Finite Group Databasebeta

← #11023875

Subgroups — #11023875

Order 768.

3130 conjugacy classes of subgroups.

The subgroup lattice has 1242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5526C211yesmaximal, characteristic, complemented
2C2×#5490C211yesmaximal, characteristic
3C22×#886C211yesmaximal, characteristic, complemented
4C22×#878C211yesmaximal, characteristic, complemented
5C3×#2342C211yesmaximal, characteristic, complemented
6#82246C211yesmaximal, characteristic, complemented
7#82108C211yesmaximal, characteristic, complemented
8#75669C212yesmaximal, complemented
9#75668C212yesmaximal, complemented
10#75666C212yesmaximal, complemented
11#75665C212yesmaximal, complemented
12#74422C212yesmaximal, complemented
13#74413C212yesmaximal, complemented
14#74135C211yesmaximal, characteristic, complemented
15#74063C211yesmaximal, characteristic, complemented
16#74032C211yesmaximal, characteristic, complemented
17#74027C211yesmaximal, characteristic, complemented
18#73847C211yesmaximal, characteristic, complemented
19#73823C211yesmaximal, characteristic, complemented
20#73594C212yesmaximal, complemented
21#73516C211yesmaximal, characteristic, complemented
22#73493C212yesmaximal, complemented
23#73446C211yesmaximal, characteristic, complemented
24#37647—31nomaximal, Sylow
25C23×#67C2211yescharacteristic
26C24×Dic3C2211yescharacteristic
27C22×#235C2211yescharacteristic
28C23×Dic6C2211yescharacteristic, complemented
29C2×C3×#117C2211yescharacteristic, complemented
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×C3×C22⋊C4C2211yescharacteristic
32C2×#953C2211yescharacteristic
33C22×#217C2211yescharacteristic
34C2×#930C2211yescharacteristic
35C2×#929C2211yescharacteristic
36C2×C4×#67C2211yescharacteristic
37C22×(C2×D3)⋊C4C2212yes—
38C22×C4⋊Dic3C2212yes—
39C22×C4⋊Dic3C2211yescharacteristic, complemented
40C22×Dic3⋊C4C2211yescharacteristic, complemented
41C22×Dic3⋊C4C2211yescharacteristic, complemented
42#5526—28no—
43C2×#897C2212yescomplemented
44C2×#897C2212yescomplemented
45C2×#886—28no—
46C2×#886C2211yescharacteristic
47C2×#886C2211yescharacteristic
48C2×#886C2211yescharacteristic
49C2×#886C2211yescharacteristic
50C2×#886C2212yes—
51C2×#886C2212yes—
52C2×#886C2211yescharacteristic
53C2×#886C2211yescharacteristic
54C2×#886C2211yescharacteristic, complemented
55C2×#886C2211yescharacteristic, complemented
56C2×#886C2211yescharacteristic, complemented
57C2×#885C2211yescharacteristic
58#5490—28no—
59C2×#884C2211yescharacteristic
60C2×#884C2211yescharacteristic
61C2×#883C2211yescharacteristic
62C2×#882C2211yescharacteristic
63C2×#67⋊C4C2211yescharacteristic
64C2×D3×C22⋊C4C2211yescharacteristic
65C2×#878—28no—
66C2×#878C2211yescharacteristic
67C2×#878C2212yes—
68C2×#878C2212yes—
69C2×#878C2212yescomplemented
70C2×#878C2212yescomplemented
71C2×#875C2212yescomplemented
72C2×#869C2212yescomplemented
73C3×#388C2212yescomplemented
74C3×#388C2212yescomplemented
