Finite Group Databasebeta

← #10972923

Subgroups — #10972923

Order 768.

5426 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×#41C211yesmaximal, characteristic, complemented
2C2×#5608C212yesmaximal, complemented
3C2×#5606C211yesmaximal, characteristic, complemented
4C3×#2615C211yesmaximal, characteristic, complemented
5#84094C211yesmaximal, characteristic, complemented
6#82723C212yesmaximal, complemented
7#82709C211yesmaximal, characteristic, complemented
8#76864C212yesmaximal, complemented
9#76780C212yesmaximal, complemented
10#76757C212yesmaximal, complemented
11#76755C214yesmaximal, complemented
12#76669C212yesmaximal, complemented
13#76668C214yesmaximal, complemented
14#74049C212yesmaximal, complemented
15#74003C212yesmaximal, complemented
16D3×#380C211yesmaximal, characteristic, complemented
17#73950C211yesmaximal, characteristic, complemented
18#35251—31nomaximal, Sylow
19C22×C3×#41C2211yescharacteristic
20C2×D3×#41—216no—
21C2×D3×#41—28no—
22C22×#239C2211yescharacteristic
23C22×D3×Q8C2211yescharacteristic
24C22×#237C2212yes—
25C22×#237C2211yescharacteristic
26C22×#237C2211yescharacteristic, complemented
27C22×D3×D4C2211yescharacteristic
28C22×D3×D4C2212yes—
29C22×#235C2211yescharacteristic
30C22×#235C2212yes—
31C23×C4×D3C2212yes—
32C23×C4×D3C2211yescharacteristic
33C2×C3×#121C2211yescharacteristic, complemented
34C2×C3×#121C2212yescomplemented
35C2×#939C2214yescomplemented
36C2×#938C2211yescharacteristic
37C2×#938C2212yescomplemented
38C2×#938C2214yescomplemented
39C2×#937C2212yes—
40C2×#937C2214yes—
41C2×D4×Dic3C2212yescomplemented
42C2×#924C2212yescomplemented
43C2×#924C2211yescharacteristic, complemented
44#5608—216no—
45#5606—28no—
46C2×#897C2211yescharacteristic
47C2×#897C2212yescomplemented
48C2×#892C2211yescharacteristic, complemented
49C2×D3×C4⋊C4C2212yescomplemented
50C2×#884C2214yescomplemented
51C2×#883C2212yescomplemented
52C2×#67⋊C4C2212yes—
53C2×D3×C22⋊C4C2212yes—
54C2×#878C2214yescomplemented
55C3×#393C2212yescomplemented
56C3×#392C2214yescomplemented
57C3×#392C2212yescomplemented
58C3×#380C2211yescharacteristic, complemented
59C3×#380C2212yescomplemented
60#5230C2212yescomplemented
61#5223C2214yescomplemented
62#5222C2214yescomplemented
63#5222C2212yescomplemented
64#5220C2214yescomplemented
65#5212C2211yescharacteristic, complemented
66#5212C2212yescomplemented
67#4987C2212yes—
68#4987C2212yescomplemented
69#4987C2212yescomplemented
70#4961C2214yescomplemented
71#4960C2212yescomplemented
72#4957C2214yescomplemented
73#4956C2214yes—
74#4956C2214yescomplemented
75#4956C2214yescomplemented
76#4955C2214yes—
77#4950C2214yescomplemented
78#4947C2212yescomplemented
