Finite Group Databasebeta

← #10823497

Subgroups — #10823497

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×C3×C4×D8C211yesmaximal, characteristic, complemented
3#82396C211yesmaximal, characteristic, complemented
4C2×#5014C211yesmaximal, characteristic, complemented
5#72044C211yesmaximal, characteristic, complemented
6#72043C211yesmaximal, characteristic, complemented
7#71609C211yesmaximal, characteristic, complemented
8#70634C211yesmaximal, characteristic, complemented
9#70618C211yesmaximal, characteristic, complemented
10#70211C211yesmaximal, characteristic, complemented
11#70207C211yesmaximal, characteristic, complemented
12#70204C211yesmaximal, characteristic, complemented
13#70164C211yesmaximal, characteristic, complemented
14C4×#821C211yesmaximal, characteristic, complemented
15#69753C211yesmaximal, characteristic, complemented
16#23580—31nomaximal, Sylow
17C22×C3×D8C2211yescharacteristic
18C2×C3×C4×D4C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×#940C2211yescharacteristic
21C2×#938C2211yescharacteristic
22C2×#938C2211yescharacteristic
23C22×#213C2211yescharacteristic
24C2×#930—21no—
25C2×#929—21no—
26#5562—24no—
27#5562—24no—
28C2×#895C2211yescharacteristic
29C2×#890C2211yescharacteristic
30C2×#884—21no—
31C2×#883—21no—
32C2×C4×D12C2211yescharacteristic
33C2×#872C2211yescharacteristic
34C3×C4×D8—24no—
35C2×C3×#107C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×C4×C8C2211yescharacteristic
39#5221C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic
42C2×#832C2211yescharacteristic
43#5213—21no—
44#5210—21no—
45C2×#821C2211yescharacteristic
46C2×#821C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic
48C2×(C2×D3)⋊C8C2211yescharacteristic
49#5014—24no—
50#4987C2211yescharacteristic
51#4972C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#808C2211yescharacteristic
54#4957—21no—
55#4945—21no—
56C4×C4⋊Dic3C2211yescharacteristic
57C2×#803C2211yescharacteristic
58#4551C2211yescharacteristic
59#4551C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#540—31no—
65C2×#442—31no—
66C2×C4×D8D311yescharacteristic, complemented
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#1762—31no—
77C4×#102—31no—
78#1750—31no—
79C22×C3×D4C2311yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4—21no—
82C23×C3×C4—21no—
83C22×#67—21no—
84C22×#67—21no—
85C22×#67—21no—
86C22×#67—21no—
87C22×D12—21no—
88C22×D12C2311yescharacteristic
89C22×C4×D3—21no—
90C22×C4×D3C2311yescharacteristic
91C2×C3×D8—22no—
92C2×C3×D8—22no—
93C2×C3×D8—22no—
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C3×C4×D4—22no—
97C3×C4×D4—22no—
98C3×C4×D4—22no—
99C3×C4×D4D414yescomplemented
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C22⋊C4—21no—
103C2×C3×C22⋊C4—21no—
104C2×C3×C42C2311yescharacteristic
105C2×#217—21no—
106C2×#217—21no—
107C2×#217—21no—
108C2×#217—21no—
109#940—22no—
110#940—22no—
111#938—22no—
112#938—22no—
113#938—22no—
114#938—22no—
115C2×#213—22no—
116C2×#213—22no—
117C2×#213—22no—
118#930—28no—
119#929—28no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4D411yescharacteristic
124C2×(C2×D3)⋊C4D411yescharacteristic
125C2×C4⋊Dic3—21no—
126C2×C4⋊Dic3C2311yescharacteristic
