Finite Group Databasebeta

← #10972927

Subgroups — #10972927

Order 768.

5426 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#235C211yesmaximal, characteristic, complemented
2C2×#5608C212yesmaximal, complemented
3C2×#5606C211yesmaximal, characteristic, complemented
4C3×#2847C211yesmaximal, characteristic, complemented
5#84031C211yesmaximal, characteristic, complemented
6#82723C211yesmaximal, characteristic, complemented
7#82709C212yesmaximal, complemented
8#82605C212yesmaximal, complemented
9#82582C212yesmaximal, complemented
10#74896C214yesmaximal, complemented
11#74887C212yesmaximal, complemented
12#74689C212yesmaximal, complemented
13#74688C214yesmaximal, complemented
14#74049C211yesmaximal, characteristic, complemented
15#74003C212yesmaximal, complemented
16D3×#380C211yesmaximal, characteristic, complemented
17#73950C212yesmaximal, complemented
18#35251—31nomaximal, Sylow
19C24×C3×C4C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×#67C2211yescharacteristic
22C22×#237C2211yescharacteristic, complemented
23C22×#235—216no—
24C22×#235—28no—
25C22×#235C2212yes—
26C22×#235C2212yes—
27C22×#235C2212yes—
28C22×#235C2212yes—
29C23×D12C2211yescharacteristic
30C23×C4×D3C2211yescharacteristic
31C23×C4×D3C2211yescharacteristic
32C23×Dic6C2211yescharacteristic
33C2×C3×#121C2211yescharacteristic
34C2×C3×#121C2212yescomplemented
35C2×C3×#120C2212yes—
36C2×#939C2214yescomplemented
37C2×#938C2211yescharacteristic, complemented
38C2×#938C2212yescomplemented
39C2×#938C2214yescomplemented
40C2×#937C2212yes—
41C2×#937C2212yes—
42C2×D4×Dic3C2212yes—
43C2×#924C2211yescharacteristic
44C2×#924C2212yescomplemented
45#5608—216no—
46#5606—28no—
47C2×#897C2212yescomplemented
48C2×#897C2211yescharacteristic, complemented
49C2×#892C2211yescharacteristic, complemented
50C2×D3×C4⋊C4C2212yescomplemented
51C2×#884C2214yescomplemented
52C2×#883C2212yescomplemented
53C2×#67⋊C4C2212yescomplemented
54C2×D3×C22⋊C4C2212yes—
55C2×#878C2214yescomplemented
56C3×#386C2212yes—
57C3×#386C2214yescomplemented
58C3×#380C2211yescharacteristic
59C3×#380C2212yescomplemented
60#5247C2212yes—
61#5223C2214yescomplemented
62#5223C2214yescomplemented
63#5220C2212yes—
64#5212C2211yescharacteristic
65#5212C2212yescomplemented
66#5210C2212yes—
67#5210C2214yescomplemented
68#4987C2212yescomplemented
69#4987C2212yescomplemented
70#4987C2212yescomplemented
71#4961C2214yescomplemented
72#4961C2214yescomplemented
73#4960C2214yescomplemented
74#4957C2214yescomplemented
75#4956C2214yescomplemented
76#4956C2214yescomplemented
77#4955C2212yes—
78#4950C2212yes—
79#4947C2214yescomplemented
80#4942C2212yes—
81#4672C2214yescomplemented
82#4668C2214yescomplemented
83#4667C2212yescomplemented