79#4942C2212yescomplemented
80#4672C2212yescomplemented
81#4668C2214yes—
82#4668C2214yescomplemented
83#4667C2212yes—
84#4665C2214yescomplemented
85D3×#95C2212yescomplemented
86#4656C2212yescomplemented
87#4646C2214yescomplemented
88C23×#41—31no—
89C2×#537—32no—
90C2×#525—31no—
91#2848—32no—
92#2847—32no—
93#2616—31no—
94#2616—31no—
95#2615—31no—
96#2615D311yescharacteristic, complemented
97#2430—32no—
98#2430—32no—
99#2410—34no—
100#2409—32no—
101#2408—32no—
102#2407—34no—
103#2311—32no—
104C2×#380—31no—
105C24×D3C2312yes—
106C24×D3C2311yescharacteristic
107C2×C3×#41—28no—
108C2×C3×#41—24no—
109C22×C3×Q8C2311yescharacteristic
110C22×C3×D4C2311yescharacteristic
111C22×C3×D4C2312yes—
112C22×C3×D4C2311yescharacteristic
113C22×C3×D4C2314yes—
114C22×C3×D4C2312yes—
115C23×C3×C4C2312yes—
116C23×C3×C4C2311yescharacteristic
117C22×#67C2312yes—
118C22×#67C2312yes—
119C22×#67C2312yes—
120C22×#67C2312yes—
121C22×#67C2312yes—
122C22×#67C2314yes—
123C23×Dic3C2312yes—
124C23×Dic3C2312yes—
125C23×Dic3C2311yescharacteristic
126D3×#41—2128no—
127C2×#239—28no—
128C2×#239—24no—
129C2×D3×Q8—24no—
130C2×D3×Q8—28no—
131C2×#237—28no—
132C2×#237—28no—
133C2×#237—28no—
134C2×#237—24no—
135C2×#237—24no—
136C2×#237—28no—
137C2×#237—28no—
138C2×D3×D4—28no—
139C2×D3×D4—28no—
140C2×D3×D4—28no—
141C2×D3×D4—28no—
142C2×D3×D4—24no—
143C2×#235—24no—
144C2×#235—28no—
145C2×#235—28no—
146C2×#235—28no—
147C2×#235D4116yescomplemented
148C22×D12C2311yescharacteristic
149C22×D12C2312yes—
150C22×C4×D3—28no—
151C22×C4×D3—28no—
152C22×C4×D3—28no—
153C22×C4×D3—28no—
154C22×C4×D3D418yescomplemented
155C22×C4×D3C2312yes—
156C22×C4×D3C2312yes—
157C22×C4×D3C2311yescharacteristic
158C22×C4×D3C2311yescharacteristic
159C22×C4×D3C2311yescharacteristic
160C22×C4×D3C2312yes—
161C22×C4×D3C2314yes—
162C22×C4×D3C2311yescharacteristic
163C22×Dic6C2311yescharacteristic
164C22×Dic6C2311yescharacteristic
165C22×Dic6C2312yes—
166C3×#121—24no—
167C3×#121—28no—
168C2×C3×C4⋊C4C2312yes—
169C2×C3×C4⋊C4C2311yescharacteristic
170C2×C3×C22⋊C4C2312yes—
171C2×C3×C22⋊C4C2314yes—
172C2×C3×C22⋊C4C2312yes—
173C2×C3×C22⋊C4C2314yes—
174C2×#217C2314yes—
175C2×#217C2314yes—
176C2×#217C2312yes—
177C2×#217C2312yes—
178C2×#217C2312yes—
179C2×#217C2314yes—
180#939—216no—
181#938—216no—
182#938—24no—
183#938—28no—
184#937—28no—
185#937—48no—
186D4×Dic3—28no—
187C2×(C2×D3)⋊C4C2312yes—
188C2×(C2×D3)⋊C4C2314yes—
189C2×(C2×D3)⋊C4C2312yes—
190C2×(C2×D3)⋊C4C2314yes—
191C2×(C2×D3)⋊C4C2314yes—
192C2×(C2×D3)⋊C4C2314yes—
193C2×C4⋊Dic3C2314yes—
194C2×C4⋊Dic3C2312yes—
195C2×C4⋊Dic3C2312yes—
196C2×C4⋊Dic3C2311yescharacteristic
197#924—24no—
198#924—28no—
199C2×Dic3⋊C4C2314yes—
200C2×Dic3⋊C4C2312yes—
201C2×Dic3⋊C4C2314yes—
