Finite Group Databasebeta

← #11258844

Subgroups — #11258844

Order 768.

2396 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#539C211yesmaximal, characteristic, complemented
2C2×#5629C211yesmaximal, characteristic, complemented
3#83117C212yesmaximal, complemented
4#83082C212yesmaximal, complemented
5#83068C212yesmaximal, complemented
6#83061C212yesmaximal, complemented
7#82909C212yesmaximal, complemented
8#82909C212yesmaximal, complemented
9#82906C212yesmaximal, complemented
10#82852C212yesmaximal, complemented
11#82831C212yesmaximal, complemented
12#82812C212yesmaximal, complemented
13#82746C211yesmaximal, characteristic, complemented
14#82722C211yesmaximal, characteristic, complemented
15#82652C211yesmaximal, characteristic, complemented
16#82413C212yesmaximal, complemented
17#82364C212yesmaximal, complemented
18#82192C211yesmaximal, characteristic, complemented
19#82182C211yesmaximal, characteristic, complemented
20#46360—31nomaximal, Sylow
21C22×#239C2211yescharacteristic
22C22×#235C2211yescharacteristic
23C3×#539—28no—
24C2×C3×#126C2212yes—
25C2×C3×#125C2212yes—
26C2×C3×#123C2212yes—
27C2×C3×#123C2212yes—
28C2×C3×C22⋊Q8C2212yes—
29C2×C3×C22⋊Q8C2211yescharacteristic
30C2×C3×#121C2211yescharacteristic
31C2×C3×C4×D4C2212yes—
32C22×C3×C4⋊C4C2211yescharacteristic
33C2×#946C2211yescharacteristic
34C2×#940C2211yescharacteristic
35C2×#936C2211yescharacteristic
36C2×#930C2211yescharacteristic
37C2×#930C2212yes—
38C2×#929C2211yescharacteristic
39C2×#929C2211yescharacteristic
40C2×C4×#67C2212yes—
41#5629—28no—
42C2×#896C2212yes—
43C2×#895C2212yes—
44C2×#895C2211yescharacteristic
45C2×D3×C4⋊C4C2211yescharacteristic
46C2×#884C2212yes—
47C2×#884C2212yes—
48#5229C2212yes—
49#5223C2212yes—
50#5223C2212yes—
51#5223C2212yes—
52#5223C2212yes—
53#5223C2212yes—
54#5213C2212yes—
55#5213C2212yes—
56#5213C2211yescharacteristic
57#5213C2211yescharacteristic
58#5213C2212yes—
59#5211C2211yescharacteristic
60#5210C2212yes—
61C4×#217C2211yescharacteristic
62#4992C2212yes—
63#4992C2212yes—
64#4992C2212yes—
65#4991C2212yes—
66#4991C2212yes—
67#4991C2212yes—
68#4990C2212yes—
69#4990C2212yes—
70#4990C2212yes—
71#4989C2212yes—
72#4989C2212yes—
73#4989C2212yes—
74#4988C2211yescharacteristic
75#4988C2212yes—
76#4988C2212yes—
77#4987C2212yes—
78#4987C2212yes—
79#4986C2212yes—
80#4985C2212yes—
81#4985C2212yes—
82#4982C2212yes—
83#4980C2212yes—
84#4980C2212yes—
85#4979C2212yes—
86Dic3×C4⋊C4C2212yes—
87#4973C2211yescharacteristic
88#4961C2212yes—
89#4961C2212yes—
