Finite Group Databasebeta

← #10829245

Subgroups — #10829245

Order 768.

1184 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5635C211yesmaximal, characteristic, complemented
2C2×#4890C211yesmaximal, characteristic, complemented
3C2×#4817C211yesmaximal, characteristic, complemented
4#73933C211yesmaximal, characteristic
5C3×#2036C211yesmaximal, characteristic, complemented
6#71699C211yesmaximal, characteristic, complemented
7#70632C211yesmaximal, characteristic, complemented
8#70275C211yesmaximal, characteristic, complemented
9#70272C211yesmaximal, characteristic, complemented
10#70222C211yesmaximal, characteristic, complemented
11#69932C211yesmaximal, characteristic, complemented
12#69917C211yesmaximal, characteristic, complemented
13#69504C211yesmaximal, characteristic, complemented
14#68880C211yesmaximal, characteristic, complemented
15#68806C211yesmaximal, characteristic, complemented
16#24130—31nomaximal, Sylow
17C2×C3×C22⋊Q8C2211yescharacteristic
18C2×#946C2211yescharacteristic
19C2×Q8×Dic3C2211yescharacteristic
20C22×#215C2211yescharacteristic
21C2×#930C2211yescharacteristic
22C2×C4×#67C2211yescharacteristic
23C22×C4⋊Dic3C2211yescharacteristic
24#5635—24no—
25#5635—24no—
26C2×#897—21no—
27C2×#895C2211yescharacteristic
28C2×#893C2211yescharacteristic
29C2×D3×C4⋊C4C2211yescharacteristic
30C2×#889—21no—
31C2×#888C2211yescharacteristic
32C2×#67⋊C4—21no—
33C2×#878—21no—
34C2×C3×#107C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×C22⋊C8C2211yescharacteristic
38C3×#380C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×#830C2211yescharacteristic
41C2×#821C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×#815C2211yescharacteristic
46C2×Dic3⋊C8C2211yescharacteristic
47#4987C2211yescharacteristic
48#4977C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#807C2211yescharacteristic
51C2×#807C2211yescharacteristic
52#4960—21no—
53#4956—21no—
54#4890—24no—
55#4817—24no—
56#4675—21no—
57#4665—21no—
58C3×#340C2211yescharacteristic
59#4551C2211yescharacteristic
60#4551C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#554—31no—
65C2×#474—31no—
66C2×#440—31no—
67#2535—31no—
68#2036—31no—
69#2036D311yescharacteristic, complemented
70#2000—31no—
71#2000—31no—
72#1993—31no—
73#1955—31no—
74#1874—31no—
75#1874—31no—
76#1852—31no—
77#1852—31no—
78#1805—31no—
79C22×C3×Q8C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C22×#67—21no—
82C22×#67D411yescharacteristic
83C23×Dic3—21no—
84C22×D12—21no—
85C22×D12C2311yescharacteristic
86C22×C4×D3—21no—
87C22×C4×D3—21no—
88C22×C4×D3C2311yescharacteristic
89C22×Dic6—21no—
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C3×C22⋊Q8—22no—
93C3×C22⋊Q8—22no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C22⋊C4—21no—
99C2×C3×C22⋊C4—21no—
100C2×#217D411yescharacteristic
101#946—22no—
102#946—22no—
103Q8×Dic3—22no—
104Q8×Dic3D414yescomplemented
105C2×#215—22no—
106C2×#215—22no—
107C2×#215—22no—
108#930—22no—
109#930—41no—
110C4×#67—22no—
111C4×#67—22no—
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4D411yescharacteristic
118C2×C4⋊Dic3—21no—
119C2×C4⋊Dic3—21no—
120C2×C4⋊Dic3—22no—
121C2×C4⋊Dic3—22no—
122C2×C4⋊Dic3C2311yescharacteristic
123C2×C4⋊Dic3C2311yescharacteristic
124C2×C4⋊Dic3C2311yescharacteristic
125C2×Dic3⋊C4—21no—
126C2×Dic3⋊C4—21no—
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4D411yescharacteristic
129C2×C4×Dic3—21no—
130C2×C4×Dic3C2311yescharacteristic
131C22×C3⋊C8C2311yescharacteristic
132C22×C3⋊C8C2311yescharacteristic
133#897—28no—
134#895—22no—
135#895—41no—
136#893—22no—
137#893—22no—
138D3×C4⋊C4—22no—
139D3×C4⋊C4—22no—
140#889—28no—
141#888—22no—
142#888D414yescomplemented