84#4665C2214yescomplemented
85D3×#95C2212yescomplemented
86#4656C2214yescomplemented
87#4646C2214yescomplemented
88C23×#41—31no—
89C2×#537—32no—
90C2×#525—31no—
91#2848—31no—
92#2848—31no—
93#2847—31no—
94#2847D311yescharacteristic, complemented
95#2616—32no—
96#2615—32no—
97#2430—34no—
98#2410—32no—
99#2410—32no—
100#2409—32no—
101#2408—32no—
102#2407—34no—
103#2311—32no—
104C2×#380—31no—
105C25×C3C2311yescharacteristic
106C24×D3C2311yescharacteristic
107C24×D3C2311yescharacteristic
108C22×C3×D4C2311yescharacteristic
109C22×C3×D4C2312yes—
110C22×C3×D4C2314yes—
111C23×C3×C4—24no—
112C23×C3×C4—28no—
113C23×C3×C4C2311yescharacteristic
114C23×C3×C4C2312yes—
115C23×C3×C4C2311yescharacteristic
116C23×C3×C4C2312yes—
117C22×#67—24no—
118C22×#67—28no—
119C22×#67—28no—
120C22×#67—24no—
121C22×#67C2312yes—
122C22×#67C2312yes—
123C22×#67C2312yes—
124C22×#67C2312yes—
125C22×#67C2312yes—
126C22×#67C2314yes—
127C22×#67C2312yes—
128C23×Dic3C2311yescharacteristic
129C23×Dic3C2312yes—
130C23×Dic3C2311yescharacteristic
131C2×#237—24no—
132C2×#237—28no—
133C2×#235—2128no—
134C2×#235—28no—
135C2×#235—28no—
136C2×#235—28no—
137C2×#235—28no—
138C2×#235—28no—
139C2×#235—28no—
140C2×#235—28no—
141C2×#235—28no—
142C2×#235—28no—
143C2×#235—28no—
144C2×#235—28no—
145C2×#235D4116yescomplemented
146C22×D12—24no—
147C22×D12—28no—
148C22×D12C2312yes—
149C22×D12C2312yes—
150C22×C4×D3—24no—
151C22×C4×D3—28no—
152C22×C4×D3—28no—
153C22×C4×D3D418yescomplemented
154C22×C4×D3C2312yes—
155C22×C4×D3C2311yescharacteristic
156C22×C4×D3C2311yescharacteristic
157C22×C4×D3C2312yes—
158C22×C4×D3C2311yescharacteristic
159C22×C4×D3C2314yes—
160C22×C4×D3C2311yescharacteristic
161C22×Dic6—24no—
162C22×Dic6—28no—
163C22×Dic6C2312yes—
164C22×Dic6C2311yescharacteristic
165C22×Dic6C2312yes—
166C3×#121—24no—
167C3×#121—28no—
168C3×#120—44no—
169C2×C3×C4⋊C4C2312yes—
170C2×C3×C4⋊C4C2311yescharacteristic
171C2×C3×C22⋊C4C2312yes—
172C2×C3×C22⋊C4C2314yes—
173C2×C3×C22⋊C4C2312yes—
174C2×C3×C22⋊C4C2314yes—
175C2×#217C2312yes—
176C2×#217C2312yes—
177C2×#217C2314yes—
178C2×#217C2312yes—
179C2×#217C2314yes—
180C2×#217C2314yes—
181#939—216no—
182#938—216no—
183#938—24no—
184#938—28no—
185#937—28no—
186#937—44no—
187D4×Dic3—28no—
188C2×(C2×D3)⋊C4C2312yes—
189C2×(C2×D3)⋊C4C2314yes—
190C2×(C2×D3)⋊C4C2312yes—
191C2×(C2×D3)⋊C4C2314yes—
192C2×(C2×D3)⋊C4C2314yes—
193C2×(C2×D3)⋊C4C2314yes—
194C2×C4⋊Dic3C2312yes—
195C2×C4⋊Dic3C2314yes—
196C2×C4⋊Dic3C2312yes—
197C2×C4⋊Dic3C2311yescharacteristic
198#924—24no—
199#924—28no—
200C2×Dic3⋊C4C2314yes—
201C2×Dic3⋊C4C2314yes—
202C2×Dic3⋊C4C2312yes—
203C2×C4×Dic3C2312yes—
204#897—24no—
205#897—28no—
206#892—24no—
207D3×C4⋊C4—28no—
208#884—216no—
