Finite Group Databasebeta

← #10830997

Subgroups — #10830997

Order 768.

1412 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#942C211yesmaximal, characteristic, complemented
2C3×#2409C211yesmaximal, characteristic, complemented
3C2×#5052C211yesmaximal, characteristic, complemented
4C2×#5049C211yesmaximal, characteristic, complemented
5#82402C211yesmaximal, characteristic
6C2×#5012C211yesmaximal, characteristic, complemented
7#72132C211yesmaximal, characteristic, complemented
8#71700C211yesmaximal, characteristic, complemented
9#71699C211yesmaximal, characteristic, complemented
10#69681C211yesmaximal, characteristic, complemented
11#69680C211yesmaximal, characteristic, complemented
12#69677C211yesmaximal, characteristic, complemented
13#69676C211yesmaximal, characteristic, complemented
14#69522C211yesmaximal, characteristic, complemented
15#69513C211yesmaximal, characteristic, complemented
16#24276—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic
18C22×#235C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22C22×#216C2211yescharacteristic
23C22×#216C2211yescharacteristic
24C2×#942—24no—
25C2×#942—24no—
26C2×#942—24no—
27C22×#215C2211yescharacteristic
28C22×#215C2211yescharacteristic
29C2×#930C2211yescharacteristic
30C2×#924C2211yescharacteristic
31C22×#208C2211yescharacteristic
32C22×#208C2211yescharacteristic
33C3×#395—21no—
34C3×#393—21no—
35C3×#391C2211yescharacteristic
36C3×#391C2211yescharacteristic
37C3×#386—21no—
38C3×#385—21no—
39C3×#380C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#835C2211yescharacteristic
42C2×#835C2211yescharacteristic
43C2×#835C2211yescharacteristic
44#5223—21no—
45#5212C2211yescharacteristic
46C2×#830C2211yescharacteristic
47C2×#830C2211yescharacteristic
48#5052—24no—
49#5049—24no—
50#5012—24no—
51#4989—21no—
52C2×#810C2211yescharacteristic
53C2×#810C2211yescharacteristic
54C2×#809C2211yescharacteristic
55C2×#809C2211yescharacteristic
56C2×#808C2211yescharacteristic
57C2×#807C2211yescharacteristic
58#4959—21no—
59#4956—21no—
60#4939C2211yescharacteristic
61#4929C2211yescharacteristic
62C2×C4⋊(C3⋊C8)C2211yescharacteristic
63C2×C4×C3⋊C8C2211yescharacteristic
64#4529C2211yescharacteristic
65#4529C2211yescharacteristic
66C22×#137—31no—
67C2×#470—31no—
68C2×#468—31no—
69C2×#436—31no—
70#2409D311yescharacteristic, complemented
71#2407—31no—
72#2056—31no—
73#2055—31no—
74#2001—31no—
75#2000—31no—
76#1969—31no—
77#1968—31no—
78#1809—31no—
79#1788—31no—
80#1787—31no—
81C22×C3×Q8—21no—
82C22×C3×Q8—22no—
83C22×C3×Q8—22no—
84C22×C3×Q8—22no—
85C22×C3×Q8—22no—
86C22×C3×Q8—41no—
87C22×C3×Q8—41no—
88C22×C3×Q8C2311yescharacteristic
89C22×C3×Q8C2311yescharacteristic
90C22×C3×D4D411yescharacteristic
91C23×C3×C4—21no—
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C22×#67—21no—
95C22×#67—21no—
96C2×#235—22no—
97C2×#235—22no—
98C2×#235—22no—
99C2×#235—22no—
100C2×#235—41no—
101C2×#235—41no—
102C22×D12C2311yescharacteristic
103C22×C4×D3—21no—
104C22×Dic6C2311yescharacteristic
105C3×C22⋊Q8—22no—
106C3×C22⋊Q8—22no—
107C3×C22⋊Q8—41no—
108C3×C22⋊Q8—41no—
109C3×C4×D4—22no—
110C3×C4×D4—22no—
111C2×C3×C4⋊C4—21no—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4D411yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4D411yescharacteristic