143#67⋊C4—28no—
144#878—28no—
145C3×#107—22no—
146C3×#103—22no—
147C3×#103—41no—
148C3×C22⋊C8—41no—
149C3×#95—21no—
150#835—41no—
151C3⋊#95—21no—
152C3⋊#95—21no—
153C3⋊#95—21no—
154#830—22no—
155#821—22no—
156#821—22no—
157(C2×D3)⋊C8—22no—
158(C2×D3)⋊C8—41no—
159#815—22no—
160Dic3⋊C8—22no—
161#809—22no—
162#807—22no—
163#807—22no—
164C22×SD16—31no—
165#554—64no—
166#554—64no—
167C2×C4⋊Q8—31no—
168C2×#125—61no—
169C2×C22⋊Q8—31no—
170C2×C22⋊Q8—61no—
171C2×C22⋊Q8—61no—
172C2×C22⋊Q8C2×D311yescharacteristic
173C2×#121—31no—
174C2×#121—31no—
175C2×C4×Q8—31no—
176C2×C4×D4—31no—
177C2×C4×D4—31no—
178C2×C4×D4—61no—
179C22×C4⋊C4—31no—
180C22×C4⋊C4—31no—
181#474—64no—
182#440—64no—
183C2×#107—31no—
184C2×#107—31no—
185C2×#107C2×D311yescharacteristic
186C2×C4⋊C8—31no—
187C2×#103—31no—
188C2×#103C2×D311yescharacteristic
189C2×#103C2×D311yescharacteristic
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×C22⋊C8—31no—
194C2×C22⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×C22⋊C8C2×D311yescharacteristic
197C2×#97—31no—
198#397—61no—
199#392—61no—
200#386—61no—
201#386—61no—
202#382—31no—
203#380—31no—
204#380C2×D311yescharacteristic
205#340—31no—
206#340—31no—
207#340—31no—
208#340—31no—
209#340—31no—
210#340C2×D311yescharacteristic
211C24×C3C2×D411yescharacteristic
212C23×D3—21no—
213C23×D3C2×D411yescharacteristic
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8C2×D412yes—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2411yescharacteristic
232C2×#67—22no—
233C2×#67—22no—
234C2×#67—22no—
235C2×#67—42no—
236C2×#67—42no—
237C2×#67—81no—
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3—24no—
241C22×Dic3—21no—
242C22×Dic3—81no—
243C22×Dic3—81no—
244C22×Dic3C2×D411yescharacteristic
245C22×Dic3C2×D411yescharacteristic
246C22×Dic3C2×D411yescharacteristic
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—42no—
253C2×D12—42no—
254C2×D12—81no—
255C2×D12#4112yes—
256C2×C4×D3—21no—
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×C4×D3—21no—
262C2×C4×D3—24no—
263C2×C4×D3—42no—
264C2×C4×D3—81no—
265C2×C4×D3—81no—
266C2×C4×D3—81no—
267C2×C4×D3—81no—
268C2×Dic6—24no—
269C2×Dic6—81no—
270C2×Dic6—81no—
271C2×C3×C8—21no—
272C2×C3×C8—21no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C3×C4⋊C4—24no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4C2×D412yes—
284C3×C22⋊C4—24no—
285C3×C22⋊C4—81no—
286#217—22no—
287#215—28no—
288(C2×D3)⋊C4—24no—
289(C2×D3)⋊C4—22no—
290(C2×D3)⋊C4—42no—
291(C2×D3)⋊C4—42no—
292(C2×D3)⋊C4—42no—
293(C2×D3)⋊C4—81no—
294C4⋊Dic3—24no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3—24no—
298C4⋊Dic3—21no—
299C4⋊Dic3—21no—
300C4⋊Dic3C2×D412yes—
301C4⋊Dic3C2×D412yes—
302Dic3⋊C4—24no—
303Dic3⋊C4—24no—
304Dic3⋊C4—24no—
305Dic3⋊C4—22no—
306C4×Dic3—24no—
307C4×Dic3C2×D412yes—
308C4×Dic3C2×D412yes—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8#4112yes—
315C22×Q8—61no—
316C22×Q8C22×D311yescharacteristic
317C22×D4—31no—
318C22×D4—31no—
319C22×D4—61no—
320C22×D4—61no—
321C23×C4—31no—
322C23×C4—61no—
323C23×C4—61no—
324C23×C4—61no—
325C23×C4C22×D311yescharacteristic
326C2×SD16—62no—
327C2×SD16—62no—
328C2×SD16—62no—
329C22×C8—31no—
330C22×C8—31no—
331C22×C8C22×D311yescharacteristic
332C22×C8C22×D311yescharacteristic
333C4⋊Q8—34no—
334C4⋊Q8—62no—
335#125—68no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338C22⋊Q8—68no—
339C22⋊Q8—68no—
340C22⋊Q8—62no—
341C22⋊Q8—62no—
342#121—62no—
343#121—62no—
344#121—121no—
345#121—121no—
346C4×Q8—34no—
347C4×Q8—62no—
348C4×D4—62no—
349C4×D4—62no—
350C4×D4—62no—
351C4×D4—62no—
352C4×D4—68no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—31no—
355C2×C4⋊C4—31no—
356C2×C4⋊C4—31no—
