Finite Group Databasebeta

← #10804160

Subgroups — #10804160

Order 768.

1426 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C22⋊Q8C211yesmaximal, characteristic
2C2×#5126C211yesmaximal, characteristic
3D3×#407C211yesmaximal, characteristic
4C3×#1901C211yesmaximal, characteristic, complemented
5#72003C211yesmaximal, characteristic, complemented
6#71698C211yesmaximal, characteristic, complemented
7#70115C212yesmaximal, complemented
8#70113C212yesmaximal, complemented
9#69986C211yesmaximal, characteristic, complemented
10#68993C212yesmaximal, complemented
11#68990C212yesmaximal, complemented
12#21753—31nomaximal, Sylow
13C22×D3×Q8C2211yescharacteristic
14C23×C4×D3C2211yescharacteristic
15C22×C3×M16C2211yescharacteristic
16C2×C3×C22⋊Q8C2211yescharacteristic
17C2×#946C2211yescharacteristic
18C2×#924C2211yescharacteristic
19C22×#208C2211yescharacteristic
20C2×D3×M16C2212yes—
21D3×C22⋊Q8—21no—
22D3×C22⋊Q8—21no—
23D3×C22⋊Q8—21no—
24D3×C22⋊Q8—21no—
25D3×C22⋊Q8—21no—
26D3×C22⋊Q8—21no—
27D3×C22⋊Q8—21no—
28D3×C22⋊Q8—21no—
29C2×#897C2211yescharacteristic
30C2×#896C412yes—
31C2×D3×C4⋊C4C412yes—
32C2×D3×C4⋊C4C2211yescharacteristic
33C2×D3×C22⋊C4C412yes—
34C2×#878C412yes—
35C2×C3×#101C2212yescomplemented
36C3×#407C2211yescharacteristic
37C2×#836C2212yescomplemented
38#5207C2211yescharacteristic
39C2×#824C2212yescomplemented
40C2×#824C2212yescomplemented
41#5126—21no—
42#5126—21no—
43#5126C2212yes—
44#5126C2212yes—
45#5126C2212yes—
46C2×(C2×D3)⋊C8—21no—
47C2×(C2×D3)⋊C8—21no—
48#4726—21no—
49#4726—21no—
50D3×C22⋊C8—21no—
51D3×C22⋊C8—21no—
52C3×#343C2212yescomplemented
53#4554C2212yescomplemented
54#4554C2212yescomplemented
55#4530C2212yescomplemented
56C22×C22⋊Q8—31no—
57C2×#407—31no—
58C2×#407—31no—
59#1901—32no—
60#1901—31no—
61#1901—32no—
62#1901—31no—
63#1901—31no—
64#1901D311yescharacteristic, complemented
65#1821—32no—
66#1784—32no—
67C24×D3C2×C411yescharacteristic
68C22×C3×Q8C2311yescharacteristic
69C23×C3×C4C2311yescharacteristic
70C23×Dic3C2×C411yescharacteristic
71C2×D3×Q8—21no—
72C2×D3×Q8—21no—
73C2×D3×Q8—21no—
74C2×D3×Q8—21no—
75C2×D3×Q8—42no—
76C2×D3×Q8—42no—
77C22×C4×D3—42no—
78C22×C4×D3—42no—
79C22×C4×D3C2×C412yes—
80C22×C4×D3C2×C412yes—
81C22×C4×D3C2×C411yescharacteristic
82C22×C4×D3C2×C411yescharacteristic
83C22×C4×D3D411yescharacteristic
84C22×C4×D3D411yescharacteristic
85C22×C4×D3D411yescharacteristic
86C22×C4×D3D411yescharacteristic
87C22×C4×D3D411yescharacteristic
88C22×C4×D3D411yescharacteristic
89C22×C4×D3D411yescharacteristic
