Finite Group Databasebeta

← #10823496

Subgroups — #10823496

Order 768.

1242 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5619C211yesmaximal, characteristic, complemented
2C2×#4869C211yesmaximal, characteristic, complemented
3C2×#4756C211yesmaximal, characteristic, complemented
4#73872C211yesmaximal, characteristic, complemented
5C3×#2034C211yesmaximal, characteristic, complemented
6#71684C211yesmaximal, characteristic, complemented
7#70566C211yesmaximal, characteristic, complemented
8#70211C211yesmaximal, characteristic, complemented
9#70209C211yesmaximal, characteristic, complemented
10#70152C211yesmaximal, characteristic, complemented
11#69961C211yesmaximal, characteristic, complemented
12#69907C211yesmaximal, characteristic, complemented
13#69523C211yesmaximal, characteristic, complemented
14#68899C211yesmaximal, characteristic, complemented
15#68780C211yesmaximal, characteristic, complemented
16#23580—31nomaximal, Sylow
17C2×C3×#121C2211yescharacteristic
18C2×#940C2211yescharacteristic
19C2×#939—21no—
20C2×#938—21no—
21C2×D4×Dic3C2211yescharacteristic
22C22×#213C2211yescharacteristic
23C2×#930C2211yescharacteristic
24C2×#930C2211yescharacteristic
25C2×#926C2211yescharacteristic
26C22×D24C2211yescharacteristic
27#5619—24no—
28#5619—24no—
29C2×#893C2211yescharacteristic
30C2×#893C2211yescharacteristic
31C2×#890C2211yescharacteristic
32C2×#886—21no—
33C2×#883—21no—
34C2×C3×#106C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×C22⋊C8C2211yescharacteristic
38C3×#380C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#830C2211yescharacteristic
41C2×#821C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×#815C2211yescharacteristic
44C2×C8×Dic3C2211yescharacteristic
45#4988C2211yescharacteristic
46Dic3×C4⋊C4C2211yescharacteristic
47#4972C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#807C2211yescharacteristic
52#4957—21no—
53#4956—21no—
54#4869—24no—
55#4756—24no—
56#4670—21no—
57#4668—21no—
58C3×#340C2211yescharacteristic
59#4551C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#540—31no—
65C2×#442—31no—
66C2×C4×D8—31no—
67#2324—31no—
68#2059—31no—
69#2041—31no—
70#2034D311yescharacteristic, complemented
71#2033—31no—
72#2025—31no—
73#2011—31no—
74#1999—31no—
75#1999—31no—
76#1762—31no—
77C4×#102—31no—
78#1750—31no—
79C22×C3×D4—21no—
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67—21no—
83C22×#67—21no—
84C22×#67—21no—
85C22×#67—21no—
86C23×Dic3—21no—
87C22×D12C2311yescharacteristic
88C22×D12C2311yescharacteristic
89C22×C4×D3—21no—
90C22×C4×D3—21no—
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C3×#121—22no—
94C3×#121—22no—
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C22⋊C4—21no—
99C2×C3×C22⋊C4—21no—
100C2×#217—21no—
101C2×#217D411yescharacteristic
102C2×#217D411yescharacteristic
103#940—22no—
104#940—22no—
105#939—28no—
106#938—28no—
107D4×Dic3—22no—
108D4×Dic3D414yescomplemented
109C2×#213—22no—
110C2×#213—22no—
111C2×#213—22no—
112#930—22no—
113#930—22no—
114#930—22no—
115#930—22no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122#926—22no—
123#926—22no—
124C2×C4⋊Dic3—21no—
125C2×C4⋊Dic3D411yescharacteristic
126C2×C4⋊Dic3D411yescharacteristic
127C2×C4⋊Dic3C2311yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×C4×Dic3—21no—
132C2×C4×Dic3C2311yescharacteristic
133C2×C4×Dic3C2311yescharacteristic
134C22×C3⋊C8C2311yescharacteristic
135C22×C3⋊C8C2311yescharacteristic
136C2×D24—22no—
137C2×D24—22no—
138C2×D24—22no—
139#893—22no—
140#893—22no—
141#893—22no—
142#893D414yescomplemented
143#890—22no—
144#890—22no—
145#886—28no—
146#883—28no—
147C3×#106—22no—
148C3×#102—22no—
149C3×#102—22no—
150C3×C22⋊C8—22no—
151C3×#95—21no—
