Finite Group Databasebeta

← #11675771

Subgroups — #11675771

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
1C3×Q8×#41C211yesmaximal, characteristic, complemented
2C2×#5579C211yesmaximal, characteristic, complemented
3#83706C212yesmaximal, complemented
4#83695C214yesmaximal, complemented
5#83693C212yesmaximal, complemented
6#83633C214yesmaximal, complemented
7#83628C212yesmaximal, complemented
8#83564C212yesmaximal, complemented
9#83350C211yesmaximal, characteristic, complemented
10#83350C212yesmaximal, complemented
11#83342C212yesmaximal, complemented
12#83341C211yesmaximal, characteristic, complemented
13C4×#949C211yesmaximal, characteristic
14C4×#949C212yesmaximal
15#82509C212yesmaximal, complemented
16#82508C211yesmaximal, characteristic, complemented
17Q8×#208C211yesmaximal, characteristic, complemented
18#61367—31nomaximal, Sylow
19C3×Q82C2211yescharacteristic, complemented
20C3×#557C2211yescharacteristic, complemented
21C3×#557C2212yescomplemented
22C3×#554—21no—
23C3×#554—22no—
24C3×#554C2211yescharacteristic, complemented
25C3×#554C2212yescomplemented
26C3×D4×Q8—21no—
27C3×D4×Q8C2211yescharacteristic, complemented
28C3×#533—21no—
29C3×#533—22no—
30C3×#533C2211yescharacteristic
31C3×#533C2212yes—
32C3×C4×#41C2211yescharacteristic
33C3×C4×#41C2212yes—
34C2×C3×C4×Q8—21no—
35C2×C3×C4×Q8C2211yescharacteristic
36C2×#949C2211yescharacteristic
37C2×#946—21no—
38#5579—21no—
39#5579—21no—
40#5579—22no—
41#5579C2212yes—
42#5579C2212yes—
43#5579C2214yes—
44C2×#896—22no—
45C2×D3×C4⋊C4—21no—
46C2×C4×D12C2212yes—
47C2×C4×D12C2211yescharacteristic
48C2×#870C2212yes—
49C2×#869C2211yescharacteristic
50#5232C2212yes—
51#5232C2211yescharacteristic
52#5087C2212yes—
53#5087C2214yes—
54#5084C2214yes—
55#5084C2212yes—
56#5081C2214yescomplemented
57#5081C2214yescomplemented
58#5080C2212yescomplemented
59#5078C2212yescomplemented
60#5066C2214yes—
61#5066C2214yes—
62#5066C2214yes—
63#5065C2214yescomplemented
64#5065C2214yescomplemented
65#5064C2214yescomplemented
66#5026C2212yes—
67#5026C2214yes—
68C4×#215C2214yes—
69C4×#215C2212yes—
70#5024C2212yescomplemented
71#5024C2214yescomplemented
72Q8×C3⋊C8C2212yescomplemented
73#5022C2214yescomplemented
74#5022C2214yescomplemented
75#5021C2212yescomplemented
76#5020C2212yescomplemented
77#5014C2214yes—
78#5014C2212yes—
79C4×#213C2212yes—
80C4×#213C2214yes—
81#5009C2214yescomplemented
82#5009C2214yescomplemented
83#5008C2212yescomplemented
84#5007C2212yescomplemented
85#5001C2211yescharacteristic
86#5001C2212yes—
87#4995C2212yes—
88#4995C2212yes—
