Finite Group Databasebeta

← #10718677

Subgroups — #10718677

Order 768.

2574 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×#67C211yesmaximal, characteristic
2C22×#885C211yesmaximal, characteristic
3C2×#4957C211yesmaximal, characteristic
4C2×#4646C211yesmaximal, characteristic, complemented
5C2×#4646C211yesmaximal, characteristic, complemented
6C3×C22⋊#95C211yesmaximal, characteristic, complemented
7#72127C211yesmaximal, characteristic, complemented
8#71549C211yesmaximal, characteristic, complemented
9#71548C211yesmaximal, characteristic, complemented
10#69429C211yesmaximal, characteristic, complemented
11#69429C211yesmaximal, characteristic, complemented
12(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
13(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
14Dic3⋊#95C211yesmaximal, characteristic, complemented
15Dic3×#95C211yesmaximal, characteristic, complemented
16#14027—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C23×Dic6C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C2×C4×#67—24no—
27C2×C4×#67—24no—
28C2×C4×#67—24no—
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×C4×Dic3C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C22×C4×Dic3C2211yescharacteristic
39C2×#885—24no—
40C2×#885—24no—
41C2×#885C418yescomplemented
42C2×C3×#95C2211yescharacteristic
43C2×C3×#95C2211yescharacteristic
44C2×C3×#95C2211yescharacteristic
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
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58#4957—24no—
59#4646—24no—
60#4646—24no—
61C22×#124—31no—
62C22×C4×D4—31no—
63C2×#391—31no—
64C2×#391—31no—
65C2×#390—31no—
66#1440—31no—
67#1440—31no—
68#1440—31no—
69#1440—31no—
70C4⋊#95—31no—
71C22⋊#95—31no—
72C22⋊#95—31no—
73C22⋊#95—31no—
74C22⋊#95D311yescharacteristic, complemented
75C4×#95—31no—
76C25×C3C2311yescharacteristic
77C24×D3C2311yescharacteristic
78C23×C3×C4—22no—
79C23×C3×C4—22no—
80C23×C3×C4—22no—
81C23×C3×C4—22no—
82C23×C3×C4—22no—
83C23×C3×C4—41no—
84C23×C3×C4—41no—
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C22×#67—22no—
92C22×#67—22no—
93C22×#67—22no—
94C22×#67—22no—
95C22×#67C2×C414yes—
96C22×#67D414yes—
97C22×#67D414yes—
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C22×C4×D3—22no—
106C22×C4×D3—22no—
107C22×C4×D3—22no—
108C22×C4×D3—22no—
109C22×C4×D3—22no—
110C22×C4×D3—41no—
111C22×C4×D3—41no—
112C22×Dic6—22no—
113C22×Dic6—22no—
114C22×Dic6—22no—
115C22×Dic6—22no—
116C22×Dic6—22no—
117C22×Dic6—22no—
118C22×Dic6C2×C414yescomplemented
119C2×C3×C22⋊C4—22no—
120C2×C3×C22⋊C4—22no—
121C2×C3×C22⋊C4—22no—
122C2×C3×C22⋊C4—22no—
123C2×C3×C22⋊C4—41no—
124C2×C3×C22⋊C4C2×C414yescomplemented
125C2×#217—22no—
126C2×#217—22no—
127C2×#217—22no—
128C2×#217—22no—
129C2×#217—22no—
130C2×#217—22no—
131C2×#217—22no—
132C2×#217—41no—
133C2×#217C2×C414yescomplemented
134C4×#67—232no—
135C2×(C2×D3)⋊C4—22no—
136C2×(C2×D3)⋊C4—22no—
137C2×(C2×D3)⋊C4—22no—
138C2×(C2×D3)⋊C4—22no—
139C2×(C2×D3)⋊C4—22no—
