Finite Group Databasebeta

← #11675121

Subgroups — #11675121

Order 768.

1878 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×#41C211yesmaximal, characteristic, complemented
2C2×#5585C211yesmaximal, characteristic, complemented
3#83708C212yesmaximal, complemented
4#83697C212yesmaximal, complemented
5#83691C214yesmaximal, complemented
6#83643C212yesmaximal, complemented
7#83639C214yesmaximal, complemented
8#83569C212yesmaximal, complemented
9#83367C211yesmaximal, characteristic, complemented
10#83350C212yesmaximal, complemented
11#83338C212yesmaximal, complemented
12#83336C211yesmaximal, characteristic, complemented
13C4×#951C211yesmaximal, characteristic, complemented
14#82527C212yesmaximal, complemented
15#82526C211yesmaximal, characteristic
16C4×#949C212yesmaximal, complemented
17Q8×#208C211yesmaximal, characteristic, complemented
18#61324—31nomaximal, Sylow
19C3×Q82C2211yescharacteristic, complemented
20C3×#557C2212yescomplemented
21C3×#557C2211yescharacteristic, complemented
22C3×#554—21no—
23C3×#554—22no—
24C3×#554C2212yescomplemented
25C3×#554C2211yescharacteristic, complemented
26C3×D4×Q8—21no—
27C3×D4×Q8C2211yescharacteristic, complemented
28C3×#533—21no—
29C3×#533—22no—
30C3×#533C2211yescharacteristic
31C3×#533C2212yes—
32C3×C4×#41C2212yes—
33C3×C4×#41C2211yescharacteristic
34C2×C3×C4×Q8—21no—
35C2×C3×C4×Q8C2211yescharacteristic
36C2×#951C2211yescharacteristic
37C2×#949C2212yes—
38C2×#947—21no—
39#5585—21no—
40#5585—21no—
41#5585—22no—
42#5585C2212yes—
43#5585C2214yes—
44#5585C2212yes—
45C2×#894—22no—
46C2×#893—21no—
47C2×#875C2212yes—
48C2×#874C2211yescharacteristic
49C2×C4×D12C2212yes—
50C2×C4×Dic6C2211yescharacteristic
51#5232C2211yescharacteristic
52#5094C2212yescomplemented
53#5091C2212yescomplemented
54#5089C2214yescomplemented
55#5089C2214yescomplemented
56#5088C2212yes—
57#5088C2212yes—
58#5087C2214yescomplemented
59#5084C2214yescomplemented
60#5068C2214yescomplemented
61#5068C2214yescomplemented
62#5067C2214yes—
63#5066C2214yescomplemented
64#5066C2214yescomplemented
65#5063C2214yescomplemented
66#5030C2212yescomplemented
67C4×#216C2212yescomplemented
68#5028C2214yescomplemented
69#5028C2214yescomplemented
70#5027C2212yes—
71#5027C2212yes—
72#5026C2214yescomplemented
73C4×#215C2214yescomplemented
74#5024C2212yescomplemented
75#5024C2214yescomplemented
76Q8×C3⋊C8C2212yescomplemented
77#5018C2212yescomplemented
78C4×#214C2212yescomplemented
79#5016C2214yescomplemented
80#5016C2214yescomplemented
81#5015C2212yes—
82#5015C2212yes—
83#5014C2214yescomplemented
84C4×#213C2214yescomplemented
85#5004C2212yes—
86#5004C2211yescharacteristic
87#5001C2212yes—
88#5001C2212yes—
89#5001C2212yes—
90#4995C2212yes—
91#4995C2211yescharacteristic
92#4924C2211yescharacteristic
