Finite Group Databasebeta

← #10823503

Subgroups — #10823503

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×#5535C211yesmaximal, characteristic, complemented
2#82236C211yesmaximal, characteristic, complemented
3C2×#4711C211yesmaximal, characteristic, complemented
4C2×C4×D24C211yesmaximal, characteristic, complemented
5C3×#1750C211yesmaximal, characteristic, complemented
6#69961C211yesmaximal, characteristic, complemented
7#69961C211yesmaximal, characteristic, complemented
8#69935C211yesmaximal, characteristic, complemented
9#69934C211yesmaximal, characteristic, complemented
10#69812C211yesmaximal, characteristic, complemented
11C4×#821C211yesmaximal, characteristic, complemented
12#68679C211yesmaximal, characteristic, complemented
13#68674C211yesmaximal, characteristic, complemented
14#68634C211yesmaximal, characteristic, complemented
15#68629C211yesmaximal, characteristic, complemented
16#23580—31nomaximal, Sylow
17C2×C3×#117C2211yescharacteristic
18C2×#930C2211yescharacteristic
19C2×#930C2211yescharacteristic
20C2×#930C2211yescharacteristic
21C22×D24C2211yescharacteristic
22C22×D24C2211yescharacteristic
23#5535—24no—
24#5535—24no—
25C2×#894—21no—
26C2×#894—21no—
27C2×#884—21no—
28C2×#884—21no—
29C2×#874C2211yescharacteristic
30C2×C4×D12C2211yescharacteristic
31C2×C4×D12C2211yescharacteristic
32C2×C4×D12C2211yescharacteristic
33C2×#870C2211yescharacteristic
34C2×C3×C22⋊C8C2211yescharacteristic
35C2×C3×C22⋊C8C2211yescharacteristic
36C2×C3×#97C2211yescharacteristic
37C2×C3×C4×C8C2211yescharacteristic
38#5212C2211yescharacteristic
39C2×#821C2211yescharacteristic
40C2×#821C2211yescharacteristic
41C2×#821C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×#821C2211yescharacteristic
44C2×#821C2211yescharacteristic
45C2×#821C2211yescharacteristic
46C2×#821C2211yescharacteristic
47C2×#818C2211yescharacteristic
48C2×#817C2211yescharacteristic
49#4990—21no—
50#4989—21no—
51#4957—21no—
52#4956—21no—
53#4939C2211yescharacteristic
54C4×C4⋊Dic3C2211yescharacteristic
55#4928C2211yescharacteristic
56#4711—24no—
57C4×D24—24no—
58C3×#336C2211yescharacteristic
59C3×#336C2211yescharacteristic
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4551C2211yescharacteristic
63#4551C2211yescharacteristic
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#1762—31no—
77C4×#102—31no—
78#1750D311yescharacteristic, complemented
79C23×C3×C4C2311yescharacteristic
80C22×#67—21no—
81C22×#67—21no—
82C22×#67—21no—
83C22×D12—21no—
84C22×D12—21no—
85C22×D12C2311yescharacteristic
86C22×D12C2311yescharacteristic
87C22×D12C2311yescharacteristic
88C22×C4×D3—21no—
89C22×C4×D3—21no—
90C22×C4×D3—21no—
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C3×#117—22no—
96C3×#117—22no—
97C2×C3×C4⋊C4D411yescharacteristic
98C2×C3×C4⋊C4D411yescharacteristic
99C2×C3×C22⋊C4D411yescharacteristic
100C2×C3×C22⋊C4D411yescharacteristic
101C2×C3×C42C2311yescharacteristic
102C2×C3×C42C2311yescharacteristic
103C2×#217—21no—
104#930—22no—
105#930—22no—
106#930—22no—
107#930—22no—
108#930—22no—
109#930—22no—
110C2×(C2×D3)⋊C4—21no—
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×C4⋊Dic3C2311yescharacteristic
119C2×C4⋊Dic3C2311yescharacteristic
120C2×C4⋊Dic3C2311yescharacteristic
121C2×C4⋊Dic3C2311yescharacteristic
122C2×C4⋊Dic3C2311yescharacteristic
123C2×Dic3⋊C4—21no—
124C2×Dic3⋊C4—21no—
125C2×Dic3⋊C4—21no—
126C2×C4×Dic3—21no—
127C2×D24—22no—
128C2×D24—22no—
129C2×D24—22no—
130C2×D24—22no—
131C2×D24—22no—
132C2×D24—22no—
133#894—28no—
134#894—28no—
135#884—28no—
136#884—28no—
137#874—22no—
138#874—22no—
139C4×D12—22no—
140C4×D12—22no—
141C4×D12—22no—
142C4×D12—22no—
143C4×D12D414yescomplemented
144C4×D12D414yescomplemented
145#870—22no—
146#870—22no—
147C3×C22⋊C8—22no—
148C3×C22⋊C8—22no—
149C3×#97—22no—
150C3×C4×C8—22no—
151C3⋊#95—21no—
152C3⋊#95—21no—
153C3⋊#95—21no—
154#821—22no—
155#821—22no—
156#821—22no—
157#821—22no—
158#821—22no—
159#821—22no—
160#821—22no—
161#821—22no—
162#818—22no—
163#817—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×D4—31no—
180C2×#117C2×D311yescharacteristic
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×#102—31no—
192C2×#102—31no—