140C2×(C2×D3)⋊C4—22no—
141C2×(C2×D3)⋊C4—22no—
142C2×(C2×D3)⋊C4—22no—
143C2×(C2×D3)⋊C4—22no—
144C2×(C2×D3)⋊C4—22no—
145C2×(C2×D3)⋊C4—22no—
146C2×(C2×D3)⋊C4—41no—
147C2×(C2×D3)⋊C4—41no—
148C2×(C2×D3)⋊C4C2×C414yescomplemented
149C2×(C2×D3)⋊C4C2×C414yescomplemented
150C2×Dic3⋊C4—22no—
151C2×Dic3⋊C4—22no—
152C2×Dic3⋊C4—22no—
153C2×Dic3⋊C4—22no—
154C2×Dic3⋊C4—22no—
155C2×Dic3⋊C4D414yes—
156C2×C4×Dic3—22no—
157C2×C4×Dic3—22no—
158C2×C4×Dic3—22no—
159C2×C4×Dic3—22no—
160C2×C4×Dic3—22no—
161C2×C4×Dic3—22no—
162C2×C4×Dic3—22no—
163C2×C4×Dic3C2×C414yescomplemented
164C2×C4×Dic3D414yes—
165#885—232no—
166C3×#95—22no—
167C3×#95—22no—
168C3×#95—22no—
169C3×#95—41no—
170C3⋊#95—22no—
171C3⋊#95—22no—
172C3⋊#95—22no—
173C3⋊#95—22no—
174C3⋊#95—22no—
175C3⋊#95—22no—
176C3⋊#95—22no—
177C3⋊#95—22no—
178C3⋊#95—22no—
179C3⋊#95—41no—
180C3⋊#95—41no—
181C3⋊#95—41no—
182C23×Q8—31no—
183C23×D4—31no—
184C24×C4—31no—
185C24×C4C2×D311yescharacteristic
186C2×#124—38no—
187C2×#124—64no—
188C2×#124—64no—
189C2×C4×D4—64no—
190C2×C4×D4—64no—
191C2×C4×D4—64no—
192C22×C4⋊C4—31no—
193C22×C4⋊C4—31no—
194C22×C22⋊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⋊C4C2×D311yescharacteristic
203C22×C22⋊C4C2×D311yescharacteristic
204C22×C42—31no—
205C22×C42—31no—
206C22×C42—31no—
207#391—64no—
208#391—64no—
209#390—64no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95—31no—
218C2×#95—31no—
219C2×#95—31no—
220C2×#95—31no—
221C2×#95—31no—
222C2×#95C2×D311yescharacteristic
223C2×#95C2×D311yescharacteristic
224C2×#95C2×D311yescharacteristic
225C2×#95C2×D311yescharacteristic
226C24×C3—21no—
227C24×C3—21no—
228C24×C3—21no—
229C24×C3—21no—
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×C3C22×C412yes—
239C24×C3C2×D412yes—
240C24×C3C2×D412yes—
241C24×C3C2411yescharacteristic
242C23×D3—21no—
243C23×D3—21no—
244C23×D3—21no—
245C23×D3—21no—
246C23×D3—21no—
247C23×D3—21no—
248C23×D3—21no—
249C23×D3—21no—
250C23×D3—21no—
251C23×D3—21no—
252C23×D3—21no—
253C23×D3—21no—
254C23×D3C22×C412yes—
255C23×D3C2×D412yes—
256C23×D3C2×D412yes—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—28no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
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—44no—
294C22×C3×C4—44no—
295C22×C3×C4—44no—
296C22×C3×C4—44no—
297C22×C3×C4—44no—
298C22×C3×C4—44no—
299C22×C3×C4C22×C412yes—
300C22×C3×C4C22×C412yes—
301C22×C3×C4C2×D412yes—
302C22×C3×C4C2×D412yes—
303C22×C3×C4#4112yes—
304C22×C3×C4#4112yes—
305C22×C3×C4#4112yes—
306C2×#67—28no—
307C2×#67—28no—
308C2×#67—28no—
309C2×#67—28no—
310C2×#67—28no—
311C2×#67—28no—
312C2×#67C22⋊C4116yes—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
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×Dic3C22×C412yes—
351C22×Dic3C22×C412yes—
352C22×Dic3C22×C412yes—
353C22×Dic3C2×D412yes—
354C22×Dic3C2×D412yes—
355C22×Dic3C2×D412yes—
356C22×Dic3C2×D412yes—
357C22×Dic3C2×D412yes—
358C22×Dic3C2×D412yes—
359C22×Dic3#4112yes—
360C22×Dic3#4112yes—
361C22×Dic3#4112yes—
