Finite Group Databasebeta

← #10733688

Subgroups — #10733688

Order 768.

2306 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#947C211yesmaximal, characteristic, complemented
2C2×C3×#393C211yesmaximal, characteristic, complemented
3C2×#5229C211yesmaximal, characteristic, complemented
4C2×#4960C211yesmaximal, characteristic
5C2×#4961C211yesmaximal, characteristic, complemented
6C2×#4957C211yesmaximal, characteristic, complemented
7#71550C211yesmaximal, characteristic, complemented
8#71550C211yesmaximal, characteristic, complemented
9#71545C211yesmaximal, characteristic, complemented
10#69429C211yesmaximal, characteristic, complemented
11#69428C211yesmaximal, characteristic, complemented
12#69427C211yesmaximal, characteristic, complemented
13#69426C211yesmaximal, characteristic, complemented
14#69408C211yesmaximal, characteristic, complemented
15#69406C211yesmaximal, characteristic, complemented
16#15317—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×D12C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C2×#947—24no—
27C2×#947—24no—
28C2×#947—24no—
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×(C2×D3)⋊C4C2211yescharacteristic
38C22×(C2×D3)⋊C4C2211yescharacteristic
39C22×C4⋊Dic3C2211yescharacteristic
40C22×Dic3⋊C4C2211yescharacteristic
41C22×C4×Dic3C2211yescharacteristic
42C22×C4×Dic3C2211yescharacteristic
43C3×#393—24no—
44C2×C3×#95C2211yescharacteristic
45C2×C3×#95C2211yescharacteristic
46C2×C3×#95C2211yescharacteristic
47#5229—24no—
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57#4961—24no—
58#4960—24no—
59#4957—24no—
60C22×#124—31no—
61C2×#394—31no—
62C2×#393D311yescharacteristic, complemented
63C2×#392—31no—
64C2×#391—31no—
65C2×#390—31no—
66#1440—31no—
67#1439—31no—
68#1439—31no—
69#1438—31no—
70#1438—31no—
71#1438—31no—
72#1437—31no—
73#1437—31no—
74#1436—31no—
75C25×C3C2311yescharacteristic
76C24×D3C2311yescharacteristic
77C24×D3C2311yescharacteristic
78C22×C3×Q8—22no—
79C22×C3×Q8—22no—
80C22×C3×Q8—22no—
81C22×C3×Q8—22no—
82C22×C3×Q8—41no—
83C22×C3×Q8—41no—
84C22×C3×Q8D414yescomplemented
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C22×#67—22no—
92C22×#67—22no—
93C22×#67—22no—
94C22×#67—22no—
95C22×#67—22no—
96C22×#67—22no—
97C22×#67—22no—
98C22×#67—22no—
99C22×#67—41no—
100C22×#67—41no—
101C22×#67—41no—
102C22×#67—41no—
103C22×#67—41no—
104C22×#67—41no—
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C23×Dic3C2311yescharacteristic
109C23×Dic3C2311yescharacteristic
110C23×Dic3C2311yescharacteristic
111C22×D12—22no—
112C22×D12—22no—
113C22×D12—22no—
114C22×D12—22no—
115C22×D12—22no—
116C22×D12—41no—
117C22×D12—41no—
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—22no—
124C2×C3×C22⋊C4—22no—
125C2×C3×C22⋊C4—41no—
126C2×C3×C22⋊C4—41no—
