Finite Group Databasebeta

← #10823508

Subgroups — #10823508

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×#5697C211yesmaximal, characteristic, complemented
2C2×#4872C211yesmaximal, characteristic, complemented
3C2×#4869C211yesmaximal, characteristic, complemented
4#76198C211yesmaximal, characteristic, complemented
5C3×#2059C211yesmaximal, characteristic, complemented
6#71743C211yesmaximal, characteristic, complemented
7#70634C211yesmaximal, characteristic, complemented
8#70581C211yesmaximal, characteristic, complemented
9#69627C211yesmaximal, characteristic, complemented
10#68886C211yesmaximal, characteristic, complemented
11#68886C211yesmaximal, characteristic, complemented
12#68782C211yesmaximal, characteristic, complemented
13#68780C211yesmaximal, characteristic, complemented
14#68674C211yesmaximal, characteristic, complemented
15#68601C211yesmaximal, characteristic, complemented
16#23580—31nomaximal, Sylow
17C2×C3×#125C2211yescharacteristic
18C22×D24C2211yescharacteristic
19C22×D24C2211yescharacteristic
20#5697—24no—
21#5697—24no—
22C2×#895—21no—
23C2×#895—21no—
24C2×#895C2211yescharacteristic
25C2×#895C2211yescharacteristic
26C2×#895C2211yescharacteristic
27C2×#894—21no—
28C2×#894—21no—
29C2×#893C2211yescharacteristic
30C2×#893C2211yescharacteristic
31C2×#893C2211yescharacteristic
32C2×#874C2211yescharacteristic
33C2×#872C2211yescharacteristic
34C2×C3×#107C2211yescharacteristic
35C2×C3×#106C2211yescharacteristic
36C3×#389C2211yescharacteristic
37C2×#821C2211yescharacteristic
38C2×#821C2211yescharacteristic
39C2×(C2×D3)⋊C8C2211yescharacteristic
40C2×(C2×D3)⋊C8C2211yescharacteristic
41C2×#815C2211yescharacteristic
42C2×C8×Dic3C2211yescharacteristic
43#4989—21no—
44#4988—21no—
45#4987C2211yescharacteristic
46Dic3×C4⋊C4C2211yescharacteristic
47C2×#809C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#809C2211yescharacteristic
53#4939C2211yescharacteristic
54#4872—24no—
55#4869—24no—
56#4669—21no—
57#4665—21no—
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#540—31no—
65C2×#442—31no—
66C2×C4×D8—31no—
67#2324—31no—
68#2059D311yescharacteristic, complemented
69#2041—31no—
70#2034—31no—
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×D12—21no—
80C22×D12—21no—
81C22×D12—21no—
82C22×D12—21no—
83C22×D12—21no—
84C22×D12C2311yescharacteristic
85C22×D12C2311yescharacteristic
86C22×D12C2311yescharacteristic
87C22×C4×D3—21no—
88C22×C4×D3—21no—
89C22×C4×D3—21no—
90C22×C4×D3C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C3×#125—22no—
94C3×#125—22no—
95C2×C3×C4⋊C4—21no—
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C42C2311yescharacteristic
103C2×(C2×D3)⋊C4—21no—
104C2×(C2×D3)⋊C4—21no—
105C2×(C2×D3)⋊C4—21no—
106C2×(C2×D3)⋊C4—21no—
107C2×(C2×D3)⋊C4—21no—
108C2×(C2×D3)⋊C4—21no—
109C2×(C2×D3)⋊C4—21no—
110C2×(C2×D3)⋊C4—21no—
111C2×(C2×D3)⋊C4—21no—
112C2×(C2×D3)⋊C4D411yescharacteristic
113C2×(C2×D3)⋊C4D411yescharacteristic
114C2×C4⋊Dic3C2311yescharacteristic
115C2×Dic3⋊C4D411yescharacteristic
116C2×Dic3⋊C4D411yescharacteristic
117C2×C4×Dic3—21no—
118C2×C4×Dic3C2311yescharacteristic
119C22×C3⋊C8C2311yescharacteristic
120C22×C3⋊C8C2311yescharacteristic
121C2×D24—22no—
122C2×D24—22no—
123C2×D24—22no—
124C2×D24—22no—
125C2×D24—22no—
126C2×D24—22no—
127#895—28no—
128#895—28no—
129#895—22no—
130#895—22no—
131#895—22no—
132#895—22no—
133#895—22no—
134#895—22no—
135#894—28no—
136#894—28no—
137#893—22no—
138#893—22no—
139#893—22no—
140#893—22no—
141#893D414yescomplemented
142#893D414yescomplemented
143#874—22no—