362C2×C4×D3—28no—
363C2×C4×D3—44no—
364C2×C4×D3—44no—
365C2×C4×D3—44no—
366C2×C4×D3—44no—
367C2×C4×D3—44no—
368C2×C4×D3—44no—
369C2×Dic6—28no—
370C2×Dic6—28no—
371C2×Dic6—28no—
372C2×Dic6—44no—
373C2×Dic6—44no—
374C2×Dic6—44no—
375C2×Dic6—44no—
376C3×C22⋊C4—28no—
377C3×C22⋊C4—44no—
378#217—28no—
379#217—28no—
380#217—44no—
381(C2×D3)⋊C4—28no—
382(C2×D3)⋊C4—28no—
383(C2×D3)⋊C4—28no—
384(C2×D3)⋊C4—44no—
385(C2×D3)⋊C4—44no—
386Dic3⋊C4—28no—
387Dic3⋊C4—44no—
388C4×Dic3—28no—
389C4×Dic3—28no—
390C4×Dic3—44no—
391C25—31no—
392C25C22×D311yescharacteristic
393C22×Q8—34no—
394C22×Q8—62no—
395C22×Q8—62no—
396C22×Q8—62no—
397C22×Q8—62no—
398C22×Q8—62no—
399C22×Q8—62no—
400C22×D4—34no—
401C22×D4—34no—
402C22×D4—34no—
403C22×D4—62no—
404C22×D4—62no—
405C22×D4—62no—
406C22×D4—62no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—22no—
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—31no—
413C23×C4—31no—
414C23×C4—31no—
415C23×C4—31no—
416C23×C4—31no—
417C23×C4—31no—
418C23×C4—31no—
419C23×C4—41no—
420C23×C4—41no—
421C23×C4—62no—
422C23×C4—62no—
423C23×C4—62no—
424C23×C4—62no—
425C23×C4—62no—
426C23×C4—121no—
427C23×C4—121no—
428C23×C4C22×D311yescharacteristic
429C23×C4C22×D311yescharacteristic
430C23×C4C22×D311yescharacteristic
431C23×C4C22×D311yescharacteristic
432C23×C4C22×D311yescharacteristic
433C23×C4C22×D311yescharacteristic
434#124—632no—
435C4×D4—632no—
436C2×C4⋊C4—34no—
437C2×C4⋊C4—62no—
438C2×C4⋊C4—62no—
439C2×C4⋊C4—62no—
440C2×C4⋊C4—62no—
441C2×C4⋊C4—62no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—34no—
447C2×C22⋊C4—34no—
448C2×C22⋊C4—34no—
449C2×C22⋊C4—41no—
450C2×C22⋊C4—62no—
451C2×C22⋊C4—62no—
452C2×C22⋊C4—62no—
453C2×C22⋊C4—62no—
454C2×C22⋊C4—62no—
455C2×C22⋊C4—62no—
456C2×C22⋊C4—62no—
457C2×C22⋊C4—62no—
458C2×C22⋊C4—62no—
459C2×C22⋊C4—62no—
460C2×C22⋊C4—62no—
461C2×C22⋊C4—62no—
462C2×C22⋊C4—62no—
463C2×C22⋊C4—62no—
464C2×C22⋊C4—62no—
465C2×C22⋊C4—62no—
466C2×C22⋊C4—62no—
467C2×C22⋊C4—62no—
468C2×C22⋊C4—121no—
469C2×C22⋊C4—121no—
470C2×C22⋊C4—121no—
471C2×C22⋊C4C4×D314yescomplemented
472C2×C42—34no—
473C2×C42—34no—
474C2×C42—62no—
475C2×C42—62no—
476C2×C42—62no—
477C2×C42—62no—
478C2×C42—62no—
479C2×C42—62no—
480C2×C42—62no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—41no—
485#95—62no—
486#95—62no—
487#95—62no—
488#95—62no—
489#95—62no—
490#95—62no—
491#95—62no—
492#95—62no—
493#95—62no—
494#95—121no—
495#95—121no—
496#95—121no—
497C23×C3—22no—
498C23×C3—22no—
499C23×C3—22no—
500C23×C3—22no—
501C23×C3—22no—
502C23×C3—22no—
503C23×C3—22no—
504C23×C3—22no—
505C23×C3—22no—
506C23×C3—22no—
507C23×C3—22no—
508C23×C3—22no—
509C23×C3—22no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—22no—
514C23×C3—22no—
515C23×C3—41no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3C2×C22⋊C414yes—
532C23×C3C23×C411yescharacteristic
533C23×C3C22×D411yescharacteristic
534C23×C3C22×D411yescharacteristic
535C23×C3C22×D411yescharacteristic
536C23×C3C22×D411yescharacteristic
