Finite Group Databasebeta

← #11664126

Subgroups — #11664126

Order 768.

2074 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3495C211yesmaximal, characteristic, complemented
2C2×#5523C211yesmaximal, characteristic, complemented
3#83475C212yesmaximal, complemented
4#83461C214yesmaximal, complemented
5#83446C214yesmaximal, complemented
6#83406C212yesmaximal, complemented
7#83368C212yesmaximal, complemented
8#83353C212yesmaximal, complemented
9#83153C212yesmaximal, complemented
10#83141C212yesmaximal, complemented
11#82926C211yesmaximal, characteristic
12#82914C211yesmaximal, characteristic, complemented
13#82735C211yesmaximal, characteristic, complemented
14C2×#5044C211yesmaximal, characteristic, complemented
15#82557C212yesmaximal, complemented
16#82547C212yesmaximal, complemented
17#82210C211yesmaximal, characteristic, complemented
18#60589—31nomaximal, Sylow
19C22×#235C2211yescharacteristic
20C3×#556—21no—
21C3×#554—21no—
22C3×#552—22no—
23C3×#552—21no—
24C3×#552—21no—
25C3×#551—22no—
26C3×#544C2211yescharacteristic, complemented
27C3×#542C2212yescomplemented
28C3×#541C2212yescomplemented
29C3×#536C2211yescharacteristic, complemented
30C3×#533C2212yes—
31C3×#529C2212yes—
32C3×#525C2211yescharacteristic
33C2×C3×C22⋊Q8C2211yescharacteristic
34C3×#520C2211yescharacteristic, complemented
35C3×#519C2211yescharacteristic, complemented
36C2×C3×#117C2211yescharacteristic
37C2×#950C2212yes—
38C2×#942C2212yes—
39C22×C4⋊Dic3C2211yescharacteristic
40#5523—21no—
41#5523—22no—
42#5523—21no—
43#5523C2214yes—
44#5523C2212yes—
45#5523C2212yes—
46C2×#892—21no—
47C2×D3×C4⋊C4—21no—
48C2×#67⋊C4—22no—
49C2×C4×D12C2212yes—
50C2×C4×Dic6C2212yes—
51#5232C2212yescomplemented
52C2×#835C2212yescomplemented
53#5207C2211yescharacteristic
54C2×#830C2211yescharacteristic
55#5091C2214yescomplemented
56#5090C2214yescomplemented
57#5087C2214yescomplemented
58#5083C2214yescomplemented
59#5066C2214yescomplemented
60#5063C2214yescomplemented
61#5057C2214yescomplemented
62#5054C2214yescomplemented
63#5050C2212yes—
64#5050C2211yescharacteristic
65#5047C2214yes—
66#5047C2212yes—
67#5046C2212yes—
68#5046C2211yescharacteristic
69#5044C2212yes—
70#5044C2212yes—
71#5044C2212yes—
72#5044C2214yescomplemented
73#5043C2212yescomplemented
74#5040C2211yescharacteristic
75#5037C2212yes—
76#5036C2211yescharacteristic
77#5034C2212yes—
78#5033C2212yescomplemented
79#5030C2214yescomplemented
80C4×#216C2214yescomplemented
81C4×#216C2214yescomplemented
82#5026C2214yescomplemented
83#5026C2214yescomplemented
84C4×#215C2214yescomplemented
85#5018C2214yescomplemented
86C4×#213C2214yescomplemented
87#5002C2212yes—
88#5000C2214yescomplemented
89#4999C2212yescomplemented
90#4997C2212yescomplemented
91#4995C2212yescomplemented
92#4966C2212yes—
93C2×#807C2212yescomplemented