357C2×C4⋊C4—31no—
358C2×C4⋊C4—62no—
359C2×C4⋊C4—62no—
360C2×C4⋊C4—62no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4—61no—
366C2×C4⋊C4—62no—
367C2×C4⋊C4C22×D311yescharacteristic
368C2×C4⋊C4C22×D311yescharacteristic
369C2×C4⋊C4C22×D311yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—31no—
373C2×C22⋊C4—31no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
377C2×C22⋊C4—61no—
378C2×C22⋊C4—61no—
379C2×C42—31no—
380C2×C42—61no—
381#107—22no—
382#107—62no—
383#107—62no—
384C4⋊C8—62no—
385#103—22no—
386#103—41no—
387#103—121no—
388#102—62no—
389#102—62no—
390#102—62no—
391C22⋊C8—41no—
392C22⋊C8—62no—
393C22⋊C8—62no—
394C22⋊C8—121no—
395#97—62no—
396#95—21no—
397#95—61no—
398#95—61no—
399#95—61no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3#13712yes—
407C23×C3C22×D411yescharacteristic
408C22×D3—21no—
409C22×D3—21no—
410C22×D3—21no—
411C22×D3—21no—
412C22×D3—21no—
413C22×D3—21no—
414C22×D3—22no—
415C22×D3—41no—
416C22×D3—41no—
417C22×D3—41no—
418C22×D3—41no—
419C22×D3—41no—
420C22×D3—41no—
421C22×D3#13712yes—
422C3×Q8—22no—
423C3×Q8—22no—
424C3×Q8—41no—
425C3×Q8—41no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4C22×D411yescharacteristic
446C2×C3×C4C22×D411yescharacteristic
447C2×C3×C4C2×#4111yescharacteristic
448C2×C3×C4C2×#4111yescharacteristic
449C2×C3×C4H(5,𝔽2)11yescharacteristic
450C2×C3×C42−1+411yescharacteristic
451#67—28no—
452#67—84no—
453C2×Dic3—21no—
454C2×Dic3—21no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—22no—
458C2×Dic3—21no—
459C2×Dic3—22no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—41no—
463C2×Dic3—41no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—84no—
470C2×Dic3#12012yes—
471C2×Dic3#12012yes—
472D12—22no—
473D12—22no—
474D12—41no—
475D12—41no—
476D12—84no—
477C4×D3—41no—
478C4×D3—41no—
479C4×D3—41no—
480C4×D3—41no—
481C4×D3—84no—
482C4×D3—84no—
483Dic6—84no—
484C3×C8—41no—
485C3×C8—41no—
486C3⋊C8—22no—
487C3⋊C8—41no—
488C24—31no—
489C24—61no—
490C24D3×D411yescharacteristic
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—64no—
497C2×Q8—241no—
498C2×Q8—241no—
499C2×Q8D3×D412yes—
500C2×D4—32no—
501C2×D4—62no—
502C2×D4—62no—
503C2×D4—62no—
504C2×D4—61no—
505C2×D4—61no—
506C2×D4—61no—
507C2×D4—61no—
508C2×D4—61no—
509C2×D4—122no—
510C2×D4—122no—
511C2×D4—122no—
512C2×D4—122no—
513C2×D4—241no—
514C2×D4—241no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—31no—
526C22×C4—31no—
527C22×C4—31no—
528C22×C4—64no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—64no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—61no—
538C22×C4—61no—
539C22×C4—122no—
540C22×C4—241no—
541C22×C4—241no—
542C22×C4—241no—
543C22×C4—241no—
544C22×C4—241no—
545C22×C4—241no—
546C22×C4D3×D411yescharacteristic
547C22×C4C23×D311yescharacteristic
548SD16—68no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—32no—
556C2×C8—61no—
557C2×C8—61no—
558C2×C8—61no—
559C2×C8—61no—
560C2×C8—61no—
561C4⋊C4—24no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—32no—
568C4⋊C4—32no—
569C4⋊C4—62no—
570C4⋊C4—64no—
571C4⋊C4—64no—
572C4⋊C4—64no—
573C4⋊C4—64no—
574C4⋊C4—64no—
575C4⋊C4—61no—
576C4⋊C4—61no—
577C4⋊C4—61no—
578C4⋊C4—61no—
579C4⋊C4D3×D412yes—
580C22⋊C4—24no—
581C22⋊C4—62no—
582C22⋊C4—64no—
583C22⋊C4—62no—
584C22⋊C4—81no—
585C22⋊C4—122no—
586C22⋊C4—122no—
587C22⋊C4—122no—
588C22⋊C4—241no—
589C42—32no—
590C42—32no—
591C42—64no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—41no—
596C22×C3—41no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3C2×#12011yescharacteristic
600C22×C3#54611yescharacteristic
601C22×C3#54711yescharacteristic
602C22×C3C2×#13711yescharacteristic
603C22×C3C2×#13711yescharacteristic