537C23×C3C2×#4111yescharacteristic
538C23×C3C2×#4111yescharacteristic
539C23×C3C2×#4111yescharacteristic
540C23×C3C2×#4111yescharacteristic
541C23×C3C2×#4111yescharacteristic
542C23×C3C2×#4111yescharacteristic
543C23×C3H(5,𝔽2)11yescharacteristic
544C23×C3H(5,𝔽2)11yescharacteristic
545C23×C32−1+411yescharacteristic
546C23×C32−1+411yescharacteristic
547C22×D3—22no—
548C22×D3—22no—
549C22×D3—22no—
550C22×D3—22no—
551C22×D3—22no—
552C22×D3—22no—
553C22×D3—22no—
554C22×D3—22no—
555C22×D3—22no—
556C22×D3—22no—
557C22×D3—22no—
558C22×D3—22no—
559C22×D3—22no—
560C22×D3—22no—
561C22×D3—22no—
562C22×D3—22no—
563C22×D3—22no—
564C22×D3—22no—
565C22×D3—41no—
566C22×D3—41no—
567C22×D3—41no—
568C22×D3—41no—
569C22×D3—41no—
570C22×D3—41no—
571C22×D3—41no—
572C22×D3—41no—
573C22×D3—41no—
574C22×D3—41no—
575C22×D3—41no—
576C22×D3—41no—
577C22×D3—41no—
578C22×D3—41no—
579C22×D3—41no—
580C22×D3—41no—
581C22×D3C2×C22⋊C414yes—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—416no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—41no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—41no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4#12414yescomplemented
625#67—232no—
626C2×Dic3—22no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—22no—
630C2×Dic3—22no—
631C2×Dic3—22no—
632C2×Dic3—22no—
633C2×Dic3—22no—
634C2×Dic3—22no—
635C2×Dic3—22no—
636C2×Dic3—22no—
637C2×Dic3—22no—
638C2×Dic3—22no—
639C2×Dic3—22no—
640C2×Dic3—22no—
641C2×Dic3—41no—
642C2×Dic3—41no—
643C2×Dic3—41no—
644C2×Dic3—41no—
645C2×Dic3—41no—
646C2×Dic3—41no—
647C2×Dic3—41no—
648C2×Dic3—41no—
649C2×Dic3—41no—
650C2×Dic3—41no—
651C2×Dic3—41no—
652C2×Dic3—41no—
653C2×Dic3—41no—
654C2×Dic3—41no—
655C2×Dic3—41no—
656C2×Dic3—41no—
657C2×Dic3—41no—
658C2×Dic3—41no—
659C2×Dic3—41no—
660C2×Dic3—41no—
661C2×Dic3—41no—
662C2×Dic3—41no—
663C2×Dic3—41no—
664C2×Dic3—41no—
665C2×Dic3—41no—
666C2×Dic3—41no—
667C2×Dic3—41no—
668C2×Dic3C2×C22⋊C414yes—
669C2×Dic3C4×D414yes—
670C2×Dic3C4×D414yes—
671C2×Dic3#12014yes—
672C2×Dic3#12114yes—
673C2×Dic3#12114yes—
674C2×Dic3#12314yes—
675C4×D3—416no—
676Dic6—416no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—21no—
689C24—32no—
690C24—32no—
691C24—32no—
692C24—61no—
693C24—61no—
694C24—61no—
695C24—61no—
696C24—61no—
697C24—61no—
698C24—61no—
699C24—61no—
700C24—61no—
701C24—61no—
702C24—61no—
703C24—61no—
704C24C2×C4×D312yes—
705C24D3×D412yes—
706C24D3×D412yes—
707C24C23×D311yescharacteristic
708C2×Q8—68no—
709C2×Q8—68no—
710C2×Q8—68no—
711C2×Q8—124no—
712C2×Q8—124no—
713C2×Q8—124no—
714C2×Q8—124no—
715C2×D4—316no—
716C2×D4—68no—
717C2×D4—68no—
718C2×D4—68no—
719C2×D4—68no—
720C2×D4—68no—
721C2×D4—68no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—28no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—32no—
759C22×C4—32no—
760C22×C4—32no—
761C22×C4—32no—
762C22×C4—32no—
763C22×C4—32no—
764C22×C4—32no—
765C22×C4—32no—
766C22×C4—32no—
767C22×C4—32no—
768C22×C4—32no—
