Finite Group Databasebeta

← #10944154

Subgroups — #10944154

Order 768.

1448 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5827C211yesmaximal, characteristic, complemented
2C2×C3×#452C211yesmaximal, characteristic, complemented
3C2×#5238C211yesmaximal, characteristic
4C2×#5185C211yesmaximal, characteristic, complemented
5C2×#5165C211yesmaximal, characteristic, complemented
6#82821C211yesmaximal, characteristic, complemented
7#72065C211yesmaximal, characteristic, complemented
8#72047C211yesmaximal, characteristic, complemented
9#71692C211yesmaximal, characteristic, complemented
10#70240C211yesmaximal, characteristic, complemented
11#70221C211yesmaximal, characteristic, complemented
12#70172C211yesmaximal, characteristic, complemented
13#70153C211yesmaximal, characteristic, complemented
14#69932C211yesmaximal, characteristic, complemented
15#69909C211yesmaximal, characteristic, complemented
16#32919—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21#5827—24no—
22#5827—24no—
23C2×#947C2211yescharacteristic
24C2×Q8×Dic3C2211yescharacteristic
25C2×Q8×Dic3C2211yescharacteristic
26C22×#215C2211yescharacteristic
27C2×D4×Dic3—21no—
28C2×D4×Dic3—21no—
29C2×D4×Dic3C2211yescharacteristic
30C2×D4×Dic3C2211yescharacteristic
31C22×#213C2211yescharacteristic
32C2×#930C2211yescharacteristic
33C2×#926—21no—
34C2×#926C2211yescharacteristic
35C22×C4⋊Dic3—21no—
36C22×C4⋊Dic3C2211yescharacteristic
37C3×#452—24no—
38C2×C3×#103C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic
41#5238—24no—
42#5229C2211yescharacteristic
43C2×#835C2211yescharacteristic
44C2×#835C2211yescharacteristic
45C2×#835C2211yescharacteristic
46C2×#832C2211yescharacteristic
47C2×#830C2211yescharacteristic
48#5185—24no—
49#5165—24no—
50C2×#821C2211yescharacteristic
51C2×#821C2211yescharacteristic
52C2×Dic3⋊C8C2211yescharacteristic
53C2×Dic3⋊C8C2211yescharacteristic
54#4994—21no—
55#4994—21no—
56#4988C2211yescharacteristic
57#4975C2211yescharacteristic
58#4959—21no—
59#4959—21no—
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4550C2211yescharacteristic
63#4550C2211yescharacteristic
64#4529C2211yescharacteristic
65#4529C2211yescharacteristic
66C2×#520—31no—
67C2×#464—31no—
68C2×#463—31no—
69C2×#452D311yescharacteristic, complemented
70C2×#449—31no—
71#2620—31no—
72#1880—31no—
73#1879—31no—
74#1878—31no—
75#1877—31no—
76#1874—31no—
77#1872—31no—
78#1803—31no—
79#1802—31no—
80#1798—31no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41D414yes—
87C22×C3×Q8C2311yescharacteristic
88C22×C3×Q8C2311yescharacteristic
89C22×C3×D4—21no—
90C22×C3×D4C2311yescharacteristic
91C23×C3×C4—21no—
92C23×C3×C4C2311yescharacteristic
93C22×#67—21no—
94C23×Dic3—21no—