127C2×#217—22no—
128C2×#217—22no—
129C2×#217—22no—
130C2×#217—22no—
131C2×#217—41no—
132C2×#217—41no—
133#947—232no—
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—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)⋊C4—41no—
155C2×(C2×D3)⋊C4—41no—
156C2×(C2×D3)⋊C4—41no—
157C2×(C2×D3)⋊C4—41no—
158C2×(C2×D3)⋊C4—41no—
159C2×(C2×D3)⋊C4—41no—
160C2×(C2×D3)⋊C4—41no—
161C2×(C2×D3)⋊C4—41no—
162C2×(C2×D3)⋊C4D414yescomplemented
163C2×(C2×D3)⋊C4D414yescomplemented
164C2×C4⋊Dic3—22no—
165C2×C4⋊Dic3—22no—
166C2×C4⋊Dic3—41no—
167C2×Dic3⋊C4—22no—
168C2×Dic3⋊C4—22no—
169C2×Dic3⋊C4—41no—
170C2×C4×Dic3—22no—
171C2×C4×Dic3—22no—
172C2×C4×Dic3—22no—
173C2×C4×Dic3—22no—
174C2×C4×Dic3—22no—
175C2×C4×Dic3—41no—
176C3×#95—22no—
177C3×#95—22no—
178C3×#95—22no—
179C3⋊#95—22no—
180C3⋊#95—22no—
181C3⋊#95—22no—
182C3⋊#95—22no—
183C3⋊#95—22no—
184C3⋊#95—41no—
185C3⋊#95—41no—
186C3⋊#95—41no—
187C3⋊#95D414yes—
188C23×Q8C2×D311yescharacteristic
189C23×D4—31no—
190C23×D4—31no—
191C23×D4—31no—
192C2×#124—64no—
193C2×#124—64no—
194C2×#124—64no—
195C22×C4⋊C4—31no—
196C22×C4⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4—31no—
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⋊C4—31no—
209C22×C22⋊C4C2×D311yescharacteristic
210C22×C22⋊C4C2×D311yescharacteristic
211C22×C22⋊C4C2×D311yescharacteristic
212C22×C42—31no—
213C22×C42—31no—
214#394—64no—
215#393—24no—
216#392—64no—
217#391—64no—
218#390—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×C3—21no—
244C24×C3—21no—
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×D3—21no—
262C23×D3—21no—
263C23×D3—21no—
264C23×D3—21no—
265C23×D3—21no—
266C23×D3—21no—
267C23×D3—21no—
268C23×D3—21no—
269C23×D3—21no—
270C23×D3—21no—
271C23×D3—21no—
272C23×D3—21no—
273C23×D3—21no—
274C23×D3—21no—
275C23×D3C2×D412yes—
276C23×D3C2×D412yes—
277C2×C3×Q8—28no—
278C2×C3×Q8—28no—
279C2×C3×Q8—44no—
280C2×C3×Q8—44no—
281C2×C3×Q8—44no—
282C2×C3×Q8—44no—
283C2×C3×Q8—44no—
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×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4C2×D412yes—
320C22×C3×C4C2×D412yes—
321C22×C3×C4C2×D412yes—
322C22×C3×C4C2×D412yes—
323C22×C3×C4C2×D412yes—
324C22×C3×C4C2×D412yes—
325C22×C3×C4#4112yes—
326C2×#67—28no—
327C2×#67—44no—
328C2×#67—44no—
329C2×#67—44no—
330C2×#67—44no—
331C2×#67—44no—
332C2×#67—44no—
333C2×#67—44no—
334C2×#67—44no—
335C2×#67—44no—
336C2×#67—44no—
337C2×#67—44no—
338C2×#67—44no—
339C2×#67—44no—
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—21no—
352C22×Dic3—21no—
353C22×Dic3—21no—
354C22×Dic3—21no—
355C22×Dic3—21no—
356C22×Dic3—21no—
357C22×Dic3—21no—
358C22×Dic3—21no—
359C22×Dic3—21no—
360C22×Dic3—21no—
361C22×Dic3—21no—
362C22×Dic3—21no—
363C22×Dic3—21no—
364C22×Dic3—21no—
365C22×Dic3—21no—
366C22×Dic3—21no—