769C22×C4—32no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—68no—
777C22×C4—61no—
778C22×C4—61no—
779C22×C4—61no—
780C22×C4—61no—
781C22×C4—61no—
782C22×C4—61no—
783C22×C4—61no—
784C22×C4—61no—
785C22×C4—61no—
786C22×C4—61no—
787C22×C4—61no—
788C22×C4—61no—
789C22×C4—61no—
790C22×C4—61no—
791C22×C4—61no—
792C22×C4—61no—
793C22×C4—61no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—61no—
797C22×C4—61no—
798C22×C4—61no—
799C22×C4—61no—
800C22×C4—61no—
801C22×C4—61no—
802C22×C4—61no—
803C22×C4—61no—
804C22×C4—61no—
805C22×C4—61no—
806C22×C4—61no—
807C22×C4—61no—
808C22×C4—61no—
809C22×C4—61no—
810C22×C4—61no—
811C22×C4—61no—
812C22×C4—61no—
813C22×C4—61no—
814C22×C4—124no—
815C22×C4—124no—
816C22×C4—124no—
817C22×C4—124no—
818C22×C4—124no—
819C22×C4—124no—
820C22×C4C2×C4×D312yes—
821C22×C4C2×C4×D312yes—
822C22×C4#23512yes—
823C22×C4#23512yes—
824C22×C4D3×D412yes—
825C22×C4D3×D412yes—
826C22×C4#23712yes—
827C4⋊C4—68no—
828C4⋊C4—124no—
829C22⋊C4—28no—
830C22⋊C4—44no—
831C22⋊C4—68no—
832C22⋊C4—68no—
833C22⋊C4—68no—
834C22⋊C4—68no—
835C22⋊C4—68no—
836C22⋊C4—124no—
837C22⋊C4—124no—
838C22⋊C4—124no—
839C42—68no—
840C42—68no—
841C42—124no—
842C22×C3—24no—
843C22×C3—24no—
844C22×C3—24no—
845C22×C3—42no—
846C22×C3—42no—
847C22×C3—42no—
848C22×C3—42no—
849C22×C3—42no—
850C22×C3—42no—
851C22×C3—42no—
852C22×C3—42no—
853C22×C3—42no—
854C22×C3—42no—
855C22×C3—42no—
856C22×C3—42no—
857C22×C3C22×C22⋊C411yescharacteristic
858C22×C3C2×C4×D411yescharacteristic
859C22×C3C2×C4×D411yescharacteristic
860C22×C3C4×#4111yescharacteristic
861C22×C3C4×#4111yescharacteristic
862C22×C3#52011yescharacteristic
863C22×C3#52011yescharacteristic
864C22×C3C2×#12011yescharacteristic
865C22×C3C2×#12111yescharacteristic
866C22×C3C2×#12111yescharacteristic
867C22×C3C2×#12311yescharacteristic
868C22×C3C2×#12411yescharacteristic
869C22×C3#52911yescharacteristic
870C22×C3#52911yescharacteristic
871C22×C3#53211yescharacteristic
872C22×C3#53511yescharacteristic
873C22×C3#53611yescharacteristic
874C22×C3#54211yescharacteristic
875C22×C3#54211yescharacteristic
876C22×C3#54611yescharacteristic
877C22×C3#54611yescharacteristic
878C22×C3#54611yescharacteristic
879C22×C3#54611yescharacteristic
880C22×C3#54611yescharacteristic
881C22×C3#54611yescharacteristic
882C22×C3#54711yescharacteristic
883C22×C3#54711yescharacteristic
884C22×C3#54711yescharacteristic
885C22×C3#54711yescharacteristic
886C22×C3#54811yescharacteristic
887C22×C3#54811yescharacteristic
888C22×C3#55611yescharacteristic
889C22×C3#55611yescharacteristic
890C22×C3#55911yescharacteristic
891C22×C3#55911yescharacteristic
892C2×D3—24no—
893C2×D3—24no—
894C2×D3—24no—
895C2×D3—42no—
896C2×D3—42no—
897C2×D3—42no—
898C2×D3—42no—
899C2×D3—42no—
900C2×D3—42no—
901C2×D3—42no—
902C2×D3—42no—
903C2×D3—42no—
904C2×D3—42no—
905C2×D3—42no—
906C2×D3—42no—
907C3×C4—24no—
908C3×C4—42no—
909C3×C4—42no—
910C3×C4—42no—
911C3×C4—42no—
912C3×C4—81no—
913Dic3—42no—
914Dic3—42no—
915Dic3—42no—
916Dic3—42no—