90#4960C2212yes—
91#4960C2212yes—
92#4960C2212yes—
93#4960C2212yes—
94#4957C2212yes—
95#4956C2212yes—
96#4956C2212yes—
97#4956C2212yes—
98#4956C2212yes—
99#4956C2212yes—
100#4953C2212yes—
101#4951C2212yes—
102#4951C2212yes—
103#4948C2212yes—
104#4945C2212yes—
105#4945C2212yes—
106#4940C2212yes—
107#4939C2212yes—
108C4×(C2×D3)⋊C4C2212yes—
109#4933C2212yes—
110C2×#539D311yescharacteristic, complemented
111C2×#537—31no—
112#2815—31no—
113#2728—32no—
114#2714—32no—
115#2703—32no—
116#2703—32no—
117#2690—32no—
118#2673—32no—
119#2591—31no—
120#2490—32no—
121#2481—32no—
122#2464—32no—
123#2461—32no—
124#2456—32no—
125#2431—31no—
126#2407—32no—
127#2406—31no—
128#2332—31no—
129C22×C3×Q8C2311yescharacteristic
130C22×C3×D4C2312yes—
131C22×C3×D4C2311yescharacteristic
132C23×C3×C4C2312yes—
133C23×C3×C4C2311yescharacteristic
134C23×C3×C4C2311yescharacteristic
135C23×C3×C4C2311yescharacteristic
136C22×#67C2311yescharacteristic
137C22×#67C2311yescharacteristic
138C22×#67C2312yes—
139C22×#67C2312yes—
140C22×#67C2312yes—
141C22×#67C2312yes—
142C22×#67C2312yes—
143C2×#239—24no—
144C2×#239—42no—
145C2×#239—42no—
146C2×#235—24no—
147C2×#235—42no—
148C2×#235—42no—
149C22×D12C2311yescharacteristic
150C22×D12C2312yes—
151C22×D12C2311yescharacteristic
152C22×D12C2312yes—
153C22×C4×D3C2311yescharacteristic
154C22×C4×D3C2312yes—
155C22×C4×D3C2311yescharacteristic
156C22×C4×D3C2312yes—
157C22×Dic6C2311yescharacteristic
158C3×#126—28no—
159C3×#125—28no—
160C3×#123—28no—
161C3×#123—28no—
162C3×C22⋊Q8—28no—
163C3×C22⋊Q8D418yescomplemented
164C3×#121—24no—
165C3×C4×D4—28no—
166C2×C3×C4⋊C4—24no—
167C2×C3×C4⋊C4C2311yescharacteristic
168C2×C3×C4⋊C4C2312yes—
169C2×C3×C4⋊C4C2312yes—
170C2×C3×C4⋊C4C2312yes—
171C2×C3×C4⋊C4C2312yes—
172C2×C3×C4⋊C4C2312yes—
173C2×C3×C4⋊C4C2312yes—
174C2×C3×C4⋊C4C2311yescharacteristic
175C2×C3×C22⋊C4C2312yes—
176C2×C3×C22⋊C4C2312yes—
177C2×C3×C22⋊C4C2312yes—
178C2×C3×C22⋊C4C2312yes—
179C2×C3×C22⋊C4C2312yes—
180C2×C3×C42C2312yes—
181C2×#217C2312yes—
182C2×#217C2312yes—
183C2×#217C2312yes—
184C2×#217C2312yes—
185C2×#217C2312yes—
186C2×#217C2311yescharacteristic
187C2×#217C2311yescharacteristic
188#946—24no—
189#940—42no—
190#936—42no—
191#930—24no—
192#930—44no—
193#929—42no—
194#929—42no—
195C4×#67—44no—
196C2×(C2×D3)⋊C4C2312yes—
197C2×(C2×D3)⋊C4C2312yes—
198C2×(C2×D3)⋊C4C2312yes—
199C2×(C2×D3)⋊C4C2312yes—
200C2×(C2×D3)⋊C4C2312yes—
201C2×(C2×D3)⋊C4C2312yes—
202C2×(C2×D3)⋊C4C2312yes—
203C2×(C2×D3)⋊C4C2312yes—
204C2×(C2×D3)⋊C4C2312yes—
205C2×(C2×D3)⋊C4C2312yes—
