Finite Group Databasebeta

← #10823499

Subgroups — #10823499

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×#5562C211yesmaximal, characteristic, complemented
2C2×C4×#213C211yesmaximal, characteristic, complemented
3C2×#4711C211yesmaximal, characteristic, complemented
4#73763C211yesmaximal, characteristic, complemented
5C3×#1762C211yesmaximal, characteristic, complemented
6#70209C211yesmaximal, characteristic, complemented
7#70204C211yesmaximal, characteristic, complemented
8#70177C211yesmaximal, characteristic, complemented
9#70176C211yesmaximal, characteristic, complemented
10#69830C211yesmaximal, characteristic, complemented
11C4×#809C211yesmaximal, characteristic, complemented
12#68899C211yesmaximal, characteristic, complemented
13#68886C211yesmaximal, characteristic, complemented
14#68828C211yesmaximal, characteristic, complemented
15#68822C211yesmaximal, characteristic, complemented
16#23580—31nomaximal, Sylow
17C2×C3×C4×D4C2211yescharacteristic
18C2×#940C2211yescharacteristic
19C2×#938C2211yescharacteristic
20C22×#213C2211yescharacteristic
21C2×#930—21no—
22C2×#929—21no—
23C22×D24C2211yescharacteristic
24#5562—24no—
25#5562—24no—
26C2×#895C2211yescharacteristic
27C2×#895C2211yescharacteristic
28C2×#890C2211yescharacteristic
29C2×#884—21no—
30C2×#883—21no—
31C2×C4×D12C2211yescharacteristic
32C2×C4×D12C2211yescharacteristic
33C2×#872C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#97C2211yescharacteristic
37C3×C4×C4⋊C4C2211yescharacteristic
38C2×#832C2211yescharacteristic
39C2×#821C2211yescharacteristic
40C2×#821C2211yescharacteristic
41C2×(C2×D3)⋊C8C2211yescharacteristic
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×#817C2211yescharacteristic
44C4×#213—24no—
45#4988C2211yescharacteristic
46#4987C2211yescharacteristic
47#4984C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#807C2211yescharacteristic
52#4940—21no—
53#4939—21no—
54C2×C4×C3⋊C8C2211yescharacteristic
55#4711—24no—
56#4668—21no—
57#4665—21no—
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
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#2034—31no—
71#2033—31no—
72#2025—31no—
73#2011—31no—
74#1999—31no—
75#1999—31no—
76#1762D311yescharacteristic, complemented
77C4×#102—31no—
78#1750—31no—
79C22×C3×D4C2311yescharacteristic
80C23×C3×C4—21no—
81C22×#67—21no—
82C22×#67—21no—
83C22×#67—21no—
84C22×D12—21no—
85C22×D12—21no—
86C22×D12C2311yescharacteristic
87C22×D12C2311yescharacteristic
88C22×C4×D3—21no—
89C22×C4×D3—21no—
90C22×C4×D3C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C3×C4×D4—22no—
94C3×C4×D4D414yescomplemented
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C22⋊C4—21no—
99C2×C3×C42—21no—
100C2×C3×C42C2311yescharacteristic
101C2×#217—21no—
102#940—22no—
103#940—22no—
104#938—22no—
105#938—22no—
106C2×#213—22no—
107C2×#213—22no—
108C2×#213—22no—
109#930—28no—
110#929—28no—
111C2×(C2×D3)⋊C4—21no—
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)⋊C4—21no—
118C2×(C2×D3)⋊C4D411yescharacteristic
119C2×(C2×D3)⋊C4D411yescharacteristic
120C2×C4⋊Dic3—21no—
121C2×C4⋊Dic3—21no—
122C2×C4⋊Dic3C2311yescharacteristic
123C2×C4⋊Dic3C2311yescharacteristic
124C2×Dic3⋊C4—21no—
125C2×Dic3⋊C4D411yescharacteristic
126C2×Dic3⋊C4D411yescharacteristic
127C2×C4×Dic3C2311yescharacteristic
128C22×C3⋊C8C2311yescharacteristic
