Finite Group Databasebeta

← #10733668

Subgroups — #10733668

Order 768.

2442 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#884C211yesmaximal, characteristic
2C2×#4991C211yesmaximal, characteristic, complemented
3C2×#4972C211yesmaximal, characteristic, complemented
4C2×#4959C211yesmaximal, characteristic, complemented
5C2×#4961C211yesmaximal, characteristic, complemented
6C2×#4957C211yesmaximal, characteristic, complemented
7C2×#4676C211yesmaximal, characteristic, complemented
8C2×#4668C211yesmaximal, characteristic, complemented
9C3×#1439C211yesmaximal, characteristic, complemented
10#71550C211yesmaximal, characteristic, complemented
11#71547C211yesmaximal, characteristic, complemented
12#69426C211yesmaximal, characteristic, complemented
13(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
14#69409C211yesmaximal, characteristic, complemented
15#69408C211yesmaximal, characteristic, complemented
16#15316—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×D12C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×Dic3⋊C4C2211yescharacteristic
41C22×C4×Dic3C2211yescharacteristic
42C2×#884—24no—
43C2×#884—24no—
44C2×#884—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
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55#4991—24no—
56#4972—24no—
57#4961—24no—
58#4959—24no—
59#4957—24no—
60#4676—24no—
61#4668—24no—
62C22×#121—31no—
63C2×#396—31no—
64C2×#394—31no—
65C2×#394—31no—
66C2×#394—31no—
67C2×#390—31no—
68C2×#389—31no—
69C2×#385—31no—
70#1441—31no—
71#1439—31no—
72#1439D311yescharacteristic, complemented
73#1438—31no—
74#1438—31no—
75#1437—31no—
76C22⋊#95—31no—
77C25×C3C2311yescharacteristic
78C24×D3C2311yescharacteristic
79C24×D3C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C22×#67—22no—
87C22×#67—22no—
88C22×#67—22no—
89C22×#67—22no—
90C22×#67—22no—
91C22×#67—22no—
92C22×#67—22no—
93C22×#67—22no—
94C22×#67—22no—
95C22×#67—41no—
96C22×#67—41no—
97C22×#67—41no—
98C22×#67—41no—
99C22×#67D414yes—
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C22×D12—22no—
107C22×D12—22no—
108C22×D12—22no—
109C22×D12—22no—
110C22×D12—22no—
111C22×D12—41no—
112C22×D12—41no—
113C22×C4×D3—22no—
114C22×C4×D3—22no—
115C22×C4×D3—22no—
116C22×C4×D3—22no—
117C22×C4×D3—22no—
118C22×C4×D3—41no—
119C22×C4×D3—41no—
120C2×C3×C4⋊C4—22no—
121C2×C3×C4⋊C4—22no—
122C2×C3×C4⋊C4—41no—
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×C3×C22⋊C4—41no—
132C2×#217—22no—
133C2×#217—22no—
134C2×#217—22no—
135C2×#217—22no—
136C2×#217—41no—
137C2×#217—41no—
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—22no—
153C2×(C2×D3)⋊C4—22no—
154C2×(C2×D3)⋊C4—22no—
155C2×(C2×D3)⋊C4—22no—
156C2×(C2×D3)⋊C4—22no—
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)⋊C4—41no—
163C2×(C2×D3)⋊C4D414yes—
164C2×(C2×D3)⋊C4D414yescomplemented
165C2×C4⋊Dic3—22no—
166C2×C4⋊Dic3—22no—
167C2×C4⋊Dic3D414yescomplemented
168C2×Dic3⋊C4—22no—