152#832—22no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155#830—22no—
156#821—22no—
157#821—22no—
158#815—22no—
159C8×Dic3—22no—
160#809—22no—
161#809—22no—
162#809—22no—
163#807—22no—
164C22×D8—31no—
165C22×D8—31no—
166#540—64no—
167#540—64no—
168C2×#127—31no—
169C2×#125—31no—
170C2×#123—61no—
171C2×#123—61no—
172C2×#121—31no—
173C2×#121—31no—
174C2×#121—61no—
175C2×#121—61no—
176C2×#121C2×D311yescharacteristic
177C2×C4×D4—31no—
178C2×C4×D4—31no—
179C2×C4×D4—31no—
180C2×#117—31no—
181#442—64no—
182C4×D8—64no—
183C2×#107—31no—
184C2×#106C2×D311yescharacteristic
185C2×#102—31no—
186C2×#102—31no—
187C2×#102—31no—
188C2×#102—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102C2×D311yescharacteristic
192C2×#102C2×D311yescharacteristic
193C2×C22⋊C8—31no—
194C2×C22⋊C8C2×D311yescharacteristic
195C2×#97—31no—
196C2×C4×C8—31no—
197#390—31no—
198#390—61no—
199#389—31no—
200#388—61no—
201#386—61no—
202#385—61no—
203#380C2×D311yescharacteristic
204C4×C4⋊C4—31no—
205#340—31no—
206#340—31no—
207#340—31no—
208#340C2×D311yescharacteristic
209#336—31no—
210#336—31no—
211C24×C3—21no—
212C24×C3C2×D411yescharacteristic
213C23×D3—21no—
214C23×D3—21no—
215C2×C3×D4—24no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—81no—
222C2×C3×D4—81no—
223C2×C3×D4C2×D412yes—
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×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2411yescharacteristic
235C2×#67—24no—
236C2×#67—24no—
237C2×#67—24no—
238C2×#67—24no—
239C2×#67—81no—
240C2×#67—81no—
241C2×#67—81no—
242C2×#67—81no—
243C2×#67—81no—
244C2×#67—81no—
245C2×#67—81no—
246C2×#67—81no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3—24no—
250C22×Dic3—81no—
251C22×Dic3—81no—
252C22×Dic3C2×D411yescharacteristic
253C22×Dic3C2×D411yescharacteristic
254C22×Dic3C2×D411yescharacteristic
255C22×Dic3C2×D411yescharacteristic
256C2×D12—21no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12C2×D412yes—
267C2×D12#4112yes—
268C2×C4×D3—24no—
269C2×C4×D3—42no—
270C2×C4×D3—81no—
271C2×C4×D3—81no—
272C2×C4×D3—81no—
273C2×C4×D3—81no—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8#4112yes—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4C2×D412yes—
286C3×C22⋊C4—24no—
287C3×C22⋊C4—81no—
288#217—24no—
289#217—22no—
290#217—22no—
291#213—28no—
292(C2×D3)⋊C4—24no—
293(C2×D3)⋊C4—24no—
294(C2×D3)⋊C4—24no—
295(C2×D3)⋊C4—42no—
296(C2×D3)⋊C4—81no—
297(C2×D3)⋊C4—81no—
298C4⋊Dic3—24no—
299C4⋊Dic3—21no—
300C4⋊Dic3—21no—
301C4⋊Dic3—22no—
302C4⋊Dic3—22no—
303C4⋊Dic3C2×D412yes—
304C4⋊Dic3#4112yes—
305Dic3⋊C4—24no—
306Dic3⋊C4—81no—
307C4×Dic3—21no—
308C4×Dic3—21no—
309C4×Dic3—81no—
310C4×Dic3C2×D412yes—
311C4×Dic3C2×D412yes—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8#4112yes—
318D24—28no—
319C22×D4—21no—
320C22×D4—31no—
321C22×D4—31no—
322C22×D4—61no—
323C22×D4—61no—
324C22×D4—61no—
325C22×D4—61no—
326C22×D4C22×D311yescharacteristic
327C23×C4—61no—
328C23×C4—61no—
329C23×C4—61no—
330C23×C4C22×D311yescharacteristic
331C2×D8—62no—
332C2×D8—62no—
333C2×D8—62no—
334C2×D8—62no—
335C2×D8—62no—
336C2×D8—62no—
337C22×C8—31no—
338C22×C8—31no—
339C22×C8C22×D311yescharacteristic
340C22×C8C22×D311yescharacteristic
341#127—62no—
342#127—62no—
343#125—62no—
344#125—62no—
345#123—68no—
346#123—68no—
347#121—22no—
348#121—22no—
349#121—62no—
350#121—62no—
351#121—62no—
352#121—62no—
353#121—68no—
354#121—68no—
355C4×D4—34no—
356C4×D4—34no—
357C4×D4—62no—
358C4×D4—62no—
359C4×D4—62no—
360C4×D4—62no—
361#117—62no—
362#117—62no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—61no—
368C2×C4⋊C4—61no—
369C2×C4⋊C4—61no—
370C2×C4⋊C4C22×D311yescharacteristic
371C2×C4⋊C4C22×D311yescharacteristic
372C2×C4⋊C4C22×D311yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—31no—