127C2×C4⋊Dic3C2311yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4D411yescharacteristic
132C2×Dic3⋊C4D411yescharacteristic
133C2×C4×Dic3—21no—
134C2×C4×Dic3C2311yescharacteristic
135C22×C3⋊C8C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137#895—22no—
138#895—22no—
139#890—22no—
140#890—22no—
141#884—28no—
142#883—28no—
143C4×D12—22no—
144C4×D12D414yescomplemented
145#872—22no—
146#872—22no—
147C3×#107—22no—
148C3×#102—22no—
149C3×#102—22no—
150C3×C4×C8—22no—
151#832—22no—
152#832—22no—
153#832—22no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157#821—22no—
158#821—22no—
159(C2×D3)⋊C8—22no—
160(C2×D3)⋊C8—22no—
161#809—22no—
162#808—22no—
163#803—22no—
164C22×D8—31no—
165C22×D8C2×D311yescharacteristic
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×D4C2×D311yescharacteristic
179C2×C4×D4C2×D311yescharacteristic
180C2×#117—31no—
181#442—64no—
182C4×D8—24no—
183C2×#107C2×D311yescharacteristic
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×#97—31no—
196C2×C4×C8C2×D311yescharacteristic
197#390—31no—
198#390—61no—
199#389—31no—
200#388—61no—
201#386—61no—
202#385—61no—
203#380—31no—
204C4×C4⋊C4—31no—
205#340—31no—
206#340—31no—
207#340—31no—
208#340—31no—
209#336—31no—
210#336—31no—
211C24×C3—21no—
212C24×C3—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×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4C2×D412yes—
226C2×C3×D4#4112yes—
227C22×C3×C4—21no—
228C22×C3×C4—24no—
229C22×C3×C4—21no—
230C22×C3×C4—42no—
231C22×C3×C4—81no—
232C22×C3×C4—81no—
233C22×C3×C4—81no—
234C22×C3×C4—81no—
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2411yescharacteristic
238C2×#67—24no—
239C2×#67—24no—
240C2×#67—24no—
241C2×#67—24no—
242C2×#67—81no—
243C2×#67—81no—
244C2×#67—81no—
245C2×#67—81no—
246C2×#67—81no—
247C2×#67—81no—
248C2×#67—81no—
249C2×#67—81no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3—21no—
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—24no—
262C2×D12—81no—
263C2×D12—81no—
264C2×D12C2×D412yes—
265C2×C4×D3—21no—
266C2×C4×D3—21no—
267C2×C4×D3—21no—
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C2×C4×D3—21no—
271C2×C4×D3—24no—
272C2×C4×D3—81no—
273C2×C4×D3—81no—
274C3×D8—28no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8#4112yes—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4C2×D412yes—
285C3×C22⋊C4—24no—
286C3×C22⋊C4—42no—
287C3×C42C2×D412yes—
288C3×C42C2×D412yes—
289#217—24no—
290#217—24no—
291#217—81no—
292#217—81no—
293#213—28no—
294(C2×D3)⋊C4—24no—
295(C2×D3)⋊C4—22no—
296(C2×D3)⋊C4—22no—
297(C2×D3)⋊C4—24no—
298(C2×D3)⋊C4—81no—
299C4⋊Dic3—24no—
300C4⋊Dic3—21no—
301C4⋊Dic3—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3C2×D412yes—
305C4⋊Dic3#4112yes—
306Dic3⋊C4—24no—
307Dic3⋊C4—22no—
308Dic3⋊C4—22no—
309Dic3⋊C4—81no—
310C4×Dic3—21no—
311C4×Dic3—21no—
312C4×Dic3—81no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8#4112yes—
319C22×D4—31no—
320C22×D4—61no—
321C22×D4—61no—
322C22×D4—61no—
323C22×D4—61no—
324C22×D4—61no—
325C22×D4C22×D311yescharacteristic
326C22×D4C22×D311yescharacteristic
327C23×C4—21no—
328C23×C4—21no—
329C23×C4—31no—
330C23×C4—61no—
331C2×D8—22no—
332C2×D8—22no—
333C2×D8—22no—
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—22no—