206C2×(C2×D3)⋊C4C2312yes—
207C2×(C2×D3)⋊C4C2312yes—
208C2×(C2×D3)⋊C4C2312yes—
209C2×(C2×D3)⋊C4C2312yes—
210C2×(C2×D3)⋊C4C2312yes—
211C2×C4⋊Dic3C2311yescharacteristic
212C2×C4⋊Dic3C2312yes—
213C2×C4⋊Dic3C2312yes—
214C2×Dic3⋊C4C2312yes—
215C2×Dic3⋊C4C2312yes—
216C2×Dic3⋊C4C2312yes—
217C2×Dic3⋊C4C2312yes—
218C2×C4×Dic3C2312yes—
219C2×C4×Dic3C2312yes—
220C2×C4×Dic3C2311yescharacteristic
221C2×C4×Dic3C2311yescharacteristic
222#896—28no—
223#895—24no—
224#895—28no—
225D3×C4⋊C4—24no—
226#884—28no—
227#884—28no—
228C3⋊#95C2312yes—
229C3⋊#95C2312yes—
230C3⋊#95C2312yes—
231C3⋊#95C2312yes—
232C3⋊#95C2312yes—
233C3⋊#95C2312yes—
234C3⋊#95C2312yes—
235C3⋊#95C2312yes—
236C3⋊#95C2312yes—
237C3⋊#95C2312yes—
238C3⋊#95C2312yes—
239C3⋊#95C2312yes—
240C3⋊#95C2312yes—
241C3⋊#95C2312yes—
242C3⋊#95C2312yes—
243C3⋊#95C2312yes—
244C3⋊#95C2312yes—
245C22×#41—31no—
246C22×#41—31no—
247#539—28no—
248#537—68no—
249C2×#127—31no—
250C2×#126C2×D312yes—
251C2×#125C2×D312yes—
252C2×#124—31no—
253C2×#123—31no—
254C2×#123—31no—
255C2×#123C2×D312yes—
256C2×#123C2×D312yes—
257C2×C22⋊Q8—31no—
258C2×C22⋊Q8—32no—
259C2×C22⋊Q8C2×D312yes—
260C2×C22⋊Q8C2×D311yescharacteristic
261C2×#121—31no—
262C2×#121—32no—
263C2×#121—32no—
264C2×#121—31no—
265C2×#121—32no—
266C2×#121—32no—
267C2×#121C2×D311yescharacteristic
268C2×C4×D4—32no—
269C2×C4×D4C2×D312yes—
270C22×C4⋊C4—31no—
271C22×C4⋊C4C2×D311yescharacteristic
272#400—32no—
273#400—32no—
274#400—32no—
275#398—32no—
276#397—32no—
277#397—32no—
278#397—32no—
279#397—32no—
280#396—32no—
281#395—32no—
282#394—32no—
283#394—32no—
284#394—32no—
285#394—32no—
286#394—32no—
287#392—32no—
288#392—32no—
289#392—32no—
290#392—32no—
291#392—32no—
292#392—32no—
293#392—32no—
294#392—32no—
295#392—32no—
296#391—32no—
297#391—31no—
298#390—32no—
299#390—31no—
300#390—32no—
301#390—32no—
302#390—32no—
303#388—32no—
304#388—32no—
305#388—32no—
306#388—32no—
307#388—32no—
308#388—32no—
309#388—32no—
310#388—32no—
311#387—32no—
312#387—32no—
313#387—32no—
314#386—32no—
315#386—32no—
316#386—31no—
317#386—31no—
318#386—32no—
319#386—32no—
320#386—32no—
321#386—32no—
322#386—32no—
323#386—32no—
324#385—32no—
325#385—32no—
326#385—32no—
327#385—32no—
328#381—31no—
329#380—32no—
330#380—32no—
331C4×C4⋊C4—32no—
332C4×C22⋊C4—31no—
333C4×C22⋊C4—32no—
334C24×C3C2412yes—
335C24×C3C2411yescharacteristic
336C23×D3C2411yescharacteristic
337C23×D3C2412yes—
338C23×D3C2411yescharacteristic
339C2×C3×Q8—41no—
340C2×C3×Q8—41no—
341C2×C3×Q8C2×D414yes—
342C2×C3×D4—24no—