169C2×Dic3⋊C4—22no—
170C2×Dic3⋊C4—22no—
171C2×Dic3⋊C4—22no—
172C2×Dic3⋊C4—22no—
173C2×Dic3⋊C4—22no—
174C2×Dic3⋊C4—22no—
175C2×Dic3⋊C4—22no—
176C2×Dic3⋊C4—22no—
177C2×Dic3⋊C4—41no—
178C2×Dic3⋊C4—41no—
179C2×Dic3⋊C4D414yes—
180C2×C4×Dic3—22no—
181C2×C4×Dic3—22no—
182C2×C4×Dic3—41no—
183#884—232no—
184C3×#95—22no—
185C3×#95—22no—
186C3×#95—41no—
187C3⋊#95—22no—
188C3⋊#95—22no—
189C3⋊#95—22no—
190C3⋊#95—22no—
191C3⋊#95—22no—
192C3⋊#95—22no—
193C3⋊#95—41no—
194C23×D4—31no—
195C23×D4—31no—
196C23×D4—31no—
197C24×C4—31no—
198C2×#121—64no—
199C2×#121—64no—
200C2×#121—64no—
201C22×C4⋊C4—31no—
202C22×C4⋊C4—31no—
203C22×C4⋊C4—31no—
204C22×C4⋊C4—31no—
205C22×C4⋊C4—31no—
206C22×C4⋊C4C2×D311yescharacteristic
207C22×C22⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4—31no—
210C22×C22⋊C4—31no—
211C22×C22⋊C4—31no—
212C22×C22⋊C4—31no—
213C22×C22⋊C4—31no—
214C22×C22⋊C4—31no—
215C22×C22⋊C4—31no—
216C22×C22⋊C4—31no—
217C22×C22⋊C4—31no—
218C22×C22⋊C4C2×D311yescharacteristic
219C22×C22⋊C4C2×D311yescharacteristic
220C22×C22⋊C4C2×D311yescharacteristic
221C22×C42—31no—
222#396—64no—
223#394—64no—
224#394—64no—
225#394—64no—
226#390—64no—
227#389—64no—
228#385—64no—
229C2×#95—31no—
230C2×#95—31no—
231C2×#95—31no—
232C2×#95—31no—
233C2×#95—31no—
234C2×#95—31no—
235C2×#95—31no—
236C2×#95C2×D311yescharacteristic
237C2×#95C2×D311yescharacteristic
238C2×#95C2×D311yescharacteristic
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×C3C2×D412yes—
254C24×C3C2411yescharacteristic
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×D3—21no—
276C23×D3—21no—
277C23×D3—21no—
278C23×D3—21no—
279C23×D3—21no—
280C23×D3—21no—
281C23×D3C2×D412yes—
282C23×D3C2×D412yes—
283C23×D3C2×D412yes—
284C23×D3#4112yes—
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×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4C2×D412yes—
323C22×C3×C4C2×D412yes—
324C22×C3×C4C2×D412yes—
325C22×C3×C4C2×D412yes—
326C22×C3×C4#4112yes—
327C2×#67—28no—
328C2×#67—28no—
329C2×#67—28no—
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—
340C2×#67—44no—
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×Dic3C2×D412yes—
375C22×Dic3C2×D412yes—
376C22×Dic3C2×D412yes—
377C22×Dic3C2×D412yes—
378C22×Dic3C2×D412yes—
379C22×Dic3C2×D412yes—
380C22×Dic3C2×D412yes—
381C22×Dic3#4112yes—
382C22×Dic3#4112yes—
383C2×D12—28no—
384C2×D12—44no—
385C2×D12—44no—
386C2×D12—44no—
387C2×D12—44no—
388C2×D12—44no—
389C2×D12—44no—
390C2×C4×D3—28no—
391C2×C4×D3—44no—
392C2×C4×D3—44no—
393C2×C4×D3—44no—
394C2×C4×D3—44no—
395C2×C4×D3—44no—
396C2×C4×D3—44no—
397C3×C4⋊C4—44no—
398C3×C22⋊C4—28no—
399C3×C22⋊C4—44no—
400C3×C22⋊C4—44no—
401#217—44no—
402#217—44no—
403(C2×D3)⋊C4—28no—
404(C2×D3)⋊C4—28no—
405(C2×D3)⋊C4—44no—
406(C2×D3)⋊C4—44no—
407(C2×D3)⋊C4—44no—
408(C2×D3)⋊C4—44no—
409(C2×D3)⋊C4—44no—
410(C2×D3)⋊C4—44no—
411(C2×D3)⋊C4—44no—
412C4⋊Dic3—28no—
413Dic3⋊C4—28no—
414Dic3⋊C4—44no—
415Dic3⋊C4—44no—