75C3×#385C2212yes—
76C3×#381C2211yescharacteristic, complemented
77C3×#380C2211yescharacteristic, complemented
78C3×#379C2211yescharacteristic
79C3×C4×C22⋊C4C2212yes—
80C3×C4×C22⋊C4C2211yescharacteristic, complemented
81#5213C2212yes—
82#5212C2212yes—
83#4994C2212yescomplemented
84#4994C2212yescomplemented
85#4994C2212yescomplemented
86#4987C2212yescomplemented
87#4984C2212yescomplemented
88#4981C2212yescomplemented
89#4961C2212yes—
90#4961C2212yes—
91#4961C2212yescomplemented
92#4958C2211yescharacteristic
93#4958C2211yescharacteristic
94#4958C2212yes—
95#4958C2211yescharacteristic, complemented
96#4958C2212yescomplemented
97#4955C2212yes—
98#4953C2212yescomplemented
99#4950C2212yes—
100#4950C2212yes—
101#4950C2211yescharacteristic, complemented
102#4950C2212yescomplemented
103#4943C2211yescharacteristic, complemented
104#4943C2211yescharacteristic, complemented
105#4943C2211yescharacteristic, complemented
106#4940C2212yescomplemented
107#4940C2212yescomplemented
108#4939C2212yescomplemented
109#4935C2212yescomplemented
110#4928C2212yescomplemented
111#4928C2212yescomplemented
112#4677C2212yescomplemented
113#4677C2212yescomplemented
114#4674C2212yescomplemented
115#4673C2212yescomplemented
116#4673C2212yescomplemented
117#4672C2212yescomplemented
118#4672C2212yescomplemented
119#4668C2212yescomplemented
120#4668C2212yescomplemented
121#4668C2212yescomplemented
122#4661C2212yescomplemented
123#4661C2212yescomplemented
124#4656C2212yescomplemented
125#4656C2212yescomplemented
126#4656C2212yescomplemented
127#4653C2212yescomplemented
128C2×#546—31no—
129C2×#536—31no—
130C22×#123—31no—
131C22×C22⋊Q8—31no—
132#2849—31no—
133#2681—32no—
134#2680—32no—
135#2674—32no—
136#2672—32no—
137#2618—31no—
138#2614—31no—
139#2501—31no—
140#2486—31no—
141#2472—32no—
142#2449—32no—
143#2440—32no—
144#2437—32no—
145#2413—31no—
146#2412—31no—
147#2406—31no—
148#2405—31no—
149#2342D311yescharacteristic, complemented
150#2322—31no—
151C25×C3C2311yescharacteristic
152C24×D3C2311yescharacteristic
153C23×C3×C4C2312yes—
154C23×C3×C4C2311yescharacteristic
155C23×C3×C4C2311yescharacteristic
156C22×#67—24no—
157C22×#67—24no—
158C22×#67—42no—
159C22×#67C2311yescharacteristic
160C22×#67C2311yescharacteristic
161C22×#67C2311yescharacteristic
162C22×#67C2311yescharacteristic
163C22×#67C2311yescharacteristic
164C22×#67C2311yescharacteristic
165C22×#67C2311yescharacteristic
166C23×Dic3—24no—
167C23×Dic3—24no—
168C23×Dic3—42no—
169C23×Dic3C2311yescharacteristic
170C23×Dic3C2311yescharacteristic
171C23×Dic3C2312yes—
172C23×Dic3C2312yes—
173C23×Dic3C2311yescharacteristic
174C23×Dic3C2311yescharacteristic
175C23×Dic3C2311yescharacteristic
176C2×#235—24no—
177C2×#235—24no—
178C2×#235—42no—
179C22×D12C2311yescharacteristic
180C22×D12C2311yescharacteristic
181C22×C4×D3C2311yescharacteristic
182C22×C4×D3C2311yescharacteristic
183C22×C4×D3C2311yescharacteristic
184C22×Dic6—24no—
185C22×Dic6—24no—
186C22×Dic6—42no—
