Finite Group Databasebeta

← #10733811

Subgroups — #10733811

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×#897C211yesmaximal, characteristic, complemented
2C2×C3×#396C211yesmaximal, characteristic, complemented
3C2×#4989C211yesmaximal, characteristic, complemented
4C2×#4979C211yesmaximal, characteristic, complemented
5C2×#4956C211yesmaximal, characteristic
6C2×#4949C211yesmaximal, characteristic, complemented
7C2×#4947C211yesmaximal, characteristic, complemented
8C2×#4957C211yesmaximal, characteristic
9#71570C211yesmaximal, characteristic, complemented
10#71564C211yesmaximal, characteristic, complemented
11#71563C211yesmaximal, characteristic, complemented
12#71550C211yesmaximal, characteristic
13#71546C211yesmaximal, characteristic, complemented
14#69428C211yesmaximal, characteristic, complemented
15#69420C211yesmaximal, characteristic, complemented
16#15325—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×Dic6C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×C4⋊Dic3C2211yescharacteristic
35C22×C4⋊Dic3C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×C4×Dic3C2211yescharacteristic
40C2×#897—24no—
41C2×#897—24no—
42C2×#897—24no—
43C3×#396—24no—
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
55C2×C3⋊#95C2211yescharacteristic
56#4989—24no—
57#4979—24no—
58#4957—24no—
59#4956—24no—
60#4949—24no—
61#4947—24no—
62C22×C22⋊Q8—31no—
63C2×#399—31no—
64C2×#396D311yescharacteristic, complemented
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#1439—31no—
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×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C22×C4×D3—22no—
100C22×C4×D3—22no—
101C22×C4×D3—22no—
102C22×C4×D3—22no—
103C22×C4×D3—22no—
104C22×C4×D3—41no—
105C22×C4×D3—41no—
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—22no—
116C2×C3×C4⋊C4—22no—
117C2×C3×C4⋊C4—22no—
118C2×C3×C4⋊C4—22no—
119C2×C3×C4⋊C4—22no—
120C2×C3×C4⋊C4—41no—
121C2×C3×C4⋊C4D414yescomplemented
122C2×C3×C22⋊C4—22no—
123C2×C3×C22⋊C4—22no—
124C2×C3×C22⋊C4—22no—
125C2×C3×C22⋊C4—22no—
126C2×C3×C22⋊C4—22no—
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4—22no—
129C2×C3×C22⋊C4—22no—
130C2×C3×C22⋊C4—41no—
131C2×#217—22no—
132C2×#217—22no—
133C2×#217—22no—
134C2×#217—22no—
135C2×#217—22no—
136C2×#217—22no—
137C2×#217—41no—
138C2×#217—41no—
139C2×#217—41no—
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—22no—
146C2×(C2×D3)⋊C4—22no—
147C2×(C2×D3)⋊C4—22no—
148C2×(C2×D3)⋊C4—22no—
149C2×(C2×D3)⋊C4—22no—
150C2×(C2×D3)⋊C4—22no—
151C2×(C2×D3)⋊C4—22no—
152C2×(C2×D3)⋊C4—41no—
153C2×(C2×D3)⋊C4—41no—
154C2×(C2×D3)⋊C4D414yes—
155C2×C4⋊Dic3—22no—
156C2×C4⋊Dic3—22no—
157C2×C4⋊Dic3—22no—
158C2×C4⋊Dic3—22no—
159C2×C4⋊Dic3—22no—
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—41no—
168C2×Dic3⋊C4—41no—
169C2×Dic3⋊C4—41no—
170C2×C4×Dic3—22no—
171C2×C4×Dic3—22no—
172C2×C4×Dic3—41no—
173#897—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⋊C4C2×D311yescharacteristic
198C22×C4⋊C4C2×D311yescharacteristic
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—24no—
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×#95—31no—
229C2×#95—31no—
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×C3—21no—
244C24×C3—21no—
245C24×C3C2×Q812yes—
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×D3C2×D412yes—
260C23×D3C2×Q812yes—
261C23×D3#4112yes—
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×C4C2×D412yes—
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—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×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×Dic3C2×D412yes—
352C22×Dic3C2×D412yes—
353C22×Dic3C2×D412yes—
354C22×Dic3C2×D412yes—
355C22×Dic3C2×D412yes—
356C22×Dic3C2×D412yes—
357C22×Dic3C2×D412yes—
358C22×Dic3C2×Q812yes—
359C22×Dic3#4112yes—
360C2×C4×D3—28no—
361C2×C4×D3—44no—
362C2×C4×D3—44no—
363C2×C4×D3—44no—
364C2×C4×D3—44no—
365C2×C4×D3—44no—
366C2×C4×D3—44no—
367C2×Dic6—28no—
368C2×Dic6—44no—
369C2×Dic6—44no—
370C2×Dic6—44no—
371C2×Dic6—44no—
372C2×Dic6—44no—