917Dic3—42no—
918Dic3—81no—
919Dic3#38618yes—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—34no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—62no—
956C23—62no—
957C23—62no—
958C23—62no—
959C23—62no—
960C23—62no—
961C23—62no—
962C23—62no—
963C23—62no—
964C23—62no—
965C23—62no—
966C23—62no—
967C23—62no—
968C23—62no—
969C23—62no—
970C23—62no—
971C23—62no—
972C23—62no—
973C23—121no—
974C23—121no—
975C23—121no—
976C23—121no—
977C23—121no—
978C23—121no—
979C23—121no—
980C23—121no—
981C23—121no—
982C23—121no—
983C23—121no—
984C23—121no—
985C23—121no—
986C23—121no—
987C23—121no—
988C23—121no—
989C23D3×C22⋊C414yes—
990C23C22×C4×D311yescharacteristic
991C23C2×#23511yescharacteristic
992C23C2×#23511yescharacteristic
993C23C2×D3×D411yescharacteristic
994C23C2×D3×D411yescharacteristic
995C23C2×D3×D411yescharacteristic
996C23C2×D3×D411yescharacteristic
997C23C2×#23711yescharacteristic
998C23#100411yescharacteristic
999C23#100411yescharacteristic
1000C23#100711yescharacteristic
1001C23D3×#4111yescharacteristic
1002C23D3×#4111yescharacteristic
1003C23D3×#4111yescharacteristic
1004C23#101011yescharacteristic
1005Q8—1216no—
1006D4—632no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—34no—
1026C2×C4—34no—
1027C2×C4—34no—
1028C2×C4—34no—
1029C2×C4—34no—
1030C2×C4—34no—
1031C2×C4—34no—
1032C2×C4—416no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—62no—
1057C2×C4—62no—
1058C2×C4—62no—
1059C2×C4—62no—
1060C2×C4—62no—
1061C2×C4—62no—
1062C2×C4—62no—
1063C2×C4—62no—
1064C2×C4—62no—
1065C2×C4—62no—
1066C2×C4—62no—
1067C2×C4—62no—
1068C2×C4—62no—
1069C2×C4—62no—
1070C2×C4—62no—
1071C2×C4—1216no—
1072C2×C4—121no—
1073C2×C4—121no—
1074C2×C4—121no—
1075C2×C4—121no—
1076C2×C4—121no—
1077C2×C4—121no—
1078C2×C4—121no—
1079C2×C4—121no—
1080C2×C4—121no—
1081C2×C4—121no—
1082C2×C4—121no—
1083C2×C4—121no—
1084C2×C4—121no—
1085C2×C4—121no—
1086C2×C4—121no—
1087C2×C4—121no—
1088C2×C4—121no—
1089C2×C4—121no—
1090C2×C4—121no—
1091C2×C4—121no—
1092C2×C4—121no—
1093C2×C4—121no—
1094C2×C4—121no—
1095C2×C4—121no—
1096C2×C4—121no—
1097C2×C4—121no—
1098C2×C4—121no—
1099C2×C4#88514yescomplemented
1100C2×C3—44no—
1101C2×C3C2×#38611yescharacteristic
1102C2×C3C4×#12411yescharacteristic
1103C2×C3#232611yescharacteristic
1104C2×C3#233911yescharacteristic
1105C2×C3#233911yescharacteristic
1106C2×C3#236711yescharacteristic
1107C2×C3#236711yescharacteristic
1108C2×C3#242711yescharacteristic
1109C2×C3#242711yescharacteristic
1110C2×C3#243211yescharacteristic
1111C2×C3#243511yescharacteristic
1112C2×C3#244711yescharacteristic
1113C2×C3#244711yescharacteristic
1114C2×C3#254411yescharacteristic
1115C2×C3#254711yescharacteristic
1116D3—44no—
1117C22—24no—
1118C22—24no—
1119C22—24no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—64no—
1133C22—64no—
1134C22—64no—
1135C22—122no—
1136C22—122no—
1137C22—122no—
1138C22—122no—
1139C22—122no—
1140C22—122no—
1141C22—122no—
1142C22—122no—
1143C22—122no—
1144C22—122no—
