Finite Group Databasebeta

← #10823501

Subgroups — #10823501

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
2C3×#2324C211yesmaximal, characteristic, complemented
3C2×#5014C211yesmaximal, characteristic, complemented
4C2×C4×#213C211yesmaximal, characteristic, complemented
5#71684C211yesmaximal, characteristic, complemented
6#71684C211yesmaximal, characteristic, complemented
7#71582C211yesmaximal, characteristic, complemented
8#69658C211yesmaximal, characteristic, complemented
9#69639C211yesmaximal, characteristic, complemented
10#69627C211yesmaximal, characteristic, complemented
11#69606C211yesmaximal, characteristic, complemented
12#69524C211yesmaximal, characteristic, complemented
13#69523C211yesmaximal, characteristic, complemented
14#69474C211yesmaximal, characteristic, complemented
15C4×#809C211yesmaximal, characteristic, complemented
16#23580—31nomaximal, Sylow
17C2×C3×#121C2211yescharacteristic
18C2×C3×C4×D4C2211yescharacteristic
19C2×C3×#117C2211yescharacteristic
20C22×#213C2211yescharacteristic
21C22×#213C2211yescharacteristic
22C2×#930C2211yescharacteristic
23C2×#930C2211yescharacteristic
24#5535—24no—
25#5535—24no—
26C2×#894—21no—
27C2×#894—21no—
28C2×#884—21no—
29C2×#884—21no—
30C2×#874C2211yescharacteristic
31C2×C4×D12C2211yescharacteristic
32C2×C4×D12C2211yescharacteristic
33C2×#870C2211yescharacteristic
34C3×#390—21no—
35C3×#390C2211yescharacteristic
36C3×#389C2211yescharacteristic
37C3×#388—21no—
38C3×#386—21no—
39C3×#385—21no—
40C3×#380C2211yescharacteristic
41C3×C4×C4⋊C4C2211yescharacteristic
42C2×#832C2211yescharacteristic
43C2×#832C2211yescharacteristic
44C2×#830C2211yescharacteristic
45C2×#830C2211yescharacteristic
46#5014—24no—
47C4×#213—24no—
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#808C2211yescharacteristic
55C2×#807C2211yescharacteristic
56C2×#803C2211yescharacteristic
57C2×C4×C3⋊C8C2211yescharacteristic
58#4529C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#540—31no—
65C2×#442—31no—
66C2×C4×D8—31no—
67#2324D311yescharacteristic, complemented
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×D4—21no—
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4—21no—
82C23×C3×C4C2311yescharacteristic
83C22×#67—21no—
84C22×#67—21no—
85C22×D12—21no—
86C22×D12—21no—
87C22×D12C2311yescharacteristic
88C22×D12C2311yescharacteristic
89C22×C4×D3—21no—
90C22×C4×D3—21no—
91C3×#121—22no—
92C3×#121—22no—
93C3×C4×D4—22no—
94C3×C4×D4—22no—
95C3×#117—22no—
96C3×#117—22no—
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4D411yescharacteristic
99C2×C3×C4⋊C4D411yescharacteristic
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C22⋊C4—21no—
104C2×C3×C22⋊C4—21no—
105C2×C3×C22⋊C4—21no—
106C2×C3×C22⋊C4—21no—
107C2×C3×C22⋊C4—21no—
108C2×C3×C22⋊C4D411yescharacteristic
109C2×C3×C22⋊C4D411yescharacteristic
110C2×C3×C42—21no—
111C2×C3×C42C2311yescharacteristic
112C2×C3×C42C2311yescharacteristic
113C2×#213—22no—
114C2×#213—22no—
115C2×#213—22no—
116C2×#213—22no—
117C2×#213—22no—
118C2×#213—22no—
119#930—22no—
120#930—22no—
121#930—22no—
122#930—22no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×C4⋊Dic3C2311yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C22×C3⋊C8C2311yescharacteristic
132C22×C3⋊C8C2311yescharacteristic
133C22×C3⋊C8C2311yescharacteristic
134C22×C3⋊C8C2311yescharacteristic
135#894—28no—
136#894—28no—
137#884—28no—
138#884—28no—
139#874—22no—
140#874—22no—
141C4×D12—22no—
142C4×D12—22no—
143C4×D12D414yescomplemented
144C4×D12D414yescomplemented
145#870—22no—
146#870—22no—
147C3×#95—21no—
148C3×#95—21no—
149C3×#95—21no—
150#832—22no—
151#832—22no—
152#830—22no—
153#830—22no—
154#809—22no—
155#809—22no—
156#809—22no—
157#809—22no—
158#809—22no—
159#809—22no—
160#808—22no—
161#807—22no—