416Dic3⋊C4—44no—
417C4×Dic3—44no—
418C25—31no—
419C25—31no—
420C25C22×D311yescharacteristic
421C22×D4—34no—
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—62no—
432C22×D4—62no—
433C22×D4—62no—
434C22×D4—62no—
435C22×D4—62no—
436C22×D4—121no—
437C22×D4—121no—
438C22×D4—121no—
439C22×D4—121no—
440C22×D4—121no—
441C22×D4—121no—
442C23×C4—31no—
443C23×C4—31no—
444C23×C4—31no—
445C23×C4—31no—
446C23×C4—31no—
447C23×C4—31no—
448C23×C4—62no—
449C23×C4—62no—
450C23×C4—62no—
451C23×C4—62no—
452C23×C4—62no—
453C23×C4—121no—
454C23×C4—121no—
455C23×C4C22×D311yescharacteristic
456C23×C4C22×D311yescharacteristic
457C23×C4C22×D311yescharacteristic
458C23×C4C22×D311yescharacteristic
459C23×C4C22×D311yescharacteristic
460C23×C4C22×D311yescharacteristic
461#121—632no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—34no—
465C2×C4⋊C4—34no—
466C2×C4⋊C4—41no—
467C2×C4⋊C4—62no—
468C2×C4⋊C4—62no—
469C2×C4⋊C4—62no—
470C2×C4⋊C4—62no—
471C2×C4⋊C4—62no—
472C2×C4⋊C4—62no—
473C2×C4⋊C4—62no—
474C2×C4⋊C4—62no—
475C2×C4⋊C4—62no—
476C2×C4⋊C4—62no—
477C2×C4⋊C4—62no—
478C2×C4⋊C4—121no—
479C2×C4⋊C4—121no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—34no—
488C2×C22⋊C4—34no—
489C2×C22⋊C4—41no—
490C2×C22⋊C4—41no—
491C2×C22⋊C4—62no—
492C2×C22⋊C4—62no—
493C2×C22⋊C4—62no—
494C2×C22⋊C4—62no—
495C2×C22⋊C4—62no—
496C2×C22⋊C4—62no—
497C2×C22⋊C4—62no—
498C2×C22⋊C4—62no—
499C2×C22⋊C4—62no—
500C2×C22⋊C4—62no—
501C2×C22⋊C4—62no—
502C2×C22⋊C4—62no—
503C2×C22⋊C4—62no—
504C2×C22⋊C4—62no—
505C2×C22⋊C4—62no—
506C2×C22⋊C4—62no—
507C2×C22⋊C4—62no—
508C2×C22⋊C4—62no—
509C2×C22⋊C4—62no—
510C2×C22⋊C4—62no—
511C2×C22⋊C4—62no—
512C2×C22⋊C4—62no—
513C2×C22⋊C4—62no—
514C2×C22⋊C4—121no—
515C2×C22⋊C4—121no—
516C2×C22⋊C4—121no—
517C2×C22⋊C4—121no—
518C2×C22⋊C4—121no—
519C2×C22⋊C4—121no—
520C2×C22⋊C4—121no—
521C2×C22⋊C4—121no—
522C2×C42—62no—
523C2×C42—62no—
524C2×C42—121no—
525#95—22no—
526#95—22no—
527#95—41no—
528#95—62no—
529#95—62no—
530#95—62no—
531#95—62no—
532#95—62no—
533#95—62no—
534#95—121no—
535C23×C3—22no—
536C23×C3—22no—
537C23×C3—22no—
538C23×C3—22no—
539C23×C3—22no—
540C23×C3—22no—
541C23×C3—22no—
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×C3C22×D411yescharacteristic
571C23×C3C22×D411yescharacteristic
572C23×C3C22×D411yescharacteristic
573C23×C3C22×D411yescharacteristic
574C23×C3C22×D411yescharacteristic
575C23×C3C2×#4111yescharacteristic
576C23×C3C2×#4111yescharacteristic
577C23×C3C2×#4111yescharacteristic
578C23×C3C2×#4111yescharacteristic
579C23×C3H(5,𝔽2)11yescharacteristic
580C23×C3H(5,𝔽2)11yescharacteristic
581C23×C3H(5,𝔽2)11yescharacteristic
582C23×C3H(5,𝔽2)11yescharacteristic
583C23×C32−1+411yescharacteristic
584C23×C32−1+411yescharacteristic
585C22×D3—22no—
586C22×D3—22no—
587C22×D3—22no—
588C22×D3—22no—
589C22×D3—22no—
590C22×D3—22no—
591C22×D3—22no—
592C22×D3—22no—
593C22×D3—22no—
594C22×D3—22no—
595C22×D3—22no—
596C22×D3—22no—