89#4995C2212yes—
90#4995C2212yes—
91#4995C2211yescharacteristic
92#4924C2211yescharacteristic
93#4924C2212yes—
94C4×#208C2211yescharacteristic
95C4×#208C2212yes—
96Q8×#41D311yescharacteristic, complemented
97C2×#554—31no—
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—
113C2×C3×#41C2311yescharacteristic
114C22×C3×Q8—21no—
115C22×C3×Q8D411yescharacteristic
116C22×D12C2311yescharacteristic
117C22×C4×D3—21no—
118C22×C4×D3—22no—
119C22×Dic6—21no—
120C3×C4⋊Q8—21no—
121C3×C4⋊Q8—22no—
122C3×C4⋊Q8—21no—
123C3×C4⋊Q8—22no—
124C3×C4⋊Q8C2311yescharacteristic
125C3×C4⋊Q8C2312yes—
126C3×C4⋊Q8C2311yescharacteristic
127C3×C4⋊Q8C2312yes—
128C3×#125—22no—
129C3×#125—22no—
130C3×#125—22no—
131C3×#125C2312yes—
132C3×#125C2312yes—
133C3×#125C2312yes—
134C3×C22⋊Q8—21no—
135C3×C22⋊Q8—22no—
136C3×C22⋊Q8—21no—
137C3×C22⋊Q8—22no—
138C3×C22⋊Q8—22no—
139C3×C22⋊Q8—21no—
140C3×C22⋊Q8—21no—
141C3×C22⋊Q8—22no—
142C3×C22⋊Q8—22no—
143C3×C22⋊Q8—22no—
144C3×C22⋊Q8—22no—
145C3×C4×Q8—21no—
146C3×C4×Q8—21no—
147C3×C4×Q8—22no—
148C3×C4×Q8—21no—
149C3×C4×Q8—22no—
150C3×C4×Q8—21no—
151C3×C4×Q8—22no—
152C3×C4×Q8D411yescharacteristic
153C3×C4×Q8D411yescharacteristic
154C3×C4×Q8D412yes—
155C3×C4×Q8C2311yescharacteristic
156C3×C4×Q8C2312yes—
157C3×C4×Q8C2311yescharacteristic
158C3×C4×Q8C2312yes—
159C3×C4×Q8C2311yescharacteristic
160C3×C4×Q8C2311yescharacteristic
161C3×C4×Q8C2312yes—
162C3×C4×D4—21no—
163C3×C4×D4—22no—
164C3×C4×D4—22no—
165C3×C4×D4—21no—
166C3×C4×D4C2311yescharacteristic
167C3×C4×D4C2311yescharacteristic
168C3×C4×D4C2312yes—
169C3×C4×D4C2312yes—
170C3×#117—21no—
171C3×#117—22no—
172C3×#117C2311yescharacteristic
173C3×#117C2312yes—
174C2×C3×C4⋊C4—21no—
175C2×C3×C4⋊C4—22no—
176C2×C3×C4⋊C4D411yescharacteristic
177C2×C3×C4⋊C4D412yes—
178C2×C3×C42—21no—
179C2×C3×C42—22no—
180C2×C3×C42C2311yescharacteristic
181C2×C3×C42C2312yes—
182#949Q818yescomplemented
183#946—22no—
184#946—22no—
185#946—24no—
186C2×#215C2312yes—
187C2×#213C2312yes—
188C2×(C2×D3)⋊C4—21no—
189C2×(C2×D3)⋊C4—22no—
190C2×C4⋊Dic3—21no—
191C2×C4⋊Dic3C2312yes—
192C2×C4⋊Dic3C2311yescharacteristic
193C2×Dic3⋊C4—22no—
194C2×Dic3⋊C4—22no—
195C2×#208C2311yescharacteristic
196C2×#208C2312yes—
197C2×#208C2311yescharacteristic
198#896—24no—
199#896—24no—
200#896—24no—
201#896—24no—
202D3×C4⋊C4—22no—
203D3×C4⋊C4—24no—
204D3×C4⋊C4—22no—
205C4×D12—22no—
206C4×D12—22no—
207C4×D12—21no—
208C4×D12—21no—
209C4×D12C2314yes—
210C4×D12C2312yes—
211C4×D12C2312yes—
212C4×D12C2314yes—
213#870—22no—
214#870—22no—
215#870C2314yes—
216#870C2314yes—
