Finite Group Databasebeta

← #10847434

Subgroups — #10847434

Order 768.

1226 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5479C211yesmaximal, characteristic, complemented
2C3×#2854C211yesmaximal, characteristic, complemented
3C2×#5038C211yesmaximal, characteristic
4C2×#5041C211yesmaximal, characteristic, complemented
5C2×#4524C211yesmaximal, characteristic, complemented
6#69660C211yesmaximal, characteristic, complemented
7#69659C211yesmaximal, characteristic, complemented
8#69657C211yesmaximal, characteristic, complemented
9#69639C211yesmaximal, characteristic, complemented
10#69631C211yesmaximal, characteristic, complemented
11#69628C211yesmaximal, characteristic, complemented
12#69626C211yesmaximal, characteristic, complemented
13#69606C211yesmaximal, characteristic, complemented
14#69515C211yesmaximal, characteristic, complemented
15#69514C211yesmaximal, characteristic, complemented
16#25500—31nomaximal, Sylow
17C2×C3×#123—21no—
18C2×C3×#121C2211yescharacteristic
19C22×C3×C42C2211yescharacteristic
20C22×#214C2211yescharacteristic
21C22×#213C2211yescharacteristic
22C2×#930C2211yescharacteristic
23C2×#929—21no—
24C2×C4×#67—21no—
25C2×#924C2211yescharacteristic
26C23×C3⋊C8C2211yescharacteristic
27C23×C3⋊C8C2211yescharacteristic
28#5479—24no—
29#5479—24no—
30C2×#876—21no—
31C2×#875C2211yescharacteristic
32C2×C4×D12C2211yescharacteristic
33C2×#872—21no—
34C2×#870C2211yescharacteristic
35C2×C4×Dic6C2211yescharacteristic
36C3×#390C2211yescharacteristic
37C3×#390C2211yescharacteristic
38C3×#389C2211yescharacteristic
39C3×#389C2211yescharacteristic
40C3×#388—21no—
41C3×#388—21no—
42C3×#386—21no—
43C3×#380C2211yescharacteristic
44C2×#832C2211yescharacteristic
45C2×#832C2211yescharacteristic
46#5041—24no—
47#5038—24no—
48C2×#810C2211yescharacteristic
49C2×#810C2211yescharacteristic
50C2×#810C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#808C2211yescharacteristic
55C2×#807C2211yescharacteristic
56#4529C2211yescharacteristic
57#4529C2211yescharacteristic
58#4529C2211yescharacteristic
59#4529C2211yescharacteristic
60#4524C2211yescharacteristic
61#4524C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#529—31no—
65C2×#466—31no—
66C2×#465—31no—
67#2854D311yescharacteristic, complemented
68#2059—31no—
69#2042—31no—
70#2025—31no—
71#2012—31no—
72#1893—31no—
73#1892—31no—
74#1880—31no—
75#1879—31no—
76#1864—31no—
77#1863—31no—
78C2×#336—31no—
79C22×C3×D4—21no—
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4D411yescharacteristic
82C23×C3×C4D411yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C22×#67—21no—
85C22×D12C2311yescharacteristic
86C22×C4×D3—21no—
87C22×Dic6C2311yescharacteristic
88C3×#123—44no—
89C3×#121—22no—
90C3×#121—22no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4C2311yescharacteristic
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C22⋊C4—21no—
97C2×C3×C22⋊C4—21no—
98C2×C3×C22⋊C4—21no—
99C2×C3×C22⋊C4—21no—
100C2×C3×C22⋊C4—21no—
101C2×C3×C22⋊C4—21no—
102C2×C3×C42—22no—
103C2×C3×C42—22no—
104C2×C3×C42D411yescharacteristic
105C2×C3×C42D411yescharacteristic
106C2×C3×C42C2311yescharacteristic
107C2×C3×C42C2311yescharacteristic
108C2×#217—21no—
109C2×#214—22no—
110C2×#214—22no—
111C2×#214—41no—
112C2×#213—22no—
113C2×#213—22no—
114C2×#213—41no—
115#930—22no—
116#930D414yes—
117#929—28no—
118C4×#67—28no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×C4⋊Dic3C2311yescharacteristic
124C2×C4⋊Dic3C2311yescharacteristic
125#924—22no—
126#924D414yes—
