Finite Group Databasebeta

← #10800989

Subgroups — #10800989

Order 768.

1476 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5827C211yesmaximal, characteristic, complemented
2C2×#5238C211yesmaximal, characteristic
3C2×#4788C211yesmaximal, characteristic, complemented
4C2×#4785C211yesmaximal, characteristic, complemented
5#73872C211yesmaximal, characteristic, complemented
6C3×#1788C211yesmaximal, characteristic, complemented
7#70240C211yesmaximal, characteristic, complemented
8#70237C211yesmaximal, characteristic, complemented
9#70220C211yesmaximal, characteristic, complemented
10#70172C211yesmaximal, characteristic, complemented
11#70169C211yesmaximal, characteristic, complemented
12Dic3×#102C211yesmaximal, characteristic, complemented
13#69932C211yesmaximal, characteristic, complemented
14#69907C211yesmaximal, characteristic, complemented
15#69505C211yesmaximal, characteristic, complemented
16#21464—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18#5827—24no—
19#5827—24no—
20C2×Q8×Dic3C2211yescharacteristic
21C2×Q8×Dic3C2211yescharacteristic
22C22×#215C2211yescharacteristic
23C2×D4×Dic3—21no—
24C2×D4×Dic3—21no—
25C2×D4×Dic3C2211yescharacteristic
26C2×D4×Dic3C2211yescharacteristic
27C22×#213C2211yescharacteristic
28C2×#930C2211yescharacteristic
29C2×#926—21no—
30C2×#926C2211yescharacteristic
31C22×C4⋊Dic3—21no—
32C22×C4⋊Dic3C2211yescharacteristic
33C2×#893C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×C22⋊C8C2211yescharacteristic
39C3×#380C2211yescharacteristic
40#5238C418yescomplemented
41C2×#835C2211yescharacteristic
42C2×#832C2211yescharacteristic
43C2×#830C2211yescharacteristic
44C2×#821C2211yescharacteristic
45C2×#821C2211yescharacteristic
46C2×#815C2211yescharacteristic
47C2×C8×Dic3C2211yescharacteristic
48#4988C2211yescharacteristic
49Dic3×C4⋊C4C2211yescharacteristic
50#4972C2211yescharacteristic
51C2×#808C2211yescharacteristic
52C2×#808C2211yescharacteristic
53#4957—21no—
54#4956—21no—
55#4788—24no—
56#4785—24no—
57#4670—21no—
58#4668—21no—
59#4551C2211yescharacteristic
60#4551C2211yescharacteristic
61#4550C2211yescharacteristic
62#4550C2211yescharacteristic
63#4529C2211yescharacteristic
64#4529C2211yescharacteristic
65C2×#520—31no—
66C2×#449—31no—
67C2×#442—31no—
68C2×C4×SD16—31no—
69#2324—31no—
70#1880—31no—
71#1879—31no—
72#1874—31no—
73#1865—31no—
74#1864—31no—
75#1853—31no—
76#1788D311yescharacteristic, complemented
77#1763—31no—
78C4×#102—31no—
79#1750—31no—
80C2×C3×#41—22no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41C2×C414yescomplemented
86C22×C3×Q8C2311yescharacteristic
87C22×C3×D4—21no—
88C22×C3×D4C2311yescharacteristic
89C23×C3×C4—21no—
90C23×C3×C4C2311yescharacteristic
91C22×#67—21no—
92C23×Dic3—21no—
93C23×Dic3—21no—
94C23×Dic3—21no—
95C22×D12C2311yescharacteristic
96C22×C4×D3—21no—
97C22×C3×C8C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C22⋊C4—21no—
102C2×#217—21no—
103C2×#217—21no—
104C2×#217D411yescharacteristic
105C2×#217D411yescharacteristic
106Q8×Dic3—22no—
107Q8×Dic3—22no—
108Q8×Dic3—22no—
109Q8×Dic3D414yescomplemented
110C2×#215—22no—
111C2×#215—22no—
112C2×#215C2×C414yescomplemented
113D4×Dic3—28no—
114D4×Dic3—28no—
