Finite Group Databasebeta

← #11675804

Subgroups — #11675804

Order 768.

1750 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#557C211yesmaximal, characteristic, complemented
2Q8×#235C211yesmaximal, characteristic
3#83695C214yesmaximal, complemented
4#83694C212yesmaximal, complemented
5#83693C212yesmaximal, complemented
6#83684C214yesmaximal, complemented
7#83683C212yesmaximal, complemented
8#83682C212yesmaximal, complemented
9#83212C211yesmaximal, characteristic
10#83207C211yesmaximal, characteristic, complemented
11#83017C212yesmaximal
12#83015C212yesmaximal, complemented
13Q8×#208C211yesmaximal, characteristic, complemented
14#82431C211yesmaximal, characteristic, complemented
15#82431C212yesmaximal, complemented
16C4×#942C211yesmaximal, characteristic
17C4×#942C212yesmaximal
18#61369—31nomaximal, Sylow
19C3×#557—21no—
20C3×#557—21no—
21C3×#557—22no—
22C3×#557C2212yes—
23C3×#557C2212yes—
24C3×#557C2214yes—
25C2×C3×C4⋊Q8—21no—
26C2×C3×C4⋊Q8C2211yescharacteristic
27C2×C3×#125—22no—
28C2×C3×#125C2212yes—
29C2×C3×C4×Q8—21no—
30C2×C3×C4×Q8C2212yes—
31C2×C3×C4×Q8C2211yescharacteristic
32C2×C3×C4×Q8C2211yescharacteristic
33Q8×#67—21no—
34C2×#942C2211yescharacteristic
35#5579C2211yescharacteristic
36#5579C2212yes—
37#5578—22no—
38#5578—21no—
39Q8×D12C2211yescharacteristic
40C4×D3×Q8—21no—
41#5567C2211yescharacteristic
42#5567C2212yes—
43Q8×Dic6C2211yescharacteristic
44#5511—21no—
45#5511—22no—
46C4×#235C2211yescharacteristic
47C4×#235C2212yes—
48#5470C2211yescharacteristic
49#5470C2212yes—
50#5225C2211yescharacteristic
51#5225C2212yes—
52#5094C2212yes—
53#5091C2212yes—
54#5087C2212yes—
55#5084C2212yes—
56#5081C2214yes—
57#5080C2212yes—
58#5078C2212yes—
59#5066C2214yes—
60#5066C2214yes—
61#5065C2214yes—
62#5065C2214yes—
63#5064C2214yes—
64#5064C2214yes—
65#5063C2214yes—
66#5063C2214yes—
67#5030C2214yes—
68#5030C2212yes—
69C4×#216C2212yes—
70C4×#216C2214yes—
71#5026C2214yes—
72#5026C2212yes—
73C4×#215C2212yes—
74C4×#215C2214yes—
75#5024C2212yes—
76#5024C2214yes—
77Q8×C3⋊C8C2212yes—
78#5022C2214yes—
79#5022C2214yes—
80#5022C2214yes—
81#5021C2212yes—
82#5021C2214yes—
83#5020C2212yes—
84#5020C2214yes—
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×#557D311yescharacteristic, complemented
98#3390—34no—
99#3388—34no—
100#3387—32no—
101#3386—32no—
102#3383—32no—
103#3381—32no—
104#3166—32no—
105#3165—31no—
106#3080—32no—
107#3079—31no—
108#3078—31no—
109#3078—32no—
110Q8×M16—31no—
111C4×#137—31no—
112C4×#137—32no—
113C22×C3×Q8—21no—
114C22×C3×Q8D411yescharacteristic
115C22×C3×Q8C2311yescharacteristic
116C2×D3×Q8—21no—
117C2×#235C2311yescharacteristic