217#869—21no—
218#869—21no—
219#869C2312yes—
220#869C2312yes—
221#835C2314yes—
222#835C2312yes—
223#832C2314yes—
224#832C2312yes—
225#809C2312yes—
226#809C2314yes—
227#809C2314yes—
228#809C2312yes—
229#808C2314yes—
230#808C2314yes—
231#808C2314yes—
232#808C2314yes—
233#808C2312yes—
234#807C2314yes—
235#807C2314yes—
236#807C2314yes—
237#807C2314yes—
238#807C2312yes—
239C4⋊(C3⋊C8)C2312yes—
240C4⋊(C3⋊C8)C2312yes—
241C4⋊(C3⋊C8)C2314yes—
242C4⋊(C3⋊C8)C2314yes—
243#803C2312yes—
244#803C2314yes—
245C4×C3⋊C8C2314yes—
246C4×C3⋊C8C2312yes—
247C2×AGL(1,ℤ/8)—31no—
248Q82C2×D311yescharacteristic, complemented
249#557C2×D311yescharacteristic, complemented
250#557C2×D312yescomplemented
251#554—21no—
252#554—22no—
253#554—32no—
254#554—32no—
255#554—34no—
256#554—61no—
257#554—62no—
258#554—61no—
259#554C2×D311yescharacteristic, complemented
260#554C2×D312yescomplemented
261D4×Q8—21no—
262D4×Q8C2×D311yescharacteristic, complemented
263#533—22no—
264#533—21no—
265#533C2×D311yescharacteristic
266#533C2×D312yes—
267C2×C4⋊Q8—31no—
268C2×#125—32no—
269C2×C22⋊Q8—61no—
270C2×C22⋊Q8—62no—
271C4×#41C2×D311yescharacteristic
272C4×#41C2×D312yes—
273C2×C4×Q8—21no—
274C2×C4×Q8C2×D311yescharacteristic
275C2×C4×D4—32no—
276C2×C4×D4—31no—
277C22×C4⋊C4—61no—
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—34no—
295#476—32no—
296#475—32no—
297#474—32no—
298#474—34no—
299#474—32no—
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—
324C23×D3—21no—
325C3×#41—22no—
326C3×#41C2×Q814yes—
327C2×C3×Q8—22no—
328C2×C3×Q8—21no—
329C2×C3×Q8—22no—
330C2×C3×Q8—21no—
331C2×C3×Q8—42no—
332C2×C3×Q8—44no—
333C2×C3×Q8C2×D411yescharacteristic
334C2×C3×Q8C2×D411yescharacteristic
335C2×C3×Q8C2×D412yes—
336C2×C3×Q8C2411yescharacteristic
337C2×C3×D4—21no—
338C2×C3×D4C2411yescharacteristic
339C22×C3×C4—21no—
340C22×C3×C4—22no—
341C22×C3×C4—21no—
342C22×C3×C4—22no—
343C22×C3×C4—21no—
344C22×C3×C4C2×D411yescharacteristic
345C22×C3×C4C2×D412yes—
346C22×C3×C4C2×D412yes—
347C22×C3×C4C2×D411yescharacteristic
348C22×C3×C4C2411yescharacteristic
349C22×Dic3—21no—
350C22×Dic3—22no—
351C2×D12—21no—
352C2×D12—22no—
353C2×D12C2×Q814yescomplemented
354C2×D12C2412yes—
355C2×C4×D3—22no—
356C2×C4×D3—22no—
357C2×C4×D3—24no—
358C2×C4×D3—24no—
359C2×C4×D3—44no—
360C2×C4×D3—84no—
361C2×Dic6—22no—
362C2×Dic6—22no—
363C2×Dic6—82no—
364C3×C4⋊C4—22no—
365C3×C4⋊C4—22no—
366C3×C4⋊C4—22no—
367C3×C4⋊C4—22no—
368C3×C4⋊C4—21no—
369C3×C4⋊C4—22no—
370C3×C4⋊C4—22no—
371C3×C4⋊C4—21no—
372C3×C4⋊C4—21no—
373C3×C4⋊C4—22no—
374C3×C4⋊C4—21no—
375C3×C4⋊C4—22no—
