—
354C22×Dic3—44no—
355C22×Dic3—44no—
356C22×Dic3—44no—
357C22×Dic3C2×D412yes—
358C22×Dic3C2×D412yes—
359C22×Dic3C2×D412yes—
360C22×Dic3C2×D412yes—
361C22×Dic3C2×D412yes—
362C22×Dic3C2×D412yes—
363C22×Dic3C2×D412yes—
364C22×Dic3C2×D412yes—
365C22×Dic3C2×Q812yes—
366C22×Dic3#4112yes—
367C2×Dic6—28no—
368C2×Dic6—44no—
369C2×Dic6—44no—
370C2×Dic6—44no—
371C2×Dic6—44no—
372C2×Dic6—44no—
373C2×Dic6—44no—
374C3×C4⋊C4—44no—
375C3×C22⋊C4—28no—
376C3×C22⋊C4—28no—
377C3×C22⋊C4—44no—
378#217—28no—
379#217—44no—
380(C2×D3)⋊C4—44no—
381(C2×D3)⋊C4—44no—
382(C2×D3)⋊C4—44no—
383(C2×D3)⋊C4—44no—
384(C2×D3)⋊C4—44no—
385(C2×D3)⋊C4—44no—
386C4⋊Dic3—28no—
387C4⋊Dic3—44no—
388C4⋊Dic3—44no—
389C4⋊Dic3—44no—
390Dic3⋊C4—28no—
391Dic3⋊C4—28no—
392Dic3⋊C4—44no—
393C4×Dic3—44no—
394C25—31no—
395C25C22×D311yescharacteristic
396C22×Q8—62no—
397C22×Q8—62no—
398C22×Q8—62no—
399C22×Q8—62no—
400C22×Q8—62no—
401C22×Q8—121no—
402C22×Q8—121no—
403C22×D4—34no—
404C22×D4—62no—
405C22×D4—62no—
406C22×D4—62no—
407C22×D4—62no—
408C22×D4—121no—
409C22×D4—121no—
410C23×C4—31no—
411C23×C4—31no—
412C23×C4—31no—
413C23×C4—31no—
414C23×C4—31no—
415C23×C4—31no—
416C23×C4—31no—
417C23×C4—62no—
418C23×C4—62no—
419C23×C4—62no—
420C23×C4—62no—
421C23×C4—62no—
422C23×C4—121no—
423C23×C4—121no—
424C23×C4C22×D311yescharacteristic
425C23×C4C22×D311yescharacteristic
426C23×C4C22×D311yescharacteristic
427C23×C4C22×D311yescharacteristic
428C23×C4C22×D311yescharacteristic
429C23×C4C22×D311yescharacteristic
430C22⋊Q8—632no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—34no—
434C2×C4⋊C4—34no—
435C2×C4⋊C4—41no—
436C2×C4⋊C4—62no—
437C2×C4⋊C4—62no—
438C2×C4⋊C4—62no—
439C2×C4⋊C4—62no—
440C2×C4⋊C4—62no—
441C2×C4⋊C4—62no—
442C2×C4⋊C4—62no—
443C2×C4⋊C4—62no—
444C2×C4⋊C4—62no—
445C2×C4⋊C4—62no—
446C2×C4⋊C4—62no—
447C2×C4⋊C4—62no—
448C2×C4⋊C4—62no—
449C2×C4⋊C4—62no—
450C2×C4⋊C4—62no—
451C2×C4⋊C4—62no—
452C2×C4⋊C4—121no—
453C2×C4⋊C4—121no—
454C2×C4⋊C4—121no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—41no—
463C2×C22⋊C4—62no—
464C2×C22⋊C4—62no—
465C2×C22⋊C4—62no—
466C2×C22⋊C4—62no—
467C2×C22⋊C4—62no—
468C2×C22⋊C4—62no—
469C2×C22⋊C4—62no—
470C2×C22⋊C4—62no—
471C2×C22⋊C4—62no—
472C2×C22⋊C4—62no—
473C2×C22⋊C4—62no—
474C2×C22⋊C4—62no—
475C2×C22⋊C4—62no—
476C2×C22⋊C4—62no—
477C2×C22⋊C4—62no—
478C2×C22⋊C4—62no—
479C2×C22⋊C4—62no—
480C2×C22⋊C4—62no—
481C2×C22⋊C4—62no—
482C2×C22⋊C4—121no—
483C2×C22⋊C4—121no—
484C2×C22⋊C4—121no—
485C2×C22⋊C4—121no—
486C2×C22⋊C4—121no—
487C2×C22⋊C4D1214yes—
488C2×C42—62no—
489C2×C42—62no—
490C2×C42—121no—
491#95—22no—
492#95—22no—
493#95—22no—
494#95—34no—
495#95—34no—
496#95—62no—
497#95—62no—
498#95—62no—
499#95—62no—
500#95—62no—
501#95—62no—
502#95—121no—
503C23×C3—22no—
504C23×C3—22no—
505C23×C3—22no—
506C23×C3—22no—
507C23×C3—22no—
508C23×C3—22no—
509C23×C3—22no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—22no—
514C23×C3—22no—
515C23×C3—22no—
516C23×C3—22no—
517C23×C3—22no—
518C23×C3—22no—
519C23×C3—22no—