95C23×Dic3—21no—
96C23×Dic3—21no—
97C22×D12C2311yescharacteristic
98C2×C3×Q16—22no—
99C2×C3×Q16—22no—
100C2×C3×Q16—22no—
101C2×C3×SD16—22no—
102C2×C3×SD16—22no—
103C2×C3×SD16—22no—
104C22×C3×C8C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C3×C22⋊Q8—22no—
107C3×C22⋊Q8—22no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C22⋊C4—21no—
111C2×#217—21no—
112C2×#217—21no—
113C2×#217D411yescharacteristic
114C2×#217D411yescharacteristic
115#947—22no—
116#947—22no—
117Q8×Dic3—22no—
118Q8×Dic3—22no—
119Q8×Dic3—22no—
120Q8×Dic3D414yescomplemented
121C2×#215—22no—
122C2×#215—22no—
123C2×#215—22no—
124D4×Dic3—28no—
125D4×Dic3—28no—
126D4×Dic3—22no—
127D4×Dic3—22no—
128D4×Dic3—22no—
129D4×Dic3D414yescomplemented
130C2×#213—22no—
131C2×#213—22no—
132C2×#213—22no—
133#930—22no—
134#930—22no—
135C2×(C2×D3)⋊C4—21no—
136C2×(C2×D3)⋊C4—21no—
137C2×(C2×D3)⋊C4—21no—
138C2×(C2×D3)⋊C4—21no—
139C2×(C2×D3)⋊C4—21no—
140#926—28no—
141#926—22no—
142#926—22no—
143C2×C4⋊Dic3—28no—
144C2×C4⋊Dic3—21no—
145C2×C4⋊Dic3—21no—
146C2×C4⋊Dic3—21no—
147C2×C4⋊Dic3—22no—
148C2×C4⋊Dic3—22no—
149C2×C4⋊Dic3D411yescharacteristic
150C2×C4⋊Dic3D411yescharacteristic
151C2×C4⋊Dic3C2311yescharacteristic
152C2×C4⋊Dic3C2311yescharacteristic
153C2×C4⋊Dic3C2311yescharacteristic
154C2×Dic3⋊C4—21no—
155C2×Dic3⋊C4—21no—
156C2×C4×Dic3—21no—
157C2×C4×Dic3—21no—
158C2×C4×Dic3C2311yescharacteristic
159C2×C4×Dic3C2311yescharacteristic
160C22×C3⋊C8C2311yescharacteristic
161C22×C3⋊C8C2311yescharacteristic
162C3×#103—22no—
163C3×#102—22no—
164C3×C22⋊C8—22no—
165#835—22no—
166#835—22no—
167#835—22no—
168#832—22no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171#830—22no—
172#821—22no—
173#821—22no—
174Dic3⋊C8—22no—
175Dic3⋊C8—22no—
176C22×#41C2×D311yescharacteristic
177C22×Q16C2×D311yescharacteristic
178C22×SD16—31no—
179C22×SD16C2×D311yescharacteristic
180C22×D8—31no—
181C2×#124—31no—
182C2×C22⋊Q8C2×D311yescharacteristic
183C2×#121—31no—
184#520—64no—
185#520—64no—
186C2×C4×Q8—31no—
187C2×C4×Q8—31no—
188C2×C4×D4—31no—
189C2×C4×D4—31no—
190C2×C4×D4—61no—
191C2×C4×D4—61no—
192C2×#117—31no—
193C2×#117—61no—
194C22×C4⋊C4—31no—
195C22×C4⋊C4—61no—
196#464—64no—
197#463—64no—
198#452—24no—
199#449—64no—
200C2×C4⋊C8—31no—
201C2×C4⋊C8—31no—
202C2×#103—31no—
203C2×#103—31no—
204C2×#103—31no—
205C2×#103C2×D311yescharacteristic
206C2×#102—31no—
207C2×#102—31no—
208C2×#102—31no—
209C2×#102C2×D311yescharacteristic
210C2×C22⋊C8—31no—
211C2×C22⋊C8C2×D311yescharacteristic
212#396—61no—
213#396—61no—
214#394—61no—
215#394—61no—
216#391—31no—
217#390—31no—
218#384—31no—
219#340—31no—
220#340—31no—
221#340—31no—
222#340—31no—
223#336—31no—
224#336—31no—
225C24×C3—21no—
226C24×C3C2×D411yescharacteristic
