Finite Group Databasebeta

← #10727867

Subgroups — #10727867

Order 768.

2278 conjugacy classes of subgroups.

The subgroup lattice has 1340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#394C211yesmaximal, characteristic, complemented
2C2×#5223C211yesmaximal, characteristic
3C2×#5221C211yesmaximal, characteristic, complemented
4C2×#4994C211yesmaximal, characteristic, complemented
5C2×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
6C2×#4948C211yesmaximal, characteristic, complemented
7C2×#4961C211yesmaximal, characteristic, complemented
8C2×#4957C211yesmaximal, characteristic, complemented
9C2×#4957C211yesmaximal, characteristic, complemented
10C2×#4945C211yesmaximal, characteristic, complemented
11#71550C211yesmaximal, characteristic, complemented
12#71547C211yesmaximal, characteristic, complemented
13#71545C211yesmaximal, characteristic, complemented
14#69420C211yesmaximal, characteristic, complemented
15#69408C211yesmaximal, characteristic, complemented
16#14815—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×C4⋊Dic3C2211yescharacteristic
37C22×C4⋊Dic3C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×Dic3⋊C4C2211yescharacteristic
41C22×C4×Dic3C2211yescharacteristic
42C22×C4×Dic3C2211yescharacteristic
43C22×C4×Dic3C2211yescharacteristic
44C3×#394—24no—
45C2×C3×#95C2211yescharacteristic
46#5223—24no—
47#5221—24no—
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55#4994—24no—
56Dic3×C4⋊C4—24no—
57#4961—24no—
58#4957—24no—
59#4957—24no—
60#4948—24no—
61#4945—24no—
62C2×#396—31no—
63C2×#396—31no—
64C2×#394—31no—
65C2×#394D311yescharacteristic, complemented
66C2×#392—31no—
67C2×#390—31no—
68C2×#390—31no—
69C2×#390—31no—
70C2×#388—31no—
71C2×C4×C4⋊C4—31no—
72#1444—31no—
73#1439—31no—
74#1438—31no—
75#1437—31no—
76#1437—31no—
77C25×C3C2311yescharacteristic
78C25×C3C2311yescharacteristic
79C24×D3C2311yescharacteristic
80C22×C3×D4—22no—
81C22×C3×D4—22no—
82C22×C3×D4—22no—
83C22×C3×D4—22no—
84C22×C3×D4—22no—
85C22×C3×D4—41no—
86C22×C3×D4—41no—
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
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—22no—
101C22×#67—22no—
102C22×#67—41no—
103C22×#67—41no—
104C22×#67—41no—
105C22×#67—41no—
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C23×Dic3C2311yescharacteristic
109C23×Dic3C2311yescharacteristic
110C23×Dic3C2311yescharacteristic
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C2×C3×C4⋊C4—22no—
114C2×C3×C4⋊C4—22no—
115C2×C3×C4⋊C4D414yescomplemented
116C2×C3×C22⋊C4—22no—
117C2×C3×C22⋊C4—22no—
118C2×C3×C22⋊C4—22no—
119C2×C3×C22⋊C4—22no—
120C2×C3×C22⋊C4—22no—
121C2×C3×C22⋊C4—22no—
122C2×C3×C22⋊C4—22no—
123C2×C3×C22⋊C4—22no—
124C2×C3×C22⋊C4—22no—
125C2×C3×C22⋊C4—22no—
126C2×C3×C22⋊C4—41no—
127C2×C3×C22⋊C4—41no—
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—22no—
139C2×#217—22no—
140C2×#217—22no—
141C2×#217—22no—
142C2×#217—22no—
143C2×#217—41no—
144C2×#217—41no—
145C2×#217D414yescomplemented
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—22no—
158C2×(C2×D3)⋊C4—22no—
159C2×(C2×D3)⋊C4—41no—
160C2×(C2×D3)⋊C4—41no—
161C2×C4⋊Dic3—22no—
162C2×C4⋊Dic3—22no—
163C2×C4⋊Dic3—22no—
164C2×C4⋊Dic3—22no—
165C2×C4⋊Dic3—41no—
166C2×C4⋊Dic3D414yescomplemented
167C2×Dic3⋊C4—22no—
168C2×Dic3⋊C4—22no—
169C2×Dic3⋊C4—22no—
170C2×Dic3⋊C4—22no—
171C2×Dic3⋊C4—22no—
172C2×Dic3⋊C4—22no—
173C2×Dic3⋊C4—41no—
174C2×Dic3⋊C4—41no—
175C2×Dic3⋊C4—41no—
176C2×C4×Dic3—22no—