367C22×Dic3—21no—
368C22×Dic3—21no—
369C22×Dic3—21no—
370C22×Dic3—21no—
371C22×Dic3—21no—
372C22×Dic3—21no—
373C22×Dic3—21no—
374C22×Dic3—21no—
375C22×Dic3C2×D412yes—
376C22×Dic3C2×D412yes—
377C22×Dic3C2×D412yes—
378C22×Dic3C2×D412yes—
379C22×Dic3#4112yes—
380C22×Dic3#4112yes—
381C22×Dic3#4112yes—
382C2×D12—28no—
383C2×D12—44no—
384C2×D12—44no—
385C2×D12—44no—
386C2×D12—44no—
387C2×D12—44no—
388C2×D12—44no—
389C3×C22⋊C4—44no—
390C3×C22⋊C4—44no—
391C3×C22⋊C4—44no—
392#217—44no—
393#217—44no—
394(C2×D3)⋊C4—28no—
395(C2×D3)⋊C4—28no—
396(C2×D3)⋊C4—28no—
397(C2×D3)⋊C4—28no—
398(C2×D3)⋊C4—44no—
399(C2×D3)⋊C4—44no—
400(C2×D3)⋊C4—44no—
401(C2×D3)⋊C4—44no—
402(C2×D3)⋊C4—44no—
403(C2×D3)⋊C4—44no—
404C4⋊Dic3—44no—
405Dic3⋊C4—44no—
406C4×Dic3—28no—
407C4×Dic3—44no—
408C25—31no—
409C25—31no—
410C25C22×D311yescharacteristic
411C22×Q8—22no—
412C22×Q8—22no—
413C22×Q8—22no—
414C22×Q8—22no—
415C22×Q8—41no—
416C22×Q8—41no—
417C22×Q8#6714yescomplemented
418C22×D4—62no—
419C22×D4—62no—
420C22×D4—62no—
421C22×D4—62no—
422C22×D4—62no—
423C22×D4—62no—
424C22×D4—62no—
425C22×D4—62no—
426C22×D4—62no—
427C22×D4—62no—
428C22×D4—62no—
429C22×D4—62no—
430C22×D4—62no—
431C22×D4—121no—
432C22×D4—121no—
433C22×D4—121no—
434C22×D4—121no—
435C22×D4—121no—
436C22×D4—121no—
437C22×D4—121no—
438C22×D4—121no—
439C23×C4—31no—
440C23×C4—31no—
441C23×C4—31no—
442C23×C4—31no—
443C23×C4—31no—
444C23×C4—31no—
445C23×C4C22×D311yescharacteristic
446C23×C4C22×D311yescharacteristic
447C23×C4C22×D311yescharacteristic
448C23×C4C22×D311yescharacteristic
449C23×C4C22×D311yescharacteristic
450C23×C4C22×D311yescharacteristic
451#124—632no—
452C2×C4⋊C4—62no—
453C2×C4⋊C4—62no—
454C2×C4⋊C4—62no—
455C2×C4⋊C4—62no—
456C2×C4⋊C4—121no—
457C2×C4⋊C4—121no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—34no—
466C2×C22⋊C4—34no—
467C2×C22⋊C4—41no—
468C2×C22⋊C4—41no—
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—62no—
484C2×C22⋊C4—62no—
485C2×C22⋊C4—62no—
486C2×C22⋊C4—62no—
487C2×C22⋊C4—62no—
488C2×C22⋊C4—62no—
489C2×C22⋊C4—62no—
490C2×C22⋊C4—62no—
491C2×C22⋊C4—121no—
492C2×C22⋊C4—121no—
493C2×C22⋊C4—121no—
494C2×C22⋊C4—121no—
495C2×C22⋊C4—121no—
496C2×C22⋊C4—121no—
497C2×C22⋊C4—121no—
498C2×C22⋊C4—121no—
499C2×C22⋊C4—121no—
500C2×C22⋊C4—121no—
501C2×C22⋊C4—121no—
502C2×C22⋊C4—121no—
503C2×C42—62no—
504C2×C42—62no—
505C2×C42—62no—
506C2×C42—62no—
507C2×C42—62no—
508C2×C42—121no—
509#95—22no—
510#95—22no—
511#95—22no—
512#95—34no—
513#95—62no—
514#95—62no—
515#95—62no—
516#95—62no—
517#95—62no—
518#95—121no—
519#95—121no—
520#95—121no—
521C23×C3—22no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—22no—
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×C3—41no—
539C23×C3—41no—
540C23×C3—41no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—41no—