120C2×C3×C22⋊C4D411yescharacteristic
121C2×C3×C42C2311yescharacteristic
122C2×#217—21no—
123C2×#217—21no—
124C2×#216—22no—
125C2×#216—22no—
126C2×#216—22no—
127C2×#216—22no—
128C2×#216—22no—
129C2×#216D414yescomplemented
130#942—232no—
131C2×#215—22no—
132C2×#215—22no—
133C2×#215—22no—
134C2×#215—22no—
135C2×#215—22no—
136C2×#215D414yescomplemented
137#930—22no—
138#930—41no—
139C2×(C2×D3)⋊C4—21no—
140C2×(C2×D3)⋊C4—21no—
141C2×(C2×D3)⋊C4—21no—
142C2×C4⋊Dic3C2311yescharacteristic
143C2×C4⋊Dic3C2311yescharacteristic
144#924—22no—
145#924—41no—
146C2×Dic3⋊C4—21no—
147C2×#208—22no—
148C2×#208—22no—
149C2×#208—22no—
150C2×#208—22no—
151C2×#208—22no—
152C2×#208D414yescomplemented
153C22×C3⋊C8C2311yescharacteristic
154C22×C3⋊C8C2311yescharacteristic
155C22×C3⋊C8C2311yescharacteristic
156C22×C3⋊C8C2311yescharacteristic
157C3×#95—21no—
158C3×#95—21no—
159C3×#95—21no—
160C3×#95—21no—
161C3×#95—21no—
162#835—22no—
163#835—22no—
164#835—41no—
165#835—41no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169#830—22no—
170#830—22no—
171#810—22no—
172#810—41no—
173#809—22no—
174#809—41no—
175#808—22no—
176#807—22no—
177C4⋊(C3⋊C8)—22no—
178C4×C3⋊C8—22no—
179C22×#41—31no—
180C23×Q8C2×D311yescharacteristic
181C2×#137—64no—
182C2×#137—64no—
183C2×#137—64no—
184C22×Q16—31no—
185C22×Q16—31no—
186C22×SD16—31no—
187C22×SD16—31no—
188C22×M16—31no—
189C22×M16—31no—
190C2×C22⋊Q8—31no—
191C2×C22⋊Q8C2×D311yescharacteristic
192C2×C22⋊Q8C2×D311yescharacteristic
193C2×#121—31no—
194C2×C4×D4C2×D311yescharacteristic
195#470—64no—
196#468—64no—
197#436—64no—
198C2×#107—31no—
199C2×#106—31no—
200C2×C4⋊C8—31no—
201C2×#103—31no—
202C2×#103—31no—
203C2×#103—31no—
204C2×#103—31no—
205C2×#103—31no—
206C2×#103—31no—
207C2×#102—31no—
208C2×#102—31no—
209C2×C22⋊C8—31no—
210C2×C22⋊C8—31no—
211C2×C4×C8—31no—
212#395—21no—
213#394—61no—
214#393—21no—
215#392—61no—
216#391—31no—
217#391C2×D311yescharacteristic
218#391C2×D311yescharacteristic
219#390—31no—
220#386—21no—
221#386—61no—
222#385—21no—
223#385—61no—
224#380—31no—
225#380C2×D311yescharacteristic
226#340—31no—
227#340—31no—
228C24×C3C2×D411yescharacteristic
229C24×C3C2×D411yescharacteristic
230C23×D3—21no—
231C2×C3×Q8—21no—
232C2×C3×Q8—21no—
233C2×C3×Q8—28no—
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×Q8—21no—
242C2×C3×Q8—42no—
243C2×C3×Q8—42no—
244C2×C3×Q8—44no—
245C2×C3×Q8—44no—
246C2×C3×Q8—44no—
247C2×C3×Q8—42no—
248C2×C3×Q8C2×D412yes—
249C2×C3×Q8C2×D412yes—
250C2×C3×D4—22no—
251C2×C3×D4—22no—
252C2×C3×D4—41no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
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×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—42no—
268C22×C3×C4—42no—
269C22×C3×C4—42no—
270C22×C3×C4C2×D412yes—
271C22×C3×C4C2×D411yescharacteristic
272C22×C3×C4C2×D411yescharacteristic
273C22×C3×C4C2×D411yescharacteristic
274C22×C3×C4C2×D411yescharacteristic
275C22×C3×C4#4112yes—
276C22×C3×C4C2411yescharacteristic
277C2×#67—42no—
278C2×#67—42no—
279C2×#67—42no—
280C2×#67—42no—
281C2×#67—42no—
282C2×#67—81no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286#235—28no—
287#235—44no—
288#235—44no—
289#235—44no—