129C22×C3⋊C8C2311yescharacteristic
130C2×D24—22no—
131C2×D24—22no—
132C2×D24—22no—
133#895—22no—
134#895—22no—
135#895—22no—
136#895—22no—
137#890—22no—
138#890—22no—
139#884—28no—
140#883—28no—
141C4×D12—22no—
142C4×D12—22no—
143C4×D12—22no—
144C4×D12D414yescomplemented
145#872—22no—
146#872—22no—
147C3×#102—22no—
148C3×#102—22no—
149C3×#97—22no—
150C3×#95—21no—
151#832—22no—
152C3⋊#95—21no—
153C3⋊#95—21no—
154#821—22no—
155#821—22no—
156(C2×D3)⋊C8—22no—
157(C2×D3)⋊C8—22no—
158#817—22no—
159#809—22no—
160#809—22no—
161#809—22no—
162#807—22no—
163C4×C3⋊C8—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—31no—
175C2×#121—61no—
176C2×#121—61no—
177C2×C4×D4—31no—
178C2×C4×D4—31no—
179C2×C4×D4C2×D311yescharacteristic
180C2×#117—31no—
181#442—64no—
182C4×D8—64no—
183C2×#107—31no—
184C2×#106—31no—
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⋊C8—31no—
195C2×#97C2×D311yescharacteristic
196C2×C4×C8—31no—
197#390—31no—
198#390—61no—
199#389—31no—
200#388—61no—
201#386—61no—
202#385—61no—
203#380—31no—
204C4×C4⋊C4C2×D311yescharacteristic
205#340—31no—
206#340—31no—
207#340C2×D311yescharacteristic
208#340C2×D311yescharacteristic
209#336—31no—
210#336—31no—
211C24×C3—21no—
212C23×D3—21no—
213C23×D3—21no—
214C23×D3C2×D411yescharacteristic
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4C2×D412yes—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—24no—
224C22×C3×C4—21no—
225C22×C3×C4—81no—
226C22×C3×C4—81no—
227C22×C3×C4C2×D411yescharacteristic
228C22×C3×C4C2×D411yescharacteristic
229C22×C3×C4C2411yescharacteristic
230C2×#67—24no—
231C2×#67—24no—
232C2×#67—24no—
233C2×#67—81no—
234C2×#67—81no—
235C2×#67—81no—
236C2×#67—81no—
237C2×#67—81no—
238C2×#67—81no—
239C22×Dic3—21no—
240C22×Dic3—21no—
241C22×Dic3C2×D411yescharacteristic
242C22×Dic3C2×D411yescharacteristic
243C22×Dic3C2×D411yescharacteristic
244C2×D12—21no—
245C2×D12—21no—
246C2×D12—21no—
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—24no—
255C2×D12—24no—
256C2×D12—81no—
257C2×D12—81no—
258C2×D12—81no—
259C2×D12—81no—
260C2×D12C2×D412yes—
261C2×D12#4112yes—
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×C4×D3—21no—
266C2×C4×D3—21no—
267C2×C4×D3—21no—
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⋊C4C2×D412yes—
285C3×C4⋊C4#4112yes—
286C3×C22⋊C4—24no—
287C3×C42—81no—
288C3×C42C2×D412yes—
289C3×C42C2×D412yes—
290#217—24no—
291#213—28no—
292(C2×D3)⋊C4—24no—
293(C2×D3)⋊C4—24no—
294(C2×D3)⋊C4—22no—
295(C2×D3)⋊C4—22no—
296(C2×D3)⋊C4—24no—
297(C2×D3)⋊C4—42no—
298(C2×D3)⋊C4—81no—
299(C2×D3)⋊C4—81no—
300(C2×D3)⋊C4—81no—
301C4⋊Dic3—24no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3—81no—
306C4⋊Dic3C2×D412yes—
307Dic3⋊C4—24no—
308Dic3⋊C4—22no—
309Dic3⋊C4—22no—
310C4×Dic3—21no—
311C4×Dic3—21no—
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—31no—
320C22×D4—31no—
321C22×D4—61no—
322C22×D4—61no—
323C22×D4—61no—
324C22×D4—61no—
325C22×D4—61no—
326C22×D4C22×D311yescharacteristic
327C23×C4—21no—
328C23×C4—31no—
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—62no—
344#125—62no—
345#123—68no—
346#123—68no—
347#121—68no—
348#121—62no—
349#121—62no—
350#121—62no—
351#121—68no—
352#121—62no—
353#121—62no—
354#121—62no—
355C4×D4—22no—
356C4×D4—34no—
357C4×D4—62no—
358C4×D4—62no—
359C4×D4—62no—
360C4×D4D1214yescomplemented