209#883—28no—
210#67⋊C4—28no—
211D3×C22⋊C4—44no—
212#878—216no—
213C3×#95C2314yes—
214C3×#95C2312yes—
215C3⋊#95C2314yes—
216C3⋊#95C2314yes—
217C3⋊#95C2314yes—
218C3⋊#95C2314yes—
219C3⋊#95C2312yes—
220C22×#41—31no—
221C22×#41—32no—
222C22×#41—32no—
223C22×#41—32no—
224C22×#41—32no—
225C22×#41—68no—
226C22×#41—616no—
227C23×Q8—31no—
228C23×D4—31no—
229C23×D4—31no—
230C23×D4—31no—
231C24×C4—31no—
232C24×C4—31no—
233C24×C4C2×D311yescharacteristic
234#537—616no—
235#525—68no—
236C2×#123—32no—
237C2×C22⋊Q8—31no—
238C2×C22⋊Q8—32no—
239C2×C22⋊Q8—32no—
240C2×C22⋊Q8—31no—
241C2×C22⋊Q8—34no—
242C2×#121—32no—
243C2×#121—31no—
244C2×#121—34no—
245C2×#121—34no—
246C2×#121—34no—
247C2×#121C2×D311yescharacteristic
248C2×#121C2×D312yescomplemented
249C2×#120—32no—
250C2×#120—32no—
251C2×#120C2×D312yes—
252C2×C4×D4—32no—
253C2×C4×D4—32no—
254C2×#117—31no—
255C22×C4⋊C4—32no—
256C22×C22⋊C4—32no—
257#395—34no—
258#394—34no—
259#394—34no—
260#394—34no—
261#393—34no—
262#392—34no—
263#392—34no—
264#392—34no—
265#391—34no—
266#390—34no—
267#386—32no—
268#386—34no—
269#386—34no—
270#386—34no—
271#386C2×D312yes—
272#386C2×D314yescomplemented
273#385—32no—
274#385—34no—
275#385—32no—
276#385—34no—
277#380—32no—
278#380—31no—
279#380—32no—
280#380—32no—
281#380—32no—
282#380—32no—
283#380—32no—
284#380C2×D311yescharacteristic
285#380C2×D312yescomplemented
286#379—32no—
287#379—32no—
288C2×#95—32no—
289C24×C3—24no—
290C24×C3—22no—
291C24×C3—22no—
292C24×C3—22no—
293C24×C3—42no—
294C24×C3C2412yes—
295C24×C3C2412yes—
296C24×C3C2411yescharacteristic
297C23×D3—22no—
298C23×D3—22no—
299C23×D3—22no—
300C23×D3—24no—
301C23×D3—24no—
302C23×D3—22no—
303C23×D3—22no—
304C23×D3—42no—
305C23×D3—42no—
306C23×D3C2×D414yes—
307C23×D3C2411yescharacteristic
308C23×D3C2412yes—
309C23×D3C2411yescharacteristic
310C2×C3×D4—24no—
311C2×C3×D4—24no—
312C2×C3×D4—24no—
313C2×C3×D4—28no—
314C2×C3×D4—22no—
315C2×C3×D4—24no—
316C2×C3×D4—44no—
317C2×C3×D4—44no—
318C22×C3×C4—232no—
319C22×C3×C4—22no—
320C22×C3×C4—24no—
321C22×C3×C4—24no—
322C22×C3×C4—24no—
323C22×C3×C4—24no—
324C22×C3×C4—24no—
325C22×C3×C4—24no—
326C22×C3×C4—24no—
327C22×C3×C4C2×D414yes—
328C22×C3×C4C2×D418yes—
329C22×C3×C4C2412yes—
330C22×C3×C4C2414yes—
331C22×C3×C4C2412yes—
332C22×C3×C4C2411yescharacteristic
333C22×C3×C4C2411yescharacteristic
334C2×#67—232no—
335C2×#67—232no—
336C2×#67—24no—
337C2×#67—24no—
338C2×#67—24no—
339C2×#67—24no—
340C2×#67—24no—
341C2×#67—24no—
342C2×#67—24no—
343C2×#67—24no—
344C2×#67—28no—
345C2×#67—28no—
346C2×#67—24no—
347C2×#67—24no—
348C2×#67—24no—
349C2×#67—24no—
350C2×#67—44no—
351C2×#67—44no—
352C2×#67—44no—
353C2×#67C2×D418yes—
354C2×#67C2×D418yes—
355C22×Dic3—22no—