202C2×C4×Dic3C2312yes—
203#897—24no—
204#897—28no—
205#892—24no—
206D3×C4⋊C4—28no—
207#884—216no—
208#883—28no—
209#67⋊C4—28no—
210D3×C22⋊C4—44no—
211#878—216no—
212C3×#95C2314yes—
213C3×#95C2312yes—
214C3⋊#95C2314yes—
215C3⋊#95C2314yes—
216C3⋊#95C2314yes—
217C3⋊#95C2312yes—
218C3⋊#95C2314yes—
219C22×#41—31no—
220C22×#41—32no—
221C22×#41—31no—
222C22×#41—31no—
223C22×#41—32no—
224C22×#41—31no—
225C22×#41—68no—
226C22×#41—616no—
227C22×#41C2×D311yescharacteristic
228C23×Q8—31no—
229C23×D4—31no—
230C23×D4—32no—
231C24×C4—31no—
232C24×C4—32no—
233#537—616no—
234#525—68no—
235C2×#123—32no—
236C2×C22⋊Q8—32no—
237C2×C22⋊Q8—31no—
238C2×C22⋊Q8—31no—
239C2×C22⋊Q8—32no—
240C2×C22⋊Q8—34no—
241C2×#121—31no—
242C2×#121—32no—
243C2×#121—34no—
244C2×#121—34no—
245C2×#121—34no—
246C2×#121C2×D312yescomplemented
247C2×#121C2×D311yescharacteristic, complemented
248C2×#120—32no—
249C2×#120—34no—
250C2×C4×D4—32no—
251C2×C4×D4—32no—
252C2×#117—31no—
253C22×C4⋊C4—32no—
254C22×C22⋊C4—32no—
255#395—32no—
256#395—32no—
257#394—34no—
258#394—32no—
259#394—34no—
260#394—32no—
261#393—32no—
262#393C2×D312yescomplemented
263#392—34no—
264#392—32no—
265#392C2×D314yescomplemented
266#392C2×D312yescomplemented
267#391—34no—
268#390—34no—
269#386—34no—
270#386—34no—
271#386—34no—
272#386—34no—
273#386—34no—
274#385—34no—
275#385—34no—
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×D312yescomplemented
285#380C2×D311yescharacteristic, complemented
286#379—34no—
287C2×#95—32no—
288C24×C3C2412yes—
289C24×C3C2411yescharacteristic
290C24×C3C2412yes—
291C23×D3—24no—
292C23×D3—24no—
293C23×D3—24no—
294C23×D3—24no—
295C23×D3—22no—
296C23×D3—22no—
297C23×D3—24no—
298C23×D3—24no—
299C23×D3—42no—
300C23×D3—42no—
301C23×D3—42no—
302C23×D3C2×D414yes—
303C23×D3C2412yes—
304C23×D3C2411yescharacteristic
305C23×D3C2411yescharacteristic
306C3×#41—232no—
307C2×C3×Q8—22no—
308C2×C3×Q8—24no—
309C2×C3×D4—24no—
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—22no—
317C2×C3×D4—24no—
318C2×C3×D4—44no—
319C2×C3×D4—44no—
320C2×C3×D4—44no—
321C22×C3×C4—24no—
322C22×C3×C4—24no—
323C22×C3×C4—24no—
324C22×C3×C4C2×D418yes—
325C22×C3×C4C2×D414yes—
326C22×C3×C4C2412yes—
327C22×C3×C4C2414yes—
328C22×C3×C4C2411yescharacteristic
329C22×C3×C4C2412yes—
330C22×C3×C4C2411yescharacteristic
331C2×#67—24no—
332C2×#67—24no—
333C2×#67—24no—
334C2×#67—24no—
335C2×#67—24no—
336C2×#67—24no—
337C2×#67—28no—
338C2×#67—24no—
339C2×#67—24no—
340C2×#67—28no—
341C2×#67—24no—
342C2×#67—24no—
343C2×#67—24no—
344C2×#67—44no—
345C2×#67—44no—
346C2×#67C2×D418yes—
347C2×#67C2×D418yes—
348C22×Dic3—24no—
349C22×Dic3—24no—
350C22×Dic3—24no—
351C22×Dic3—24no—
352C22×Dic3—28no—