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—31no—
375C2×C22⋊C4—31no—
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—21no—
385C2×C42—31no—
386C2×C42C22×D311yescharacteristic
387#107—62no—
388#106—62no—
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—62no—
398C22⋊C8—62no—
399#97—22no—
400C4×C8—62no—
401#95—21no—
402#95—61no—
403#95—61no—
404C23×C3—22no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3C22×D411yescharacteristic
412C22×D3—21no—
413C22×D3—22no—
414C22×D3—22no—
415C22×D3—21no—
416C22×D3—21no—
417C22×D3—21no—
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—21no—
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—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
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—84no—
451C2×C3×C4#12012yes—
452C2×C3×C4#12012yes—
453C2×C3×C4C22×D411yescharacteristic
454C2×C3×C4C22×D411yescharacteristic
455C2×C3×C4C2×#4111yescharacteristic
456C2×C3×C4C2×#4111yescharacteristic
457C2×C3×C4C2×#4111yescharacteristic
458C2×C3×C4C2×#4111yescharacteristic
459#67—84no—
460#67—84no—
461#67—84no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—22no—
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477D12—22no—
478D12—22no—
479D12—22no—
480D12—22no—
481D12—41no—
482D12—41no—
483D12—41no—
484D12—41no—
485D12—84no—
486D12—84no—
487C4×D3—41no—
488C4×D3—41no—
489C4×D3—41no—
490C4×D3—41no—
491C4×D3—84no—
492C4×D3—84no—
493C3×C8—22no—
494C3×C8—41no—
495C3⋊C8—22no—
496C3⋊C8—41no—
497C24—21no—
498C24—31no—
499C24—61no—
500C24—61no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—32no—
507C2×D4—32no—
508C2×D4—64no—
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—241no—
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×D4C2×D1212yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—24no—
537C22×C4—21no—
538C22×C4—31no—
539C22×C4—31no—
540C22×C4—31no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4—61no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—64no—
549C22×C4—61no—
550C22×C4—81no—
551C22×C4—81no—
552C22×C4—122no—
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—21no—
567C2×C8—32no—
568C2×C8—61no—
569C2×C8—61no—
570C2×C8—61no—
571C2×C8—61no—
572C2×C8—61no—
573C2×C8#23512yes—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—32no—
579C4⋊C4—64no—
580C4⋊C4—64no—
581C4⋊C4—62no—
582C4⋊C4—62no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—241no—
587C4⋊C4C2×D1212yes—
588C4⋊C4#23512yes—
589C22⋊C4—24no—
590C22⋊C4—64no—
591C22⋊C4—64no—
592C22⋊C4—64no—
593C22⋊C4—62no—
594C22⋊C4—62no—
595C22⋊C4—64no—
596C22⋊C4—122no—
597C22⋊C4—241no—
598C22⋊C4—241no—
599C22⋊C4—241no—
600C42—61no—
601C42—61no—
602C42—81no—
603C42C2×D1212yes—
604C42D3×D412yes—
605C22×C3—42no—
606C22×C3—42no—
607C22×C3—42no—
608C22×C3—81no—
609C22×C3—81no—
610C22×C3—81no—
611C22×C3—81no—
612C22×C3C2×#12011yescharacteristic
613C22×C3#52511yescharacteristic
614C22×C3#53211yescharacteristic
615C22×C3#57611yescharacteristic
616C22×C3#57611yescharacteristic
617C22×C3#57611yescharacteristic
618C22×C3#57711yescharacteristic
619C2×D3—41no—
620C2×D3—42no—
621C2×D3—41no—
622C2×D3—42no—
623C2×D3—41no—
624C2×D3—42no—
625C2×D3—42no—
626C2×D3—41no—
627C2×D3—41no—
628C2×D3—41no—
629C2×D3—42no—
630C2×D3—42no—
631C2×D3—41no—
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—22no—
641C3×C4—22no—
