Finite Group Databasebeta

← #11634164

Subgroups — #11634164

Order 768.

3338 conjugacy classes of subgroups.

The subgroup lattice has 1330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#550C211yesmaximal, characteristic, complemented
2C2×#5824C211yesmaximal, characteristic, complemented
3C2×#5832C211yesmaximal, characteristic, complemented
4C2×#5599C211yesmaximal, characteristic, complemented
5#84097C211yesmaximal, characteristic, complemented
6#84092C211yesmaximal, characteristic, complemented
7#83187C211yesmaximal, characteristic, complemented
8#83182C212yesmaximal, complemented
9#83177C211yesmaximal, characteristic, complemented
10#83177C212yesmaximal, complemented
11#82683C212yesmaximal, complemented
12#82669C211yesmaximal, characteristic, complemented
13#82657C212yesmaximal, complemented
14#82650C212yesmaximal, complemented
15#82646C211yesmaximal, characteristic, complemented
16#82642C212yesmaximal, complemented
17Dic3×#121C211yesmaximal, characteristic, complemented
18#82495C211yesmaximal, characteristic, complemented
19#82465C211yesmaximal, characteristic, complemented
20#82402C211yesmaximal, characteristic, complemented
21#82364C212yesmaximal, complemented
22#82340C212yesmaximal, complemented
23C4×#939C211yesmaximal, characteristic, complemented
24#59051—31nomaximal, Sylow
25C22×C3×#41C2211yescharacteristic
26C22×C3×#41C2211yescharacteristic
27C22×#237C2211yescharacteristic
28C22×#235C2211yescharacteristic
29C3×#550—28no—
30C2×C3×#127C2212yes—
31C2×C3×#127C2211yescharacteristic
32C2×C3×#121C2212yes—
33C2×C3×#121C2211yescharacteristic
34C2×C3×#121C2212yes—
35C2×C3×#121C2211yescharacteristic
36C2×C3×C4×Q8C2211yescharacteristic
37C2×C3×C4×D4C2211yescharacteristic
38C2×C3×C4×D4C2212yes—
39#5832—28no—
40#5824—28no—
41C2×#947C2211yescharacteristic
42C2×#946C2211yescharacteristic
43C2×#944C2211yescharacteristic
44C2×#940C2211yescharacteristic
45C2×#940C2212yes—
46C2×#940C2211yescharacteristic
47C2×#940C2212yes—
48C2×#939C2211yescharacteristic
49C2×#939C2212yes—
50C2×#939C2212yes—
51C2×#939C2212yes—
52C2×#939C2212yes—
53C2×#939C2212yes—
54C2×#939C2212yes—
55C2×#938C2211yescharacteristic
56C2×#936C2211yescharacteristic
57C2×#935C2212yes—
58C2×D4×Dic3C2211yescharacteristic
59C2×D4×Dic3C2212yes—
60C2×#930C2211yescharacteristic
61C2×#929C2212yes—
62C2×C4×#67C2211yescharacteristic
63C2×C4×#67C2211yescharacteristic
64C2×C4×#67C2212yes—
65C2×C4×#67C2212yes—
66C2×#924C2211yescharacteristic
67C22×Dic3⋊C4C2212yes—
68C22×C4×Dic3C2211yescharacteristic
69#5599—28no—
70C2×#895C2211yescharacteristic
71C2×#887C2211yescharacteristic
72C2×#884C2212yes—
73C2×#67⋊C4C2212yes—
74#5229C2211yescharacteristic
75#5223C2212yes—
76#5223C2212yes—
77#5223C2212yes—
78#5223C2212yes—
79#5223C2212yes—
80#5223C2212yes—
81#5223C2212yes—
82#5223C2212yes—
83#5223C2212yes—
84#5222C2212yes—
85#5222C2212yes—
86#5221C2211yescharacteristic
87#5221C2211yescharacteristic
88#5221C2212yes—
89#5220C2211yescharacteristic
90#5220C2212yes—
91#5220C2212yes—
92#5220C2212yes—
93#5213C2212yes—
94#5213C2212yes—
95#5213C2212yes—
96#5212C2211yescharacteristic
97#5210C2212yes—
98C4×#217C2211yescharacteristic
99#4994C2212yes—
100#4991C2212yes—
101#4990C2211yescharacteristic
102#4989C2212yes—
103#4984C2211yescharacteristic
104#4978C2212yes—
105#4976C2212yes—
106#4976C2211yescharacteristic
107Dic3×C4⋊C4C2211yescharacteristic
108#4960C2212yes—