353C22×Dic3—24no—
354C22×Dic3C2×D414yes—
355C22×Dic3C2412yes—
356C22×Dic3C2414yes—
357C22×Dic3C2412yes—
358C22×Dic3C2412yes—
359C22×Dic3C2411yescharacteristic
360C22×Dic3C2411yescharacteristic
361#239—232no—
362D3×Q8—232no—
363#237—232no—
364#237—264no—
365#237—416no—
366D3×D4—264no—
367D3×D4—232no—
368#235—232no—
369#235—264no—
370C2×D12—24no—
371C2×D12—24no—
372C2×D12—24no—
373C2×D12—22no—
374C2×D12C2×D418yes—
375C2×C4×D3—264no—
376C2×C4×D3—24no—
377C2×C4×D3—24no—
378C2×C4×D3—24no—
379C2×C4×D3—24no—
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—232no—
388C2×C4×D3—28no—
389C2×C4×D3—44no—
390C2×C4×D3—44no—
391C2×C4×D3C2×D414yes—
392C2×C4×D3C2×D414yes—
393C2×C4×D3C2×D414yes—
394C2×C4×D3C2×D418yes—
395C2×C4×D3C2×D418yes—
396C2×C4×D3C2×D414yes—
397C2×Dic6—22no—
398C2×Dic6—24no—
399C2×Dic6—24no—
400C2×Dic6—24no—
401C2×Dic6—22no—
402C2×Dic6—24no—
403C2×Dic6C2×D418yes—
404C3×C4⋊C4—24no—
405C3×C4⋊C4—22no—
406C3×C22⋊C4—28no—
407C3×C22⋊C4—24no—
408C3×C22⋊C4—42no—
409C3×C22⋊C4—44no—
410#217—24no—
411#217—28no—
412#217—28no—
413#217—24no—
414#217—42no—
415#217—44no—
416(C2×D3)⋊C4—24no—
417(C2×D3)⋊C4—24no—
418(C2×D3)⋊C4—28no—
419(C2×D3)⋊C4—28no—
420(C2×D3)⋊C4—44no—
421(C2×D3)⋊C4—44no—
422C4⋊Dic3—24no—
423C4⋊Dic3—22no—
424C4⋊Dic3—28no—
425C4⋊Dic3—24no—
426Dic3⋊C4—28no—
427Dic3⋊C4—24no—
428Dic3⋊C4—28no—
429C4×Dic3—24no—
430C25—31no—
431C25—32no—
432C2×#41—24no—
433C2×#41—28no—
434C2×#41—316no—
435C2×#41—68no—
436C2×#41—68no—
437C2×#41—68no—
438C2×#41—68no—
439C2×#41—64no—
440C2×#41—64no—
441C2×#41—68no—
442C2×#41—64no—
443C2×#41—68no—
444C2×#41—68no—
445C2×#41—68no—
446C2×#41—68no—
447C2×#41—6128no—
448C2×#41—64no—
449C22×Q8—32no—
450C22×Q8—31no—
451C22×Q8—31no—
452C22×Q8—64no—
453C22×Q8—68no—
454C22×Q8C22×D311yescharacteristic
455C22×D4—32no—
456C22×D4—32no—
457C22×D4—32no—
458C22×D4—32no—
459C22×D4—32no—
460C22×D4—34no—
461C22×D4—32no—
462C22×D4—31no—
463C22×D4—64no—
464C22×D4—68no—
465C22×D4—68no—
466C22×D4—68no—
467C22×D4—68no—
468C22×D4C22×D311yescharacteristic
469C22×D4C22×D311yescharacteristic
470C22×D4C22×D312yes—
471C22×D4C22×D312yes—
472C22×D4C22×D314yes—
473C23×C4—31no—
474C23×C4—31no—
475C23×C4—38no—
476C23×C4—31no—
477C23×C4—31no—
478C23×C4—32no—
479C23×C4—31no—
480C23×C4—32no—
481C23×C4—32no—
482C23×C4—32no—
483C23×C4—32no—
484C23×C4—34no—
485C23×C4—68no—
486C23×C4—68no—
487C23×C4—68no—
488C23×C4—68no—
489C23×C4C22×D311yescharacteristic
490C23×C4C22×D312yes—
491#123—68no—
492C22⋊Q8—616no—
493C22⋊Q8—64no—
494C22⋊Q8—68no—
495C22⋊Q8—64no—
496C22⋊Q8—68no—
497#121—24no—
498#121—28no—
499#121—616no—
500#121—64no—
501#121—68no—
502#121—616no—
503#121—616no—
504#120—68no—
505#120—128no—
506C4×D4—68no—
