Finite Group Databasebeta

← #10740297

Subgroups — #10740297

Order 768.

2138 conjugacy classes of subgroups.

The subgroup lattice has 1324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5223C211yesmaximal, characteristic
2C2×#4959C211yesmaximal, characteristic, complemented
3C2×#4949C211yesmaximal, characteristic, complemented
4C2×#4948C211yesmaximal, characteristic, complemented
5C2×#4957C211yesmaximal, characteristic, complemented
6C2×#4957C211yesmaximal, characteristic, complemented
7C2×#4945C211yesmaximal, characteristic, complemented
8C2×#4652C211yesmaximal, characteristic, complemented
9C3×#1438C211yesmaximal, characteristic, complemented
10#72131C211yesmaximal, characteristic, complemented
11#71550C211yesmaximal, characteristic, complemented
12#71545C211yesmaximal, characteristic, complemented
13#69428C211yesmaximal, characteristic, complemented
14#69427C211yesmaximal, characteristic, complemented
15#69406C211yesmaximal, characteristic, complemented
16#15776—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×C4⋊Dic3C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×C4×Dic3C2211yescharacteristic
41C22×C4×Dic3C2211yescharacteristic
42C2×C3×#95C2211yescharacteristic
43C2×C3×#95C2211yescharacteristic
44#5223—24no—
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53#4959—24no—
54#4957—24no—
55#4957—24no—
56#4949—24no—
57#4948—24no—
58#4945—24no—
59#4652—24no—
60C2×#399—31no—
61C2×#396—31no—
62C2×#394—31no—
63C2×#392—31no—
64C2×#390—31no—
65C2×#390—31no—
66C2×#388—31no—
67C2×#387—31no—
68#1439—31no—
69#1439—31no—
70#1438—31no—
71#1438—31no—
72#1438D311yescharacteristic, complemented
73#1437—31no—
74#1436—31no—
75C25×C3C2311yescharacteristic
76C25×C3C2311yescharacteristic
77C24×D3C2311yescharacteristic
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—22no—
81C22×C3×D4—41no—
82C22×C3×D4—41no—
83C22×C3×D4—41no—
84C22×C3×D4—41no—
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C22×#67—22no—
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—22no—
100C22×#67—41no—
101C22×#67—41no—
102C22×#67—41no—
103C22×#67—41no—
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C23×Dic3C2311yescharacteristic
109C23×Dic3C2311yescharacteristic
110C23×Dic3C2311yescharacteristic
111C2×C3×C22⋊C4—22no—
112C2×C3×C22⋊C4—22no—
113C2×C3×C22⋊C4—22no—
114C2×C3×C22⋊C4—22no—
115C2×C3×C22⋊C4—22no—
116C2×C3×C22⋊C4—22no—
117C2×C3×C22⋊C4—22no—
118C2×C3×C22⋊C4—41no—
119C2×C3×C22⋊C4—41no—
120C2×C3×C22⋊C4—41no—
121C2×C3×C22⋊C4—41no—
122C2×C3×C22⋊C4—41no—
123C2×#217—22no—
124C2×#217—22no—
125C2×#217—22no—
126C2×#217—22no—
127C2×#217—22no—
128C2×#217—22no—
129C2×#217—22no—
130C2×#217—22no—
131C2×#217—22no—
132C2×#217—22no—
133C2×#217—22no—
134C2×#217—22no—
135C2×#217—22no—
136C2×#217—22no—
137C2×#217—22no—
138C2×#217—41no—
139C2×#217—41no—
140C2×#217—41no—
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—41no—
151C2×(C2×D3)⋊C4—41no—
152C2×(C2×D3)⋊C4—41no—
153C2×(C2×D3)⋊C4—41no—
154C2×(C2×D3)⋊C4—41no—
155C2×(C2×D3)⋊C4—41no—
156C2×C4⋊Dic3—22no—
157C2×C4⋊Dic3—22no—