343C2×C3×D4—22no—
344C2×C3×D4—42no—
345C2×C3×D4—42no—
346C2×C3×D4—41no—
347C2×C3×D4—41no—
348C22×C3×C4—22no—
349C22×C3×C4—22no—
350C22×C3×C4—24no—
351C22×C3×C4—41no—
352C22×C3×C4—41no—
353C22×C3×C4—42no—
354C22×C3×C4—42no—
355C22×C3×C4—41no—
356C22×C3×C4—41no—
357C22×C3×C4—42no—
358C22×C3×C4C2×D414yes—
359C22×C3×C4C2412yes—
360C22×C3×C4C2412yes—
361C22×C3×C4C2412yes—
362C22×C3×C4C2411yescharacteristic
363C22×C3×C4C2411yescharacteristic
364C22×C3×C4C2412yes—
365C22×C3×C4C2412yes—
366C2×#67—22no—
367C2×#67—22no—
368C2×#67—22no—
369C2×#67—24no—
370C2×#67—24no—
371C2×#67—22no—
372C2×#67—42no—
373C2×#67—41no—
374C2×#67—41no—
375C2×#67—42no—
376C2×#67—42no—
377C2×#67—42no—
378C2×#67—42no—
379C2×#67—42no—
380C2×#67—42no—
381C2×#67—42no—
382C2×#67—42no—
383C2×#67—42no—
384C2×#67—42no—
385C2×#67—42no—
386C2×#67—42no—
387C22×Dic3C2412yes—
388C22×Dic3C2412yes—
389C22×Dic3C2412yes—
390C22×Dic3C2412yes—
391C22×Dic3C2412yes—
392C22×Dic3C2411yescharacteristic
393C22×Dic3C2411yescharacteristic
394#239—416no—
395#235—416no—
396C2×D12—24no—
397C2×D12—22no—
398C2×D12—24no—
399C2×D12—22no—
400C2×D12—22no—
401C2×D12—24no—
402C2×D12—41no—
403C2×D12—42no—
404C2×D12—41no—
405C2×D12—41no—
406C2×D12—42no—
407C2×D12—42no—
408C2×C4×D3—22no—
409C2×C4×D3—22no—
410C2×C4×D3—22no—
411C2×C4×D3—24no—
412C2×C4×D3—22no—
413C2×C4×D3—24no—
414C2×C4×D3—24no—
415C2×C4×D3—41no—
416C2×C4×D3—41no—
417C2×C4×D3—42no—
418C2×C4×D3—42no—
419C2×C4×D3—42no—
420C2×Dic6—22no—
421C2×Dic6—22no—
422C2×Dic6—41no—
423C3×C4⋊C4—24no—
424C3×C4⋊C4—24no—
425C3×C4⋊C4—24no—
426C3×C4⋊C4—22no—
427C3×C4⋊C4—24no—
428C3×C4⋊C4—24no—
429C3×C4⋊C4C2×D414yes—
430C3×C4⋊C4C2×D418yes—
431C3×C22⋊C4—24no—
432C3×C22⋊C4—24no—
433C3×C22⋊C4—24no—
434C3×C22⋊C4—24no—
435C3×C22⋊C4C2×D418yes—
436C3×C42—24no—
437#217—24no—
438#217—41no—
439#217—41no—
440#217—42no—
441#217—42no—
442#217—42no—
443#217—42no—
444(C2×D3)⋊C4—24no—
445(C2×D3)⋊C4—24no—
446(C2×D3)⋊C4—24no—
447(C2×D3)⋊C4—24no—
448(C2×D3)⋊C4—42no—
449(C2×D3)⋊C4—42no—
450(C2×D3)⋊C4—42no—
451(C2×D3)⋊C4—42no—
452(C2×D3)⋊C4—42no—
453(C2×D3)⋊C4—42no—
454(C2×D3)⋊C4—42no—
455(C2×D3)⋊C4—42no—
456(C2×D3)⋊C4—42no—
457(C2×D3)⋊C4—42no—
458(C2×D3)⋊C4—42no—
459C4⋊Dic3—22no—
460C4⋊Dic3—42no—
461C4⋊Dic3—42no—
462Dic3⋊C4—24no—
463Dic3⋊C4—24no—
464Dic3⋊C4—24no—
465Dic3⋊C4—42no—
466C4×Dic3—42no—
467C4×Dic3—42no—
468C4×Dic3—41no—
469C4×Dic3—41no—
470C2×#41—64no—
471C2×#41—64no—
472C2×#41—122no—
473C2×#41—122no—
474C2×#41—122no—
475C2×#41—122no—
476C22×Q8—31no—
477C22×Q8C22×D311yescharacteristic