94#4926C2212yes—
95#4925C2212yes—
96#3495D311yescharacteristic, complemented
97C2×#520—31no—
98#3124—34no—
99#3120—34no—
100#3117—32no—
101#3110—32no—
102#3105—32no—
103#3104—32no—
104#3092—31no—
105C2×#484—31no—
106#3083—32no—
107#3046—32no—
108#3007—31no—
109#3002—31no—
110#2951—32no—
111#2947—32no—
112#2924—31no—
113C2×C3×#41C2311yescharacteristic
114C22×C3×Q8C2311yescharacteristic
115C23×C3×C4C2311yescharacteristic
116C22×#67—21no—
117C23×Dic3—21no—
118C2×#235—21no—
119C2×#235—21no—
120C2×#235—28no—
121C2×#235C2312yes—
122C2×#235C2312yes—
123C22×D12C2311yescharacteristic
124C22×C4×D3—21no—
125C22×C4×D3—22no—
126C22×Dic6C2311yescharacteristic
127C3×C4⋊Q8—21no—
128C3×C4⋊Q8C2312yes—
129C3×C4⋊Q8C2312yes—
130C3×#126—22no—
131C3×#126—22no—
132C3×#126—22no—
133C3×#126—22no—
134C3×#125—22no—
135C3×#125—22no—
136C3×#125—21no—
137C3×#125—22no—
138C3×#125C2312yes—
139C3×#124—22no—
140C3×#124C2312yes—
141C3×#123—21no—
142C3×#123—22no—
143C3×#123—22no—
144C3×#123—22no—
145C3×C22⋊Q8—21no—
146C3×C22⋊Q8—21no—
147C3×C22⋊Q8—22no—
148C3×C22⋊Q8—21no—
149C3×C22⋊Q8—21no—
150C3×C22⋊Q8—22no—
151C3×C22⋊Q8—22no—
152C3×C22⋊Q8C2311yescharacteristic
153C3×C22⋊Q8C2312yes—
154C3×C22⋊Q8C2311yescharacteristic
155C3×C22⋊Q8C2312yes—
156C3×#121C2311yescharacteristic
157C3×#121C2311yescharacteristic
158C3×#120—21no—
159C3×C4×Q8—21no—
160C3×C4×Q8—21no—
161C3×C4×Q8—22no—
162C3×C4×Q8C2312yes—
163C3×C4×Q8C2312yes—
164C3×C4×Q8C2312yes—
165C3×C4×D4—21no—
166C3×C4×D4—21no—
167C3×C4×D4—22no—
168C3×C4×D4—22no—
169C3×C4×D4C2312yes—
170C3×#117—22no—
171C3×#117—21no—
172C3×#117—22no—
173C3×#117—22no—
174C3×#117D411yescharacteristic
175C3×#117D412yes—
176C3×#117D411yescharacteristic
177C3×#117C2311yescharacteristic
178C3×#117C2311yescharacteristic
179C3×#117C2311yescharacteristic
180C3×#117C2312yes—
181C2×C3×C4⋊C4—21no—
182C2×C3×C4⋊C4—21no—
183C2×C3×C4⋊C4D411yescharacteristic
184C2×C3×C4⋊C4D411yescharacteristic
185C2×C3×C4⋊C4C2311yescharacteristic
186C2×C3×C22⋊C4—21no—
187C2×C3×C22⋊C4D412yes—
188C2×C3×C42C2312yes—
189#950—28no—
190C2×#216C2312yes—
191C2×#216C2314yes—
192#942—28no—
193C2×#215C2314yes—
194C2×#215C2312yes—
195C2×#214C2312yes—
196C2×#213C2312yes—
197C2×(C2×D3)⋊C4—22no—
198C2×C4⋊Dic3—21no—
199C2×C4⋊Dic3—21no—
200C2×C4⋊Dic3—21no—
201C2×C4⋊Dic3C2312yes—
202C2×C4⋊Dic3C2312yes—
203C2×C4⋊Dic3C2312yes—
204C2×Dic3⋊C4—22no—
205C2×C4×Dic3—22no—
206C2×#208C2312yes—
207C22×C3⋊C8C2312yes—
208#892—22no—
209#892—22no—
210#892—24no—
211D3×C4⋊C4—22no—
212D3×C4⋊C4—24no—
213D3×C4⋊C4—22no—
214#67⋊C4—24no—
215#67⋊C4—24no—
216#67⋊C4—24no—
217#67⋊C4—24no—
218C4×D12—22no—
219C4×D12—22no—
220C4×D12C2314yes—
221C4×D12C2314yes—
222C4×Dic6—22no—
223C4×Dic6—22no—
224C4×Dic6C2314yes—
225C4×Dic6C2314yes—
226#835C2314yes—
227#835C2314yes—
228#835C2314yes—
229#832C2314yes—
