Finite Group Databasebeta

← #10827361

Subgroups — #10827361

Order 768.

1338 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5558C211yesmaximal, characteristic, complemented
2C2×#5172C211yesmaximal, characteristic, complemented
3C2×#4804C211yesmaximal, characteristic, complemented
4#76618C211yesmaximal, characteristic, complemented
5C3×#1877C211yesmaximal, characteristic, complemented
6#72054C211yesmaximal, characteristic, complemented
7#71613C211yesmaximal, characteristic, complemented
8#70268C211yesmaximal, characteristic, complemented
9#70204C211yesmaximal, characteristic, complemented
10#70202C211yesmaximal, characteristic, complemented
11#69669C211yesmaximal, characteristic, complemented
12#68880C211yesmaximal, characteristic, complemented
13#68813C211yesmaximal, characteristic, complemented
14#68679C211yesmaximal, characteristic, complemented
15#68668C211yesmaximal, characteristic, complemented
16#23962—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C2×#938C2211yescharacteristic
22C2×#938C2211yescharacteristic
23C22×#213C2211yescharacteristic
24C2×#929—21no—
25C2×C4×#67—21no—
26C22×D3×C8C2211yescharacteristic
27#5558—24no—
28#5558—24no—
29C2×#895C2211yescharacteristic
30C2×#892C2211yescharacteristic
31C2×D3×C4⋊C4C2211yescharacteristic
32C2×#884—21no—
33C2×#879—21no—
34C2×C4×D12C2211yescharacteristic
35C2×#870C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C3×#391C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#832C2211yescharacteristic
42#5172—24no—
43C2×#821C2211yescharacteristic
44C2×#821C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic
48#4987C2211yescharacteristic
49C2×#809C2211yescharacteristic
50#4939C2211yescharacteristic
51#4804—24no—
52#4672—21no—
53#4671—21no—
54#4668—21no—
55#4665—21no—
56C3×#340C2211yescharacteristic
57C3×#336C2211yescharacteristic
58#4551C2211yescharacteristic
59#4551C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#553—31no—
65C2×#449—31no—
66C2×#416—31no—
67#2407—31no—
68#2026—31no—
69#2025—31no—
70#2000—31no—
71#1999—31no—
72#1893—31no—
73#1879—31no—
74#1877D311yescharacteristic, complemented
75#1874—31no—
76#1872—31no—
77#1869—31no—
78#1825—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4—21no—
82C22×#67—21no—
83C22×#67—21no—
84C2×#239—22no—
85C2×#239—22no—
86C2×#239—22no—
87C2×#239—22no—
88C2×#239—41no—
89C2×#239—41no—
90C22×D12—21no—
91C22×D12—21no—
92C22×D12D411yescharacteristic
93C22×D12C2311yescharacteristic
94C22×C4×D3—21no—
95C22×C4×D3—21no—
96C22×C4×D3C2311yescharacteristic
97C22×C4×D3C2311yescharacteristic
98C2×C3×SD16—22no—
99C2×C3×SD16—22no—
100C2×C3×SD16—41no—
101C22×C3×C8C2311yescharacteristic
102C22×C3×C8C2311yescharacteristic
103C3×C4×D4—22no—
104C3×C4×D4—22no—
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C22⋊C4—21no—
108C2×C3×C42C2311yescharacteristic
109C2×#217—21no—
110C2×#217—21no—
111#946—22no—
112#946—41no—
113#938—22no—
114#938—22no—
115#938—22no—
116#938D414yescomplemented
117C2×#213—22no—
118C2×#213—22no—
119C2×#213—41no—
120#929—28no—
121C4×#67—28no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4D411yescharacteristic
129C2×(C2×D3)⋊C4D411yescharacteristic
130C2×C4⋊Dic3D411yescharacteristic