597C22×D3—22no—
598C22×D3—22no—
599C22×D3—22no—
600C22×D3—22no—
601C22×D3—22no—
602C22×D3—22no—
603C22×D3—22no—
604C22×D3—22no—
605C22×D3—22no—
606C22×D3—22no—
607C22×D3—22no—
608C22×D3—22no—
609C22×D3—22no—
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—
641C22×D3—41no—
642C22×D3—41no—
643C22×D3—41no—
644C22×D3—41no—
645C22×D3—41no—
646C22×D3—41no—
647C22×D3—41no—
648C22×D3—41no—
649C22×D3—41no—
650C22×D3—41no—
651C22×D3—41no—
652C22×D3—41no—
653C22×D3—41no—
654C22×D3#12114yes—
655C2×C3×C4—22no—
656C2×C3×C4—22no—
657C2×C3×C4—22no—
658C2×C3×C4—22no—
659C2×C3×C4—22no—
660C2×C3×C4—22no—
661C2×C3×C4—22no—
662C2×C3×C4—22no—
663C2×C3×C4—22no—
664C2×C3×C4—22no—
665C2×C3×C4—22no—
666C2×C3×C4—22no—
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—41no—
683C2×C3×C4—41no—
684C2×C3×C4—41no—
685C2×C3×C4—41no—
686C2×C3×C4—41no—
687C2×C3×C4—41no—
688C2×C3×C4—41no—
689C2×C3×C4—41no—
690C2×C3×C4—41no—
691C2×C3×C4—41no—
692C2×C3×C4—41no—
693C2×C3×C4—41no—
694C2×C3×C4—41no—
695C2×C3×C4—41no—
696C2×C3×C4#12114yescomplemented
697#67—416no—
698#67—416no—
699C2×Dic3—22no—
700C2×Dic3—22no—
701C2×Dic3—22no—
702C2×Dic3—22no—
703C2×Dic3—22no—
704C2×Dic3—22no—
705C2×Dic3—22no—
706C2×Dic3—22no—
707C2×Dic3—22no—
708C2×Dic3—22no—
709C2×Dic3—22no—
710C2×Dic3—22no—
711C2×Dic3—22no—
712C2×Dic3—22no—
713C2×Dic3—22no—
714C2×Dic3—22no—
715C2×Dic3—22no—
716C2×Dic3—22no—
717C2×Dic3—22no—
718C2×Dic3—22no—
719C2×Dic3—22no—
720C2×Dic3—41no—
721C2×Dic3—41no—
722C2×Dic3—41no—
723C2×Dic3—41no—
724C2×Dic3—41no—
725C2×Dic3—41no—
726C2×Dic3—41no—
727C2×Dic3—41no—
728C2×Dic3—41no—
729C2×Dic3—41no—
730C2×Dic3—41no—
731C2×Dic3—41no—
732C2×Dic3—41no—
733C2×Dic3—41no—
734C2×Dic3—41no—
735C2×Dic3—41no—
736C2×Dic3—41no—
737C2×Dic3—41no—
738C2×Dic3—41no—
739C2×Dic3#12014yes—
740C2×Dic3#12114yes—
741D12—416no—
742C4×D3—416no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—32no—
758C24—32no—
759C24—32no—
760C24—32no—
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—61no—
774C24—61no—
775C24—61no—
776C24—61no—
777C24—61no—
778C24—61no—
779C24—61no—
780C24—61no—
781C24—61no—
782C24—61no—
783C24—61no—
784C24—61no—
785C24—61no—
786C24—61no—
787C24D3×D412yes—
788C24C23×D311yescharacteristic
789C2×D4—68no—
790C2×D4—68no—
791C2×D4—68no—
792C2×D4—68no—
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—
803C2×D4—124no—
804C2×D4—124no—
805C2×D4—124no—
806C2×D4—124no—
807C2×D4—124no—
808C2×D4—124no—
809C2×D4—124no—
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—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—32no—
848C22×C4—32no—
849C22×C4—32no—
850C22×C4—32no—
851C22×C4—32no—
852C22×C4—32no—
853C22×C4—32no—
854C22×C4—32no—
855C22×C4—32no—
856C22×C4—68no—
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×C4—61no—
881C22×C4—61no—
882C22×C4—61no—
883C22×C4—61no—
884C22×C4—61no—
885C22×C4—61no—
886C22×C4—61no—
887C22×C4—61no—
888C22×C4—61no—
889C22×C4—61no—