230#830C2311yescharacteristic
231#830C2312yes—
232#830C2311yescharacteristic
233#830C2312yes—
234#830C2312yes—
235#810C2314yes—
236#810C2312yes—
237#810C2312yes—
238#809C2314yes—
239#809C2312yes—
240#809C2312yes—
241#808C2314yes—
242#807C2314yes—
243#807C2314yes—
244#807C2314yes—
245C4⋊(C3⋊C8)C2314yes—
246C4⋊(C3⋊C8)C2314yes—
247#803C2314yes—
248C4×C3⋊C8C2314yes—
249C22×#41—31no—
250C2×#137—32no—
251C2×#135—32no—
252#556—21no—
253#554—21no—
254#552—22no—
255#552—21no—
256#552—21no—
257#551—22no—
258#544C2×D311yescharacteristic, complemented
259#542C2×D312yescomplemented
260#541C2×D312yescomplemented
261#536C2×D311yescharacteristic, complemented
262#533C2×D312yes—
263#529C2×D312yes—
264#525C2×D311yescharacteristic
265C2×C22⋊Q8C2×D311yescharacteristic
266#520—32no—
267#520—34no—
268#520—32no—
269#520—62no—
270#520—61no—
271#520—61no—
272#520C2×D311yescharacteristic, complemented
273#519C2×D311yescharacteristic, complemented
274C2×C4×Q8—32no—
275C2×C4×D4—32no—
276C2×C4×D4—62no—
277C2×#117—61no—
278C2×#117C2×D311yescharacteristic
279C22×C4⋊C4—31no—
280C22×C4⋊C4—61no—
281#484—32no—
282#484—32no—
283#484—34no—
284#484—32no—
285#483—32no—
286#481—32no—
287#480—32no—
288#479—34no—
289#478—34no—
290#477—34no—
291#474—34no—
292#464—34no—
293#463—34no—
294#462—34no—
295#461—34no—
296#452—32no—
297#452—34no—
298#451—31no—
299#451—32no—
300#450—32no—
301#450—31no—
302#449—32no—
303#448—31no—
304#447—31no—
305#441—34no—
306#440—34no—
307#440—34no—
308#440—34no—
309C4×Q16—34no—
310C4×Q16—34no—
311C4×SD16—34no—
312C4×D8—34no—
313#433—34no—
314#432—32no—
315#431—32no—
316#428—32no—
317C2×#107—32no—
318#424—32no—
319#417—32no—
320#417—32no—
321#416—32no—
322C2×#103—32no—
323#407—31no—
324C2×C22⋊C8—31no—
325#405—32no—
326C24×C3C2×D411yescharacteristic
327C23×D3—21no—
328C3×#41—24no—
329C2×C3×Q8—21no—
330C2×C3×Q8—22no—
331C2×C3×Q8—24no—
332C2×C3×Q8C2412yes—
333C2×C3×Q8C2411yescharacteristic
334C2×C3×D4—21no—
335C2×C3×D4—21no—
336C2×C3×D4—21no—
337C2×C3×D4C2411yescharacteristic
338C22×C3×C4—24no—
339C22×C3×C4—21no—
340C22×C3×C4—21no—
341C22×C3×C4—21no—
342C22×C3×C4—22no—
343C22×C3×C4C2×D412yes—
344C22×C3×C4C2×D411yescharacteristic
345C22×C3×C4C2×D411yescharacteristic
346C22×C3×C4C2×D411yescharacteristic
347C22×C3×C4C2×D412yes—
348C22×C3×C4C2411yescharacteristic
349C22×C3×C4C2411yescharacteristic
350C22×C3×C4C2411yescharacteristic
351C2×#67—28no—
352C2×#67—22no—
353C2×#67—22no—
354C22×Dic3—21no—
355C22×Dic3—22no—
356C22×Dic3—22no—
357C22×Dic3—22no—
358C22×Dic3—82no—
359#235—28no—
360#235—28no—
361#235—24no—
362#235—24no—
363#235—24no—
364#235#4118yes—
365C2×D12—21no—
366C2×D12—24no—
367C2×D12C2412yes—
368C2×C4×D3—28no—
369C2×C4×D3—22no—
370C2×C4×D3—22no—
371C2×C4×D3—24no—
372C2×C4×D3—24no—
373C2×C4×D3—84no—
374C2×Dic6—21no—
375C2×Dic6—24no—
