Finite Group Databasebeta

← #11664266

Subgroups — #11664266

Order 768.

2130 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2#85850C211yesmaximal, characteristic, complemented
3#84102C212yesmaximal, complemented
4#82569C214yesmaximal, complemented
5#82567C212yesmaximal, complemented
6#82557C212yesmaximal, complemented
7#82541C214yesmaximal, complemented
8#82537C212yesmaximal, complemented
9#82534C212yesmaximal, complemented
10#82531C212yesmaximal, complemented
11#82525C211yesmaximal, characteristic, complemented
12#82515C211yesmaximal, characteristic, complemented
13#82508C211yesmaximal, characteristic, complemented
14#82315C212yesmaximal, complemented
15#82308C212yesmaximal, complemented
16#82307C211yesmaximal, characteristic, complemented
17C2×#5007C211yesmaximal, characteristic, complemented
18#60596—31nomaximal, Sylow
19C2×C3×H(5,𝔽2)C2211yescharacteristic
20C3×#520—21no—
21C3×#520C2211yescharacteristic
22C3×#520C2212yes—
23C3×#520C2211yescharacteristic
24C3×#518—21no—
25C3×#518—22no—
26C3×#518C2211yescharacteristic
27C3×#518C2212yes—
28C3×C4×#41—21no—
29C3×C4×#41C2211yescharacteristic
30C3×C4×#41C2212yes—
31C3×C4×#41C2211yescharacteristic
32C2×C3×C4×D4—21no—
33C2×C3×C4×D4—22no—
34C2×C3×C4×D4C2211yescharacteristic
35C2×C3×C4×D4C2212yes—
36#5833C2212yes—
37C2×#950C2212yes—
38C2×#932C2212yes—
39#5584—21no—
40#5579—21no—
41#5565—22no—
42#5563—21no—
43#5552—22no—
44#5551—21no—
45#5534C2214yescomplemented
46#5523C2212yescomplemented
47#5477C2211yescharacteristic, complemented
48#5477C2212yescomplemented
49#5470C2212yescomplemented
50C2×#869C2211yescharacteristic, complemented
51#5239C2214yes—
52#5238C2214yes—
53#5234C2212yes—
54#5232C2212yes—
55#5218C2214yes—
56#5217C2214yes—
57C2×#832C2212yes—
58#5031C2211yescharacteristic, complemented
59C4×#216C2214yescomplemented
60#5028C2212yescomplemented
61#5027C2211yescharacteristic, complemented
62#5026C2214yescomplemented
63#5021C2212yescomplemented
64#5020C2212yescomplemented
65#5019C2211yescharacteristic, complemented
66#5019C2212yescomplemented
67#5018C2214yescomplemented
68#5018C2214yescomplemented
69C4×#214C2214yescomplemented
70#5016C2212yescomplemented
71#5016C2214yescomplemented
72#5015C2211yescharacteristic, complemented
73#5015C2212yescomplemented
74#5014C2214yescomplemented
75C4×#213C2214yescomplemented
76C4×#213C2214yescomplemented
77#5008C2212yescomplemented
78#5007C2212yescomplemented
79#5007C2212yescomplemented
80#5007C2212yescomplemented
81#5007C2214yescomplemented
82#5003C2214yescomplemented
83#5002C2212yescomplemented