193C2×C22⋊C8C2×D311yescharacteristic
194C2×C22⋊C8C2×D311yescharacteristic
195C2×#97C2×D311yescharacteristic
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#336C2×D311yescharacteristic
210#336C2×D311yescharacteristic
211C24×C3C2×D411yescharacteristic
212C23×D3—21no—
213C23×D3—21no—
214C23×D3—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4C2×D411yescharacteristic
222C22×C3×C4C2×D411yescharacteristic
223C22×C3×C4C2×D411yescharacteristic
224C22×C3×C4C2×D411yescharacteristic
225C22×C3×C4C2×D411yescharacteristic
226C22×C3×C4C2411yescharacteristic
227C2×#67—24no—
228C2×#67—24no—
229C2×#67—24no—
230C2×#67—81no—
231C2×#67—81no—
232C2×#67—81no—
233C2×#67—81no—
234C2×#67—81no—
235C2×#67—81no—
236C22×Dic3—21no—
237C22×Dic3—21no—
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3—21no—
241C2×D12—21no—
242C2×D12—21no—
243C2×D12—21no—
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—21no—
255C2×D12—21no—
256C2×D12—24no—
257C2×D12—24no—
258C2×D12—81no—
259C2×D12—81no—
260C2×D12—81no—
261C2×D12—81no—
262C2×D12C2×D412yes—
263C2×D12C2×D412yes—
264C2×D12#4112yes—
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—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8#4112yes—
285C2×C3×C8#4112yes—
286C3×C4⋊C4—22no—
287C3×C4⋊C4—22no—
288C3×C22⋊C4—22no—
289C3×C22⋊C4—22no—
290C3×C42—21no—
291C3×C42—21no—
292C3×C42C2×D412yes—
293C3×C42C2×D412yes—
294#217—81no—
295(C2×D3)⋊C4—24no—
296(C2×D3)⋊C4—24no—
297(C2×D3)⋊C4—24no—
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—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3—21no—
310C4⋊Dic3C2×D412yes—
311C4⋊Dic3C2×D412yes—
312C4⋊Dic3#4112yes—
313Dic3⋊C4—24no—
314Dic3⋊C4—24no—
315Dic3⋊C4—81no—
316C4×Dic3—81no—
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—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×C8C22×D311yescharacteristic
338C22×C8C22×D311yescharacteristic
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—68no—
349#121—62no—
350#121—62no—
351#121—62no—
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—22no—
362#117—22no—
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⋊C4D1211yescharacteristic
372C2×C4⋊C4D1211yescharacteristic
373C2×C22⋊C4—61no—
374C2×C22⋊C4—61no—
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⋊C4D1211yescharacteristic
383C2×C22⋊C4D1211yescharacteristic
384C2×C42—61no—
385C2×C42C22×D311yescharacteristic
386C2×C42C22×D311yescharacteristic
387#107—62no—
388#106—62no—
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—22no—
398C22⋊C8—22no—
399#97—22no—
400C4×C8—22no—
401#95—61no—
402#95—61no—
403#95—61no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3C22×D411yescharacteristic
412C22×D3—22no—
413C22×D3—22no—
414C22×D3—22no—
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—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4#12012yes—
451C2×C3×C4#12012yes—
452C2×C3×C4C22×D411yescharacteristic
453C2×C3×C4C22×D411yescharacteristic
454C2×C3×C4C2×#4111yescharacteristic
455C2×C3×C4C2×#4111yescharacteristic
456C2×C3×C4C2×#4111yescharacteristic
457C2×C3×C4C2×#4111yescharacteristic
458#67—84no—
459#67—84no—
460#67—84no—
461C2×Dic3—22no—
462C2×Dic3—22no—
463C2×Dic3—22no—
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—41no—
475C2×Dic3—41no—
476D12—22no—
477D12—22no—
478D12—22no—
479D12—22no—
480D12—22no—
481D12—22no—
482D12—41no—
483D12—41no—
484D12—41no—
485D12—41no—
486D12—41no—
487D12—41no—
488D12—84no—
489D12—84no—
490C4×D3—84no—
491C4×D3—84no—
492C4×D3—84no—
493C3×C8—22no—
494C3×C8—22no—
495C3×C8—41no—
496C3×C8—41no—
497C24—61no—
498C24—61no—
499C24—61no—
500C24C2×D1211yescharacteristic
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—21no—
539C22×C4—21no—
540C22×C4—61no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4—64no—
544C22×C4—64no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—122no—
548C22×C4—241no—
549C22×C4—241no—
550C22×C4—241no—
551C22×C4—241no—
552C22×C4—241no—
553C22×C4—241no—
554C22×C4C2×D1211yescharacteristic
555C22×C4C2×D1211yescharacteristic
556C22×C4C2×D1211yescharacteristic
557C22×C4C2×D1211yescharacteristic
558C22×C4C2×D1211yescharacteristic
559C22×C4C23×D311yescharacteristic
560D8—68no—