109#4959C2212yes—
110#4958C2211yescharacteristic
111#4957C2211yescharacteristic
112#4957C2212yes—
113#4956C2212yes—
114#4951C2212yes—
115#4948C2212yes—
116#4945C2211yescharacteristic
117#4944C2212yes—
118#4942C2211yescharacteristic
119Dic3×C22⋊C4C2212yes—
120#4940C2212yes—
121#4939C2212yes—
122#4939C2211yescharacteristic
123C4×(C2×D3)⋊C4C2211yescharacteristic
124#4933C2212yes—
125C4×Dic3⋊C4C2211yescharacteristic
126C4×Dic3⋊C4C2212yes—
127#4929C2211yescharacteristic
128C2×#550—31no—
129C2×#550D311yescharacteristic, complemented
130C2×#547—31no—
131C2×#532—31no—
132#2673—32no—
133#2673—32no—
134#2541—31no—
135#2541—32no—
136#2541—31no—
137#2456—32no—
138#2456—32no—
139#2431—31no—
140#2431—31no—
141#2428—32no—
142#2426—31no—
143#2426—31no—
144#2416—32no—
145#2407—31no—
146#2407—31no—
147#2365—31no—
148#2361—32no—
149C4×#121—31no—
150C4×#121—31no—
151C2×C3×#41—24no—
152C2×C3×#41—24no—
153C2×C3×#41—24no—
154C2×C3×#41—24no—
155C2×C3×#41—42no—
156C2×C3×#41—42no—
157C22×C3×Q8C2311yescharacteristic
158C22×C3×D4C2311yescharacteristic
159C22×C3×D4C2312yes—
160C22×C3×D4C2312yes—
161C22×C3×D4C2311yescharacteristic
162C22×C3×D4C2312yes—
163C22×C3×D4C2311yescharacteristic
164C22×C3×D4C2312yes—
165C22×C3×D4C2312yes—
166C22×C3×D4C2312yes—
167C23×C3×C4C2311yescharacteristic
168C23×C3×C4C2312yes—
169C23×C3×C4C2312yes—
170C23×C3×C4C2311yescharacteristic
171C22×#67C2311yescharacteristic
172C22×#67C2312yes—
173C22×#67C2312yes—
174C22×#67C2312yes—
175C22×#67C2312yes—
176C22×#67C2311yescharacteristic
177C22×#67C2312yes—
178C22×#67C2312yes—
179C22×#67C2312yes—
180C22×#67C2312yes—
181C23×Dic3C2312yes—
182C23×Dic3C2311yescharacteristic
183C23×Dic3C2312yes—
184C23×Dic3C2311yescharacteristic
185C2×#237—24no—
186C2×#237—24no—
187C2×#237—42no—
188C2×#235—24no—
189C2×#235—24no—
190C2×#235—42no—
191C22×D12C2311yescharacteristic
192C22×D12C2312yes—
193C22×C4×D3C2311yescharacteristic
194C22×C4×D3C2312yes—
195C22×Dic6C2311yescharacteristic
196C3×#127—28no—
197C3×#127—24no—
198C3×#121—28no—
199C3×#121—24no—
200C3×#121—28no—
201C3×#121D418yescomplemented
202C3×C4×Q8—24no—
203C3×C4×D4—24no—
204C3×C4×D4—28no—
205C2×C3×C4⋊C4C2312yes—
206C2×C3×C4⋊C4C2311yescharacteristic
207C2×C3×C4⋊C4C2311yescharacteristic
208C2×C3×C22⋊C4C2311yescharacteristic
209C2×C3×C22⋊C4C2312yes—
210C2×C3×C22⋊C4C2311yescharacteristic
211C2×C3×C22⋊C4C2312yes—
212C2×C3×C42C2311yescharacteristic
213C2×C3×C42C2312yes—
214C2×#217C2311yescharacteristic
215C2×#217C2312yes—
216C2×#217C2312yes—
217C2×#217C2311yescharacteristic
218C2×#217C2311yescharacteristic
219C2×#217C2312yes—
220C2×#217C2312yes—
221C2×#217C2312yes—
222C2×#217C2312yes—
223C2×#217C2312yes—
224C2×#217C2312yes—
225C2×#217C2311yescharacteristic
226C2×#217C2312yes—
227C2×#217C2312yes—
228#947—24no—
229#946—24no—
230#944D418yescomplemented
231#940—28no—
232#940—24no—
233#940—24no—
234#940—44no—
235#939—28no—
236#939—28no—
237#939—28no—
238#939—28no—
239#939—24no—
240#939—28no—
241#939—44no—
242#938—42no—
243#936—24no—
244#935—28no—
245D4×Dic3—24no—
246D4×Dic3—44no—
247#930—42no—
248#929—28no—
249C4×#67—24no—
250C4×#67—28no—
251C4×#67—28no—
252C4×#67—24no—
253C2×(C2×D3)⋊C4C2311yescharacteristic
254C2×(C2×D3)⋊C4C2312yes—
255C2×(C2×D3)⋊C4C2312yes—
256C2×(C2×D3)⋊C4C2312yes—
257C2×(C2×D3)⋊C4C2312yes—
258C2×(C2×D3)⋊C4C2312yes—
259C2×(C2×D3)⋊C4C2311yescharacteristic
260C2×(C2×D3)⋊C4C2311yescharacteristic
261C2×(C2×D3)⋊C4C2311yescharacteristic