376C3×C4⋊C4—22no—
377C3×C4⋊C4—22no—
378C3×C4⋊C4C2×D411yescharacteristic
379C3×C4⋊C4C2×D412yes—
380C3×C4⋊C4C2×D411yescharacteristic
381C3×C4⋊C4C2×D412yes—
382C3×C4⋊C4C2×D412yes—
383C3×C4⋊C4C2×D412yes—
384C3×C4⋊C4C2×D412yes—
385C3×C4⋊C4C2411yescharacteristic
386C3×C4⋊C4C2412yes—
387C3×C4⋊C4C2412yes—
388C3×C4⋊C4C2411yescharacteristic
389C3×C22⋊C4—21no—
390C3×C22⋊C4—22no—
391C3×C22⋊C4—22no—
392C3×C22⋊C4—22no—
393C3×C22⋊C4—21no—
394C3×C22⋊C4—21no—
395C3×C42—21no—
396C3×C42—22no—
397C3×C42—22no—
398C3×C42—21no—
399C3×C42—22no—
400C3×C42—21no—
401C3×C42C2×D411yescharacteristic
402C3×C42C2×D411yescharacteristic
403C3×C42C2×D412yes—
404C3×C42C2×D412yes—
405C3×C42C2411yescharacteristic
406C3×C42C2412yes—
407C3×C42C2411yescharacteristic
408C3×C42C2412yes—
409#215C2×Q818yescomplemented
410#213C2×Q818yescomplemented
411(C2×D3)⋊C4—22no—
412(C2×D3)⋊C4—22no—
413(C2×D3)⋊C4—24no—
414(C2×D3)⋊C4—24no—
415C4⋊Dic3—22no—
416C4⋊Dic3—22no—
417C4⋊Dic3—22no—
418C4⋊Dic3—21no—
419C4⋊Dic3C2414yes—
420C4⋊Dic3C2412yes—
421Dic3⋊C4—24no—
422Dic3⋊C4—24no—
423Dic3⋊C4—24no—
424Dic3⋊C4—24no—
425#208—22no—
426#208—24no—
427#208C2×Q814yescomplemented
428C2×C3⋊C8C2414yes—
429C2×C3⋊C8C2412yes—
430C2×C3⋊C8C2412yes—
431C2×#41C22×D311yescharacteristic
432C22×Q8—21no—
433C22×Q8—61no—
434C22×Q8#6711yescharacteristic
435C22×D4—31no—
436C23×C4—61no—
437C23×C4—62no—
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—22no—
446C4⋊Q8—21no—
447C4⋊Q8—22no—
448C4⋊Q8—32no—
449C4⋊Q8—32no—
450C4⋊Q8—61no—
451C4⋊Q8—61no—
452C4⋊Q8C22×D311yescharacteristic
453C4⋊Q8C22×D312yes—
454C4⋊Q8C22×D312yes—
455C4⋊Q8C22×D311yescharacteristic
456#125—22no—
457#125—22no—
458#125—22no—
459#125—34no—
460#125—34no—
461#125—62no—
462#125—62no—
463#125C22×D312yes—
464#125C22×D312yes—
465#125C22×D312yes—
466C22⋊Q8—21no—
467C22⋊Q8—22no—
468C22⋊Q8—21no—
469C22⋊Q8—22no—
470C22⋊Q8—21no—
471C22⋊Q8—22no—
472C22⋊Q8—21no—
473C22⋊Q8—22no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476C22⋊Q8—22no—
477C22⋊Q8—62no—
478C22⋊Q8—62no—
479C22⋊Q8—64no—
480C22⋊Q8—64no—
481C22⋊Q8—64no—
482C22⋊Q8—64no—
483C22⋊Q8—64no—
484C4×Q8—21no—
485C4×Q8—21no—
486C4×Q8—22no—
487C4×Q8—22no—
488C4×Q8—21no—
489C4×Q8—22no—
490C4×Q8—21no—
491C4×Q8#6711yescharacteristic
492C4×Q8#6712yes—
493C4×Q8#6711yescharacteristic
494C4×Q8C22×D312yes—
495C4×Q8C22×D311yescharacteristic
496C4×Q8C22×D311yescharacteristic
497C4×Q8C22×D312yes—
498C4×Q8C22×D311yescharacteristic
499C4×Q8C22×D311yescharacteristic
500C4×Q8C22×D312yes—
501C4×D4—21no—
502C4×D4—22no—
503C4×D4—21no—
504C4×D4—22no—
505C4×D4—32no—