376C2×Dic6C2412yes—
377C3×C4⋊C4—21no—
378C3×C4⋊C4—22no—
379C3×C4⋊C4—22no—
380C3×C4⋊C4—22no—
381C3×C4⋊C4—22no—
382C3×C4⋊C4—22no—
383C3×C4⋊C4—22no—
384C3×C4⋊C4—22no—
385C3×C4⋊C4—22no—
386C3×C4⋊C4—21no—
387C3×C4⋊C4—22no—
388C3×C4⋊C4—21no—
389C3×C4⋊C4—22no—
390C3×C4⋊C4C2×D411yescharacteristic
391C3×C4⋊C4C2×D412yes—
392C3×C4⋊C4C2×D411yescharacteristic
393C3×C4⋊C4C2×D411yescharacteristic
394C3×C4⋊C4C2×D411yescharacteristic
395C3×C4⋊C4C2×D412yes—
396C3×C4⋊C4C2412yes—
397C3×C4⋊C4C2411yescharacteristic
398C3×C4⋊C4C2411yescharacteristic
399C3×C22⋊C4—22no—
400C3×C22⋊C4—22no—
401C3×C22⋊C4—21no—
402C3×C22⋊C4—21no—
403C3×C22⋊C4—21no—
404C3×C22⋊C4—21no—
405C3×C22⋊C4—22no—
406C3×C22⋊C4—22no—
407C3×C22⋊C4—21no—
408C3×C22⋊C4—22no—
409C3×C22⋊C4C2×D412yes—
410C3×C22⋊C4C2×D412yes—
411C3×C22⋊C4C2×D412yes—
412C3×C22⋊C4C2×D412yes—
413C3×C42—22no—
414C3×C42—22no—
415C3×C42—22no—
416C3×C42—21no—
417C3×C42C2×D412yes—
418C3×C42C2×D412yes—
419C3×C42C2412yes—
420C3×C42C2412yes—
421#216—28no—
422#216—24no—
423#215—28no—
424#215—24no—
425#214—24no—
426#213—24no—
427(C2×D3)⋊C4—24no—
428(C2×D3)⋊C4—24no—
429C4⋊Dic3—22no—
430C4⋊Dic3—22no—
431C4⋊Dic3—22no—
432C4⋊Dic3C2414yes—
433Dic3⋊C4—24no—
434Dic3⋊C4—24no—
435C4×Dic3—24no—
436C4×Dic3—24no—
437#208—24no—
438C2×C3⋊C8—24no—
439C2×C3⋊C8C2412yes—
440C2×C3⋊C8C2414yes—
441C2×C3⋊C8C2412yes—
442C2×#41—32no—
443C2×#41—32no—
444C2×#41—68no—
445C2×#41—61no—
446C2×#41—61no—
447C2×#41C22×D311yescharacteristic
448C22×Q8—31no—
449C22×Q8C22×D311yescharacteristic
450C22×D4—31no—
451C22×D4—61no—
452C23×C4—61no—
453C23×C4—61no—
454C23×C4—62no—
455C23×C4C22×D311yescharacteristic
456#137—68no—
457#135—68no—
458C2×Q16—32no—
459C2×Q16—34no—
460C2×SD16—32no—
461C2×SD16—34no—
462C2×SD16—32no—
463C2×D8—32no—
464C2×M16—32no—
465C22×C8—32no—
466C4⋊Q8—21no—
467C4⋊Q8C22×D312yes—
468C4⋊Q8C22×D312yes—
469#126—22no—
470#126—22no—
471#126—22no—
472#126—22no—
473#125—22no—
474#125—22no—
475#125—21no—
476#125—22no—
477#125C22×D312yes—
478#124—22no—
479#124C22×D312yes—
480#123—21no—
481#123—22no—
482#123—22no—
483#123—22no—
484C22⋊Q8—21no—
485C22⋊Q8—21no—
486C22⋊Q8—22no—
487C22⋊Q8—21no—
488C22⋊Q8—21no—
489C22⋊Q8—22no—
490C22⋊Q8—22no—
491C22⋊Q8C22×D312yes—
492C22⋊Q8C22×D312yes—
493C22⋊Q8C22×D311yescharacteristic
494C22⋊Q8C22×D311yescharacteristic
495#121C22×D311yescharacteristic
496#121C22×D311yescharacteristic
497#120—21no—
498C4×Q8—21no—
499C4×Q8—21no—
500C4×Q8—22no—
501C4×Q8—34no—
502C4×Q8—34no—
503C4×Q8—62no—
504C4×Q8—62no—
505C4×Q8C22×D312yes—
506C4×Q8C22×D312yes—
507C4×Q8C22×D312yes—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—34no—
513C4×D4—34no—
514C4×D4—64no—
515C4×D4—64no—
516C4×D4—64no—
517C4×D4—64no—
518C4×D4—62no—
519C4×D4—62no—
520C4×D4C22×D312yes—
521#117—22no—
522#117—21no—
523#117—22no—
524#117—22no—
525#117—62no—