520C23×C3—22no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3C22⋊Q814yes—
538C23×C3C22×D411yescharacteristic
539C23×C3C22×D411yescharacteristic
540C23×C3C22×D411yescharacteristic
541C23×C3C22×D411yescharacteristic
542C23×C3C22×D411yescharacteristic
543C23×C3C22×Q811yescharacteristic
544C23×C3C2×#4111yescharacteristic
545C23×C3C2×#4111yescharacteristic
546C23×C3C2×#4111yescharacteristic
547C23×C3H(5,𝔽2)11yescharacteristic
548C23×C3H(5,𝔽2)11yescharacteristic
549C23×C3H(5,𝔽2)11yescharacteristic
550C23×C32−1+411yescharacteristic
551C23×C32−1+411yescharacteristic
552C23×C32−1+411yescharacteristic
553C22×D3—22no—
554C22×D3—22no—
555C22×D3—22no—
556C22×D3—22no—
557C22×D3—22no—
558C22×D3—22no—
559C22×D3—22no—
560C22×D3—41no—
561C22×D3—41no—
562C22×D3—41no—
563C22×D3—41no—
564C22×D3—41no—
565C22×D3—41no—
566C22×D3—41no—
567C22×D3—41no—
568C22×D3—41no—
569C22×D3—41no—
570C22×D3—41no—
571C22×D3—41no—
572C22×D3—41no—
573C22×D3—41no—
574C22×D3—41no—
575C22×D3—41no—
576C22×D3—41no—
577C22×D3—41no—
578C22×D3—41no—
579C22×D3—41no—
580C22×D3—41no—
581C22×D3—41no—
582C22×D3—41no—
583C22×D3—41no—
584C22×D3—41no—
585C22×D3—41no—
586C22×D3—41no—
587C22×D3—41no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—22no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—41no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—41no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—41no—
626C2×C3×C4—41no—
627C2×C3×C4—41no—
628C2×C3×C4—41no—
629C2×C3×C4#12014yes—
630#67—416no—
631C2×Dic3—22no—
632C2×Dic3—22no—
633C2×Dic3—22no—
634C2×Dic3—22no—
635C2×Dic3—22no—
636C2×Dic3—22no—
637C2×Dic3—22no—
638C2×Dic3—22no—
639C2×Dic3—22no—
640C2×Dic3—22no—
641C2×Dic3—22no—
642C2×Dic3—22no—
643C2×Dic3—22no—
644C2×Dic3—22no—
645C2×Dic3—22no—
646C2×Dic3—22no—
647C2×Dic3—22no—
648C2×Dic3—22no—
649C2×Dic3—22no—
650C2×Dic3—22no—
651C2×Dic3—22no—
652C2×Dic3—22no—
653C2×Dic3—22no—
654C2×Dic3—22no—
655C2×Dic3—416no—
656C2×Dic3—41no—
657C2×Dic3—41no—
658C2×Dic3—41no—
659C2×Dic3—41no—
660C2×Dic3—41no—
661C2×Dic3—41no—
662C2×Dic3—41no—
663C2×Dic3—41no—
664C2×Dic3—41no—
665C2×Dic3—41no—
666C2×Dic3—41no—
667C2×Dic3—41no—
668C2×Dic3—41no—
669C2×Dic3—41no—
670C2×Dic3—41no—
671C2×Dic3—41no—
672C2×Dic3—41no—
673C2×Dic3—41no—
674C2×Dic3—41no—
675C2×Dic3—41no—
676C2×Dic3—41no—
677C2×Dic3—41no—
678C2×Dic3—41no—
679C2×Dic3C22⋊Q814yescomplemented
680C2×Dic3#12714yes—
681Dic6—416no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—21no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—32no—
695C24—61no—
696C24—61no—
697C24—61no—
698C24—61no—
699C24—61no—
700C24—61no—
701C24—61no—
702C24—61no—
703C24—61no—
704C24—61no—
705C24—61no—
706C24—61no—
707C24—61no—
708C24—61no—
709C24C2×D1212yes—
710C24#23712yes—
711C24D3×Q812yes—
712C24C23×D311yescharacteristic
713C2×Q8—68no—
714C2×Q8—124no—
715C2×Q8—124no—
716C2×Q8—124no—
717C2×Q8—124no—
718C2×Q8—124no—
719C2×Q8—124no—
720C2×D4—68no—
721C2×D4—68no—
722C2×D4—124no—
723C2×D4—124no—
724C2×D4—124no—