93#4924C2212yes—
94C4×#208C2212yes—
95C4×#208C2211yescharacteristic
96C2×#559—31no—
97Q8×#41D311yescharacteristic, complemented
98#3375—32no—
99#3373—32no—
100#3371—34no—
101#3370—34no—
102#3365—32no—
103#3361—32no—
104#3140—32no—
105#3138—31no—
106#3078—31no—
107#3077—32no—
108#3040—32no—
109#3038—31no—
110Q8×M16—31no—
111C4×#137—31no—
112C4×AGL(1,ℤ/8)—32no—
113C2×C3×#41C2311yescharacteristic
114C22×C3×Q8—21no—
115C22×C3×Q8D411yescharacteristic
116C22×D12—21no—
117C22×D12—21no—
118C22×D12C2312yes—
119C22×C4×D3—22no—
120C22×Dic6C2311yescharacteristic
121C3×C4⋊Q8—21no—
122C3×C4⋊Q8—22no—
123C3×C4⋊Q8—21no—
124C3×C4⋊Q8—22no—
125C3×C4⋊Q8C2312yes—
126C3×C4⋊Q8C2311yescharacteristic
127C3×C4⋊Q8C2312yes—
128C3×C4⋊Q8C2311yescharacteristic
129C3×#125—22no—
130C3×#125—22no—
131C3×#125—22no—
132C3×#125C2312yes—
133C3×#125C2312yes—
134C3×#125C2312yes—
135C3×C22⋊Q8—21no—
136C3×C22⋊Q8—22no—
137C3×C22⋊Q8—21no—
138C3×C22⋊Q8—22no—
139C3×C22⋊Q8—21no—
140C3×C22⋊Q8—22no—
141C3×C22⋊Q8—21no—
142C3×C22⋊Q8—22no—
143C3×C22⋊Q8—22no—
144C3×C22⋊Q8—22no—
145C3×C22⋊Q8—22no—
146C3×C4×Q8—21no—
147C3×C4×Q8—21no—
148C3×C4×Q8—22no—
149C3×C4×Q8—21no—
150C3×C4×Q8—22no—
151C3×C4×Q8—21no—
152C3×C4×Q8—22no—
153C3×C4×Q8D411yescharacteristic
154C3×C4×Q8D411yescharacteristic
155C3×C4×Q8D412yes—
156C3×C4×Q8C2312yes—
157C3×C4×Q8C2311yescharacteristic
158C3×C4×Q8C2312yes—
159C3×C4×Q8C2311yescharacteristic
160C3×C4×Q8C2311yescharacteristic
161C3×C4×Q8C2311yescharacteristic
162C3×C4×Q8C2312yes—
163C3×C4×D4—21no—
164C3×C4×D4—22no—
165C3×C4×D4—21no—
166C3×C4×D4—22no—
167C3×C4×D4C2312yes—
168C3×C4×D4C2312yes—
169C3×C4×D4C2311yescharacteristic
170C3×C4×D4C2311yescharacteristic
171C3×#117—21no—
172C3×#117—22no—
173C3×#117C2312yes—
174C3×#117C2311yescharacteristic
175C2×C3×C4⋊C4—21no—
176C2×C3×C4⋊C4—22no—
177C2×C3×C4⋊C4D411yescharacteristic
178C2×C3×C4⋊C4D412yes—
179C2×C3×C42—21no—
180C2×C3×C42—22no—
181C2×C3×C42C2311yescharacteristic
182C2×C3×C42C2312yes—
183#951—24no—
184#949—28no—
185#947—22no—
186#947—22no—
187#947—24no—
188C2×#216C2312yes—
189C2×#215C2314yes—
190C2×#214C2312yes—
191C2×#213C2314yes—
192C2×(C2×D3)⋊C4—22no—
193C2×(C2×D3)⋊C4—22no—
194C2×(C2×D3)⋊C4—22no—
195C2×C4⋊Dic3C2311yescharacteristic
196C2×Dic3⋊C4—21no—
197C2×C4×Dic3—21no—
198C2×#208C2311yescharacteristic
199C2×#208C2311yescharacteristic
200C2×#208C2312yes—
201#894—24no—
202#894—24no—
203#894—24no—
204#894—24no—
205#893—22no—
206#893—24no—
207#893—22no—
208#875—22no—
209#875—22no—
210#875C2314yes—
211#875C2314yes—
212#874—21no—
213#874—21no—
214#874C2312yes—
215#874C2312yes—
216C4×D12—22no—
217C4×D12—22no—
218C4×D12C2314yes—
219C4×D12C2314yes—
220C4×Dic6—21no—
221C4×Dic6—21no—
222C4×Dic6C2312yes—
223C4×Dic6C2312yes—
224#835C2312yes—
225#832C2312yes—
226#810C2314yes—