357C4×D4—22no—
358C4×D4—34no—
359C4×D4—62no—
360C4×D4#6714yescomplemented
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—31no—
368C2×C4⋊C4—61no—
369C2×C4⋊C4—61no—
370C2×C4⋊C4—61no—
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—61no—
386C2×C42C22×D311yescharacteristic
387#107—22no—
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—62no—
400C4×C8—22no—
401#95—61no—
402#95—61no—
403#95—61no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3C22×D411yescharacteristic
419C22×D3—21no—
420C22×D3—22no—
421C22×D3—21no—
422C22×D3—21no—
423C22×D3—21no—
424C22×D3—21no—
425C22×D3—21no—
426C22×D3—21no—
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—22no—
436C3×D4—22no—
437C3×D4—41no—
438C3×D4—41no—
439C3×D4—41no—
440C3×D4—41no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—22no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—84no—
452C2×C3×C4—84no—
453C2×C3×C4#12012yes—
454C2×C3×C4#12012yes—
455C2×C3×C4C22×D411yescharacteristic
456C2×C3×C4C22×D411yescharacteristic
457C2×C3×C4C2×#4111yescharacteristic
458C2×C3×C4C2×#4111yescharacteristic
459C2×C3×C4C2×#4111yescharacteristic
460C2×C3×C4C2×#4111yescharacteristic
461#67—84no—
462#67—84no—
463#67—84no—
464#67—84no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—22no—
469C2×Dic3—22no—
470C2×Dic3—21no—
471C2×Dic3—21no—
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—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483D12—22no—
484D12—22no—
485D12—41no—
486D12—41no—
487D12—84no—
488C4×D3—41no—
489C4×D3—41no—
490C4×D3—41no—
491C4×D3—41no—
492C4×D3—84no—
493C3×C8—22no—
494C3×C8—41no—
495C3⋊C8—22no—
496C3⋊C8—41no—
497C24—21no—
498C24—21no—
499C24—31no—
500C24—61no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—32no—
512C2×D4—64no—
513C2×D4—64no—
514C2×D4—64no—
515C2×D4—64no—
516C2×D4—64no—
517C2×D4—61no—
518C2×D4—61no—
519C2×D4—61no—
520C2×D4—61no—
521C2×D4—61no—
522C2×D4—241no—
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#23512yes—
533C2×D4C2×#6712yes—
534C22×C4—21no—
535C22×C4—24no—
536C22×C4—21no—
537C22×C4—31no—
538C22×C4—31no—
539C22×C4—31no—
540C22×C4—42no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4—61no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—64no—
550C22×C4—61no—
551C22×C4—81no—
552C22×C4—81no—
553C22×C4—81no—
554C22×C4—81no—
555C22×C4—241no—
556C22×C4—241no—
557C22×C4D3×D411yescharacteristic
558C22×C4D3×D411yescharacteristic
559C22×C4C23×D311yescharacteristic
560D8—28no—
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—32no—
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—61no—
587C4⋊C4—241no—
588C4⋊C4C2×#6712yes—
589C22⋊C4—24no—
590C22⋊C4—42no—
591C22⋊C4—64no—
592C22⋊C4—64no—
593C22⋊C4—64no—
594C22⋊C4—62no—
595C22⋊C4—62no—
596C22⋊C4—64no—
597C22⋊C4—241no—
598C22⋊C4—241no—
599C22⋊C4—241no—
600C42—61no—
601C42—61no—
602C42—241no—
603C42D3×D412yes—
604C42C2×#6712yes—
605C22×C3—42no—
606C22×C3—42no—
607C22×C3—42no—
608C22×C3—42no—
609C22×C3—42no—
610C22×C3—42no—
611C22×C3—81no—
612C22×C3—81no—
613C22×C3—81no—
614C22×C3—81no—
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—41no—
627C2×D3—41no—
628C2×D3—41no—
629C2×D3—42no—
630C2×D3—41no—
631C2×D3—41no—
632C2×D3—41no—
633C2×D3—42no—
634C2×D3—42no—