227C23×D3—21no—
228C3×#41—28no—
229C3×#41—28no—
230C3×#41—28no—
231C3×#41—28no—
232C2×C3×Q8—21no—
233C2×C3×Q8—21no—
234C2×C3×Q8—21no—
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C2×C3×Q8—21no—
241C2×C3×Q8C2×D412yes—
242C2×C3×Q8C2×D412yes—
243C2×C3×Q8#4112yes—
244C2×C3×D4—24no—
245C2×C3×D4—24no—
246C2×C3×D4—24no—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4C2×D412yes—
251C2×C3×D4C2×D412yes—
252C2×C3×D4#4112yes—
253C22×C3×C4—24no—
254C22×C3×C4—24no—
255C22×C3×C4—21no—
256C22×C3×C4—24no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4C2×D411yescharacteristic
264C22×C3×C4C2×D412yes—
265C22×C3×C4#4112yes—
266C22×C3×C4C2411yescharacteristic
267C2×#67—42no—
268C2×#67—81no—
269C2×#67—81no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—24no—
273C22×Dic3—24no—
274C22×Dic3—24no—
275C22×Dic3—21no—
276C22×Dic3—81no—
277C22×Dic3—81no—
278C22×Dic3—81no—
279C22×Dic3—81no—
280C22×Dic3—81no—
281C22×Dic3—81no—
282C22×Dic3C2×D411yescharacteristic
283C22×Dic3C2×D411yescharacteristic
284C22×Dic3C2×D411yescharacteristic
285C22×Dic3C2×D411yescharacteristic
286C2×D12—21no—
287C2×D12—21no—
288C2×D12—21no—
289C2×D12—21no—
290C2×D12—21no—
291C2×D12—21no—
292C3×Q16—44no—
293C3×SD16—44no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8—21no—
297C2×C3×C8—21no—
298C2×C3×C8—21no—
299C2×C3×C8—21no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—42no—
303C3×C22⋊C4—42no—
304#217—24no—
305#217—22no—
306#217—22no—
307#217—24no—
308#215—44no—
309#213—44no—
310(C2×D3)⋊C4—42no—
311(C2×D3)⋊C4—42no—
312(C2×D3)⋊C4—42no—
313(C2×D3)⋊C4—81no—
314(C2×D3)⋊C4—81no—
315C4⋊Dic3—24no—
316C4⋊Dic3—24no—
317C4⋊Dic3—21no—
318C4⋊Dic3—21no—
319C4⋊Dic3—22no—
320C4⋊Dic3—24no—
321C4⋊Dic3—22no—
322C4⋊Dic3—21no—
323C4⋊Dic3—21no—
324C4⋊Dic3C2×D412yes—
325C4⋊Dic3C2×D412yes—
326Dic3⋊C4—81no—
327Dic3⋊C4—81no—
328C4×Dic3—24no—
329C4×Dic3—21no—
330C4×Dic3—21no—
331C4×Dic3—24no—
332C4×Dic3C2×D412yes—
333C4×Dic3C2×D412yes—
334C2×C3⋊C8—21no—
335C2×C3⋊C8—21no—
336C2×C3⋊C8—21no—
337C2×C3⋊C8—21no—
338C2×C3⋊C8—21no—
339C2×C3⋊C8—21no—
340C2×#41—22no—
341C2×#41—22no—
342C2×#41—22no—
343C2×#41—22no—
344C2×#41—22no—
345C2×#41#6714yes—
346C22×Q8C22×D311yescharacteristic
347C22×Q8C22×D311yescharacteristic
348C22×D4—21no—
349C22×D4—31no—
350C22×D4—61no—
351C22×D4C22×D311yescharacteristic
352C23×C4—21no—
353C23×C4—61no—
354C23×C4—61no—
355C23×C4—61no—
356C23×C4C22×D311yescharacteristic
357C2×Q16—22no—
358C2×Q16—22no—
359C2×Q16—22no—
360C2×SD16—22no—
361C2×SD16—22no—
362C2×SD16—22no—
363C2×SD16—62no—
364C2×SD16—62no—
365C2×SD16—62no—
366C2×D8—62no—
367C2×D8—62no—
368C2×D8—62no—
369C22×C8—31no—
370C22×C8—31no—
371C22×C8C22×D311yescharacteristic
372C22×C8C22×D311yescharacteristic