177C2×C4×Dic3—22no—
178C2×C4×Dic3—22no—
179C2×C4×Dic3—22no—
180C2×C4×Dic3—22no—
181C2×C4×Dic3—22no—
182C2×C4×Dic3—41no—
183C2×C4×Dic3—41no—
184C2×C4×Dic3D414yescomplemented
185C3×#95—22no—
186C3⋊#95—22no—
187C3⋊#95—22no—
188C3⋊#95—22no—
189C3⋊#95—22no—
190C3⋊#95—22no—
191C3⋊#95—22no—
192C3⋊#95D414yes—
193C23×D4—31no—
194C23×D4—31no—
195C23×D4C2×D311yescharacteristic
196C22×C4⋊C4—31no—
197C22×C4⋊C4—31no—
198C22×C4⋊C4—31no—
199C22×C4⋊C4—31no—
200C22×C4⋊C4—31no—
201C22×C4⋊C4C2×D311yescharacteristic
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⋊C4—31no—
210C22×C22⋊C4—31no—
211C22×C22⋊C4—31no—
212C22×C22⋊C4—31no—
213C22×C22⋊C4C2×D311yescharacteristic
214C22×C22⋊C4C2×D311yescharacteristic
215C22×C22⋊C4C2×D311yescharacteristic
216C22×C22⋊C4C2×D311yescharacteristic
217C22×C42—31no—
218C22×C42—31no—
219C22×C42—31no—
220#396—64no—
221#396—64no—
222#394—24no—
223#394—64no—
224#392—64no—
225#390—64no—
226#390—64no—
227#390—64no—
228#388—64no—
229C4×C4⋊C4—64no—
230C2×#95—31no—
231C2×#95—31no—
232C2×#95—31no—
233C2×#95—31no—
234C2×#95—31no—
235C2×#95—31no—
236C2×#95—31no—
237C2×#95C2×D311yescharacteristic
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—21no—
259C24×C3—21no—
260C24×C3—21no—
261C24×C3—21no—
262C24×C3—21no—
263C24×C3—21no—
264C24×C3—21no—
265C24×C3—21no—
266C24×C3C2×D412yes—
267C24×C3#4112yes—
268C24×C3C2411yescharacteristic
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×D3—21no—
282C23×D3—21no—
283C23×D3#4112yes—
284C2×C3×D4—28no—
285C2×C3×D4—44no—
286C2×C3×D4—44no—
287C2×C3×D4—44no—
288C2×C3×D4—44no—
289C2×C3×D4—44no—
290C2×C3×D4—44no—
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—28no—
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×Dic3—21no—
376C22×Dic3—21no—
377C22×Dic3—21no—
378C22×Dic3C2×D412yes—
379C22×Dic3C2×D412yes—
380C22×Dic3C2×D412yes—
381C22×Dic3C2×D412yes—
382C22×Dic3C2×D412yes—
383C22×Dic3C2×D412yes—
384C22×Dic3C2×D412yes—
385C22×Dic3C2×D412yes—
386C22×Dic3#4112yes—
387C22×Dic3#4112yes—
388C22×Dic3#4112yes—
389C3×C4⋊C4—28no—
390C3×C22⋊C4—44no—
391C3×C22⋊C4—44no—
392C3×C22⋊C4—44no—
393C3×C22⋊C4—44no—
394#217—28no—
395#217—44no—
396#217—44no—
397#217—44no—
398#217—44no—
399#217—44no—
400(C2×D3)⋊C4—44no—
401(C2×D3)⋊C4—44no—
402(C2×D3)⋊C4—44no—
403(C2×D3)⋊C4—44no—
404(C2×D3)⋊C4—44no—
405C4⋊Dic3—28no—
406C4⋊Dic3—44no—
407Dic3⋊C4—44no—
408Dic3⋊C4—44no—
409Dic3⋊C4—44no—
410C4×Dic3—28no—
411C4×Dic3—44no—
412C4×Dic3—44no—
413C25—31no—
414C25C22×D311yescharacteristic
415C25C22×D311yescharacteristic
416C22×D4—22no—
417C22×D4—22no—
418C22×D4—22no—
419C22×D4—22no—
420C22×D4—22no—
421C22×D4—41no—
422C22×D4—41no—
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—121no—
434C22×D4—121no—
435C22×D4—121no—
436C22×D4—121no—
437C23×C4—31no—
438C23×C4—31no—
439C23×C4—31no—
440C23×C4—31no—
441C23×C4—31no—
442C23×C4—31no—
443C23×C4—31no—
444C23×C4C22×D311yescharacteristic
445C23×C4C22×D311yescharacteristic
446C23×C4C22×D311yescharacteristic
447C23×C4C22×D311yescharacteristic
448C23×C4C22×D311yescharacteristic
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—34no—
452C2×C4⋊C4—62no—
453C2×C4⋊C4—62no—
454C2×C4⋊C4—62no—
455C2×C4⋊C4—62no—
456C2×C4⋊C4—62no—
457C2×C4⋊C4—62no—
458C2×C4⋊C4—62no—
459C2×C4⋊C4—62no—
460C2×C4⋊C4—62no—
461C2×C4⋊C4—62no—
462C2×C4⋊C4—121no—
463C2×C4⋊C4—121no—
464C2×C4⋊C4—121no—
465C2×C4⋊C4—121no—
466C2×C4⋊C4#6714yescomplemented
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—34no—