131C2×C4⋊Dic3C2311yescharacteristic
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4—21no—
138C2×C4×Dic3—21no—
139C22×C3⋊C8C2311yescharacteristic
140C22×C3⋊C8C2311yescharacteristic
141C2×D3×C8—22no—
142C2×D3×C8—41no—
143C2×D3×C8—41no—
144#895—22no—
145#895—41no—
146#892—22no—
147#892D414yescomplemented
148D3×C4⋊C4—22no—
149D3×C4⋊C4—22no—
150#884—28no—
151#879—28no—
152C4×D12—22no—
153C4×D12—22no—
154#870—22no—
155#870—22no—
156C3×#103—22no—
157C3×#102—41no—
158C3×#95—21no—
159C3×#95—21no—
160#835—22no—
161#835—22no—
162#832—41no—
163C3⋊#95—21no—
164#821—22no—
165#821—22no—
166(C2×D3)⋊C8—22no—
167(C2×D3)⋊C8—41no—
168(C2×D3)⋊C8—41no—
169#809—22no—
170C22×#41—31no—
171C22×SD16C2×D311yescharacteristic
172C22×D8—31no—
173C23×C8—31no—
174#553—64no—
175#553—64no—
176C2×#126—61no—
177C2×#125—31no—
178C2×#123—61no—
179C2×C22⋊Q8—31no—
180C2×#121—31no—
181C2×#121—31no—
182C2×#121—31no—
183C2×#121—61no—
184C2×C4×D4—31no—
185C2×C4×D4—61no—
186C2×C4×D4C2×D311yescharacteristic
187C2×#117—31no—
188C22×C4⋊C4—31no—
189#449—64no—
190#416—64no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103C2×D311yescharacteristic
194C2×#102—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102C2×D311yescharacteristic
199C2×C22⋊C8—31no—
200C2×C22⋊C8—31no—
201C2×C22⋊C8—31no—
202#394—61no—
203#392—61no—
204#391C2×D311yescharacteristic
205#390—31no—
206#386—61no—
207#385—61no—
208#380—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340C2×D311yescharacteristic
215#336—31no—
216#336C2×D311yescharacteristic
217C24×C3—21no—
218C23×D3—21no—
219C23×D3C2×D411yescharacteristic
220C23×D3C2×D411yescharacteristic
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8#4112yes—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4C2×D412yes—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—24no—
236C22×C3×C4—21no—
237C22×C3×C4—81no—
238C22×C3×C4—81no—
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2411yescharacteristic
242C2×#67—24no—
243C2×#67—24no—
244C2×#67—42no—
245C2×#67—42no—
246C2×#67—81no—
247C2×#67—81no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251C22×Dic3C2×D411yescharacteristic
252C22×Dic3C2×D411yescharacteristic
253#239—28no—
254#239—44no—
255#239—44no—
256#239—44no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12—22no—
262C2×D12—22no—
263C2×D12—21no—
264C2×D12—41no—
265C2×D12—42no—
266C2×D12—42no—
267C2×D12—42no—
268C2×D12—42no—
269C2×D12—42no—
270C2×D12—81no—
271C2×D12#4112yes—
272C2×C4×D3—21no—
273C2×C4×D3—21no—
274C2×C4×D3—21no—
275C2×C4×D3—21no—
276C2×C4×D3—21no—
277C2×C4×D3—21no—
278C2×C4×D3—21no—
279C2×C4×D3—21no—
280C2×C4×D3—21no—
281C2×C4×D3—21no—
282C2×C4×D3—24no—
283C2×C4×D3—42no—
284C2×C4×D3—42no—
285C2×C4×D3—42no—
286C2×C4×D3—81no—
287C2×C4×D3—81no—
288C2×C4×D3C2×D412yes—
289C2×C4×D3C2×D412yes—
290C3×SD16—44no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8—21no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4C2×D412yes—
301C3×C22⋊C4—24no—
302C3×C42—21no—
303C3×C42—21no—
304#217—24no—
305#217—24no—
306#213—44no—
307(C2×D3)⋊C4—22no—
308(C2×D3)⋊C4—24no—
309(C2×D3)⋊C4—22no—
310(C2×D3)⋊C4—42no—
311(C2×D3)⋊C4—42no—
312(C2×D3)⋊C4—42no—
313(C2×D3)⋊C4—81no—