1145C22—122no—
1146C22—122no—
1147C22C4×#23511yescharacteristic
1148C22C2×D3×C22⋊C411yescharacteristic
1149C22#549011yescharacteristic
1150C22#549011yescharacteristic
1151C22#549011yescharacteristic
1152C22C2×#88511yescharacteristic
1153C22#550411yescharacteristic
1154C22#550711yescharacteristic
1155C22#550711yescharacteristic
1156C22#552811yescharacteristic
1157C22#553311yescharacteristic
1158C22C4×#23711yescharacteristic
1159C22#553811yescharacteristic
1160C22C4×D3×D411yescharacteristic
1161C22C4×D3×D411yescharacteristic
1162C22#554611yescharacteristic
1163C22#554811yescharacteristic
1164C22#555211yescharacteristic
1165C22#555911yescharacteristic
1166C22D3×#12011yescharacteristic
1167C22#559111yescharacteristic
1168C22#559111yescharacteristic
1169C22#559211yescharacteristic
1170C22D3×#12111yescharacteristic
1171C22D3×#12111yescharacteristic
1172C22#561011yescharacteristic
1173C22#561111yescharacteristic
1174C22#562811yescharacteristic
1175C22#563311yescharacteristic
1176C22#564011yescharacteristic
1177C22#564111yescharacteristic
1178C22D3×#12311yescharacteristic
1179C22#565511yescharacteristic
1180C22#566211yescharacteristic
1181C22#566411yescharacteristic
1182C4—24no—
1183C4—38no—
1184C4—42no—
1185C4—42no—
1186C4—42no—
1187C4—42no—
1188C4—81no—
1189C4—122no—
1190C4—122no—
1191C4—122no—
1192C4—122no—
1193C4—122no—
1194C4—241no—
1195C3#1402711yescharacteristic, complemented, Sylow
1196C2—44no—
1197C2—124no—
1198C2#7336811yescharacteristic
1199C2C4×#88511yescharacteristic
1200C2#7347211yescharacteristic
1201C2#7382711yescharacteristic
1202C2#7389511yescharacteristic
1203C2#7393711yescharacteristic
1204C2#7406811yescharacteristic
1205C2#7438611yescharacteristic
1206C2#7439811yescharacteristic
1207C2#7441111yescharacteristic
1208C2#7442011yescharacteristic
1209C2#7467211yescharacteristic
1210C2#7469711yescharacteristic
1211C2#7475311yescharacteristic
1212C2D3×#38611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×C22⋊#95C2
socle, cosocleC24×C3C24
prime radicalC23×#67C22
hypercenterC22⋊#95D3
hypocenterC3#14027
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#4646C2semidirect
5. C2×#4646C2semidirect
6. C3×C22⋊#95C2semidirect
7. #72127C2semidirect
8. #71549C2semidirect
9. #71548C2semidirect
10. #69429C2semidirect
11. #69429C2semidirect
12. (C2×D3)⋊#95C2semidirect
13. (C2×D3)⋊#95C2semidirect
14. Dic3⋊#95C2semidirect
15. Dic3×#95C2semidirect
41. C2×#885C4semidirect
74. C22⋊#95D3semidirect
118. C22×Dic6C2×C4semidirect
124. C2×C3×C22⋊C4C2×C4semidirect
133. C2×#217C2×C4semidirect
148. C2×(C2×D3)⋊C4C2×C4semidirect
149. C2×(C2×D3)⋊C4C2×C4semidirect
163. C2×C4×Dic3C2×C4semidirect
471. C2×C22⋊C4C4×D3semidirect
624. C2×C3×C4#124semidirect
1099. C2×C4#885semidirect
1195. C3#14027semidirect

Maximal subgroups

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

subgroupindex
C22×C4×#672
C22×#8852
C2×#49572
C2×#46462
C3×C22⋊#952
#721272
#715492
#715482
#694292
(C2×D3)⋊#952
Dic3⋊#952
Dic3×#952
#140273