373C2×Dic6—44no—
374C3×C4⋊C4—28no—
375C3×C4⋊C4—44no—
376C3×C4⋊C4—44no—
377C3×C22⋊C4—44no—
378C3×C22⋊C4—44no—
379C3×C22⋊C4—44no—
380#217—44no—
381#217—44no—
382#217—44no—
383(C2×D3)⋊C4—28no—
384(C2×D3)⋊C4—28no—
385(C2×D3)⋊C4—28no—
386(C2×D3)⋊C4—44no—
387(C2×D3)⋊C4—44no—
388C4⋊Dic3—28no—
389C4⋊Dic3—28no—
390Dic3⋊C4—44no—
391Dic3⋊C4—44no—
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—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—34no—
439C2×C4⋊C4—41no—
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—121no—
452C2×C4⋊C4—121no—
453C2×C4⋊C4—121no—
454C2×C4⋊C4#6714yescomplemented
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—22no—
463C2×C22⋊C4—34no—
464C2×C22⋊C4—41no—
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—62no—
483C2×C22⋊C4—121no—
484C2×C22⋊C4—121no—
485C2×C22⋊C4—121no—
486C2×C22⋊C4—121no—
487C2×C22⋊C4—121no—
488C2×C42—62no—
489C2×C42—62no—
490C2×C42—121no—
491#95—22no—
492#95—34no—
493#95—34no—
494#95—62no—
495#95—62no—
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—41no—
511C23×C3—41no—
512C23×C3—41no—
513C23×C3—41no—
514C23×C3—41no—
515C23×C3—41no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
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×C3—41no—
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—22no—
561C22×D3—22no—
562C22×D3—22no—
563C22×D3—22no—
564C22×D3—22no—
565C22×D3—22no—
566C22×D3—22no—
567C22×D3—22no—
568C22×D3—22no—
569C22×D3—22no—
570C22×D3—22no—
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×D3C22⋊Q814yes—
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#12014yes—
629C2×C3×C4#12714yes—
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—41no—
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
680C4×D3—416no—
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—21no—
695C24—21no—
696C24—32no—
697C24—32no—
698C24—32no—
699C24—61no—
700C24—61no—
701C24—61no—
702C24—61no—
703C24—61no—
704C24—61no—
705C24—61no—
706C24—61no—
707C24—61no—
708C24—61no—
709C24—61no—
710C24—61no—
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—32no—
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—68no—
771C22×C4—61no—
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—61no—
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—124no—
812C22×C4—124no—
813C22×C4—124no—
814C22×C4—124no—
815C22×C4—124no—
816C22×C4—124no—
817C22×C4D3×D412yes—
818C22×C4D3×D412yes—
819C22×C4D3×D412yes—
820C22×C4D3×D412yes—
821C22×C4#23712yes—
822C22×C4C2×#6712yes—
823C22×C4C2×#6712yes—
824C22×C4C2×#6712yes—
825C4⋊C4—28no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C4⋊C4—68no—
829C4⋊C4—68no—
830C4⋊C4—124no—
831C4⋊C4—124no—
832C4⋊C4—124no—
833C22⋊C4—44no—
834C22⋊C4—44no—
835C22⋊C4—44no—
836C22⋊C4—68no—
837C22⋊C4—68no—
838C22⋊C4—68no—
839C22⋊C4—124no—
840C22⋊C4—124no—
841C22⋊C4—124no—
842C22⋊C4—124no—
843C22⋊C4—124no—
844C42—124no—
845C22×C3—42no—
846C22×C3—42no—
847C22×C3—42no—
848C22×C3—42no—
849C22×C3—42no—
850C22×C3—42no—
851C22×C3—42no—
852C22×C3—81no—
853C22×C3—81no—
854C22×C3—81no—
855C22×C3—81no—
856C22×C3—81no—
857C22×C3—81no—
858C22×C3—81no—
859C22×C3—81no—
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—24no—
896C2×D3—24no—
897C2×D3—24no—
898C2×D3—42no—
899C2×D3—42no—
900C2×D3—42no—
901C2×D3—42no—
902C2×D3—42no—
903C2×D3—42no—
904C2×D3—42no—
905C2×D3—42no—
906C2×D3—42no—
907C2×D3—42no—
908C2×D3—42no—
909C2×D3—42no—
910C3×C4—24no—
911C3×C4—24no—
912C3×C4—42no—
913C3×C4—42no—
914C3×C4—81no—
915C3×C4—81no—
916Dic3—24no—
917Dic3—42no—
918Dic3—42no—
919Dic3—42no—
920Dic3—42no—
921Dic3—42no—
922Dic3—42no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—34no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
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—41no—
958C23—41no—
959C23—62no—
960C23—62no—
961C23—62no—
962C23—62no—
963C23—62no—
964C23—62no—
965C23—62no—
966C23—62no—
967C23—62no—
968C23—62no—
969C23—62no—
970C23—62no—
971C23—62no—
972C23—62no—
973C23—62no—
974C23—62no—
975C23—62no—
976C23—62no—