227#810C2314yes—
228#810C2312yes—
229#810C2312yes—
230#809C2314yes—
231#809C2314yes—
232#809C2314yes—
233#809C2314yes—
234#809C2314yes—
235#809C2314yes—
236#808C2314yes—
237#808C2312yes—
238#807C2314yes—
239#807C2312yes—
240C4⋊(C3⋊C8)C2312yes—
241C4⋊(C3⋊C8)C2312yes—
242C4⋊(C3⋊C8)C2314yes—
243C4⋊(C3⋊C8)C2314yes—
244#803C2314yes—
245#803C2312yes—
246C4×C3⋊C8C2314yes—
247C4×C3⋊C8C2312yes—
248C2×#137—31no—
249C2×AGL(1,ℤ/8)—32no—
250#559—32no—
251#559—34no—
252#559—32no—
253#559—61no—
254#559—62no—
255#559—61no—
256Q82C2×D311yescharacteristic, complemented
257#557C2×D311yescharacteristic, complemented
258#557C2×D312yescomplemented
259#554—21no—
260#554—22no—
261#554C2×D311yescharacteristic, complemented
262#554C2×D312yescomplemented
263D4×Q8—21no—
264D4×Q8C2×D311yescharacteristic, complemented
265#533—22no—
266#533—21no—
267#533C2×D312yes—
268#533C2×D311yescharacteristic
269C2×#127—31no—
270C2×#124—32no—
271C2×#124—61no—
272C2×#123—62no—
273C4×#41C2×D312yes—
274C4×#41C2×D311yescharacteristic
275C2×C4×Q8—21no—
276C2×C4×Q8—31no—
277C2×C4×Q8C2×D311yescharacteristic
278C2×C4×D4—32no—
279C2×C4×D4—61no—
280#490—34no—
281#489—34no—
282#489—34no—
283#488—34no—
284#488—34no—
285#486—32no—
286#486—32no—
287#479—34no—
288#478—34no—
289#478—34no—
290#477—32no—
291#476—34no—
292#475—32no—
293#474—34no—
294#464—34no—
295#464—34no—
296#463—34no—
297#463—34no—
298#460—32no—
299#460—32no—
300#459—32no—
301#459—32no—
302#446—34no—
303#446—32no—
304C8×Q8—32no—
305#442—34no—
306#441—32no—
307#440—34no—
308#440—32no—
309C4×Q16—32no—
310C4×SD16—34no—
311C4×SD16—32no—
312C4×D8—34no—
313#428—31no—
314#428—32no—
315#423—32no—
316#423—31no—
317#419—32no—
318#419—31no—
319#418—32no—
320#418—32no—
321#418—32no—
322#417—31no—
323C4×M16—31no—
324C4×M16—32no—
325C23×D3—22no—
326C3×#41—22no—
327C3×#41#4114yes—
328C2×C3×Q8—22no—
329C2×C3×Q8—21no—
330C2×C3×Q8—21no—
331C2×C3×Q8—22no—
332C2×C3×Q8—42no—
333C2×C3×Q8—44no—
334C2×C3×Q8C2×D411yescharacteristic
335C2×C3×Q8C2×D411yescharacteristic
336C2×C3×Q8C2×D412yes—
337C2×C3×Q8C2411yescharacteristic
338C2×C3×D4—21no—
339C2×C3×D4C2411yescharacteristic
340C22×C3×C4—21no—
341C22×C3×C4—22no—
342C22×C3×C4—21no—
343C22×C3×C4—21no—
344C22×C3×C4—22no—
345C22×C3×C4C2×D411yescharacteristic
346C22×C3×C4C2×D411yescharacteristic
347C22×C3×C4C2×D412yes—
348C22×C3×C4C2×D412yes—
349C22×C3×C4C2411yescharacteristic
350C22×Dic3—21no—
351C22×Dic3—21no—
352C2×D12—24no—
353C2×D12—24no—
354C2×D12—22no—
355C2×D12—22no—
356C2×D12—22no—
357C2×D12—22no—
358C2×D12—22no—
359C2×D12—44no—
360C2×D12—82no—
361C2×D12C2414yes—
362C2×C4×D3—24no—
363C2×C4×D3—24no—
364C2×C4×D3—84no—
365C2×Dic6—22no—
366C2×Dic6—22no—
367C2×Dic6—21no—
368C2×Dic6C2412yes—
369C3×C4⋊C4—22no—
370C3×C4⋊C4—22no—
371C3×C4⋊C4—22no—