478C22×D4—31no—
479C22×D4—31no—
480C22×D4—32no—
481C22×D4—32no—
482C22×D4—32no—
483C22×D4—32no—
484C22×D4—32no—
485C22×D4—32no—
486C22×D4—31no—
487C22×D4—32no—
488C22×D4—31no—
489C22×D4C22×D312yes—
490C22×D4C22×D311yescharacteristic
491C23×C4—31no—
492C23×C4—32no—
493C23×C4—32no—
494C23×C4—31no—
495C23×C4C22×D311yescharacteristic
496C23×C4C22×D311yescharacteristic
497C23×C4C22×D312yes—
498C23×C4C22×D311yescharacteristic
499#127—122no—
500#126—28no—
501#125—28no—
502#124—122no—
503#123—28no—
504#123—28no—
505#123—122no—
506#123—122no—
507C22⋊Q8—28no—
508C22⋊Q8—64no—
509C22⋊Q8—68no—
510C22⋊Q8#6718yescomplemented
511#121—24no—
512#121—64no—
513#121—64no—
514#121—68no—
515#121—68no—
516#121—68no—
517#121—124no—
518C4×D4—28no—
519C4×D4—124no—
520C2×C4⋊C4—24no—
521C2×C4⋊C4—32no—
522C2×C4⋊C4—31no—
523C2×C4⋊C4—32no—
524C2×C4⋊C4—32no—
525C2×C4⋊C4—32no—
526C2×C4⋊C4—32no—
527C2×C4⋊C4—32no—
528C2×C4⋊C4—64no—
529C2×C4⋊C4C22×D312yes—
530C2×C4⋊C4C22×D312yes—
531C2×C4⋊C4C22×D312yes—
532C2×C4⋊C4C22×D311yescharacteristic
533C2×C4⋊C4C22×D312yes—
534C2×C4⋊C4C22×D312yes—
535C2×C4⋊C4C22×D311yescharacteristic
536C2×C4⋊C4C22×D312yes—
537C2×C22⋊C4—32no—
538C2×C22⋊C4—32no—
539C2×C22⋊C4—32no—
540C2×C22⋊C4—32no—
541C2×C22⋊C4—32no—
542C2×C22⋊C4—31no—
543C2×C22⋊C4—31no—
544C2×C22⋊C4—32no—
545C2×C22⋊C4—32no—
546C2×C22⋊C4—32no—
547C2×C22⋊C4—32no—
548C2×C22⋊C4—32no—
549C2×C22⋊C4—32no—
550C2×C22⋊C4—32no—
551C2×C22⋊C4—32no—
552C2×C22⋊C4—32no—
553C2×C22⋊C4—32no—
554C2×C22⋊C4—32no—
555C2×C22⋊C4—32no—
556C2×C22⋊C4—32no—
557C2×C22⋊C4—32no—
558C2×C22⋊C4—32no—
559C2×C22⋊C4C22×D312yes—
560C2×C22⋊C4C22×D312yes—
561C2×C22⋊C4C22×D312yes—
562C2×C22⋊C4C22×D312yes—
563C2×C22⋊C4C22×D312yes—
564C2×C42—32no—
565C2×C42—31no—
566C2×C42—31no—
567C2×C42—32no—
568C2×C42C22×D312yes—
569#95—32no—
570#95—32no—
571#95—32no—
572#95—32no—
573#95—32no—
574#95—32no—
575#95—32no—
576#95—32no—
577#95—32no—
578#95—32no—
579#95—32no—
580#95—32no—
581#95—32no—
582#95—32no—
583#95—32no—
584#95—32no—
585#95—32no—
586C23×C3—21no—
587C23×C3—21no—
588C23×C3—22no—
589C23×C3—22no—
590C23×C3—22no—
591C23×C3—22no—
592C23×C3—22no—
593C23×C3—22no—
594C23×C3—22no—
595C23×C3—22no—
596C23×C3—22no—
597C23×C3C22×D412yes—
598C23×C3C2511yescharacteristic
599C22×D3—21no—
600C22×D3—21no—
601C22×D3—22no—
602C22×D3—22no—
603C22×D3—22no—
604C22×D3—21no—
605C22×D3—21no—
606C22×D3—22no—
607C22×D3—22no—
608C22×D3—21no—
609C22×D3—22no—
610C22×D3—22no—
611C22×D3—22no—
612C22×D3—22no—
613C22×D3—22no—
614C22×D3—22no—
615C22×D3H(5,𝔽2)12yes—