546C23×C3—41no—
547C23×C3—41no—
548C23×C3—41no—
549C23×C3—41no—
550C23×C3—41no—
551C23×C3—41no—
552C23×C3—41no—
553C23×C3—41no—
554C23×C3—41no—
555C23×C3—41no—
556C23×C3C22×D411yescharacteristic
557C23×C3C22×D411yescharacteristic
558C23×C3C22×D411yescharacteristic
559C23×C3C22×D411yescharacteristic
560C23×C3C2×#4111yescharacteristic
561C23×C3C2×#4111yescharacteristic
562C23×C3C2×#4111yescharacteristic
563C23×C3C2×#4111yescharacteristic
564C23×C3C2×#4111yescharacteristic
565C23×C3H(5,𝔽2)11yescharacteristic
566C23×C3H(5,𝔽2)11yescharacteristic
567C23×C3H(5,𝔽2)11yescharacteristic
568C23×C3H(5,𝔽2)11yescharacteristic
569C23×C3H(5,𝔽2)11yescharacteristic
570C23×C32−1+411yescharacteristic
571C22×D3—22no—
572C22×D3—22no—
573C22×D3—22no—
574C22×D3—22no—
575C22×D3—22no—
576C22×D3—22no—
577C22×D3—22no—
578C22×D3—22no—
579C22×D3—22no—
580C22×D3—22no—
581C22×D3—22no—
582C22×D3—22no—
583C22×D3—22no—
584C22×D3—22no—
585C22×D3—41no—
586C22×D3—41no—
587C22×D3—41no—
588C22×D3—41no—
589C22×D3—41no—
590C22×D3—41no—
591C22×D3—41no—
592C22×D3—41no—
593C22×D3—41no—
594C22×D3—41no—
595C22×D3—41no—
596C22×D3—41no—
597C22×D3—41no—
598C22×D3—41no—
599C22×D3—41no—
600C22×D3—41no—
601C22×D3—41no—
602C22×D3—41no—
603C22×D3—41no—
604C22×D3—41no—
605C22×D3—41no—
606C22×D3—41no—
607C22×D3—41no—
608C22×D3—41no—
609C22×D3—41no—
610C22×D3—41no—
611C22×D3—41no—
612C22×D3—41no—
613C22×D3—41no—
614C22×D3—41no—
615C22×D3—41no—
616C22×D3—41no—
617C22×D3—41no—
618C22×D3—41no—
619C22×D3—41no—
620C22×D3—41no—
621C22×D3—41no—
622C22×D3—41no—
623C22×D3—41no—
624C22×D3—41no—
625C22×D3—41no—
626C22×D3—41no—
627C22×D3—41no—
628C22×D3—41no—
629C22×D3—41no—
630C22×D3—41no—
631C22×D3—41no—
632C22×D3—41no—
633C22×D3—41no—
634C22×D3—41no—
635C22×D3—41no—
636C22×D3—41no—
637C22×D3—41no—
638C22×D3—41no—
639C22×D3—41no—
640C22×D3—41no—
641C3×Q8—416no—
642C2×C3×C4—22no—
643C2×C3×C4—22no—
644C2×C3×C4—22no—
645C2×C3×C4—22no—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4—22no—
654C2×C3×C4—22no—
655C2×C3×C4—22no—
656C2×C3×C4—22no—
657C2×C3×C4—41no—
658C2×C3×C4—41no—
659C2×C3×C4—41no—
660C2×C3×C4—41no—
661C2×C3×C4—41no—
662C2×C3×C4—41no—
663C2×C3×C4—41no—
664C2×C3×C4—41no—
665C2×C3×C4—41no—
666C2×C3×C4—41no—
667C2×C3×C4—41no—
668C2×C3×C4—41no—
669C2×C3×C4—41no—
670C2×C3×C4—41no—
671C2×C3×C4—41no—
672C2×C3×C4—41no—
673C2×C3×C4—41no—
674C2×C3×C4—41no—
675C2×C3×C4—41no—
676C2×C3×C4—41no—
677C2×C3×C4—41no—
678C2×C3×C4—41no—
679C2×C3×C4—41no—
680C2×C3×C4—41no—
681C2×C3×C4—41no—
682C2×C3×C4#12014yes—
683C2×C3×C4#12114yes—
684#67—416no—
685#67—416no—
686C2×Dic3—22no—
687C2×Dic3—22no—
688C2×Dic3—22no—
689C2×Dic3—22no—
690C2×Dic3—22no—
691C2×Dic3—22no—
692C2×Dic3—22no—
693C2×Dic3—22no—
694C2×Dic3—22no—
695C2×Dic3—22no—
696C2×Dic3—22no—
