Finite Group Databasebeta

← #10727866

Subgroups — #10727866

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×#390C211yesmaximal, characteristic, complemented
2C2×#5223C211yesmaximal, characteristic
3C2×#5222C211yesmaximal, characteristic, complemented
4C2×#4994C211yesmaximal, characteristic, complemented
5C2×#4959C211yesmaximal, characteristic, complemented
6C2×#4948C211yesmaximal, characteristic, complemented
7C2×#4957C211yesmaximal, characteristic, complemented
8C2×#4957C211yesmaximal, characteristic, complemented
9C2×#4951C211yesmaximal, characteristic, complemented
10C2×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
11#71568C211yesmaximal, characteristic, complemented
12#71550C211yesmaximal, characteristic, complemented
13#71547C211yesmaximal, characteristic, complemented
14#71545C211yesmaximal, characteristic, complemented
15#71537C211yesmaximal, 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×C3×C42C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×C4⋊Dic3C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×Dic3⋊C4C2211yescharacteristic
41C22×Dic3⋊C4C2211yescharacteristic
42C22×C4×Dic3C2211yescharacteristic
43C22×C4×Dic3C2211yescharacteristic
44C3×#390—24no—
45#5223—24no—
46#5222—24no—
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#4994—24no—
56#4959—24no—
57#4957—24no—
58#4957—24no—
59#4951—24no—
60#4948—24no—
61C4×Dic3⋊C4—24no—
62C2×#396—31no—
63C2×#396—31no—
64C2×#394—31no—
65C2×#394—31no—
66C2×#392—31no—
67C2×#390—31no—
68C2×#390—31no—
69C2×#390D311yescharacteristic, complemented
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⋊C4—41no—
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—41no—
126C2×C3×C22⋊C4—41no—
127C2×C3×C22⋊C4D414yescomplemented
128C2×C3×C42—22no—
129C2×C3×C42—22no—
130C2×C3×C42—41no—
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—22no—
144C2×#217—22no—
145C2×#217—22no—
146C2×#217—22no—
147C2×#217—41no—
148C2×#217—41no—
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—22no—
160C2×(C2×D3)⋊C4—22no—
161C2×(C2×D3)⋊C4—22no—
162C2×(C2×D3)⋊C4—41no—
163C2×(C2×D3)⋊C4—41no—
164C2×C4⋊Dic3—22no—
165C2×C4⋊Dic3—22no—
166C2×C4⋊Dic3—22no—
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—22no—
174C2×Dic3⋊C4—41no—
175C2×Dic3⋊C4—41no—
176C2×Dic3⋊C4—41no—
177C2×Dic3⋊C4D414yescomplemented
178C2×Dic3⋊C4D414yescomplemented
179C2×C4×Dic3—22no—
180C2×C4×Dic3—22no—
181C2×C4×Dic3—22no—
182C2×C4×Dic3—22no—
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×C42C2×D311yescharacteristic
220#396—64no—
221#396—64no—
222#394—64no—
223#394—64no—
224#392—64no—
225#390—24no—
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×#95—31no—
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×C4C2×D412yes—
319C22×C3×C4C2×D412yes—
320C22×C3×C4C2×D412yes—
321C22×C3×C4C2×D412yes—
322C22×C3×C4C2×D412yes—
323C22×C3×C4C2×D412yes—
324C22×C3×C4#4112yes—
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×Dic3—21no—
379C22×Dic3C2×D412yes—
380C22×Dic3C2×D412yes—
381C22×Dic3C2×D412yes—
382C22×Dic3C2×D412yes—
383C22×Dic3C2×D412yes—
384C22×Dic3C2×D412yes—
385C22×Dic3C2×D412yes—
386C22×Dic3C2×D412yes—
387C22×Dic3#4112yes—
388C22×Dic3#4112yes—
389C3×C4⋊C4—44no—
390C3×C22⋊C4—28no—
391C3×C22⋊C4—44no—
392C3×C22⋊C4—44no—
393C3×C22⋊C4—44no—
394C3×C42—44no—
395#217—44no—
396#217—44no—
397#217—44no—
398#217—44no—
399#217—44no—
400#217—44no—
401(C2×D3)⋊C4—44no—
402(C2×D3)⋊C4—44no—
403(C2×D3)⋊C4—44no—
404(C2×D3)⋊C4—44no—
405(C2×D3)⋊C4—44no—
406C4⋊Dic3—44no—
407Dic3⋊C4—28no—
408Dic3⋊C4—28no—
409Dic3⋊C4—44no—
410Dic3⋊C4—44no—
411C4×Dic3—28no—
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—34no—
453C2×C4⋊C4—41no—
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—62no—
463C2×C4⋊C4—62no—
464C2×C4⋊C4—121no—
465C2×C4⋊C4—121no—
466C2×C4⋊C4—121no—
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—41no—
477C2×C22⋊C4—41no—
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—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—121no—
508C2×C22⋊C4—121no—
509C2×C22⋊C4—121no—
510C2×C22⋊C4—121no—
511C2×C22⋊C4#6714yescomplemented
512C2×C42—22no—
513C2×C42—22no—
514C2×C42—34no—
515C2×C42—41no—
516C2×C42—62no—
517C2×C42—62no—
518C2×C42—62no—
519C2×C42—62no—
520C2×C42—121no—
521#95—34no—
522#95—62no—
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—22no—
666C2×C3×C4—22no—
667C2×C3×C4—22no—
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#12114yes—
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—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—41no—
728C2×Dic3—41no—
729C2×Dic3—41no—
730C2×Dic3—41no—