84#5000C2214yescomplemented
85#4997C2212yescomplemented
86#4996C2214yescomplemented
87#4995C2212yescomplemented
88#4970C2214yescomplemented
89#4967C2214yescomplemented
90#4966C2212yescomplemented
91C2×#807C2212yescomplemented
92#4926C2212yescomplemented
93#4925C2212yescomplemented
94#4924C2211yescharacteristic, complemented
95C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
96#3511—31no—
97C4×H(5,𝔽2)D311yescharacteristic, complemented
98#3124—34no—
99#3118—34no—
100#3115—32no—
101#3110—32no—
102#3107—32no—
103#3100—32no—
104#3098—32no—
105#3079—31no—
106C2×#474—31no—
107#3036—31no—
108#3035—31no—
109#3012—32no—
110#2951—32no—
111#2946—32no—
112#2925—31no—
113C3×H(5,𝔽2)—24no—
114C3×H(5,𝔽2)—24no—
115C2×C3×#41—21no—
116C2×C3×#41C2312yes—
117C2×C3×#41C2311yescharacteristic
118C2×C3×#41C2311yescharacteristic
119C22×C3×D4—21no—
120C22×C3×D4—22no—
121C22×C3×D4C2312yes—
122C22×C3×D4C2311yescharacteristic
123C23×C3×C4—22no—
124C23×C3×C4—21no—
125C2×#235—22no—
126C2×#235C2312yes—
127C22×Dic6—21no—
128C3×C4×Q8—21no—
129C3×C4×Q8D411yescharacteristic
130C3×C4×Q8D411yescharacteristic
131C3×C4×Q8C2311yescharacteristic
132C3×C4×Q8C2311yescharacteristic
133C3×C4×Q8C2312yes—
134C3×C4×D4—21no—
135C3×C4×D4—22no—
136C3×C4×D4—22no—
137C3×C4×D4—21no—
138C3×C4×D4—21no—
139C3×C4×D4—22no—
140C3×C4×D4—21no—
141C3×C4×D4—22no—
142C3×C4×D4—21no—
143C3×C4×D4—22no—
144C3×C4×D4—22no—
145C3×C4×D4—22no—
146C3×C4×D4—22no—
147C3×C4×D4—22no—
148C3×C4×D4—21no—
149C3×C4×D4—21no—
150C3×C4×D4—22no—
151C3×C4×D4D411yescharacteristic
152C3×C4×D4D412yes—
153C3×C4×D4D411yescharacteristic
154C3×C4×D4D412yes—
155C3×C4×D4C2311yescharacteristic
156C3×C4×D4C2312yes—
157C3×C4×D4C2312yes—
158C3×C4×D4C2311yescharacteristic
159C3×C4×D4C2312yes—
160C3×C4×D4C2312yes—
161C3×C4×D4C2312yes—
162C3×#117—21no—
163C3×#117—22no—
164C3×#117—21no—
165C3×#117—22no—
166C3×#117C2311yescharacteristic
167C3×#117C2312yes—
168C3×#117C2311yescharacteristic
169C3×#117C2312yes—
170C2×C3×C4⋊C4—21no—
171C2×C3×C4⋊C4—22no—
172C2×C3×C4⋊C4C2311yescharacteristic
173C2×C3×C4⋊C4C2312yes—
174C2×C3×C22⋊C4—21no—
175C2×C3×C22⋊C4—22no—
176C2×C3×C22⋊C4—22no—
177C2×C3×C22⋊C4—22no—
178C2×C3×C22⋊C4—22no—
179C2×C3×C42—22no—
180C2×C3×C42—21no—
181C2×C3×C42C2311yescharacteristic
182C2×C3×C42C2312yes—
183#950—28no—
184#946—22no—
185C2×#216C2312yes—
186C2×#215C2312yes—
187#939—24no—
188#938—22no—
189C2×#214C2312yes—
190C2×#214C2314yes—
191#932—28no—
192C2×#213C2312yes—
193C2×#213C2314yes—
194#930—21no—
195#930—22no—
196#930—21no—
197#930C2314yes—
198#926—22no—
199C2×C4⋊Dic3—21no—
