Finite Group Databasebeta

← #11675776

Subgroups — #11675776

Order 768.

1826 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#554C211yesmaximal, characteristic, complemented
2Q8×#235C211yesmaximal, characteristic, complemented
3#83633C214yesmaximal, complemented
4#83632C214yesmaximal, complemented
5#83631C212yesmaximal, complemented
6#83630C212yesmaximal, complemented
7#83629C212yesmaximal, complemented
8#83628C212yesmaximal, complemented
9#83212C211yesmaximal, characteristic, complemented
10#83207C211yesmaximal, characteristic, complemented
11#83017C212yesmaximal, complemented
12#83015C212yesmaximal, complemented
13Q8×#208C211yesmaximal, characteristic, complemented
14#82296C211yesmaximal, characteristic, complemented
15#82296C212yesmaximal, complemented
16C4×#932C211yesmaximal, characteristic
17C4×#932C212yesmaximal
18#61367—31nomaximal, Sylow
19C3×#554—21no—
20C3×#554—21no—
21C3×#554—22no—
22C3×#554C2212yes—
23C3×#554C2212yes—
24C3×#554C2214yes—
25C2×C3×C4⋊Q8C2211yescharacteristic
26C2×C3×#125C2212yes—
27C2×C3×C22⋊Q8—21no—
28C2×C3×C22⋊Q8—22no—
29C2×C3×C4×Q8C2211yescharacteristic
30C2×C3×C4×D4C2212yes—
31C2×C3×C4×D4C2211yescharacteristic
32C22×C3×C4⋊C4—21no—
33Q8×#67—21no—
34C2×#932C2211yescharacteristic
35#5579C2211yescharacteristic, complemented
36#5579C2212yescomplemented
37#5578—22no—
38#5578—21no—
39Q8×D12C2211yescharacteristic, complemented
40C4×D3×Q8—21no—
41#5567C2211yescharacteristic, complemented
42#5567C2212yescomplemented
43Q8×Dic6C2211yescharacteristic, complemented
44#5511—21no—
45#5511—22no—
46C4×#235C2211yescharacteristic
47C4×#235C2212yes—
48#5470C2211yescharacteristic
49#5470C2212yes—
50#5215C2211yescharacteristic
51#5215C2212yes—
52#5094C2212yescomplemented
53#5091C2212yescomplemented
54#5087C2212yescomplemented
55#5084C2212yescomplemented
56#5081C2214yescomplemented
57#5080C2212yescomplemented
58#5078C2212yescomplemented
59#5066C2214yescomplemented
60#5066C2214yescomplemented
61#5065C2214yescomplemented
62#5065C2214yescomplemented
63#5064C2214yescomplemented
64#5064C2214yescomplemented
65#5063C2214yescomplemented
66#5063C2214yescomplemented
67#5024C2212yescomplemented
68#5024C2214yescomplemented
69Q8×C3⋊C8C2212yescomplemented
70#5018C2214yes—
71#5018C2212yes—
72C4×#214C2212yes—
73C4×#214C2214yes—
74#5014C2214yes—
75#5014C2212yes—
76C4×#213C2212yes—
77C4×#213C2214yes—
78#5009C2214yes—
79#5009C2214yes—
80#5009C2214yes—
81#5008C2212yes—
82#5008C2214yes—
83#5007C2212yes—
84#5007C2214yes—
85#4966C2212yes—
86#4966C2211yescharacteristic
87#4964C2212yes—
88#4964C2212yes—
89#4964C2212yes—
90#4964C2211yescharacteristic
91#4964C2212yes—