290C2×D12—21no—
291C2×D12—21no—
292C2×D12—21no—
293C2×D12—21no—
294C2×D12—21no—
295C2×D12C2×D412yes—
296C2×C4×D3—42no—
297C2×C4×D3—42no—
298C2×C4×D3—42no—
299C2×Dic6—21no—
300C2×Dic6—21no—
301C2×Dic6—21no—
302C2×Dic6—21no—
303C2×Dic6—21no—
304C2×Dic6C2×D412yes—
305C3×C4⋊C4—22no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4—21no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—42no—
311C3×C4⋊C4—42no—
312C3×C22⋊C4—22no—
313C3×C22⋊C4—22no—
314C3×C22⋊C4—42no—
315C3×C22⋊C4—42no—
316C3×C22⋊C4—42no—
317C3×C42—21no—
318C3×C42—21no—
319#217—42no—
320#217—81no—
321#216—28no—
322#216—28no—
323#215—28no—
324#215—28no—
325(C2×D3)⋊C4—42no—
326(C2×D3)⋊C4—42no—
327(C2×D3)⋊C4—81no—
328C4⋊Dic3—21no—
329C4⋊Dic3—21no—
330C4⋊Dic3—21no—
331C4⋊Dic3—21no—
332Dic3⋊C4—42no—
333#208—28no—
334#208—44no—
335C2×C3⋊C8—21no—
336C2×C3⋊C8—21no—
337C2×C3⋊C8—21no—
338C2×C3⋊C8—21no—
339C2×C3⋊C8—21no—
340C2×C3⋊C8—21no—
341C2×C3⋊C8—21no—
342C2×C3⋊C8—21no—
343C2×C3⋊C8C2×D412yes—
344C2×C3⋊C8C2×D412yes—
345C2×C3⋊C8C2×D412yes—
346C2×C3⋊C8C2×D412yes—
347C2×#41—62no—
348C2×#41—62no—
349C2×#41—62no—
350C2×#41—62no—
351C2×#41—121no—
352C2×#41—121no—
353C22×Q8—21no—
354C22×Q8—22no—
355C22×Q8—22no—
356C22×Q8—22no—
357C22×Q8—22no—
358C22×Q8—31no—
359C22×Q8—41no—
360C22×Q8—41no—
361C22×Q8C22×D311yescharacteristic
362C22×Q8C22×D311yescharacteristic
363C22×D4—31no—
364C22×D4—61no—
365C22×D4—61no—
366C22×D4#6711yescharacteristic
367C23×C4—21no—
368C23×C4—61no—
369C23×C4C22×D311yescharacteristic
370C23×C4C22×D311yescharacteristic
371#137—632no—
372C2×Q16—34no—
373C2×Q16—62no—
374C2×Q16—62no—
375C2×Q16—62no—
376C2×Q16—62no—
377C2×Q16—62no—
378C2×SD16—34no—
379C2×SD16—62no—
380C2×SD16—62no—
381C2×SD16—62no—
382C2×SD16—62no—
383C2×SD16—62no—
384C2×M16—34no—
385C2×M16—62no—
386C2×M16—62no—
387C2×M16—62no—
388C2×M16—62no—
389C2×M16—62no—
390C22×C8—31no—
391C22×C8—31no—
392C22×C8—31no—
393C22×C8—31no—
394C22⋊Q8—22no—
395C22⋊Q8—22no—
396C22⋊Q8—41no—
397C22⋊Q8—41no—
398C22⋊Q8—62no—
399C22⋊Q8—121no—
400#121—62no—
401#121—121no—
402C4×D4—22no—
403C4×D4—22no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—31no—
407C2×C4⋊C4—31no—
408C2×C4⋊C4—61no—
409C2×C4⋊C4#6711yescharacteristic
410C2×C4⋊C4C22×D311yescharacteristic
411C2×C4⋊C4C22×D311yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—61no—
416C2×C22⋊C4—61no—
417C2×C22⋊C4—61no—
418C2×C22⋊C4—61no—
419C2×C22⋊C4—61no—
420C2×C22⋊C4#6711yescharacteristic
421C2×C22⋊C4#6711yescharacteristic
422C2×C42C22×D311yescharacteristic
423#107—62no—
424#106—62no—
425C4⋊C8—62no—
426#103—62no—
427#103—62no—
428#103—62no—
429#103—121no—
430#103—121no—
431#103—121no—
432#102—62no—
433#102—121no—
434C22⋊C8—62no—
435C22⋊C8—62no—
436C4×C8—62no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—61no—
443#95—61no—
444#95—61no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—21no—
450C23×C3—21no—
451C23×C3—21no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—21no—
457C23×C3—21no—
458C23×C3#12112yes—
459C23×C3C22×D411yescharacteristic
460C22×D3—22no—
461C22×D3—41no—
462C22×D3—41no—
463C22×D3—41no—
464C22×D3—41no—
465C22×D3—41no—
466C22×D3—41no—
467C3×Q8—22no—
468C3×Q8—22no—
469C3×Q8—22no—
470C3×Q8—22no—
471C3×Q8—48no—
472C3×Q8—41no—