507C4×D4—68no—
508#117—64no—
509C2×C4⋊C4—32no—
510C2×C4⋊C4—34no—
511C2×C4⋊C4—31no—
512C2×C4⋊C4—32no—
513C2×C4⋊C4—32no—
514C2×C4⋊C4—34no—
515C2×C4⋊C4—34no—
516C2×C4⋊C4—68no—
517C2×C4⋊C4C22×D312yes—
518C2×C4⋊C4C22×D311yescharacteristic
519C2×C22⋊C4—32no—
520C2×C22⋊C4—32no—
521C2×C22⋊C4—34no—
522C2×C22⋊C4—34no—
523C2×C22⋊C4—34no—
524C2×C22⋊C4—32no—
525C2×C22⋊C4—32no—
526C2×C22⋊C4—34no—
527C2×C22⋊C4—32no—
528C2×C22⋊C4—34no—
529C2×C22⋊C4—34no—
530C2×C22⋊C4—34no—
531C2×C22⋊C4—124no—
532C2×C22⋊C4C22×D312yes—
533C2×C22⋊C4C22×D314yes—
534C2×C22⋊C4C22×D312yes—
535C2×C22⋊C4C22×D314yes—
536C2×C42—32no—
537#95—34no—
538#95—32no—
539#95—34no—
540#95—34no—
541#95—34no—
542#95C22×D312yes—
543#95C22×D314yes—
544C23×C3—22no—
545C23×C3—22no—
546C23×C3—22no—
547C23×C3—21no—
548C23×C3—22no—
549C23×C3—21no—
550C23×C3—22no—
551C23×C3—22no—
552C23×C3—22no—
553C23×C3—22no—
554C23×C3—22no—
555C23×C3—24no—
556C23×C3—22no—
557C23×C3—22no—
558C23×C3—24no—
559C23×C3C22×D414yes—
560C23×C3C22×D412yes—
561C23×C3C2511yescharacteristic
562C22×D3—22no—
563C22×D3—21no—
564C22×D3—21no—
565C22×D3—22no—
566C22×D3—22no—
567C22×D3—216no—
568C22×D3—22no—
569C22×D3—22no—
570C22×D3—22no—
571C22×D3—22no—
572C22×D3—22no—
573C22×D3—22no—
574C22×D3—28no—
575C22×D3—28no—
576C22×D3—44no—
577C22×D3—48no—
578C22×D3—48no—
579C22×D3—48no—
580C22×D3—48no—
581C22×D3—48no—
582C22×D3—48no—
583C22×D3—48no—
584C22×D3—48no—
585C22×D3C22×D414yes—
586C22×D3C22×D412yes—
587C22×D3C22×D414yes—
588C22×D3C22×D412yes—
589C22×D3H(5,𝔽2)12yes—
590C22×D32−1+412yes—
591C3×Q8—28no—
592C3×D4—28no—
593C3×D4—216no—
594C3×D4—48no—
595C3×D4—44no—
596C3×D4—88no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—216no—
601C2×C3×C4—28no—
602C2×C3×C4—22no—
603C2×C3×C4—24no—
604C2×C3×C4—24no—
605C2×C3×C4—24no—
606C2×C3×C4—24no—
607C2×C3×C4C22×D412yes—
608C2×C3×C4C22×D414yes—
609C2×C3×C4C22×D412yes—
610C2×C3×C4C22×D414yes—
611#67—216no—
612#67—216no—
613#67—216no—
614#67—48no—
615#67—48no—
616#67—88no—
617C2×Dic3—216no—
618C2×Dic3—22no—
619C2×Dic3—22no—
620C2×Dic3—22no—
621C2×Dic3—28no—
622C2×Dic3—22no—
623C2×Dic3—24no—
624C2×Dic3—22no—
625C2×Dic3—24no—
626C2×Dic3—24no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—24no—
630C2×Dic3—48no—
631C2×Dic3C22×D414yes—
632C2×Dic3C22×D412yes—
633C2×Dic3C22×D412yes—
634C2×Dic3C22×D414yes—
635D12—28no—
636D12—216no—
637C4×D3—216no—
638C4×D3—216no—
639C4×D3—28no—
640C4×D3—28no—
641C4×D3—216no—
642C4×D3—28no—
643C4×D3—88no—
644C4×D3#120116yescomplemented
645Dic6—28no—
646Dic6—216no—
647Dic6—44no—
648C24—31no—
649C24—31no—
650C24—32no—
651C24—34no—
652C24—62no—
653C24—64no—
654C24—64no—
655C24—64no—
656C24—62no—
657C24—64no—
658C24—64no—
659C24—64no—