200C2×C4⋊Dic3C2312yes—
201#924—22no—
202#924C2314yes—
203C2×#208C2312yes—
204C22×C3⋊C8C2312yes—
205#898—24no—
206#896—24no—
207#892—22no—
208D3×C4⋊C4—22no—
209#885—24no—
210#883—24no—
211#67⋊C4—24no—
212#875—22no—
213#875C2312yes—
214#874C2311yescharacteristic
215C4×D12—21no—
216C4×D12—21no—
217C4×D12—22no—
218C4×D12C2314yes—
219#870—22no—
220#869—21no—
221#869—21no—
222#869C2311yescharacteristic
223#869C2312yes—
224#869C2312yes—
225C4×Dic6—22no—
226C4×Dic6C2314yes—
227#835C2314yes—
228#832C2314yes—
229#832C2314yes—
230#832C2314yes—
231#830C2314yes—
232#830C2314yes—
233#810C2314yes—
234#810C2312yes—
235#810C2312yes—
236#809C2314yes—
237#809C2312yes—
238#809C2312yes—
239#808C2314yes—
240#807C2314yes—
241#807C2314yes—
242#807C2314yes—
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×H(5,𝔽2)C2×D311yescharacteristic
251C2×AGL(1,ℤ/8)—32no—
252C2×#135—32no—
253#556—61no—
254#555—61no—
255#554—61no—
256#553—62no—
257#548—62no—
258#547—61no—
259#542—34no—
260#537—32no—
261#533—32no—
262#532—32no—
263#532—31no—
264C2×C4⋊Q8—31no—
265#520—21no—
266#520—32no—
267#520C2×D312yes—
268#520C2×D311yescharacteristic
269#520C2×D311yescharacteristic
270#518—22no—
271#518—21no—
272#518C2×D312yes—
273#518C2×D311yescharacteristic
274C4×#41—21no—
275C4×#41C2×D311yescharacteristic
276C4×#41C2×D312yes—
277C4×#41C2×D311yescharacteristic
278C2×C4×D4—21no—
279C2×C4×D4—22no—
280C2×C4×D4C2×D312yes—
281C2×C4×D4C2×D311yescharacteristic
282#485—34no—
283#484—34no—
284#482—34no—
285#480—34no—
286#477—32no—
287#476—32no—
288#475—32no—
289#474—32no—
290#474—32no—
291#474—32no—
292#474—34no—
293#464—32no—
294#463—32no—
295#463—34no—
296#462—31no—
297#461—32no—
298#461—31no—
299#460—31no—
300#459—31no—
301#459—32no—
302#452—34no—
303#450—34no—
304#449—34no—
305#447—34no—
306#442—34no—
307#440—34no—
308#440—34no—
309#440—34no—
310C4×Q16—34no—
311C4×SD16—34no—
312C4×D8—34no—
313C4×D8—34no—
314#433—34no—
315#432—32no—
316#431—32no—
317#428—32no—
318C2×#107—32no—
319#423—31no—
320C2×C4⋊C8—31no—
321#417—32no—
322#417—32no—
323#416—32no—
324C2×#102—32no—
325#408—32no—
326#405—32no—
327C24×C3—22no—
328C24×C3—21no—
329C3×#41—28no—
330C3×#41—24no—
331C3×#41—24no—
332C3×#41—22no—
333C3×#41—22no—
334C3×#41—22no—
335C3×#41#4114yescomplemented
336C2×C3×Q8C2×D411yescharacteristic
337C2×C3×Q8C2411yescharacteristic
338C2×C3×D4—216no—
339C2×C3×D4—28no—
340C2×C3×D4—22no—
341C2×C3×D4—21no—
342C2×C3×D4—24no—
343C2×C3×D4—24no—
344C2×C3×D4—22no—
345C2×C3×D4—21no—
346C2×C3×D4—22no—
347C2×C3×D4C2×D411yescharacteristic
348C2×C3×D4C2×D412yes—