697C2×Dic3—22no—
698C2×Dic3—22no—
699C2×Dic3—22no—
700C2×Dic3—22no—
701C2×Dic3—22no—
702C2×Dic3—22no—
703C2×Dic3—22no—
704C2×Dic3—41no—
705C2×Dic3—41no—
706C2×Dic3—41no—
707C2×Dic3—41no—
708C2×Dic3—41no—
709C2×Dic3—41no—
710C2×Dic3—41no—
711C2×Dic3—41no—
712C2×Dic3—41no—
713C2×Dic3—41no—
714C2×Dic3—41no—
715C2×Dic3—41no—
716C2×Dic3—41no—
717C2×Dic3—41no—
718C2×Dic3—41no—
719C2×Dic3—41no—
720C2×Dic3—41no—
721C2×Dic3—41no—
722C2×Dic3—41no—
723C2×Dic3—41no—
724C2×Dic3—41no—
725C2×Dic3—41no—
726C2×Dic3—41no—
727C2×Dic3#12414yescomplemented
728D12—416no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—32no—
744C24—32no—
745C24—61no—
746C24—61no—
747C24—61no—
748C24—61no—
749C24—61no—
750C24—61no—
751C24—61no—
752C24—61no—
753C24—61no—
754C24—61no—
755C24—61no—
756C24—61no—
757C24—61no—
758C24—61no—
759C24—61no—
760C24—61no—
761C24—61no—
762C24—61no—
763C24—61no—
764C24—61no—
765C24—61no—
766C24—61no—
767C24—61no—
768C24—61no—
769C24—61no—
770C24—61no—
771C24—61no—
772C24—61no—
773C24#23912yes—
774C24C23×D311yescharacteristic
775C2×Q8—28no—
776C2×Q8—28no—
777C2×Q8—44no—
778C2×Q8—44no—
779C2×Q8—44no—
780C2×Q8—44no—
781C2×Q8—44no—
782C2×D4—68no—
783C2×D4—68no—
784C2×D4—124no—
785C2×D4—124no—
786C2×D4—124no—
787C2×D4—124no—
788C2×D4—124no—
789C2×D4—124no—
790C2×D4—124no—
791C2×D4—124no—
792C2×D4—124no—
793C2×D4—124no—
794C2×D4—124no—
795C2×D4—124no—
796C2×D4—124no—
797C2×D4—124no—
798C2×D4—124no—
799C2×D4—124no—
800C2×D4—124no—
801C2×D4—124no—
802C2×D4—124no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—32no—
839C22×C4—32no—
840C22×C4—32no—
841C22×C4—32no—
842C22×C4—32no—
843C22×C4—32no—
844C22×C4—32no—
845C22×C4—61no—
846C22×C4—61no—
847C22×C4—61no—
848C22×C4—61no—
849C22×C4—61no—
850C22×C4—61no—
851C22×C4—61no—
852C22×C4—61no—
853C22×C4—61no—
854C22×C4—61no—
855C22×C4—61no—
856C22×C4—61no—
857C22×C4—61no—
858C22×C4—61no—
859C22×C4—61no—
860C22×C4—61no—
861C22×C4—61no—
862C22×C4—61no—
863C22×C4—61no—
864C22×C4—61no—
865C22×C4—61no—
866C22×C4—61no—
867C22×C4—61no—
868C22×C4—61no—
869C22×C4—61no—
870C22×C4—61no—
871C22×C4—61no—
872C22×C4—61no—
873C22×C4—61no—
874C22×C4—61no—
875C22×C4—61no—
876C22×C4—61no—
877C22×C4—61no—
878C22×C4—61no—
879C22×C4—61no—
880C22×C4D3×D412yes—
881C22×C4D3×D412yes—
882C22×C4D3×D412yes—
883C22×C4#23712yes—
884C22×C4C2×#6712yes—
885C22×C4C2×#6712yes—
886C22×C4C2×#6712yes—
887C4⋊C4—124no—
888C4⋊C4—124no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—68no—
893C22⋊C4—68no—
894C22⋊C4—68no—
895C22⋊C4—68no—
896C22⋊C4—124no—
897C22⋊C4—124no—
898C22⋊C4—124no—
899C22⋊C4—124no—
900C22⋊C4—124no—
901C22⋊C4—124no—
902C22⋊C4—124no—
903C22⋊C4—124no—
904C42—68no—
905C42—124no—
906C22×C3—42no—
907C22×C3—42no—
908C22×C3—42no—
909C22×C3—42no—
910C22×C3—42no—