478C2×C22⋊C4—41no—
479C2×C22⋊C4—41no—
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—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—121no—
509C2×C22⋊C4—121no—
510C2×C22⋊C4—121no—
511C2×C22⋊C4—121no—
512C2×C42—34no—
513C2×C42—62no—
514C2×C42—62no—
515C2×C42—62no—
516C2×C42—62no—
517C2×C42—62no—
518C2×C42—62no—
519C2×C42—121no—
520C2×C42—121no—
521#95—22no—
522#95—34no—
523#95—62no—
524#95—62no—
525#95—62no—
526#95—62no—
527#95—62no—
528#95—62no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—22no—
532C23×C3—22no—
533C23×C3—22no—
534C23×C3—22no—
535C23×C3—22no—
536C23×C3—22no—
537C23×C3—22no—
538C23×C3—22no—
539C23×C3—22no—
540C23×C3—22no—
541C23×C3—22no—
542C23×C3—22no—
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×C3—41no—
586C23×C3—41no—
587C23×C3—41no—
588C23×C3—41no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3—41no—
593C23×C3—41no—
594C23×C3—41no—
595C23×C3—41no—
596C23×C3—41no—
597C23×C3—41no—
598C23×C3—41no—
599C23×C3C22×D411yescharacteristic
600C23×C3C22×D411yescharacteristic
601C23×C3C22×D411yescharacteristic
602C23×C3C22×D411yescharacteristic
603C23×C3C22×D411yescharacteristic
604C23×C3C2×#4111yescharacteristic
605C23×C3C2×#4111yescharacteristic
606C23×C3C2×#4111yescharacteristic
607C23×C3C2×#4111yescharacteristic
608C23×C3C2×#4111yescharacteristic
609C23×C3C2×#4111yescharacteristic
610C23×C3H(5,𝔽2)11yescharacteristic
611C23×C3H(5,𝔽2)11yescharacteristic
612C23×C3H(5,𝔽2)11yescharacteristic
613C23×C32−1+411yescharacteristic
614C22×D3—22no—
615C22×D3—22no—
616C22×D3—22no—
617C22×D3—22no—
618C22×D3—22no—
619C22×D3—22no—
620C22×D3—22no—
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—
649C3×D4—416no—
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—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—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—41no—
683C2×C3×C4#12114yes—
684C2×C3×C4#12714yes—
685#67—416no—
686#67—416no—
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—22no—
705C2×Dic3—22no—
706C2×Dic3—22no—
707C2×Dic3—22no—
708C2×Dic3—22no—
709C2×Dic3—22no—
710C2×Dic3—22no—
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—41no—
728C2×Dic3—41no—
729C2×Dic3—41no—
730C2×Dic3—41no—
731C2×Dic3—41no—
732C2×Dic3—41no—
733C2×Dic3#12114yes—
734C2×Dic3#12114yes—
735C2×Dic3#12114yes—
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—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—32no—
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—
779C24D3×D412yes—
780C24#23712yes—
781C24C23×D311yescharacteristic
782C2×D4—28no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—68no—
790C2×D4—68no—
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—32no—
832C22×C4—32no—
833C22×C4—32no—
834C22×C4—32no—
835C22×C4—32no—
836C22×C4—32no—
837C22×C4—32no—
838C22×C4—32no—
839C22×C4—32no—
840C22×C4—32no—
841C22×C4—32no—
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×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—28no—
888C4⋊C4—68no—
889C4⋊C4—124no—
890C4⋊C4—124no—
891C4⋊C4—124no—
892C4⋊C4—124no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—68no—
898C22⋊C4—124no—
899C22⋊C4—124no—
900C22⋊C4—124no—
901C22⋊C4—124no—
902C22⋊C4—124no—
903C22⋊C4—124no—
904C22⋊C4—124no—
905C22⋊C4—124no—
906C22⋊C4—124no—
907C22⋊C4—124no—
908C42—68no—
909C42—124no—
910C42—124no—
911C22×C3—42no—
912C22×C3—42no—
913C22×C3—42no—
914C22×C3—42no—
915C22×C3—42no—
