Finite Group Databasebeta

← #11664218

Subgroups — #11664218

Order 768.

1990 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×#3509C211yesmaximal, characteristic, complemented
2C4×#1010C211yesmaximal, characteristic
3#83451C214yesmaximal, complemented
4#83446C214yesmaximal, complemented
5#83411C212yesmaximal
6#83397C212yesmaximal, complemented
7#83369C212yesmaximal, complemented
8#83368C212yesmaximal, complemented
9#83367C211yesmaximal, characteristic, complemented
10#83354C212yesmaximal, complemented
11#83352C212yesmaximal, complemented
12#83349C211yesmaximal, characteristic, complemented
13C2×#5090C211yesmaximal, characteristic, complemented
14#83209C211yesmaximal, characteristic, complemented
15#82549C212yesmaximal, complemented
16#82547C212yesmaximal, complemented
17#82515C211yesmaximal, characteristic, complemented
18#60594—31nomaximal, Sylow
19C2×#1010C2211yescharacteristic
20C3×#557—21no—
21C3×#557—21no—
22C3×#556—21no—
23C3×#556—21no—
24C3×#552—22no—
25C3×#552—22no—
26C3×#541C2214yes—
27C3×#536C2212yes—
28C3×#533C2212yes—
29C3×#533C2212yes—
30C3×#533C2211yescharacteristic
31C2×C3×C4⋊Q8C2211yescharacteristic
32C3×#519C2212yes—
33C3×C4×#41C2211yescharacteristic
34#5827C2211yescharacteristic
35C22×#216C2212yes—
36C2×#942C2212yes—
37#5572—21no—
38C4×D3×Q8—21no—
39#5546—22no—
40#5546—21no—
41C4×#237—22no—
42C4×#237—21no—
43#5523C2211yescharacteristic
44#5523C2212yes—
45#5516C2211yescharacteristic
46#5516C2212yes—
47C4×#235C2211yescharacteristic
48C4×#235C2212yes—
49C2×C4×Dic6C2211yescharacteristic
50C2×C4×Dic6C2212yes—
51#5234C2212yes—
52#5225C2212yes—
53C2×#835C2212yes—
54#5094C2211yescharacteristic
55#5094C2212yes—
56#5091C2211yescharacteristic
57#5091C2212yes—
58#5090C2212yes—
59#5090C2212yes—
60#5090C2212yes—
61#5090C2212yes—
62#5090C2214yes—
63#5087C2211yescharacteristic
64#5084C2211yescharacteristic
65#5083C2212yes—
66#5083C2212yes—
67#5066C2212yes—
68#5063C2212yes—
69#5063C2214yes—
70#5050C2214yes—
71#5050C2214yes—
72#5047C2214yes—
73#5047C2214yes—
74#5045C2214yes—
75#5045C2214yes—
76#5044C2214yes—
77#5043C2214yes—
78#5030C2214yes—
79#5030C2214yes—
80#5030C2214yes—
81C4×#216C2214yes—
82C4×#216C2214yes—
83C4×#216C2214yes—
84#5026C2214yes—
85C4×#215C2214yes—
86#5004C2212yes—
87#5002C2212yes—
88#5000C2214yes—
89#4998C2212yes—
90#4997C2212yes—
91#4995C2212yes—
92#4926C2212yes—
93#4925C2212yes—
94#4924C2211yescharacteristic
95C2×C4⋊(C3⋊C8)C2211yescharacteristic
96#3509D311yescharacteristic, complemented
97C4×2−1+4—31no—
98#3127—34no—
99#3120—34no—
100#3116—32no—