92#4924C2211yescharacteristic
93#4924C2212yes—
94C4×#208C2211yescharacteristic
95C4×#208C2212yes—
96Q8×#41—31no—
97C2×#554D311yescharacteristic, complemented
98#3389—34no—
99#3388—34no—
100#3385—32no—
101#3384—32no—
102#3381—32no—
103#3380—32no—
104#3166—32no—
105#3165—31no—
106#3080—32no—
107#3079—31no—
108#3077—31no—
109#3077—32no—
110Q8×M16—31no—
111C4×AGL(1,ℤ/8)—31no—
112C4×AGL(1,ℤ/8)—32no—
113C22×C3×Q8—21no—
114C22×C3×Q8D411yescharacteristic
115C22×C3×D4C2311yescharacteristic
116C23×C3×C4—21no—
117C23×C3×C4—22no—
118C2×D3×Q8—21no—
119C2×#235C2311yescharacteristic
120C3×C4⋊Q8—21no—
121C3×C4⋊Q8—21no—
122C3×C4⋊Q8C2312yes—
123C3×C4⋊Q8C2312yes—
124C3×#125—22no—
125C3×#125—22no—
126C3×#125C2314yes—
127C3×#125C2314yes—
128C3×C22⋊Q8—22no—
129C3×C22⋊Q8—22no—
130C3×C22⋊Q8—24no—
131C3×C22⋊Q8—24no—
132C3×C22⋊Q8—24no—
133C3×C22⋊Q8—24no—
134C3×C22⋊Q8—24no—
135C3×C4×Q8D411yescharacteristic
136C3×C4×Q8D412yes—
137C3×C4×Q8D411yescharacteristic
138C3×C4×Q8C2311yescharacteristic
139C3×C4×Q8C2311yescharacteristic
140C3×C4×Q8C2312yes—
141C3×C4×D4—22no—
142C3×C4×D4—21no—
143C3×C4×D4—22no—
144C3×C4×D4—21no—
145C3×C4×D4C2312yes—
146C3×C4×D4C2314yes—
147C3×C4×D4C2314yes—
148C3×C4×D4C2312yes—
149C2×C3×C4⋊C4—22no—
150C2×C3×C4⋊C4—21no—
151C2×C3×C4⋊C4—22no—
152C2×C3×C4⋊C4—22no—
153C2×C3×C4⋊C4—22no—
154C2×C3×C4⋊C4—24no—
155C2×C3×C4⋊C4D411yescharacteristic
156C2×C3×C4⋊C4D412yes—
157C2×C3×C4⋊C4C2311yescharacteristic
158C2×C3×C4⋊C4C2312yes—
159C2×C3×C22⋊C4—21no—
160C2×C3×C22⋊C4—22no—
161C2×C3×C42C2312yes—
162C2×C3×C42C2311yescharacteristic
163#946—21no—
164#946—22no—
165Q8×Dic3—21no—
166#944—21no—
167#944—22no—
168C2×#214C2312yes—
169#932Q818yescomplemented
170C2×#213C2312yes—
171C4×#67—21no—
172C4×#67—22no—
173C4×#67—21no—
174C4×#67—22no—
175#926C2312yes—
176#926C2311yescharacteristic
177#924—21no—
178#924—22no—
179#924—21no—
180#924—22no—
181C2×#208C2311yescharacteristic
182C2×#208C2312yes—
183C2×#208C2311yescharacteristic
184#897—21no—
185#897—22no—
186#896—22no—
187#896—22no—
188#896—22no—
189D3×C4⋊C4—21no—
190D3×C4⋊C4—22no—
191#889—22no—
192#889—22no—
193#889—22no—
194#888—21no—
195#888—22no—
196#887—21no—
197#887—22no—
198C4×D12C2311yescharacteristic
199C4×D12C2312yes—
200C4×D12C2312yes—
201C4×D12C2311yescharacteristic
202#872—22no—
203#872—21no—
204C42×D3—22no—
205C42×D3—21no—
206#870C2312yes—
207#870C2312yes—
208#870C2312yes—
209#869C2312yes—
210#869C2311yescharacteristic
211#869C2311yescharacteristic
212#869C2312yes—
213C4×Dic6—22no—
214C4×Dic6—21no—
215C4×Dic6—22no—
216C4×Dic6—21no—
217C4×Dic6C2311yescharacteristic
218C4×Dic6C2312yes—
219C4×Dic6C2312yes—
220C4×Dic6C2311yescharacteristic
221#832C2312yes—