660C24—122no—
661C24—122no—
662C24—122no—
663C24C23×D312yes—
664C24C23×D311yescharacteristic
665C24C23×D312yes—
666#41—232no—
667#41—664no—
668#41—632no—
669#41—632no—
670#41—664no—
671#41—632no—
672#41—1216no—
673C2×Q8—22no—
674C2×Q8—24no—
675C2×Q8—38no—
676C2×Q8—64no—
677C2×Q8—64no—
678C2×Q8—64no—
679C2×Q8—632no—
680C2×Q8—62no—
681C2×Q8—62no—
682C2×Q8—64no—
683C2×D4—24no—
684C2×D4—24no—
685C2×D4—24no—
686C2×D4—24no—
687C2×D4—28no—
688C2×D4—22no—
689C2×D4—24no—
690C2×D4—22no—
691C2×D4—24no—
692C2×D4—38no—
693C2×D4—38no—
694C2×D4—38no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—64no—
699C2×D4—64no—
700C2×D4—64no—
701C2×D4—64no—
702C2×D4—64no—
703C2×D4—64no—
704C2×D4—632no—
705C2×D4—664no—
706C2×D4—64no—
707C2×D4—64no—
708C2×D4—64no—
709C2×D4—64no—
710C2×D4—64no—
711C2×D4—64no—
712C2×D4—64no—
713C2×D4—68no—
714C2×D4—64no—
715C2×D4—68no—
716C2×D4—62no—
717C2×D4—124no—
718C2×D4—124no—
719C22×C4—24no—
720C22×C4—24no—
721C22×C4—24no—
722C22×C4—31no—
723C22×C4—38no—
724C22×C4—34no—
725C22×C4—34no—
726C22×C4—31no—
727C22×C4—32no—
728C22×C4—34no—
729C22×C4—34no—
730C22×C4—38no—
731C22×C4—34no—
732C22×C4—32no—
733C22×C4—34no—
734C22×C4—32no—
735C22×C4—64no—
736C22×C4—64no—
737C22×C4—64no—
738C22×C4—632no—
739C22×C4—64no—
740C22×C4—64no—
741C22×C4—64no—
742C22×C4—664no—
743C22×C4—68no—
744C22×C4—64no—
745C22×C4—64no—
746C22×C4—64no—
747C22×C4—64no—
748C22×C4—68no—
749C22×C4—64no—
750C22×C4—64no—
751C22×C4—64no—
752C22×C4—64no—
753C22×C4—64no—
754C22×C4—64no—
755C22×C4—124no—
756C22×C4—124no—
757C22×C4D3×D414yes—
758C22×C4D3×D418yes—
759C22×C4C23×D312yes—
760C22×C4C23×D314yes—
761C22×C4C23×D311yescharacteristic
762C22×C4C23×D312yes—
763C22×C4C23×D311yescharacteristic
764C4⋊C4—24no—
765C4⋊C4—22no—
766C4⋊C4—68no—
767C4⋊C4—64no—
768C4⋊C4—68no—
769C4⋊C4—64no—
770C4⋊C4—62no—
771C4⋊C4—64no—
772C4⋊C4—68no—
773C22⋊C4—24no—
774C22⋊C4—28no—
775C22⋊C4—42no—
776C22⋊C4—44no—
777C22⋊C4—68no—
778C22⋊C4—64no—
779C22⋊C4—64no—
780C22⋊C4—68no—
781C22⋊C4—64no—
782C22⋊C4—68no—
783C22⋊C4—64no—
784C22⋊C4—68no—
785C22⋊C4—124no—
786C22⋊C4—124no—
787C22⋊C4—122no—
788C22⋊C4—124no—
789C42—64no—
790C22×C3—24no—
791C22×C3—22no—
792C22×C3—22no—
793C22×C3—22no—
794C22×C3—24no—
795C22×C3—24no—
796C22×C3—42no—
797C22×C3—42no—
798C22×C3—42no—
799C22×C3—42no—
800C22×C3—42no—
801C22×C3—42no—
802C22×C3—42no—
803C22×C3—42no—
804C22×C3—42no—
805C22×C3—44no—
806C22×C3—44no—
807C22×C3C23×D411yescharacteristic
808C22×C3C23×D412yes—
809C22×C3C2×H(5,𝔽2)11yescharacteristic
810C22×C3C2×2−1+411yescharacteristic
811C22×C3#58512yes—
812C2×D3—22no—
813C2×D3—22no—
814C2×D3—22no—
815C2×D3—22no—
816C2×D3—24no—
817C2×D3—24no—
818C2×D3—24no—
819C2×D3—24no—