262C2×(C2×D3)⋊C4C2312yes—
263C2×(C2×D3)⋊C4C2312yes—
264C2×C4⋊Dic3C2311yescharacteristic
265C2×C4⋊Dic3C2311yescharacteristic
266C2×C4⋊Dic3C2312yes—
267#924—24no—
268C2×Dic3⋊C4—28no—
269C2×Dic3⋊C4C2311yescharacteristic
270C2×Dic3⋊C4C2312yes—
271C2×Dic3⋊C4C2312yes—
272C2×Dic3⋊C4C2311yescharacteristic
273C2×Dic3⋊C4C2312yes—
274C2×Dic3⋊C4C2311yescharacteristic
275C2×Dic3⋊C4C2312yes—
276C2×Dic3⋊C4C2312yes—
277C2×Dic3⋊C4C2311yescharacteristic
278C2×C4×Dic3—24no—
279C2×C4×Dic3C2312yes—
280C2×C4×Dic3C2312yes—
281C2×C4×Dic3C2311yescharacteristic
282C2×C4×Dic3C2311yescharacteristic
283C2×C4×Dic3C2311yescharacteristic
284C2×C4×Dic3C2311yescharacteristic
285C2×C4×Dic3C2311yescharacteristic
286#895—24no—
287#887—24no—
288#884—28no—
289#67⋊C4—28no—
290C3⋊#95C2312yes—
291C3⋊#95C2312yes—
292C3⋊#95C2311yescharacteristic
293C3⋊#95C2311yescharacteristic
294C3⋊#95C2312yes—
295C3⋊#95C2312yes—
296C3⋊#95C2312yes—
297C3⋊#95C2311yescharacteristic
298C3⋊#95C2311yescharacteristic
299C3⋊#95C2312yes—
300C3⋊#95C2312yes—
301C3⋊#95C2311yescharacteristic
302C3⋊#95C2311yescharacteristic
303C22×#41—31no—
304C22×#41—31no—
305C22×#41C2×D311yescharacteristic
306C22×#41C2×D311yescharacteristic
307#550—28no—
308#550—68no—
309#547—68no—
310#532—68no—
311C2×C4⋊Q8—31no—
312C2×#127—32no—
313C2×#127—31no—
314C2×#127—31no—
315C2×#127—32no—
316C2×#127C2×D312yes—
317C2×#127C2×D311yescharacteristic
318C2×#124—31no—
319C2×#124—31no—
320C2×#123—32no—
321C2×#123—32no—
322C2×C22⋊Q8—31no—
323C2×C22⋊Q8—31no—
324C2×#121—32no—
325C2×#121—32no—
326C2×#121—32no—
327C2×#121—32no—
328C2×#121—32no—
329C2×#121—31no—
330C2×#121—31no—
331C2×#121—32no—
332C2×#121—31no—
333C2×#121—31no—
334C2×#121—32no—
335C2×#121C2×D312yes—
336C2×#121C2×D311yescharacteristic
337C2×#121C2×D312yes—
338C2×#121C2×D311yescharacteristic
339C2×C4×Q8—31no—
340C2×C4×Q8C2×D311yescharacteristic
341C2×C4×D4—31no—
342C2×C4×D4—32no—
343C2×C4×D4—31no—
344C2×C4×D4—32no—
345C2×C4×D4—31no—
346C2×C4×D4—32no—
347C2×C4×D4—32no—
348C2×C4×D4C2×D312yes—
349C2×C4×D4C2×D311yescharacteristic
350C22×C4⋊C4—32no—
351C22×C42—31no—
352#396—32no—
353#396—32no—
354#394—32no—
355#394—32no—
356#394—32no—
357#394—32no—
358#392—32no—
359#392—32no—
360#392—32no—
361#392—32no—
362#392—32no—
363#392—32no—
364#392—32no—
365#392—32no—
366#392—32no—
367#392—32no—
368#391—31no—
369#391—31no—
370#390—31no—
371#390—32no—
372#390—31no—
373#390—32no—
374#390—31no—
375#390—31no—
376#390—32no—
377#389—31no—
378#389—32no—
379#389—31no—
380#388—31no—
381#388—32no—
382#388—31no—
383#388—32no—
384#388—32no—
385#387—32no—
386#387—32no—
387#386—32no—
388#386—32no—
389#386—31no—
390#386—32no—
391#386—32no—
392#386—32no—
393#386—32no—
394#386—32no—
395#386—31no—
396#385—32no—
397#385—32no—
398#380—31no—
399#380—31no—
400C4×C4⋊C4—31no—
401C4×C4⋊C4—32no—
402C4×C4⋊C4—31no—
403C4×C22⋊C4—31no—
404C4×C22⋊C4—32no—
405C4×C22⋊C4—31no—
406C24×C3C2411yescharacteristic
407C24×C3C2412yes—
408C24×C3C2412yes—
409C24×C3C2411yescharacteristic
410C23×D3C2411yescharacteristic
411C23×D3C2412yes—
412C3×#41—416no—
413C3×#41—416no—
414C2×C3×Q8—22no—
415C2×C3×Q8—22no—
416C2×C3×Q8C2×D414yes—
417C2×C3×D4—22no—
418C2×C3×D4—24no—
419C2×C3×D4—24no—
420C2×C3×D4—24no—
421C2×C3×D4—24no—
422C2×C3×D4—22no—
423C2×C3×D4—24no—
424C2×C3×D4—22no—
425C2×C3×D4—24no—
426C2×C3×D4—22no—
427C2×C3×D4—24no—
428C2×C3×D4—22no—
429C2×C3×D4—24no—
430C2×C3×D4—22no—
431C2×C3×D4—22no—