890C22×C4—124no—
891C22×C4—124no—
892C22×C4—124no—
893C22×C4—124no—
894C22×C4—124no—
895C22×C4—124no—
896C22×C4#23512yes—
897C22×C4D3×D412yes—
898C22×C4D3×D412yes—
899C22×C4D3×D412yes—
900C22×C4D3×D412yes—
901C4⋊C4—44no—
902C4⋊C4—68no—
903C4⋊C4—68no—
904C4⋊C4—124no—
905C4⋊C4—124no—
906C4⋊C4—124no—
907C22⋊C4—28no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—68no—
911C22⋊C4—68no—
912C22⋊C4—124no—
913C22⋊C4—124no—
914C22⋊C4—124no—
915C22⋊C4—124no—
916C22⋊C4—124no—
917C22⋊C4—124no—
918C22⋊C4—124no—
919C22⋊C4—124no—
920C22⋊C4—124no—
921C42—124no—
922C22×C3—42no—
923C22×C3—42no—
924C22×C3—42no—
925C22×C3—42no—
926C22×C3—42no—
927C22×C3—42no—
928C22×C3—42no—
929C22×C3—81no—
930C22×C3—81no—
931C22×C3—81no—
932C22×C3—81no—
933C22×C3—81no—
934C22×C3—81no—
935C22×C3—81no—
936C22×C3—81no—
937C22×C3C2×#12011yescharacteristic
938C22×C3C2×#12111yescharacteristic
939C22×C3C2×#12111yescharacteristic
940C22×C3C2×#12111yescharacteristic
941C22×C3#52911yescharacteristic
942C22×C3#53211yescharacteristic
943C22×C3#53411yescharacteristic
944C22×C3#53511yescharacteristic
945C22×C3#53611yescharacteristic
946C22×C3#53711yescharacteristic
947C22×C3#53711yescharacteristic
948C22×C3#53811yescharacteristic
949C22×C3#53911yescharacteristic
950C22×C3#54011yescharacteristic
951C22×C3#54211yescharacteristic
952C22×C3D4211yescharacteristic
953C22×C3D4211yescharacteristic
954C22×C3D4211yescharacteristic
955C22×C3D4211yescharacteristic
956C22×C3#54611yescharacteristic
957C22×C3#54611yescharacteristic
958C22×C3#54611yescharacteristic
959C22×C3#54611yescharacteristic
960C22×C3#54611yescharacteristic
961C22×C3#54711yescharacteristic
962C22×C3#54711yescharacteristic
963C22×C3#54711yescharacteristic
964C22×C3#54811yescharacteristic
965C22×C3#54811yescharacteristic
966C22×C3#54811yescharacteristic
967C22×C3#55011yescharacteristic
968C22×C3#55311yescharacteristic
969C22×C3#55311yescharacteristic
970C22×C3#56211yescharacteristic
971C22×C3#56211yescharacteristic
972C2×D3—24no—
973C2×D3—24no—
974C2×D3—24no—
975C2×D3—42no—
976C2×D3—42no—
977C2×D3—42no—
978C2×D3—42no—
979C2×D3—42no—
980C2×D3—42no—
981C2×D3—42no—
982C2×D3—42no—
983C2×D3—42no—
984C2×D3—42no—
985C2×D3—42no—
986C2×D3—42no—
987C2×D3—42no—
988C2×D3—42no—
989C2×D3—42no—
990C2×D3—42no—
991C2×D3—42no—
992C2×D3—42no—
993C2×D3—42no—
994C2×D3—81no—
995C2×D3—81no—
996C2×D3—81no—
997C2×D3—81no—
998C2×D3—81no—
999C2×D3—81no—
1000C2×D3—81no—
1001C2×D3—81no—
1002C3×C4—24no—
1003C3×C4—42no—
1004C3×C4—42no—
1005C3×C4—81no—
1006C3×C4—81no—
1007C3×C4—81no—
1008Dic3—24no—
1009Dic3—24no—
1010Dic3—42no—
1011Dic3—42no—
1012Dic3—42no—
1013Dic3—81no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—34no—
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—62no—
1051C23—62no—
1052C23—62no—
1053C23—62no—
1054C23—62no—
1055C23—62no—
1056C23—62no—
1057C23—62no—
1058C23—62no—
1059C23—62no—
1060C23—62no—
1061C23—62no—