616C3×Q8—44no—
617C3×D4—48no—
618C3×D4—82no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—22no—
622C2×C3×C4—22no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—22no—
626C2×C3×C4—22no—
627C2×C3×C4—22no—
628C2×C3×C4—22no—
629C2×C3×C4—22no—
630C2×C3×C4—22no—
631C2×C3×C4—22no—
632C2×C3×C4—22no—
633C2×C3×C4—22no—
634C2×C3×C4—22no—
635C2×C3×C4—22no—
636C2×C3×C4—44no—
637C2×C3×C4—44no—
638C2×C3×C4—84no—
639C2×C3×C4—82no—
640C2×C3×C4C22×D414yes—
641C2×C3×C4C22×D414yes—
642C2×C3×C4C22×D412yes—
643C2×C3×C4C22×D412yes—
644#67—44no—
645#67—44no—
646#67—48no—
647#67—84no—
648#67—84no—
649#67—84no—
650#67—84no—
651C2×Dic3—21no—
652C2×Dic3—21no—
653C2×Dic3—22no—
654C2×Dic3—21no—
655C2×Dic3—22no—
656C2×Dic3—22no—
657C2×Dic3—22no—
658C2×Dic3—21no—
659C2×Dic3—22no—
660C2×Dic3—21no—
661C2×Dic3—22no—
662C2×Dic3—22no—
663C2×Dic3—22no—
664C2×Dic3—22no—
665C2×Dic3—22no—
666C2×Dic3—22no—
667C2×Dic3—22no—
668C2×Dic3—22no—
669C2×Dic3—22no—
670C2×Dic3—22no—
671C2×Dic3H(5,𝔽2)12yes—
672D12—44no—
673D12—48no—
674D12—44no—
675D12—84no—
676C4×D3—28no—
677C4×D3—48no—
678C4×D3—44no—
679C4×D3—84no—
680Dic6—44no—
681C24—31no—
682C24—32no—
683C24—31no—
684C24C23×D312yes—
685C24C23×D311yescharacteristic
686#41—1216no—
687#41—1216no—
688C2×Q8—41no—
689C2×Q8—41no—
690C2×Q8—62no—
691C2×Q8—62no—
692C2×Q8—121no—
693C2×Q8C2×#6714yes—
694C2×D4—24no—
695C2×D4—22no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—41no—
699C2×D4—41no—
700C2×D4—64no—
701C2×D4—62no—
702C2×D4—62no—
703C2×D4—62no—
704C2×D4—62no—
705C2×D4—62no—
706C2×D4—64no—
707C2×D4—64no—
708C2×D4—62no—
709C2×D4—64no—
710C2×D4—62no—
711C2×D4—64no—
712C2×D4—122no—
713C2×D4—121no—
714C2×D4—121no—
715C2×D4—121no—
716C2×D4—122no—
717C2×D4—122no—
718C2×D4—122no—
719C2×D4—121no—
720C2×D4—121no—
721C2×D4—122no—
722C2×D4—122no—
723C2×D4—122no—
724C2×D4—122no—
725C2×D4—122no—
726C2×D4—122no—
727C2×D4—122no—
728C2×D4—122no—
729C2×D4—122no—
730C2×D4—122no—
731C2×D4—122no—
732C2×D4—122no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—24no—
736C22×C4—31no—
737C22×C4—32no—
738C22×C4—32no—
739C22×C4—32no—
740C22×C4—32no—
741C22×C4—32no—
742C22×C4—31no—
743C22×C4—41no—
744C22×C4—41no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—41no—
749C22×C4—41no—
750C22×C4—62no—
751C22×C4—64no—
752C22×C4—62no—
753C22×C4—62no—
754C22×C4—64no—
755C22×C4—62no—
756C22×C4—64no—
757C22×C4—122no—
758C22×C4—121no—
759C22×C4—121no—
760C22×C4—122no—
761C22×C4—122no—
762C22×C4C2×#6714yes—
763C22×C4C23×D312yes—
764C22×C4C23×D312yes—