118C3×C4⋊Q8—22no—
119C3×C4⋊Q8—22no—
120C3×C4⋊Q8—24no—
121C3×C4⋊Q8—21no—
122C3×C4⋊Q8—21no—
123C3×C4⋊Q8C2312yes—
124C3×C4⋊Q8C2312yes—
125C3×#125—24no—
126C3×#125—24no—
127C3×#125—24no—
128C3×#125—24no—
129C3×#125—22no—
130C3×#125—22no—
131C3×#125C2314yes—
132C3×#125C2314yes—
133C3×C4×Q8—22no—
134C3×C4×Q8—22no—
135C3×C4×Q8—24no—
136C3×C4×Q8—22no—
137C3×C4×Q8—22no—
138C3×C4×Q8—21no—
139C3×C4×Q8—21no—
140C3×C4×Q8D411yescharacteristic
141C3×C4×Q8D412yes—
142C3×C4×Q8D411yescharacteristic
143C3×C4×Q8C2312yes—
144C3×C4×Q8C2314yes—
145C3×C4×Q8C2314yes—
146C3×C4×Q8C2312yes—
147C3×C4×Q8C2311yescharacteristic
148C3×C4×Q8C2311yescharacteristic
149C3×C4×Q8C2312yes—
150C2×C3×C4⋊C4—22no—
151C2×C3×C4⋊C4—21no—
152C2×C3×C4⋊C4—22no—
153C2×C3×C4⋊C4—21no—
154C2×C3×C4⋊C4—22no—
155C2×C3×C4⋊C4D411yescharacteristic
156C2×C3×C4⋊C4D412yes—
157C2×C3×C4⋊C4C2311yescharacteristic
158C2×C3×C4⋊C4C2312yes—
159C2×C3×C42—22no—
160C2×C3×C42—21no—
161C2×C3×C42C2312yes—
162C2×C3×C42C2311yescharacteristic
163#946—21no—
164#946—22no—
165Q8×Dic3—21no—
166#944—21no—
167#944—22no—
168C2×#216C2312yes—
169#942Q818yescomplemented
170C2×#215C2312yes—
171C4×#67—22no—
172C4×#67—21no—
173C4×#67—21no—
174C4×#67—22no—
175#926C2312yes—
176#926C2311yescharacteristic
177#924—22no—
178#924—21no—
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#835C2312yes—
222#835C2314yes—
223#835C2314yes—
224#835C2312yes—
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×#137—31no—
248Q82—31no—
249#557—21no—
250#557—22no—
251#557—21no—
252#557—31no—
253#557—32no—
254#557C2×D312yes—
255#557C2×D312yes—
256#557C2×D314yes—
257#554—31no—
258#554—32no—
259#554—61no—
260#554—62no—
261D4×Q8—31no—
262D4×Q8—61no—
263#533—31no—
264#533—32no—
265#533—62no—
266#533—61no—
267C2×C4⋊Q8—21no—
268C2×C4⋊Q8C2×D311yescharacteristic
269C2×#125—22no—
270C2×#125C2×D312yes—
271C4×#41—31no—
272C4×#41—32no—
273C2×C4×Q8—21no—
274C2×C4×Q8—61no—
275C2×C4×Q8C2×D312yes—
276C2×C4×Q8C2×D311yescharacteristic
277C2×C4×Q8C2×D311yescharacteristic
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#479—34no—
288#479—34no—
289#479—34no—
290#478—34no—
291#478—34no—
292#477—32no—
293#477—32no—
294#477—34no—
295#476—32no—
296#475—32no—
297#475—32no—
298#475—34no—
299#474—32no—
300#446—32no—
301#446—34no—
302C8×Q8—32no—
303#441—34no—
304#441—32no—
305#440—34no—
306#440—32no—
307C4×Q16—32no—
308C4×Q16—34no—
309C4×SD16—32no—
310C4×SD16—34no—
311#428—32no—
312#428—32no—
313#428—32no—
314#428—32no—
315#428—31no—
316#423—31no—
317#423—32no—
318#419—32no—
319#419—31no—
320#417—32no—
321#417—31no—
322C4×M16—31no—
323C4×M16—32no—
324C2×C3×Q8—21no—