1062C23—62no—
1063C23—62no—
1064C23—62no—
1065C23—62no—
1066C23—62no—
1067C23—62no—
1068C23—62no—
1069C23—62no—
1070C23—62no—
1071C23—62no—
1072C23—62no—
1073C23—62no—
1074C23—62no—
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—
1103C23—121no—
1104C23—121no—
1105C23—121no—
1106C23—121no—
1107C23—121no—
1108C23—121no—
1109C23—121no—
1110C23—121no—
1111C23—121no—
1112C23—121no—
1113C23—121no—
1114C23—121no—
1115C23—121no—
1116C23—121no—
1117C23—121no—
1118C23—121no—
1119C23C2×#23511yescharacteristic
1120C23C2×D3×D411yescharacteristic
1121C23C2×D3×D411yescharacteristic
1122C23C2×D3×D411yescharacteristic
1123C23C2×D3×D411yescharacteristic
1124C23C2×D3×D411yescharacteristic
1125C23#100411yescharacteristic
1126C23#100411yescharacteristic
1127C23#100711yescharacteristic
1128C23D3×#4111yescharacteristic
1129C23D3×#4111yescharacteristic
1130C23D3×#4111yescharacteristic
1131C23#100911yescharacteristic
1132C23#100911yescharacteristic
1133C23#101011yescharacteristic
1134D4—1216no—
1135D4—1216no—
1136D4—1216no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—34no—
1150C2×C4—34no—
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—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—62no—
1181C2×C4—62no—
1182C2×C4—62no—
1183C2×C4—62no—
1184C2×C4—62no—
1185C2×C4—62no—
1186C2×C4—62no—
1187C2×C4—62no—
1188C2×C4—62no—
1189C2×C4—62no—
1190C2×C4—62no—
1191C2×C4—62no—
1192C2×C4—62no—
1193C2×C4—62no—
1194C2×C4—62no—
1195C2×C4—62no—
1196C2×C4—62no—
1197C2×C4—62no—
1198C2×C4—62no—
1199C2×C4—62no—
1200C2×C4—62no—
1201C2×C4—1216no—
1202C2×C4—121no—
1203C2×C4—121no—
1204C2×C4—121no—
1205C2×C4—121no—
1206C2×C4—121no—
1207C2×C4—121no—
1208C2×C4—121no—
1209C2×C4—121no—
1210C2×C4—121no—
1211C2×C4—121no—
1212C2×C4—121no—
1213C2×C4—121no—
1214C2×C4—121no—
1215C2×C4—121no—
1216C2×C4—121no—
1217C2×C4—121no—
1218C2×C4—121no—
1219C2×C4—121no—
1220C2×C4—121no—
1221C2×C4#88414yescomplemented
1222C2×C3—82no—
1223C2×C3#240811yescharacteristic
1224C2×C3#241011yescharacteristic
1225C2×C3#241611yescharacteristic
1226C2×C3#241611yescharacteristic
1227C2×C3#242511yescharacteristic
1228C2×C3#242611yescharacteristic
1229C2×C3#242811yescharacteristic
1230C2×C3#243211yescharacteristic
1231C2×C3#255911yescharacteristic
1232C2×C3#267211yescharacteristic
1233C2×C3#267611yescharacteristic
1234C2×C3#268111yescharacteristic
1235C2×C3#268211yescharacteristic
1236C2×C3#270111yescharacteristic
1237C2×C3#271111yescharacteristic
1238D3—44no—
1239D3—82no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—64no—
1248C22—64no—
1249C22—64no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—122no—
1259C22—122no—
1260C22—122no—
1261C22—122no—
1262C22—122no—
1263C22—122no—
1264C22—122no—
1265C22—122no—
1266C22—122no—
1267C22—122no—
1268C22—122no—
1269C22—122no—
1270C22—122no—
1271C22—122no—
1272C22—122no—
1273C22—122no—
1274C22—122no—
1275C22—122no—
1276C22—122no—