765C22×C4C23×D312yes—
766C22×C4C23×D311yescharacteristic
767C22×C4C23×D311yescharacteristic
768C22×C4C23×D312yes—
769C22×C4C23×D312yes—
770C4⋊C4—24no—
771C4⋊C4—24no—
772C4⋊C4—24no—
773C4⋊C4—22no—
774C4⋊C4—24no—
775C4⋊C4—24no—
776C4⋊C4—64no—
777C4⋊C4—64no—
778C4⋊C4—62no—
779C4⋊C4—64no—
780C4⋊C4—122no—
781C4⋊C4—122no—
782C4⋊C4—122no—
783C4⋊C4C2×#6714yes—
784C4⋊C4C2×#6718yes—
785C22⋊C4—24no—
786C22⋊C4—24no—
787C22⋊C4—24no—
788C22⋊C4—24no—
789C22⋊C4—64no—
790C22⋊C4—64no—
791C22⋊C4—64no—
792C22⋊C4—64no—
793C22⋊C4—64no—
794C22⋊C4—122no—
795C22⋊C4—122no—
796C22⋊C4—122no—
797C22⋊C4—122no—
798C22⋊C4—122no—
799C22⋊C4—122no—
800C22⋊C4—122no—
801C22⋊C4—122no—
802C22⋊C4—122no—
803C22⋊C4—122no—
804C22⋊C4—122no—
805C22⋊C4—121no—
806C22⋊C4—121no—
807C22⋊C4—122no—
808C22⋊C4—122no—
809C22⋊C4—122no—
810C22⋊C4—122no—
811C22⋊C4C2×#6718yes—
812C42—24no—
813C42—122no—
814C42—121no—
815C42—121no—
816C42—122no—
817C22×C3—22no—
818C22×C3—22no—
819C22×C3—22no—
820C22×C3—42no—
821C22×C3—42no—
822C22×C3—42no—
823C22×C3—42no—
824C22×C3—42no—
825C22×C3—42no—
826C22×C3—42no—
827C22×C3—42no—
828C22×C3—42no—
829C22×C3C23×D411yescharacteristic
830C22×C3C2×H(5,𝔽2)11yescharacteristic
831C22×C3C2×H(5,𝔽2)11yescharacteristic
832C22×C3#58512yes—
833C22×C3#58512yes—
834C2×D3—22no—
835C2×D3—24no—
836C2×D3—41no—
837C2×D3—41no—
838C2×D3—42no—
839C2×D3—42no—
840C2×D3—41no—
841C2×D3—42no—
842C2×D3—41no—
843C2×D3—41no—
844C2×D3—42no—
845C2×D3—42no—
846C2×D3—42no—
847C2×D3—42no—
848C2×D3—42no—
849C2×D3—42no—
850C2×D3—42no—
851C3×C4—22no—
852C3×C4—22no—
853C3×C4—24no—
854C3×C4—24no—
855C3×C4—42no—
856C3×C4—42no—
857C3×C4—42no—
858Dic3—22no—
859Dic3—41no—
860Dic3—42no—
861Dic3—42no—
862Dic3—42no—
863Dic3—42no—
864Dic3—42no—
865C23—22no—
866C23—21no—
867C23—21no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—32no—
877C23—62no—
878C23—61no—
879C23—62no—
880C23—61no—
881C23—62no—
882C23—62no—
883C23—62no—
884C23—61no—
885C23—62no—
886C23—62no—
887C23—61no—
888C23—62no—
889C23—62no—
890C23—62no—
891C23—61no—
892C23—62no—
893C23C22×#6712yes—
894C23C24×D311yescharacteristic
895Q8—44no—
896Q8—124no—
897D4—48no—
898D4—82no—
899D4—124no—
900D4—128no—
901D4—124no—
902D4—124no—
903D4—124no—
904D4—128no—
905D4—244no—
906D4—244no—
907D4—244no—
908D4—244no—
909D4—244no—
910C2×C4—22no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—22no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—32no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—68no—
931C2×C4—61no—
932C2×C4—61no—
933C2×C4—62no—