349C2×C3×D4#4114yescomplemented
350C2×C3×D4C2411yescharacteristic
351C2×C3×D4C2412yes—
352C22×C3×C4—22no—
353C22×C3×C4—21no—
354C22×C3×C4—22no—
355C22×C3×C4—21no—
356C22×C3×C4—22no—
357C22×C3×C4—21no—
358C22×C3×C4—22no—
359C22×C3×C4—21no—
360C22×C3×C4—22no—
361C22×C3×C4—22no—
362C22×C3×C4—22no—
363C22×C3×C4—82no—
364C22×C3×C4—84no—
365C22×C3×C4C2×D412yes—
366C22×C3×C4C2×D411yescharacteristic
367C22×C3×C4C2×D411yescharacteristic
368C22×C3×C4C2×D412yes—
369C22×C3×C4C2412yes—
370C22×C3×C4C2411yescharacteristic
371C2×#67—22no—
372C2×#67—24no—
373C22×Dic3—22no—
374#235—24no—
375#235—24no—
376#235—84no—
377C2×D12—21no—
378C2×D12—21no—
379C2×D12C2412yes—
380C2×C4×D3—22no—
381C2×C4×D3—24no—
382C2×Dic6—22no—
383C2×Dic6—22no—
384C2×Dic6—82no—
385C2×Dic6C2412yes—
386C3×C4⋊C4—22no—
387C3×C4⋊C4—21no—
388C3×C4⋊C4—22no—
389C3×C4⋊C4—21no—
390C3×C4⋊C4—21no—
391C3×C4⋊C4C2×D411yescharacteristic
392C3×C4⋊C4C2×D411yescharacteristic
393C3×C4⋊C4C2×D412yes—
394C3×C4⋊C4C2×D412yes—
395C3×C4⋊C4C2412yes—
396C3×C4⋊C4C2411yescharacteristic
397C3×C4⋊C4C2411yescharacteristic
398C3×C22⋊C4—22no—
399C3×C22⋊C4—21no—
400C3×C22⋊C4—22no—
401C3×C22⋊C4—21no—
402C3×C22⋊C4—22no—
403C3×C22⋊C4—22no—
404C3×C22⋊C4—22no—
405C3×C22⋊C4—21no—
406C3×C22⋊C4—22no—
407C3×C22⋊C4C2×D412yes—
408C3×C22⋊C4C2×D412yes—
409C3×C22⋊C4C2×D412yes—
410C3×C42—21no—
411C3×C42—22no—
412C3×C42—21no—
413C3×C42—22no—
414C3×C42—21no—
415C3×C42C2×D412yes—
416C3×C42C2×D411yescharacteristic
417C3×C42C2×D411yescharacteristic
418C3×C42C2×D412yes—
419C3×C42C2412yes—
420C3×C42C2411yescharacteristic
421C3×C42C2411yescharacteristic
422#217—24no—
423#216—24no—
424#215—24no—
425#214—28no—
426#214—24no—
427#213—28no—
428#213—24no—
429(C2×D3)⋊C4—24no—
430(C2×D3)⋊C4—22no—
431(C2×D3)⋊C4—22no—
432(C2×D3)⋊C4—24no—
433C4⋊Dic3—21no—
434C4⋊Dic3—22no—
435C4⋊Dic3—22no—
436C4⋊Dic3—22no—
437C4⋊Dic3—21no—
438C4⋊Dic3C2414yes—
439Dic3⋊C4—24no—
440Dic3⋊C4—24no—
441C4×Dic3—24no—
442#208—24no—
443C2×C3⋊C8—24no—
444C2×C3⋊C8C2412yes—
445C2×C3⋊C8C2414yes—
446C2×C3⋊C8C2412yes—
447H(5,𝔽2)—24no—
448H(5,𝔽2)—24no—
449C2×#41—21no—
450C2×#41—32no—
451C2×#41—62no—
452C2×#41C22×D312yes—
453C2×#41C22×D311yescharacteristic
454C2×#41C22×D311yescharacteristic
455C22×Q8—61no—
456C22×D4—22no—
457C22×D4—21no—
458C22×D4C22×D312yes—
459C22×D4C22×D311yescharacteristic
460C23×C4—21no—
461C23×C4—22no—
462AGL(1,ℤ/8)—68no—
463#135—68no—
464C2×Q16—32no—
465C2×SD16—32no—
466C2×SD16—32no—
467C2×SD16—34no—
468C2×D8—32no—
469C2×D8—34no—
470C2×M16—32no—
471C22×C8—32no—
472C4⋊Q8—32no—
473C4⋊Q8—32no—
474C4⋊Q8—31no—