222#832C2314yes—
223#832C2314yes—
224#832C2312yes—
225#810C2312yes—
226#810C2314yes—
227#809C2312yes—
228#809C2314yes—
229#808C2314yes—
230#808C2314yes—
231#808C2314yes—
232#808C2312yes—
233#808C2314yes—
234#807C2314yes—
235#807C2314yes—
236#807C2314yes—
237#807C2312yes—
238#807C2314yes—
239C4⋊(C3⋊C8)C2312yes—
240C4⋊(C3⋊C8)C2314yes—
241C4⋊(C3⋊C8)C2314yes—
242C4⋊(C3⋊C8)C2312yes—
243#803C2314yes—
244#803C2312yes—
245C4×C3⋊C8C2314yes—
246C4×C3⋊C8C2312yes—
247C2×AGL(1,ℤ/8)—31no—
248Q82—31no—
249#557—31no—
250#557—32no—
251#554—21no—
252#554—22no—
253#554—21no—
254#554—31no—
255#554—32no—
256#554—61no—
257#554—62no—
258#554C2×D312yes—
259#554C2×D312yes—
260#554C2×D314yes—
261D4×Q8—31no—
262D4×Q8—61no—
263#533—31no—
264#533—32no—
265#533—62no—
266#533—61no—
267C2×C4⋊Q8C2×D311yescharacteristic
268C2×#125C2×D312yes—
269C2×C22⋊Q8—21no—
270C2×C22⋊Q8—22no—
271C4×#41—31no—
272C4×#41—32no—
273C2×C4×Q8—61no—
274C2×C4×Q8C2×D311yescharacteristic
275C2×C4×D4C2×D312yes—
276C2×C4×D4C2×D311yescharacteristic
277C22×C4⋊C4—21no—
278#501—34no—
279#501—34no—
280#501—34no—
281#500—32no—
282#499—34no—
283#499—34no—
284#498—32no—
285#479—34no—
286#479—34no—
287#478—34no—
288#478—34no—
289#478—34no—
290#478—34no—
291#478—34no—
292#477—32no—
293#476—32no—
294#476—32no—
295#476—34no—
296#475—32no—
297#474—32no—
298#474—32no—
299#474—34no—
300#446—32no—
301#446—34no—
302C8×Q8—32no—
303#442—34no—
304#442—32no—
305#440—34no—
306#440—32no—
307C4×SD16—32no—
308C4×SD16—34no—
309C4×D8—32no—
310C4×D8—34no—
311#428—32no—
312#428—32no—
313#428—32no—
314#428—32no—
315#428—31no—
316#423—31no—
317#423—32no—
318#418—32no—
319#418—31no—
320#417—32no—
321#417—31no—
322C4×M16—31no—
323C4×M16—32no—
324C24×C3—21no—
325C2×C3×Q8—22no—
326C2×C3×Q8—22no—
327C2×C3×Q8—42no—
328C2×C3×Q8—82no—
329C2×C3×Q8C2×D411yescharacteristic
330C2×C3×Q8C2×D411yescharacteristic
331C2×C3×Q8C2×D412yes—
332C2×C3×D4—21no—
333C2×C3×D4—22no—
334C2×C3×D4C2×Q814yescomplemented
335C2×C3×D4C2412yes—
336C22×C3×C4—21no—
337C22×C3×C4—22no—
338C22×C3×C4—22no—
339C22×C3×C4—22no—
340C22×C3×C4—24no—
341C22×C3×C4—24no—
342C22×C3×C4—44no—
343C22×C3×C4—84no—
344C22×C3×C4C2×D411yescharacteristic
345C22×C3×C4C2×D412yes—
346C22×C3×C4C2×D411yescharacteristic
347C22×C3×C4C2×D412yes—
348C22×C3×C4C2411yescharacteristic
349C2×#67—21no—
350D3×Q8—44no—
351#235—22no—
352#235C2×Q814yes—
353C2×D12C2411yescharacteristic
354C2×C4×D3—21no—
355C2×C4×D3—22no—
356C2×C4×D3—21no—
357C2×C4×D3—21no—
358C2×C4×D3—22no—
359C2×Dic6—22no—
360C2×Dic6—21no—
361C2×Dic6—21no—
362C2×Dic6—22no—
363C2×Dic6C2411yescharacteristic
364C3×C4⋊C4—24no—
365C3×C4⋊C4—24no—
366C3×C4⋊C4—22no—