604C22×C3#57611yescharacteristic
605C22×C3#57611yescharacteristic
606C2×D3—22no—
607C2×D3—22no—
608C2×D3—22no—
609C2×D3—41no—
610C2×D3—41no—
611C2×D3—41no—
612C2×D3—41no—
613C2×D3—42no—
614C2×D3—42no—
615C2×D3—42no—
616C2×D3—81no—
617C2×D3—81no—
618C2×D3—81no—
619C2×D3—81no—
620C3×C4—41no—
621C3×C4—42no—
622C3×C4—42no—
623C3×C4—81no—
624C3×C4—81no—
625C3×C4#52511yescharacteristic
626C3×C4#53711yescharacteristic
627C3×C4#54811yescharacteristic
628C3×C4#55011yescharacteristic
629Dic3—22no—
630Dic3—22no—
631Dic3—41no—
632Dic3—42no—
633Dic3—42no—
634Dic3—81no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—32no—
642C23—61no—
643C23—61no—
644C23—61no—
645C23—61no—
646C23—61no—
647C23—61no—
648C23—62no—
649C23—121no—
650C23—121no—
651C23—121no—
652C23—121no—
653C23—121no—
654C23—121no—
655C23#91812yes—
656C23C2×D3×D411yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—41no—
660Q8—41no—
661Q8—244no—
662D4—68no—
663D4—62no—
664D4—62no—
665D4—121no—
666D4—121no—
667D4—244no—
668D4—244no—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—32no—
675C2×C4—32no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—244no—
711C2×C4—244no—
712C2×C4—244no—
713C2×C4C2×D3×D411yescharacteristic
714C2×C4C2×D3×D411yescharacteristic
715C2×C4#100411yescharacteristic
716C2×C4D3×#4111yescharacteristic
717C2×C4D3×#4111yescharacteristic
718C2×C4#101011yescharacteristic
719C8—41no—
720C8—41no—
721C8—62no—
722C8—121no—
723C2×C3—42no—
724C2×C3#240711yescharacteristic
725C2×C3#300411yescharacteristic
726C2×C3#300811yescharacteristic
727C2×C3#331411yescharacteristic
728C2×C3#331411yescharacteristic
729C2×C3#334611yescharacteristic
730C2×C3#334611yescharacteristic
731D3—42no—
732D3—82no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—62no—
741C22—62no—
742C22—62no—
743C22—121no—
744C22—121no—
745C22—121no—
746C22—121no—
747C22—122no—
748C22—122no—
749C22—122no—
750C22—241no—
751C22—241no—
752C22—241no—
753C22—241no—
754C22D3×#12011yescharacteristic
755C22#561011yescharacteristic
756C22#565511yescharacteristic
757C22C2×#91811yescharacteristic
758C22#576911yescharacteristic
759C22#577411yescharacteristic
760C22D3×#13711yescharacteristic
761C4—41no—
762C4—42no—
763C4—42no—
764C4—62no—
765C4—62no—
766C4—81no—
767C4—81no—
768C4—121no—
769C4—122no—
770C4—122no—
771C4—241no—
772C4#559711yescharacteristic
773C4#559911yescharacteristic
774C4#565611yescharacteristic
775C4#567711yescharacteristic
776C3#2413011yescharacteristic, complemented, Sylow
777C2—42no—
778C2—122no—
779C2—242no—
780C2#7689411yescharacteristic
781C2#8008511yescharacteristic
782C2#8018311yescharacteristic
783C2#8077711yescharacteristic
784C2#8082311yescharacteristic
785C2#8147811yescharacteristic
786C2#8153511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2036C2
socleC23×C3C22×D4
prime radical#73933C2
hypercenter#2036D3
hypocenterC3#24130
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2036

Complements

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

NH ≅ G/Ntype
1. C2×#5635C2semidirect
2. C2×#4890C2semidirect
3. C2×#4817C2semidirect
5. C3×#2036C2semidirect
6. #71699C2semidirect
7. #70632C2semidirect
8. #70275C2semidirect
9. #70272C2semidirect
10. #70222C2semidirect
11. #69932C2semidirect
12. #69917C2semidirect
13. #69504C2semidirect
14. #68880C2semidirect
15. #68806C2semidirect
69. #2036D3semidirect
104. Q8×Dic3D4semidirect
142. #888D4semidirect
776. C3#24130semidirect

Maximal subgroups

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

subgroupindex
C2×#56352
C2×#48902
C2×#48172
#739332
C3×#20362
#716992
#706322
#702752
#702722
#702222
#699322
#699172
#695042
#688802
#688062
#241303