90C22×C4×D3D411yescharacteristic
91C22×C4×D3C2311yescharacteristic
92C22×C4×D3C2311yescharacteristic
93C22×Dic6C2×C412yes—
94C22×Dic6C2311yescharacteristic
95C2×C3×M16—21no—
96C2×C3×M16—42no—
97C2×C3×M16C2312yes—
98C2×C3×M16C2312yes—
99C22×C3×C8—21no—
100C3×C22⋊Q8—21no—
101C3×C22⋊Q8—21no—
102C3×C22⋊Q8—21no—
103C3×C22⋊Q8—21no—
104C2×C3×C4⋊C4C2×C412yes—
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C22⋊C4C2×C412yes—
107C2×#217C2×C412yes—
108#946—21no—
109#946—21no—
110#946—21no—
111#946—21no—
112C2×(C2×D3)⋊C4C2×C412yes—
113C2×(C2×D3)⋊C4C2×C412yes—
114C2×C4⋊Dic3C2×C412yes—
115C2×C4⋊Dic3C2311yescharacteristic
116#924—21no—
117#924—21no—
118#924—21no—
119#924—21no—
120C2×Dic3⋊C4C2×C412yes—
121C2×Dic3⋊C4C2×C412yes—
122C2×Dic3⋊C4C2×C412yes—
123C2×#208—21no—
124C2×#208—42no—
125C2×#208C2312yes—
126C2×#208C2312yes—
127C22×C3⋊C8—21no—
128D3×M16—42no—
129D3×M16—42no—
130C2×ΓL(1,𝔽25)—22no—
131C2×D3×C8—22no—
132#897—21no—
133#897—21no—
134#897—21no—
135#897—21no—
136#896—22no—
137#896—22no—
138#896—22no—
139#896—22no—
140D3×C4⋊C4—22no—
141D3×C4⋊C4—22no—
142D3×C4⋊C4—22no—
143D3×C4⋊C4—22no—
144D3×C4⋊C4—21no—
145D3×C4⋊C4—21no—
146D3×C4⋊C4—21no—
147D3×C4⋊C4—21no—
148D3×C22⋊C4—22no—
149D3×C22⋊C4—22no—
150D3×C22⋊C4—22no—
151D3×C22⋊C4—22no—
152#878—22no—
153#878—22no—
154#878—22no—
155#878—22no—
156C3×#101—42no—
157C3×C22⋊C8—21no—
158C3×C22⋊C8—21no—
159#836—42no—
160#830—21no—
161#830—21no—
162#824—42no—
163#824—42no—
164(C2×D3)⋊C8—22no—
165(C2×D3)⋊C8—22no—
166(C2×D3)⋊C8—22no—
167(C2×D3)⋊C8—22no—
168(C2×D3)⋊C8—22no—
169(C2×D3)⋊C8—22no—
170C23×Q8—31no—
171C24×C4—31no—
172C22×M16—31no—
173C22×M16—32no—
174C22×M16C2×D311yescharacteristic
175C2×C22⋊Q8—31no—
176C2×C22⋊Q8—31no—
177C2×C22⋊Q8—32no—
178C2×C22⋊Q8—31no—
179C2×C22⋊Q8—32no—
180C2×C22⋊Q8—61no—
181C2×C22⋊Q8—61no—
182C2×C22⋊Q8—61no—
183C2×C22⋊Q8—61no—
184C2×C22⋊Q8—61no—
185C2×C22⋊Q8—61no—
186C2×C22⋊Q8—61no—
187C2×C22⋊Q8—61no—
188C2×C22⋊Q8C2×D311yescharacteristic
189C22×C4⋊C4—32no—
190C22×C4⋊C4—31no—
191C22×C22⋊C4—32no—
192C2×#101—32no—
193C2×#101—32no—
194C2×#101—32no—
195C2×#101C2×D312yescomplemented
196#407—31no—
197#407—32no—
198#407—32no—
199#407—32no—
200#407—61no—
201#407—61no—
202#407—61no—
203#407—61no—
204#407C2×D311yescharacteristic
205C2×C22⋊C8—61no—
206C2×C22⋊C8—61no—
207C2×C22⋊C8—61no—
208C2×C22⋊C8—61no—
209#343—32no—
210#343—32no—
211#343—32no—
212#343C2×D312yescomplemented
213C24×C3C22×C411yescharacteristic
214C23×D3—24no—
215C23×D3—42no—
216C23×D3—42no—