642C3×C4—42no—
643C3×C4—42no—
644C3×C4—81no—
645C3×C4#52511yescharacteristic
646C3×C4#52511yescharacteristic
647C3×C4#53211yescharacteristic
648C3×C4#53211yescharacteristic
649Dic3—41no—
650Dic3—41no—
651Dic3—42no—
652Dic3—41no—
653Dic3—81no—
654C23—22no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—62no—
662C23—61no—
663C23—61no—
664C23—61no—
665C23—61no—
666C23—61no—
667C23—62no—
668C23—61no—
669C23—61no—
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—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—22no—
705C2×C4—22no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—62no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—84no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—244no—
734C2×C4—244no—
735C2×C4#88212yes—
736C2×C4#88212yes—
737C2×C4C22×D1211yescharacteristic
738C2×C4C2×#23511yescharacteristic
739C2×C4C2×#23511yescharacteristic
740C2×C4C2×D3×D411yescharacteristic
741C2×C4D3×#4111yescharacteristic
742C2×C4D3×#4111yescharacteristic
743C8—22no—
744C8—41no—
745C8—62no—
746C8—121no—
747C2×C3—82no—
748C2×C3#238811yescharacteristic
749C2×C3#300811yescharacteristic
750C2×C3#301211yescharacteristic
751C2×C3#311911yescharacteristic
752C2×C3#312211yescharacteristic
753C2×C3#317611yescharacteristic
754C2×C3#317911yescharacteristic
755D3—81no—
756D3—82no—
757D3—82no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—121no—
766C22—122no—
767C22—122no—
768C22—121no—
769C22—121no—
770C22—122no—
771C22—121no—
772C22—122no—
773C22—122no—
774C22—121no—
775C22—121no—
776C22—122no—
777C22—121no—
778C22—241no—
779C22—241no—
780C22—241no—
781C22—241no—
782C22—241no—
783C22—241no—
784C22—241no—
785C22—241no—
786C22C2×#88211yescharacteristic
787C22#554711yescharacteristic
788C22#554811yescharacteristic
789C22#577411yescharacteristic
790C22#577411yescharacteristic
791C22#577411yescharacteristic
792C22#577811yescharacteristic
793C4—22no—
794C4—22no—
795C4—42no—
796C4—42no—
797C4—81no—
798C4—121no—
799C4—122no—
800C4—121no—
801C4—121no—
802C4—241no—
803C4#547711yescharacteristic
804C4#552411yescharacteristic
805C4#554711yescharacteristic
806C4#554811yescharacteristic
807C3#2358011yescharacteristic, complemented, Sylow
808C2—82no—
809C2—241no—
810C2—242no—
811C2—242no—
812C2#7358011yescharacteristic
813C2#7888611yescharacteristic
814C2#7892811yescharacteristic
815C2#7977011yescharacteristic
816C2#7981211yescharacteristic
817C2#7986011yescharacteristic
818C2#7987411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1762C2
socleC23×C3C22×D4
hypercenter#1762D3
hypocenterC3#23580
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
1. C2×#5562C2semidirect
2. C2×C4×#213C2semidirect
3. C2×#4711C2semidirect
4. #73763C2semidirect
5. C3×#1762C2semidirect
6. #70209C2semidirect
7. #70204C2semidirect
8. #70177C2semidirect
9. #70176C2semidirect
10. #69830C2semidirect
11. C4×#809C2semidirect
12. #68899C2semidirect
13. #68886C2semidirect
14. #68828C2semidirect
15. #68822C2semidirect
76. #1762D3semidirect
94. C3×C4×D4D4semidirect
144. C4×D12D4semidirect
360. C4×D4D12semidirect
807. C3#23580semidirect

Maximal subgroups

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

subgroupindex
C2×#55622
C2×C4×#2132
C2×#47112
#737632
C3×#17622
#702092
#702042
#701772
#701762
#698302
C4×#8092
#688992
#688862
#688282
#688222
#235803