162#803—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—61no—
175C2×#121—61no—
176C2×#121C2×D311yescharacteristic
177C2×C4×D4—31no—
178C2×C4×D4—31no—
179C2×C4×D4C2×D311yescharacteristic
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⋊C8—31no—
194C2×C22⋊C8—31no—
195C2×#97—31no—
196C2×C4×C8—31no—
197#390—21no—
198#390C2×D311yescharacteristic
199#389C2×D311yescharacteristic
200#388—21no—
201#386—21no—
202#385—21no—
203#380C2×D311yescharacteristic
204C4×C4⋊C4C2×D311yescharacteristic
205#340—31no—
206#340—31no—
207#340—31no—
208#340—31no—
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×D4#4112yes—
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×C4—42no—
234C22×C3×C4—81no—
235C22×C3×C4—81no—
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2411yescharacteristic
242C2×#67—24no—
243C2×#67—24no—
244C2×#67—81no—
245C2×#67—81no—
246C2×#67—81no—
247C2×#67—81no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—21no—
260C2×D12—24no—
261C2×D12—24no—
262C2×D12—81no—
263C2×D12—81no—
264C2×D12—81no—
265C2×D12—81no—
266C2×D12C2×D412yes—
267C2×D12C2×D412yes—
268C2×C4×D3—24no—
269C2×C4×D3—24no—
270C2×C4×D3—81no—
271C2×C4×D3—81no—
272C2×C4×D3—81no—
273C2×C4×D3—81no—
274C3×C4⋊C4—22no—
275C3×C4⋊C4—22no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—81no—
282C3×C4⋊C4#4112yes—
283C3×C22⋊C4—24no—
284C3×C22⋊C4—22no—
285C3×C22⋊C4—22no—
286C3×C22⋊C4—42no—
287C3×C22⋊C4—81no—
288C3×C22⋊C4—81no—
289C3×C22⋊C4—81no—
290C3×C42—21no—
291C3×C42—21no—
292C3×C42—81no—
293C3×C42C2×D412yes—
294C3×C42C2×D412yes—
295#213—28no—
296#213—28no—
297(C2×D3)⋊C4—24no—
298(C2×D3)⋊C4—24no—
299(C2×D3)⋊C4—24no—
300(C2×D3)⋊C4—24no—
301C4⋊Dic3—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3C2×D412yes—
304C4⋊Dic3C2×D412yes—
305Dic3⋊C4—24no—
306Dic3⋊C4—24no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—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—
318C2×C3⋊C8#4112yes—
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—21no—
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×C8—31no—
340C22×C8—31no—
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—68no—
350#121—68no—
351#121—62no—
352#121—62no—
353#121—62no—
354#121—62no—
355C4×D4—22no—
356C4×D4—22no—
357C4×D4—34no—
358C4×D4—34no—
359C4×D4—62no—
360C4×D4—62no—
361#117—22no—
362#117—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—61no—
367C2×C4⋊C4—61no—
368C2×C4⋊C4#6711yescharacteristic
369C2×C4⋊C4#6711yescharacteristic
370C2×C4⋊C4C22×D311yescharacteristic
371C2×C4⋊C4C22×D311yescharacteristic
372C2×C4⋊C4C22×D311yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C22⋊C4#6711yescharacteristic
383C2×C22⋊C4#6711yescharacteristic
384C2×C42—21no—
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—62no—
398C22⋊C8—62no—
399#97—62no—
400C4×C8—62no—
401#95—21no—
402#95—21no—
403#95—21no—
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—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—22no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—84no—
465C2×C3×C4#12012yes—
466C2×C3×C4#12012yes—
467C2×C3×C4C22×D411yescharacteristic
468C2×C3×C4C22×D411yescharacteristic
469C2×C3×C4C2×#4111yescharacteristic
470C2×C3×C4C2×#4111yescharacteristic
471C2×C3×C4C2×#4111yescharacteristic
472C2×C3×C4C2×#4111yescharacteristic
473#67—84no—
474#67—84no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481D12—22no—
482D12—22no—
483D12—22no—
484D12—22no—
485D12—41no—
486D12—41no—
487D12—41no—
488D12—41no—
489D12—84no—
490D12—84no—
491C4×D3—84no—
492C4×D3—84no—
493C3⋊C8—22no—
494C3⋊C8—22no—
495C3⋊C8—41no—
496C3⋊C8—41no—
497C24—21no—
498C24—61no—
499C24—61no—
500C24C2×#6711yescharacteristic
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×D4#23512yes—
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—42no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—64no—