158C2×C4⋊Dic3—41no—
159C2×Dic3⋊C4—22no—
160C2×Dic3⋊C4—22no—
161C2×Dic3⋊C4—22no—
162C2×Dic3⋊C4—22no—
163C2×Dic3⋊C4—22no—
164C2×Dic3⋊C4—22no—
165C2×Dic3⋊C4—22no—
166C2×Dic3⋊C4—41no—
167C2×Dic3⋊C4—41no—
168C2×Dic3⋊C4—41no—
169C2×Dic3⋊C4D414yescomplemented
170C2×Dic3⋊C4D414yescomplemented
171C2×C4×Dic3—22no—
172C2×C4×Dic3—22no—
173C2×C4×Dic3—22no—
174C2×C4×Dic3—22no—
175C2×C4×Dic3—41no—
176C2×C4×Dic3—41no—
177C3×#95—22no—
178C3×#95—41no—
179C3⋊#95—22no—
180C3⋊#95—22no—
181C3⋊#95—22no—
182C3⋊#95—22no—
183C3⋊#95—22no—
184C3⋊#95—41no—
185C3⋊#95D414yes—
186C3⋊#95D414yescomplemented
187C23×D4—31no—
188C23×D4—31no—
189C23×D4C2×D311yescharacteristic
190C22×C4⋊C4—31no—
191C22×C4⋊C4—31no—
192C22×C4⋊C4—31no—
193C22×C4⋊C4—31no—
194C22×C4⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊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⋊C4C2×D311yescharacteristic
207C22×C22⋊C4C2×D311yescharacteristic
208C22×C22⋊C4C2×D311yescharacteristic
209C22×C22⋊C4C2×D311yescharacteristic
210C22×C42—31no—
211C22×C42—31no—
212#399—64no—
213#396—64no—
214#394—64no—
215#392—64no—
216#390—64no—
217#390—64no—
218#388—64no—
219#387—64no—
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
230C24×C3—21no—
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—21no—
246C24×C3—21no—
247C24×C3—21no—
248C24×C3—21no—
249C24×C3—21no—
250C24×C3—21no—
251C24×C3—21no—
252C24×C3—21no—
253C24×C3—21no—
254C24×C3—21no—
255C24×C3—21no—
256C24×C3—21no—
257C24×C3—21no—
258C24×C3#4112yes—
259C24×C3#4112yes—
260C24×C3C2411yescharacteristic
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×D3#4112yes—
276C2×C3×D4—44no—
277C2×C3×D4—44no—
278C2×C3×D4—44no—
279C2×C3×D4—44no—
280C2×C3×D4—44no—
281C2×C3×D4—44no—
282C2×C3×D4—44no—
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×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×C4C2×D412yes—
315C22×C3×C4C2×D412yes—
316C22×C3×C4C2×D412yes—
317C22×C3×C4C2×D412yes—
318C2×#67—28no—
319C2×#67—28no—
320C2×#67—44no—
321C2×#67—44no—
322C2×#67—44no—
323C2×#67—44no—
324C2×#67—44no—
325C2×#67—44no—
326C2×#67—44no—
327C2×#67—44no—
328C2×#67—44no—
329C2×#67—44no—
330C2×#67—44no—
331C2×#67—44no—
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—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×Dic3C2×D412yes—
372C22×Dic3C2×D412yes—
373C22×Dic3C2×D412yes—
374C22×Dic3C2×D412yes—
375C22×Dic3C2×D412yes—
376C22×Dic3C2×D412yes—
377C22×Dic3C2×D412yes—
378C22×Dic3C2×D412yes—
379C22×Dic3#4112yes—
380C22×Dic3#4112yes—
381C3×C22⋊C4—44no—
382C3×C22⋊C4—44no—
383C3×C22⋊C4—44no—
384C3×C22⋊C4—44no—
385#217—28no—
386#217—44no—
387#217—44no—
388#217—44no—
389#217—44no—
390#217—44no—
391(C2×D3)⋊C4—44no—
392(C2×D3)⋊C4—44no—
393(C2×D3)⋊C4—44no—
394(C2×D3)⋊C4—44no—
395(C2×D3)⋊C4—44no—
396C4⋊Dic3—44no—
397Dic3⋊C4—28no—
398Dic3⋊C4—44no—
399Dic3⋊C4—44no—
400Dic3⋊C4—44no—
401C4×Dic3—44no—
402C4×Dic3—44no—
403C25—31no—
404C25C22×D311yescharacteristic
405C25C22×D311yescharacteristic
406C22×D4—22no—
407C22×D4—22no—
408C22×D4—22no—
409C22×D4—41no—
410C22×D4—41no—
411C22×D4—41no—