144#874—22no—
145#872—22no—
146#872—22no—
147C3×#107—22no—
148C3×#106—22no—
149C3×#95—21no—
150C3⋊#95—21no—
151C3⋊#95—21no—
152#821—22no—
153#821—22no—
154(C2×D3)⋊C8—22no—
155(C2×D3)⋊C8—22no—
156#815—22no—
157C8×Dic3—22no—
158#809—22no—
159#809—22no—
160#809—22no—
161#809—22no—
162#809—22no—
163#809—22no—
164C22×D8—31no—
165C22×D8—31no—
166#540—64no—
167#540—64no—
168C2×#127—31no—
169C2×#125C2×D311yescharacteristic
170C2×#123—61no—
171C2×#123—61no—
172C2×#121—31no—
173C2×#121—31no—
174C2×#121—31no—
175C2×#121—61no—
176C2×#121—61no—
177C2×C4×D4—31no—
178C2×C4×D4—31no—
179C2×C4×D4—31no—
180C2×#117—31no—
181#442—64no—
182C4×D8—64no—
183C2×#107C2×D311yescharacteristic
184C2×#106C2×D311yescharacteristic
185C2×#102—31no—
186C2×#102—31no—
187C2×#102—31no—
188C2×#102—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×C22⋊C8—31no—
194C2×C22⋊C8—31no—
195C2×#97—31no—
196C2×C4×C8—31no—
197#390—31no—
198#390—61no—
199#389C2×D311yescharacteristic
200#388—61no—
201#386—61no—
202#385—61no—
203#380—31no—
204C4×C4⋊C4—31no—
205#340—31no—
206#340—31no—
207#340C2×D311yescharacteristic
208#340C2×D311yescharacteristic
209#336—31no—
210#336C2×D311yescharacteristic
211C23×D3—21no—
212C23×D3—21no—
213C23×D3—21no—
214C23×D3C2×D411yescharacteristic
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4C2×D411yescharacteristic
220C22×C3×C4C2×D411yescharacteristic
221C22×C3×C4C2411yescharacteristic
222C22×Dic3—21no—
223C22×Dic3C2×D411yescharacteristic
224C22×Dic3C2×D411yescharacteristic
225C22×Dic3C2×D411yescharacteristic
226C2×D12—21no—
227C2×D12—21no—
228C2×D12—21no—
229C2×D12—21no—
230C2×D12—21no—
231C2×D12—21no—
232C2×D12—21no—
233C2×D12—21no—
234C2×D12—21no—
235C2×D12—21no—
236C2×D12—21no—
237C2×D12—21no—
238C2×D12—21no—
239C2×D12—21no—
240C2×D12—21no—
241C2×D12—24no—
242C2×D12—24no—
243C2×D12—24no—
244C2×D12—24no—
245C2×D12—24no—
246C2×D12—81no—
247C2×D12—81no—
248C2×D12—81no—
249C2×D12—81no—
250C2×D12—81no—
251C2×D12—81no—
252C2×D12—81no—
253C2×D12—81no—
254C2×D12—81no—
255C2×D12—81no—
256C2×D12C2×D412yes—
257C2×D12C2×D412yes—
258C2×D12#4112yes—
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—24no—
267C2×C4×D3—42no—
268C2×C4×D3—81no—
269C2×C4×D3—81no—
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#4112yes—
279C2×C3×C8#4112yes—
280C3×C4⋊C4—24no—
281C3×C4⋊C4—24no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—81no—
288C3×C4⋊C4C2×D412yes—
289C3×C4⋊C4C2×D412yes—
290C3×C4⋊C4#4112yes—
291C3×C42—21no—
292C3×C42—21no—
293(C2×D3)⋊C4—24no—
294(C2×D3)⋊C4—24no—
295(C2×D3)⋊C4—24no—
296(C2×D3)⋊C4—22no—
297(C2×D3)⋊C4—22no—
298(C2×D3)⋊C4—24no—
299(C2×D3)⋊C4—24no—
300(C2×D3)⋊C4—42no—
301(C2×D3)⋊C4—81no—
302(C2×D3)⋊C4—81no—
303(C2×D3)⋊C4—81no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306Dic3⋊C4—22no—
307Dic3⋊C4—22no—
308C4×Dic3—81no—
309C4×Dic3C2×D412yes—
310C4×Dic3C2×D412yes—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317D24—28no—
318D24—28no—
319C22×D4—31no—
320C22×D4—31no—
321C22×D4—31no—
322C22×D4—61no—
323C22×D4—61no—
324C22×D4—61no—
325C22×D4—61no—
326C22×D4—61no—
327C23×C4—31no—
328C23×C4—61no—
329C23×C4—61no—
330C23×C4—61no—
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—22no—
344#125—22no—
345#123—68no—
346#123—68no—
347#121—62no—
348#121—62no—
349#121—62no—
350#121—68no—
351#121—68no—
352#121—62no—
353#121—62no—
354#121—62no—
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—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4C22×D311yescharacteristic
370C2×C4⋊C4C22×D311yescharacteristic