475C4⋊Q8—61no—
476C4⋊Q8—61no—
477#127—31no—
478#126—64no—
479#125—62no—
480#124—32no—
481#124—64no—
482#124—62no—
483#123—64no—
484C22⋊Q8—34no—
485C22⋊Q8—62no—
486C22⋊Q8—62no—
487C22⋊Q8—64no—
488#121—34no—
489#121—62no—
490#121—64no—
491#121—61no—
492#121—61no—
493#121—62no—
494C4×Q8—21no—
495C4×Q8—34no—
496C4×Q8—62no—
497C4×Q8#6711yescharacteristic
498C4×Q8#6711yescharacteristic
499C4×Q8C22×D311yescharacteristic
500C4×Q8C22×D312yes—
501C4×Q8C22×D311yescharacteristic
502C4×D4—22no—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4—22no—
506C4×D4—21no—
507C4×D4—22no—
508C4×D4—21no—
509C4×D4—22no—
510C4×D4—21no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—22no—
515C4×D4—21no—
516C4×D4—22no—
517C4×D4—22no—
518C4×D4—21no—
519C4×D4—34no—
520C4×D4—64no—
521C4×D4—61no—
522C4×D4—62no—
523C4×D4—61no—
524C4×D4#6711yescharacteristic
525C4×D4#6712yes—
526C4×D4#6712yes—
527C4×D4#6711yescharacteristic
528C4×D4C22×D311yescharacteristic
529C4×D4C22×D312yes—
530C4×D4C22×D312yes—
531C4×D4C22×D312yes—
532C4×D4C22×D312yes—
533C4×D4C22×D312yes—
534C4×D4C22×D311yescharacteristic
535#117—21no—
536#117—22no—
537#117—22no—
538#117—21no—
539#117—62no—
540#117—62no—
541#117C22×D311yescharacteristic
542#117C22×D312yes—
543#117C22×D311yescharacteristic
544#117C22×D312yes—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—32no—
548C2×C4⋊C4—61no—
549C2×C4⋊C4—62no—
550C2×C4⋊C4C22×D311yescharacteristic
551C2×C4⋊C4C22×D312yes—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C42—21no—
558C2×C42—22no—
559C2×C42C22×D311yescharacteristic
560C2×C42C22×D312yes—
561#107—34no—
562#107—34no—
563#107—34no—
564#106—34no—
565C4⋊C8—31no—
566C4⋊C8—31no—
567C4⋊C8—32no—
568C4⋊C8—32no—
569C4⋊C8—32no—
570#103—34no—
571#103—32no—
572#103—32no—
573#103—34no—
574#102—34no—
575#102—34no—
576#102—34no—
577#102—32no—
578#102—32no—
579#102—34no—
580C22⋊C8—34no—
581C22⋊C8—34no—
582#97—34no—
583C4×C8—34no—
584C23×C3—28no—
585C23×C3—22no—
586C23×C3—21no—
587C23×C3—24no—
588C23×C3—81no—
589C23×C3—82no—
590C23×C3—81no—
591C23×C3—82no—
592C23×C3C22×D412yes—
593C23×C3C22×D411yescharacteristic
594C22×D3—22no—
595C3×Q8—22no—
596C3×Q8—21no—
597C3×Q8C2×#4112yes—
598C3×D4—28no—
599C3×D4—28no—
600C3×D4—24no—
601C3×D4—24no—
602C3×D4—22no—
603C3×D4—24no—
604C3×D4—22no—
605C3×D4—21no—
606C3×D4C2×#4112yes—
607C3×D4C2×#4114yes—
608C2×C3×C4—28no—
609C2×C3×C4—21no—
610C2×C3×C4—24no—
611C2×C3×C4—22no—
612C2×C3×C4—24no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—21no—
616C2×C3×C4—22no—
617C2×C3×C4—21no—
618C2×C3×C4—41no—
619C2×C3×C4—42no—