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×C4×Dic3—21no—
132C22×C3⋊C8—22no—
133C22×C3⋊C8—22no—
134C22×C3⋊C8—22no—
135C22×C3⋊C8—22no—
136C22×C3⋊C8—41no—
137C22×C3⋊C8—41no—
138C22×C3⋊C8C2311yescharacteristic
139C22×C3⋊C8C2311yescharacteristic
140C22×C3⋊C8C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142#876—28no—
143#875—22no—
144#875—22no—
145C4×D12—22no—
146C4×D12—22no—
147#872—28no—
148#870—22no—
149#870—22no—
150C4×Dic6—22no—
151C4×Dic6—22no—
152C3×#95—21no—
153C3×#95—21no—
154C3×#95—21no—
155#832—22no—
156#832—22no—
157#810—22no—
158#810—22no—
159#810—41no—
160#809—22no—
161#809—22no—
162#809—41no—
163#808—22no—
164#807—22no—
165C22×SD16—31no—
166C22×D8—31no—
167C23×C8—31no—
168C23×C8—31no—
169#529—64no—
170#529—64no—
171C2×#126—61no—
172C2×#125—31no—
173C2×#124—31no—
174C2×#123—21no—
175C2×#123—61no—
176C2×C22⋊Q8—31no—
177C2×#121—31no—
178C2×#121C2×D311yescharacteristic
179C2×C4×Q8—31no—
180C2×C4×D4—31no—
181C2×C4×D4—61no—
182C2×#117—61no—
183C22×C42C2×D311yescharacteristic
184#466—64no—
185#465—64no—
186C2×#107—31no—
187C2×#106—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×#102—31no—
196#390C2×D311yescharacteristic
197#390C2×D311yescharacteristic
198#389C2×D311yescharacteristic
199#389C2×D311yescharacteristic
200#388—21no—
201#388—21no—
202#386—21no—
203#380C2×D311yescharacteristic
204#340—31no—
205#340—31no—
206#340—31no—
207#340—31no—
208#336—31no—
209#336—31no—
210#336—31no—
211#336—31no—
212C24×C3—21no—
213C24×C3C2×D411yescharacteristic
214C23×D3—21no—
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—42no—
222C2×C3×D4—42no—
223C2×C3×D4—42no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—41no—
237C22×C3×C4C2×D412yes—
238C22×C3×C4C2×D412yes—
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2411yescharacteristic
245C2×#67—24no—
246C2×#67—42no—
247C2×#67—42no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12C2×D412yes—
257C2×C4×D3—24no—
258C2×C4×D3—42no—
259C2×C4×D3—42no—
260C2×Dic6—21no—
261C2×Dic6—21no—
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6C2×D412yes—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—42no—
273C3×C4⋊C4—42no—
274C3×C22⋊C4—42no—
275C3×C22⋊C4—42no—
276C3×C22⋊C4—42no—
277C3×C22⋊C4—42no—
278C3×C22⋊C4—42no—
279C3×C22⋊C4—42no—
280C3×C42—22no—
281C3×C42—22no—
282C3×C42—21no—
283C3×C42—21no—
284C3×C42—21no—
285C3×C42—21no—
286#217—24no—
287#214—44no—
288#213—44no—
289(C2×D3)⋊C4—24no—
290(C2×D3)⋊C4—24no—
291(C2×D3)⋊C4—24no—
292(C2×D3)⋊C4—24no—
293C4⋊Dic3—21no—
294C4⋊Dic3—21no—
295C4⋊Dic3C2×D412yes—
296C4⋊Dic3C2×D412yes—
297Dic3⋊C4—24no—
298Dic3⋊C4—24no—
299Dic3⋊C4—24no—
300Dic3⋊C4—24no—
301C4×Dic3—24no—
302C2×C3⋊C8—21no—
303C2×C3⋊C8—21no—
304C2×C3⋊C8—21no—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—44no—
313C2×C3⋊C8—44no—
314C2×C3⋊C8#4112yes—
315C2×C3⋊C8#4112yes—
316C22×Q8—31no—
317C22×D4—21no—
318C22×D4—31no—
319C22×D4—61no—
320C22×D4C22×D311yescharacteristic
321C23×C4—61no—
322C23×C4#6711yescharacteristic
323C23×C4#6711yescharacteristic
324C23×C4C22×D311yescharacteristic
325C2×SD16—62no—
326C2×SD16—62no—
327C2×SD16—121no—
328C2×D8—62no—
329C2×D8—62no—
330C2×D8—121no—
331C22×C8—31no—
332C22×C8—31no—
333C22×C8—31no—
334C22×C8—31no—
335C22×C8—62no—
336C22×C8—62no—
337C22×C8—62no—
338C22×C8—62no—
339C22×C8—121no—
340C22×C8—121no—
341#126—68no—
342#125—62no—
343#125—62no—
344#124—62no—
345#124—62no—
346#123—44no—
347#123—68no—
348C22⋊Q8—34no—
349C22⋊Q8—62no—
350#121—22no—
351#121—22no—
352#121—34no—