432C2×C3×D4—42no—
433C2×C3×D4—42no—
434C2×C3×D4—42no—
435C2×C3×D4—41no—
436C2×C3×D4—42no—
437C2×C3×D4—42no—
438C2×C3×D4—42no—
439C2×C3×D4—42no—
440C2×C3×D4—42no—
441C2×C3×D4—42no—
442C2×C3×D4C2×D414yes—
443C2×C3×D4C2×D418yes—
444C22×C3×C4—22no—
445C22×C3×C4—22no—
446C22×C3×C4—24no—
447C22×C3×C4—24no—
448C22×C3×C4—22no—
449C22×C3×C4—24no—
450C22×C3×C4—24no—
451C22×C3×C4—22no—
452C22×C3×C4—22no—
453C22×C3×C4—42no—
454C22×C3×C4—42no—
455C22×C3×C4C2×D414yes—
456C22×C3×C4C2411yescharacteristic
457C22×C3×C4C2411yescharacteristic
458C22×C3×C4C2412yes—
459C22×C3×C4C2411yescharacteristic
460C22×C3×C4C2412yes—
461C22×C3×C4C2411yescharacteristic
462C22×C3×C4C2411yescharacteristic
463C2×#67—24no—
464C2×#67—24no—
465C2×#67—22no—
466C2×#67—24no—
467C2×#67—24no—
468C2×#67—22no—
469C2×#67—24no—
470C2×#67—24no—
471C2×#67—24no—
472C2×#67—24no—
473C2×#67—24no—
474C2×#67—22no—
475C2×#67—22no—
476C2×#67—24no—
477C2×#67—24no—
478C2×#67—22no—
479C2×#67—42no—
480C2×#67—42no—
481C2×#67—42no—
482C2×#67—42no—
483C2×#67—42no—
484C2×#67—41no—
485C2×#67—42no—
486C2×#67—42no—
487C2×#67—42no—
488C2×#67—42no—
489C2×#67—42no—
490C2×#67—42no—
491C2×#67—42no—
492C2×#67—42no—
493C22×Dic3—24no—
494C22×Dic3—22no—
495C22×Dic3—22no—
496C22×Dic3—24no—
497C22×Dic3—24no—
498C22×Dic3—24no—
499C22×Dic3—22no—
500C22×Dic3—22no—
501C22×Dic3—24no—
502C22×Dic3—42no—
503C22×Dic3—41no—
504C22×Dic3—41no—
505C22×Dic3C2412yes—
506C22×Dic3C2411yescharacteristic
507C22×Dic3C2411yescharacteristic
508C22×Dic3C2411yescharacteristic
509C22×Dic3C2411yescharacteristic
510C22×Dic3C2412yes—
511C22×Dic3C2411yescharacteristic
512C22×Dic3C2412yes—
513C22×Dic3C2411yescharacteristic
514C22×Dic3C2411yescharacteristic
515#237—416no—
516#235—416no—
517C2×D12—22no—
518C2×D12—22no—
519C2×D12—22no—
520C2×D12—24no—
521C2×D12—42no—
522C2×D12—42no—
523C2×C4×D3—24no—
524C2×C4×D3—22no—
525C2×C4×D3—22no—
526C2×C4×D3—22no—
527C2×C4×D3—24no—
528C2×C4×D3—42no—
529C2×Dic6—22no—
530C2×Dic6—22no—
531C2×Dic6C2×D414yes—
532C3×C4⋊C4—22no—
533C3×C4⋊C4—24no—
534C3×C4⋊C4C2×D414yes—
535C3×C22⋊C4—22no—
536C3×C22⋊C4—22no—
537C3×C22⋊C4—24no—
538C3×C22⋊C4C2×D418yes—
539C3×C42—24no—
540C3×C42—22no—
541#217—22no—
542#217—24no—
543#217—22no—
544#217—24no—
545#217—24no—
546#217—24no—
547#217—24no—
548#217—22no—
549#217—42no—
550#217—42no—
551#217—42no—
552#217—42no—
553#217—41no—
554#217—42no—
555(C2×D3)⋊C4—24no—
556(C2×D3)⋊C4—22no—
557(C2×D3)⋊C4—24no—
558(C2×D3)⋊C4—24no—
559(C2×D3)⋊C4—24no—
560(C2×D3)⋊C4—22no—
561(C2×D3)⋊C4—24no—
562(C2×D3)⋊C4—22no—
563(C2×D3)⋊C4—41no—
564(C2×D3)⋊C4—42no—
565(C2×D3)⋊C4—42no—
566C4⋊Dic3—22no—
567C4⋊Dic3—22no—
568C4⋊Dic3—42no—
569Dic3⋊C4—22no—
570Dic3⋊C4—24no—
571Dic3⋊C4—24no—
572Dic3⋊C4—22no—
573Dic3⋊C4—24no—
574Dic3⋊C4—22no—
575Dic3⋊C4C2×D418yes—
576Dic3⋊C4C2×D418yes—
577Dic3⋊C4#4114yescomplemented
578C4×Dic3—24no—
579C4×Dic3—22no—
580C4×Dic3—22no—
581C4×Dic3—22no—
582C4×Dic3—22no—
583C4×Dic3—24no—
584C4×Dic3C2×D414yes—
585C2×#41—24no—
586C2×#41—24no—
587C2×#41—24no—
588C2×#41—24no—
589C2×#41—42no—
590C2×#41—42no—
591C2×#41—64no—
592C2×#41—64no—
593C2×#41—64no—
594C2×#41—64no—
595C2×#41—122no—
596C2×#41—122no—
597C22×Q8—31no—
598C22×Q8C22×D311yescharacteristic
599C22×D4—31no—
600C22×D4—32no—
601C22×D4—31no—
602C22×D4—32no—
603C22×D4—32no—
604C22×D4—32no—
605C22×D4—32no—
606C22×D4—32no—
607C22×D4—32no—
608C22×D4—32no—
609C22×D4—31no—
610C22×D4—32no—