376C2×C22⋊C4—31no—
377C2×C22⋊C4—61no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4—61no—
384C2×C42—31no—
385C2×C42—31no—
386C2×C42—61no—
387#107—62no—
388#106—22no—
389#102—22no—
390#102—22no—
391#102—62no—
392#102—62no—
393#102—62no—
394#102—62no—
395#102—62no—
396#102—62no—
397C22⋊C8—22no—
398C22⋊C8—62no—
399#97—62no—
400C4×C8—62no—
401#95—21no—
402#95—61no—
403#95—61no—
404C23×C3—21no—
405C23×C3—22no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3C22×D411yescharacteristic
419C22×D3—22no—
420C22×D3—22no—
421C22×D3—41no—
422C22×D3—41no—
423C22×D3—41no—
424C22×D3—41no—
425C22×D3—41no—
426C22×D3—41no—
427C22×D3—41no—
428C22×D3—41no—
429C22×D3—41no—
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—41no—
433C3×D4—22no—
434C3×D4—22no—
435C3×D4—41no—
436C3×D4—41no—
437C3×D4—84no—
438C2×C3×C4—22no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4C22×D411yescharacteristic
455C2×C3×C4C22×D411yescharacteristic
456C2×C3×C4C2×#4111yescharacteristic
457C2×C3×C4C2×#4111yescharacteristic
458C2×C3×C4C2×#4111yescharacteristic
459C2×C3×C4C2×#4111yescharacteristic
460#67—84no—
461#67—84no—
462#67—84no—
463#67—84no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—84no—
481C2×Dic3#12012yes—
482C2×Dic3#12012yes—
483D12—22no—
484D12—22no—
485D12—22no—
486D12—22no—
487D12—41no—
488D12—41no—
489D12—41no—
490D12—41no—
491C4×D3—84no—
492C4×D3—84no—
493C3×C8—22no—
494C3×C8—41no—
495C3⋊C8—22no—
496C3⋊C8—41no—
497C24—21no—
498C24—61no—
499C24—61no—
500C24D3×D411yescharacteristic
501C2×D4—24no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—32no—
508C2×D4—32no—
509C2×D4—64no—
510C2×D4—64no—
511C2×D4—64no—
512C2×D4—64no—
513C2×D4—61no—
514C2×D4—61no—
515C2×D4—61no—
516C2×D4—61no—
517C2×D4—61no—
518C2×D4—61no—
519C2×D4—61no—
520C2×D4—61no—
521C2×D4—61no—
522C2×D4—61no—
523C2×D4—81no—
524C2×D4—81no—
525C2×D4—241no—
526C2×D4—241no—
527C2×D4—241no—
528C2×D4—241no—
529C2×D4—241no—
530C2×D4—241no—
531C2×D4—241no—
532C2×D4—241no—
533C2×D4D3×D412yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—31no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—31no—
547C22×C4—64no—
548C22×C4—64no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—122no—
552C22×C4—241no—
553C22×C4—241no—
554C22×C4—241no—
555C22×C4—241no—
556C22×C4—241no—
557C22×C4—241no—
558C22×C4D3×D411yescharacteristic
559C22×C4C23×D311yescharacteristic
560D8—68no—
561D8—68no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—32no—
568C2×C8—61no—
569C2×C8—61no—
570C2×C8—61no—
571C2×C8—61no—
572C2×C8—61no—
573C2×C8#23712yes—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—32no—
580C4⋊C4—32no—
581C4⋊C4—62no—
582C4⋊C4—62no—
583C4⋊C4—64no—
584C4⋊C4—64no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—241no—
588C4⋊C4D3×D412yes—
589C22⋊C4—24no—
590C22⋊C4—64no—
591C22⋊C4—64no—
592C22⋊C4—64no—
593C22⋊C4—62no—
594C22⋊C4—62no—
595C22⋊C4—64no—
596C22⋊C4—81no—
597C22⋊C4—122no—
598C22⋊C4—241no—
599C22⋊C4—241no—
600C42—32no—
601C42—32no—
602C42—61no—
603C42—61no—
604C42—241no—
605C22×C3—41no—
606C22×C3—41no—
607C22×C3—41no—
608C22×C3—42no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—42no—
612C22×C3—41no—
613C22×C3—42no—
614C22×C3—41no—
615C22×C3—81no—
616C22×C3—81no—
617C22×C3—81no—
618C22×C3—81no—
619C22×C3C2×#12011yescharacteristic
620C22×C3#52511yescharacteristic
621C22×C3#53211yescharacteristic
622C22×C3#57611yescharacteristic
623C22×C3#57611yescharacteristic
624C22×C3#57611yescharacteristic
625C22×C3#57711yescharacteristic
626C2×D3—42no—
627C2×D3—42no—
628C2×D3—42no—
629C2×D3—42no—
630C2×D3—42no—
631C2×D3—42no—
632C2×D3—81no—
633C2×D3—81no—
634C2×D3—81no—
635C2×D3—81no—
636C2×D3—81no—
637C2×D3—81no—
638C2×D3—81no—
639C2×D3—81no—