372C3×C4⋊C4—22no—
373C3×C4⋊C4—21no—
374C3×C4⋊C4—21no—
375C3×C4⋊C4—21no—
376C3×C4⋊C4—22no—
377C3×C4⋊C4—22no—
378C3×C4⋊C4—21no—
379C3×C4⋊C4—22no—
380C3×C4⋊C4—22no—
381C3×C4⋊C4—22no—
382C3×C4⋊C4—22no—
383C3×C4⋊C4C2×D411yescharacteristic
384C3×C4⋊C4C2×D412yes—
385C3×C4⋊C4C2×D411yescharacteristic
386C3×C4⋊C4C2×D412yes—
387C3×C4⋊C4C2×D412yes—
388C3×C4⋊C4C2×D412yes—
389C3×C4⋊C4C2×D412yes—
390C3×C4⋊C4C2412yes—
391C3×C4⋊C4C2411yescharacteristic
392C3×C4⋊C4C2412yes—
393C3×C4⋊C4C2411yescharacteristic
394C3×C22⋊C4—22no—
395C3×C22⋊C4—21no—
396C3×C22⋊C4—21no—
397C3×C22⋊C4—21no—
398C3×C22⋊C4—22no—
399C3×C22⋊C4—22no—
400C3×C42—21no—
401C3×C42—22no—
402C3×C42—21no—
403C3×C42—22no—
404C3×C42—22no—
405C3×C42—21no—
406C3×C42C2×D411yescharacteristic
407C3×C42C2×D411yescharacteristic
408C3×C42C2×D412yes—
409C3×C42C2×D412yes—
410C3×C42C2411yescharacteristic
411C3×C42C2412yes—
412C3×C42C2411yescharacteristic
413C3×C42C2412yes—
414#216—24no—
415#215—28no—
416#214—24no—
417#213—28no—
418(C2×D3)⋊C4—24no—
419(C2×D3)⋊C4—24no—
420(C2×D3)⋊C4—24no—
421(C2×D3)⋊C4—24no—
422(C2×D3)⋊C4—24no—
423(C2×D3)⋊C4—24no—
424C4⋊Dic3—21no—
425C4⋊Dic3C2412yes—
426Dic3⋊C4—22no—
427Dic3⋊C4—22no—
428C4×Dic3—22no—
429C4×Dic3—22no—
430#208—24no—
431#208—22no—
432#208—22no—
433C2×C3⋊C8C2412yes—
434C2×C3⋊C8C2412yes—
435C2×C3⋊C8C2414yes—
436C2×#41C22×D311yescharacteristic
437C22×Q8—21no—
438C22×Q8—31no—
439C22×Q8#6711yescharacteristic
440C22×D4—32no—
441C22×D4—61no—
442C22×D4—61no—
443C23×C4—62no—
444#137—64no—
445AGL(1,ℤ/8)—68no—
446C2×Q16—32no—
447C2×SD16—34no—
448C2×SD16—32no—
449C2×D8—34no—
450C2×M16—32no—
451C2×M16—31no—
452C2×M16—31no—
453C4⋊Q8—21no—
454C4⋊Q8—22no—
455C4⋊Q8—21no—
456C4⋊Q8—22no—
457C4⋊Q8C22×D311yescharacteristic
458C4⋊Q8C22×D312yes—
459C4⋊Q8C22×D312yes—
460C4⋊Q8C22×D311yescharacteristic
461#127—32no—
462#127—32no—
463#127—61no—
464#127—61no—
465#125—22no—
466#125—22no—
467#125—22no—
468#125C22×D312yes—
469#125C22×D312yes—
470#125C22×D312yes—
471#124—34no—
472#124—34no—
473#124—62no—
474#124—62no—
475#124—64no—
476#124—62no—
477#124—62no—
478#123—64no—
479#123—64no—
480#123—64no—
481#123—64no—
482C22⋊Q8—21no—
483C22⋊Q8—22no—
484C22⋊Q8—21no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—21no—
488C22⋊Q8—21no—
489C22⋊Q8—22no—
490C22⋊Q8—22no—
491C22⋊Q8—22no—
492C22⋊Q8—22no—
493C4×Q8—21no—
494C4×Q8—21no—
495C4×Q8—22no—
496C4×Q8—22no—
497C4×Q8—21no—
498C4×Q8—22no—
499C4×Q8—21no—
500C4×Q8—32no—
501C4×Q8—32no—
502C4×Q8—61no—
503C4×Q8—61no—
504C4×Q8#6711yescharacteristic
505C4×Q8#6712yes—
506C4×Q8#6711yescharacteristic
507C4×Q8C22×D312yes—
508C4×Q8C22×D311yescharacteristic
509C4×Q8C22×D311yescharacteristic
510C4×Q8C22×D312yes—
511C4×Q8C22×D311yescharacteristic
512C4×Q8C22×D311yescharacteristic
513C4×Q8C22×D312yes—