356C22×Dic3—24no—
357C22×Dic3—24no—
358C22×Dic3—28no—
359C22×Dic3—24no—
360C22×Dic3C2×D414yes—
361C22×Dic3C2412yes—
362C22×Dic3C2414yes—
363C22×Dic3C2412yes—
364C22×Dic3C2411yescharacteristic
365C22×Dic3C2412yes—
366C22×Dic3C2411yescharacteristic
367#237—416no—
368#235—264no—
369#235—264no—
370#235—264no—
371#235—264no—
372C2×D12—232no—
373C2×D12—24no—
374C2×D12—24no—
375C2×D12—24no—
376C2×D12—24no—
377C2×D12—24no—
378C2×D12C2×D418yes—
379C2×C4×D3—232no—
380C2×C4×D3—24no—
381C2×C4×D3—24no—
382C2×C4×D3—24no—
383C2×C4×D3—24no—
384C2×C4×D3—24no—
385C2×C4×D3—24no—
386C2×C4×D3—24no—
387C2×C4×D3—24no—
388C2×C4×D3—232no—
389C2×C4×D3—28no—
390C2×C4×D3—44no—
391C2×C4×D3—44no—
392C2×C4×D3C2×D414yes—
393C2×C4×D3C2×D414yes—
394C2×C4×D3C2×D418yes—
395C2×C4×D3C2×D414yes—
396C2×C4×D3C2×D418yes—
397C2×C4×D3C2×D414yes—
398C2×Dic6—232no—
399C2×Dic6—24no—
400C2×Dic6—24no—
401C2×Dic6—24no—
402C2×Dic6—24no—
403C2×Dic6—24no—
404C2×Dic6—22no—
405C2×Dic6—24no—
406C2×Dic6C2×D418yes—
407C3×C4⋊C4—24no—
408C3×C4⋊C4—22no—
409C3×C22⋊C4—24no—
410C3×C22⋊C4—28no—
411C3×C22⋊C4—24no—
412C3×C22⋊C4—44no—
413#217—24no—
414#217—28no—
415#217—24no—
416#217—28no—
417#217—24no—
418#217—44no—
419(C2×D3)⋊C4—24no—
420(C2×D3)⋊C4—24no—
421(C2×D3)⋊C4—28no—
422(C2×D3)⋊C4—44no—
423(C2×D3)⋊C4—44no—
424(C2×D3)⋊C4—44no—
425C4⋊Dic3—24no—
426C4⋊Dic3—22no—
427C4⋊Dic3—28no—
428C4⋊Dic3—24no—
429Dic3⋊C4—28no—
430Dic3⋊C4—24no—
431Dic3⋊C4—28no—
432C4×Dic3—24no—
433C25—31no—
434C25—31no—
435C25C22×D311yescharacteristic
436C2×#41—316no—
437C2×#41—68no—
438C2×#41—68no—
439C2×#41—68no—
440C2×#41—68no—
441C2×#41—68no—
442C2×#41—68no—
443C2×#41—68no—
444C2×#41—68no—
445C2×#41—68no—
446C2×#41—68no—
447C2×#41—6128no—
448C2×#41—64no—
449C2×#41—68no—
450C2×#41—68no—
451C22×Q8—32no—
452C22×Q8—31no—
453C22×Q8—32no—
454C22×Q8—64no—
455C22×Q8—68no—
456C22×D4—32no—
457C22×D4—32no—
458C22×D4—32no—
459C22×D4—32no—
460C22×D4—32no—
461C22×D4—32no—
462C22×D4—34no—
463C22×D4—32no—
464C22×D4—32no—
465C22×D4—68no—
466C22×D4—64no—
467C22×D4—64no—
468C22×D4—68no—
469C22×D4—68no—
470C22×D4—64no—
471C22×D4C22×D312yes—
472C22×D4C22×D311yescharacteristic
473C22×D4C22×D314yes—
474C23×C4—24no—
475C23×C4—28no—
476C23×C4—31no—
477C23×C4—31no—
478C23×C4—38no—
479C23×C4—31no—
480C23×C4—31no—
481C23×C4—32no—
482C23×C4—31no—
483C23×C4—32no—
484C23×C4—31no—
485C23×C4—32no—
486C23×C4—34no—
487C23×C4—68no—
488C23×C4—68no—
489C23×C4—64no—
490C23×C4C22×D311yescharacteristic
491C23×C4C22×D312yes—
492C23×C4C22×D311yescharacteristic
493C23×C4C22×D312yes—
494#123—68no—
495C22⋊Q8—616no—
496C22⋊Q8—64no—
497C22⋊Q8—68no—
498C22⋊Q8—64no—
499C22⋊Q8—68no—
500#121—24no—
501#121—28no—
502#121—616no—
503#121—64no—
504#121—68no—
505#121—616no—