561D8—68no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8#23512yes—
573C2×C8#23512yes—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—32no—
577C4⋊C4—32no—
578C4⋊C4—32no—
579C4⋊C4—64no—
580C4⋊C4—64no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—61no—
588C4⋊C4—241no—
589C22⋊C4—22no—
590C22⋊C4—22no—
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—241no—
603C42D3×D412yes—
604C42D3×D412yes—
605C22×C3—41no—
606C22×C3—41no—
607C22×C3—41no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3C2×#12011yescharacteristic
613C22×C3#52511yescharacteristic
614C22×C3#53211yescharacteristic
615C22×C3#57611yescharacteristic
616C22×C3#57611yescharacteristic
617C22×C3#57611yescharacteristic
618C22×C3#57711yescharacteristic
619C2×D3—42no—
620C2×D3—42no—
621C2×D3—42no—
622C2×D3—42no—
623C2×D3—42no—
624C2×D3—42no—
625C2×D3—42no—
626C2×D3—42no—
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—22no—
641C3×C4—22no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4#52511yescharacteristic
646C3×C4#52511yescharacteristic
647C3×C4#53211yescharacteristic
648C3×C4#53211yescharacteristic
649Dic3—42no—
650Dic3—42no—
651Dic3—42no—
652Dic3—81no—
653Dic3—81no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—62no—
662C23—62no—
663C23—62no—
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—
682C23C22×D1211yescharacteristic
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—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—121no—
721C2×C4—121no—
722C2×C4—121no—
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—244no—
733C2×C4—244no—
734C2×C4—244no—
735C2×C4#88212yes—
736C2×C4#88212yes—
737C2×C4C2×#23511yescharacteristic
738C2×C4C2×#23511yescharacteristic
739C2×C4C2×D3×D411yescharacteristic
740C2×C4C2×D3×D411yescharacteristic
741C2×C4D3×#4111yescharacteristic
742C2×C4D3×#4111yescharacteristic
743C8—22no—
744C8—22no—
745C8—41no—
746C8—41no—
747C2×C3—81no—
748C2×C3#238811yescharacteristic
749C2×C3#300811yescharacteristic
750C2×C3#301211yescharacteristic
751C2×C3#311911yescharacteristic
752C2×C3#312211yescharacteristic
753C2×C3#317611yescharacteristic
754C2×C3#317911yescharacteristic
755D3—82no—
756D3—82no—
757D3—82no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—122no—
766C22—122no—
767C22—122no—
768C22—122no—
769C22—122no—
770C22—122no—
771C22—122no—
772C22—122no—
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—
786C22#547711yescharacteristic
787C22C2×#88211yescharacteristic
788C22#552411yescharacteristic
789C22#575111yescharacteristic
790C22#575211yescharacteristic
791C22#575211yescharacteristic
792C22#575211yescharacteristic
793C4—22no—
794C4—22no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—122no—
799C4—122no—
800C4—122no—
801C4—241no—
802C4—241no—
803C4#554711yescharacteristic
804C4#554711yescharacteristic
805C4#554811yescharacteristic
806C4#554811yescharacteristic
807C3#2358011yescharacteristic, complemented, Sylow
808C2—81no—
809C2—242no—
810C2—242no—
811C2—242no—
812C2#7358011yescharacteristic
813C2#7856911yescharacteristic
814C2#7857811yescharacteristic
815C2#7867011yescharacteristic
816C2#7867211yescharacteristic
817C2#7938411yescharacteristic
818C2#7938611yescharacteristic
subgroupG/H
centerC23C22×D12
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1750C2
socleC23×C3C22×D4
hypercenter#1750D3
hypocenterC3#23580
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#117 ◁ #1750

Complements

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

NH ≅ G/Ntype
1. C2×#5535C2semidirect
2. #82236C2semidirect
3. C2×#4711C2semidirect
4. C2×C4×D24C2semidirect
5. C3×#1750C2semidirect
6. #69961C2semidirect
7. #69961C2semidirect
8. #69935C2semidirect
9. #69934C2semidirect
10. #69812C2semidirect
11. C4×#821C2semidirect
12. #68679C2semidirect
13. #68674C2semidirect
14. #68634C2semidirect
15. #68629C2semidirect
78. #1750D3semidirect
143. C4×D12D4semidirect
144. C4×D12D4semidirect
807. C3#23580semidirect

Maximal subgroups

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

subgroupindex
C2×#55352
#822362
C2×#47112
C2×C4×D242
C3×#17502
#699612
#699352
#699342
#698122
C4×#8212
#686792
#686742
#686342
#686292
#235803