353#121—62no—
354C4×Q8—62no—
355C4×Q8—62no—
356C4×D4—62no—
357C4×D4—62no—
358C4×D4—68no—
359#117—68no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4—61no—
366C2×C4⋊C4—61no—
367C2×C4⋊C4—61no—
368C2×C4⋊C4C22×D311yescharacteristic
369C2×C4⋊C4C22×D311yescharacteristic
370C2×C4⋊C4C22×D311yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—61no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—61no—
385C2×C42#6711yescharacteristic
386C2×C42#6711yescharacteristic
387C2×C42C22×D311yescharacteristic
388C2×C42C22×D311yescharacteristic
389#107—62no—
390#106—62no—
391#103—62no—
392#103—62no—
393#103—121no—
394#102—62no—
395#102—62no—
396#102—62no—
397#102—62no—
398#102—121no—
399#95—21no—
400#95—21no—
401#95—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3#12012yes—
414C23×C3#13512yes—
415C23×C3AGL(1,ℤ/8)12yes—
416C23×C3C22×D411yescharacteristic
417C22×D3—22no—
418C22×D3—41no—
419C22×D3—41no—
420C22×D3—41no—
421C22×D3—41no—
422C22×D3—41no—
423C22×D3—41no—
424C3×D4—41no—
425C3×D4—41no—
426C3×D4—41no—
427C3×D4—41no—
428C3×D4—84no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
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—44no—
447C2×C3×C4—44no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4#12012yes—
458C2×C3×C4#13512yes—
459C2×C3×C4C22×D411yescharacteristic
460C2×C3×C4C22×D411yescharacteristic
461C2×C3×C4C2×#4111yescharacteristic
462C2×C3×C4C2×#4111yescharacteristic
463C2×C3×C4H(5,𝔽2)11yescharacteristic
464C2×C3×C42−1+411yescharacteristic
465#67—48no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475D12—22no—
476D12—22no—
477D12—41no—
478D12—41no—
479C4×D3—48no—
480Dic6—22no—
481Dic6—22no—
482Dic6—41no—
483Dic6—41no—
484C3⋊C8—22no—
485C3⋊C8—22no—
486C3⋊C8—41no—
487C3⋊C8—41no—
488C24—21no—
489C24—61no—
490C24C2×#6711yescharacteristic
491C2×Q8—32no—
492C2×Q8—61no—
493C2×Q8—61no—
494C2×Q8—61no—
495C2×Q8—61no—
496C2×Q8—61no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—32no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—64no—
508C2×D4—61no—
509C2×D4—61no—
510C2×D4—61no—
511C2×D4—61no—
512C2×D4—61no—
513C2×D4—122no—
514C2×D4—122no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—41no—
528C22×C4—64no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—122no—
533C22×C4—122no—
534C22×C4D3×D412yes—
535C22×C4D3×D412yes—
536C22×C4C2×#6711yescharacteristic
537C22×C4C2×#6711yescharacteristic
538C22×C4C2×#6711yescharacteristic
539C22×C4C2×#6711yescharacteristic
540C22×C4C2×#6711yescharacteristic
541C22×C4C23×D311yescharacteristic
542SD16—124no—
543D8—124no—
544C2×C8—32no—
545C2×C8—32no—
546C2×C8—61no—
547C2×C8—61no—
548C2×C8—61no—
549C2×C8—61no—
550C2×C8—61no—
551C2×C8—61no—
552C2×C8—61no—
553C2×C8—61no—
554C2×C8—61no—
555C2×C8—61no—
556C2×C8—124no—
557C2×C8—124no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—32no—
565C4⋊C4—32no—
566C4⋊C4—42no—
567C4⋊C4—42no—
568C4⋊C4—64no—
569C4⋊C4—64no—
570C4⋊C4—64no—
571C4⋊C4—64no—
572C4⋊C4—61no—
573C4⋊C4—61no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—64no—
581C22⋊C4—64no—
582C22⋊C4—64no—
583C22⋊C4—64no—
584C22⋊C4—64no—
585C42—22no—
586C42—22no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—64no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3—81no—
599C22×C3—81no—
600C22×C3—81no—
601C22×C3—81no—
602C22×C3—81no—
603C22×C3—81no—
604C22×C3—81no—
605C22×C3#44914yes—
606C22×C3C2×#12011yescharacteristic
607C22×C3#53211yescharacteristic
608C22×C3#53711yescharacteristic
609C22×C3C2×#13511yescharacteristic