526#117—62no—
527#117—64no—
528#117#6711yescharacteristic
529#117#6712yes—
530#117#6711yescharacteristic
531#117C22×D311yescharacteristic
532#117C22×D311yescharacteristic
533#117C22×D311yescharacteristic
534#117C22×D312yes—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—32no—
538C2×C4⋊C4—32no—
539C2×C4⋊C4—32no—
540C2×C4⋊C4—61no—
541C2×C4⋊C4—61no—
542C2×C4⋊C4—61no—
543C2×C4⋊C4—62no—
544C2×C4⋊C4—62no—
545C2×C4⋊C4—64no—
546C2×C4⋊C4—62no—
547C2×C4⋊C4#6711yescharacteristic
548C2×C4⋊C4#6711yescharacteristic
549C2×C4⋊C4C22×D311yescharacteristic
550C2×C22⋊C4—21no—
551C2×C22⋊C4—62no—
552C2×C22⋊C4#6712yes—
553C2×C42—62no—
554C2×C42C22×D312yes—
555#107—34no—
556#107—34no—
557#107—34no—
558#106—34no—
559C4⋊C8—34no—
560C4⋊C8—34no—
561#103—34no—
562#103—34no—
563#103—34no—
564#103—32no—
565#103—32no—
566#103—34no—
567#102—34no—
568#102—32no—
569#102—32no—
570#102—34no—
571C22⋊C8—31no—
572C22⋊C8—31no—
573C22⋊C8—32no—
574C22⋊C8—32no—
575C22⋊C8—32no—
576#97—34no—
577C4×C8—34no—
578C23×C3—22no—
579C23×C3—22no—
580C23×C3—21no—
581C23×C3—41no—
582C23×C3C22×D411yescharacteristic
583C23×C3C22×D411yescharacteristic
584C23×C3C22×D411yescharacteristic
585C22×D3—24no—
586C22×D3—22no—
587C22×D3—42no—
588C22×D3—42no—
589C3×Q8—24no—
590C3×Q8—22no—
591C3×Q8—42no—
592C3×Q8—82no—
593C3×D4—22no—
594C3×D4—42no—
595C3×D4—42no—
596C3×D4—81no—
597C2×C3×C4—22no—
598C2×C3×C4—24no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—22no—
606C2×C3×C4—21no—
607C2×C3×C4—22no—
608C2×C3×C4—42no—
609C2×C3×C4—42no—
610C2×C3×C4—42no—
611C2×C3×C4—82no—
612C2×C3×C4—81no—
613C2×C3×C4C22×D412yes—
614C2×C3×C4C22×D412yes—
615C2×C3×C4C22×D412yes—
616C2×C3×C4C22×D412yes—
617C2×C3×C4C22×D411yescharacteristic
618C2×C3×C4C22×D411yescharacteristic
619C2×C3×C4C22×D411yescharacteristic
620C2×C3×C4C2×#4114yes—
621C2×C3×C4C2511yescharacteristic
622#67—28no—
623#67—28no—
624C2×Dic3—24no—
625C2×Dic3—22no—
626C2×Dic3—24no—
627C2×Dic3—44no—
628C2×Dic3—82no—
629C2×Dic3—82no—
630D12—24no—
631D12—22no—
632D12C2×#4114yes—
633C4×D3—28no—
634C4×D3—28no—
635C4×D3—84no—
636C4×D3—84no—
637Dic6—24no—
638Dic6—22no—
639Dic6C2×#4114yes—
640C3⋊C8—22no—
641C3⋊C8—22no—
642C3⋊C8—24no—
643C24—61no—
644C24C2×#6711yescharacteristic
645#41—24no—
646#41—38no—
647#41—64no—
648#41—64no—
649#41—68no—
650#41—68no—
651#41—64no—
652C2×Q8—21no—
653C2×Q8—22no—
654C2×Q8—24no—
655C2×Q8—32no—
656C2×Q8—64no—
657C2×Q8—61no—
658C2×Q8C23×D312yes—
659C2×Q8C23×D311yescharacteristic
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—32no—
664C2×D4—64no—
665C2×D4—68no—
666C2×D4—62no—
667C2×D4—62no—
668C2×D4—61no—
669C2×D4C23×D311yescharacteristic
670C22×C4—24no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—22no—
675C22×C4—68no—
676C22×C4—61no—
677C22×C4—62no—
678C22×C4—62no—
679C22×C4—62no—
680C22×C4—62no—