325C2×C3×Q8—22no—
326C2×C3×Q8—22no—
327C2×C3×Q8—22no—
328C2×C3×Q8—42no—
329C2×C3×Q8—44no—
330C2×C3×Q8C2×D411yescharacteristic
331C2×C3×Q8C2×D411yescharacteristic
332C2×C3×Q8C2×D412yes—
333C2×C3×Q8C2×Q814yescomplemented
334C2×C3×Q8C2412yes—
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4—22no—
338C22×C3×C4C2×D411yescharacteristic
339C22×C3×C4C2×D412yes—
340C22×C3×C4C2×D411yescharacteristic
341C22×C3×C4C2×D412yes—
342C22×C3×C4C2411yescharacteristic
343C2×#67—21no—
344D3×Q8—44no—
345#235—22no—
346#235C2×Q814yes—
347C2×D12C2411yescharacteristic
348C2×C4×D3—21no—
349C2×C4×D3—22no—
350C2×C4×D3—21no—
351C2×C4×D3—22no—
352C2×C4×D3—21no—
353C2×Dic6—22no—
354C2×Dic6—21no—
355C2×Dic6—22no—
356C2×Dic6—21no—
357C2×Dic6C2411yescharacteristic
358C3×C4⋊C4—24no—
359C3×C4⋊C4—24no—
360C3×C4⋊C4—22no—
361C3×C4⋊C4—22no—
362C3×C4⋊C4—24no—
363C3×C4⋊C4—24no—
364C3×C4⋊C4—22no—
365C3×C4⋊C4—22no—
366C3×C4⋊C4—24no—
367C3×C4⋊C4—24no—
368C3×C4⋊C4—21no—
369C3×C4⋊C4—22no—
370C3×C4⋊C4C2×D411yescharacteristic
371C3×C4⋊C4C2×D412yes—
372C3×C4⋊C4C2×D411yescharacteristic
373C3×C4⋊C4C2×D412yes—
374C3×C4⋊C4C2×D412yes—
375C3×C4⋊C4C2×D412yes—
376C3×C4⋊C4C2×D412yes—
377C3×C4⋊C4C2412yes—
378C3×C4⋊C4C2414yes—
379C3×C42—24no—
380C3×C42—24no—
381C3×C42—22no—
382C3×C42—22no—
383C3×C42C2×D412yes—
384C3×C42C2×D411yescharacteristic
385C3×C42C2×D412yes—
386C3×C42C2×D411yescharacteristic
387C3×C42C2411yescharacteristic
388C3×C42C2412yes—
389C3×C42C2412yes—
390C3×C42C2411yescharacteristic
391#217—21no—
392#217—22no—
393#216C2×Q818yescomplemented
394#215C2×Q818yescomplemented
395(C2×D3)⋊C4—22no—
396(C2×D3)⋊C4—21no—
397(C2×D3)⋊C4—21no—
398(C2×D3)⋊C4—22no—
399C4⋊Dic3—22no—
400C4⋊Dic3—21no—
401C4⋊Dic3—22no—
402C4⋊Dic3—21no—
403C4⋊Dic3C2412yes—
404C4⋊Dic3C2411yescharacteristic
405C4⋊Dic3C2412yes—
406C4⋊Dic3C2411yescharacteristic
407Dic3⋊C4—22no—
408Dic3⋊C4—22no—
409Dic3⋊C4—22no—
410Dic3⋊C4—22no—
411Dic3⋊C4—22no—
412Dic3⋊C4—22no—
413Dic3⋊C4—22no—
414Dic3⋊C4—21no—
415Dic3⋊C4—21no—
416Dic3⋊C4—22no—
417C4×Dic3—21no—
418C4×Dic3—22no—
419C4×Dic3—22no—
420C4×Dic3—21no—
421C4×Dic3—22no—
422C4×Dic3—21no—
423#208—22no—
424#208—24no—
425#208C2×Q814yescomplemented
426C2×C3⋊C8C2414yes—
427C2×C3⋊C8C2412yes—
428C2×C3⋊C8C2412yes—
429C2×#41—31no—
430C22×Q8—21no—
431C22×Q8—61no—
432C22×Q8#6711yescharacteristic
433C22×Q8C22×D311yescharacteristic
434#137—38no—
435C2×Q16—32no—
436C2×SD16—32no—
437C2×M16—31no—
438C2×M16—31no—
439C2×M16—32no—
440C4⋊Q8—22no—
441C4⋊Q8—22no—
442C4⋊Q8—24no—
443C4⋊Q8—21no—
444C4⋊Q8—21no—
445C4⋊Q8—31no—
446C4⋊Q8—32no—
447C4⋊Q8—32no—
448C4⋊Q8—31no—
449C4⋊Q8—61no—
450C4⋊Q8—62no—
451C4⋊Q8—61no—