187C22×Dic6C2311yescharacteristic
188C22×Dic6C2312yes—
189C22×Dic6C2312yes—
190C3×#117—24no—
191C2×C3×C4⋊C4C2312yes—
192C2×C3×C4⋊C4C2312yes—
193C2×C3×C22⋊C4—24no—
194C2×C3×C22⋊C4D418yes—
195C2×C3×C22⋊C4C2311yescharacteristic
196C2×C3×C22⋊C4C2311yescharacteristic
197C2×C3×C22⋊C4C2311yescharacteristic
198C2×C3×C22⋊C4C2312yes—
199C2×C3×C22⋊C4C2312yes—
200C2×C3×C22⋊C4C2312yes—
201C2×C3×C22⋊C4C2311yescharacteristic
202C2×C3×C22⋊C4C2311yescharacteristic
203C2×C3×C22⋊C4C2311yescharacteristic
204C2×C3×C22⋊C4C2311yescharacteristic
205C2×C3×C22⋊C4C2311yescharacteristic
206C2×C3×C42C2312yes—
207C2×C3×C42C2312yes—
208#953—24no—
209C2×#217—24no—
210C2×#217C2311yescharacteristic
211C2×#217C2311yescharacteristic
212C2×#217C2312yes—
213C2×#217C2311yescharacteristic
214C2×#217C2312yes—
215#930—24no—
216#929—24no—
217C4×#67—24no—
218C2×(C2×D3)⋊C4—28no—
219C2×(C2×D3)⋊C4C2312yes—
220C2×(C2×D3)⋊C4C2312yes—
221C2×(C2×D3)⋊C4C2312yes—
222C2×(C2×D3)⋊C4C2311yescharacteristic
223C2×(C2×D3)⋊C4C2311yescharacteristic
224C2×(C2×D3)⋊C4C2311yescharacteristic
225C2×(C2×D3)⋊C4C2312yes—
226C2×(C2×D3)⋊C4C2311yescharacteristic
227C2×(C2×D3)⋊C4C2311yescharacteristic
228C2×(C2×D3)⋊C4C2312yes—
229C2×(C2×D3)⋊C4C2312yes—
230C2×(C2×D3)⋊C4C2312yes—
231C2×(C2×D3)⋊C4C2312yes—
232C2×(C2×D3)⋊C4C2312yes—
233C2×(C2×D3)⋊C4C2312yes—
234C2×(C2×D3)⋊C4C2312yes—
235C2×(C2×D3)⋊C4C2312yes—
236C2×C4⋊Dic3—24no—
237C2×C4⋊Dic3—28no—
238C2×C4⋊Dic3C2312yes—
239C2×C4⋊Dic3C2312yes—
240C2×C4⋊Dic3C2311yescharacteristic
241C2×C4⋊Dic3C2312yes—
242C2×C4⋊Dic3C2312yes—
243C2×C4⋊Dic3C2312yes—
244C2×C4⋊Dic3C2312yes—
245C2×C4⋊Dic3C2312yes—
246C2×C4⋊Dic3C2312yes—
247C2×C4⋊Dic3C2312yes—
248C2×C4⋊Dic3C2312yes—
249C2×C4⋊Dic3C2312yes—
250C2×C4⋊Dic3C2312yes—
251C2×Dic3⋊C4—24no—
252C2×Dic3⋊C4—24no—
253C2×Dic3⋊C4C2312yes—
254C2×Dic3⋊C4C2311yescharacteristic
255C2×Dic3⋊C4C2311yescharacteristic
256C2×Dic3⋊C4C2312yes—
257C2×Dic3⋊C4C2311yescharacteristic
258C2×Dic3⋊C4C2312yes—
259C2×Dic3⋊C4C2312yes—
260C2×C4×Dic3C2311yescharacteristic
261#897—28no—
262#897—28no—
263#886—24no—
264#886—24no—
265#886—24no—
266#886—24no—
267#886—24no—
268#886—24no—
269#886—28no—
270#886—28no—
271#886—42no—
272#886—42no—
273#886D418yescomplemented
274#885—24no—
275#884—24no—
276#884—24no—
277#883—24no—
278#882—24no—
279#67⋊C4—24no—
280D3×C22⋊C4—24no—
281#878—28no—
282#878—28no—
283#878—28no—
284#878—28no—
285#878—24no—
286#875—28no—
287#869—28no—
288C3×#95C2312yes—
289C3×#95C2312yes—
290C3×#95C2312yes—
291C3×#95C2312yes—
292C3⋊#95C2312yes—
293C3⋊#95C2312yes—
294C3⋊#95C2312yes—
295C3⋊#95C2312yes—
296C3⋊#95C2312yes—
297C3⋊#95C2312yes—
298C3⋊#95C2312yes—
299C3⋊#95C2312yes—
300C3⋊#95C2312yes—
301C3⋊#95C2312yes—
302C22×#41—31no—
303C23×Q8—31no—
304C23×D4—31no—
305C24×C4—31no—
306#546—68no—
307#536—68no—
308C2×C4⋊Q8—32no—
309C2×#124—31no—
310C2×#124—32no—
311C2×#123—31no—
312C2×#123—31no—
313C2×#123—31no—
314C2×#123—31no—
315C2×#123—31no—
316C2×#123—31no—
317C2×#123—31no—