820C2×D3—24no—
821C2×D3—24no—
822C2×D3—24no—
823C2×D3—416no—
824C2×D3—432no—
825C2×D3—42no—
826C2×D3—42no—
827C2×D3—42no—
828C2×D3—42no—
829C2×D3C2×#12014yes—
830C2×D3#53714yescomplemented
831C3×C4—22no—
832C3×C4—24no—
833C3×C4—42no—
834C3×C4—44no—
835C3×C4C2×#12014yes—
836Dic3—24no—
837Dic3—22no—
838Dic3—42no—
839Dic3—42no—
840Dic3—44no—
841Dic3C2×#12014yes—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—21no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—21no—
851C23—22no—
852C23—22no—
853C23—24no—
854C23—22no—
855C23—24no—
856C23—22no—
857C23—32no—
858C23—32no—
859C23—34no—
860C23—32no—
861C23—32no—
862C23—34no—
863C23—68no—
864C23—68no—
865C23—616no—
866C23—62no—
867C23—61no—
868C23—62no—
869C23—62no—
870C23—61no—
871C23—62no—
872C23—62no—
873C23—62no—
874C23—62no—
875C23—62no—
876C23—62no—
877C23—124no—
878C23—128no—
879C23—128no—
880C23—128no—
881C23—128no—
882C23—128no—
883C23—128no—
884C23—128no—
885C23—128no—
886C23C2×D3×D412yes—
887C23C2×D3×D414yes—
888C23C24×D311yescharacteristic
889Q8—28no—
890Q8—616no—
891Q8—68no—
892Q8—124no—
893D4—28no—
894D4—216no—
895D4—48no—
896D4—44no—
897D4—616no—
898D4—68no—
899D4—616no—
900D4—616no—
901D4—616no—
902D4—88no—
903D4—128no—
904D4—128no—
905D4—248no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—28no—
910C2×C4—216no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—32no—
917C2×C4—34no—
918C2×C4—316no—
919C2×C4—32no—
920C2×C4—34no—
921C2×C4—68no—
922C2×C4—68no—
923C2×C4—616no—
924C2×C4—616no—
925C2×C4—68no—
926C2×C4—616no—
927C2×C4—62no—
928C2×C4—62no—
929C2×C4—62no—
930C2×C4—68no—
931C2×C4—616no—
932C2×C4—62no—
933C2×C4—64no—
934C2×C4—62no—
935C2×C4—64no—
936C2×C4—64no—
937C2×C4—62no—
938C2×C4—64no—
939C2×C4—62no—
940C2×C4—128no—
941C2×C4—248no—
942C2×C4C2×D3×D412yes—
943C2×C4C2×D3×D414yes—
944C2×C4C2×D3×D412yes—
945C2×C4C2×D3×D414yes—
946C2×C3—42no—
947C2×C3—44no—
948C2×C3—82no—
949C2×C3C22×#12011yescharacteristic
950C2×C3C2×#53711yescharacteristic
951C2×C3#344911yescharacteristic
952C2×C3#348812yes—
953C2×C3#348912yes—
954D3—24no—
955D3—24no—
956D3—44no—
957C22—22no—
958C22—24no—
959C22—22no—
960C22—24no—
961C22—22no—
962C22—24no—
963C22—34no—
964C22—34no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22—44no—
973C22—42no—
974C22—44no—
975C22—42no—
976C22—62no—
977C22—62no—
978C22—64no—
979C22—64no—
980C22—62no—
981C22—64no—
982C22—64no—
983C22—62no—
984C22—64no—
985C22—64no—
986C22—64no—
987C22—1216no—
988C22—1232no—
989C22—122no—
990C22—122no—
991C22—122no—
992C22—122no—
993C22C22×D3×D411yescharacteristic
994C22C22×D3×D412yes—
995C22D3×H(5,𝔽2)11yescharacteristic
996C22#596612yes—
997C22D3×2−1+411yescharacteristic
998C4—22no—