452C4⋊Q8—62no—
453C4⋊Q8C22×D312yes—
454C4⋊Q8C22×D312yes—
455#125—24no—
456#125—24no—
457#125—24no—
458#125—24no—
459#125—22no—
460#125—22no—
461#125—32no—
462#125—32no—
463#125—32no—
464#125—62no—
465#125—62no—
466#125—62no—
467#125C22×D314yes—
468#125C22×D314yes—
469C22⋊Q8—61no—
470C22⋊Q8—62no—
471C22⋊Q8—61no—
472C22⋊Q8—62no—
473C22⋊Q8—62no—
474C22⋊Q8—61no—
475C22⋊Q8—61no—
476C22⋊Q8—62no—
477C22⋊Q8—62no—
478C22⋊Q8—62no—
479C22⋊Q8—62no—
480C4×Q8—22no—
481C4×Q8—24no—
482C4×Q8—22no—
483C4×Q8—22no—
484C4×Q8—22no—
485C4×Q8—21no—
486C4×Q8—21no—
487C4×Q8—32no—
488C4×Q8—31no—
489C4×Q8—31no—
490C4×Q8—32no—
491C4×Q8—61no—
492C4×Q8—61no—
493C4×Q8—62no—
494C4×Q8—62no—
495C4×Q8—61no—
496C4×Q8—62no—
497C4×Q8—61no—
498C4×Q8#6711yescharacteristic
499C4×Q8#6712yes—
500C4×Q8#6711yescharacteristic
501C4×Q8C22×D312yes—
502C4×Q8C22×D314yes—
503C4×Q8C22×D314yes—
504C4×Q8C22×D312yes—
505C4×Q8C22×D311yescharacteristic
506C4×Q8C22×D311yescharacteristic
507C4×Q8C22×D312yes—
508C4×D4—31no—
509C4×D4—32no—
510C4×D4—32no—
511C4×D4—31no—
512C4×D4—61no—
513C4×D4—62no—
514C4×D4—62no—
515C4×D4—61no—
516#117—31no—
517#117—32no—
518#117—62no—
519#117—61no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—22no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—22no—
525C2×C4⋊C4—61no—
526C2×C4⋊C4—62no—
527C2×C4⋊C4#6711yescharacteristic
528C2×C4⋊C4#6712yes—
529C2×C4⋊C4C22×D311yescharacteristic
530C2×C4⋊C4C22×D312yes—
531C2×C42—22no—
532C2×C42—21no—
533C2×C42—62no—
534C2×C42—61no—
535C2×C42C22×D312yes—
536C2×C42C22×D311yescharacteristic
537#107—32no—
538#107—34no—
539#107—34no—
540#107—34no—
541#107—34no—
542#106—34no—
543#106—32no—
544#106—34no—
545#106—34no—
546#106—34no—
547C4⋊C8—32no—
548C4⋊C8—34no—
549C4⋊C8—34no—
550C4⋊C8—32no—
551#103—34no—
552#103—32no—
553#103—32no—
554#103—34no—
555#103—34no—
556#103—32no—
557#102—34no—
558#102—32no—
559#97—32no—
560#97—34no—
561C4×C8—32no—
562C4×C8—34no—
563C23×C3C22×D411yescharacteristic
564C22×D3—21no—
565C3×Q8—24no—
566C3×Q8—22no—
567C3×Q8—22no—
568C3×Q8—22no—
569C3×Q8—42no—
570C3×Q8—44no—
571C3×Q8—44no—
572C3×Q8C22×Q814yes—
573C2×C3×C4—24no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—24no—
578C2×C3×C4—42no—
579C2×C3×C4—41no—
580C2×C3×C4—42no—
581C2×C3×C4—42no—
582C2×C3×C4—44no—
583C2×C3×C4C22×D412yes—
584C2×C3×C4C22×D411yescharacteristic
585C2×C3×C4C22×D412yes—
586C2×C3×C4C22×D411yescharacteristic
587C2×C3×C4C22×D412yes—
588C2×C3×C4C22×D412yes—
589C2×C3×C4C22×D411yescharacteristic
590C2×C3×C4C22×D411yescharacteristic
591C2×C3×C4C22×D411yescharacteristic
592C2×C3×C4C22×Q812yes—
593C2×C3×C42−1+412yes—
594C2×C3×C4C2511yescharacteristic