101#3113—32no—
102#3107—32no—
103#3104—32no—
104#3097—32no—
105#3078—31no—
106#3076—31no—
107#3039—31no—
108C2×#462—31no—
109#3011—32no—
110#2950—32no—
111#2947—32no—
112#2925—31no—
113C2×C3×#41C2311yescharacteristic
114C22×C3×Q8C2312yes—
115#1010—24no—
116#1010—24no—
117C2×D3×Q8—21no—
118C2×#237—22no—
119C2×#237—21no—
120C2×#235C2312yes—
121C2×#235C2311yescharacteristic
122C22×Dic6C2312yes—
123C22×Dic6C2311yescharacteristic
124C3×C4⋊Q8—22no—
125C3×C4⋊Q8—21no—
126C3×C4⋊Q8—21no—
127C3×C4⋊Q8C2312yes—
128C3×C4⋊Q8C2312yes—
129C3×C4⋊Q8C2311yescharacteristic
130C3×C4⋊Q8C2311yescharacteristic
131C3×#126—24no—
132C3×#126—24no—
133C3×#125—24no—
134C3×#125—24no—
135C3×#125—22no—
136C3×#125—22no—
137C3×#125C2312yes—
138C3×#124—22no—
139C3×#123—24no—
140C3×C22⋊Q8—21no—
141C3×C22⋊Q8—21no—
142C3×C22⋊Q8—22no—
143C3×C22⋊Q8—22no—
144C3×C22⋊Q8C2314yes—
145C3×C22⋊Q8C2314yes—
146C3×C4×Q8—22no—
147C3×C4×Q8—22no—
148C3×C4×Q8—22no—
149C3×C4×Q8—22no—
150C3×C4×Q8—21no—
151C3×C4×Q8—21no—
152C3×C4×Q8D411yescharacteristic
153C3×C4×Q8D411yescharacteristic
154C3×C4×Q8C2314yes—
155C3×C4×Q8C2314yes—
156C3×C4×D4D412yes—
157C3×C4×D4D411yescharacteristic
158C3×C4×D4D412yes—
159C3×C4×D4D411yescharacteristic
160C3×#117—22no—
161C3×#117—22no—
162C3×#117—24no—
163C3×#117C2312yes—
164C3×#117C2311yescharacteristic
165C3×#117C2312yes—
166C2×C3×C4⋊C4—21no—
167C2×C3×C4⋊C4—21no—
168C2×C3×C42C2311yescharacteristic
169C2×C3×C42C2312yes—
170Q8×Dic3—21no—
171C2×#216—28no—
172C2×#216C2314yes—
173C2×#216C2314yes—
174C2×#216C2314yes—
175#942—28no—
176C2×#215C2314yes—
177D4×Dic3—22no—
178D4×Dic3—21no—
179C4×#67—21no—
180C4×#67—22no—
181C4×#67—21no—
182C4×#67—22no—
183#926C2311yescharacteristic
184#926C2312yes—
185C2×C4⋊Dic3C2311yescharacteristic
186C2×C4⋊Dic3C2312yes—
187C2×Dic3⋊C4—21no—
188C2×Dic3⋊C4—22no—
189C2×C4×Dic3—21no—
190C2×C4×Dic3—22no—
191C2×#208C2312yes—
192C22×C3⋊C8C2312yes—
193#892—21no—
194#892—22no—
195D3×C4⋊C4—21no—
196D3×C4⋊C4—22no—
197#887—21no—
198#887—22no—
199#887—21no—
200#887—22no—
201#67⋊C4—22no—
202#67⋊C4—22no—
203#67⋊C4—22no—
204#877—22no—
205#877—22no—
206#877—22no—
207C4×D12C2311yescharacteristic
208C4×D12C2312yes—
209C4×D12C2311yescharacteristic
210#872—22no—
211#872—21no—
212C42×D3—22no—
213C42×D3—21no—
214C4×Dic6—22no—
215C4×Dic6—21no—
216C4×Dic6—22no—
217C4×Dic6—21no—
218C4×Dic6C2312yes—
219C4×Dic6C2311yescharacteristic
220C4×Dic6C2312yes—
221C4×Dic6C2312yes—
222C4×Dic6C2312yes—
223C4×Dic6C2312yes—
224C4×Dic6C2311yescharacteristic
225#835C2314yes—
226#835C2314yes—
227#835C2314yes—
228#835C2314yes—