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—121no—
993C23C2×D3×D411yescharacteristic
994C23C2×D3×D411yescharacteristic
995C23C2×D3×D411yescharacteristic
996C23C2×D3×D411yescharacteristic
997C23C2×#23711yescharacteristic
998C23#100411yescharacteristic
999C23C2×D3×Q811yescharacteristic
1000C23#100711yescharacteristic
1001C23D3×#4111yescharacteristic
1002C23D3×#4111yescharacteristic
1003C23#100911yescharacteristic
1004C23#100911yescharacteristic
1005C23#101011yescharacteristic
1006C23#101011yescharacteristic
1007C23C22×#6711yescharacteristic
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—41no—
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—62no—
1052C2×C4—62no—
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—1216no—
1076C2×C4—121no—
1077C2×C4—121no—
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#93714yes—
1101C2×C4#94014yes—
1102C2×C3—82no—
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—44no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—64no—
1127C22—64no—
1128C22—64no—
1129C22—81no—
1130C22—81no—
1131C22—81no—
1132C22—81no—
1133C22—81no—
1134C22—81no—
1135C22—81no—
1136C22—81no—
1137C22—122no—
1138C22—122no—
1139C22—122no—
1140C22—122no—
1141C22—122no—
1142C22—122no—
1143C22—122no—
1144C22—122no—
1145C22—122no—
1146C22—122no—
1147C22—122no—
1148C22—122no—
1149C22#559611yescharacteristic
1150C22#559711yescharacteristic
1151C22#559811yescharacteristic
1152C22#560611yescharacteristic
1153C22#560811yescharacteristic
1154C22#560911yescharacteristic
1155C22#560911yescharacteristic
1156C22#560911yescharacteristic
1157C22#560911yescharacteristic
1158C22#561011yescharacteristic
1159C22#561111yescharacteristic
1160C22#561211yescharacteristic
1161C22D3×C22⋊Q811yescharacteristic
1162C22D3×C22⋊Q811yescharacteristic
1163C22#562811yescharacteristic
1164C22#562811yescharacteristic
1165C22#563111yescharacteristic
1166C22#563211yescharacteristic
1167C22#563211yescharacteristic
1168C22#563311yescharacteristic
1169C22#563411yescharacteristic
1170C22#563511yescharacteristic
1171C22#564311yescharacteristic
1172C22#564711yescharacteristic
1173C22#570511yescharacteristic
1174C22#570711yescharacteristic
1175C22#571011yescharacteristic
1176C22#571211yescharacteristic
1177C22C2×#93711yescharacteristic
1178C22C2×#94011yescharacteristic
1179C22#580611yescharacteristic
1180C22Q8×#6711yescharacteristic
1181C22#582411yescharacteristic
1182C22#583011yescharacteristic
1183C22#583111yescharacteristic
1184C4—24no—
1185C4—24no—
1186C4—42no—
1187C4—42no—
1188C4—64no—
1189C4—81no—
1190C4—81no—
1191C4—122no—
1192C4—122no—
1193C4—122no—
1194C4—122no—
1195C4—122no—
1196C4—122no—
1197C3#1532511yescharacteristic, complemented, Sylow
1198C2—82no—
1199C2—124no—
1200C2#7729011yescharacteristic
1201C2#7729511yescharacteristic
1202C2#7741811yescharacteristic
1203C2#7741911yescharacteristic
1204C2#7742611yescharacteristic
1205C2#7742711yescharacteristic
1206C2#7743111yescharacteristic
1207C2#7743311yescharacteristic
1208C2#8265111yescharacteristic
1209C2#8265311yescharacteristic
1210C2#8266811yescharacteristic
1211C2#8275111yescharacteristic
1212C2#8278011yescharacteristic
1213C2#8279711yescharacteristic
1214C2#8310011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#396C2
prime radicalC23×#67C22
hypercenterC2×#396D3
hypocenterC3#15325
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#897C2semidirect
2. C2×C3×#396C2semidirect
3. C2×#4989C2semidirect
4. C2×#4979C2semidirect
6. C2×#4949C2semidirect
7. C2×#4947C2semidirect
9. #71570C2semidirect
10. #71564C2semidirect
11. #71563C2semidirect
13. #71546C2semidirect
14. #69428C2semidirect
15. #69420C2semidirect
64. C2×#396D3semidirect
91. C22×#67Q8semidirect
121. C2×C3×C4⋊C4D4semidirect
160. C2×C4⋊Dic3D4semidirect
185. C3⋊#95D4semidirect
454. C2×C4⋊C4#67semidirect
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×#8972
C2×C3×#3962
C2×#49892
C2×#49792
C2×#49562
C2×#49492
C2×#49472
C2×#49572
#715702
#715642
#715632
#715502
#715462
#694282
#694202
#153253