367C3×C4⋊C4—22no—
368C3×C4⋊C4—24no—
369C3×C4⋊C4—24no—
370C3×C4⋊C4—21no—
371C3×C4⋊C4—22no—
372C3×C4⋊C4C2×D411yescharacteristic
373C3×C4⋊C4C2×D412yes—
374C3×C4⋊C4C2×D411yescharacteristic
375C3×C4⋊C4C2×D412yes—
376C3×C4⋊C4C2×D412yes—
377C3×C4⋊C4C2×D412yes—
378C3×C4⋊C4C2×D412yes—
379C3×C4⋊C4C2412yes—
380C3×C4⋊C4C2414yes—
381C3×C22⋊C4—22no—
382C3×C22⋊C4—22no—
383C3×C22⋊C4—24no—
384C3×C22⋊C4—24no—
385C3×C42C2×D412yes—
386C3×C42C2×D411yescharacteristic
387C3×C42C2×D412yes—
388C3×C42C2×D411yescharacteristic
389C3×C42C2411yescharacteristic
390C3×C42C2412yes—
391C3×C42C2412yes—
392C3×C42C2411yescharacteristic
393#217—22no—
394#217—21no—
395#214C2×Q818yescomplemented
396#213C2×Q818yescomplemented
397(C2×D3)⋊C4—21no—
398(C2×D3)⋊C4—22no—
399(C2×D3)⋊C4—22no—
400(C2×D3)⋊C4—21no—
401C4⋊Dic3—22no—
402C4⋊Dic3—21no—
403C4⋊Dic3—21no—
404C4⋊Dic3—22no—
405C4⋊Dic3C2412yes—
406C4⋊Dic3C2411yescharacteristic
407C4⋊Dic3C2412yes—
408C4⋊Dic3C2411yescharacteristic
409Dic3⋊C4—22no—
410Dic3⋊C4—22no—
411Dic3⋊C4—22no—
412Dic3⋊C4—22no—
413Dic3⋊C4—22no—
414Dic3⋊C4—22no—
415Dic3⋊C4—21no—
416Dic3⋊C4—22no—
417Dic3⋊C4—22no—
418Dic3⋊C4—21no—
419C4×Dic3—21no—
420C4×Dic3—22no—
421C4×Dic3—21no—
422C4×Dic3—22no—
423C4×Dic3—22no—
424C4×Dic3—21no—
425#208—22no—
426#208—24no—
427#208C2×Q814yescomplemented
428C2×C3⋊C8C2414yes—
429C2×C3⋊C8C2412yes—
430C2×C3⋊C8C2412yes—
431C2×#41—31no—
432C22×Q8—21no—
433C22×Q8—61no—
434C22×Q8#6711yescharacteristic
435C22×D4C22×D311yescharacteristic
436C23×C4—21no—
437C23×C4—22no—
438AGL(1,ℤ/8)—38no—
439C2×SD16—32no—
440C2×D8—32no—
441C2×M16—31no—
442C2×M16—31no—
443C2×M16—32no—
444C4⋊Q8—21no—
445C4⋊Q8—21no—
446C4⋊Q8—31no—
447C4⋊Q8—32no—
448C4⋊Q8—32no—
449C4⋊Q8—31no—
450C4⋊Q8—61no—
451C4⋊Q8—62no—
452C4⋊Q8—61no—
453C4⋊Q8—62no—
454C4⋊Q8C22×D312yes—
455C4⋊Q8C22×D312yes—
456#125—22no—
457#125—22no—
458#125—32no—
459#125—32no—
460#125—32no—
461#125—62no—
462#125—62no—
463#125—62no—
464#125C22×D314yes—
465#125C22×D314yes—
466C22⋊Q8—22no—
467C22⋊Q8—22no—
468C22⋊Q8—24no—
469C22⋊Q8—24no—
470C22⋊Q8—24no—
471C22⋊Q8—24no—
472C22⋊Q8—24no—
473C22⋊Q8—61no—
474C22⋊Q8—62no—
475C22⋊Q8—61no—
476C22⋊Q8—62no—
477C22⋊Q8—61no—
478C22⋊Q8—62no—
479C22⋊Q8—61no—
480C22⋊Q8—62no—
481C22⋊Q8—62no—
482C22⋊Q8—62no—
483C22⋊Q8—62no—
484C4×Q8—32no—
485C4×Q8—31no—
486C4×Q8—31no—
487C4×Q8—32no—
488C4×Q8—61no—
489C4×Q8—61no—
490C4×Q8—62no—
491C4×Q8—62no—
492C4×Q8—61no—
493C4×Q8—62no—
494C4×Q8—61no—
495C4×Q8#6711yescharacteristic
496C4×Q8#6712yes—
497C4×Q8#6711yescharacteristic
498C4×Q8C22×D311yescharacteristic
499C4×Q8C22×D311yescharacteristic
500C4×Q8C22×D312yes—
501C4×D4—22no—
502C4×D4—21no—
503C4×D4—22no—
504C4×D4—21no—