681C22×C4—62no—
682C22×C4—64no—
683C22×C4—64no—
684C22×C4—244no—
685C22×C4—242no—
686C22×C4C2×#6712yes—
687C22×C4C2×#6711yescharacteristic
688C22×C4C2×#6711yescharacteristic
689C22×C4C2×#6711yescharacteristic
690C22×C4C2×#6712yes—
691C22×C4C23×D311yescharacteristic
692C22×C4C23×D311yescharacteristic
693C22×C4C23×D311yescharacteristic
694Q16—64no—
695Q16—68no—
696SD16—64no—
697SD16—64no—
698SD16—68no—
699D8—64no—
700M16—64no—
701C2×C8—32no—
702C2×C8—34no—
703C2×C8—32no—
704C2×C8—64no—
705C4⋊C4—21no—
706C4⋊C4—22no—
707C4⋊C4—22no—
708C4⋊C4—22no—
709C4⋊C4—22no—
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—21no—
715C4⋊C4—22no—
716C4⋊C4—21no—
717C4⋊C4—22no—
718C4⋊C4—34no—
719C4⋊C4—62no—
720C4⋊C4—62no—
721C4⋊C4—62no—
722C4⋊C4—64no—
723C4⋊C4—64no—
724C4⋊C4C2×#6711yescharacteristic
725C4⋊C4C2×#6712yes—
726C4⋊C4C2×#6711yescharacteristic
727C4⋊C4C2×#6711yescharacteristic
728C4⋊C4C2×#6711yescharacteristic
729C4⋊C4C2×#6712yes—
730C4⋊C4C23×D311yescharacteristic
731C4⋊C4C23×D312yes—
732C4⋊C4C23×D311yescharacteristic
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—21no—
742C22⋊C4—22no—
743C22⋊C4—64no—
744C22⋊C4—64no—
745C22⋊C4C2×#6712yes—
746C22⋊C4C2×#6712yes—
747C22⋊C4C2×#6712yes—
748C22⋊C4C2×#6712yes—
749C42—22no—
750C42—22no—
751C42—22no—
752C42—21no—
753C42—64no—
754C42—64no—
755C42C2×#6712yes—
756C42C2×#6712yes—
757C42C23×D312yes—
758C42C23×D312yes—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—21no—
765C22×C3—21no—
766C22×C3—44no—
767C22×C3—41no—
768C22×C3—41no—
769C22×C3—41no—
770C22×C3#52512yes—
771C22×C3#57812yes—
772C22×C3C23×D411yescharacteristic
773C2×D3—24no—
774C2×D3—48no—
775C2×D3—42no—
776C2×D3—42no—
777C3×C4—22no—
778C3×C4—22no—
779C3×C4—21no—
780C3×C4—21no—
781C3×C4—22no—
782C3×C4—22no—
783C3×C4—42no—
784C3×C4—41no—
785C3×C4—41no—
786C3×C4—42no—
787C3×C4—41no—
788C3×C4#52512yes—
789C3×C4C22×#4112yes—
790Dic3—24no—
791Dic3—44no—
792C23—22no—
793C23—22no—
794C23—21no—
795C23—41no—
796C23—64no—
797C23—62no—
798C23—122no—
799C23—122no—
800C23C22×#6711yescharacteristic
801C23C22×#6711yescharacteristic
802C23C22×#6711yescharacteristic
803Q8—24no—
804Q8—22no—
805Q8—34no—
806Q8—42no—
807Q8—64no—
808Q8—62no—
809Q8—82no—
810D4—22no—
811D4—34no—
812D4—42no—
813D4—42no—
814D4—64no—
815D4—68no—
816D4—68no—
817D4—62no—
818D4—81no—
819C2×C4—22no—
820C2×C4—24no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—22no—
828C2×C4—21no—
829C2×C4—22no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—68no—
834C2×C4—64no—
835C2×C4—62no—
836C2×C4—68no—
837C2×C4—64no—
838C2×C4—82no—
839C2×C4—81no—
840C2×C4—124no—
841C2×C4—244no—
842C2×C4—244no—
843C2×C4—242no—
844C2×C4—242no—
845C2×C4D3×#4114yes—
846C2×C4C22×#6712yes—
847C2×C4C22×#6712yes—
848C2×C4C22×#6712yes—
849C2×C4C22×#6711yescharacteristic
850C2×C4C22×#6712yes—