473C3×Q8—41no—
474C3×Q8—41no—
475C3×Q8—41no—
476C3×D4—44no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—48no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4#12112yes—
509C2×C3×C4#13712yescomplemented
510C2×C3×C4C22×D411yescharacteristic
511C2×C3×C4C22×D411yescharacteristic
512C2×C3×C4C22×D411yescharacteristic
513C2×C3×C4C2×#4111yescharacteristic
514C2×C3×C4H(5,𝔽2)11yescharacteristic
515C2×C3×C4H(5,𝔽2)11yescharacteristic
516#67—48no—
517#67—84no—
518C2×Dic3—22no—
519C2×Dic3—41no—
520C2×Dic3—41no—
521C2×Dic3—41no—
522C2×Dic3—41no—
523C2×Dic3—41no—
524C2×Dic3—41no—
525C2×Dic3—41no—
526C2×Dic3—41no—
527D12—22no—
528D12—22no—
529D12—41no—
530D12—41no—
531C4×D3—48no—
532Dic6—22no—
533Dic6—22no—
534Dic6—41no—
535Dic6—41no—
536C3⋊C8—22no—
537C3⋊C8—41no—
538C3⋊C8—41no—
539C3⋊C8#12014yes—
540C24—61no—
541C24C2×#6711yescharacteristic
542C24C2×#6711yescharacteristic
543#41—68no—
544#41—124no—
545#41—124no—
546#41—124no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—28no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—32no—
559C2×Q8—42no—
560C2×Q8—42no—
561C2×Q8—44no—
562C2×Q8—44no—
563C2×Q8—44no—
564C2×Q8—42no—
565C2×Q8—61no—
566C2×Q8—61no—
567C2×Q8—61no—
568C2×Q8—61no—
569C2×Q8—61no—
570C2×Q8D3×D412yes—
571C2×Q8D3×D412yes—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—32no—
575C2×D4—41no—
576C2×D4—61no—
577C2×D4—61no—
578C2×D4—61no—
579C2×D4—61no—
580C2×D4—61no—
581C2×D4—122no—
582C2×D4—122no—
583C2×D4—122no—
584C2×D4—122no—
585C2×D4—122no—
586C2×D4—241no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—122no—
608C22×C4—122no—
609C22×C4—122no—
610C22×C4D3×D412yes—
611C22×C4#23712yes—
612C22×C4C2×#6711yescharacteristic
613C22×C4C2×#6711yescharacteristic
614C22×C4C2×#6711yescharacteristic
615C22×C4C2×#6711yescharacteristic
616C22×C4C23×D311yescharacteristic
617Q16—68no—
618Q16—68no—
619SD16—68no—
620SD16—68no—
621M16—68no—
622M16—124no—
623C2×C8—32no—
624C2×C8—32no—
625C2×C8—32no—
626C2×C8—32no—
627C2×C8—61no—
628C2×C8—61no—
629C2×C8—61no—
630C2×C8—61no—
631C2×C8—61no—
632C2×C8—61no—
633C2×C8—61no—
634C2×C8—61no—
635C4⋊C4—22no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—42no—
641C4⋊C4—42no—
642C4⋊C4—61no—
643C4⋊C4—61no—
644C4⋊C4—61no—
645C4⋊C4—61no—
646C4⋊C4—122no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—122no—
653C22⋊C4—122no—
654C22⋊C4—122no—
655C22⋊C4—241no—
656C22⋊C4—241no—
657C42—21no—
658C42—21no—
659C22×C3—22no—
660C22×C3—22no—
661C22×C3—22no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3C2×#12111yescharacteristic
674C22×C3D4211yescharacteristic
675C22×C3D4211yescharacteristic
676C22×C3C2×#13711yescharacteristic
677C22×C3#57511yescharacteristic
678C22×C3#57711yescharacteristic
679C22×C3#57811yescharacteristic
680C2×D3—42no—
681C2×D3—42no—
682C2×D3—42no—
683C2×D3—81no—
684C2×D3—81no—
685C2×D3—81no—
686C2×D3—81no—
687C3×C4—22no—
688C3×C4—22no—
689C3×C4—41no—
690C3×C4—42no—
691C3×C4—42no—
692C3×C4—41no—
693C3×C4—81no—
694C3×C4—81no—
695C3×C4C2×#12011yescharacteristic
696C3×C4#53511yescharacteristic
697C3×C4#54611yescharacteristic
698C3×C4#54611yescharacteristic
699Dic3—42no—
700Dic3—81no—
701Dic3—81no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—62no—
716C23—121no—