412C22×D4—41no—
413C22×D4—62no—
414C22×D4—62no—
415C22×D4—62no—
416C22×D4—62no—
417C22×D4—62no—
418C22×D4—62no—
419C22×D4—62no—
420C22×D4—62no—
421C22×D4—62no—
422C22×D4—62no—
423C22×D4—121no—
424C22×D4—121no—
425C22×D4—121no—
426C22×D4—121no—
427C23×C4—31no—
428C23×C4—31no—
429C23×C4—31no—
430C23×C4—31no—
431C23×C4—31no—
432C23×C4—31no—
433C23×C4—31no—
434C23×C4C22×D311yescharacteristic
435C23×C4C22×D311yescharacteristic
436C23×C4C22×D311yescharacteristic
437C23×C4C22×D311yescharacteristic
438C23×C4C22×D311yescharacteristic
439C2×C4⋊C4—34no—
440C2×C4⋊C4—34no—
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—121no—
451C2×C4⋊C4—121no—
452C2×C4⋊C4—121no—
453C2×C4⋊C4—121no—
454C2×C22⋊C4—22no—
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—41no—
462C2×C22⋊C4—41no—
463C2×C22⋊C4—41no—
464C2×C22⋊C4—41no—
465C2×C22⋊C4—41no—
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—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—121no—
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×C42—62no—
500C2×C42—62no—
501C2×C42—62no—
502C2×C42—62no—
503C2×C42—121no—
504C2×C42—121no—
505#95—22no—
506#95—34no—
507#95—34no—
508#95—41no—
509#95—62no—
510#95—62no—
511#95—62no—
512#95—62no—
513#95—62no—
514#95—121no—
515C23×C3—22no—
516C23×C3—22no—
517C23×C3—22no—
518C23×C3—22no—
519C23×C3—22no—
520C23×C3—22no—
521C23×C3—22no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—22no—
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×C3—41no—
557C23×C3—41no—
558C23×C3—41no—
559C23×C3—41no—
560C23×C3—41no—
561C23×C3—41no—
562C23×C3—41no—
563C23×C3—41no—
564C23×C3—41no—
565C23×C3—41no—
566C23×C3—41no—
567C23×C3—41no—
568C23×C3—41no—
569C23×C3—41no—
570C23×C3—41no—
571C23×C3—41no—
572C23×C3—41no—
573C23×C3—41no—
574C23×C3—41no—
575C23×C3—41no—
576C23×C3—41no—
577C23×C3—41no—
578C23×C3—41no—
579C23×C3—41no—
580C23×C3—41no—
581C23×C3—41no—
582C23×C3—41no—
583C23×C3—41no—
584C23×C3—41no—
585C23×C3C22×D411yescharacteristic
586C23×C3C22×D411yescharacteristic
587C23×C3C22×D411yescharacteristic
588C23×C3C22×D411yescharacteristic
589C23×C3C2×#4111yescharacteristic
590C23×C3C2×#4111yescharacteristic
591C23×C3C2×#4111yescharacteristic
592C23×C3C2×#4111yescharacteristic
593C23×C3C2×#4111yescharacteristic
594C23×C3H(5,𝔽2)11yescharacteristic
595C23×C3H(5,𝔽2)11yescharacteristic
596C23×C3H(5,𝔽2)11yescharacteristic
597C23×C3H(5,𝔽2)11yescharacteristic
598C23×C3H(5,𝔽2)11yescharacteristic
599C23×C32−1+411yescharacteristic
600C22×D3—22no—
601C22×D3—22no—
602C22×D3—22no—
603C22×D3—22no—
604C22×D3—22no—
605C22×D3—22no—
606C22×D3—22no—
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—
635C3×D4—416no—
636C2×C3×C4—22no—
637C2×C3×C4—22no—
638C2×C3×C4—22no—
639C2×C3×C4—22no—
640C2×C3×C4—22no—
641C2×C3×C4—22no—
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—41no—
649C2×C3×C4—41no—
650C2×C3×C4—41no—
651C2×C3×C4—41no—
652C2×C3×C4—41no—
653C2×C3×C4—41no—
654C2×C3×C4—41no—
655C2×C3×C4—41no—
656C2×C3×C4—41no—
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—
671#67—416no—
672#67—416no—