217C23×D3C22⋊C411yescharacteristic
218C23×D3C22⋊C411yescharacteristic
219C23×D3C22⋊C411yescharacteristic
220C23×D3C22⋊C411yescharacteristic
221C23×D3C22×C411yescharacteristic
222C23×D3C22×C411yescharacteristic
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—22no—
226C2×C3×Q8—22no—
227C22×C3×C4—22no—
228C22×C3×C4—22no—
229C22×C3×C4C22×C412yes—
230C22×C3×C4C22×C411yescharacteristic
231C22×C3×C4C22×C412yes—
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2411yescharacteristic
237C22×Dic3—42no—
238C22×Dic3C22⋊C411yescharacteristic
239C22×Dic3C22⋊C411yescharacteristic
240C22×Dic3C22⋊C411yescharacteristic
241C22×Dic3C22⋊C411yescharacteristic
242C22×Dic3C22×C412yes—
243C22×Dic3C22×C411yescharacteristic
244C22×Dic3C22×C411yescharacteristic
245C22×Dic3C22×C412yes—
246D3×Q8—42no—
247D3×Q8—42no—
248D3×Q8—42no—
249D3×Q8—42no—
250D3×Q8—44no—
251D3×Q8—44no—
252C2×C4×D3—22no—
253C2×C4×D3—22no—
254C2×C4×D3—22no—
255C2×C4×D3—22no—
256C2×C4×D3—22no—
257C2×C4×D3—22no—
258C2×C4×D3—22no—
259C2×C4×D3—22no—
260C2×C4×D3—42no—
261C2×C4×D3—42no—
262C2×C4×D3—42no—
263C2×C4×D3—42no—
264C2×C4×D3—41no—
265C2×C4×D3—41no—
266C2×C4×D3—41no—
267C2×C4×D3—41no—
268C2×C4×D3—41no—
269C2×C4×D3—41no—
270C2×C4×D3—41no—
271C2×C4×D3—41no—
272C2×C4×D3—42no—
273C2×C4×D3—42no—
274C2×C4×D3—44no—
275C2×C4×D3—44no—
276C2×C4×D3C22⋊C411yescharacteristic
277C2×C4×D3C22⋊C411yescharacteristic
278C2×C4×D3C22⋊C411yescharacteristic
279C2×C4×D3C22⋊C411yescharacteristic
280C2×C4×D3C22⋊C411yescharacteristic
281C2×C4×D3C22⋊C411yescharacteristic
282C2×C4×D3C22⋊C411yescharacteristic
283C2×C4×D3C22⋊C411yescharacteristic
284C2×C4×D3C2×D411yescharacteristic
285C2×C4×D3C2×D411yescharacteristic
286C2×C4×D3C2×D411yescharacteristic
287C2×C4×D3C2×D411yescharacteristic
288C2×C4×D3C2×D411yescharacteristic
289C2×C4×D3C2×D411yescharacteristic
290C2×C4×D3C2×D411yescharacteristic
291C2×C4×D3C2×D411yescharacteristic
292C2×Dic6—21no—
293C2×Dic6—21no—
294C2×Dic6—22no—
295C2×Dic6—22no—
296C2×Dic6—22no—
297C2×Dic6—22no—
298C2×Dic6—44no—
299C3×M16—22no—
300C3×M16—22no—
301C3×M16—22no—
302C3×M16—22no—
303C3×M16—42no—
304C2×C3×C8—22no—
305C2×C3×C8—22no—
306C2×C3×C8—42no—
307C3×C4⋊C4—22no—
308C3×C4⋊C4—22no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—21no—
311C3×C22⋊C4—22no—
312C3×C22⋊C4—22no—
313#217—22no—
314#217—22no—
315(C2×D3)⋊C4—22no—
316(C2×D3)⋊C4—22no—
317(C2×D3)⋊C4—22no—
318(C2×D3)⋊C4—22no—
319C4⋊Dic3—21no—
320C4⋊Dic3—21no—
321C4⋊Dic3—22no—
322C4⋊Dic3—22no—
323Dic3⋊C4—22no—
324Dic3⋊C4—22no—