506C4×D4—34no—
507C4×D4—34no—
508C4×D4—32no—
509C4×D4—62no—
510C4×D4—61no—
511C4×D4—62no—
512C4×D4—61no—
513C4×D4C22×D311yescharacteristic
514C4×D4C22×D312yes—
515C4×D4C22×D312yes—
516C4×D4C22×D311yescharacteristic
517#117—22no—
518#117—21no—
519#117C22×D311yescharacteristic
520#117C22×D312yes—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—22no—
523C2×C4⋊C4—31no—
524C2×C4⋊C4—32no—
525C2×C4⋊C4—62no—
526C2×C4⋊C4—61no—
527C2×C4⋊C4—62no—
528C2×C4⋊C4—62no—
529C2×C4⋊C4—64no—
530C2×C4⋊C4—62no—
531C2×C4⋊C4#6711yescharacteristic
532C2×C4⋊C4#6712yes—
533C2×C22⋊C4—61no—
534C2×C22⋊C4—62no—
535C2×C42—22no—
536C2×C42—21no—
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—34no—
558#102—32no—
559#102—32no—
560#102—34no—
561#97—34no—
562#97—32no—
563C4×C8—32no—
564C4×C8—34no—
565C23×C3—21no—
566C23×C3C22×D411yescharacteristic
567C22×D3—24no—
568C22×D3—22no—
569C22×D3—42no—
570C22×D3—42no—
571C3×Q8—22no—
572C3×Q8—22no—
573C3×Q8—21no—
574C3×Q8—42no—
575C3×Q8—44no—
576C3×Q8—42no—
577C3×Q8—81no—
578C3×Q8—82no—
579C3×Q8C22×Q812yes—
580C3×D4—24no—
581C3×D4—21no—
582C3×D4C22×Q812yes—
583C2×C3×C4—21no—
584C2×C3×C4—24no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—21no—
588C2×C3×C4—22no—
589C2×C3×C4—21no—
590C2×C3×C4—41no—
591C2×C3×C4—42no—
592C2×C3×C4—42no—
593C2×C3×C4—44no—
594C2×C3×C4—42no—
595C2×C3×C4—81no—
596C2×C3×C4—82no—
597C2×C3×C4C22×D412yes—
598C2×C3×C4C22×D412yes—
599C2×C3×C4C22×D412yes—
600C2×C3×C4C22×D412yes—
601C2×C3×C4C22×D411yescharacteristic
602C2×C3×C4C22×D411yescharacteristic
603C2×C3×C4C22×D411yescharacteristic
604C2×C3×C4C22×D411yescharacteristic
605C2×C3×C4C22×D411yescharacteristic
606C2×C3×C4C22×Q812yes—
607C2×C3×C42−1+412yes—
608C2×C3×C4C2511yescharacteristic
609C2×Dic3—22no—
610C2×Dic3—24no—
611C2×Dic3—44no—
612C2×Dic3—42no—
613D12—24no—
614D12—22no—
615D12C22×Q814yes—
616C4×D3—44no—
617C4×D3—44no—
618C4×D3—84no—
619C4×D3—84no—
620Dic6—82no—
621Dic6—82no—
622C3⋊C8—24no—
623C3⋊C8—22no—
624C3⋊C8C22×Q814yes—
625C24—61no—
626#41—22no—
627#41D3×Q814yes—
628C2×Q8—22no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—22no—
632C2×Q8—42no—
633C2×Q8—44no—
634C2×Q8—62no—
635C2×Q8—62no—
636C2×Q8—242no—
637C2×Q8C2×#6711yescharacteristic
638C2×Q8C2×#6711yescharacteristic
639C2×Q8C2×#6712yes—
640C2×Q8C23×D311yescharacteristic
641C2×D4—21no—
642C2×D4—34no—
643C2×D4—32no—
644C2×D4—62no—
645C2×D4—61no—
646C2×D4C23×D311yescharacteristic
647C22×C4—21no—
648C22×C4—22no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—22no—
652C22×C4—61no—
653C22×C4—62no—
654C22×C4—62no—