314(C2×D3)⋊C4—81no—
315C4⋊Dic3—21no—
316C4⋊Dic3—21no—
317C4⋊Dic3—22no—
318C4⋊Dic3—21no—
319C4⋊Dic3—21no—
320C4⋊Dic3C2×D412yes—
321C4⋊Dic3C2×D412yes—
322Dic3⋊C4—24no—
323Dic3⋊C4—24no—
324Dic3⋊C4—24no—
325Dic3⋊C4—42no—
326C4×Dic3—24no—
327C2×C3⋊C8—21no—
328C2×C3⋊C8—21no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8—21no—
332C2×C3⋊C8—21no—
333D3×C8—44no—
334C2×#41—62no—
335C2×#41—62no—
336C2×#41—62no—
337C2×#41—62no—
338C2×#41—121no—
339C2×#41—121no—
340C22×Q8C22×D311yescharacteristic
341C22×D4—31no—
342C22×D4—31no—
343C22×D4—61no—
344C22×D4—61no—
345C22×D4—61no—
346C22×D4—61no—
347C22×D4C22×D311yescharacteristic
348C23×C4—21no—
349C23×C4—31no—
350C23×C4—31no—
351C23×C4—61no—
352C23×C4—61no—
353C2×SD16—22no—
354C2×SD16—22no—
355C2×SD16—41no—
356C2×D8—62no—
357C2×D8—62no—
358C2×D8—121no—
359C22×C8—31no—
360C22×C8—31no—
361C22×C8—62no—
362C22×C8—121no—
363C22×C8—121no—
364C22×C8C22×D311yescharacteristic
365C22×C8C22×D311yescharacteristic
366#126—68no—
367#125—62no—
368#125—62no—
369#123—68no—
370C22⋊Q8—62no—
371C22⋊Q8—121no—
372#121—34no—
373#121—68no—
374#121—62no—
375#121—62no—
376#121—62no—
377#121—62no—
378#121—121no—
379C4×D4—22no—
380C4×D4—22no—
381C4×D4—62no—
382C4×D4—62no—
383C4×D4—68no—
384#117—34no—
385#117—62no—
386C2×C4⋊C4—31no—
387C2×C4⋊C4—31no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—62no—
391C2×C4⋊C4—61no—
392C2×C4⋊C4—61no—
393C2×C4⋊C4—61no—
394C2×C4⋊C4—62no—
395C2×C4⋊C4—61no—
396C2×C4⋊C4C22×D311yescharacteristic
397C2×C4⋊C4C22×D311yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—31no—
400C2×C22⋊C4—31no—
401C2×C22⋊C4—61no—
402C2×C22⋊C4—61no—
403C2×C22⋊C4—61no—
404C2×C22⋊C4—61no—
405C2×C22⋊C4—61no—
406C2×C22⋊C4—61no—
407C2×C22⋊C4—61no—
408C2×C22⋊C4—61no—
409C2×C42—61no—
410C2×C42C22×D311yescharacteristic
411#103—22no—
412#103—62no—
413#103—62no—
414#102—41no—
415#102—62no—
416#102—62no—
417#102—62no—
418#102—121no—
419C22⋊C8—62no—
420C22⋊C8—121no—
421C22⋊C8—121no—
422#95—21no—
423#95—21no—
424#95—61no—
425C23×C3—22no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3C22×D411yescharacteristic
433C22×D3—21no—
434C22×D3—21no—
435C22×D3—21no—
436C22×D3—21no—
437C22×D3—21no—
438C22×D3—21no—
439C22×D3—21no—
440C22×D3—21no—
441C22×D3—21no—
442C22×D3—21no—
443C22×D3—21no—
444C22×D3—21no—
445C22×D3—22no—
446C22×D3—41no—
447C22×D3—41no—
448C22×D3—41no—
449C22×D3—41no—
450C22×D3—41no—
451C22×D3—41no—
452C22×D3#12012yes—
453C22×D3#13512yes—
454C3×Q8—22no—
455C3×Q8—22no—
456C3×Q8—41no—
457C3×Q8—41no—
458C3×D4—22no—
459C3×D4—22no—
460C3×D4—41no—
461C3×D4—41no—
462C2×C3×C4—22no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—22no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—84no—
478C2×C3×C4C22×D411yescharacteristic
479C2×C3×C4C22×D411yescharacteristic
480C2×C3×C4C2×#4111yescharacteristic
481C2×C3×C4C2×#4111yescharacteristic
482C2×C3×C4H(5,𝔽2)11yescharacteristic
483C2×C3×C4H(5,𝔽2)11yescharacteristic
484#67—48no—
485#67—84no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498C2×Dic3—41no—
499C2×Dic3—41no—
500C2×Dic3#12012yes—
501D12—22no—
502D12—22no—
503D12—44no—
504D12—48no—
505D12—41no—
506D12—41no—
507D12—84no—
508C4×D3—22no—
509C4×D3—22no—
510C4×D3—22no—