595#67—24no—
596C2×Dic3—21no—
597C2×Dic3—22no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—22no—
601D12—21no—
602D12C22×Q812yes—
603C4×D3—24no—
604C4×D3—44no—
605C4×D3—42no—
606C4×D3—82no—
607C4×D3—81no—
608Dic6—21no—
609Dic6—44no—
610Dic6—42no—
611Dic6—82no—
612Dic6—81no—
613Dic6C22×Q812yes—
614C3⋊C8—24no—
615C3⋊C8—22no—
616C3⋊C8C22×Q814yes—
617#41—34no—
618#41—62no—
619C2×Q8—22no—
620C2×Q8—21no—
621C2×Q8—22no—
622C2×Q8—22no—
623C2×Q8—31no—
624C2×Q8—42no—
625C2×Q8—44no—
626C2×Q8—62no—
627C2×Q8—61no—
628C2×Q8—62no—
629C2×Q8—61no—
630C2×Q8—124no—
631C2×Q8D3×Q814yescomplemented
632C2×Q8C2×#6711yescharacteristic
633C2×Q8C2×#6711yescharacteristic
634C2×Q8C2×#6712yes—
635C2×Q8C23×D312yes—
636C2×D4—31no—
637C2×D4—61no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—22no—
641C22×C4—61no—
642C22×C4—62no—
643C22×C4—61no—
644C22×C4—62no—
645C22×C4—61no—
646C22×C4C2×#6711yescharacteristic
647C22×C4C2×#6712yes—
648C22×C4C2×#6711yescharacteristic
649C22×C4C2×#6712yes—
650C22×C4C23×D311yescharacteristic
651Q16—38no—
652SD16—38no—
653M16—34no—
654M16—62no—
655M16—64no—
656C2×C8—32no—
657C2×C8—32no—
658C2×C8—34no—
659C4⋊C4—24no—
660C4⋊C4—24no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—24no—
664C4⋊C4—24no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—24no—
668C4⋊C4—24no—
669C4⋊C4—21no—
670C4⋊C4—22no—
671C4⋊C4—32no—
672C4⋊C4—31no—
673C4⋊C4—31no—
674C4⋊C4—32no—
675C4⋊C4—62no—
676C4⋊C4—62no—
677C4⋊C4—62no—
678C4⋊C4—62no—
679C4⋊C4—61no—
680C4⋊C4—62no—
681C4⋊C4—61no—
682C4⋊C4—62no—
683C4⋊C4—61no—
684C4⋊C4—62no—
685C4⋊C4—62no—
686C4⋊C4—62no—
687C4⋊C4—62no—
688C4⋊C4—61no—
689C4⋊C4C2×#6711yescharacteristic
690C4⋊C4C2×#6712yes—
691C4⋊C4C2×#6712yes—
692C4⋊C4C2×#6711yescharacteristic
693C4⋊C4C2×#6712yes—
694C4⋊C4C2×#6712yes—
695C4⋊C4C2×#6712yes—
696C4⋊C4C23×D312yes—
697C4⋊C4C23×D314yes—
698C22⋊C4—61no—
699C22⋊C4—62no—
700C22⋊C4—62no—
701C22⋊C4—61no—
702C22⋊C4—62no—
703C22⋊C4—61no—
704C42—24no—
705C42—24no—
706C42—22no—
707C42—22no—
708C42—62no—
709C42—61no—
710C42—62no—
711C42—61no—
712C42—62no—
713C42—61no—
714C42C2×#6712yes—
715C42C2×#6711yescharacteristic
716C42C2×#6712yes—
717C42C2×#6711yescharacteristic
718C42C23×D312yes—
719C42C23×D311yescharacteristic
720C42C23×D311yescharacteristic
721C42C23×D312yes—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3D4×Q812yes—
725C22×C3C23×D411yescharacteristic
726C2×D3—22no—
727C2×D3—41no—
728C2×D3—41no—
729C3×C4—22no—
730C3×C4—21no—
731C3×C4—22no—
732C3×C4—21no—
733C3×C4—24no—
734C3×C4—22no—
735C3×C4—21no—
736C3×C4—22no—
737C3×C4—42no—
738C3×C4—44no—
739C3×C4D4×Q812yes—
740C3×C4#57512yes—