611C22×D4C22×D311yescharacteristic
612C22×D4C22×D312yes—
613C22×D4C22×D311yescharacteristic
614C22×D4C22×D312yes—
615C22×D4C22×D312yes—
616C22×D4C22×D311yescharacteristic
617C22×D4C22×D312yes—
618C22×D4C22×D312yes—
619C22×D4C22×D312yes—
620C23×C4—32no—
621C23×C4—31no—
622C23×C4—32no—
623C23×C4—31no—
624C23×C4—31no—
625C23×C4—32no—
626C23×C4C22×D311yescharacteristic
627C23×C4C22×D312yes—
628C23×C4C22×D312yes—
629C23×C4C22×D311yescharacteristic
630C4⋊Q8—38no—
631#127—28no—
632#127—24no—
633#127—64no—
634#127—68no—
635#127—64no—
636#127—124no—
637#124—64no—
638#124—64no—
639#123—68no—
640#123—68no—
641C22⋊Q8—64no—
642C22⋊Q8—64no—
643#121—28no—
644#121—24no—
645#121—28no—
646#121—68no—
647#121—68no—
648#121—68no—
649#121—68no—
650#121—64no—
651#121—68no—
652#121—64no—
653#121—68no—
654#121—122no—
655#121—122no—
656#121—124no—
657#121#6718yescomplemented
658C4×Q8—24no—
659C4×Q8—64no—
660C4×D4—24no—
661C4×D4—28no—
662C4×D4—64no—
663C4×D4—64no—
664C4×D4—68no—
665C4×D4—68no—
666C4×D4—64no—
667C4×D4—68no—
668C4×D4—124no—
669C2×C4⋊C4—32no—
670C2×C4⋊C4—32no—
671C2×C4⋊C4—31no—
672C2×C4⋊C4—31no—
673C2×C4⋊C4—32no—
674C2×C4⋊C4—32no—
675C2×C4⋊C4—31no—
676C2×C4⋊C4—31no—
677C2×C4⋊C4—32no—
678C2×C4⋊C4—31no—
679C2×C4⋊C4—31no—
680C2×C4⋊C4—32no—
681C2×C4⋊C4—68no—
682C2×C4⋊C4C22×D311yescharacteristic
683C2×C4⋊C4C22×D312yes—
684C2×C4⋊C4C22×D311yescharacteristic
685C2×C22⋊C4—31no—
686C2×C22⋊C4—32no—
687C2×C22⋊C4—32no—
688C2×C22⋊C4—32no—
689C2×C22⋊C4—31no—
690C2×C22⋊C4—32no—
691C2×C22⋊C4—31no—
692C2×C22⋊C4—32no—
693C2×C22⋊C4—31no—
694C2×C22⋊C4—32no—
695C2×C22⋊C4—32no—
696C2×C22⋊C4—32no—
697C2×C22⋊C4—31no—
698C2×C22⋊C4—32no—
699C2×C22⋊C4—31no—
700C2×C22⋊C4—32no—
701C2×C22⋊C4—32no—
702C2×C22⋊C4—32no—
703C2×C22⋊C4—32no—
704C2×C22⋊C4—32no—
705C2×C22⋊C4—32no—
706C2×C22⋊C4—31no—
707C2×C22⋊C4—32no—
708C2×C22⋊C4—32no—
709C2×C22⋊C4—31no—
710C2×C22⋊C4C22×D311yescharacteristic
711C2×C22⋊C4C22×D311yescharacteristic
712C2×C22⋊C4C22×D312yes—
713C2×C22⋊C4C22×D312yes—
714C2×C42—31no—
715C2×C42—31no—
716C2×C42—31no—
717C2×C42—31no—
718C2×C42—32no—
719C2×C42—32no—
720C2×C42—31no—
721C2×C42—64no—
722C2×C42C22×D311yescharacteristic
723C2×C42C22×D312yes—
724#95—32no—
725#95—31no—
726#95—31no—
727#95—31no—
728#95—31no—
729#95—32no—
730#95—32no—
731#95—32no—
732#95—31no—
733#95—32no—
734#95—31no—
735#95—32no—
736#95—32no—
737C23×C3—22no—
738C23×C3—21no—
739C23×C3—22no—
740C23×C3—21no—
741C23×C3—21no—
742C23×C3—22no—
743C23×C3—22no—
744C23×C3—21no—
745C23×C3—22no—
746C23×C3—21no—
747C23×C3—21no—
748C23×C3—22no—
749C23×C3—21no—
750C23×C3—22no—
751C23×C3—21no—
752C23×C3—22no—
753C23×C3—21no—
754C23×C3—22no—
755C23×C3—22no—
756C23×C3—22no—
757C23×C3—21no—
758C23×C3—21no—
759C23×C3—21no—
760C23×C3—22no—
761C23×C3—21no—
762C23×C3—22no—
763C23×C3C22×D412yes—
764C23×C3C22×D414yes—
765C23×C3C2511yescharacteristic
766C22×D3—21no—
767C22×D3—22no—
768C22×D3—22no—
769C22×D3—21no—
770C22×D3—21no—
771C22×D3—22no—
772C22×D3—22no—
773C22×D3—22no—
774C22×D3—21no—
775C22×D3—21no—
776C22×D3—21no—
777C22×D3—22no—
778C22×D3—22no—
779C22×D3—21no—
780C3×Q8—28no—
781C3×D4—28no—
782C3×D4—48no—
783C3×D4—48no—
784C3×D4—44no—
785C3×D4—48no—
786C3×D4—48no—
787C3×D4—44no—
788C3×D4—84no—
789C3×D4—84no—
790C2×C3×C4—21no—
791C2×C3×C4—21no—
792C2×C3×C4—22no—
793C2×C3×C4—22no—
794C2×C3×C4—21no—
795C2×C3×C4—22no—
796C2×C3×C4—22no—
797C2×C3×C4—21no—
798C2×C3×C4—28no—
799C2×C3×C4—21no—
800C2×C3×C4—21no—