620C2×C3×C4—44no—
621C2×C3×C4—42no—
622C2×C3×C4—82no—
623C2×C3×C4—81no—
624C2×C3×C4—82no—
625C2×C3×C4—82no—
626C2×C3×C4—82no—
627C2×C3×C4—81no—
628C2×C3×C4—82no—
629C2×C3×C4C22×D412yes—
630C2×C3×C4C22×D412yes—
631C2×C3×C4C22×D412yes—
632C2×C3×C4C22×D411yescharacteristic
633C2×C3×C4C22×D411yescharacteristic
634C2×C3×C4C22×D411yescharacteristic
635C2×C3×C4C22×D411yescharacteristic
636C2×C3×C4C22×D411yescharacteristic
637C2×C3×C4C2×#4112yes—
638C2×C3×C4C2×#4112yes—
639C2×C3×C4C2511yescharacteristic
640#67—44no—
641#67—84no—
642C2×Dic3—22no—
643C2×Dic3—24no—
644C2×Dic3—82no—
645D12—22no—
646D12—22no—
647D12—42no—
648D12—42no—
649C4×D3—44no—
650C4×D3—84no—
651Dic6—22no—
652Dic6—22no—
653Dic6—44no—
654Dic6—82no—
655C3⋊C8—22no—
656C3⋊C8—22no—
657C3⋊C8—24no—
658C24—22no—
659C24—21no—
660#41—28no—
661#41—24no—
662#41—24no—
663#41—22no—
664#41—22no—
665#41—22no—
666#41—64no—
667#41—64no—
668#41—244no—
669#41#23514yescomplemented
670C2×Q8—32no—
671C2×Q8—62no—
672C2×Q8—62no—
673C2×Q8—242no—
674C2×Q8C2×#6711yescharacteristic
675C2×Q8C23×D311yescharacteristic
676C2×D4—216no—
677C2×D4—28no—
678C2×D4—22no—
679C2×D4—21no—
680C2×D4—24no—
681C2×D4—24no—
682C2×D4—22no—
683C2×D4—22no—
684C2×D4—21no—
685C2×D4—32no—
686C2×D4—62no—
687C2×D4—64no—
688C2×D4—61no—
689C2×D4—61no—
690C2×D4#23514yescomplemented
691C2×D4C2×#6712yes—
692C2×D4C2×#6711yescharacteristic
693C2×D4C23×D311yescharacteristic
694C2×D4C23×D312yes—
695C22×C4—22no—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—62no—
707C22×C4—62no—
708C22×C4—64no—
709C22×C4—82no—
710C22×C4—84no—
711C22×C4C2×#6711yescharacteristic
712C22×C4C2×#6712yes—
713C22×C4C2×#6711yescharacteristic
714C22×C4C2×#6712yes—
715C22×C4C23×D312yes—
716C22×C4C23×D311yescharacteristic
717Q16—64no—
718SD16—64no—
719SD16—64no—
720SD16—68no—
721D8—64no—
722D8—68no—
723M16—64no—
724C2×C8—32no—
725C2×C8—34no—
726C2×C8—32no—
727C2×C8—64no—
728C4⋊C4—21no—
729C4⋊C4—22no—
730C4⋊C4—22no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—34no—
734C4⋊C4—62no—
735C4⋊C4—62no—
736C4⋊C4—64no—
737C4⋊C4—62no—
738C4⋊C4—61no—
739C4⋊C4—61no—
740C4⋊C4—64no—
741C4⋊C4C2×#6711yescharacteristic
742C4⋊C4C2×#6712yes—
743C4⋊C4C2×#6711yescharacteristic
744C4⋊C4C2×#6712yes—
745C4⋊C4C23×D311yescharacteristic
746C4⋊C4C23×D311yescharacteristic
747C4⋊C4C23×D312yes—
748C22⋊C4—22no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—22no—
752C22⋊C4—22no—
753C22⋊C4—22no—
754C22⋊C4—22no—
755C22⋊C4—22no—
756C22⋊C4—21no—
757C22⋊C4—64no—
758C22⋊C4—64no—
759C22⋊C4—64no—
760C22⋊C4—62no—
761C22⋊C4—62no—
762C22⋊C4C2×#6712yes—