717C23—121no—
718C23—121no—
719C23—121no—
720C23—121no—
721C23—121no—
722C23#93912yes—
723C23C22×#6711yescharacteristic
724Q8—22no—
725Q8—22no—
726Q8—22no—
727Q8—22no—
728Q8—48no—
729Q8—41no—
730Q8—41no—
731Q8—41no—
732Q8—41no—
733Q8—62no—
734Q8—62no—
735Q8—121no—
736Q8—121no—
737D4—44no—
738D4—62no—
739D4—62no—
740D4—128no—
741D4—121no—
742D4—121no—
743D4—244no—
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—22no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—48no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—62no—
776C2×C4—128no—
777C2×C4—121no—
778C2×C4—121no—
779C2×C4—121no—
780C2×C4—121no—
781C2×C4—121no—
782C2×C4—121no—
783C2×C4—121no—
784C2×C4—121no—
785C2×C4#93912yes—
786C2×C4#94212yescomplemented
787C2×C4C2×D3×D411yescharacteristic
788C2×C4C2×D3×D411yescharacteristic
789C2×C4C2×D3×D411yescharacteristic
790C2×C4C2×#23711yescharacteristic
791C2×C4#100411yescharacteristic
792C2×C4#100411yescharacteristic
793C8—34no—
794C8—62no—
795C8—121no—
796C8—121no—
797C2×C3—42no—
798C2×C3—81no—
799C2×C3#240811yescharacteristic
800C2×C3#305611yescharacteristic
801C2×C3#306311yescharacteristic
802C2×C3#327511yescharacteristic
803C2×C3#327611yescharacteristic
804C2×C3#327711yescharacteristic
805C2×C3#327811yescharacteristic
806D3—82no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—122no—
822C22—122no—
823C22—122no—
824C22—241no—
825C22—241no—
826C22—241no—
827C22—241no—
828C22D4×#6711yescharacteristic
829C22D4×#6711yescharacteristic
830C22C2×#93911yescharacteristic
831C22C2×#94211yescharacteristic
832C22#582211yescharacteristic
833C22#583711yescharacteristic
834C22#583811yescharacteristic
835C4—22no—
836C4—22no—
837C4—41no—
838C4—42no—
839C4—42no—
840C4—41no—
841C4—81no—
842C4—81no—
843C4—122no—
844C4—241no—
845C4—241no—
846C4D3×#12011yescharacteristic
847C4#559111yescharacteristic
848C4#559111yescharacteristic
849C4#559211yescharacteristic
850C3#2427611yescharacteristic, complemented, Sylow
851C2—42no—
852C2—81no—
853C2—242no—
854C2#8258211yescharacteristic
855C2#8273211yescharacteristic
856C2#8340011yescharacteristic
857C2#8354411yescharacteristic
858C2#8354811yescharacteristic
859C2#8356011yescharacteristic
860C2#8356611yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2409C2
socleC23×C3C22×D4
prime radical#82402C2
hypercenter#2409D3
hypocenterC3#24276
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2409

Complements

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

NH ≅ G/Ntype
1. C22×#942C2semidirect
2. C3×#2409C2semidirect
3. C2×#5052C2semidirect
4. C2×#5049C2semidirect
6. C2×#5012C2semidirect
7. #72132C2semidirect
8. #71700C2semidirect
9. #71699C2semidirect
10. #69681C2semidirect
11. #69680C2semidirect
12. #69677C2semidirect
13. #69676C2semidirect
14. #69522C2semidirect
15. #69513C2semidirect
70. #2409D3semidirect
129. C2×#216D4semidirect
136. C2×#215D4semidirect
152. C2×#208D4semidirect
509. C2×C3×C4#137semidirect
786. C2×C4#942semidirect
850. C3#24276semidirect

Maximal subgroups

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

subgroupindex
C22×#9422
C3×#24092
C2×#50522
C2×#50492
#824022
C2×#50122
#721322
#717002
#716992
#696812
#696802
#696772
#696762
#695222
#695132
#242763