655C22×C4—62no—
656C22×C4—64no—
657C22×C4—64no—
658C22×C4—124no—
659C22×C4—244no—
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—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—21no—
678C4⋊C4—22no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—22no—
682C4⋊C4—21no—
683C4⋊C4—22no—
684C4⋊C4—22no—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—32no—
688C4⋊C4—34no—
689C4⋊C4—61no—
690C4⋊C4—62no—
691C4⋊C4—64no—
692C4⋊C4—64no—
693C4⋊C4—62no—
694C4⋊C4—62no—
695C4⋊C4—64no—
696C4⋊C4—64no—
697C4⋊C4C2×#6711yescharacteristic
698C4⋊C4C2×#6712yes—
699C4⋊C4C2×#6712yes—
700C4⋊C4C2×#6711yescharacteristic
701C4⋊C4C2×#6712yes—
702C4⋊C4C2×#6712yes—
703C4⋊C4C2×#6712yes—
704C4⋊C4C23×D311yescharacteristic
705C4⋊C4C23×D312yes—
706C4⋊C4C23×D312yes—
707C4⋊C4C23×D311yescharacteristic
708C22⋊C4—21no—
709C22⋊C4—22no—
710C22⋊C4—22no—
711C22⋊C4—21no—
712C22⋊C4—21no—
713C22⋊C4—22no—
714C22⋊C4—62no—
715C22⋊C4—62no—
716C22⋊C4—64no—
717C22⋊C4—64no—
718C42—22no—
719C42—21no—
720C42—21no—
721C42—22no—
722C42—22no—
723C42—21no—
724C42C2×#6712yes—
725C42C2×#6711yescharacteristic
726C42C2×#6712yes—
727C42C2×#6711yescharacteristic
728C42C23×D312yes—
729C42C23×D311yescharacteristic
730C42C23×D312yes—
731C42C23×D311yescharacteristic
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—22no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3D4×Q812yes—
738C22×C3C23×D411yescharacteristic
739C2×D3—24no—
740C2×D3—48no—
741C2×D3—42no—
742C2×D3—42no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—22no—
746C3×C4—22no—
747C3×C4—22no—
748C3×C4—21no—
749C3×C4—22no—
750C3×C4—22no—
751C3×C4—41no—
752C3×C4—42no—
753C3×C4—42no—
754C3×C4—41no—
755C3×C4D4×Q812yes—
756C3×C4#57512yes—
757C3×C4C23×Q811yescharacteristic
758C3×C4C2×2−1+411yescharacteristic
759Dic3—44no—
760Dic3—42no—
761C23—21no—
762C23—62no—
763C23—64no—
764C23—122no—
765C23—122no—
766C23C22×#6711yescharacteristic
767Q8—21no—
768Q8—22no—
769Q8—22no—
770Q8—42no—
771Q8—44no—
772Q8—42no—
773Q8—82no—
774Q8—81no—
775Q8—242no—
776Q8—242no—
777Q8C2×D3×Q812yes—
778D4—24no—
779D4—21no—
780D4—34no—
781D4—62no—
782D4—64no—
783D4C2×D3×Q812yes—
784C2×C4—21no—
785C2×C4—24no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—21no—
789C2×C4—22no—
790C2×C4—21no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—44no—
795C2×C4—42no—
796C2×C4—62no—
797C2×C4—64no—
798C2×C4—82no—
799C2×C4—81no—
800C2×C4—124no—
801C2×C4—122no—
802C2×C4—124no—
803C2×C4—124no—
804C2×C4—244no—
805C2×C4—244no—
806C2×C4C2×D3×Q812yes—
807C2×C4#100712yes—
808C2×C4C22×#6711yescharacteristic