801C2×C3×C4—21no—
802C2×C3×C4—21no—
803C2×C3×C4—21no—
804C2×C3×C4—21no—
805C2×C3×C4—48no—
806C2×C3×C4—48no—
807C2×C3×C4—44no—
808C2×C3×C4C22×D414yes—
809C2×C3×C4C22×D412yes—
810C2×C3×C4C22×D414yes—
811C2×C3×C4C22×D412yes—
812C2×C3×C4C22×D412yes—
813C2×C3×C4C2×#4112yes—
814C2×C3×C4H(5,𝔽2)12yes—
815#67—48no—
816#67—48no—
817#67—48no—
818#67—44no—
819#67—48no—
820#67—44no—
821#67—48no—
822#67—84no—
823#67—84no—
824#67—84no—
825C2×Dic3—21no—
826C2×Dic3—22no—
827C2×Dic3—22no—
828C2×Dic3—21no—
829C2×Dic3—21no—
830C2×Dic3—21no—
831C2×Dic3—21no—
832C2×Dic3—21no—
833C2×Dic3—21no—
834C2×Dic3—21no—
835C2×Dic3—22no—
836C2×Dic3—21no—
837C2×Dic3—21no—
838C2×Dic3—22no—
839C2×Dic3—22no—
840C2×Dic3—21no—
841C2×Dic3—22no—
842C2×Dic3—21no—
843C2×Dic3—22no—
844C2×Dic3—21no—
845C2×Dic3—21no—
846C2×Dic3—21no—
847C2×Dic3—22no—
848C2×Dic3—21no—
849C2×Dic3—48no—
850C2×Dic3—44no—
851C2×Dic3—44no—
852C2×Dic3—48no—
853C2×Dic3C22×D412yes—
854C2×Dic3C22×D414yes—
855C2×Dic3C22×D412yes—
856C2×Dic3C2×#4112yes—
857C2×Dic3C2×#4112yes—
858C2×Dic3H(5,𝔽2)12yes—
859D12—44no—
860D12—84no—
861C4×D3—48no—
862C4×D3—44no—
863Dic6—28no—
864C24—31no—
865C24—32no—
866C24C23×D311yescharacteristic
867C24C23×D312yes—
868C24C23×D312yes—
869C24C23×D311yescharacteristic
870#41—416no—
871#41—416no—
872#41—1216no—
873#41—1216no—
874C2×Q8—22no—
875C2×Q8—22no—
876C2×Q8—34no—
877C2×Q8—62no—
878C2×Q8—62no—
879C2×Q8D3×D414yes—
880C2×D4—22no—
881C2×D4—24no—
882C2×D4—24no—
883C2×D4—24no—
884C2×D4—24no—
885C2×D4—22no—
886C2×D4—24no—
887C2×D4—24no—
888C2×D4—22no—
889C2×D4—22no—
890C2×D4—22no—
891C2×D4—24no—
892C2×D4—22no—
893C2×D4—22no—
894C2×D4—24no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—41no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—62no—
906C2×D4—64no—
907C2×D4—64no—
908C2×D4—64no—
909C2×D4—64no—
910C2×D4—62no—
911C2×D4—64no—
912C2×D4—64no—
913C2×D4—62no—
914C2×D4—64no—
915C2×D4—62no—
916C2×D4—62no—
917C2×D4—64no—
918C2×D4—64no—
919C2×D4—64no—
920C2×D4—64no—
921C2×D4—62no—
922C2×D4—62no—
923C2×D4—62no—
924C2×D4—64no—
925C2×D4—122no—
926C2×D4—122no—
927C2×D4—122no—
928C2×D4—122no—
929C2×D4—122no—
930C2×D4—122no—
931C2×D4—121no—
932C2×D4—122no—
933C2×D4—122no—
934C2×D4—122no—
935C2×D4—122no—
936C2×D4—122no—
937C2×D4—122no—
938C2×D4—122no—
939C2×D4—122no—
940C2×D4—122no—
941C2×D4C2×#6714yes—
942C2×D4C2×#6718yes—
943C22×C4—22no—
944C22×C4—22no—
945C22×C4—24no—
946C22×C4—24no—
947C22×C4—24no—
948C22×C4—22no—
949C22×C4—22no—
950C22×C4—24no—
951C22×C4—22no—
952C22×C4—31no—
953C22×C4—31no—
954C22×C4—31no—
955C22×C4—32no—
956C22×C4—32no—
957C22×C4—31no—
958C22×C4—31no—
959C22×C4—31no—
960C22×C4—32no—
961C22×C4—31no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—64no—
965C22×C4—62no—
966C22×C4—62no—
967C22×C4—64no—
968C22×C4—64no—
969C22×C4—62no—
970C22×C4—64no—
971C22×C4—64no—
972C22×C4—62no—
973C22×C4—64no—
974C22×C4—62no—
975C22×C4—62no—
976C22×C4—64no—
977C22×C4—62no—
978C22×C4—122no—
979C22×C4—122no—
980C22×C4—121no—
981C22×C4—121no—
982C22×C4C2×#6714yes—
983C22×C4C23×D311yescharacteristic
984C22×C4C23×D311yescharacteristic
985C22×C4C23×D312yes—
986C22×C4C23×D311yescharacteristic
987C22×C4C23×D312yes—
988C22×C4C23×D311yescharacteristic
989C22×C4C23×D311yescharacteristic
990C4⋊C4—22no—
991C4⋊C4—24no—
992C4⋊C4—38no—
993C4⋊C4—38no—
994C4⋊C4—34no—
995C4⋊C4—62no—
996C4⋊C4—64no—
997C4⋊C4—62no—
998C4⋊C4—64no—
999C4⋊C4—62no—
1000C4⋊C4—62no—