1277C22—241no—
1278C22—241no—
1279C22—241no—
1280C22—241no—
1281C22—241no—
1282C22—241no—
1283C22—241no—
1284C22—241no—
1285C22C2×#88411yescharacteristic
1286C22#550711yescharacteristic
1287C22#553011yescharacteristic
1288C22#554011yescharacteristic
1289C22#554811yescharacteristic
1290C22#555211yescharacteristic
1291C22#556211yescharacteristic
1292C22D3×#12011yescharacteristic
1293C22#558911yescharacteristic
1294C22#559011yescharacteristic
1295C22#559711yescharacteristic
1296C22#559911yescharacteristic
1297C22D3×#12111yescharacteristic
1298C22D3×#12111yescharacteristic
1299C22#560911yescharacteristic
1300C22#560911yescharacteristic
1301C22#561011yescharacteristic
1302C22#561211yescharacteristic
1303C22#562811yescharacteristic
1304C22#562911yescharacteristic
1305C22#563311yescharacteristic
1306C22#563311yescharacteristic
1307C22#564011yescharacteristic
1308C22#564711yescharacteristic
1309C22#565411yescharacteristic
1310C22#565411yescharacteristic
1311C22#565511yescharacteristic
1312C22#565511yescharacteristic
1313C22#566711yescharacteristic
1314C22#567411yescharacteristic
1315C22#567611yescharacteristic
1316C22#567811yescharacteristic
1317C22#570611yescharacteristic
1318C22#570711yescharacteristic
1319C22#571711yescharacteristic
1320C4—24no—
1321C4—42no—
1322C4—42no—
1323C4—64no—
1324C4—64no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—122no—
1329C4—122no—
1330C4—122no—
1331C4—241no—
1332C3#1531611yescharacteristic, complemented, Sylow
1333C2—82no—
1334C2—124no—
1335C2—242no—
1336C2#7388711yescharacteristic
1337C2#7441111yescharacteristic
1338C2#7463611yescharacteristic
1339C2#7469211yescharacteristic
1340C2#7569111yescharacteristic
1341C2#7588811yescharacteristic
1342C2#7644411yescharacteristic
1343C2#7675511yescharacteristic
1344C2#7682211yescharacteristic
1345C2#7689511yescharacteristic
1346C2#7700711yescharacteristic
1347C2#7728611yescharacteristic
1348C2#7743111yescharacteristic
1349C2#7767211yescharacteristic
1350C2#7811411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1439C2
prime radicalC22×#884C2
hypercenter#1439D3
hypocenterC3#15316
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#4991C2semidirect
3. C2×#4972C2semidirect
4. C2×#4959C2semidirect
5. C2×#4961C2semidirect
6. C2×#4957C2semidirect
7. C2×#4676C2semidirect
8. C2×#4668C2semidirect
9. C3×#1439C2semidirect
10. #71550C2semidirect
11. #71547C2semidirect
12. #69426C2semidirect
13. (C2×D3)⋊#95C2semidirect
14. #69409C2semidirect
15. #69408C2semidirect
72. #1439D3semidirect
164. C2×(C2×D3)⋊C4D4semidirect
167. C2×C4⋊Dic3D4semidirect
696. C2×C3×C4#121semidirect
1221. C2×C4#884semidirect
1332. C3#15316semidirect

Maximal subgroups

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

subgroupindex
C22×#8842
C2×#49912
C2×#49722
C2×#49592
C2×#49612
C2×#49572
C2×#46762
C2×#46682
C3×#14392
#715502
#715472
#694262
(C2×D3)⋊#952
#694092
#694082
#153163