851C2×C4C22×#6711yescharacteristic
852C2×C4C22×#6711yescharacteristic
853C2×C4C24×D311yescharacteristic
854C8—62no—
855C8—62no—
856C8—64no—
857C2×C3—22no—
858C2×C3—22no—
859C2×C3—41no—
860C2×C3—81no—
861C2×C3C2×#52511yescharacteristic
862C2×C3C2×#57811yescharacteristic
863C2×C3#358511yescharacteristic
864D3—44no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—44no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—64no—
877C22—128no—
878C22—122no—
879C22—122no—
880C22#582812yes—
881C22#583812yes—
882C22C23×#6711yescharacteristic
883C4—22no—
884C4—22no—
885C4—21no—
886C4—21no—
887C4—22no—
888C4—22no—
889C4—42no—
890C4—41no—
891C4—41no—
892C4—42no—
893C4—41no—
894C4—64no—
895C4—124no—
896C4#582812yes—
897C4C2×D3×#4112yes—
898C3#6058911yescharacteristic, complemented, Sylow
899C2—22no—
900C2—22no—
901C2—41no—
902C2—81no—
903C2—124no—
904C2C2×#582811yescharacteristic
905C2C2×#583811yescharacteristic
906C2#8729811yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3495C2
socleC22×C3C23×D4
prime radical#82926C2
hypercenter#3495D3
hypocenterC3#60589
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3495

Complements

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

NH ≅ G/Ntype
1. C3×#3495C2semidirect
2. C2×#5523C2semidirect
3. #83475C2semidirect
4. #83461C2semidirect
5. #83446C2semidirect
6. #83406C2semidirect
7. #83368C2semidirect
8. #83353C2semidirect
9. #83153C2semidirect
10. #83141C2semidirect
12. #82914C2semidirect
13. #82735C2semidirect
14. C2×#5044C2semidirect
15. #82557C2semidirect
16. #82547C2semidirect
17. #82210C2semidirect
26. C3×#544C22semidirect
27. C3×#542C22semidirect
28. C3×#541C22semidirect
29. C3×#536C22semidirect
34. C3×#520C22semidirect
35. C3×#519C22semidirect
51. #5232C22semidirect
52. C2×#835C22semidirect
55. #5091C22semidirect
56. #5090C22semidirect
57. #5087C22semidirect
58. #5083C22semidirect
59. #5066C22semidirect
60. #5063C22semidirect
61. #5057C22semidirect
62. #5054C22semidirect
72. #5044C22semidirect
73. #5043C22semidirect
78. #5033C22semidirect
79. #5030C22semidirect
80. C4×#216C22semidirect
81. C4×#216C22semidirect
82. #5026C22semidirect
83. #5026C22semidirect
84. C4×#215C22semidirect
85. #5018C22semidirect
86. C4×#213C22semidirect
88. #5000C22semidirect
89. #4999C22semidirect
90. #4997C22semidirect
91. #4995C22semidirect
93. C2×#807C22semidirect
96. #3495D3semidirect
258. #544C2×D3semidirect
259. #542C2×D3semidirect
260. #541C2×D3semidirect
261. #536C2×D3semidirect
272. #520C2×D3semidirect
273. #519C2×D3semidirect
898. C3#60589semidirect

Maximal subgroups

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

subgroupindex
C3×#34952
C2×#55232
#834752
#834612
#834462
#834062
#833682
#833532
#831532
#831412
#829262
#829142
#827352
C2×#50442
#825572
#825472
#822102
#605893