999C4—24no—
1000C4—34no—
1001C4—42no—
1002C4—44no—
1003C4—62no—
1004C4—64no—
1005C4—124no—
1006C4—122no—
1007C4—122no—
1008C4D3×#12014yes—
1009C3#3525111yescharacteristic, complemented, Sylow
1010C2—42no—
1011C2—44no—
1012C2—64no—
1013C2—64no—
1014C2—82no—
1015C2—124no—
1016C2C2×D3×#12011yescharacteristic
1017C2#8631311yescharacteristic
1018C2#8633112yes—
1019C2D3×#53711yescharacteristic
1020C2#8638012yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2615C2
hypercenter#2615D3
hypocenterC3#35251
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2615

Complements

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

NH ≅ G/Ntype
1. C22×D3×#41C2semidirect
2. C2×#5608C2semidirect
3. C2×#5606C2semidirect
4. C3×#2615C2semidirect
5. #84094C2semidirect
6. #82723C2semidirect
7. #82709C2semidirect
8. #76864C2semidirect
9. #76780C2semidirect
10. #76757C2semidirect
11. #76755C2semidirect
12. #76669C2semidirect
13. #76668C2semidirect
14. #74049C2semidirect
15. #74003C2semidirect
16. D3×#380C2semidirect
17. #73950C2semidirect
26. C22×#237C22semidirect
33. C2×C3×#121C22semidirect
34. C2×C3×#121C22semidirect
35. C2×#939C22semidirect
37. C2×#938C22semidirect
38. C2×#938C22semidirect
41. C2×D4×Dic3C22semidirect
42. C2×#924C22semidirect
43. C2×#924C22semidirect
47. C2×#897C22semidirect
48. C2×#892C22semidirect
49. C2×D3×C4⋊C4C22semidirect
50. C2×#884C22semidirect
51. C2×#883C22semidirect
54. C2×#878C22semidirect
55. C3×#393C22semidirect
56. C3×#392C22semidirect
57. C3×#392C22semidirect
58. C3×#380C22semidirect
59. C3×#380C22semidirect
60. #5230C22semidirect
61. #5223C22semidirect
62. #5222C22semidirect
63. #5222C22semidirect
64. #5220C22semidirect
65. #5212C22semidirect
66. #5212C22semidirect
68. #4987C22semidirect
69. #4987C22semidirect
70. #4961C22semidirect
71. #4960C22semidirect
72. #4957C22semidirect
74. #4956C22semidirect
75. #4956C22semidirect
77. #4950C22semidirect
78. #4947C22semidirect
79. #4942C22semidirect
80. #4672C22semidirect
82. #4668C22semidirect
84. #4665C22semidirect
85. D3×#95C22semidirect
86. #4656C22semidirect
87. #4646C22semidirect
96. #2615D3semidirect
147. C2×#235D4semidirect
154. C22×C4×D3D4semidirect
246. C2×#121C2×D3semidirect
247. C2×#121C2×D3semidirect
262. #393C2×D3semidirect
265. #392C2×D3semidirect
266. #392C2×D3semidirect
284. #380C2×D3semidirect
285. #380C2×D3semidirect
644. C4×D3#120semidirect
830. C2×D3#537semidirect
1009. C3#35251semidirect

Maximal subgroups

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

subgroupindex
C22×D3×#412
C2×#56082
C2×#56062
C3×#26152
#840942
#827232
#827092
#768642
#767802
#767572
#767552
#766692
#766682
#740492
#740032
D3×#3802
#739502
#352513