325Dic3⋊C4—22no—
326Dic3⋊C4—22no—
327Dic3⋊C4—22no—
328Dic3⋊C4—22no—
329#208—22no—
330#208—22no—
331#208—22no—
332#208—22no—
333#208—42no—
334C2×C3⋊C8—22no—
335C2×C3⋊C8—22no—
336C2×C3⋊C8—42no—
337ΓL(1,𝔽25)—44no—
338D3×C8—44no—
339C25—31no—
340C22×Q8—32no—
341C22×Q8—31no—
342C22×Q8—61no—
343C22×Q8—61no—
344C22×Q8—61no—
345C22×Q8—61no—
346C22×Q8—122no—
347C22×Q8—122no—
348C22×Q8C22×D311yescharacteristic
349C23×C4—31no—
350C23×C4—31no—
351C23×C4—31no—
352C23×C4—31no—
353C23×C4—31no—
354C23×C4—31no—
355C23×C4—31no—
356C23×C4—31no—
357C23×C4—31no—
358C23×C4—31no—
359C23×C4—31no—
360C23×C4—31no—
361C23×C4—31no—
362C23×C4—32no—
363C23×C4—32no—
364C23×C4—122no—
365C23×C4—122no—
366C23×C4C22×D311yescharacteristic
367C2×M16—21no—
368C2×M16—32no—
369C2×M16—32no—
370C2×M16—42no—
371C2×M16—62no—
372C2×M16—61no—
373C2×M16—122no—
374C2×M16—122no—
375C2×M16—122no—
376C2×M16C22×D312yes—
377C2×M16C22×D312yes—
378C22×C8—21no—
379C22×C8—62no—
380C22×C8—61no—
381C22⋊Q8—21no—
382C22⋊Q8—21no—
383C22⋊Q8—21no—
384C22⋊Q8—21no—
385C22⋊Q8—62no—
386C22⋊Q8—62no—
387C22⋊Q8—62no—
388C22⋊Q8—62no—
389C22⋊Q8—62no—
390C22⋊Q8—62no—
391C22⋊Q8—62no—
392C22⋊Q8—62no—
393C22⋊Q8—61no—
394C22⋊Q8—61no—
395C22⋊Q8—61no—
396C22⋊Q8—61no—
397C22⋊Q8—61no—
398C22⋊Q8—61no—
399C22⋊Q8—61no—
400C22⋊Q8—61no—
401C22⋊Q8—61no—
402C22⋊Q8—61no—
403C22⋊Q8—61no—
404C22⋊Q8—61no—
405C2×C4⋊C4—32no—
406C2×C4⋊C4—32no—
407C2×C4⋊C4—32no—
408C2×C4⋊C4—32no—
409C2×C4⋊C4—31no—
410C2×C4⋊C4—62no—
411C2×C4⋊C4—62no—
412C2×C4⋊C4—62no—
413C2×C4⋊C4—62no—
414C2×C4⋊C4—61no—
415C2×C4⋊C4—61no—
416C2×C4⋊C4—61no—
417C2×C4⋊C4—61no—
418C2×C4⋊C4C4×D312yes—
419C2×C4⋊C4C22×D311yescharacteristic
420C2×C22⋊C4—32no—
421C2×C22⋊C4—32no—
422C2×C22⋊C4—32no—
423C2×C22⋊C4—62no—
424C2×C22⋊C4—62no—
425C2×C22⋊C4—62no—
426C2×C22⋊C4—62no—
427C2×C22⋊C4C4×D312yes—
428#101—42no—
429#101—122no—
430#101—122no—
431#101—122no—
432C22⋊C8—21no—
433C22⋊C8—21no—
434C22⋊C8—62no—
435C22⋊C8—62no—
436C22⋊C8—62no—
437C22⋊C8—62no—
438C22⋊C8—62no—
439C22⋊C8—62no—
440C22⋊C8—61no—
441C22⋊C8—61no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—41no—
445C23×C3C2×C22⋊C411yescharacteristic
446C23×C3C2×C22⋊C411yescharacteristic
447C23×C3C23×C411yescharacteristic
448C22×D3—22no—
449C22×D3—22no—
450C22×D3—22no—
451C22×D3—22no—
452C22×D3—22no—
453C22×D3—22no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—41no—
459C22×D3—41no—
460C22×D3—41no—
461C22×D3—41no—
462C22×D3—41no—
463C22×D3—41no—
464C22×D3—41no—
465C22×D3—416no—
466C22×D3#10114yescomplemented