673C2×Dic3—22no—
674C2×Dic3—22no—
675C2×Dic3—22no—
676C2×Dic3—22no—
677C2×Dic3—22no—
678C2×Dic3—22no—
679C2×Dic3—22no—
680C2×Dic3—22no—
681C2×Dic3—22no—
682C2×Dic3—22no—
683C2×Dic3—22no—
684C2×Dic3—22no—
685C2×Dic3—22no—
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—41no—
698C2×Dic3—41no—
699C2×Dic3—41no—
700C2×Dic3—41no—
701C2×Dic3—41no—
702C2×Dic3—41no—
703C2×Dic3—41no—
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#12114yes—
721C2×Dic3#12714yes—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
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—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—32no—
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#23512yes—
766C24#23712yes—
767C24C23×D311yescharacteristic
768C2×D4—44no—
769C2×D4—44no—
770C2×D4—44no—
771C2×D4—44no—
772C2×D4—44no—
773C2×D4—44no—
774C2×D4—44no—
775C2×D4—68no—
776C2×D4—68no—
777C2×D4—124no—
778C2×D4—124no—
779C2×D4—124no—
780C2×D4—124no—
781C2×D4—124no—
782C2×D4—124no—
783C2×D4—124no—
784C2×D4—124no—
785C2×D4—124no—
786C2×D4—124no—
787C2×D4—124no—
788C2×D4—124no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
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—32no—
821C22×C4—32no—
822C22×C4—32no—
823C22×C4—32no—
824C22×C4—32no—
825C22×C4—32no—
826C22×C4—32no—
827C22×C4—32no—
828C22×C4—32no—
829C22×C4—32no—
830C22×C4—61no—
831C22×C4—61no—
832C22×C4—61no—
833C22×C4—61no—
834C22×C4—61no—
835C22×C4—61no—
836C22×C4—61no—
837C22×C4—61no—
838C22×C4—61no—
839C22×C4—61no—
840C22×C4—61no—
841C22×C4—61no—
842C22×C4—61no—
843C22×C4—61no—
844C22×C4—61no—
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×C4D3×D412yes—
870C22×C4D3×D412yes—
871C22×C4D3×D412yes—
872C22×C4D3×D412yes—
873C4⋊C4—68no—
874C4⋊C4—124no—
875C4⋊C4—124no—
876C4⋊C4—124no—
877C4⋊C4—124no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—68no—
883C22⋊C4—124no—
884C22⋊C4—124no—
885C22⋊C4—124no—
886C22⋊C4—124no—
887C22⋊C4—124no—
888C22⋊C4—124no—
889C22⋊C4—124no—
890C22⋊C4—124no—
891C22⋊C4—124no—
892C22⋊C4—124no—
893C42—124no—
894C42—124no—
895C22×C3—42no—
896C22×C3—42no—
897C22×C3—42no—
898C22×C3—42no—
899C22×C3—42no—
900C22×C3—42no—
901C22×C3—42no—
902C22×C3—42no—
903C22×C3—42no—
904C22×C3—42no—
905C22×C3—42no—
906C22×C3—42no—
907C22×C3—42no—
908C22×C3—42no—
909C22×C3—81no—
910C22×C3—81no—
911C22×C3—81no—
912C22×C3—81no—
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×C3—81no—
922C22×C3—81no—
923C22×C3—81no—
924C22×C3—81no—
925C22×C3C2×#12111yescharacteristic
926C22×C3#52511yescharacteristic
927C22×C3#52511yescharacteristic
928C22×C3#52511yescharacteristic
929C22×C3#52911yescharacteristic
930C22×C3C2×#12711yescharacteristic
931C22×C3#53411yescharacteristic
932C22×C3#53511yescharacteristic
933C22×C3#53511yescharacteristic
934C22×C3#53711yescharacteristic
935C22×C3#53811yescharacteristic
936C22×C3#53811yescharacteristic
937C22×C3#53911yescharacteristic
938C22×C3#54011yescharacteristic
939C22×C3#54211yescharacteristic
940C22×C3D4211yescharacteristic
941C22×C3D4211yescharacteristic
942C22×C3#54611yescharacteristic