731C2×Dic3—41no—
732C2×Dic3—41no—
733C2×Dic3#12114yes—
734C2×Dic3#12114yes—
735C2×Dic3#12714yes—
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—
779C24#23512yes—
780C24C2×#6712yes—
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—32no—
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—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×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#23512yes—
880C22×C4D3×D412yes—
881C22×C4D3×D412yes—
882C22×C4D3×D412yes—
883C22×C4D3×D412yes—
884C22×C4#23712yes—
885C22×C4C2×#6712yes—
886C22×C4C2×#6712yes—
887C4⋊C4—44no—
888C4⋊C4—68no—
889C4⋊C4—68no—
890C4⋊C4—124no—
891C4⋊C4—124no—
892C4⋊C4—124no—
893C22⋊C4—28no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—124no—
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—44no—
909C42—68no—
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—42no—
995C3×C4—81no—
996Dic3—24no—
997Dic3—24no—
998Dic3—24no—
999Dic3—42no—
1000Dic3—81no—
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×#23511yescharacteristic
1109C23C2×#23511yescharacteristic
1110C23C2×D3×D411yescharacteristic
1111C23C2×D3×D411yescharacteristic
1112C23C2×D3×D411yescharacteristic
1113C23C2×D3×D411yescharacteristic
1114C23C2×#23711yescharacteristic
1115C23#100411yescharacteristic
1116C23#100411yescharacteristic
1117C23#100411yescharacteristic
1118C23D3×#4111yescharacteristic
1119C23D3×#4111yescharacteristic
1120C23D3×#4111yescharacteristic
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—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—34no—
1145C2×C4—34no—
1146C2×C4—34no—
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—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—121no—
1205C2×C4—121no—
1206C2×C4—121no—
1207C2×C4—121no—
1208C2×C4#88414yes—
1209C2×C4#93914yes—
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—
1273C22C2×#88411yescharacteristic
1274C22#549011yescharacteristic
1275C22#549011yescharacteristic
1276C22#549411yescharacteristic
1277C22#553811yescharacteristic
1278C22#554711yescharacteristic
1279C22#554811yescharacteristic
1280C22#554811yescharacteristic
1281C22#555211yescharacteristic
1282C22#555611yescharacteristic
1283C22#555711yescharacteristic
1284C22#556111yescharacteristic
1285C22#559711yescharacteristic
1286C22#559811yescharacteristic
1287C22#560111yescharacteristic
1288C22D3×#12111yescharacteristic
1289C22D3×#12111yescharacteristic
1290C22#561011yescharacteristic
1291C22#561211yescharacteristic
1292C22#561311yescharacteristic
1293C22#566811yescharacteristic
1294C22#566911yescharacteristic
1295C22#567711yescharacteristic
1296C22#567911yescharacteristic
1297C22D3×#12711yescharacteristic
1298C22#571511yescharacteristic
1299C22#571811yescharacteristic
1300C22#571811yescharacteristic
1301C22#579111yescharacteristic
1302C22D4×#6711yescharacteristic
1303C22D4×#6711yescharacteristic
1304C22D4×#6711yescharacteristic
1305C22C2×#93911yescharacteristic
1306C22#582411yescharacteristic
1307C22#582811yescharacteristic
1308C4—24no—
1309C4—24no—
1310C4—42no—
1311C4—42no—
1312C4—64no—
1313C4—64no—
1314C4—64no—
1315C4—81no—
1316C4—122no—
1317C4—241no—
1318C4—241no—
1319C4—241no—
1320C3#1481511yescharacteristic, complemented, Sylow
1321C2—82no—
1322C2—82no—
1323C2—242no—
1324C2#7631211yescharacteristic
1325C2#7634711yescharacteristic
1326C2#7635511yescharacteristic
1327C2#7637711yescharacteristic
1328C2#7643711yescharacteristic
1329C2#7644311yescharacteristic
1330C2#7645511yescharacteristic
1331C2#7647611yescharacteristic
1332C2#8210911yescharacteristic
1333C2#8234511yescharacteristic
1334C2#8236711yescharacteristic
1335C2#8264211yescharacteristic
1336C2#8270711yescharacteristic
1337C2#8296411yescharacteristic
1338C2#8317711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#390C2
prime radicalC2×#5223C2
hypercenterC2×#390D3
hypocenterC3#14815
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C2×C3×#390C2semidirect
3. C2×#5222C2semidirect
4. C2×#4994C2semidirect
5. C2×#4959C2semidirect
6. C2×#4948C2semidirect
7. C2×#4957C2semidirect
8. C2×#4957C2semidirect
9. C2×#4951C2semidirect
10. C2×C4×Dic3⋊C4C2semidirect
11. #71568C2semidirect
12. #71550C2semidirect
13. #71547C2semidirect
14. #71545C2semidirect
15. #71537C2semidirect
69. C2×#390D3semidirect
127. C2×C3×C22⋊C4D4semidirect
177. C2×Dic3⋊C4D4semidirect
178. C2×Dic3⋊C4D4semidirect
184. C2×C4×Dic3D4semidirect
511. C2×C22⋊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×#3902
C2×#52232
C2×#52222
C2×#49942
C2×#49592
C2×#49482
C2×#49572
C2×#49512
C2×C4×Dic3⋊C42
#715682
#715502
#715472
#715452
#715372
#148153