506#121—616no—
507#120—44no—
508#120—68no—
509#120—124no—
510C4×D4—68no—
511C4×D4—68no—
512#117—64no—
513C2×C4⋊C4—32no—
514C2×C4⋊C4—34no—
515C2×C4⋊C4—31no—
516C2×C4⋊C4—32no—
517C2×C4⋊C4—32no—
518C2×C4⋊C4—34no—
519C2×C4⋊C4—34no—
520C2×C4⋊C4—68no—
521C2×C4⋊C4C22×D312yes—
522C2×C4⋊C4C22×D311yescharacteristic
523C2×C22⋊C4—32no—
524C2×C22⋊C4—32no—
525C2×C22⋊C4—32no—
526C2×C22⋊C4—34no—
527C2×C22⋊C4—34no—
528C2×C22⋊C4—32no—
529C2×C22⋊C4—32no—
530C2×C22⋊C4—34no—
531C2×C22⋊C4—34no—
532C2×C22⋊C4—34no—
533C2×C22⋊C4—34no—
534C2×C22⋊C4—34no—
535C2×C22⋊C4—124no—
536C2×C22⋊C4C22×D312yes—
537C2×C22⋊C4C22×D312yes—
538C2×C22⋊C4C22×D314yes—
539C2×C22⋊C4C22×D314yes—
540C2×C42—32no—
541#95—32no—
542#95—34no—
543#95—34no—
544#95—34no—
545#95—34no—
546#95C22×D312yes—
547#95C22×D314yes—
548C23×C3—22no—
549C23×C3—22no—
550C23×C3—28no—
551C23×C3—22no—
552C23×C3—22no—
553C23×C3—22no—
554C23×C3—22no—
555C23×C3—22no—
556C23×C3—22no—
557C23×C3—22no—
558C23×C3—24no—
559C23×C3—22no—
560C23×C3—22no—
561C23×C3—24no—
562C23×C3—48no—
563C23×C3—48no—
564C23×C3—44no—
565C23×C3—44no—
566C23×C3C22×D414yes—
567C23×C3C22×D412yes—
568C23×C3H(5,𝔽2)12yes—
569C23×C32−1+412yes—
570C23×C3C2511yescharacteristic
571C22×D3—21no—
572C22×D3—21no—
573C22×D3—22no—
574C22×D3—28no—
575C22×D3—28no—
576C22×D3—22no—
577C22×D3—22no—
578C22×D3—22no—
579C22×D3—21no—
580C22×D3—22no—
581C22×D3—21no—
582C22×D3—22no—
583C22×D3—22no—
584C22×D3—22no—
585C22×D3—22no—
586C22×D3—28no—
587C22×D3—44no—
588C22×D3—48no—
589C22×D3—48no—
590C22×D3—48no—
591C22×D3—48no—
592C22×D3—44no—
593C22×D3—44no—
594C22×D3C22×D414yes—
595C22×D3C22×D412yes—
596C22×D3C22×D412yes—
597C22×D3C22×D414yes—
598C3×D4—48no—
599C3×D4—44no—
600C3×D4—88no—
601C2×C3×C4—28no—
602C2×C3×C4—216no—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—22no—
606C2×C3×C4—28no—
607C2×C3×C4—216no—
608C2×C3×C4—22no—
609C2×C3×C4—24no—
610C2×C3×C4—22no—
611C2×C3×C4—24no—
612C2×C3×C4—22no—
613C2×C3×C4—24no—
614C2×C3×C4C22×D414yes—
615C2×C3×C4C22×D412yes—
616C2×C3×C4C22×D412yes—
617C2×C3×C4C22×D414yes—
618#67—216no—
619#67—216no—
620#67—216no—
621#67—216no—
622#67—48no—
623#67—48no—
624#67—88no—
625C2×Dic3—28no—
626C2×Dic3—22no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—28no—
630C2×Dic3—22no—
631C2×Dic3—24no—
632C2×Dic3—22no—
633C2×Dic3—24no—
634C2×Dic3—24no—
635C2×Dic3—24no—
636C2×Dic3—24no—
637C2×Dic3—48no—
638C2×Dic3C22×D412yes—
639C2×Dic3C22×D414yes—
640C2×Dic3C22×D412yes—
641C2×Dic3C22×D414yes—
642D12—216no—
643D12—216no—
644C4×D3—216no—
645C4×D3—28no—
646C4×D3—216no—
647C4×D3—28no—
648C4×D3—28no—
649C4×D3—88no—
650C4×D3#120116yescomplemented
651Dic6—216no—
652Dic6—216no—
653Dic6—44no—
654C24—24no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—31no—