911C22×C3—42no—
912C22×C3—42no—
913C22×C3—81no—
914C22×C3—81no—
915C22×C3—81no—
916C22×C3—81no—
917C22×C3—81no—
918C22×C3—81no—
919C22×C3—81no—
920C22×C3—81no—
921C22×C3C2×#12011yescharacteristic
922C22×C3C2×#12111yescharacteristic
923C22×C3#52511yescharacteristic
924C22×C3C2×#12411yescharacteristic
925C22×C3#52911yescharacteristic
926C22×C3#53211yescharacteristic
927C22×C3#53411yescharacteristic
928C22×C3#53511yescharacteristic
929C22×C3#53511yescharacteristic
930C22×C3#53711yescharacteristic
931C22×C3#53811yescharacteristic
932C22×C3#53811yescharacteristic
933C22×C3#53811yescharacteristic
934C22×C3#54211yescharacteristic
935C22×C3#54211yescharacteristic
936C22×C3D4211yescharacteristic
937C22×C3D4211yescharacteristic
938C22×C3#54611yescharacteristic
939C22×C3#54611yescharacteristic
940C22×C3#54611yescharacteristic
941C22×C3#54611yescharacteristic
942C22×C3#54611yescharacteristic
943C22×C3#54611yescharacteristic
944C22×C3#54711yescharacteristic
945C22×C3#54811yescharacteristic
946C22×C3#54811yescharacteristic
947C22×C3#55011yescharacteristic
948C22×C3#55011yescharacteristic
949C22×C3#55011yescharacteristic
950C22×C3#55111yescharacteristic
951C22×C3#55511yescharacteristic
952C22×C3#55911yescharacteristic
953C22×C3#55911yescharacteristic
954C22×C3H(3,𝔽4)11yescharacteristic
955C22×C3#56211yescharacteristic
956C2×D3—42no—
957C2×D3—42no—
958C2×D3—42no—
959C2×D3—42no—
960C2×D3—42no—
961C2×D3—42no—
962C2×D3—42no—
963C2×D3—42no—
964C2×D3—42no—
965C2×D3—42no—
966C2×D3—42no—
967C2×D3—42no—
968C2×D3—42no—
969C2×D3—42no—
970C2×D3—81no—
971C2×D3—81no—
972C2×D3—81no—
973C2×D3—81no—
974C2×D3—81no—
975C2×D3—81no—
976C2×D3—81no—
977C2×D3—81no—
978C2×D3—81no—
979C2×D3—81no—
980C2×D3—81no—
981C2×D3—81no—
982C2×D3—81no—
983C2×D3—81no—
984C2×D3—81no—
985C2×D3—81no—
986C3×C4—24no—
987C3×C4—24no—
988C3×C4—42no—
989C3×C4—81no—
990C3×C4—81no—
991C3×C4—81no—
992Dic3—24no—
993Dic3—42no—
994Dic3—42no—
995Dic3—42no—
996Dic3—42no—
997Dic3—81no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—62no—
1034C23—62no—
1035C23—62no—
1036C23—62no—
1037C23—62no—
1038C23—62no—
1039C23—62no—
1040C23—62no—
1041C23—62no—
1042C23—62no—
1043C23—62no—
1044C23—62no—
1045C23—62no—
1046C23—62no—
1047C23—121no—
1048C23—121no—
1049C23—121no—
1050C23—121no—
1051C23—121no—
1052C23—121no—
1053C23—121no—
1054C23—121no—
1055C23—121no—
1056C23—121no—
1057C23—121no—
1058C23—121no—
1059C23—121no—
1060C23—121no—
1061C23—121no—
1062C23—121no—
1063C23—121no—
1064C23—121no—
1065C23—121no—
1066C23—121no—
1067C23—121no—
1068C23—121no—
1069C23—121no—
1070C23—121no—
1071C23—121no—
1072C23—121no—
1073C23—121no—
1074C23—121no—
1075C23—121no—
1076C23—121no—
1077C23—121no—
1078C23—121no—
1079C23—121no—
1080C23—121no—
1081C23—121no—
1082C23—121no—
1083C23—121no—