943C22×C3#54611yescharacteristic
944C22×C3#54611yescharacteristic
945C22×C3#54611yescharacteristic
946C22×C3#54611yescharacteristic
947C22×C3#54611yescharacteristic
948C22×C3#54811yescharacteristic
949C22×C3#54811yescharacteristic
950C22×C3#54811yescharacteristic
951C22×C3#55011yescharacteristic
952C22×C3#55011yescharacteristic
953C22×C3#55011yescharacteristic
954C22×C3#55111yescharacteristic
955C22×C3#55111yescharacteristic
956C22×C3#55111yescharacteristic
957C22×C3#55311yescharacteristic
958C22×C3#56011yescharacteristic
959C22×C3#56211yescharacteristic
960C2×D3—42no—
961C2×D3—42no—
962C2×D3—42no—
963C2×D3—42no—
964C2×D3—42no—
965C2×D3—42no—
966C2×D3—42no—
967C2×D3—81no—
968C2×D3—81no—
969C2×D3—81no—
970C2×D3—81no—
971C2×D3—81no—
972C2×D3—81no—
973C2×D3—81no—
974C2×D3—81no—
975C3×C4—42no—
976C3×C4—42no—
977C3×C4—42no—
978C3×C4—42no—
979C3×C4—81no—
980Dic3—24no—
981Dic3—24no—
982Dic3—42no—
983Dic3—42no—
984Dic3—42no—
985Dic3—42no—
986Dic3—81no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
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—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—62no—
1058C23—62no—
1059C23—62no—
1060C23—62no—
1061C23—62no—
1062C23—62no—
1063C23—62no—
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—
1092C23C2×#23511yescharacteristic
1093C23C2×D3×D411yescharacteristic
1094C23C2×D3×D411yescharacteristic
1095C23C2×D3×D411yescharacteristic
1096C23C2×D3×D411yescharacteristic
1097C23C2×#23711yescharacteristic
1098C23#100411yescharacteristic
1099C23#100411yescharacteristic
1100C23#100411yescharacteristic
1101C23#100411yescharacteristic
1102C23#100411yescharacteristic
1103C23D3×#4111yescharacteristic
1104C23D3×#4111yescharacteristic
1105C23D3×#4111yescharacteristic
1106C23#101011yescharacteristic
1107D4—416no—
1108D4—1216no—
1109D4—1216no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—34no—
1123C2×C4—34no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
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—62no—
1148C2×C4—62no—
1149C2×C4—62no—
1150C2×C4—62no—
1151C2×C4—62no—
1152C2×C4—62no—
1153C2×C4—62no—
1154C2×C4—62no—
1155C2×C4—62no—
1156C2×C4—62no—
1157C2×C4—62no—
1158C2×C4—62no—
1159C2×C4—62no—
1160C2×C4—62no—
1161C2×C4—62no—
1162C2×C4—62no—
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—121no—
1172C2×C4—121no—
1173C2×C4—121no—
1174C2×C4—121no—
1175C2×C4—121no—
1176C2×C4—121no—
1177C2×C4—121no—
1178C2×C4—121no—
1179C2×C4—121no—
1180C2×C4—121no—
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×C3—82no—
1195C2×C3—82no—
1196C2×C3#241111yescharacteristic
1197C2×C3#242611yescharacteristic
1198C2×C3#245611yescharacteristic
1199C2×C3#246311yescharacteristic
1200C2×C3#246711yescharacteristic
1201C2×C3#247111yescharacteristic
1202C2×C3#253911yescharacteristic
1203C2×C3#254011yescharacteristic
1204C2×C3#254111yescharacteristic
1205C2×C3#267311yescharacteristic
1206C2×C3#267611yescharacteristic
1207C2×C3#268511yescharacteristic
1208C2×C3#270511yescharacteristic
1209C2×C3#271111yescharacteristic