115D4×Dic3—22no—
116D4×Dic3—22no—
117D4×Dic3—22no—
118D4×Dic3D414yescomplemented
119C2×#213—22no—
120C2×#213—22no—
121C2×#213C2×C414yescomplemented
122#930—22no—
123#930C2×C414yescomplemented
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128#926—28no—
129#926—22no—
130#926—22no—
131C2×C4⋊Dic3—28no—
132C2×C4⋊Dic3—21no—
133C2×C4⋊Dic3—21no—
134C2×C4⋊Dic3—21no—
135C2×C4⋊Dic3—22no—
136C2×C4⋊Dic3—22no—
137C2×C4⋊Dic3D411yescharacteristic
138C2×C4⋊Dic3D411yescharacteristic
139C2×C4⋊Dic3C2311yescharacteristic
140C2×C4⋊Dic3C2311yescharacteristic
141C2×C4⋊Dic3C2311yescharacteristic
142C2×Dic3⋊C4—21no—
143C2×C4×Dic3—21no—
144C2×C4×Dic3—21no—
145C2×C4×Dic3—21no—
146C2×C4×Dic3C2311yescharacteristic
147C2×C4×Dic3C2311yescharacteristic
148C22×C3⋊C8C2311yescharacteristic
149C22×C3⋊C8C2311yescharacteristic
150#893—22no—
151#893—22no—
152C3×#103—22no—
153C3×#103—22no—
154C3×#102—22no—
155C3×#102—22no—
156C3×C22⋊C8—22no—
157C3×#95—21no—
158#835C2×C414yescomplemented
159#832C2×C414yescomplemented
160C3⋊#95—21no—
161C3⋊#95—21no—
162#830C2×C414yescomplemented
163#821—22no—
164#821—22no—
165#815—22no—
166C8×Dic3—22no—
167#808—22no—
168#808—22no—
169C22×#41C2×D311yescharacteristic
170C22×SD16—31no—
171C22×D8—31no—
172C2×#121—31no—
173#520—64no—
174#520—64no—
175C2×C4×Q8—31no—
176C2×C4×Q8—31no—
177C2×C4×D4—31no—
178C2×C4×D4—31no—
179C2×C4×D4—31no—
180C2×C4×D4—61no—
181C2×C4×D4—61no—
182C2×#117—31no—
183C2×#117—61no—
184C22×C4⋊C4—31no—
185C22×C4⋊C4—61no—
186#449—38no—
187#442—64no—
188C4×SD16—64no—
189C2×#106—31no—
190C2×#106—31no—
191C2×#103—31no—
192C2×#103C2×D311yescharacteristic
193C2×#103C2×D311yescharacteristic
194C2×#102—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102C2×D311yescharacteristic
198C2×#102C2×D311yescharacteristic
199C2×C22⋊C8—31no—
200C2×C22⋊C8C2×D311yescharacteristic
201C2×#97—31no—
202C2×C4×C8—31no—
203#390—31no—
204#390—61no—
205#389—31no—
206#388—61no—
207#386—61no—
208#385—61no—
209#380C2×D311yescharacteristic
210C4×C4⋊C4—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#336—31no—
216#336—31no—
217C24×C3—21no—
218C24×C3C2×D411yescharacteristic
219C23×D3—21no—
220C3×#41—28no—
221C3×#41—28no—
222C3×#41—28no—
223C3×#41—28no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8C22×C412yes—
228C2×C3×Q8C2×D412yes—
229C2×C3×Q8#4112yes—
230C2×C3×D4—24no—
231C2×C3×D4—24no—
232C2×C3×D4—24no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4C22×C412yes—
237C2×C3×D4C2×D412yes—
238C2×C3×D4#4112yes—
239C22×C3×C4—24no—
240C22×C3×C4—24no—
241C22×C3×C4—21no—
242C22×C3×C4—24no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4C22×C412yes—
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4#4112yes—
252C22×C3×C4C2411yescharacteristic
253C2×#67—24no—
254C2×#67—81no—
255C2×#67—81no—
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3—24no—
260C22×Dic3—24no—
261C22×Dic3—24no—
262C22×Dic3—81no—
263C22×Dic3—81no—
264C22×Dic3—81no—
265C22×Dic3—81no—
266C22×Dic3—81no—
267C22×Dic3—81no—
268C22×Dic3C2×D411yescharacteristic
269C22×Dic3C2×D411yescharacteristic
270C22×Dic3C2×D411yescharacteristic
271C22×Dic3C2×D411yescharacteristic
272C2×D12—21no—
273C2×D12—21no—