1084C23—121no—
1085C23—121no—
1086C23—121no—
1087C23—121no—
1088C23—121no—
1089C23—121no—
1090C23—121no—
1091C23—121no—
1092C23—121no—
1093C23—121no—
1094C23—121no—
1095C23—121no—
1096C23—121no—
1097C23—121no—
1098C23—121no—
1099C23—121no—
1100C23—121no—
1101C23—121no—
1102C23—121no—
1103C23C2×D3×D411yescharacteristic
1104C23C2×D3×D411yescharacteristic
1105C23C2×D3×D411yescharacteristic
1106C23C2×#23711yescharacteristic
1107C23#100411yescharacteristic
1108C23#100411yescharacteristic
1109C23C2×#23911yescharacteristic
1110C23#100711yescharacteristic
1111C23D3×#4111yescharacteristic
1112C23D3×#4111yescharacteristic
1113C23D3×#4111yescharacteristic
1114C23#100911yescharacteristic
1115C23#100911yescharacteristic
1116C23#100911yescharacteristic
1117C23C22×#6711yescharacteristic
1118Q8—416no—
1119D4—1216no—
1120D4—1216no—
1121D4—1216no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—34no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—62no—
1164C2×C4—62no—
1165C2×C4—62no—
1166C2×C4—62no—
1167C2×C4—62no—
1168C2×C4—62no—
1169C2×C4—62no—
1170C2×C4—62no—
1171C2×C4—62no—
1172C2×C4—62no—
1173C2×C4—62no—
1174C2×C4—62no—
1175C2×C4—62no—
1176C2×C4—62no—
1177C2×C4—62no—
1178C2×C4—62no—
1179C2×C4—62no—
1180C2×C4—62no—
1181C2×C4—121no—
1182C2×C4—121no—
1183C2×C4—121no—
1184C2×C4—121no—
1185C2×C4—121no—
1186C2×C4—121no—
1187C2×C4—121no—
1188C2×C4—121no—
1189C2×C4—121no—
1190C2×C4—121no—
1191C2×C4—121no—
1192C2×C4—121no—
1193C2×C4—121no—
1194C2×C4—121no—
1195C2×C4—121no—
1196C2×C4—121no—
1197C2×C4—121no—
1198C2×C4—121no—
1199C2×C4—121no—
1200C2×C4—121no—
1201C2×C4—121no—
1202C2×C4—121no—
1203C2×C4—121no—
1204C2×C4#93714yes—
1205C2×C4#93914yes—
1206C2×C3—82no—
1207C2×C3#240711yescharacteristic
1208C2×C3#241011yescharacteristic
1209C2×C3#242611yescharacteristic
1210C2×C3#243111yescharacteristic
1211C2×C3#245911yescharacteristic
1212C2×C3#247211yescharacteristic
1213C2×C3#249111yescharacteristic
1214C2×C3#254811yescharacteristic
1215C2×C3#255711yescharacteristic
1216C2×C3#267011yescharacteristic
1217C2×C3#267611yescharacteristic
1218C2×C3#271011yescharacteristic
1219C2×C3#271211yescharacteristic
1220C2×C3#273011yescharacteristic
1221C2×C3#273311yescharacteristic
1222D3—82no—
1223D3—82no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—122no—
1240C22—122no—
1241C22—122no—
1242C22—122no—
1243C22—122no—
1244C22—122no—
1245C22—122no—
1246C22—122no—
1247C22—122no—
1248C22—122no—
1249C22—122no—
1250C22—122no—
1251C22—122no—
1252C22—122no—
1253C22—241no—
1254C22—241no—
1255C22—241no—
1256C22—241no—
1257C22—241no—
1258C22—241no—
1259C22—241no—
1260C22—241no—
1261C22—241no—
1262C22—241no—
1263C22—241no—
1264C22—241no—
1265C22—241no—
1266C22—241no—
1267C22—241no—
1268C22—241no—
1269C22#559011yescharacteristic