916C22×C3—42no—
917C22×C3—42no—
918C22×C3—42no—
919C22×C3—42no—
920C22×C3—42no—
921C22×C3—42no—
922C22×C3—42no—
923C22×C3—42no—
924C22×C3—42no—
925C22×C3—81no—
926C22×C3—81no—
927C22×C3—81no—
928C22×C3—81no—
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×C3—81no—
938C22×C3—81no—
939C22×C3—81no—
940C22×C3—81no—
941C22×C3C2×#12111yescharacteristic
942C22×C3C2×#12111yescharacteristic
943C22×C3C2×#12111yescharacteristic
944C22×C3C2×#12111yescharacteristic
945C22×C3#52511yescharacteristic
946C22×C3#52511yescharacteristic
947C22×C3#52511yescharacteristic
948C22×C3#52911yescharacteristic
949C22×C3#52911yescharacteristic
950C22×C3C2×#12711yescharacteristic
951C22×C3#53211yescharacteristic
952C22×C3#53211yescharacteristic
953C22×C3#53211yescharacteristic
954C22×C3#53511yescharacteristic
955C22×C3#53711yescharacteristic
956C22×C3#53811yescharacteristic
957C22×C3#53811yescharacteristic
958C22×C3#54211yescharacteristic
959C22×C3#54211yescharacteristic
960C22×C3D4211yescharacteristic
961C22×C3D4211yescharacteristic
962C22×C3D4211yescharacteristic
963C22×C3#54611yescharacteristic
964C22×C3#54611yescharacteristic
965C22×C3#54611yescharacteristic
966C22×C3#54611yescharacteristic
967C22×C3#54711yescharacteristic
968C22×C3#54811yescharacteristic
969C22×C3#54811yescharacteristic
970C22×C3#54811yescharacteristic
971C22×C3#55011yescharacteristic
972C22×C3#55011yescharacteristic
973C22×C3#55111yescharacteristic
974C22×C3#55111yescharacteristic
975C22×C3#55311yescharacteristic
976C2×D3—42no—
977C2×D3—42no—
978C2×D3—42no—
979C2×D3—42no—
980C2×D3—42no—
981C2×D3—42no—
982C2×D3—42no—
983C2×D3—81no—
984C2×D3—81no—
985C2×D3—81no—
986C2×D3—81no—
987C2×D3—81no—
988C2×D3—81no—
989C2×D3—81no—
990C2×D3—81no—
991C3×C4—24no—
992C3×C4—24no—
993C3×C4—42no—
994C3×C4—81no—
995C3×C4—81no—
996Dic3—24no—
997Dic3—24no—
998Dic3—24no—
999Dic3—42no—
1000Dic3—42no—
1001Dic3—81no—
1002Dic3—81no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
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—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—62no—
1074C23—62no—
1075C23—62no—
1076C23—62no—
1077C23—62no—
1078C23—62no—
1079C23—62no—
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—
1108C23C2×D3×D411yescharacteristic
1109C23C2×D3×D411yescharacteristic
1110C23C2×D3×D411yescharacteristic
1111C23C2×D3×D411yescharacteristic
1112C23C2×#23711yescharacteristic
1113C23C2×#23711yescharacteristic
1114C23#100411yescharacteristic
1115C23#100411yescharacteristic
1116C23D3×#4111yescharacteristic
1117C23D3×#4111yescharacteristic
1118C23D3×#4111yescharacteristic
1119C23D3×#4111yescharacteristic
1120C23#100911yescharacteristic
1121C23#101011yescharacteristic
1122C23C22×#6711yescharacteristic
1123D4—416no—
1124D4—1216no—
1125D4—1216no—
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—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—34no—
1142C2×C4—34no—
1143C2×C4—34no—
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—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—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—62no—
1182C2×C4—62no—
1183C2×C4—62no—
1184C2×C4—62no—
1185C2×C4—62no—
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—121no—
1205C2×C4—121no—
1206C2×C4—121no—
1207C2×C4—121no—
1208C2×C4#93914yes—
1209C2×C4#94014yes—
1210C2×C3—82no—
1211C2×C3—82no—
1212C2×C3#239211yescharacteristic
1213C2×C3#241111yescharacteristic