1001C4⋊C4—62no—
1002C4⋊C4—64no—
1003C4⋊C4—122no—
1004C4⋊C4C2×#6714yes—
1005C22⋊C4—22no—
1006C22⋊C4—22no—
1007C22⋊C4—24no—
1008C22⋊C4—62no—
1009C22⋊C4—64no—
1010C22⋊C4—64no—
1011C22⋊C4—64no—
1012C22⋊C4—62no—
1013C22⋊C4—64no—
1014C22⋊C4—62no—
1015C22⋊C4—64no—
1016C22⋊C4—62no—
1017C22⋊C4—64no—
1018C22⋊C4—64no—
1019C22⋊C4—64no—
1020C22⋊C4—62no—
1021C22⋊C4—64no—
1022C22⋊C4—62no—
1023C22⋊C4—64no—
1024C22⋊C4—122no—
1025C22⋊C4—122no—
1026C22⋊C4—121no—
1027C22⋊C4—122no—
1028C22⋊C4—122no—
1029C22⋊C4—122no—
1030C22⋊C4—122no—
1031C22⋊C4—122no—
1032C22⋊C4—121no—
1033C22⋊C4C2×#6718yes—
1034C42—24no—
1035C42—22no—
1036C42—34no—
1037C42—62no—
1038C42—62no—
1039C42—64no—
1040C42—62no—
1041C42—64no—
1042C42—62no—
1043C22×C3—24no—
1044C22×C3—22no—
1045C22×C3—24no—
1046C22×C3—22no—
1047C22×C3—24no—
1048C22×C3—22no—
1049C22×C3—42no—
1050C22×C3—41no—
1051C22×C3—41no—
1052C22×C3—42no—
1053C22×C3—42no—
1054C22×C3—41no—
1055C22×C3—41no—
1056C22×C3—42no—
1057C22×C3—42no—
1058C22×C3—41no—
1059C22×C3—41no—
1060C22×C3—42no—
1061C22×C3—42no—
1062C22×C3—41no—
1063C22×C3—42no—
1064C22×C3—41no—
1065C22×C3—41no—
1066C22×C3—42no—
1067C22×C3—42no—
1068C22×C3—41no—
1069C22×C3—41no—
1070C22×C3—42no—
1071C22×C3C23×D411yescharacteristic
1072C22×C3C23×D411yescharacteristic
1073C22×C3C22×#4111yescharacteristic
1074C22×C3C2×H(5,𝔽2)11yescharacteristic
1075C22×C3C2×H(5,𝔽2)11yescharacteristic
1076C22×C3#58511yescharacteristic
1077C22×C3#58511yescharacteristic
1078C2×D3—42no—
1079C2×D3—41no—
1080C2×D3—41no—
1081C2×D3—42no—
1082C2×D3—42no—
1083C2×D3—41no—
1084C2×D3—42no—
1085C2×D3—41no—
1086C2×D3—41no—
1087C2×D3—42no—
1088C2×D3—42no—
1089C2×D3—41no—
1090C2×D3—41no—
1091C2×D3—42no—
1092C3×C4—22no—
1093C3×C4—24no—
1094C3×C4—22no—
1095C3×C4—24no—
1096C3×C4—41no—
1097C3×C4—41no—
1098C3×C4D4214yes—
1099Dic3—24no—
1100Dic3—22no—
1101Dic3—22no—
1102Dic3—41no—
1103Dic3—41no—
1104Dic3—42no—
1105Dic3—41no—
1106Dic3—41no—
1107Dic3—42no—
1108Dic3#55014yescomplemented
1109C23—22no—
1110C23—21no—
1111C23—21no—
1112C23—22no—
1113C23—22no—
1114C23—21no—
1115C23—22no—
1116C23—21no—
1117C23—21no—
1118C23—22no—
1119C23—21no—
1120C23—22no—
1121C23—21no—
1122C23—22no—
1123C23—22no—
1124C23—21no—
1125C23—22no—
1126C23—21no—
1127C23—21no—
1128C23—22no—
1129C23—22no—
1130C23—21no—
1131C23—21no—
1132C23—22no—
1133C23—21no—
1134C23—22no—
1135C23—61no—
1136C23—62no—
1137C23—62no—
1138C23—61no—
1139C23—62no—
1140C23—61no—
1141C23—61no—
1142C23—62no—
1143C23—62no—
1144C23—61no—
1145C23—61no—
1146C23—62no—
1147C23—61no—
1148C23—62no—
1149C23C22×#6712yes—
1150C23C22×#6714yes—
1151C23C24×D311yescharacteristic
1152Q8—28no—
1153Q8—68no—
1154D4—28no—
1155D4—48no—
1156D4—48no—
1157D4—48no—
1158D4—48no—
1159D4—44no—
1160D4—44no—
1161D4—84no—
1162D4—84no—
1163D4—124no—
1164D4—128no—
1165D4—128no—
1166D4—128no—
1167D4—128no—
1168D4—124no—
1169D4—128no—
1170D4—124no—
1171D4—244no—
1172D4—244no—
1173D4—244no—
1174D4—244no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—22no—
1178C2×C4—21no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—21no—
1182C2×C4—22no—
1183C2×C4—28no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—32no—
1191C2×C4—32no—
1192C2×C4—32no—
1193C2×C4—32no—
1194C2×C4—34no—
1195C2×C4—32no—
1196C2×C4—48no—
1197C2×C4—48no—
1198C2×C4—44no—
1199C2×C4—62no—
1200C2×C4—61no—
1201C2×C4—61no—
1202C2×C4—61no—
1203C2×C4—61no—
1204C2×C4—62no—
1205C2×C4—61no—
1206C2×C4—61no—