659C24—31no—
660C24—32no—
661C24—34no—
662C24—42no—
663C24—64no—
664C24—64no—
665C24—62no—
666C24—62no—
667C24—62no—
668C24—62no—
669C24—62no—
670C24—122no—
671C24—122no—
672C24C23×D312yes—
673C24C23×D312yes—
674C24C23×D311yescharacteristic
675#41—664no—
676#41—664no—
677#41—664no—
678#41—664no—
679#41—1216no—
680C2×Q8—38no—
681C2×Q8—64no—
682C2×Q8—64no—
683C2×Q8—64no—
684C2×Q8—64no—
685C2×Q8—632no—
686C2×Q8—64no—
687C2×Q8—62no—
688C2×Q8—64no—
689C2×D4—24no—
690C2×D4—24no—
691C2×D4—24no—
692C2×D4—28no—
693C2×D4—22no—
694C2×D4—24no—
695C2×D4—38no—
696C2×D4—38no—
697C2×D4—38no—
698C2×D4—44no—
699C2×D4—44no—
700C2×D4—64no—
701C2×D4—64no—
702C2×D4—64no—
703C2×D4—64no—
704C2×D4—632no—
705C2×D4—64no—
706C2×D4—64no—
707C2×D4—64no—
708C2×D4—64no—
709C2×D4—64no—
710C2×D4—64no—
711C2×D4—64no—
712C2×D4—64no—
713C2×D4—632no—
714C2×D4—632no—
715C2×D4—64no—
716C2×D4—64no—
717C2×D4—64no—
718C2×D4—64no—
719C2×D4—68no—
720C2×D4—68no—
721C2×D4—64no—
722C2×D4—124no—
723C2×D4—124no—
724C2×D4—124no—
725C22×C4—232no—
726C22×C4—22no—
727C22×C4—24no—
728C22×C4—24no—
729C22×C4—24no—
730C22×C4—24no—
731C22×C4—24no—
732C22×C4—24no—
733C22×C4—24no—
734C22×C4—31no—
735C22×C4—38no—
736C22×C4—34no—
737C22×C4—34no—
738C22×C4—31no—
739C22×C4—32no—
740C22×C4—34no—
741C22×C4—34no—
742C22×C4—38no—
743C22×C4—34no—
744C22×C4—32no—
745C22×C4—34no—
746C22×C4—32no—
747C22×C4—64no—
748C22×C4—64no—
749C22×C4—632no—
750C22×C4—64no—
751C22×C4—64no—
752C22×C4—632no—
753C22×C4—68no—
754C22×C4—64no—
755C22×C4—64no—
756C22×C4—64no—
757C22×C4—68no—
758C22×C4—62no—
759C22×C4—64no—
760C22×C4—64no—
761C22×C4—64no—
762C22×C4—64no—
763C22×C4—124no—
764C22×C4—124no—
765C22×C4D3×D414yes—
766C22×C4D3×D418yes—
767C22×C4C23×D312yes—
768C22×C4C23×D314yes—
769C22×C4C23×D311yescharacteristic
770C22×C4C23×D312yes—
771C22×C4C23×D311yescharacteristic
772C4⋊C4—24no—
773C4⋊C4—22no—
774C4⋊C4—68no—
775C4⋊C4—64no—
776C4⋊C4—68no—
777C4⋊C4—64no—
778C4⋊C4—62no—
779C4⋊C4—64no—
780C4⋊C4—68no—
781C22⋊C4—24no—
782C22⋊C4—24no—
783C22⋊C4—28no—
784C22⋊C4—44no—
785C22⋊C4—64no—
786C22⋊C4—64no—
787C22⋊C4—68no—
788C22⋊C4—64no—
789C22⋊C4—68no—
790C22⋊C4—64no—
791C22⋊C4—68no—
792C22⋊C4—64no—
793C22⋊C4—124no—
794C22⋊C4—124no—
795C22⋊C4—124no—
796C22⋊C4—124no—
797C42—64no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—24no—
801C22×C3—24no—
802C22×C3—24no—
803C22×C3—24no—
804C22×C3—24no—
805C22×C3—416no—
806C22×C3—42no—
807C22×C3—42no—
808C22×C3—42no—
809C22×C3—42no—
810C22×C3—42no—
811C22×C3—42no—
812C22×C3—42no—
813C22×C3—44no—
814C22×C3—44no—
815C22×C3#53714yescomplemented
816C22×C3C23×D411yescharacteristic
817C22×C3C23×D412yes—
818C22×C3C2×H(5,𝔽2)11yescharacteristic