229#830C2314yes—
230#830C2314yes—
231#810C2312yes—
232#810C2312yes—
233#810C2314yes—
234#810C2314yes—
235#809C2312yes—
236#809C2312yes—
237#808C2314yes—
238#808C2312yes—
239#808C2312yes—
240#807C2314yes—
241#807C2312yes—
242#807C2312yes—
243C4⋊(C3⋊C8)C2311yescharacteristic
244C4⋊(C3⋊C8)C2311yescharacteristic
245C4⋊(C3⋊C8)C2312yes—
246C4⋊(C3⋊C8)C2312yes—
247C4⋊(C3⋊C8)C2312yes—
248#803C2314yes—
249C4×C3⋊C8C2314yes—
250C2×2−1+4—31no—
251C2×#137—32no—
252C22×Q16—32no—
253#557—21no—
254#557—21no—
255#556—21no—
256#556—21no—
257#552—22no—
258#552—22no—
259#541C2×D314yes—
260#536C2×D312yes—
261#533C2×D312yes—
262#533C2×D312yes—
263#533C2×D311yescharacteristic
264C2×C4⋊Q8C2×D311yescharacteristic
265#520—31no—
266#520—32no—
267#520—31no—
268#520—62no—
269#520—61no—
270#519—32no—
271#519—31no—
272#519—61no—
273#519C2×D312yes—
274C4×#41—31no—
275C4×#41—32no—
276C4×#41—62no—
277C4×#41—61no—
278C4×#41C2×D311yescharacteristic
279C2×C4×Q8—31no—
280C2×C4×Q8—32no—
281C2×C4×Q8—61no—
282#485—34no—
283#485—34no—
284#484—34no—
285#483—34no—
286#479—32no—
287#479—34no—
288#478—32no—
289#477—31no—
290#477—32no—
291#476—31no—
292#475—31no—
293#475—32no—
294#474—31no—
295#462—32no—
296#462—32no—
297#462—32no—
298#462—34no—
299#462—32no—
300#461—32no—
301#461—32no—
302#452—34no—
303#452—34no—
304#451—34no—
305#451—34no—
306#441—34no—
307#441—34no—
308#441—34no—
309#440—34no—
310C4×Q16—34no—
311C4×Q16—34no—
312C4×Q16—34no—
313C4×SD16—34no—
314#433—34no—
315#432—32no—
316#431—32no—
317#428—32no—
318#427—32no—
319#423—31no—
320C2×C4⋊C8—31no—
321#419—32no—
322#419—32no—
323#416—32no—
324C2×#103—32no—
325#408—32no—
326#405—32no—
327C3×#41—22no—
328C3×#41—22no—
329C2×C3×Q8—21no—
330C2×C3×Q8—21no—
331C2×C3×Q8—22no—
332C2×C3×Q8—24no—
333C2×C3×Q8—24no—
334C2×C3×Q8C2×D411yescharacteristic
335C2×C3×Q8C2414yes—
336C2×C3×D4C2×D412yes—
337C2×C3×D4C2×D411yescharacteristic
338C22×C3×C4—22no—
339C22×C3×C4C2×D411yescharacteristic
340C22×C3×C4C2×D412yes—
341C22×C3×C4C2×D411yescharacteristic
342C22×C3×C4C2×D412yes—
343C22×C3×C4C2412yes—
344C22×C3×C4C2411yescharacteristic
345C2×#67—22no—
346C2×#67—21no—
347C22×Dic3—22no—
348C22×Dic3—21no—
349C22×Dic3—22no—
350C22×Dic3—21no—
351D3×Q8—28no—
352#237—216no—
353#237—28no—
354#235—22no—
355#235—24no—
356#235—24no—
357#235#4114yes—
358C2×D12C2411yescharacteristic
359C2×C4×D3—22no—
360C2×C4×D3—21no—
361C2×C4×D3—21no—
362C2×C4×D3—22no—
363C2×C4×D3—21no—
364C2×Dic6—22no—
365C2×Dic6—21no—
366C2×Dic6—22no—
367C2×Dic6—24no—
368C2×Dic6—24no—
369C2×Dic6#4114yes—
370C2×Dic6C2411yescharacteristic