373#124—62no—
374#124—62no—
375C22⋊Q8—22no—
376C22⋊Q8—22no—
377#121—62no—
378#121—62no—
379C4×Q8—34no—
380C4×Q8—62no—
381C4×Q8—62no—
382C4×Q8—62no—
383C4×D4—34no—
384C4×D4—62no—
385C4×D4—62no—
386C4×D4—68no—
387C4×D4—68no—
388C4×D4—62no—
389#117—62no—
390#117—62no—
391#117—68no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—62no—
399C2×C4⋊C4—62no—
400C2×C4⋊C4—61no—
401C2×C4⋊C4—61no—
402C2×C4⋊C4—68no—
403C2×C4⋊C4—61no—
404C2×C4⋊C4—61no—
405C2×C4⋊C4—61no—
406C2×C4⋊C4C22×D311yescharacteristic
407C2×C22⋊C4—21no—
408C2×C22⋊C4—31no—
409C2×C22⋊C4—31no—
410C2×C22⋊C4—61no—
411C2×C22⋊C4—61no—
412C2×C22⋊C4—61no—
413C2×C22⋊C4—61no—
414C2×C22⋊C4—61no—
415C2×C22⋊C4—61no—
416C2×C22⋊C4—61no—
417C2×C42—31no—
418C2×C42—31no—
419C2×C42—61no—
420C2×C42—61no—
421C4⋊C8—62no—
422C4⋊C8—62no—
423#103—22no—
424#103—62no—
425#103—62no—
426#103—62no—
427#102—22no—
428#102—62no—
429#102—62no—
430#102—62no—
431C22⋊C8—22no—
432C22⋊C8—62no—
433#95—61no—
434#95—61no—
435C23×C3—21no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—21no—
439C23×C3—22no—
440C23×C3—21no—
441C23×C3—21no—
442C23×C3—21no—
443C23×C3—21no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3#12112yes—
449C23×C3C22×D411yescharacteristic
450C22×D3—41no—
451C22×D3—41no—
452C22×D3—41no—
453C22×D3—41no—
454C22×D3—41no—
455C22×D3—41no—
456C22×D3—41no—
457C3×Q8—22no—
458C3×Q8—22no—
459C3×Q8—22no—
460C3×Q8—41no—
461C3×Q8—41no—
462C3×Q8—41no—
463C3×Q8—41no—
464C3×Q8#12114yes—
465C3×D4—216no—
466C3×D4—22no—
467C3×D4—22no—
468C3×D4—22no—
469C3×D4#12114yes—
470C2×C3×C4—216no—
471C2×C3×C4—22no—
472C2×C3×C4—21no—
473C2×C3×C4—22no—
474C2×C3×C4—21no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4#12112yes—
487C2×C3×C4C22×D411yescharacteristic
488C2×C3×C4C22×D411yescharacteristic
489C2×C3×C4C22×D411yescharacteristic
490C2×C3×C4C2×#4111yescharacteristic
491C2×C3×C4C2×#4111yescharacteristic
492C2×C3×C4C2×#4111yescharacteristic
493#67—84no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—41no—
507C2×Dic3—41no—
508C2×Dic3—41no—
509C2×Dic3—41no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3—41no—
513C2×Dic3—84no—
514C2×Dic3—84no—
515C2×Dic3—84no—
516C2×Dic3#12012yes—
517C2×Dic3#12012yes—
518D12—41no—
519D12—41no—
520D12—41no—
521D12—41no—
522C3×C8—41no—
523C3×C8—41no—
524C3⋊C8—41no—
525C3⋊C8—41no—
526C24—21no—
527C24—61no—
528C24D3×D411yescharacteristic
529#41—28no—
530#41—28no—
531#41—28no—
532#41—28no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8D3×D412yes—
543C2×Q8#23712yes—
544C2×Q8C2×#6712yes—
545C2×D4—24no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—61no—
552C2×D4—61no—
553C2×D4—61no—
554C2×D4—61no—
555C2×D4—61no—
556C2×D4—61no—
557C2×D4—122no—