610C22×C3C2×#13511yescharacteristic
611C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
612C22×C3#57511yescharacteristic
613C2×D3—42no—
614C2×D3—42no—
615C2×D3—42no—
616C2×D3—81no—
617C2×D3—81no—
618C2×D3—81no—
619C2×D3—81no—
620C3×C4—22no—
621C3×C4—22no—
622C3×C4—41no—
623C3×C4—41no—
624C3×C4—41no—
625C3×C4—81no—
626C3×C4—81no—
627C3×C4—81no—
628C3×C4#54611yescharacteristic
629C3×C4#54611yescharacteristic
630C3×C4#54711yescharacteristic
631C3×C4#54711yescharacteristic
632Dic3—42no—
633Dic3—42no—
634Dic3—42no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—62no—
647C23—121no—
648C23—121no—
649C23—121no—
650C23—121no—
651C23—121no—
652C23—121no—
653C23#93212yes—
654C23#93712yes—
655C23#95012yes—
656C23C22×#6711yescharacteristic
657Q8—62no—
658Q8—62no—
659Q8—121no—
660Q8—121no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—62no—
666D4—62no—
667D4—84no—
668D4—128no—
669D4—121no—
670D4—121no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—62no—
700C2×C4—62no—
701C2×C4—62no—
702C2×C4—128no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4#93712yes—
710C2×C4#95012yes—
711C2×C4C2×D3×D411yescharacteristic
712C2×C4C2×D3×D411yescharacteristic
713C2×C4D3×#4111yescharacteristic
714C2×C4D3×#4111yescharacteristic
715C2×C4#100911yescharacteristic
716C2×C4#101011yescharacteristic
717C8—62no—
718C8—62no—
719C8—121no—
720C8—121no—
721C2×C3—24no—
722C2×C3—161no—
723C2×C3#243011yescharacteristic
724C2×C3C2×#44911yescharacteristic
725C2×C3#300211yescharacteristic
726C2×C3#316811yescharacteristic
727C2×C3#318011yescharacteristic
728C2×C3#324711yescharacteristic
729C2×C3#325011yescharacteristic
730D3—82no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—122no—
745C22—122no—
746C22—122no—
747C22—241no—
748C22—241no—
749C22—241no—
750C22—241no—
751C22#503714yes—
752C22C2×#93211yescharacteristic
753C22C2×#93711yescharacteristic
754C22C2×#95011yescharacteristic
755C22C2×#95011yescharacteristic
756C22#582211yescharacteristic
757C22#583211yescharacteristic
758C22#583311yescharacteristic
759C4—22no—
760C4—22no—
761C4—41no—
762C4—41no—
763C4—41no—
764C4—81no—
765C4—81no—
766C4—81no—
767C4—122no—
768C4—122no—
769C4—122no—
770C4#565411yescharacteristic
771C4#565411yescharacteristic
772C4#565511yescharacteristic
773C4#565511yescharacteristic
774C3#2550011yescharacteristic, complemented, Sylow
775C2—24no—
776C2—161no—
777C2—242no—
778C2C2×#503711yescharacteristic
779C2#8284811yescharacteristic
780C2#8292611yescharacteristic
781C2#8313411yescharacteristic
782C2#8314911yescharacteristic
783C2#8329311yescharacteristic
784C2#8331111yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2854C2
socleC23×C3C22×D4
prime radicalC2×#5038C2
hypercenter#2854D3
hypocenterC3#25500
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2854

Complements

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

NH ≅ G/Ntype
1. C2×#5479C2semidirect
2. C3×#2854C2semidirect
4. C2×#5041C2semidirect
5. C2×#4524C2semidirect
6. #69660C2semidirect
7. #69659C2semidirect
8. #69657C2semidirect
9. #69639C2semidirect
10. #69631C2semidirect
11. #69628C2semidirect
12. #69626C2semidirect
13. #69606C2semidirect
14. #69515C2semidirect
15. #69514C2semidirect
67. #2854D3semidirect
774. C3#25500semidirect

Maximal subgroups

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

subgroupindex
C2×#54792
C3×#28542
C2×#50382
C2×#50412
C2×#45242
#696602
#696592
#696572
#696392
#696312
#696282
#696262
#696062
#695152
#695142
#255003