635C2×D3—41no—
636C2×D3—81no—
637C2×D3—81no—
638C2×D3—81no—
639C2×D3—81no—
640C3×C4—22no—
641C3×C4—22no—
642C3×C4—42no—
643C3×C4—81no—
644C3×C4#52511yescharacteristic
645C3×C4#52511yescharacteristic
646C3×C4#53211yescharacteristic
647C3×C4#53211yescharacteristic
648Dic3—42no—
649Dic3—41no—
650Dic3—41no—
651Dic3—42no—
652Dic3—41no—
653Dic3—81no—
654C23—22no—
655C23—22no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—61no—
669C23—61no—
670C23—61no—
671C23—61no—
672C23—62no—
673C23—61no—
674C23—61no—
675C23—61no—
676C23—121no—
677C23—121no—
678C23—121no—
679C23—121no—
680C23—121no—
681C23—121no—
682C23C2×D3×D411yescharacteristic
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—62no—
692D4—62no—
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—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—62no—
718C2×C4—61no—
719C2×C4—62no—
720C2×C4—61no—
721C2×C4—84no—
722C2×C4—84no—
723C2×C4—121no—
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—121no—
734C2×C4—244no—
735C2×C4#93712yes—
736C2×C4#93712yes—
737C2×C4C2×#23511yescharacteristic
738C2×C4C2×#23511yescharacteristic
739C2×C4C2×D3×D411yescharacteristic
740C2×C4D3×#4111yescharacteristic
741C2×C4D3×#4111yescharacteristic
742C2×C4C22×#6711yescharacteristic
743C8—22no—
744C8—41no—
745C8—62no—
746C8—121no—
747C2×C3—82no—
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—81no—
757D3—82no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—121no—
773C22—122no—
774C22—122no—
775C22—121no—
776C22—121no—
777C22—122no—
778C22—121no—
779C22—121no—
780C22—121no—
781C22—121no—
782C22—241no—
783C22—241no—
784C22—241no—
785C22—241no—
786C22#554711yescharacteristic
787C22#554811yescharacteristic
788C22#575711yescharacteristic
789C22#575711yescharacteristic
790C22#576911yescharacteristic
791C22#577011yescharacteristic
792C22C2×#93711yescharacteristic
793C4—22no—
794C4—22no—
795C4—42no—
796C4—81no—
797C4—121no—
798C4—121no—
799C4—122no—
800C4—121no—
801C4—122no—
802C4—241no—
803C4#554711yescharacteristic
804C4#554811yescharacteristic
805C4#579111yescharacteristic
806C4#583211yescharacteristic
807C3#2358011yescharacteristic, complemented, Sylow
808C2—82no—
809C2—82no—
810C2—241no—
811C2—242no—
812C2#7959511yescharacteristic
813C2#7959611yescharacteristic
814C2#7960111yescharacteristic
815C2#7960211yescharacteristic
816C2#8240011yescharacteristic
817C2#8383311yescharacteristic
818C2#8391211yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×C4×D8C2
socleC23×C3C22×D4
hypercenterC2×C4×D8D3
hypocenterC3#23580
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#5562C2semidirect
2. C2×C3×C4×D8C2semidirect
3. #82396C2semidirect
4. C2×#5014C2semidirect
5. #72044C2semidirect
6. #72043C2semidirect
7. #71609C2semidirect
8. #70634C2semidirect
9. #70618C2semidirect
10. #70211C2semidirect
11. #70207C2semidirect
12. #70204C2semidirect
13. #70164C2semidirect
14. C4×#821C2semidirect
15. #69753C2semidirect
66. C2×C4×D8D3semidirect
99. C3×C4×D4D4semidirect
144. C4×D12D4semidirect
360. C4×D4#67semidirect
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×C3×C4×D82
#823962
C2×#50142
#720442
#720432
#716092
#706342
#706182
#702112
#702072
#702042
#701642
C4×#8212
#697532
#235803