371C2×C4⋊C4C22×D311yescharacteristic
372C2×C4⋊C4C22×D311yescharacteristic
373C2×C22⋊C4—31no—
374C2×C22⋊C4—31no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
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—61no—
386C2×C42C22×D311yescharacteristic
387#107—22no—
388#106—22no—
389#102—62no—
390#102—62no—
391#102—62no—
392#102—62no—
393#102—62no—
394#102—62no—
395#102—62no—
396#102—62no—
397C22⋊C8—62no—
398C22⋊C8—62no—
399#97—62no—
400C4×C8—62no—
401#95—21no—
402#95—61no—
403#95—61no—
404C23×C3C22×D411yescharacteristic
405C22×D3—21no—
406C22×D3—22no—
407C22×D3—22no—
408C22×D3—22no—
409C22×D3—21no—
410C22×D3—21no—
411C22×D3—21no—
412C22×D3—21no—
413C22×D3—21no—
414C22×D3—21no—
415C22×D3—41no—
416C22×D3—41no—
417C22×D3—41no—
418C22×D3—41no—
419C22×D3—41no—
420C22×D3—41no—
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—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—21no—
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×C4C22×D411yescharacteristic
452C2×C3×C4C22×D411yescharacteristic
453C2×C3×C4C2×#4111yescharacteristic
454C2×C3×C4C2×#4111yescharacteristic
455C2×C3×C4C2×#4111yescharacteristic
456C2×C3×C4C2×#4111yescharacteristic
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3#12012yes—
468C2×Dic3#12012yes—
469D12—22no—
470D12—22no—
471D12—22no—
472D12—22no—
473D12—22no—
474D12—22no—
475D12—41no—
476D12—41no—
477D12—41no—
478D12—41no—
479D12—41no—
480D12—41no—
481D12—84no—
482D12—84no—
483D12—84no—
484D12—84no—
485D12—84no—
486C4×D3—41no—
487C4×D3—41no—
488C4×D3—41no—
489C4×D3—41no—
490C4×D3—84no—
491C4×D3—84no—
492C4×D3—84no—
493C3×C8—22no—
494C3×C8—22no—
495C3⋊C8—41no—
496C3⋊C8—41no—
497C24—31no—
498C24—61no—
499C24—61no—
500C24—61no—
501C2×D4—32no—
502C2×D4—32no—
503C2×D4—32no—
504C2×D4—64no—
505C2×D4—64no—
506C2×D4—64no—
507C2×D4—64no—
508C2×D4—64no—
509C2×D4—61no—
510C2×D4—61no—
511C2×D4—61no—
512C2×D4—61no—
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—61no—
524C2×D4—241no—
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×D4—241no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—31no—
539C22×C4—31no—
540C22×C4—31no—
541C22×C4—64no—
542C22×C4—64no—
543C22×C4—61no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—122no—
551C22×C4—241no—
552C22×C4—241no—
553C22×C4—241no—
554C22×C4—241no—
555C22×C4—241no—
556C22×C4—241no—
557C22×C4D3×D411yescharacteristic
558C22×C4D3×D411yescharacteristic
559C22×C4C23×D311yescharacteristic
560D8—68no—
561D8—68no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—61no—
567C2×C8—61no—
568C2×C8—61no—
569C2×C8—61no—
570C2×C8—61no—
571C2×C8—61no—
572C2×C8#23912yes—
573C2×C8#23912yes—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—62no—
582C4⋊C4—62no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—81no—
586C4⋊C4D3×D412yes—
587C4⋊C4D3×D412yes—
588C4⋊C4#23912yes—
589C22⋊C4—62no—
590C22⋊C4—62no—
591C22⋊C4—64no—
592C22⋊C4—64no—
593C22⋊C4—64no—
594C22⋊C4—64no—
595C22⋊C4—64no—
596C22⋊C4—122no—
597C22⋊C4—241no—
598C22⋊C4—241no—
599C22⋊C4—241no—
600C42—21no—
601C42—21no—
602C42—32no—
603C42—32no—
604C42—241no—
605C22×C3C2×#12011yescharacteristic
606C22×C3#52511yescharacteristic
607C22×C3#53211yescharacteristic
608C22×C3#57611yescharacteristic
609C22×C3#57611yescharacteristic
610C22×C3#57611yescharacteristic
611C22×C3#57711yescharacteristic
612C2×D3—41no—
613C2×D3—42no—
614C2×D3—41no—
615C2×D3—42no—
616C2×D3—41no—
617C2×D3—42no—
618C2×D3—42no—
619C2×D3—42no—
620C2×D3—41no—
621C2×D3—41no—
622C2×D3—42no—
623C2×D3—41no—
624C2×D3—42no—
625C2×D3—42no—
626C2×D3—41no—