274C2×D12—21no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12C22×C412yes—
278C2×C4×D3—42no—
279C2×C4×D3—81no—
280C2×C4×D3—81no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C22⋊C4—81no—
292#217—24no—
293#217—22no—
294#217—22no—
295#217—24no—
296#215—28no—
297#213—28no—
298(C2×D3)⋊C4—24no—
299(C2×D3)⋊C4—42no—
300(C2×D3)⋊C4—81no—
301(C2×D3)⋊C4—81no—
302C4⋊Dic3—24no—
303C4⋊Dic3—24no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
307C4⋊Dic3—22no—
308C4⋊Dic3—24no—
309C4⋊Dic3—22no—
310C4⋊Dic3C22×C412yes—
311C4⋊Dic3C2×D412yes—
312C4⋊Dic3C2×D412yes—
313Dic3⋊C4—81no—
314C4×Dic3—24no—
315C4×Dic3—21no—
316C4×Dic3—21no—
317C4×Dic3—24no—
318C4×Dic3—81no—
319C4×Dic3C2×D412yes—
320C4×Dic3C2×D412yes—
321C2×C3⋊C8—21no—
322C2×C3⋊C8—21no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8C22×C412yes—
326C2×C3⋊C8C22×C412yes—
327C2×#41—22no—
328C2×#41—22no—
329C2×#41—22no—
330C2×#41—22no—
331C2×#41—22no—
332C2×#41C4×D314yescomplemented
333C22×Q8C22×D311yescharacteristic
334C22×D4—21no—
335C22×D4—31no—
336C22×D4—61no—
337C22×D4C22×D311yescharacteristic
338C23×C4—21no—
339C23×C4—61no—
340C23×C4—61no—
341C23×C4—61no—
342C23×C4—61no—
343C23×C4C22×D311yescharacteristic
344C2×SD16—34no—
345C2×SD16—62no—
346C2×SD16—62no—
347C2×D8—34no—
348C2×D8—62no—
349C2×D8—62no—
350C22×C8—31no—
351C22×C8—31no—
352C22×C8C22×D311yescharacteristic
353C22×C8C22×D311yescharacteristic
354#121—34no—
355#121—62no—
356C4×Q8—34no—
357C4×Q8—62no—
358C4×Q8—62no—
359C4×Q8—62no—
360C4×D4—34no—
361C4×D4—62no—
362C4×D4—62no—
363C4×D4—62no—
364C4×D4—62no—
365C4×D4—68no—
366C4×D4—68no—
367C4×D4—62no—
368#117—62no—
369#117—62no—
370#117—68no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—31no—
376C2×C4⋊C4—62no—
377C2×C4⋊C4—62no—
378C2×C4⋊C4—61no—
379C2×C4⋊C4—61no—
380C2×C4⋊C4—68no—
381C2×C4⋊C4—61no—
382C2×C4⋊C4—61no—
383C2×C4⋊C4C22×D311yescharacteristic
384C2×C4⋊C4C22×D311yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—31no—
387C2×C22⋊C4—31no—
388C2×C22⋊C4—61no—
389C2×C22⋊C4—61no—
390C2×C22⋊C4—61no—
391C2×C22⋊C4—61no—
392C2×C22⋊C4—61no—
393C2×C22⋊C4—61no—
394C2×C42—31no—
395C2×C42—31no—
396C2×C42—61no—
397C2×C42—61no—
398C2×C42—61no—
399#106—62no—
400#106—62no—
401#103—22no—
402#103—22no—
403#103—34no—
404#102—22no—
405#102—22no—
406#102—34no—
407#102—62no—
408#102—62no—
409C22⋊C8—22no—
410C22⋊C8—34no—
411#97—62no—
412C4×C8—62no—
413#95—21no—
414#95—61no—
415#95—61no—
416C23×C3—22no—
417C23×C3—21no—
418C23×C3—22no—
419C23×C3—21no—
420C23×C3—22no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3C4×D412yes—
430C23×C3C22×D411yescharacteristic
431C22×D3—22no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C22×D3—41no—
438C3×Q8—22no—
439C3×Q8—22no—
440C3×Q8—22no—
441C3×Q8C4×D414yes—
442C3×D4—216no—
443C3×D4—22no—
444C3×D4—22no—
445C3×D4—22no—
446C3×D4C4×D414yes—
447C2×C3×C4—216no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
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×C4C4×D412yes—
464C2×C3×C4C23×C411yescharacteristic
465C2×C3×C4C22×D411yescharacteristic
466C2×C3×C4C22×D411yescharacteristic
467C2×C3×C4C2×#4111yescharacteristic
468C2×C3×C4C2×#4111yescharacteristic
469C2×C3×C4C2×#4111yescharacteristic