1214C2×C3#241611yescharacteristic
1215C2×C3#242411yescharacteristic
1216C2×C3#242411yescharacteristic
1217C2×C3#242611yescharacteristic
1218C2×C3#242611yescharacteristic
1219C2×C3#246111yescharacteristic
1220C2×C3#246111yescharacteristic
1221C2×C3#254011yescharacteristic
1222C2×C3#254111yescharacteristic
1223C2×C3#255411yescharacteristic
1224C2×C3#255411yescharacteristic
1225C2×C3#266211yescharacteristic
1226C2×C3#285611yescharacteristic
1227D3—82no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
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—241no—
1266C22—241no—
1267C22—241no—
1268C22—241no—
1269C22—241no—
1270C22—241no—
1271C22—241no—
1272C22—241no—
1273C22#558611yescharacteristic
1274C22#559011yescharacteristic
1275C22#559111yescharacteristic
1276C22#559311yescharacteristic
1277C22#559611yescharacteristic
1278C22#559611yescharacteristic
1279C22#559811yescharacteristic
1280C22#559911yescharacteristic
1281C22D3×#12111yescharacteristic
1282C22D3×#12111yescharacteristic
1283C22D3×#12111yescharacteristic
1284C22#560611yescharacteristic
1285C22#560711yescharacteristic
1286C22#560811yescharacteristic
1287C22#560911yescharacteristic
1288C22#561211yescharacteristic
1289C22#564911yescharacteristic
1290C22#565511yescharacteristic
1291C22#565611yescharacteristic
1292C22#565711yescharacteristic
1293C22#565811yescharacteristic
1294C22#565911yescharacteristic
1295C22#566111yescharacteristic
1296C22#566211yescharacteristic
1297C22#567611yescharacteristic
1298C22#567711yescharacteristic
1299C22#568011yescharacteristic
1300C22#568211yescharacteristic
1301C22D4×#6711yescharacteristic
1302C22C2×#93911yescharacteristic
1303C22C2×#94011yescharacteristic
1304C22#580611yescharacteristic
1305C22#583111yescharacteristic
1306C22#583211yescharacteristic
1307C22#583411yescharacteristic
1308C4—24no—
1309C4—24no—
1310C4—42no—
1311C4—64no—
1312C4—64no—
1313C4—64no—
1314C4—81no—
1315C4—81no—
1316C4—122no—
1317C4—122no—
1318C4—241no—
1319C4—241no—
1320C3#1481511yescharacteristic, complemented, Sylow
1321C2—82no—
1322C2—82no—
1323C2—242no—
1324C2#7689011yescharacteristic
1325C2#7689811yescharacteristic
1326C2#7690111yescharacteristic
1327C2#7691511yescharacteristic
1328C2#7694811yescharacteristic
1329C2#7699611yescharacteristic
1330C2#7710911yescharacteristic
1331C2#7711311yescharacteristic
1332C2#8258711yescharacteristic
1333C2#8266811yescharacteristic
1334C2#8266911yescharacteristic
1335C2#8270011yescharacteristic
1336C2#8285211yescharacteristic
1337C2#8286111yescharacteristic
1338C2#8299511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#394C2
prime radicalC2×#5223C2
hypercenterC2×#394D3
hypocenterC3#14815
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C2×C3×#394C2semidirect
3. C2×#5221C2semidirect
4. C2×#4994C2semidirect
5. C2×Dic3×C4⋊C4C2semidirect
6. C2×#4948C2semidirect
7. C2×#4961C2semidirect
8. C2×#4957C2semidirect
9. C2×#4957C2semidirect
10. C2×#4945C2semidirect
11. #71550C2semidirect
12. #71547C2semidirect
13. #71545C2semidirect
14. #69420C2semidirect
15. #69408C2semidirect
65. C2×#394D3semidirect
115. C2×C3×C4⋊C4D4semidirect
145. C2×#217D4semidirect
166. C2×C4⋊Dic3D4semidirect
184. C2×C4×Dic3D4semidirect
466. C2×C4⋊C4#67semidirect
1320. C3#14815semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3942
C2×#52232
C2×#52212
C2×#49942
C2×Dic3×C4⋊C42
C2×#49482
C2×#49612
C2×#49572
C2×#49452
#715502
#715472
#715452
#694202
#694082
#148153