505C4×D4—31no—
506C4×D4—32no—
507C4×D4—32no—
508C4×D4—31no—
509C4×D4—61no—
510C4×D4—62no—
511C4×D4—61no—
512C4×D4—62no—
513C4×D4C22×D312yes—
514C4×D4C22×D314yes—
515C4×D4C22×D314yes—
516C4×D4C22×D312yes—
517#117—31no—
518#117—32no—
519#117—62no—
520#117—61no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—22no—
524C2×C4⋊C4—22no—
525C2×C4⋊C4—24no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—61no—
528C2×C4⋊C4—62no—
529C2×C4⋊C4#6711yescharacteristic
530C2×C4⋊C4#6712yes—
531C2×C4⋊C4C22×D311yescharacteristic
532C2×C4⋊C4C22×D312yes—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—22no—
535C2×C42—62no—
536C2×C42—61no—
537C2×C42C22×D312yes—
538C2×C42C22×D311yescharacteristic
539#107—32no—
540#107—34no—
541#107—34no—
542#107—34no—
543#107—34no—
544#106—34no—
545#106—32no—
546#106—34no—
547#106—34no—
548#106—34no—
549C4⋊C8—32no—
550C4⋊C8—34no—
551C4⋊C8—32no—
552C4⋊C8—34no—
553#103—34no—
554#103—32no—
555#102—34no—
556#102—32no—
557#102—32no—
558#102—34no—
559#102—34no—
560#102—32no—
561#97—32no—
562#97—34no—
563C4×C8—32no—
564C4×C8—34no—
565C23×C3—24no—
566C23×C3—22no—
567C23×C3—42no—
568C23×C3—42no—
569C23×C3C22×D411yescharacteristic
570C22×D3—21no—
571C3×Q8—22no—
572C3×Q8—22no—
573C3×Q8—42no—
574C3×Q8—82no—
575C3×Q8—82no—
576C3×D4—24no—
577C3×D4—22no—
578C3×D4C22×Q814yes—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—24no—
582C2×C3×C4—42no—
583C2×C3×C4—42no—
584C2×C3×C4—41no—
585C2×C3×C4—44no—
586C2×C3×C4—42no—
587C2×C3×C4—44no—
588C2×C3×C4—44no—
589C2×C3×C4—84no—
590C2×C3×C4—84no—
591C2×C3×C4C22×D411yescharacteristic
592C2×C3×C4C22×D412yes—
593C2×C3×C4C22×D412yes—
594C2×C3×C4C22×D412yes—
595C2×C3×C4C22×D411yescharacteristic
596C2×C3×C4C22×D411yescharacteristic
597C2×C3×C4C22×D412yes—
598C2×C3×C4C22×D411yescharacteristic
599C2×C3×C4C22×D411yescharacteristic
600C2×C3×C4C22×Q812yes—
601C2×C3×C42−1+412yes—
602C2×C3×C4C2511yescharacteristic
603#67—24no—
604C2×Dic3—21no—
605C2×Dic3—22no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—22no—
609D12—21no—
610D12C22×Q812yes—
611C4×D3—24no—
612C4×D3—44no—
613C4×D3—42no—
614C4×D3—82no—
615C4×D3—81no—
616Dic6—21no—
617Dic6—44no—
618Dic6—42no—
619Dic6—82no—
620Dic6—81no—
621Dic6C22×Q812yes—
622C3⋊C8—24no—
623C3⋊C8—22no—
624C3⋊C8C22×Q814yes—
625C24—21no—
626#41—34no—
627#41—62no—
628C2×Q8—22no—
629C2×Q8—22no—
630C2×Q8—31no—
631C2×Q8—42no—
632C2×Q8—62no—
633C2×Q8—61no—
634C2×Q8—61no—
635C2×Q8—62no—
636C2×Q8—82no—
637C2×Q8—124no—
638C2×Q8C2×#6711yescharacteristic
639C2×Q8C2×#6711yescharacteristic
640C2×Q8C2×#6712yes—
641C2×D4—22no—
642C2×D4—21no—
643C2×D4—31no—
644C2×D4—61no—
645C2×D4D3×Q814yescomplemented