558C2×D4—241no—
559C2×D4—241no—
560C2×D4D3×D412yes—
561C2×D4#23712yes—
562C2×D4C2×#6712yes—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—31no—
576C22×C4—31no—
577C22×C4—64no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—64no—
581C22×C4—64no—
582C22×C4—61no—
583C22×C4—241no—
584C22×C4—241no—
585C22×C4—241no—
586C22×C4—241no—
587C22×C4—241no—
588C22×C4—241no—
589C22×C4D3×D411yescharacteristic
590C22×C4#23712yes—
591C22×C4C2×#6712yes—
592C22×C4C23×D311yescharacteristic
593Q16—44no—
594SD16—44no—
595SD16—124no—
596D8—124no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—61no—
604C2×C8—61no—
605C2×C8—61no—
606C2×C8—61no—
607C2×C8—61no—
608C2×C8—61no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—32no—
612C4⋊C4—32no—
613C4⋊C4—42no—
614C4⋊C4—62no—
615C4⋊C4—62no—
616C4⋊C4—64no—
617C4⋊C4—64no—
618C4⋊C4—64no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—241no—
624C4⋊C4—241no—
625C22⋊C4—42no—
626C22⋊C4—62no—
627C22⋊C4—62no—
628C22⋊C4—64no—
629C22⋊C4—64no—
630C22⋊C4—122no—
631C22⋊C4—122no—
632C22⋊C4—122no—
633C22⋊C4—241no—
634C22⋊C4—241no—
635C42—32no—
636C42—32no—
637C42—64no—
638C42—64no—
639C42—61no—
640C42—61no—
641C22×C3—22no—
642C22×C3—24no—
643C22×C3—22no—
644C22×C3—22no—
645C22×C3—41no—
646C22×C3—42no—
647C22×C3—41no—
648C22×C3—42no—
649C22×C3—41no—
650C22×C3—42no—
651C22×C3—41no—
652C22×C3—42no—
653C22×C3—42no—
654C22×C3—42no—
655C22×C3C2×#12011yescharacteristic
656C22×C3C2×#12111yescharacteristic
657C22×C3#52511yescharacteristic
658C22×C3#57611yescharacteristic
659C22×C3#57711yescharacteristic
660C22×C3#57711yescharacteristic
661C22×C3#57811yescharacteristic
662C2×D3—81no—
663C2×D3—81no—
664C2×D3—81no—
665C2×D3—81no—
666C2×D3—81no—
667C2×D3—81no—
668C2×D3—81no—
669C3×C4—22no—
670C3×C4—24no—
671C3×C4—81no—
672C3×C4—81no—
673C3×C4C2×#12111yescharacteristic
674C3×C4C2×#12111yescharacteristic
675C3×C4#52511yescharacteristic
676C3×C4#52511yescharacteristic
677Dic3—22no—
678Dic3—22no—
679Dic3—41no—
680Dic3—42no—
681Dic3—42no—
682Dic3—41no—
683Dic3—81no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—22no—
689C23—21no—
690C23—22no—
691C23—21no—
692C23—22no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—121no—
698C23—121no—
699C23—121no—
700C23—121no—
701C23—121no—
702C23—121no—
703C23—121no—
704C23#93912yes—
705C23C2×D3×D411yescharacteristic
706Q8—22no—
707Q8—22no—
708Q8—22no—
709Q8—41no—
710Q8—41no—
711Q8—41no—
712Q8—41no—
713Q8#93914yes—
714D4—216no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—121no—
719D4—121no—
720D4—121no—
721D4—121no—
722D4—244no—
723D4#93914yes—
724C2×C4—216no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—32no—