511C4×D3—22no—
512C4×D3—48no—
513C4×D3—41no—
514C4×D3—41no—
515C4×D3—41no—
516C4×D3—41no—
517C4×D3—84no—
518C3×C8—41no—
519C3×C8—41no—
520C3⋊C8—41no—
521C3⋊C8—41no—
522C24—21no—
523C24—31no—
524C24—31no—
525C24—61no—
526#41—68no—
527#41—124no—
528#41—124no—
529#41—124no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8#23512yes—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—32no—
542C2×D4—62no—
543C2×D4—62no—
544C2×D4—64no—
545C2×D4—64no—
546C2×D4—61no—
547C2×D4—61no—
548C2×D4—61no—
549C2×D4—61no—
550C2×D4—61no—
551C2×D4—121no—
552C2×D4—122no—
553C2×D4—122no—
554C2×D4—122no—
555C2×D4—122no—
556C2×D4—122no—
557C2×D4—122no—
558C2×D4—122no—
559C2×D4—241no—
560C2×D4—241no—
561C2×D4—241no—
562C2×D4D3×D412yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—21no—
567C22×C4—31no—
568C22×C4—32no—
569C22×C4—32no—
570C22×C4—31no—
571C22×C4—64no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—61no—
575C22×C4—61no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—81no—
586C22×C4—81no—
587C22×C4—122no—
588C22×C4—122no—
589C22×C4—122no—
590C22×C4—241no—
591C22×C4—241no—
592C22×C4D3×D411yescharacteristic
593C22×C4D3×D411yescharacteristic
594C22×C4C23×D311yescharacteristic
595SD16—44no—
596D8—124no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—61no—
604C2×C8—61no—
605C2×C8—61no—
606C2×C8—61no—
607C2×C8—61no—
608C2×C8—61no—
609C2×C8—124no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—32no—
614C4⋊C4—32no—
615C4⋊C4—62no—
616C4⋊C4—64no—
617C4⋊C4—64no—
618C4⋊C4—64no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—122no—
624C4⋊C4D3×D412yes—
625C22⋊C4—24no—
626C22⋊C4—62no—
627C22⋊C4—62no—
628C22⋊C4—64no—
629C22⋊C4—64no—
630C22⋊C4—64no—
631C22⋊C4—122no—
632C22⋊C4—122no—
633C22⋊C4—122no—
634C22⋊C4—241no—
635C22⋊C4—241no—
636C42—21no—
637C42—21no—
638C42—64no—
639C22×C3—42no—
640C22×C3—42no—
641C22×C3—42no—
642C22×C3—81no—
643C22×C3—81no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3C2×#12011yescharacteristic
647C22×C3#54611yescharacteristic
648C22×C3#54611yescharacteristic
649C22×C3C2×#13511yescharacteristic
650C22×C3#57511yescharacteristic
651C22×C3#57611yescharacteristic
652C22×C3#57711yescharacteristic
653C2×D3—22no—
654C2×D3—22no—
655C2×D3—22no—
656C2×D3—22no—
657C2×D3—22no—
658C2×D3—22no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—42no—
668C2×D3—42no—
669C2×D3—42no—
670C2×D3—81no—
671C2×D3—81no—
672C2×D3—81no—
673C2×D3—81no—
674C3×C4—42no—
675C3×C4—41no—
676C3×C4—42no—
677C3×C4—41no—
678C3×C4—81no—
679C3×C4#52511yescharacteristic
680C3×C4#53511yescharacteristic
681C3×C4#54611yescharacteristic
682C3×C4#54611yescharacteristic
683Dic3—22no—
684Dic3—41no—
685Dic3—42no—
686Dic3—42no—
687Dic3—81no—
688C23—22no—
689C23—32no—
690C23—32no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—61no—
698C23—61no—
699C23—61no—
700C23—61no—
701C23—61no—
702C23—61no—
703C23—61no—
704C23—61no—
705C23—61no—
706C23—61no—
707C23—61no—
708C23—61no—
709C23—62no—
710C23—121no—
711C23—121no—
712C23—121no—
713C23—121no—
714C23—121no—
715C23—121no—
716C23C2×D3×D411yescharacteristic
717Q8—22no—
718Q8—22no—
719Q8—41no—
720Q8—41no—
721D4—22no—
722D4—22no—
723D4—41no—
724D4—41no—
725D4—62no—