646C2×D4C23×D312yes—
647C22×C4—21no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—24no—
652C22×C4—24no—
653C22×C4—44no—
654C22×C4—61no—
655C22×C4—62no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—62no—
659C22×C4—84no—
660C22×C4C2×#6711yescharacteristic
661C22×C4C2×#6712yes—
662C22×C4C2×#6711yescharacteristic
663C22×C4C2×#6712yes—
664C22×C4C23×D311yescharacteristic
665SD16—38no—
666D8—38no—
667M16—34no—
668M16—62no—
669M16—64no—
670C2×C8—32no—
671C2×C8—32no—
672C2×C8—34no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—24no—
678C4⋊C4—24no—
679C4⋊C4—21no—
680C4⋊C4—22no—
681C4⋊C4—31no—
682C4⋊C4—32no—
683C4⋊C4—32no—
684C4⋊C4—31no—
685C4⋊C4—62no—
686C4⋊C4—62no—
687C4⋊C4—62no—
688C4⋊C4—62no—
689C4⋊C4—61no—
690C4⋊C4—62no—
691C4⋊C4—61no—
692C4⋊C4—61no—
693C4⋊C4—62no—
694C4⋊C4—62no—
695C4⋊C4—62no—
696C4⋊C4—62no—
697C4⋊C4—61no—
698C4⋊C4—62no—
699C4⋊C4C2×#6711yescharacteristic
700C4⋊C4C2×#6712yes—
701C4⋊C4C2×#6711yescharacteristic
702C4⋊C4C2×#6712yes—
703C4⋊C4C2×#6712yes—
704C4⋊C4C2×#6712yes—
705C4⋊C4C2×#6712yes—
706C4⋊C4C23×D312yes—
707C4⋊C4C23×D314yes—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—61no—
713C22⋊C4—62no—
714C22⋊C4—62no—
715C22⋊C4—61no—
716C22⋊C4—61no—
717C22⋊C4—62no—
718C42—62no—
719C42—61no—
720C42—61no—
721C42—62no—
722C42—62no—
723C42—61no—
724C42C2×#6712yes—
725C42C2×#6711yescharacteristic
726C42C2×#6712yes—
727C42C2×#6711yescharacteristic
728C42C23×D312yes—
729C42C23×D311yescharacteristic
730C42C23×D311yescharacteristic
731C42C23×D312yes—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—24no—
735C22×C3—48no—
736C22×C3—42no—
737C22×C3—42no—
738C22×C3D4×Q812yes—
739C22×C3C23×D411yescharacteristic
740C2×D3—22no—
741C2×D3—41no—
742C2×D3—41no—
743C3×C4—22no—
744C3×C4—21no—
745C3×C4—22no—
746C3×C4—21no—
747C3×C4—22no—
748C3×C4—21no—
749C3×C4—22no—
750C3×C4—44no—
751C3×C4—42no—
752C3×C4D4×Q812yes—
753C3×C4#57512yes—
754C3×C4C23×Q811yescharacteristic
755C3×C4C2×2−1+411yescharacteristic
756Dic3—22no—
757Dic3—41no—
758Dic3—42no—
759Dic3—41no—
760Dic3—42no—
761C23—22no—
762C23—24no—
763C23—42no—
764C23—42no—
765C23—61no—
766C23C22×#6711yescharacteristic
767Q8—22no—
768Q8—22no—
769Q8—32no—
770Q8—42no—
771Q8—61no—
772Q8—82no—
773Q8—82no—
774Q8—124no—
775Q8—122no—
776Q8—242no—
777Q8—241no—
778D4—22no—
779D4—24no—
780D4—32no—
781D4—64no—
782D4—61no—
783D4C2×D3×Q814yes—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—44no—
791C2×C4—42no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—61no—
795C2×C4—64no—
796C2×C4—62no—
797C2×C4—61no—
798C2×C4—62no—
799C2×C4—61no—
800C2×C4—84no—
801C2×C4—84no—
802C2×C4—124no—
803C2×C4—122no—
804C2×C4—242no—