725C2×D4—124no—
726C2×D4—124no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—32no—
763C22×C4—32no—
764C22×C4—32no—
765C22×C4—32no—
766C22×C4—32no—
767C22×C4—32no—
768C22×C4—32no—
769C22×C4—32no—
770C22×C4—32no—
771C22×C4—32no—
772C22×C4—61no—
773C22×C4—61no—
774C22×C4—61no—
775C22×C4—61no—
776C22×C4—61no—
777C22×C4—61no—
778C22×C4—61no—
779C22×C4—61no—
780C22×C4—68no—
781C22×C4—61no—
782C22×C4—61no—
783C22×C4—61no—
784C22×C4—61no—
785C22×C4—61no—
786C22×C4—61no—
787C22×C4—61no—
788C22×C4—61no—
789C22×C4—61no—
790C22×C4—61no—
791C22×C4—61no—
792C22×C4—61no—
793C22×C4—61no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—61no—
797C22×C4—61no—
798C22×C4—61no—
799C22×C4—61no—
800C22×C4—61no—
801C22×C4—61no—
802C22×C4—61no—
803C22×C4—61no—
804C22×C4—61no—
805C22×C4—61no—
806C22×C4—61no—
807C22×C4—61no—
808C22×C4—61no—
809C22×C4—61no—
810C22×C4—61no—
811C22×C4—61no—
812C22×C4—124no—
813C22×C4—124no—
814C22×C4—124no—
815C22×C4—124no—
816C22×C4—124no—
817C22×C4—124no—
818C22×C4C2×D1212yes—
819C22×C4C2×D1212yes—
820C22×C4D3×D412yes—
821C22×C4D3×D412yes—
822C22×C4D3×D412yes—
823C22×C4D3×D412yes—
824C22×C4#23712yes—
825C4⋊C4—44no—
826C4⋊C4—68no—
827C4⋊C4—68no—
828C4⋊C4—68no—
829C4⋊C4—124no—
830C4⋊C4—124no—
831C4⋊C4—124no—
832C4⋊C4—124no—
833C22⋊C4—28no—
834C22⋊C4—28no—
835C22⋊C4—44no—
836C22⋊C4—68no—
837C22⋊C4—124no—
838C22⋊C4—124no—
839C22⋊C4—124no—
840C22⋊C4—124no—
841C22⋊C4—124no—
842C22⋊C4—124no—
843C22⋊C4—124no—
844C42—124no—
845C22×C3—24no—
846C22×C3—24no—
847C22×C3—24no—
848C22×C3—42no—
849C22×C3—42no—
850C22×C3—42no—
851C22×C3—42no—
852C22×C3—42no—
853C22×C3—42no—
854C22×C3—42no—
855C22×C3—42no—
856C22×C3—42no—
857C22×C3—42no—
858C22×C3—42no—
859C22×C3—42no—
860C22×C3C2×#12011yescharacteristic
861C22×C3C2×C22⋊Q811yescharacteristic
862C22×C3C2×C22⋊Q811yescharacteristic
863C22×C3#52511yescharacteristic
864C22×C3C2×#12711yescharacteristic
865C22×C3#53211yescharacteristic
866C22×C3#53511yescharacteristic
867C22×C3#53611yescharacteristic
868C22×C3#53611yescharacteristic
869C22×C3#53711yescharacteristic
870C22×C3#53711yescharacteristic
871C22×C3#53911yescharacteristic
872C22×C3#54211yescharacteristic
873C22×C3#54211yescharacteristic
874C22×C3#54311yescharacteristic
875C22×C3D4211yescharacteristic
876C22×C3D4211yescharacteristic
877C22×C3D4211yescharacteristic
878C22×C3D4211yescharacteristic
879C22×C3#54611yescharacteristic
880C22×C3#54611yescharacteristic
881C22×C3#54611yescharacteristic
882C22×C3#54711yescharacteristic
883C22×C3#54711yescharacteristic
884C22×C3#54711yescharacteristic
885C22×C3#54811yescharacteristic
886C22×C3#54811yescharacteristic
887C22×C3#54811yescharacteristic
888C22×C3D4×Q811yescharacteristic
889C22×C3D4×Q811yescharacteristic
890C22×C3D4×Q811yescharacteristic
891C22×C3#55111yescharacteristic
892C22×C3#55411yescharacteristic
893C22×C3#56211yescharacteristic
894C22×C3#56311yescharacteristic
895C2×D3—42no—
896C2×D3—42no—
897C2×D3—42no—
898C2×D3—42no—
899C2×D3—42no—
900C2×D3—42no—