318C2×#123—32no—
319C2×#123—32no—
320C2×#123—31no—
321C2×#123—31no—
322C2×#123—31no—
323C2×#123—31no—
324C2×#123—68no—
325C2×C22⋊Q8—32no—
326C2×C22⋊Q8—32no—
327C2×C22⋊Q8—32no—
328C2×C22⋊Q8—32no—
329C2×C22⋊Q8—32no—
330C2×C22⋊Q8—32no—
331C2×C22⋊Q8—31no—
332C2×C22⋊Q8—68no—
333C2×#121—31no—
334C2×#121—31no—
335C2×#121—31no—
336C2×#120—31no—
337C2×#120—31no—
338C2×C4×D4—31no—
339C2×C4×D4—31no—
340C2×#117C2×D311yescharacteristic, complemented
341C22×C4⋊C4—31no—
342C22×C4⋊C4—31no—
343C22×C4⋊C4—31no—
344C22×C4⋊C4—32no—
345C22×C22⋊C4—31no—
346C22×C22⋊C4—32no—
347C22×C22⋊C4—31no—
348C22×C22⋊C4C2×D311yescharacteristic
349C22×C22⋊C4C2×D311yescharacteristic
350#399—32no—
351#399—32no—
352#398—32no—
353#398—32no—
354#398—32no—
355#397—32no—
356#397—32no—
357#396—32no—
358#396—32no—
359#396—32no—
360#395—32no—
361#395—32no—
362#395—32no—
363#394—32no—
364#394—32no—
365#394—32no—
366#394—32no—
367#394—32no—
368#393—32no—
369#393—32no—
370#390—32no—
371#389—32no—
372#389—32no—
373#389—32no—
374#388—32no—
375#388—32no—
376#388C2×D312yescomplemented
377#388C2×D312yescomplemented
378#387—32no—
379#386—32no—
380#386—31no—
381#386—32no—
382#386—32no—
383#386—31no—
384#386—31no—
385#385—31no—
386#385—32no—
387#385—32no—
388#385—32no—
389#385—32no—
390#385—32no—
391#385—32no—
392#385C2×D312yes—
393#384—32no—
394#381—31no—
395#381—31no—
396#381—31no—
397#381C2×D311yescharacteristic, complemented
398#380—32no—
399#380—32no—
400#380C2×D311yescharacteristic, complemented
401#379—32no—
402#379C2×D311yescharacteristic
403C4×C22⋊C4C2×D312yes—
404C4×C22⋊C4C2×D311yescharacteristic, complemented
405C24×C3—22no—
406C24×C3—22no—
407C24×C3—24no—
408C24×C3—42no—
409C24×C3C2×D414yes—
410C24×C3C2411yescharacteristic
411C24×C3C2411yescharacteristic
412C24×C3C2411yescharacteristic
413C23×D3—22no—
414C23×D3—24no—
415C23×D3—22no—
416C23×D3—41no—
417C23×D3—42no—
418C23×D3C2411yescharacteristic
419C23×D3C2411yescharacteristic
420C23×D3C2411yescharacteristic
421C22×C3×C4—22no—
422C22×C3×C4—22no—
423C22×C3×C4—24no—
424C22×C3×C4—24no—
425C22×C3×C4—42no—
426C22×C3×C4—42no—
427C22×C3×C4C2×D414yes—
428C22×C3×C4C2×D414yes—
429C22×C3×C4C2412yes—
430C22×C3×C4C2412yes—
431C22×C3×C4C2412yes—
432C22×C3×C4C2412yes—
433C22×C3×C4C2411yescharacteristic
434C22×C3×C4C2411yescharacteristic
435C22×C3×C4C2411yescharacteristic
436C22×C3×C4C2411yescharacteristic
437C2×#67—22no—
438C2×#67—22no—
439C2×#67—22no—
440C2×#67—22no—
441C2×#67—22no—
442C2×#67—22no—
443C2×#67—22no—
444C2×#67—22no—
445C2×#67—22no—
446C2×#67—22no—
447C2×#67—22no—
448C2×#67—24no—
449C2×#67—22no—
450C2×#67—22no—
451C2×#67—22no—
452C2×#67—41no—
453C2×#67—41no—
454C2×#67—42no—
455C2×#67—416no—
456C2×#67C2×D414yes—
457C22×Dic3—22no—
458C22×Dic3—22no—
459C22×Dic3—24no—
460C22×Dic3—24no—
461C22×Dic3—22no—
462C22×Dic3—22no—
463C22×Dic3—22no—
464C22×Dic3—22no—
465C22×Dic3—22no—
466C22×Dic3—22no—
467C22×Dic3—22no—
468C22×Dic3—22no—
469C22×Dic3—24no—
470C22×Dic3—22no—