809C2×C4C22×#6712yes—
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—42no—
823C2×C3C2×D4×Q811yescharacteristic
824C2×C3C2×#57511yescharacteristic
825C2×C3#358511yescharacteristic
826D3—44no—
827C22—21no—
828C22—21no—
829C22—22no—
830C22—41no—
831C22—41no—
832C22—64no—
833C22—128no—
834C22—122no—
835C22—122no—
836C22Q8×#6712yes—
837C22C23×#6711yescharacteristic
838C4—22no—
839C4—21no—
840C4—22no—
841C4—21no—
842C4—22no—
843C4—21no—
844C4—22no—
845C4—22no—
846C4—42no—
847C4—41no—
848C4—42no—
849C4—41no—
850C4—124no—
851C4—122no—
852C4Q8×#6712yes—
853C4#582212yes—
854C4C22×D3×Q811yescharacteristic
855C4C2×#100711yescharacteristic
856C3#6136711yescharacteristic, complemented, Sylow
857C2—22no—
858C2—42no—
859C2—124no—
860C2C2×Q8×#6711yescharacteristic
861C2C2×#582211yescharacteristic
862C2#8729811yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×Q8×#41C2
socleC22×C3C23×D4
prime radicalC2×#949C22
hypercenterQ8×#41D3
hypocenterC3#61367
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ Q8×#41

Complements

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

NH ≅ G/Ntype
1. C3×Q8×#41C2semidirect
2. C2×#5579C2semidirect
3. #83706C2semidirect
4. #83695C2semidirect
5. #83693C2semidirect
6. #83633C2semidirect
7. #83628C2semidirect
8. #83564C2semidirect
9. #83350C2semidirect
10. #83350C2semidirect
11. #83342C2semidirect
12. #83341C2semidirect
15. #82509C2semidirect
16. #82508C2semidirect
17. Q8×#208C2semidirect
19. C3×Q82C22semidirect
20. C3×#557C22semidirect
21. C3×#557C22semidirect
24. C3×#554C22semidirect
25. C3×#554C22semidirect
27. C3×D4×Q8C22semidirect
56. #5081C22semidirect
57. #5081C22semidirect
58. #5080C22semidirect
59. #5078C22semidirect
63. #5065C22semidirect
64. #5065C22semidirect
65. #5064C22semidirect
70. #5024C22semidirect
71. #5024C22semidirect
72. Q8×C3⋊C8C22semidirect
73. #5022C22semidirect
74. #5022C22semidirect
75. #5021C22semidirect
76. #5020C22semidirect
81. #5009C22semidirect
82. #5009C22semidirect
83. #5008C22semidirect
84. #5007C22semidirect
96. Q8×#41D3semidirect
182. #949Q8semidirect
248. Q82C2×D3semidirect
249. #557C2×D3semidirect
250. #557C2×D3semidirect
259. #554C2×D3semidirect
260. #554C2×D3semidirect
262. D4×Q8C2×D3semidirect
353. C2×D12C2×Q8semidirect
409. #215C2×Q8semidirect
410. #213C2×Q8semidirect
427. #208C2×Q8semidirect
856. C3#61367semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×#412
C2×#55792
#837062
#836952
#836932
#836332
#836282
#835642
#833502
#833422
#833412
C4×#9492
#825092
#825082
Q8×#2082
#613673