1207C2×C4—62no—
1208C2×C4—61no—
1209C2×C4—62no—
1210C2×C4—61no—
1211C2×C4—61no—
1212C2×C4—62no—
1213C2×C4—61no—
1214C2×C4—62no—
1215C2×C4—62no—
1216C2×C4—62no—
1217C2×C4—61no—
1218C2×C4—61no—
1219C2×C4—61no—
1220C2×C4—61no—
1221C2×C4—61no—
1222C2×C4—61no—
1223C2×C4—128no—
1224C2×C4—124no—
1225C2×C4—128no—
1226C2×C4—128no—
1227C2×C4—124no—
1228C2×C4—124no—
1229C2×C4C2×D3×D414yes—
1230C2×C4C2×D3×D412yes—
1231C2×C4#100412yes—
1232C2×C4D3×#4112yes—
1233C2×C4C22×#6714yes—
1234C2×C4C22×#6712yes—
1235C2×C4C22×#6712yes—
1236C2×C3—44no—
1237C2×C3—42no—
1238C2×C3—82no—
1239C2×C3—81no—
1240C2×C3C2×D4211yescharacteristic
1241C2×C3C2×#55011yescharacteristic
1242C2×C3D4×#4111yescharacteristic
1243C2×C3#348711yescharacteristic
1244C2×C3#349611yescharacteristic
1245C2×C3#351711yescharacteristic
1246C2×C3#354611yescharacteristic
1247D3—82no—
1248D3—81no—
1249C22—22no—
1250C22—24no—
1251C22—24no—
1252C22—22no—
1253C22—22no—
1254C22—24no—
1255C22—41no—
1256C22—42no—
1257C22—41no—
1258C22—42no—
1259C22—42no—
1260C22—41no—
1261C22—41no—
1262C22—42no—
1263C22—42no—
1264C22—41no—
1265C22—41no—
1266C22—42no—
1267C22—41no—
1268C22—42no—
1269C22—42no—
1270C22—41no—
1271C22—41no—
1272C22—42no—
1273C22—41no—
1274C22—42no—
1275C22—42no—
1276C22—41no—
1277C22—122no—
1278C22—121no—
1279C22—121no—
1280C22—122no—
1281C22—121no—
1282C22—122no—
1283C22—122no—
1284C22—121no—
1285C22—121no—
1286C22—122no—
1287C22—121no—
1288C22—122no—
1289C22—122no—
1290C22—121no—
1291C22C22×D3×D411yescharacteristic
1292C22C2×#100411yescharacteristic
1293C22C2×D3×#4111yescharacteristic
1294C22#596411yescharacteristic
1295C22D3×H(5,𝔽2)11yescharacteristic
1296C22#596611yescharacteristic
1297C22C23×#6711yescharacteristic
1298C4—22no—
1299C4—24no—
1300C4—22no—
1301C4—24no—
1302C4—34no—
1303C4—41no—
1304C4—41no—
1305C4—64no—
1306C4—62no—
1307C4—62no—
1308C4—121no—
1309C4—121no—
1310C4—122no—
1311C4—121no—
1312C4—122no—
1313C4—121no—
1314C4D4×#6714yes—
1315C3#5905111yescharacteristic, complemented, Sylow
1316C2—42no—
1317C2—44no—
1318C2—81no—
1319C2—82no—
1320C2—241no—
1321C2—242no—
1322C2#8677411yescharacteristic
1323C2#8677911yescharacteristic
1324C2D3×#55011yescharacteristic
1325C2#8678311yescharacteristic
1326C2C2×D4×#6711yescharacteristic
1327C2#41×#6711yescharacteristic
1328C2#8728111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×#550C2
hypercenterC2×#550D3
hypocenterC3#59051
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×C3×#550C2semidirect
2. C2×#5824C2semidirect
3. C2×#5832C2semidirect
4. C2×#5599C2semidirect
5. #84097C2semidirect
6. #84092C2semidirect
7. #83187C2semidirect
8. #83182C2semidirect
9. #83177C2semidirect
10. #83177C2semidirect
11. #82683C2semidirect
12. #82669C2semidirect
13. #82657C2semidirect
14. #82650C2semidirect
15. #82646C2semidirect
16. #82642C2semidirect
17. Dic3×#121C2semidirect
18. #82495C2semidirect
19. #82465C2semidirect
20. #82402C2semidirect
21. #82364C2semidirect
22. #82340C2semidirect
23. C4×#939C2semidirect
129. C2×#550D3semidirect
201. C3×#121D4semidirect
230. #944D4semidirect
577. Dic3⋊C4#41semidirect
657. #121#67semidirect
1108. Dic3#550semidirect
1315. C3#59051semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5502
C2×#58242
C2×#58322
C2×#55992
#840972
#840922
#831872
#831822
#831772
#826832
#826692
#826572
#826502
#826462
#826422
Dic3×#1212
#824952
#824652
#824022
#823642
#823402
C4×#9392
#590513