763C22⋊C4C2×#6712yes—
764C22⋊C4C2×#6712yes—
765C42—21no—
766C42—22no—
767C42—21no—
768C42—22no—
769C42—21no—
770C42—64no—
771C42C2×#6711yescharacteristic
772C42C2×#6712yes—
773C42C2×#6712yes—
774C42C2×#6711yescharacteristic
775C42C23×D312yes—
776C42C23×D311yescharacteristic
777C42C23×D311yescharacteristic
778C22×C3—21no—
779C22×C3—21no—
780C22×C3—22no—
781C22×C3—22no—
782C22×C3—24no—
783C22×C3—22no—
784C22×C3—22no—
785C22×C3—42no—
786C22×C3—41no—
787C22×C3—42no—
788C22×C3—41no—
789C22×C3—84no—
790C22×C3—88no—
791C22×C3#52512yes—
792C22×C3C23×D411yescharacteristic
793C2×D3—42no—
794C2×D3—42no—
795C2×D3—42no—
796C3×C4—21no—
797C3×C4—22no—
798C3×C4—21no—
799C3×C4—22no—
800C3×C4—22no—
801C3×C4—21no—
802C3×C4—22no—
803C3×C4—41no—
804C3×C4—42no—
805C3×C4—41no—
806C3×C4#52512yes—
807C3×C4#57612yes—
808C3×C4C22×#4111yescharacteristic
809C3×C4C22×#4111yescharacteristic
810Dic3—42no—
811Dic3—44no—
812C23—28no—
813C23—22no—
814C23—21no—
815C23—24no—
816C23—62no—
817C23—81no—
818C23—82no—
819C23—81no—
820C23—82no—
821C23C22×#6712yes—
822C23C22×#6711yescharacteristic
823Q8—21no—
824Q8—22no—
825Q8—62no—
826Q8—62no—
827Q8—124no—
828Q8—242no—
829Q8C2×#23512yes—
830D4—28no—
831D4—28no—
832D4—24no—
833D4—24no—
834D4—22no—
835D4—21no—
836D4—24no—
837D4—22no—
838D4—62no—
839D4—62no—
840D4—122no—
841D4—124no—
842D4—122no—
843D4—244no—
844D4C2×#23512yes—
845D4C2×#23514yes—
846C2×C4—28no—
847C2×C4—21no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—24no—
851C2×C4—22no—
852C2×C4—24no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—44no—
859C2×C4—42no—
860C2×C4—62no—
861C2×C4—64no—
862C2×C4—82no—
863C2×C4—82no—
864C2×C4—82no—
865C2×C4—82no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—82no—
869C2×C4—124no—
870C2×C4—244no—
871C2×C4—242no—
872C2×C4C2×#23512yes—
873C2×C4C2×#23512yes—
874C2×C4C22×#6712yes—
875C2×C4C22×#6712yes—
876C2×C4C22×#6711yescharacteristic
877C2×C4C22×#6711yescharacteristic
878C2×C4C22×#6711yescharacteristic
879C2×C4C22×#6712yes—
880C2×C4C22×#6711yescharacteristic
881C2×C4C22×#6711yescharacteristic
882C2×C4C24×D311yescharacteristic
883C8—62no—
884C8—62no—
885C8—64no—
886C2×C3—22no—
887C2×C3—42no—
888C2×C3—44no—
889C2×C3—42no—
890C2×C3C2×#52511yescharacteristic
891C2×C3C2×#57611yescharacteristic
892C2×C3#358611yescharacteristic
893D3—82no—
894C22—21no—
895C22—21no—
896C22—22no—
897C22—22no—
898C22—24no—
899C22—22no—
900C22—22no—
901C22—42no—
902C22—41no—
903C22—42no—
904C22—41no—
905C22—84no—
906C22—88no—
907C22—122no—
908C22—122no—
909C22—122no—
910C22#579112yes—