726D4—62no—
727D4—124no—
728D4—128no—
729D4—128no—
730D4—121no—
731D4—121no—
732D4—244no—
733D4—244no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—32no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—62no—
753C2×C4—62no—
754C2×C4—62no—
755C2×C4—62no—
756C2×C4—61no—
757C2×C4—62no—
758C2×C4—61no—
759C2×C4—62no—
760C2×C4—61no—
761C2×C4—84no—
762C2×C4—128no—
763C2×C4—121no—
764C2×C4—121no—
765C2×C4—121no—
766C2×C4—121no—
767C2×C4—121no—
768C2×C4—121no—
769C2×C4—121no—
770C2×C4—121no—
771C2×C4—121no—
772C2×C4—121no—
773C2×C4—121no—
774C2×C4—244no—
775C2×C4C2×#23511yescharacteristic
776C2×C4C2×D3×D411yescharacteristic
777C2×C4C2×D3×D411yescharacteristic
778C2×C4#100411yescharacteristic
779C2×C4D3×#4111yescharacteristic
780C2×C4#100911yescharacteristic
781C8—41no—
782C8—41no—
783C8—121no—
784C8—121no—
785C2×C3—82no—
786C2×C3#240411yescharacteristic
787C2×C3#300211yescharacteristic
788C2×C3#301211yescharacteristic
789C2×C3#329711yescharacteristic
790C2×C3#330111yescharacteristic
791C2×C3#330711yescharacteristic
792C2×C3#330911yescharacteristic
793D3—42no—
794D3—42no—
795D3—82no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—62no—
800C22—62no—
801C22—62no—
802C22—62no—
803C22—62no—
804C22—62no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—121no—
810C22—121no—
811C22—121no—
812C22—121no—
813C22—121no—
814C22—121no—
815C22—121no—
816C22—121no—
817C22—122no—
818C22—122no—
819C22—122no—
820C22—241no—
821C22—241no—
822C22—241no—
823C22—241no—
824C22#555011yescharacteristic
825C22D3×#12011yescharacteristic
826C22#561211yescharacteristic
827C22#576211yescharacteristic
828C22D3×#13511yescharacteristic
829C22#577411yescharacteristic
830C22#577711yescharacteristic
831C4—41no—
832C4—42no—
833C4—41no—
834C4—42no—
835C4—62no—
836C4—81no—
837C4—122no—
838C4—122no—
839C4—121no—
840C4—241no—
841C4#549011yescharacteristic
842C4#554711yescharacteristic
843C4#560711yescharacteristic
844C4#565411yescharacteristic
845C3#2396211yescharacteristic, complemented, Sylow
846C2—82no—
847C2—122no—
848C2—122no—
849C2—242no—
850C2#7488611yescharacteristic
851C2#7967911yescharacteristic
852C2#7979911yescharacteristic
853C2#8014911yescharacteristic
854C2#8022611yescharacteristic
855C2#8045211yescharacteristic
856C2#8055911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1877C2
socleC23×C3C22×D4
hypercenter#1877D3
hypocenterC3#23962
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1877

Complements

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

NH ≅ G/Ntype
1. C2×#5558C2semidirect
2. C2×#5172C2semidirect
3. C2×#4804C2semidirect
4. #76618C2semidirect
5. C3×#1877C2semidirect
6. #72054C2semidirect
7. #71613C2semidirect
8. #70268C2semidirect
9. #70204C2semidirect
10. #70202C2semidirect
11. #69669C2semidirect
12. #68880C2semidirect
13. #68813C2semidirect
14. #68679C2semidirect
15. #68668C2semidirect
74. #1877D3semidirect
116. #938D4semidirect
147. #892D4semidirect
845. C3#23962semidirect

Maximal subgroups

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

subgroupindex
C2×#55582
C2×#51722
C2×#48042
#766182
C3×#18772
#720542
#716132
#702682
#702042
#702022
#696692
#688802
#688132
#686792
#686682
#239623