819C22×C3C2×2−1+411yescharacteristic
820C22×C3#58512yes—
821C2×D3—22no—
822C2×D3—22no—
823C2×D3—24no—
824C2×D3—24no—
825C2×D3—24no—
826C2×D3—22no—
827C2×D3—22no—
828C2×D3—22no—
829C2×D3—24no—
830C2×D3—24no—
831C2×D3—416no—
832C2×D3—416no—
833C2×D3—42no—
834C2×D3—42no—
835C2×D3—42no—
836C2×D3—42no—
837C2×D3—42no—
838C2×D3—42no—
839C2×D3C2×#12014yes—
840C3×C4—24no—
841C3×C4—22no—
842C3×C4—42no—
843C3×C4—44no—
844C3×C4C2×#12014yes—
845Dic3—22no—
846Dic3—24no—
847Dic3—42no—
848Dic3—42no—
849Dic3—44no—
850Dic3C2×#12014yes—
851C23—22no—
852C23—22no—
853C23—28no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—24no—
862C23—22no—
863C23—22no—
864C23—24no—
865C23—32no—
866C23—34no—
867C23—32no—
868C23—34no—
869C23—48no—
870C23—48no—
871C23—44no—
872C23—44no—
873C23—68no—
874C23—68no—
875C23—61no—
876C23—61no—
877C23—62no—
878C23—62no—
879C23—62no—
880C23—62no—
881C23—61no—
882C23—62no—
883C23—62no—
884C23—61no—
885C23—62no—
886C23—62no—
887C23—62no—
888C23—68no—
889C23—124no—
890C23—128no—
891C23—128no—
892C23—128no—
893C23—128no—
894C23—124no—
895C23—124no—
896C23C2×D3×D414yes—
897C23C2×D3×D412yes—
898C23#100412yes—
899C23#101012yes—
900C23C24×D311yescharacteristic
901Q8—616no—
902Q8—616no—
903Q8—124no—
904D4—48no—
905D4—44no—
906D4—616no—
907D4—616no—
908D4—616no—
909D4—616no—
910D4—616no—
911D4—616no—
912D4—88no—
913D4—128no—
914D4—128no—
915D4—248no—
916C2×C4—28no—
917C2×C4—216no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—28no—
922C2×C4—216no—
923C2×C4—22no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—24no—
929C2×C4—32no—
930C2×C4—34no—
931C2×C4—316no—
932C2×C4—32no—
933C2×C4—34no—
934C2×C4—68no—
935C2×C4—68no—
936C2×C4—616no—
937C2×C4—68no—
938C2×C4—68no—
939C2×C4—62no—
940C2×C4—62no—
941C2×C4—62no—
942C2×C4—68no—
943C2×C4—616no—
944C2×C4—62no—
945C2×C4—64no—
946C2×C4—62no—
947C2×C4—64no—
948C2×C4—64no—
949C2×C4—64no—
950C2×C4—64no—
951C2×C4—128no—
952C2×C4—248no—
953C2×C4C2×D3×D412yes—
954C2×C4C2×D3×D414yes—
955C2×C4C2×D3×D412yes—
956C2×C4C2×D3×D414yes—
957C2×C3—24no—
958C2×C3—44no—
959C2×C3—82no—
960C2×C3C22×#12011yescharacteristic
961C2×C3C2×#53711yescharacteristic
962C2×C3#344911yescharacteristic
963C2×C3#348812yes—
964C2×C3#348912yes—
965D3—24no—
966D3—42no—
967D3—44no—
968C22—22no—
969C22—24no—
970C22—22no—
971C22—24no—
972C22—24no—
973C22—24no—
974C22—24no—
975C22—34no—
976C22—416no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—44no—
983C22—42no—
984C22—42no—
985C22—44no—
986C22—62no—
987C22—64no—
988C22—62no—
989C22—64no—
990C22—62no—
991C22—64no—
992C22—62no—
993C22—64no—
994C22—62no—
995C22—64no—
996C22—1216no—
997C22—1216no—
998C22—122no—
999C22—122no—
1000C22—122no—
1001C22—122no—