371C2×Dic6C2412yes—
372C3×C4⋊C4—22no—
373C3×C4⋊C4—22no—
374C3×C4⋊C4—22no—
375C3×C4⋊C4—22no—
376C3×C4⋊C4—21no—
377C3×C4⋊C4—21no—
378C3×C4⋊C4—24no—
379C3×C4⋊C4—24no—
380C3×C4⋊C4—22no—
381C3×C4⋊C4—22no—
382C3×C4⋊C4—24no—
383C3×C4⋊C4—24no—
384C3×C4⋊C4C2×D411yescharacteristic
385C3×C4⋊C4C2×D412yes—
386C3×C4⋊C4C2×D411yescharacteristic
387C3×C4⋊C4C2×D412yes—
388C3×C4⋊C4C2412yes—
389C3×C4⋊C4C2412yes—
390C3×C22⋊C4—22no—
391C3×C22⋊C4—24no—
392C3×C22⋊C4—24no—
393C3×C22⋊C4C2×D412yes—
394C3×C22⋊C4C2×D412yes—
395C3×C22⋊C4C2×D412yes—
396C3×C42—24no—
397C3×C42—24no—
398C3×C42—22no—
399C3×C42C2×D412yes—
400C3×C42C2×D411yescharacteristic
401C3×C42C2×D412yes—
402C3×C42C2×D411yescharacteristic
403C3×C42C2412yes—
404C3×C42C2411yescharacteristic
405C3×C42C2411yescharacteristic
406#217—22no—
407#217—21no—
408#216—28no—
409#216—28no—
410#216—28no—
411#215—28no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—22no—
414(C2×D3)⋊C4—21no—
415C4⋊Dic3—22no—
416C4⋊Dic3—21no—
417C4⋊Dic3C2412yes—
418C4⋊Dic3C2411yescharacteristic
419C4⋊Dic3C2411yescharacteristic
420Dic3⋊C4—21no—
421Dic3⋊C4—22no—
422Dic3⋊C4—22no—
423Dic3⋊C4—22no—
424Dic3⋊C4—22no—
425Dic3⋊C4—22no—
426Dic3⋊C4—21no—
427C4×Dic3—21no—
428C4×Dic3—22no—
429C4×Dic3—22no—
430C4×Dic3—22no—
431C4×Dic3—22no—
432C4×Dic3—22no—
433C4×Dic3—21no—
434C4×Dic3—22no—
435C4×Dic3—21no—
436#208—24no—
437C2×C3⋊C8—24no—
438C2×C3⋊C8C2412yes—
439C2×C3⋊C8C2414yes—
440C2×C3⋊C8C2412yes—
4412−1+4—64no—
4422−1+4—64no—
443C2×#41—31no—
444C2×#41—32no—
445C2×#41—62no—
446C2×#41—61no—
447C2×#41C22×D311yescharacteristic
448C22×Q8—31no—
449C22×Q8—32no—
450C22×Q8—61no—
451C22×Q8C22×D312yes—
452#137—68no—
453C2×Q16—34no—
454C2×Q16—34no—
455C2×Q16—34no—
456C2×Q16—68no—
457C2×SD16—34no—
458C2×M16—32no—
459C22×C8—32no—
460C4⋊Q8—22no—
461C4⋊Q8—21no—
462C4⋊Q8—21no—
463C4⋊Q8C22×D312yes—
464C4⋊Q8C22×D312yes—
465C4⋊Q8C22×D311yescharacteristic
466C4⋊Q8C22×D311yescharacteristic
467#126—24no—
468#126—24no—
469#125—24no—
470#125—24no—
471#125—22no—
472#125—22no—
473#125C22×D312yes—
474#124—22no—
475#123—24no—
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478C22⋊Q8—22no—
479C22⋊Q8—22no—
480C22⋊Q8C22×D314yes—
481C22⋊Q8C22×D314yes—
482C4×Q8—22no—
483C4×Q8—22no—
484C4×Q8—22no—
485C4×Q8—22no—
486C4×Q8—21no—
487C4×Q8—21no—
488C4×Q8—32no—
489C4×Q8—31no—
490C4×Q8—32no—
491C4×Q8—32no—
492C4×Q8—32no—
493C4×Q8—32no—
494C4×Q8—31no—
495C4×Q8—61no—
496C4×Q8—61no—
497C4×Q8—62no—
498C4×Q8—61no—
499C4×Q8—62no—
500C4×Q8—62no—
501C4×Q8—61no—
502C4×Q8—62no—
503C4×Q8—61no—
504C4×Q8#6711yescharacteristic
