Finite Group Databasebeta

← #10829243

Subgroups — #10829243

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×#5164C211yesmaximal, characteristic, complemented
3#82666C211yesmaximal, characteristic
4C2×#4759C211yesmaximal, characteristic, complemented
5C3×#2000C211yesmaximal, characteristic, complemented
6#72054C211yesmaximal, characteristic, complemented
7#71695C211yesmaximal, characteristic, complemented
8#71677C211yesmaximal, characteristic, complemented
9#70244C211yesmaximal, characteristic, complemented
10#70222C211yesmaximal, characteristic, complemented
11#70200C211yesmaximal, characteristic, complemented
12#69927C211yesmaximal, characteristic, complemented
13#69917C211yesmaximal, characteristic, complemented
14#68874C211yesmaximal, characteristic, complemented
15#68806C211yesmaximal, characteristic, complemented
16#24130—31nomaximal, Sylow
17C22×C3×SD16C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C2×Q8×Dic3C2211yescharacteristic
22C2×#938C2211yescharacteristic
23C2×D4×Dic3C2211yescharacteristic
24C2×C4×#67C2211yescharacteristic
25C22×C4⋊Dic3C2211yescharacteristic
26#5635—24no—
27#5635—24no—
28C2×#897—21no—
29C2×D3×C4⋊C4C2211yescharacteristic
30C2×#889—21no—
31C2×#888C2211yescharacteristic
32C2×#67⋊C4—21no—
33C2×#878—21no—
34C2×C3×#103C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×C22⋊C8C2211yescharacteristic
37C2×#835C2211yescharacteristic
38C2×#835C2211yescharacteristic
39#5223—21no—
40#5220—21no—
41C2×#832C2211yescharacteristic
42C2×#832C2211yescharacteristic
43#5212C2211yescharacteristic
44C2×#830C2211yescharacteristic
45#5164—24no—
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic
48C2×#818C2211yescharacteristic
49C2×#818C2211yescharacteristic
50C2×#815C2211yescharacteristic
51C2×Dic3⋊C8C2211yescharacteristic
52#4987C2211yescharacteristic
53#4977C2211yescharacteristic
54C2×#807C2211yescharacteristic
55#4958—21no—
56#4952—21no—
57#4759—24no—
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#2036—31no—
70#2000—31no—
71#2000D311yescharacteristic, complemented
72#1993—31no—
73#1955—31no—
74#1874—31no—
75#1874—31no—
76#1852—31no—
77#1852—31no—
78#1805—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67—21no—
84C22×#67D411yescharacteristic
85C23×Dic3—21no—
86C23×Dic3—21no—
87C22×C4×D3—21no—
88C22×C4×D3C2311yescharacteristic
89C22×Dic6—21no—
90C2×C3×SD16—22no—
91C2×C3×SD16—22no—
92C2×C3×SD16—22no—
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C3×C22⋊Q8—22no—
96C3×C22⋊Q8—22no—
97C3×#121—22no—
98C3×#121—41no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C22⋊C4—21no—
103C2×C3×C22⋊C4—21no—
104C2×#217—21no—
105C2×#217—21no—
106C2×#217—21no—
107C2×#217D411yescharacteristic
108#946—22no—
109#946—22no—
110Q8×Dic3—22no—
111Q8×Dic3D414yescomplemented
112#938—22no—
113#938—41no—
114D4×Dic3—22no—
115D4×Dic3—22no—
116C4×#67—22no—
117C4×#67—22no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4D411yescharacteristic
121C2×C4⋊Dic3—21no—
122C2×C4⋊Dic3—21no—
123C2×C4⋊Dic3—22no—
124C2×C4⋊Dic3—22no—
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×C4⋊Dic3C2311yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4D411yescharacteristic
133C2×C4×Dic3—21no—
134C2×C4×Dic3C2311yescharacteristic
135C22×C3⋊C8C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137#897—28no—
138D3×C4⋊C4—22no—
139D3×C4⋊C4—22no—
140#889—28no—
141#888—22no—
142#888D414yescomplemented
143#67⋊C4—28no—
144#878—28no—
145C3×#103—41no—
146C3×#102—22no—
147C3×C22⋊C8—22no—
148#835—22no—
149#835—41no—
150#832—22no—
151#832—22no—
152C3⋊#95—21no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156#830—41no—
157(C2×D3)⋊C8—22no—
158(C2×D3)⋊C8—41no—
159#818—22no—
160#818—22no—
161#815—22no—
162Dic3⋊C8—22no—
163#807—22no—
164C22×SD16C2×D311yescharacteristic
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×#121C2×D311yescharacteristic
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×#107—31no—
186C2×C4⋊C8—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103C2×D311yescharacteristic
190C2×#102—31no—
191C2×#102—31no—
192C2×#102C2×D311yescharacteristic
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#380—31no—