901C2×D3—42no—
902C2×D3—81no—
903C2×D3—81no—
904C2×D3—81no—
905C2×D3—81no—
906C2×D3—81no—
907C2×D3—81no—
908C2×D3—81no—
909C2×D3—81no—
910C3×C4—24no—
911C3×C4—42no—
912C3×C4—42no—
913C3×C4—42no—
914C3×C4—42no—
915C3×C4—81no—
916Dic3—24no—
917Dic3—24no—
918Dic3—42no—
919Dic3—42no—
920Dic3—42no—
921Dic3—42no—
922Dic3—81no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—62no—
958C23—62no—
959C23—62no—
960C23—62no—
961C23—62no—
962C23—62no—
963C23—62no—
964C23—121no—
965C23—121no—
966C23—121no—
967C23—121no—
968C23—121no—
969C23—121no—
970C23—121no—
971C23—121no—
972C23—121no—
973C23—121no—
974C23—121no—
975C23—121no—
976C23—121no—
977C23—121no—
978C23—121no—
979C23—121no—
980C23—121no—
981C23—121no—
982C23—121no—
983C23—121no—
984C23—121no—
985C23—121no—
986C23—121no—
987C23—121no—
988C23—121no—
989C23—121no—
990C23—121no—
991C23—121no—
992C23#89714yes—
993C23C22×D1211yescharacteristic
994C23C2×D3×D411yescharacteristic
995C23C2×D3×D411yescharacteristic
996C23C2×D3×D411yescharacteristic
997C23C2×D3×D411yescharacteristic
998C23C2×#23711yescharacteristic
999C23C2×#23711yescharacteristic
1000C23#100411yescharacteristic
1001C23C2×D3×Q811yescharacteristic
1002C23D3×#4111yescharacteristic
1003C23#100911yescharacteristic
1004C23#100911yescharacteristic
1005C23#101011yescharacteristic
1006C23#101011yescharacteristic
1007C23#101011yescharacteristic
1008Q8—1216no—
1009D4—1216no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—34no—
1029C2×C4—34no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—62no—
1054C2×C4—62no—
1055C2×C4—62no—
1056C2×C4—62no—
1057C2×C4—62no—
1058C2×C4—62no—
1059C2×C4—62no—
1060C2×C4—62no—
1061C2×C4—62no—
1062C2×C4—62no—
1063C2×C4—62no—
1064C2×C4—62no—
1065C2×C4—62no—
1066C2×C4—62no—
1067C2×C4—62no—
1068C2×C4—62no—
1069C2×C4—62no—
1070C2×C4—62no—
1071C2×C4—62no—
1072C2×C4—62no—
1073C2×C4—62no—
1074C2×C4—62no—
1075C2×C4—62no—
1076C2×C4—62no—
1077C2×C4—1216no—
1078C2×C4—121no—
1079C2×C4—121no—
1080C2×C4—121no—
1081C2×C4—121no—
1082C2×C4—121no—
1083C2×C4—121no—
1084C2×C4—121no—
1085C2×C4—121no—
1086C2×C4—121no—
1087C2×C4—121no—
1088C2×C4—121no—
1089C2×C4—121no—
1090C2×C4—121no—
1091C2×C4—121no—
1092C2×C4—121no—
1093C2×C4—121no—
1094C2×C4—121no—
1095C2×C4—121no—
1096C2×C4—121no—
1097C2×C4—121no—
1098C2×C4—121no—
1099C2×C4—121no—
1100C2×C4—121no—
1101C2×C4#88214yes—
1102C2×C3—44no—
1103C2×C3#240911yescharacteristic
1104C2×C3#243011yescharacteristic
1105C2×C3#243311yescharacteristic
1106C2×C3#243711yescharacteristic
1107C2×C3#244911yescharacteristic
1108C2×C3#245211yescharacteristic
1109C2×C3#246111yescharacteristic
1110C2×C3#254011yescharacteristic
1111C2×C3#254211yescharacteristic
1112C2×C3#267211yescharacteristic
1113C2×C3#267411yescharacteristic
1114C2×C3#268111yescharacteristic
1115C2×C3#268311yescharacteristic
1116C2×C3#269211yescharacteristic
1117C2×C3#272311yescharacteristic
1118D3—82no—
1119C22—24no—
1120C22—24no—
1121C22—24no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—122no—