547C22×C4—64no—
548C22×C4—81no—
549C22×C4—81no—
550C22×C4—241no—
551C22×C4—241no—
552C22×C4—241no—
553C22×C4—241no—
554C22×C4C2×#6711yescharacteristic
555C22×C4C2×#6711yescharacteristic
556C22×C4C2×#6711yescharacteristic
557C22×C4C2×#6711yescharacteristic
558C22×C4C2×#6711yescharacteristic
559C22×C4C23×D311yescharacteristic
560D8—68no—
561D8—68no—
562C2×C8—32no—
563C2×C8—32no—
564C2×C8—61no—
565C2×C8—61no—
566C2×C8—61no—
567C2×C8—61no—
568C2×C8—61no—
569C2×C8—61no—
570C2×C8—61no—
571C2×C8—61no—
572C2×C8—61no—
573C2×C8—61no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—32no—
582C4⋊C4—32no—
583C4⋊C4—64no—
584C4⋊C4—64no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—81no—
588C4⋊C4#23512yes—
589C22⋊C4—24no—
590C22⋊C4—22no—
591C22⋊C4—22no—
592C22⋊C4—42no—
593C22⋊C4—64no—
594C22⋊C4—64no—
595C22⋊C4—64no—
596C22⋊C4—64no—
597C22⋊C4—81no—
598C22⋊C4—81no—
599C22⋊C4—81no—
600C42—21no—
601C42—21no—
602C42—81no—
603C42D3×D412yes—
604C42D3×D412yes—
605C22×C3—41no—
606C22×C3—42no—
607C22×C3—41no—
608C22×C3—42no—
609C22×C3—41no—
610C22×C3—42no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
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—22no—
641C3×C4—22no—
642C3×C4—42no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—81no—
647C3×C4—81no—
648C3×C4#52511yescharacteristic
649C3×C4#52511yescharacteristic
650C3×C4#53211yescharacteristic
651C3×C4#53211yescharacteristic
652Dic3—42no—
653Dic3—42no—
654C23—22no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
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—
682C23C22×#6711yescharacteristic
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—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—84no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—244no—
734C2×C4—244no—
735C2×C4#93712yes—
736C2×C4#93712yes—
737C2×C4C2×#23511yescharacteristic
738C2×C4C2×#23511yescharacteristic
739C2×C4C2×D3×D411yescharacteristic
740C2×C4C2×D3×D411yescharacteristic
741C2×C4D3×#4111yescharacteristic
742C2×C4D3×#4111yescharacteristic
743C8—62no—
744C8—62no—
745C8—121no—
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—41no—
760C22—42no—
761C22—41no—
762C22—42no—
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—
786C22#579111yescharacteristic
787C22C2×#93711yescharacteristic
788C22#583211yescharacteristic
789C22#583511yescharacteristic
790C22#583511yescharacteristic
791C22#583511yescharacteristic
792C22#583711yescharacteristic
793C4—22no—
794C4—22no—
795C4—42no—
796C4—41no—
797C4—41no—
798C4—41no—
799C4—81no—
800C4—81no—
801C4—122no—
802C4—122no—
803C4#554711yescharacteristic
804C4#554711yescharacteristic
805C4#554811yescharacteristic
806C4#554811yescharacteristic
807C3#2358011yescharacteristic, complemented, Sylow
808C2—81no—
809C2—82no—
810C2—242no—
811C2—242no—
812C2#8240011yescharacteristic
813C2#8254211yescharacteristic
814C2#8256811yescharacteristic
815C2#8338311yescharacteristic
816C2#8342411yescharacteristic
817C2#8343211yescharacteristic
818C2#8345911yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2324C2
socleC23×C3C22×D4
hypercenter#2324D3
hypocenterC3#23580
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
1. C2×#5535C2semidirect
2. C3×#2324C2semidirect
3. C2×#5014C2semidirect
4. C2×C4×#213C2semidirect
5. #71684C2semidirect
6. #71684C2semidirect
7. #71582C2semidirect
8. #69658C2semidirect
9. #69639C2semidirect
10. #69627C2semidirect
11. #69606C2semidirect
12. #69524C2semidirect
13. #69523C2semidirect
14. #69474C2semidirect
15. C4×#809C2semidirect
67. #2324D3semidirect
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
C3×#23242
C2×#50142
C2×C4×#2132
#716842
#715822
#696582
#696392
#696272
#696062
#695242
#695232
#694742
C4×#8092
#235803