470#67—84no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—22no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—84no—
491C2×Dic3—84no—
492C2×Dic3—84no—
493C2×Dic3#12012yes—
494C2×Dic3#12012yes—
495D12—22no—
496D12—22no—
497D12—41no—
498D12—41no—
499C4×D3—84no—
500C3×C8—41no—
501C3×C8—41no—
502C3⋊C8—22no—
503C3⋊C8—22no—
504C24—21no—
505C24—61no—
506C24D3×D411yescharacteristic
507#41—28no—
508#41—28no—
509#41—28no—
510#41—28no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8C2×C4×D312yes—
515C2×Q8D3×D412yes—
516C2×Q8#23712yes—
517C2×D4—24no—
518C2×D4—24no—
519C2×D4—24no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—32no—
524C2×D4—64no—
525C2×D4—61no—
526C2×D4—61no—
527C2×D4—61no—
528C2×D4—61no—
529C2×D4—61no—
530C2×D4—241no—
531C2×D4—241no—
532C2×D4C2×C4×D312yes—
533C2×D4D3×D412yes—
534C2×D4#23712yes—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—21no—
538C22×C4—24no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—31no—
546C22×C4—31no—
547C22×C4—31no—
548C22×C4—31no—
549C22×C4—64no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—64no—
554C22×C4—64no—
555C22×C4—122no—
556C22×C4—241no—
557C22×C4—241no—
558C22×C4—241no—
559C22×C4—241no—
560C22×C4—241no—
561C22×C4—241no—
562C22×C4—241no—
563C22×C4—241no—
564C22×C4C2×C4×D312yes—
565C22×C4D3×D411yescharacteristic
566C22×C4#23712yes—
567C22×C4C23×D311yescharacteristic
568SD16—68no—
569D8—68no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—32no—
577C2×C8—32no—
578C2×C8—61no—
579C2×C8—61no—
580C2×C8—61no—
581C2×C8—61no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—32no—
587C4⋊C4—32no—
588C4⋊C4—32no—
589C4⋊C4—62no—
590C4⋊C4—62no—
591C4⋊C4—64no—
592C4⋊C4—64no—
593C4⋊C4—64no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—241no—
598C22⋊C4—62no—
599C22⋊C4—62no—
600C22⋊C4—64no—
601C22⋊C4—64no—
602C22⋊C4—64no—
603C22⋊C4—81no—
604C22⋊C4—122no—
605C22⋊C4—241no—
606C22⋊C4—241no—
607C42—32no—
608C42—32no—
609C42—64no—
610C42—64no—
611C42—61no—
612C42—61no—
613C42—241no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—24no—
618C22×C3—41no—
619C22×C3—42no—
620C22×C3—41no—
621C22×C3—42no—
622C22×C3—42no—
623C22×C3—42no—
624C22×C3—41no—
625C22×C3—42no—
626C22×C3—41no—
627C22×C3—42no—
628C22×C3C2×C4×D411yescharacteristic
629C22×C3C2×#12011yescharacteristic
630C22×C3#52511yescharacteristic
631C22×C3#57611yescharacteristic
632C22×C3#57711yescharacteristic
633C22×C3#57711yescharacteristic
634C22×C3#57711yescharacteristic
635C2×D3—42no—
636C2×D3—42no—
637C2×D3—42no—
638C2×D3—81no—
639C2×D3—81no—
640C2×D3—81no—
641C2×D3—81no—
642C3×C4—22no—
643C3×C4—24no—
644C3×C4—81no—
645C3×C4—81no—
646C3×C4C2×C4×D411yescharacteristic
647C3×C4C2×C4×D411yescharacteristic
648C3×C4#52511yescharacteristic
649C3×C4#52511yescharacteristic
650Dic3—22no—
651Dic3—22no—
652Dic3—42no—
653Dic3—41no—
654Dic3—41no—
655Dic3—42no—
656Dic3—42no—
657C23—22no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—22no—
664C23—21no—
665C23—22no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—62no—
671C23—121no—
672C23—121no—
673C23—121no—
674C23—121no—
675C23—121no—
676C23—121no—
677C23#67⋊C412yes—
678C23C2×D3×D411yescharacteristic
679Q8—22no—