505C4×Q8#6711yescharacteristic
506C4×Q8C22×D314yes—
507C4×Q8C22×D314yes—
508C4×D4—31no—
509C4×D4—32no—
510C4×D4—31no—
511C4×D4—62no—
512C4×D4—61no—
513C4×D4—61no—
514C4×D4—62no—
515C4×D4—61no—
516C4×D4—62no—
517C4×D4—62no—
518C4×D4—62no—
519C4×D4—62no—
520C4×D4#6712yes—
521C4×D4#6711yescharacteristic
522C4×D4#6712yes—
523C4×D4#6711yescharacteristic
524#117—22no—
525#117—22no—
526#117—24no—
527#117—31no—
528#117—32no—
529#117—61no—
530#117—62no—
531#117—62no—
532#117—62no—
533#117—62no—
534#117—62no—
535#117—61no—
536#117C22×D312yes—
537#117C22×D311yescharacteristic
538#117C22×D312yes—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—31no—
542C2×C4⋊C4—32no—
543C2×C4⋊C4—61no—
544C2×C4⋊C4—62no—
545C2×C4⋊C4—61no—
546C2×C4⋊C4—62no—
547C2×C42—61no—
548C2×C42—62no—
549C2×C42—62no—
550C2×C42—61no—
551C2×C42C22×D311yescharacteristic
552C2×C42C22×D312yes—
553#107—32no—
554#107—32no—
555#107—34no—
556#106—32no—
557#106—32no—
558#106—34no—
559C4⋊C8—31no—
560C4⋊C8—31no—
561C4⋊C8—32no—
562C4⋊C8—32no—
563C4⋊C8—32no—
564#103—34no—
565#103—34no—
566#103—34no—
567#103—34no—
568#103—32no—
569#103—32no—
570#103—34no—
571#103—34no—
572#102—32no—
573#102—32no—
574C22⋊C8—34no—
575C22⋊C8—34no—
576#97—34no—
577C4×C8—34no—
578C23×C3C22×D412yes—
579C23×C3C22×D411yescharacteristic
580C22×D3—21no—
581C3×Q8—22no—
582C3×Q8—24no—
583C3×Q8—24no—
584C3×Q8—42no—
585C3×Q8—44no—
586C3×Q8—42no—
587C3×D4—24no—
588C3×D4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—24no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
595C2×C3×C4—24no—
596C2×C3×C4—41no—
597C2×C3×C4—42no—
598C2×C3×C4—44no—
599C2×C3×C4C22×D412yes—
600C2×C3×C4C22×D411yescharacteristic
601C2×C3×C4C22×D412yes—
602C2×C3×C4C22×D411yescharacteristic
603C2×C3×C4C22×D412yes—
604C2×C3×C4C22×D411yescharacteristic
605C2×C3×C4C22×D411yescharacteristic
606C2×C3×C4C22×D411yescharacteristic
607C2×C3×C4C2×#4112yes—
608C2×C3×C4C2×#4112yes—
609C2×C3×C4C2511yescharacteristic
610#67—28no—
611#67—24no—
612C2×Dic3—28no—
613C2×Dic3—24no—
614C2×Dic3—21no—
615C2×Dic3—22no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—22no—
619C2×Dic3—81no—
620C2×Dic3—82no—
621D12—21no—
622D12C2×#4112yes—
623C4×D3—28no—
624C4×D3—24no—
625C4×D3—42no—
626C4×D3—82no—
627C4×D3—81no—
628Dic6—28no—
629Dic6—24no—
630Dic6—22no—
631Dic6—21no—
632Dic6C2×#4112yes—
633Dic6C2×#4114yes—
634C3⋊C8—22no—
635C3⋊C8—22no—
636C3⋊C8—24no—
637#41—22no—
638#41—22no—
639#41—34no—
640#41—64no—
641#41—64no—
642#41—616no—
643#41—68no—
644#41—62no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—22no—