514C4×D4—21no—
515C4×D4—22no—
516C4×D4—22no—
517C4×D4—21no—
518C4×D4—34no—
519C4×D4—34no—
520C4×D4—62no—
521C4×D4—64no—
522C4×D4—62no—
523C4×D4—62no—
524C4×D4—62no—
525C4×D4C22×D311yescharacteristic
526C4×D4C22×D312yes—
527C4×D4C22×D312yes—
528C4×D4C22×D311yescharacteristic
529#117—22no—
530#117—21no—
531#117C22×D312yes—
532#117C22×D311yescharacteristic
533C2×C4⋊C4—21no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—31no—
536C2×C4⋊C4—61no—
537C2×C4⋊C4#6711yescharacteristic
538C2×C4⋊C4#6712yes—
539C2×C22⋊C4—62no—
540C2×C22⋊C4—62no—
541C2×C22⋊C4—62no—
542C2×C42—22no—
543C2×C42—21no—
544C2×C42—61no—
545C2×C42C22×D312yes—
546C2×C42C22×D311yescharacteristic
547#107—34no—
548#107—32no—
549#106—32no—
550#106—34no—
551C4⋊C8—32no—
552C4⋊C8—34no—
553C4⋊C8—32no—
554C4⋊C8—34no—
555#103—32no—
556#103—32no—
557#103—32no—
558#103—34no—
559#103—34no—
560#102—32no—
561#102—34no—
562#102—34no—
563#102—34no—
564#102—34no—
565#102—34no—
566#102—34no—
567#97—32no—
568#97—34no—
569C4×C8—34no—
570C4×C8—32no—
571C23×C3—21no—
572C23×C3C22×D411yescharacteristic
573C22×D3—24no—
574C22×D3—44no—
575C22×D3—44no—
576C22×D3—44no—
577C3×Q8—22no—
578C3×Q8—22no—
579C3×Q8—21no—
580C3×Q8—42no—
581C3×Q8—44no—
582C3×Q8—42no—
583C3×Q8—82no—
584C3×Q8—81no—
585C3×Q8C2×#4112yes—
586C3×D4—24no—
587C3×D4—21no—
588C3×D4C2×#4112yes—
589C2×C3×C4—21no—
590C2×C3×C4—24no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—21no—
594C2×C3×C4—22no—
595C2×C3×C4—21no—
596C2×C3×C4—42no—
597C2×C3×C4—41no—
598C2×C3×C4—42no—
599C2×C3×C4—44no—
600C2×C3×C4—42no—
601C2×C3×C4—82no—
602C2×C3×C4—81no—
603C2×C3×C4C22×D411yescharacteristic
604C2×C3×C4C22×D411yescharacteristic
605C2×C3×C4C22×D411yescharacteristic
606C2×C3×C4C22×D412yes—
607C2×C3×C4C22×D412yes—
608C2×C3×C4C22×D412yes—
609C2×C3×C4C22×D412yes—
610C2×C3×C4C22×D411yescharacteristic
611C2×C3×C4C22×D411yescharacteristic
612C2×C3×C4C2×#4112yes—
613C2×C3×C42−1+412yes—
614C2×C3×C4C2511yescharacteristic
615C2×Dic3—22no—
616C2×Dic3—22no—
617C2×Dic3—42no—
618C2×Dic3—42no—
619D12—24no—
620D12—24no—
621D12—44no—
622D12—44no—
623D12—44no—
624D12—82no—
625D12—82no—
626C4×D3—84no—
627C4×D3—84no—
628Dic6—22no—
629Dic6—22no—
630Dic6—42no—
631C3⋊C8—24no—
632C3⋊C8—22no—
633C3⋊C8—22no—
634C24—62no—
635#41—22no—
636#41#23914yes—
637C2×Q8—22no—
638C2×Q8—21no—
639C2×Q8—22no—
640C2×Q8—21no—
641C2×Q8—32no—
642C2×Q8—42no—
643C2×Q8—44no—
644C2×Q8—61no—
645C2×Q8—62no—
646C2×Q8—62no—
647C2×Q8C2×#6711yescharacteristic
648C2×Q8C2×#6711yescharacteristic
649C2×Q8C2×#6712yes—
650C2×Q8C23×D311yescharacteristic
651C2×D4—21no—
652C2×D4—34no—
653C2×D4—64no—
654C2×D4—64no—
655C2×D4—62no—
656C2×D4—62no—
657C2×D4—62no—
658C2×D4—62no—
659C2×D4—62no—
660C2×D4—124no—
661C2×D4—242no—
662C2×D4C23×D311yescharacteristic