911C22C23×#6711yescharacteristic
912C4—21no—
913C4—22no—
914C4—21no—
915C4—22no—
916C4—22no—
917C4—22no—
918C4—21no—
919C4—41no—
920C4—41no—
921C4—42no—
922C4—122no—
923C4—124no—
924C4#579112yes—
925C4#583512yes—
926C4C22×#23511yescharacteristic
927C4C22×#23511yescharacteristic
928C3#6059611yescharacteristic, complemented, Sylow
929C2—22no—
930C2—42no—
931C2—44no—
932C2—42no—
933C2—242no—
934C2C2×#579111yescharacteristic
935C2C2×#583511yescharacteristic
936C2#8729911yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×C4×H(5,𝔽2)C2
socleC22×C3C23×D4
hypercenterC4×H(5,𝔽2)D3
hypocenterC3#60596
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×#41 ◁ C4×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C3×C4×H(5,𝔽2)C2semidirect
2. #85850C2semidirect
3. #84102C2semidirect
4. #82569C2semidirect
5. #82567C2semidirect
6. #82557C2semidirect
7. #82541C2semidirect
8. #82537C2semidirect
9. #82534C2semidirect
10. #82531C2semidirect
11. #82525C2semidirect
12. #82515C2semidirect
13. #82508C2semidirect
14. #82315C2semidirect
15. #82308C2semidirect
16. #82307C2semidirect
17. C2×#5007C2semidirect
45. #5534C22semidirect
46. #5523C22semidirect
47. #5477C22semidirect
48. #5477C22semidirect
49. #5470C22semidirect
50. C2×#869C22semidirect
58. #5031C22semidirect
59. C4×#216C22semidirect
60. #5028C22semidirect
61. #5027C22semidirect
62. #5026C22semidirect
63. #5021C22semidirect
64. #5020C22semidirect
65. #5019C22semidirect
66. #5019C22semidirect
67. #5018C22semidirect
68. #5018C22semidirect
69. C4×#214C22semidirect
70. #5016C22semidirect
71. #5016C22semidirect
72. #5015C22semidirect
73. #5015C22semidirect
74. #5014C22semidirect
75. C4×#213C22semidirect
76. C4×#213C22semidirect
77. #5008C22semidirect
78. #5007C22semidirect
79. #5007C22semidirect
80. #5007C22semidirect
81. #5007C22semidirect
82. #5003C22semidirect
83. #5002C22semidirect
84. #5000C22semidirect
85. #4997C22semidirect
86. #4996C22semidirect
87. #4995C22semidirect
88. #4970C22semidirect
89. #4967C22semidirect
90. #4966C22semidirect
91. C2×#807C22semidirect
92. #4926C22semidirect
93. #4925C22semidirect
94. #4924C22semidirect
95. C2×C4⋊(C3⋊C8)C22semidirect
97. C4×H(5,𝔽2)D3semidirect
335. C3×#41#41semidirect
349. C2×C3×D4#41semidirect
669. #41#235semidirect
690. C2×D4#235semidirect
928. C3#60596semidirect

Maximal subgroups

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

subgroupindex
C3×C4×H(5,𝔽2)2
#858502
#841022
#825692
#825672
#825572
#825412
#825372
#825342
#825312
#825252
#825152
#825082
#823152
#823082
#823072
C2×#50072
#605963