467C22×D3C2×C22⋊C411yescharacteristic
468C22×D3C2×C22⋊C411yescharacteristic
469C22×D3C2×C22⋊C411yescharacteristic
470C22×D3C2×C22⋊C411yescharacteristic
471C3×Q8—41no—
472C3×Q8—41no—
473C3×Q8—42no—
474C2×C3×C4—22no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—24no—
484C2×C3×C4—42no—
485C2×C3×C4C2×C22⋊C411yescharacteristic
486C2×C3×C4C2×C22⋊C411yescharacteristic
487C2×C3×C4C22×D411yescharacteristic
488C2×C3×C4C22×D411yescharacteristic
489C2×C3×C4H(5,𝔽2)12yes—
490C2×C3×C4H(5,𝔽2)12yes—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—24no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498C2×Dic3—41no—
499C2×Dic3—41no—
500C2×Dic3—42no—
501C2×Dic3C2×C22⋊C411yescharacteristic
502C2×Dic3C2×C22⋊C411yescharacteristic
503C2×Dic3C2×C22⋊C411yescharacteristic
504C2×Dic3C2×C22⋊C411yescharacteristic
505C4×D3—22no—
506C4×D3—22no—
507C4×D3—21no—
508C4×D3—21no—
509C4×D3—21no—
510C4×D3—21no—
511C4×D3—21no—
512C4×D3—21no—
513C4×D3—21no—
514C4×D3—21no—
515C4×D3—22no—
516C4×D3—22no—
517C4×D3—41no—
518C4×D3—41no—
519C4×D3—41no—
520C4×D3—41no—
521C4×D3—41no—
522C4×D3—41no—
523C4×D3—41no—
524C4×D3—41no—
525C4×D3—44no—
526C4×D3—44no—
527C4×D3—44no—
528C4×D3—44no—
529Dic6—44no—
530Dic6—44no—
531Dic6—41no—
532Dic6—41no—
533Dic6—42no—
534C3×C8—42no—
535C3×C8—42no—
536C3⋊C8—42no—
537C3⋊C8—42no—
538C24—31no—
539C24—31no—
540C24—31no—
541C24—31no—
542C24—31no—
543C24—31no—
544C24—64no—
545C24—122no—
546C24—122no—
547C24C2×C4×D311yescharacteristic
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—62no—
553C2×Q8—62no—
554C2×Q8—61no—
555C2×Q8—61no—
556C2×Q8—62no—
557C2×Q8—62no—
558C2×Q8—124no—
559C2×Q8—122no—
560C2×Q8—122no—
561C2×Q8—122no—
562C2×Q8—122no—
563C2×Q8—124no—
564C2×Q8—124no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—31no—
568C22×C4—31no—
569C22×C4—31no—
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—31no—
576C22×C4—31no—
577C22×C4—31no—
578C22×C4—31no—
579C22×C4—31no—
580C22×C4—31no—
581C22×C4—31no—
582C22×C4—31no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—31no—
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—32no—
590C22×C4—32no—
591C22×C4—62no—
592C22×C4—62no—
593C22×C4—62no—
594C22×C4—62no—
595C22×C4—62no—
596C22×C4—62no—
597C22×C4—62no—
598C22×C4—62no—
599C22×C4—121no—
600C22×C4—121no—
601C22×C4—121no—
602C22×C4—121no—
603C22×C4—121no—
604C22×C4—121no—
605C22×C4—121no—
606C22×C4—121no—
607C22×C4—122no—
608C22×C4—122no—
609C22×C4—122no—
610C22×C4—122no—
611C22×C4—122no—
612C22×C4—122no—