1135C22—122no—
1136C22—122no—
1137C22—122no—
1138C22—122no—
1139C22—122no—
1140C22—122no—
1141C22—241no—
1142C22—241no—
1143C22—241no—
1144C22—241no—
1145C22—241no—
1146C22—241no—
1147C22—241no—
1148C22—241no—
1149C22C2×#88211yescharacteristic
1150C22C2×#89711yescharacteristic
1151C22#552611yescharacteristic
1152C22D4×D1211yescharacteristic
1153C22D4×D1211yescharacteristic
1154C22#555411yescharacteristic
1155C22#555511yescharacteristic
1156C22#558611yescharacteristic
1157C22#559111yescharacteristic
1158C22#559111yescharacteristic
1159C22#559611yescharacteristic
1160C22#559711yescharacteristic
1161C22#559811yescharacteristic
1162C22#559811yescharacteristic
1163C22#559811yescharacteristic
1164C22#560811yescharacteristic
1165C22#560911yescharacteristic
1166C22#560911yescharacteristic
1167C22D3×C22⋊Q811yescharacteristic
1168C22#563211yescharacteristic
1169C22#563211yescharacteristic
1170C22#563211yescharacteristic
1171C22#563411yescharacteristic
1172C22#563511yescharacteristic
1173C22#564811yescharacteristic
1174C22#565511yescharacteristic
1175C22#565511yescharacteristic
1176C22#565811yescharacteristic
1177C22#566511yescharacteristic
1178C22#567411yescharacteristic
1179C22#568211yescharacteristic
1180C22#568411yescharacteristic
1181C22#571011yescharacteristic
1182C22#571211yescharacteristic
1183C22D3×#12711yescharacteristic
1184C4—24no—
1185C4—42no—
1186C4—42no—
1187C4—42no—
1188C4—42no—
1189C4—64no—
1190C4—64no—
1191C4—81no—
1192C4—122no—
1193C4—122no—
1194C4—122no—
1195C4—122no—
1196C4—241no—
1197C3#1532511yescharacteristic, complemented, Sylow
1198C2—44no—
1199C2—242no—
1200C2#7401711yescharacteristic
1201C2#7441311yescharacteristic
1202C2#7442211yescharacteristic
1203C2#7469911yescharacteristic
1204C2#7566511yescharacteristic
1205C2#7566611yescharacteristic
1206C2#7631411yescharacteristic
1207C2#7668711yescharacteristic
1208C2#7682511yescharacteristic
1209C2#7691511yescharacteristic
1210C2#7700611yescharacteristic
1211C2#7729011yescharacteristic
1212C2#7743311yescharacteristic
1213C2#7759411yescharacteristic
1214C2#7803711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1439C2
prime radicalC23×#67C22
hypercenter#1439D3
hypocenterC3#15325
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×#878C2semidirect
2. C2×#4994C2semidirect
5. C2×#4950C2semidirect
6. C2×#4677C2semidirect
7. C2×#4673C2semidirect
8. C2×#4656C2semidirect
9. C3×#1439C2semidirect
10. #71563C2semidirect
12. #71546C2semidirect
13. #69428C2semidirect
14. #69420C2semidirect
15. #69405C2semidirect
73. #1439D3semidirect
91. C22×#67Q8semidirect
160. C2×C4⋊Dic3D4semidirect
169. C2×Dic3⋊C4D4semidirect
185. C3⋊#95D4semidirect
679. C2×Dic3C22⋊Q8semidirect
1197. C3#15325semidirect

Maximal subgroups

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

subgroupindex
C22×#8782
C2×#49942
C2×#49572
C2×#49582
C2×#49502
C2×#46772
C2×#46732
C2×#46562
C3×#14392
#715632
#715502
#715462
#694282
#694202
#694052
#153253