805C2×C4—241no—
806C2×C4C2×D3×Q812yes—
807C2×C4#100712yes—
808C2×C4C22×#6712yes—
809C2×C4C22×#6711yescharacteristic
810C2×C4C22×#6712yes—
811C2×C4C22×#6712yes—
812C2×C4C22×#6711yescharacteristic
813C2×C4C22×#6711yescharacteristic
814C2×C4C22×#6712yes—
815C2×C4C22×#6711yescharacteristic
816C2×C4C22×#6711yescharacteristic
817C2×C4C24×D311yescharacteristic
818C8—34no—
819C8—62no—
820C8—64no—
821C2×C3—22no—
822C2×C3—44no—
823C2×C3C2×D4×Q811yescharacteristic
824C2×C3C2×#57511yescharacteristic
825C2×C3#358511yescharacteristic
826D3—42no—
827C22—21no—
828C22—21no—
829C22—24no—
830C22—48no—
831C22—42no—
832C22—42no—
833C22—62no—
834C22—121no—
835C22—121no—
836C22Q8×#6712yes—
837C22C23×#6711yescharacteristic
838C4—21no—
839C4—22no—
840C4—22no—
841C4—22no—
842C4—22no—
843C4—21no—
844C4—21no—
845C4—42no—
846C4—44no—
847C4—62no—
848C4—122no—
849C4—121no—
850C4—122no—
851C4—121no—
852C4Q8×#6712yes—
853C4#582212yes—
854C4C22×D3×Q811yescharacteristic
855C4C2×#100711yescharacteristic
856C3#6136711yescharacteristic, complemented, Sylow
857C2—22no—
858C2—44no—
859C2—122no—
860C2C2×Q8×#6711yescharacteristic
861C2C2×#582211yescharacteristic
862C2#8727711yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#554C2
socleC22×C3C23×D4
prime radicalC2×#932C22
hypercenterC2×#554D3
hypocenterC3#61367
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×C3×#554C2semidirect
2. Q8×#235C2semidirect
3. #83633C2semidirect
4. #83632C2semidirect
5. #83631C2semidirect
6. #83630C2semidirect
7. #83629C2semidirect
8. #83628C2semidirect
9. #83212C2semidirect
10. #83207C2semidirect
11. #83017C2semidirect
12. #83015C2semidirect
13. Q8×#208C2semidirect
14. #82296C2semidirect
15. #82296C2semidirect
35. #5579C22semidirect
36. #5579C22semidirect
39. Q8×D12C22semidirect
41. #5567C22semidirect
42. #5567C22semidirect
43. Q8×Dic6C22semidirect
52. #5094C22semidirect
53. #5091C22semidirect
54. #5087C22semidirect
55. #5084C22semidirect
56. #5081C22semidirect
57. #5080C22semidirect
58. #5078C22semidirect
59. #5066C22semidirect
60. #5066C22semidirect
61. #5065C22semidirect
62. #5065C22semidirect
63. #5064C22semidirect
64. #5064C22semidirect
65. #5063C22semidirect
66. #5063C22semidirect
67. #5024C22semidirect
68. #5024C22semidirect
69. Q8×C3⋊C8C22semidirect
97. C2×#554D3semidirect
169. #932Q8semidirect
334. C2×C3×D4C2×Q8semidirect
395. #214C2×Q8semidirect
396. #213C2×Q8semidirect
427. #208C2×Q8semidirect
645. C2×D4D3×Q8semidirect
856. C3#61367semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5542
Q8×#2352
#836332
#836322
#836312
#836302
#836292
#836282
#832122
#832072
#830172
#830152
Q8×#2082
#822962
C4×#9322
#613673