613C22×C4—124no—
614C22×C4—124no—
615C22×C4—122no—
616C22×C4C2×C4×D312yes—
617C22×C4C2×C4×D311yescharacteristic
618C22×C4C2×C4×D312yes—
619C22×C4D3×D411yescharacteristic
620C22×C4D3×D411yescharacteristic
621C22×C4D3×D411yescharacteristic
622C22×C4D3×D411yescharacteristic
623C22×C4C23×D311yescharacteristic
624M16—22no—
625M16—22no—
626M16—22no—
627M16—22no—
628M16—42no—
629M16—62no—
630M16—62no—
631M16—62no—
632M16—62no—
633M16—124no—
634M16—122no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—42no—
638C2×C8—62no—
639C2×C8—62no—
640C2×C8—124no—
641C2×C8—122no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—62no—
647C4⋊C4—62no—
648C4⋊C4—62no—
649C4⋊C4—62no—
650C4⋊C4—62no—
651C4⋊C4—62no—
652C4⋊C4—62no—
653C4⋊C4—62no—
654C4⋊C4—61no—
655C4⋊C4—61no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—62no—
659C22⋊C4—62no—
660C22⋊C4—62no—
661C22⋊C4—62no—
662C22⋊C4—62no—
663C22⋊C4—62no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—44no—
672C22×C3C2×#10112yes—
673C22×C3C22×C22⋊C411yescharacteristic
674C22×C3#51812yes—
675C2×D3—28no—
676C2×D3—21no—
677C2×D3—21no—
678C2×D3—21no—
679C2×D3—21no—
680C2×D3—21no—
681C2×D3—21no—
682C2×D3—21no—
683C2×D3—21no—
684C2×D3—21no—
685C2×D3—44no—
686C2×D3—44no—
687C2×D3—44no—
688C2×D3—44no—
689C2×D3—44no—
690C2×D3C2×#10112yes—
691C2×D3C2×#10112yes—
692C2×D3#41312yes—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—42no—
696C3×C4—42no—
697C3×C4#53411yescharacteristic
698C3×C4#53411yescharacteristic
699C3×C4#53412yes—
700Dic3—21no—
701Dic3—21no—
702Dic3—21no—
703Dic3—21no—
704Dic3—42no—
705Dic3—42no—
706C23—22no—
707C23—22no—
708C23—31no—
709C23—31no—
710C23—31no—
711C23—34no—
712C23—31no—
713C23—41no—
714C23—62no—
715C23—62no—
716C23—62no—
717C23—62no—
718C23—62no—
719C23—62no—
720C23—62no—
721C23—62no—
722C23—62no—
723C23—62no—
724C23—121no—
725C23—121no—
726C23—121no—
727C23—121no—
728C23—121no—
729C23—121no—
730C23—121no—
731C23—1216no—
732C23D3×C22⋊C411yescharacteristic
733C23D3×C22⋊C411yescharacteristic
734C23C22×C4×D311yescharacteristic
735Q8—41no—
736Q8—41no—
737Q8—42no—
738Q8—124no—
739Q8—124no—
740Q8—121no—
741Q8—121no—
742Q8—122no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—31no—
754C2×C4—31no—
755C2×C4—31no—
756C2×C4—31no—
757C2×C4—42no—
758C2×C4—62no—
759C2×C4—62no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—62no—
769C2×C4—62no—
770C2×C4—62no—
771C2×C4—62no—
772C2×C4—62no—
773C2×C4—62no—
774C2×C4—64no—
775C2×C4—121no—
776C2×C4—121no—
777C2×C4—121no—