735C2×C4—32no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—62no—
752C2×C4—62no—
753C2×C4—61no—
754C2×C4—121no—
755C2×C4—121no—
756C2×C4—121no—
757C2×C4—121no—
758C2×C4—121no—
759C2×C4—121no—
760C2×C4—121no—
761C2×C4—244no—
762C2×C4—244no—
763C2×C4—244no—
764C2×C4#93912yes—
765C2×C4C2×D3×D411yescharacteristic
766C2×C4C2×D3×D411yescharacteristic
767C2×C4C2×#23711yescharacteristic
768C2×C4C2×#23711yescharacteristic
769C2×C4C2×#23711yescharacteristic
770C2×C4C22×#6711yescharacteristic
771C8—41no—
772C8—41no—
773C8—121no—
774C8—121no—
775C2×C3—42no—
776C2×C3—44no—
777C2×C3#284711yescharacteristic
778C2×C3#301211yescharacteristic
779C2×C3#301311yescharacteristic
780C2×C3#304511yescharacteristic
781C2×C3#304611yescharacteristic
782C2×C3#312411yescharacteristic
783C2×C3#312511yescharacteristic
784D3—161no—
785C22—22no—
786C22—22no—
787C22—24no—
788C22—22no—
789C22—42no—
790C22—41no—
791C22—42no—
792C22—41no—
793C22—42no—
794C22—41no—
795C22—42no—
796C22—41no—
797C22—42no—
798C22—42no—
799C22—241no—
800C22—241no—
801C22—241no—
802C22—241no—
803C22—241no—
804C22—241no—
805C22—241no—
806C22#558611yescharacteristic
807C22D3×#12011yescharacteristic
808C22#576911yescharacteristic
809C22#577011yescharacteristic
810C22#577811yescharacteristic
811C22#577911yescharacteristic
812C22C2×#93911yescharacteristic
813C4—22no—
814C4—24no—
815C4—62no—
816C4—62no—
817C4—81no—
818C4—81no—
819C4—121no—
820C4—122no—
821C4—122no—
822C4—121no—
823C4—241no—
824C4#558611yescharacteristic
825C4#558611yescharacteristic
826C4C2×#93911yescharacteristic
827C4C2×#93911yescharacteristic
828C3#3291911yescharacteristic, complemented, Sylow
829C2—42no—
830C2—44no—
831C2—481no—
832C2#8021811yescharacteristic
833C2#8021911yescharacteristic
834C2#8023111yescharacteristic
835C2#8023211yescharacteristic
836C2#8260111yescharacteristic
837C2#8390111yescharacteristic
838C2#8397111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#452C2
socleC23×C3C22×D4
prime radicalC2×#5238C2
hypercenterC2×#452D3
hypocenterC3#32919
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#5827C2semidirect
2. C2×C3×#452C2semidirect
4. C2×#5185C2semidirect
5. C2×#5165C2semidirect
6. #82821C2semidirect
7. #72065C2semidirect
8. #72047C2semidirect
9. #71692C2semidirect
10. #70240C2semidirect
11. #70221C2semidirect
12. #70172C2semidirect
13. #70153C2semidirect
14. #69932C2semidirect
15. #69909C2semidirect
69. C2×#452D3semidirect
120. Q8×Dic3D4semidirect
129. D4×Dic3D4semidirect
828. C3#32919semidirect

Maximal subgroups

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

subgroupindex
C2×#58272
C2×C3×#4522
C2×#52382
C2×#51852
C2×#51652
#828212
#720652
#720472
#716922
#702402
#702212
#701722
#701532
#699322
#699092
#329193