663C22×C4—21no—
664C22×C4—22no—
665C22×C4—21no—
666C22×C4—22no—
667C22×C4—21no—
668C22×C4—61no—
669C22×C4—61no—
670C22×C4—64no—
671C22×C4—64no—
672C22×C4—244no—
673C22×C4C2×#6711yescharacteristic
674C22×C4C2×#6712yes—
675C22×C4C2×#6712yes—
676C22×C4C2×#6711yescharacteristic
677C22×C4C23×D311yescharacteristic
678Q16—64no—
679SD16—68no—
680SD16—64no—
681D8—68no—
682M16—64no—
683M16—62no—
684M16—62no—
685C2×C8—32no—
686C2×C8—32no—
687C2×C8—34no—
688C4⋊C4—22no—
689C4⋊C4—22no—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—22no—
695C4⋊C4—22no—
696C4⋊C4—21no—
697C4⋊C4—22no—
698C4⋊C4—21no—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4—22no—
702C4⋊C4—32no—
703C4⋊C4—61no—
704C4⋊C4—62no—
705C4⋊C4—62no—
706C4⋊C4C2×#6711yescharacteristic
707C4⋊C4C2×#6712yes—
708C4⋊C4C2×#6712yes—
709C4⋊C4C2×#6711yescharacteristic
710C4⋊C4C2×#6712yes—
711C4⋊C4C2×#6712yes—
712C4⋊C4C2×#6712yes—
713C4⋊C4C23×D312yes—
714C4⋊C4C23×D311yescharacteristic
715C4⋊C4C23×D312yes—
716C4⋊C4C23×D311yescharacteristic
717C22⋊C4—22no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—22no—
721C22⋊C4—22no—
722C22⋊C4—21no—
723C22⋊C4—64no—
724C22⋊C4—64no—
725C22⋊C4—64no—
726C22⋊C4—64no—
727C22⋊C4—64no—
728C22⋊C4—64no—
729C42—22no—
730C42—21no—
731C42—22no—
732C42—21no—
733C42—22no—
734C42—21no—
735C42—62no—
736C42—62no—
737C42C2×#6712yes—
738C42C2×#6711yescharacteristic
739C42C2×#6712yes—
740C42C2×#6711yescharacteristic
741C42C23×D312yes—
742C42C23×D311yescharacteristic
743C42C23×D312yes—
744C42C23×D311yescharacteristic
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—22no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3#54812yes—
751C22×C3C23×D411yescharacteristic
752C2×D3—44no—
753C2×D3—44no—
754C2×D3—44no—
755C2×D3—88no—
756C3×C4—22no—
757C3×C4—22no—
758C3×C4—21no—
759C3×C4—21no—
760C3×C4—22no—
761C3×C4—21no—
762C3×C4—22no—
763C3×C4—22no—
764C3×C4—42no—
765C3×C4—41no—
766C3×C4—42no—
767C3×C4—41no—
768C3×C4#54812yes—
769C3×C4#57512yes—
770C3×C4C22×#4111yescharacteristic
771C3×C4C2×2−1+411yescharacteristic
772Dic3—42no—
773Dic3—42no—
774C23—21no—
775C23—64no—
776C23—124no—
777C23—124no—
778C23—124no—
779C23C22×#6711yescharacteristic
780Q8—21no—
781Q8—22no—
782Q8—22no—
783Q8—42no—
784Q8—44no—
785Q8—42no—
786Q8—62no—
787Q8—62no—
788Q8—82no—
789Q8—81no—
790Q8—122no—
791Q8C2×#23912yes—
792D4—24no—
793D4—21no—
794D4—64no—
795D4—64no—
796D4—124no—
797D4—124no—
798D4—124no—
799D4—242no—
800D4—242no—
801D4C2×#23912yes—
802C2×C4—21no—
803C2×C4—24no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—44no—
813C2×C4—42no—
814C2×C4—62no—
815C2×C4—62no—
816C2×C4—82no—
817C2×C4—81no—
818C2×C4—122no—
819C2×C4—122no—
820C2×C4—244no—
821C2×C4—244no—
822C2×C4C2×#23912yes—
823C2×C4#100712yes—
824C2×C4C22×#6712yes—
825C2×C4C22×#6712yes—