648C2×Q8—24no—
649C2×Q8—24no—
650C2×Q8—34no—
651C2×Q8—32no—
652C2×Q8—31no—
653C2×Q8—64no—
654C2×Q8—64no—
655C2×Q8—68no—
656C2×Q8—62no—
657C2×Q8—62no—
658C2×Q8—61no—
659C2×Q8C2×#6711yescharacteristic
660C2×Q8C23×D314yes—
661C2×D4—31no—
662C2×D4—62no—
663C2×D4—61no—
664C2×D4C2×#6712yes—
665C2×D4C2×#6711yescharacteristic
666C22×C4—22no—
667C22×C4—62no—
668C22×C4—61no—
669C22×C4—62no—
670C22×C4—61no—
671C22×C4—62no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—62no—
675C22×C4—61no—
676C22×C4C2×#6711yescharacteristic
677C22×C4C2×#6712yes—
678C22×C4C2×#6711yescharacteristic
679C22×C4C2×#6712yes—
680C22×C4C23×D312yes—
681C22×C4C23×D311yescharacteristic
682Q16—68no—
683Q16—68no—
684Q16—68no—
685SD16—68no—
686M16—64no—
687C2×C8—32no—
688C2×C8—34no—
689C2×C8—32no—
690C2×C8—64no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4—22no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—24no—
698C4⋊C4—24no—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4—24no—
702C4⋊C4—24no—
703C4⋊C4—32no—
704C4⋊C4—31no—
705C4⋊C4—31no—
706C4⋊C4—62no—
707C4⋊C4—61no—
708C4⋊C4—62no—
709C4⋊C4—62no—
710C4⋊C4—62no—
711C4⋊C4—62no—
712C4⋊C4—61no—
713C4⋊C4—62no—
714C4⋊C4—61no—
715C4⋊C4C2×#6711yescharacteristic
716C4⋊C4C2×#6712yes—
717C4⋊C4C2×#6711yescharacteristic
718C4⋊C4C2×#6712yes—
719C4⋊C4C23×D312yes—
720C4⋊C4C23×D312yes—
721C22⋊C4—22no—
722C22⋊C4—24no—
723C22⋊C4—24no—
724C22⋊C4—62no—
725C22⋊C4—61no—
726C22⋊C4—61no—
727C22⋊C4—62no—
728C22⋊C4—61no—
729C22⋊C4C2×#6712yes—
730C22⋊C4C2×#6712yes—
731C22⋊C4C2×#6712yes—
732C42—24no—
733C42—24no—
734C42—22no—
735C42—62no—
736C42—61no—
737C42—62no—
738C42—61no—
739C42—62no—
740C42—61no—
741C42—62no—
742C42—62no—
743C42—62no—
744C42C2×#6712yes—
745C42C2×#6711yescharacteristic
746C42C2×#6712yes—
747C42C2×#6711yescharacteristic
748C42C23×D312yes—
749C42C23×D311yescharacteristic
750C42C23×D311yescharacteristic
751C22×C3—21no—
752C22×C3—21no—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3#52512yes—
757C22×C3C23×D411yescharacteristic
758C2×D3—22no—
759C2×D3—41no—
760C2×D3—41no—
761C3×C4—22no—
762C3×C4—21no—
763C3×C4—21no—
764C3×C4—22no—
765C3×C4—22no—
766C3×C4—21no—
767C3×C4—42no—
768C3×C4—44no—
769C3×C4—42no—
770C3×C4#52512yes—
771C3×C4#57812yes—
772C3×C4C22×#4111yescharacteristic
773C3×C4C22×#4111yescharacteristic
774Dic3—22no—
775Dic3—24no—
776Dic3—42no—
777Dic3—41no—
778Dic3—41no—
779C23—61no—
780C23C22×#6712yes—
781C23C22×#6711yescharacteristic
782Q8—22no—
783Q8—24no—
784Q8—24no—
785Q8—34no—
786Q8—32no—
787Q8—42no—
788Q8—44no—
789Q8—42no—