778C2×C4—121no—
779C2×C4—121no—
780C2×C4—121no—
781C2×C4—121no—
782C2×C4—121no—
783C2×C4—124no—
784C2×C4—124no—
785C2×C4—124no—
786C2×C4—124no—
787C2×C4—121no—
788C2×C4—121no—
789C2×C4—121no—
790C2×C4—121no—
791C2×C4—122no—
792C2×C4D3×C22⋊C411yescharacteristic
793C2×C4D3×C22⋊C411yescharacteristic
794C2×C4C2×D3×D411yescharacteristic
795C2×C4C2×D3×D411yescharacteristic
796C2×C4#100412yes—
797C2×C4#100912yes—
798C8—42no—
799C8—42no—
800C8—122no—
801C8—122no—
802C2×C3—22no—
803C2×C3—22no—
804C2×C3—41no—
805C2×C3#230811yescharacteristic
806C2×C3C22×#10111yescharacteristic
807C2×C3C2×#41311yescharacteristic
808D3—22no—
809D3—22no—
810D3—22no—
811D3—41no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—32no—
820C22—32no—
821C22—32no—
822C22—44no—
823C22—68no—
824C22—61no—
825C22—61no—
826C22—61no—
827C22—61no—
828C22—61no—
829C22—61no—
830C22—61no—
831C22—61no—
832C22—61no—
833C22—124no—
834C22—124no—
835C22—124no—
836C22—124no—
837C22—124no—
838C22D3×#10112yes—
839C22C2×D3×C22⋊C411yescharacteristic
840C22#554512yes—
841C4—21no—
842C4—21no—
843C4—42no—
844C4—42no—
845C4—61no—
846C4—61no—
847C4—61no—
848C4—61no—
849C4—122no—
850C4—122no—
851C4#558911yescharacteristic
852C4#560512yes—
853C4#565311yescharacteristic
854C3#2175311yescharacteristic, complemented, Sylow
855C2—22no—
856C2—22no—
857C2—41no—
858C2—62no—
859C2—62no—
860C2—62no—
861C2—121no—
862C2#7487411yescharacteristic
863C2C2×D3×#10111yescharacteristic
864C2D3×#41311yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊C4
commutatorC23×C3C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1901C2
socleC22×C3C22×C22⋊C4
prime radicalC24×D3C2×C4
cosocleC22×C3×C4C24
hypercenter#1901D3
hypocenterC3#21753
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1901

Complements

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

NH ≅ G/Ntype
4. C3×#1901C2semidirect
5. #72003C2semidirect
6. #71698C2semidirect
7. #70115C2semidirect
8. #70113C2semidirect
9. #69986C2semidirect
10. #68993C2semidirect
11. #68990C2semidirect
35. C2×C3×#101C22semidirect
37. C2×#836C22semidirect
39. C2×#824C22semidirect
40. C2×#824C22semidirect
52. C3×#343C22semidirect
53. #4554C22semidirect
54. #4554C22semidirect
55. #4530C22semidirect
64. #1901D3semidirect
195. C2×#101C2×D3semidirect
212. #343C2×D3semidirect
466. C22×D3#101semidirect
854. C3#21753semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C22⋊Q82
C2×#51262
D3×#4072
C3×#19012
#720032
#716982
#701152
#701132
#699862
#689932
#689902
#217533