826C2×C4C22×#6711yescharacteristic
827C2×C4C22×#6711yescharacteristic
828C2×C4C22×#6712yes—
829C2×C4C22×#6712yes—
830C2×C4C22×#6711yescharacteristic
831C2×C4C22×#6711yescharacteristic
832C2×C4C22×#6711yescharacteristic
833C2×C4C24×D311yescharacteristic
834C8—64no—
835C8—62no—
836C8—62no—
837C2×C3—22no—
838C2×C3—42no—
839C2×C3C2×#54811yescharacteristic
840C2×C3C2×#57511yescharacteristic
841C2×C3#358511yescharacteristic
842D3—84no—
843C22—21no—
844C22—21no—
845C22—22no—
846C22—41no—
847C22—41no—
848C22—124no—
849C22—124no—
850C22—124no—
851C22—248no—
852C22#581712yes—
853C22C23×#6711yescharacteristic
854C4—22no—
855C4—21no—
856C4—22no—
857C4—21no—
858C4—22no—
859C4—21no—
860C4—22no—
861C4—22no—
862C4—42no—
863C4—41no—
864C4—42no—
865C4—41no—
866C4—122no—
867C4—122no—
868C4#581712yes—
869C4#582212yes—
870C4C22×#23911yescharacteristic
871C4C2×#100711yescharacteristic
872C3#6132411yescharacteristic, complemented, Sylow
873C2—22no—
874C2—42no—
875C2—244no—
876C2C2×#581711yescharacteristic
877C2C2×#582211yescharacteristic
878C2#8729811yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×Q8×#41C2
socleC22×C3C23×D4
prime radical#82526C2
hypercenterQ8×#41D3
hypocenterC3#61324
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×#5585C2semidirect
3. #83708C2semidirect
4. #83697C2semidirect
5. #83691C2semidirect
6. #83643C2semidirect
7. #83639C2semidirect
8. #83569C2semidirect
9. #83367C2semidirect
10. #83350C2semidirect
11. #83338C2semidirect
12. #83336C2semidirect
13. C4×#951C2semidirect
14. #82527C2semidirect
16. C4×#949C2semidirect
17. Q8×#208C2semidirect
19. C3×Q82C22semidirect
20. C3×#557C22semidirect
21. C3×#557C22semidirect
24. C3×#554C22semidirect
25. C3×#554C22semidirect
27. C3×D4×Q8C22semidirect
52. #5094C22semidirect
53. #5091C22semidirect
54. #5089C22semidirect
55. #5089C22semidirect
58. #5087C22semidirect
59. #5084C22semidirect
60. #5068C22semidirect
61. #5068C22semidirect
63. #5066C22semidirect
64. #5066C22semidirect
65. #5063C22semidirect
66. #5030C22semidirect
67. C4×#216C22semidirect
68. #5028C22semidirect
69. #5028C22semidirect
72. #5026C22semidirect
73. C4×#215C22semidirect
74. #5024C22semidirect
75. #5024C22semidirect
76. Q8×C3⋊C8C22semidirect
77. #5018C22semidirect
78. C4×#214C22semidirect
79. #5016C22semidirect
80. #5016C22semidirect
83. #5014C22semidirect
84. C4×#213C22semidirect
97. Q8×#41D3semidirect
256. Q82C2×D3semidirect
257. #557C2×D3semidirect
258. #557C2×D3semidirect
261. #554C2×D3semidirect
262. #554C2×D3semidirect
264. D4×Q8C2×D3semidirect
872. C3#61324semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×#412
C2×#55852
#837082
#836972
#836912
#836432
#836392
#835692
#833672
#833502
#833382
#833362
C4×#9512
#825272
#825262
C4×#9492
Q8×#2082
#613243