790Q8—68no—
791Q8—62no—
792Q8—61no—
793Q8—64no—
794D4—24no—
795D4—22no—
796D4—32no—
797D4—68no—
798D4—64no—
799D4—61no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—24no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—24no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—44no—
810C2×C4—68no—
811C2×C4—68no—
812C2×C4—62no—
813C2×C4—61no—
814C2×C4—64no—
815C2×C4—64no—
816C2×C4—61no—
817C2×C4—62no—
818C2×C4—61no—
819C2×C4—122no—
820C2×C4—242no—
821C2×C4—241no—
822C2×C4—241no—
823C2×C4—242no—
824C2×C4D3×#4112yes—
825C2×C4D3×#4112yes—
826C2×C4C22×#6712yes—
827C2×C4C22×#6712yes—
828C2×C4C22×#6711yescharacteristic
829C2×C4C22×#6712yes—
830C2×C4C22×#6711yescharacteristic
831C2×C4C22×#6711yescharacteristic
832C2×C4C22×#6711yescharacteristic
833C2×C4C22×#6711yescharacteristic
834C2×C4C24×D311yescharacteristic
835C8—62no—
836C8—62no—
837C8—64no—
838C2×C3—22no—
839C2×C3—42no—
840C2×C3C2×#52511yescharacteristic
841C2×C3C2×#57811yescharacteristic
842C2×C3#358611yescharacteristic
843D3—42no—
844C22—21no—
845C22—21no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—62no—
850C22—121no—
851C22—121no—
852C22#582812yes—
853C22C23×#6711yescharacteristic
854C4—22no—
855C4—21no—
856C4—22no—
857C4—21no—
858C4—22no—
859C4—21no—
860C4—44no—
861C4—42no—
862C4—42no—
863C4—64no—
864C4—62no—
865C4—122no—
866C4—121no—
867C4—121no—
868C4#582812yes—
869C4#583812yes—
870C4C2×D3×#4111yescharacteristic
871C4C2×D3×#4111yescharacteristic
872C3#6059411yescharacteristic, complemented, Sylow
873C2—22no—
874C2—42no—
875C2—122no—
876C2C2×#582811yescharacteristic
877C2#8728711yescharacteristic
878C2C2×#583811yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3509C2
socleC22×C3C23×D4
prime radicalC2×#1010C22
hypercenter#3509D3
hypocenterC3#60594
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3509

Complements

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

NH ≅ G/Ntype
1. C3×#3509C2semidirect
3. #83451C2semidirect
4. #83446C2semidirect
6. #83397C2semidirect
7. #83369C2semidirect
8. #83368C2semidirect
9. #83367C2semidirect
10. #83354C2semidirect
11. #83352C2semidirect
12. #83349C2semidirect
13. C2×#5090C2semidirect
14. #83209C2semidirect
15. #82549C2semidirect
16. #82547C2semidirect
17. #82515C2semidirect
96. #3509D3semidirect
872. C3#60594semidirect

Maximal subgroups

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

subgroupindex
C3×#35092
C4×#10102
#834512
#834462
#834112
#833972
#833692
#833682
#833672
#833542
#833522
#833492
C2×#50902
#832092
#825492
#825472
#825152
#605943