205#340—31no—
206#340—31no—
207#340—31no—
208#340—31no—
209#340—31no—
210#340C2×D311yescharacteristic
211C24×C3—21no—
212C24×C3C2×D411yescharacteristic
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—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—42no—
226C2×C3×D4—42no—
227C2×C3×D4—81no—
228C2×C3×D4#4112yes—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2411yescharacteristic
240C2×#67—22no—
241C2×#67—22no—
242C2×#67—22no—
243C2×#67—42no—
244C2×#67—42no—
245C2×#67—81no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—24no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251C22×Dic3—42no—
252C22×Dic3—81no—
253C22×Dic3—81no—
254C22×Dic3—81no—
255C22×Dic3—81no—
256C22×Dic3C2×D411yescharacteristic
257C22×Dic3C2×D411yescharacteristic
258C22×Dic3C2×D411yescharacteristic
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×C4×D3—21no—
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×C4×D3—24no—
266C2×C4×D3—81no—
267C2×C4×D3—81no—
268C2×Dic6—24no—
269C2×Dic6—81no—
270C2×Dic6—81no—
271C3×SD16—28no—
272C2×C3×C8—21no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8#4112yes—
278C3×C4⋊C4—24no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4C2×D412yes—
283C3×C22⋊C4—24no—
284C3×C22⋊C4—42no—
285#217—22no—
286#217—42no—
287#217—42no—
288#217—81no—
289(C2×D3)⋊C4—24no—
290(C2×D3)⋊C4—22no—
291(C2×D3)⋊C4—81no—
292C4⋊Dic3—24no—
293C4⋊Dic3—21no—
294C4⋊Dic3—21no—
295C4⋊Dic3—24no—
296C4⋊Dic3—21no—
297C4⋊Dic3—21no—
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—21no—
315C22×Q8—61no—
316C22×Q8C22×D311yescharacteristic
317C22×D4—21no—
318C22×D4—31no—
319C22×D4—61no—
320C22×D4C22×D311yescharacteristic
321C23×C4—31no—
322C23×C4—61no—
323C23×C4—61no—
324C23×C4—61no—
325C23×C4C22×D311yescharacteristic
326C2×SD16—22no—
327C2×SD16—22no—
328C2×SD16—22no—
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—22no—
343#121—41no—
344#121—62no—
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—31no—
359C2×C4⋊C4—62no—
360C2×C4⋊C4—62no—
361C2×C4⋊C4—62no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4—61no—
366C2×C4⋊C4—61no—
367C2×C4⋊C4—62no—
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—62no—
382#107—62no—
383#107—62no—
384C4⋊C8—62no—
385#103—41no—
386#103—62no—
387#103—121no—
388#102—22no—
389#102—62no—
390#102—62no—
391C22⋊C8—22no—
392C22⋊C8—62no—
393C22⋊C8—121no—
394C22⋊C8—121no—
395#97—62no—
396#95—61no—
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—22no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3#13712yes—
414C23×C3C22×D411yescharacteristic
415C22×D3—21no—
416C22×D3—21no—
417C22×D3—21no—
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—21no—
421C22×D3#13712yes—
422C3×Q8—22no—
423C3×Q8—22no—
424C3×Q8—41no—
425C3×Q8—41no—
426C3×D4—22no—
427C3×D4—22no—
428C3×D4—41no—
429C3×D4—41no—
430C3×D4—84no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
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×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4C22×D411yescharacteristic
448C2×C3×C4C22×D411yescharacteristic
449C2×C3×C4C2×#4111yescharacteristic
450C2×C3×C4C2×#4111yescharacteristic
451C2×C3×C4H(5,𝔽2)11yescharacteristic
452C2×C3×C42−1+411yescharacteristic
453#67—28no—
454#67—84no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—22no—
460C2×Dic3—21no—
461C2×Dic3—22no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—84no—
475C2×Dic3—84no—
476C2×Dic3#12012yes—
477C2×Dic3#12012yes—
478C4×D3—41no—
479C4×D3—41no—
480C4×D3—41no—
481C4×D3—41no—
482C4×D3—84no—
483Dic6—84no—
484C3×C8—22no—
485C3×C8—41no—
486C3⋊C8—41no—
487C3⋊C8—41no—
488C24—21no—
489C24—31no—
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—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—62no—
508C2×D4—62no—
509C2×D4—62no—
510C2×D4—81no—
511C2×D4—122no—
512C2×D4—122no—
513C2×D4—241no—
514C2×D4#23712yes—
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—31no—
525C22×C4—31no—
526C22×C4—31no—
527C22×C4—64no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—64no—
531C22×C4—61no—
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—28no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—61no—