1210C2×C3#273011yescharacteristic
1211D3—82no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—122no—
1243C22—122no—
1244C22—122no—
1245C22—122no—
1246C22—122no—
1247C22—122no—
1248C22—122no—
1249C22—241no—
1250C22—241no—
1251C22—241no—
1252C22—241no—
1253C22—241no—
1254C22—241no—
1255C22—241no—
1256C22—241no—
1257C22#549011yescharacteristic
1258C22#549411yescharacteristic
1259C22#549511yescharacteristic
1260C22#554711yescharacteristic
1261C22#554711yescharacteristic
1262C22#555211yescharacteristic
1263C22#555611yescharacteristic
1264C22#558911yescharacteristic
1265C22#559011yescharacteristic
1266C22#559011yescharacteristic
1267C22#559111yescharacteristic
1268C22#559111yescharacteristic
1269C22#559211yescharacteristic
1270C22#559311yescharacteristic
1271C22#559511yescharacteristic
1272C22#559711yescharacteristic
1273C22#559811yescharacteristic
1274C22#559911yescharacteristic
1275C22#559911yescharacteristic
1276C22#559911yescharacteristic
1277C22D3×#12111yescharacteristic
1278C22#560611yescharacteristic
1279C22#561011yescharacteristic
1280C22#561211yescharacteristic
1281C22#561211yescharacteristic
1282C22#561511yescharacteristic
1283C22#562111yescharacteristic
1284C22#564911yescharacteristic
1285C22#566011yescharacteristic
1286C22#566111yescharacteristic
1287C22#566211yescharacteristic
1288C22#567711yescharacteristic
1289C22#567911yescharacteristic
1290C22D3×#12711yescharacteristic
1291C22#571511yescharacteristic
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—42no—
1296C4—64no—
1297C4—64no—
1298C4—81no—
1299C4—122no—
1300C4—122no—
1301C4—122no—
1302C4—122no—
1303C4—241no—
1304C3#1577611yescharacteristic, complemented, Sylow
1305C2—82no—
1306C2—82no—
1307C2—242no—
1308C2#7383811yescharacteristic
1309C2#7472411yescharacteristic
1310C2#7482911yescharacteristic
1311C2#7489911yescharacteristic
1312C2#7490011yescharacteristic
1313C2#7634711yescharacteristic
1314C2#7643711yescharacteristic
1315C2#7668811yescharacteristic
1316C2#7671111yescharacteristic
1317C2#7671411yescharacteristic
1318C2#7675811yescharacteristic
1319C2#7690111yescharacteristic
1320C2#7692111yescharacteristic
1321C2#7702511yescharacteristic
1322C2#7703411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1438C2
prime radicalC2×#5223C2
hypercenter#1438D3
hypocenterC3#15776
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#4959C2semidirect
3. C2×#4949C2semidirect
4. C2×#4948C2semidirect
5. C2×#4957C2semidirect
6. C2×#4957C2semidirect
7. C2×#4945C2semidirect
8. C2×#4652C2semidirect
9. C3×#1438C2semidirect
10. #72131C2semidirect
11. #71550C2semidirect
12. #71545C2semidirect
13. #69428C2semidirect
14. #69427C2semidirect
15. #69406C2semidirect
72. #1438D3semidirect
169. C2×Dic3⋊C4D4semidirect
170. C2×Dic3⋊C4D4semidirect
186. C3⋊#95D4semidirect
1304. C3#15776semidirect

Maximal subgroups

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

subgroupindex
C2×#52232
C2×#49592
C2×#49492
C2×#49482
C2×#49572
C2×#49452
C2×#46522
C3×#14382
#721312
#715502
#715452
#694282
#694272
#694062
#157763