934C2×C4—62no—
935C2×C4—62no—
936C2×C4—62no—
937C2×C4—62no—
938C2×C4—62no—
939C2×C4—62no—
940C2×C4—62no—
941C2×C4—61no—
942C2×C4—61no—
943C2×C4—62no—
944C2×C4—62no—
945C2×C4—62no—
946C2×C4—62no—
947C2×C4—62no—
948C2×C4—62no—
949C2×C4—62no—
950C2×C4—61no—
951C2×C4—84no—
952C2×C4—82no—
953C2×C4—128no—
954C2×C4—124no—
955C2×C4—244no—
956C2×C4C22×#6714yes—
957C2×C4C22×#6712yes—
958C2×C4C22×#6714yes—
959C2×C4C22×#6712yes—
960C2×C3—42no—
961C2×C3—82no—
962C2×C3#348411yescharacteristic
963C2×C3#348711yescharacteristic
964C2×C3#350011yescharacteristic
965C2×C3#353912yes—
966C2×C3#356012yes—
967D3—42no—
968D3—82no—
969D3—81no—
970C22—22no—
971C22—22no—
972C22—22no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—64no—
983C22—62no—
984C22—122no—
985C22—121no—
986C22—121no—
987C22—122no—
988C22—122no—
989C22—122no—
990C22—122no—
991C22—122no—
992C22—122no—
993C22—122no—
994C22—121no—
995C22—122no—
996C22—121no—
997C22—121no—
998C22—122no—
999C22#596412yes—
1000C22D3×H(5,𝔽2)11yescharacteristic
1001C22D3×H(5,𝔽2)11yescharacteristic
1002C22#596812yes—
1003C22C23×#6711yescharacteristic
1004C4—22no—
1005C4—22no—
1006C4—24no—
1007C4—24no—
1008C4—42no—
1009C4—42no—
1010C4—42no—
1011C4—62no—
1012C4—122no—
1013C4—122no—
1014C4—122no—
1015C4—122no—
1016C4—121no—
1017C4—122no—
1018C3#4636011yescharacteristic, complemented, Sylow
1019C2—42no—
1020C2—82no—
1021C2—122no—
1022C2—242no—
1023C2—241no—
1024C2#8643612yes—
1025C2#8646512yes—
1026C2#8727411yescharacteristic
1027C2#8728411yescharacteristic
1028C2#8729311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×#539C2
hypercenterC2×#539D3
hypocenterC3#46360
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#539

Complements

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

NH ≅ G/Ntype
1. C2×C3×#539C2semidirect
2. C2×#5629C2semidirect
3. #83117C2semidirect
4. #83082C2semidirect
5. #83068C2semidirect
6. #83061C2semidirect
7. #82909C2semidirect
8. #82909C2semidirect
9. #82906C2semidirect
10. #82852C2semidirect
11. #82831C2semidirect
12. #82812C2semidirect
13. #82746C2semidirect
14. #82722C2semidirect
15. #82652C2semidirect
16. #82413C2semidirect
17. #82364C2semidirect
18. #82192C2semidirect
19. #82182C2semidirect
110. C2×#539D3semidirect
163. C3×C22⋊Q8D4semidirect
510. C22⋊Q8#67semidirect
1018. C3#46360semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5392
C2×#56292
#831172
#830822
#830682
#830612
#829092
#829062
#828522
#828312
#828122
#827462
#827222
#826522
#824132
#823642
#821922
#821822
#463603