741C3×C4C23×Q811yescharacteristic
742C3×C4C2×2−1+411yescharacteristic
743Dic3—22no—
744Dic3—41no—
745Dic3—42no—
746Dic3—41no—
747Dic3—42no—
748C23—61no—
749C23C22×#6711yescharacteristic
750Q8—22no—
751Q8—24no—
752Q8—22no—
753Q8—22no—
754Q8—32no—
755Q8—42no—
756Q8—44no—
757Q8—44no—
758Q8—61no—
759Q8—124no—
760Q8—122no—
761Q8—242no—
762Q8—241no—
763Q8C2×D3×Q814yes—
764D4—32no—
765D4—64no—
766D4—61no—
767C2×C4—22no—
768C2×C4—24no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—41no—
775C2×C4—44no—
776C2×C4—42no—
777C2×C4—61no—
778C2×C4—64no—
779C2×C4—62no—
780C2×C4—61no—
781C2×C4—62no—
782C2×C4—61no—
783C2×C4—124no—
784C2×C4—122no—
785C2×C4—242no—
786C2×C4—241no—
787C2×C4C2×D3×Q812yes—
788C2×C4#100712yes—
789C2×C4C22×#6712yes—
790C2×C4C22×#6712yes—
791C2×C4C22×#6711yescharacteristic
792C2×C4C22×#6711yescharacteristic
793C2×C4C22×#6712yes—
794C2×C4C22×#6712yes—
795C2×C4C22×#6711yescharacteristic
796C2×C4C22×#6711yescharacteristic
797C2×C4C22×#6711yescharacteristic
798C2×C4C24×D311yescharacteristic
799C8—34no—
800C8—62no—
801C8—64no—
802C2×C3—22no—
803C2×C3C2×D4×Q811yescharacteristic
804C2×C3C2×#57511yescharacteristic
805C2×C3#358611yescharacteristic
806D3—42no—
807C22—21no—
808C22—21no—
809C22—62no—
810C22—121no—
811C22—121no—
812C22Q8×#6712yes—
813C22C23×#6711yescharacteristic
814C4—24no—
815C4—21no—
816C4—22no—
817C4—22no—
818C4—22no—
819C4—21no—
820C4—22no—
821C4—21no—
822C4—44no—
823C4—42no—
824C4—62no—
825C4—122no—
826C4—121no—
827C4—122no—
828C4—121no—
829C4Q8×#6712yes—
830C4#582212yes—
831C4C22×D3×Q811yescharacteristic
832C4C2×#100711yescharacteristic
833C3#6136911yescharacteristic, complemented, Sylow
834C2—22no—
835C2—122no—
836C2C2×Q8×#6711yescharacteristic
837C2C2×#582211yescharacteristic
838C2#8728711yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#557C2
socleC22×C3C23×D4
prime radicalC2×#235C23
hypercenterC2×#557D3
hypocenterC3#61369
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. C2×C3×#557C2semidirect
3. #83695C2semidirect
4. #83694C2semidirect
5. #83693C2semidirect
6. #83684C2semidirect
7. #83683C2semidirect
8. #83682C2semidirect
10. #83207C2semidirect
12. #83015C2semidirect
13. Q8×#208C2semidirect
14. #82431C2semidirect
15. #82431C2semidirect
97. C2×#557D3semidirect
169. #942Q8semidirect
333. C2×C3×Q8C2×Q8semidirect
393. #216C2×Q8semidirect
394. #215C2×Q8semidirect
425. #208C2×Q8semidirect
631. C2×Q8D3×Q8semidirect
833. C3#61369semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5572
Q8×#2352
#836952
#836942
#836932
#836842
#836832
#836822
#832122
#832072
#830172
#830152
Q8×#2082
#824312
C4×#9422
#613693