640C3×C4—41no—
641C3×C4—42no—
642C3×C4—81no—
643C3×C4—81no—
644C3×C4#52511yescharacteristic
645C3×C4#52511yescharacteristic
646C3×C4#53211yescharacteristic
647C3×C4#53211yescharacteristic
648Dic3—22no—
649Dic3—22no—
650Dic3—42no—
651Dic3—41no—
652Dic3—42no—
653Dic3—41no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—22no—
660C23—21no—
661C23—21no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—62no—
669C23—62no—
670C23—121no—
671C23—121no—
672C23—121no—
673C23—121no—
674C23—121no—
675C23—121no—
676C23—121no—
677C23—121no—
678C23—121no—
679C23—121no—
680C23—121no—
681C23—121no—
682C23C2×D3×D411yescharacteristic
683D4—22no—
684D4—22no—
685D4—41no—
686D4—41no—
687D4—62no—
688D4—62no—
689D4—62no—
690D4—62no—
691D4—84no—
692D4—121no—
693D4—121no—
694D4—121no—
695D4—121no—
696D4—244no—
697D4—244no—
698D4—244no—
699D4—244no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—32no—
705C2×C4—32no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—62no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—62no—
730C2×C4—121no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—121no—
734C2×C4—244no—
735C2×C4—244no—
736C2×C4—244no—
737C2×C4C2×D3×D411yescharacteristic
738C2×C4C2×D3×D411yescharacteristic
739C2×C4C2×#23711yescharacteristic
740C2×C4D3×#4111yescharacteristic
741C2×C4D3×#4111yescharacteristic
742C2×C4D3×#4111yescharacteristic
743C8—22no—
744C8—41no—
745C8—62no—
746C8—121no—
747C2×C3—81no—
748C2×C3—82no—
749C2×C3#238811yescharacteristic
750C2×C3#300811yescharacteristic
751C2×C3#301211yescharacteristic
752C2×C3#311911yescharacteristic
753C2×C3#312211yescharacteristic
754C2×C3#317611yescharacteristic
755C2×C3#317911yescharacteristic
756D3—82no—
757D3—82no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—41no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—122no—
773C22—122no—
774C22—122no—
775C22—122no—
776C22—122no—
777C22—122no—
778C22—241no—
779C22—241no—
780C22—241no—
781C22—241no—
782C22—241no—
783C22—241no—
784C22—241no—
785C22—241no—
786C22D3×#12011yescharacteristic
787C22#559611yescharacteristic
788C22#565611yescharacteristic
789C22#576211yescharacteristic
790C22#576911yescharacteristic
791C22#577411yescharacteristic
792C22#577411yescharacteristic
793C4—42no—
794C4—41no—
795C4—62no—
796C4—62no—
797C4—81no—
798C4—81no—
799C4—121no—
800C4—122no—
801C4—121no—
802C4—122no—
803C4#559611yescharacteristic
804C4#560611yescharacteristic
805C4#565611yescharacteristic
806C4#566811yescharacteristic
807C3#2358011yescharacteristic, complemented, Sylow
808C2—81no—
809C2—82no—
810C2—242no—
811C2—242no—
812C2#7688911yescharacteristic
813C2#8008511yescharacteristic
814C2#8014911yescharacteristic
815C2#8063711yescharacteristic
816C2#8085011yescharacteristic
817C2#8131211yescharacteristic
818C2#8135411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2034C2
socleC23×C3C22×D4
hypercenter#2034D3
hypocenterC3#23580
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2034

Complements

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

NH ≅ G/Ntype
1. C2×#5619C2semidirect
2. C2×#4869C2semidirect
3. C2×#4756C2semidirect
4. #73872C2semidirect
5. C3×#2034C2semidirect
6. #71684C2semidirect
7. #70566C2semidirect
8. #70211C2semidirect
9. #70209C2semidirect
10. #70152C2semidirect
11. #69961C2semidirect
12. #69907C2semidirect
13. #69523C2semidirect
14. #68899C2semidirect
15. #68780C2semidirect
70. #2034D3semidirect
108. D4×Dic3D4semidirect
142. #893D4semidirect
807. C3#23580semidirect

Maximal subgroups

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

subgroupindex
C2×#56192
C2×#48692
C2×#47562
#738722
C3×#20342
#716842
#705662
#702112
#702092
#701522
#699612
#699072
#695232
#688992
#687802
#235803