555C2×C8—61no—
556C2×C8—61no—
557C2×C8—61no—
558C2×C8—61no—
559C2×C8—61no—
560C2×C8#23712yes—
561C4⋊C4—24no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—32no—
566C4⋊C4—32no—
567C4⋊C4—62no—
568C4⋊C4—64no—
569C4⋊C4—64no—
570C4⋊C4—64no—
571C4⋊C4—64no—
572C4⋊C4—64no—
573C4⋊C4—61no—
574C4⋊C4—61no—
575C4⋊C4—61no—
576C4⋊C4—61no—
577C4⋊C4—61no—
578C4⋊C4—61no—
579C4⋊C4D3×D412yes—
580C22⋊C4—24no—
581C22⋊C4—42no—
582C22⋊C4—62no—
583C22⋊C4—64no—
584C22⋊C4—62no—
585C22⋊C4—122no—
586C22⋊C4—122no—
587C22⋊C4—241no—
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×C3—42no—
600C22×C3—42no—
601C22×C3—42no—
602C22×C3—81no—
603C22×C3—81no—
604C22×C3—81no—
605C22×C3—81no—
606C22×C3C2×#12011yescharacteristic
607C22×C3#54611yescharacteristic
608C22×C3#54711yescharacteristic
609C22×C3C2×#13711yescharacteristic
610C22×C3C2×#13711yescharacteristic
611C22×C3#57611yescharacteristic
612C22×C3#57611yescharacteristic
613C2×D3—22no—
614C2×D3—22no—
615C2×D3—22no—
616C2×D3—41no—
617C2×D3—41no—
618C2×D3—41no—
619C2×D3—41no—
620C3×C4—41no—
621C3×C4—42no—
622C3×C4—42no—
623C3×C4—81no—
624C3×C4#52511yescharacteristic
625C3×C4#53711yescharacteristic
626C3×C4#54811yescharacteristic
627C3×C4#55011yescharacteristic
628Dic3—22no—
629Dic3—22no—
630Dic3—41no—
631Dic3—42no—
632Dic3—42no—
633Dic3—81no—
634Dic3—81no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—22no—
642C23—32no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—61no—
650C23—61no—
651C23—61no—
652C23—61no—
653C23—61no—
654C23—61no—
655C23#91512yes—
656C23C2×D3×D411yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—41no—
660Q8—41no—
661Q8—244no—
662D4—22no—
663D4—22no—
664D4—41no—
665D4—41no—
666D4—68no—
667D4—84no—
668D4—244no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—21no—
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—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—121no—
697C2×C4—121no—
698C2×C4—121no—
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×C4C2×#23711yescharacteristic
716C2×C4C2×#23711yescharacteristic
717C2×C4#100411yescharacteristic
718C2×C4#101011yescharacteristic
719C8—22no—
720C8—41no—
721C8—121no—
722C8—121no—
723C2×C3—42no—
724C2×C3—82no—
725C2×C3#240711yescharacteristic
726C2×C3#300411yescharacteristic
727C2×C3#300811yescharacteristic
728C2×C3#331411yescharacteristic
729C2×C3#331411yescharacteristic
730C2×C3#334611yescharacteristic
731C2×C3#334611yescharacteristic
732D3—42no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—62no—
744C22—62no—
745C22—62no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—121no—
751C22—121no—
752C22—121no—
753C22—121no—
754C22D3×#12011yescharacteristic
755C22#559111yescharacteristic
756C22#561111yescharacteristic
757C22C2×#91511yescharacteristic
758C22#576911yescharacteristic
759C22#577411yescharacteristic
760C22D3×#13711yescharacteristic
761C4—41no—
762C4—42no—
763C4—42no—
764C4—62no—
765C4—62no—
766C4—81no—
767C4—121no—
768C4—122no—
769C4—122no—
770C4—241no—
771C4—241no—
772C4#558611yescharacteristic
773C4#559711yescharacteristic
774C4#559811yescharacteristic
775C4#571811yescharacteristic
776C3#2413011yescharacteristic, complemented, Sylow
777C2—42no—
778C2—82no—
779C2—122no—
780C2#7666811yescharacteristic
781C2#8003911yescharacteristic
782C2#8008511yescharacteristic
783C2#8016311yescharacteristic
784C2#8025211yescharacteristic
785C2#8065211yescharacteristic
786C2#8083011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2000C2
socleC23×C3C22×D4
prime radical#82666C2
hypercenter#2000D3
hypocenterC3#24130
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
1. C2×#5635C2semidirect
2. C2×#5164C2semidirect
4. C2×#4759C2semidirect
5. C3×#2000C2semidirect
6. #72054C2semidirect
7. #71695C2semidirect
8. #71677C2semidirect
9. #70244C2semidirect
10. #70222C2semidirect
11. #70200C2semidirect
12. #69927C2semidirect
13. #69917C2semidirect
14. #68874C2semidirect
15. #68806C2semidirect
71. #2000D3semidirect
111. 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×#51642
#826662
C2×#47592
C3×#20002
#720542
#716952
#716772
#702442
#702222
#702002
#699272
#699172
#688742
#688062
#241303