1002C22—122no—
1003C22—122no—
1004C22#560814yescomplemented
1005C22C22×D3×D411yescharacteristic
1006C22C22×D3×D412yes—
1007C22C2×#100411yescharacteristic
1008C22C2×#101011yescharacteristic
1009C22#596412yes—
1010C4—22no—
1011C4—24no—
1012C4—34no—
1013C4—42no—
1014C4—44no—
1015C4—62no—
1016C4—64no—
1017C4—122no—
1018C4—122no—
1019C4—124no—
1020C4D3×#12014yes—
1021C3#3525111yescharacteristic, complemented, Sylow
1022C2—24no—
1023C2—44no—
1024C2—64no—
1025C2—82no—
1026C2—122no—
1027C2—124no—
1028C2C2×D3×#12011yescharacteristic
1029C2C2×#560811yescharacteristic
1030C2#8594912yes—
1031C2#8603511yescharacteristic
1032C2#8604212yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2847C2
hypercenter#2847D3
hypocenterC3#35251
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2847

Complements

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

NH ≅ G/Ntype
1. C23×#235C2semidirect
2. C2×#5608C2semidirect
3. C2×#5606C2semidirect
4. C3×#2847C2semidirect
5. #84031C2semidirect
6. #82723C2semidirect
7. #82709C2semidirect
8. #82605C2semidirect
9. #82582C2semidirect
10. #74896C2semidirect
11. #74887C2semidirect
12. #74689C2semidirect
13. #74688C2semidirect
14. #74049C2semidirect
15. #74003C2semidirect
16. D3×#380C2semidirect
17. #73950C2semidirect
22. C22×#237C22semidirect
34. C2×C3×#121C22semidirect
36. C2×#939C22semidirect
37. C2×#938C22semidirect
38. C2×#938C22semidirect
39. C2×#938C22semidirect
44. C2×#924C22semidirect
47. C2×#897C22semidirect
48. C2×#897C22semidirect
49. C2×#892C22semidirect
50. C2×D3×C4⋊C4C22semidirect
51. C2×#884C22semidirect
52. C2×#883C22semidirect
53. C2×#67⋊C4C22semidirect
55. C2×#878C22semidirect
57. C3×#386C22semidirect
59. C3×#380C22semidirect
61. #5223C22semidirect
62. #5223C22semidirect
65. #5212C22semidirect
67. #5210C22semidirect
68. #4987C22semidirect
69. #4987C22semidirect
70. #4987C22semidirect
71. #4961C22semidirect
72. #4961C22semidirect
73. #4960C22semidirect
74. #4957C22semidirect
75. #4956C22semidirect
76. #4956C22semidirect
79. #4947C22semidirect
81. #4672C22semidirect
82. #4668C22semidirect
83. #4667C22semidirect
84. #4665C22semidirect
85. D3×#95C22semidirect
86. #4656C22semidirect
87. #4646C22semidirect
94. #2847D3semidirect
145. C2×#235D4semidirect
153. C22×C4×D3D4semidirect
248. C2×#121C2×D3semidirect
272. #386C2×D3semidirect
285. #380C2×D3semidirect
650. C4×D3#120semidirect
815. C22×C3#537semidirect
1004. C22#5608semidirect
1021. C3#35251semidirect

Maximal subgroups

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

subgroupindex
C23×#2352
C2×#56082
C2×#56062
C3×#28472
#840312
#827232
#827092
#826052
#825822
#748962
#748872
#746892
#746882
#740492
#740032
D3×#3802
#739502
#352513