1270C22#559011yescharacteristic
1271C22#559111yescharacteristic
1272C22#559111yescharacteristic
1273C22#562411yescharacteristic
1274C22#562711yescharacteristic
1275C22#562911yescharacteristic
1276C22#563011yescharacteristic
1277C22#563011yescharacteristic
1278C22#563111yescharacteristic
1279C22#563311yescharacteristic
1280C22#563711yescharacteristic
1281C22#564011yescharacteristic
1282C22#564311yescharacteristic
1283C22#564411yescharacteristic
1284C22#564711yescharacteristic
1285C22#566811yescharacteristic
1286C22#567011yescharacteristic
1287C22D3×#12411yescharacteristic
1288C22#567411yescharacteristic
1289C22#567411yescharacteristic
1290C22#567611yescharacteristic
1291C22#567611yescharacteristic
1292C22#567811yescharacteristic
1293C22#567811yescharacteristic
1294C22#568111yescharacteristic
1295C22#568111yescharacteristic
1296C22#568311yescharacteristic
1297C22C2×#93711yescharacteristic
1298C22C2×#93911yescharacteristic
1299C22#580411yescharacteristic
1300C22#581711yescharacteristic
1301C22#583411yescharacteristic
1302C22#583411yescharacteristic
1303C22#583411yescharacteristic
1304C4—24no—
1305C4—24no—
1306C4—42no—
1307C4—64no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—122no—
1312C4—122no—
1313C4—122no—
1314C4—122no—
1315C4—241no—
1316C3#1531711yescharacteristic, complemented, Sylow
1317C2—82no—
1318C2—242no—
1319C2—242no—
1320C2#7678611yescharacteristic
1321C2#7679011yescharacteristic
1322C2#7679211yescharacteristic
1323C2#7679711yescharacteristic
1324C2#7682211yescharacteristic
1325C2#7682911yescharacteristic
1326C2#7687311yescharacteristic
1327C2#7688011yescharacteristic
1328C2#8260611yescharacteristic
1329C2#8275511yescharacteristic
1330C2#8280611yescharacteristic
1331C2#8281211yescharacteristic
1332C2#8295811yescharacteristic
1333C2#8297411yescharacteristic
1334C2#8299111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#393C2
prime radicalC2×#4960C2
hypercenterC2×#393D3
hypocenterC3#15317
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C22×#947C2semidirect
2. C2×C3×#393C2semidirect
3. C2×#5229C2semidirect
5. C2×#4961C2semidirect
6. C2×#4957C2semidirect
7. #71550C2semidirect
8. #71550C2semidirect
9. #71545C2semidirect
10. #69429C2semidirect
11. #69428C2semidirect
12. #69427C2semidirect
13. #69426C2semidirect
14. #69408C2semidirect
15. #69406C2semidirect
62. C2×#393D3semidirect
84. C22×C3×Q8D4semidirect
162. C2×(C2×D3)⋊C4D4semidirect
163. C2×(C2×D3)⋊C4D4semidirect
417. C22×Q8#67semidirect
727. C2×Dic3#124semidirect
1316. C3#15317semidirect

Maximal subgroups

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

subgroupindex
C22×#9472
C2×C3×#3932
C2×#52292
C2×#49602
C2×#49612
C2×#49572
#715502
#715452
#694292
#694282
#694272
#694262
#694082
#694062
#153173