627C2×D3—42no—
628C2×D3—81no—
629C2×D3—81no—
630C2×D3—81no—
631C2×D3—81no—
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—42no—
641C3×C4—42no—
642C3×C4—41no—
643C3×C4—42no—
644C3×C4—41no—
645C3×C4—81no—
646C3×C4#52511yescharacteristic
647C3×C4#52511yescharacteristic
648C3×C4#53211yescharacteristic
649C3×C4#53211yescharacteristic
650Dic3—22no—
651Dic3—22no—
652Dic3—41no—
653Dic3—81no—
654C23—61no—
655C23—61no—
656C23—61no—
657C23—61no—
658C23—61no—
659C23—62no—
660C23—62no—
661C23—61no—
662C23—62no—
663C23—61no—
664C23—121no—
665C23—121no—
666C23—121no—
667C23—121no—
668C23—121no—
669C23—121no—
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—62no—
684D4—62no—
685D4—62no—
686D4—62no—
687D4—62no—
688D4—62no—
689D4—121no—
690D4—121no—
691D4—121no—
692D4—121no—
693D4—121no—
694D4—121no—
695D4—244no—
696D4—244no—
697D4—244no—
698D4—244no—
699D4—244no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—32no—
710C2×C4—32no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
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×#23911yescharacteristic
740C2×C4C2×#23911yescharacteristic
741C2×C4C2×#23911yescharacteristic
742C2×C4D3×#4111yescharacteristic
743C8—22no—
744C8—22no—
745C8—121no—
746C8—121no—
747C2×C3#238811yescharacteristic
748C2×C3#300811yescharacteristic
749C2×C3#301211yescharacteristic
750C2×C3#311911yescharacteristic
751C2×C3#312211yescharacteristic
752C2×C3#317611yescharacteristic
753C2×C3#317911yescharacteristic
754D3—81no—
755D3—82no—
756D3—82no—
757D3—82no—
758C22—121no—
759C22—121no—
760C22—122no—
761C22—122no—
762C22—121no—
763C22—122no—
764C22—121no—
765C22—122no—
766C22—122no—
767C22—122no—
768C22—122no—
769C22—121no—
770C22—122no—
771C22—121no—
772C22—121no—
773C22—122no—
774C22—241no—
775C22—241no—
776C22—241no—
777C22—241no—
778C22—241no—
779C22—241no—
780C22—241no—
781C22—241no—
782C22—241no—
783C22—241no—
784C22—241no—
785C22—241no—
786C22D3×#12011yescharacteristic
787C22#562711yescharacteristic
788C22#572511yescharacteristic
789C22#576911yescharacteristic
790C22#576911yescharacteristic
791C22#577411yescharacteristic
792C22#577811yescharacteristic
793C4—41no—
794C4—42no—
795C4—41no—
796C4—42no—
797C4—42no—
798C4—62no—
799C4—62no—
800C4—81no—
801C4—121no—
802C4—241no—
803C4#562711yescharacteristic
804C4#562711yescharacteristic
805C4#572511yescharacteristic
806C4#572511yescharacteristic
807C3#2358011yescharacteristic, complemented, Sylow
808C2—241no—
809C2—242no—
810C2—242no—
811C2—242no—
812C2#7716911yescharacteristic
813C2#8008511yescharacteristic
814C2#8023111yescharacteristic
815C2#8114611yescharacteristic
816C2#8120811yescharacteristic
817C2#8190911yescharacteristic
818C2#8196111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2059C2
socleC23×C3C22×D4
hypercenter#2059D3
hypocenterC3#23580
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2059

Complements

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

NH ≅ G/Ntype
1. C2×#5697C2semidirect
2. C2×#4872C2semidirect
3. C2×#4869C2semidirect
4. #76198C2semidirect
5. C3×#2059C2semidirect
6. #71743C2semidirect
7. #70634C2semidirect
8. #70581C2semidirect
9. #69627C2semidirect
10. #68886C2semidirect
11. #68886C2semidirect
12. #68782C2semidirect
13. #68780C2semidirect
14. #68674C2semidirect
15. #68601C2semidirect
68. #2059D3semidirect
141. #893D4semidirect
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×#56972
C2×#48722
C2×#48692
#761982
C3×#20592
#717432
#706342
#705812
#696272
#688862
#687822
#687802
#686742
#686012
#235803