680Q8—22no—
681Q8—22no—
682Q8#67⋊C414yes—
683D4—216no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—62no—
688D4—62no—
689D4—121no—
690D4—121no—
691D4—244no—
692D4#67⋊C414yes—
693C2×C4—216no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—32no—
704C2×C4—32no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—62no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—61no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—244no—
731C2×C4—244no—
732C2×C4—244no—
733C2×C4—244no—
734C2×C4#67⋊C412yes—
735C2×C4C22×C4×D311yescharacteristic
736C2×C4C2×D3×D411yescharacteristic
737C2×C4C2×D3×D411yescharacteristic
738C2×C4C2×#23711yescharacteristic
739C2×C4C2×#23711yescharacteristic
740C2×C4C2×#23711yescharacteristic
741C8—41no—
742C8—41no—
743C8—62no—
744C8—62no—
745C2×C3—42no—
746C2×C3—44no—
747C2×C3C4×#12011yescharacteristic
748C2×C3#294611yescharacteristic
749C2×C3#295211yescharacteristic
750C2×C3#301011yescharacteristic
751C2×C3#301211yescharacteristic
752C2×C3#311911yescharacteristic
753C2×C3#312511yescharacteristic
754D3—82no—
755C22—22no—
756C22—22no—
757C22—24no—
758C22—22no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—42no—
769C22—122no—
770C22—122no—
771C22—122no—
772C22—241no—
773C22—241no—
774C22—241no—
775C22—241no—
776C22C2×#67⋊C411yescharacteristic
777C22#558611yescharacteristic
778C22D3×#12011yescharacteristic
779C22#576911yescharacteristic
780C22#577011yescharacteristic
781C22#577511yescharacteristic
782C22#577811yescharacteristic
783C4—22no—
784C4—24no—
785C4—62no—
786C4—62no—
787C4—81no—
788C4—81no—
789C4—121no—
790C4—122no—
791C4—122no—
792C4—121no—
793C4—122no—
794C4C2×#67⋊C411yescharacteristic
795C4C2×#67⋊C411yescharacteristic
796C4#558611yescharacteristic
797C4#558611yescharacteristic
798C3#2146411yescharacteristic, complemented, Sylow
799C2—42no—
800C2—44no—
801C2—242no—
802C2#7381811yescharacteristic
803C2#7882011yescharacteristic
804C2#7886911yescharacteristic
805C2#8007211yescharacteristic
806C2#8008611yescharacteristic
807C2#8021911yescharacteristic
808C2#8023111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1788C2
socleC23×C3C22×D4
prime radicalC2×#5238C2
cosocleC22×C3×C4C24
hypercenter#1788D3
hypocenterC3#21464
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
1. C2×#5827C2semidirect
3. C2×#4788C2semidirect
4. C2×#4785C2semidirect
5. #73872C2semidirect
6. C3×#1788C2semidirect
7. #70240C2semidirect
8. #70237C2semidirect
9. #70220C2semidirect
10. #70172C2semidirect
11. #70169C2semidirect
12. Dic3×#102C2semidirect
13. #69932C2semidirect
14. #69907C2semidirect
15. #69505C2semidirect
40. #5238C4semidirect
76. #1788D3semidirect
85. C2×C3×#41C2×C4semidirect
109. Q8×Dic3D4semidirect
112. C2×#215C2×C4semidirect
118. D4×Dic3D4semidirect
121. C2×#213C2×C4semidirect
123. #930C2×C4semidirect
158. #835C2×C4semidirect
159. #832C2×C4semidirect
162. #830C2×C4semidirect
332. C2×#41C4×D3semidirect
798. C3#21464semidirect

Maximal subgroups

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

subgroupindex
C2×#58272
C2×#52382
C2×#47882
C2×#47852
#738722
C3×#17882
#702402
#702372
#702202
#701722
#701692
Dic3×#1022
#699322
#699072
#695052
#214643