471C22×Dic3—24no—
472C22×Dic3—42no—
473C22×Dic3—42no—
474C22×Dic3—42no—
475C22×Dic3—41no—
476C22×Dic3—416no—
477C22×Dic3C2×D414yes—
478C22×Dic3C2411yescharacteristic
479C22×Dic3C2411yescharacteristic
480C22×Dic3C2412yes—
481C22×Dic3C2411yescharacteristic
482C22×Dic3C2412yes—
483C22×Dic3C2411yescharacteristic
484C22×Dic3C2412yes—
485C22×Dic3C2411yescharacteristic
486C22×Dic3C2412yes—
487#235—416no—
488C2×D12—22no—
489C2×D12—22no—
490C2×D12—22no—
491C2×D12—41no—
492C2×D12—42no—
493C2×C4×D3—22no—
494C2×C4×D3—22no—
495C2×C4×D3—22no—
496C2×C4×D3—22no—
497C2×C4×D3—22no—
498C2×C4×D3—41no—
499C2×C4×D3—41no—
500C2×C4×D3—42no—
501C2×Dic6—24no—
502C2×Dic6—24no—
503C2×Dic6—22no—
504C2×Dic6—22no—
505C2×Dic6—24no—
506C2×Dic6—24no—
507C2×Dic6—42no—
508C2×Dic6—42no—
509C2×Dic6—41no—
510C2×Dic6—416no—
511C3×C4⋊C4—24no—
512C3×C4⋊C4—42no—
513C3×C22⋊C4—22no—
514C3×C22⋊C4—22no—
515C3×C22⋊C4—22no—
516C3×C22⋊C4—24no—
517C3×C22⋊C4—24no—
518C3×C22⋊C4—42no—
519C3×C22⋊C4C2×D414yes—
520C3×C22⋊C4C2×D414yes—
521C3×C22⋊C4C2×D414yes—
522C3×C22⋊C4C2×D414yes—
523C3×C22⋊C4C2×D414yes—
524C3×C42—24no—
525C3×C42—42no—
526#217—24no—
527#217—24no—
528#217—22no—
529#217—22no—
530#217—22no—
531(C2×D3)⋊C4—24no—
532(C2×D3)⋊C4—24no—
533(C2×D3)⋊C4—24no—
534(C2×D3)⋊C4—22no—
535(C2×D3)⋊C4—22no—
536(C2×D3)⋊C4—22no—
537(C2×D3)⋊C4—22no—
538(C2×D3)⋊C4—22no—
539(C2×D3)⋊C4—24no—
540(C2×D3)⋊C4—24no—
541(C2×D3)⋊C4—24no—
542(C2×D3)⋊C4—42no—
543(C2×D3)⋊C4—42no—
544(C2×D3)⋊C4—42no—
545(C2×D3)⋊C4—42no—
546(C2×D3)⋊C4—42no—
547(C2×D3)⋊C4C2×D418yes—
548C4⋊Dic3—24no—
549C4⋊Dic3—24no—
550C4⋊Dic3—24no—
551C4⋊Dic3—22no—
552C4⋊Dic3—24no—
553C4⋊Dic3—24no—
554C4⋊Dic3—24no—
555C4⋊Dic3—24no—
556C4⋊Dic3—24no—
557C4⋊Dic3—42no—
558C4⋊Dic3—42no—
559C4⋊Dic3—42no—
560C4⋊Dic3C2×D418yes—
561Dic3⋊C4—24no—
562Dic3⋊C4—24no—
563Dic3⋊C4—24no—
564Dic3⋊C4—24no—
565Dic3⋊C4—22no—
566Dic3⋊C4—22no—
567Dic3⋊C4—22no—
568C4×Dic3—22no—
569C25—31no—
570C25C22×D311yescharacteristic
571C2×#41—64no—
572C2×#41—64no—
573C2×#41—122no—
574C22×Q8—32no—
575C22×Q8—32no—
576C22×Q8—31no—
577C22×Q8—64no—
578C22×Q8—64no—
579C22×Q8—122no—
580C22×D4—31no—
581C22×D4—31no—
582C22×D4—31no—
583C22×D4—31no—
584C22×D4—31no—
585C22×D4—31no—
586C22×D4—31no—
587C22×D4—31no—
588C22×D4—31no—
589C22×D4—64no—
590C22×D4—64no—
591C22×D4—122no—
592C23×C4—31no—
593C23×C4—31no—
594C23×C4—31no—
595C23×C4—32no—
596C23×C4—31no—
597C23×C4—32no—
598C23×C4—31no—
599C23×C4—31no—
600C23×C4—31no—
601C23×C4—31no—
602C23×C4—64no—
603C23×C4—64no—
604C23×C4—122no—
605C23×C4C22×D312yes—
606C23×C4C22×D311yescharacteristic
607C23×C4C22×D311yescharacteristic
608C4⋊Q8—68no—
609#124—68no—
610#124—64no—
611#123—38no—
612#123—68no—
613#123—68no—
614#123—64no—
615#123—64no—
616#123—64no—
617#123—64no—
618#123—64no—
619#123—64no—
620#123—64no—
621#123—64no—
622#123—122no—
623#123—122no—
624C22⋊Q8—68no—
625C22⋊Q8—68no—
626C22⋊Q8—68no—
627C22⋊Q8—68no—
628C22⋊Q8—68no—
629C22⋊Q8—68no—
630C22⋊Q8—64no—
631#121—64no—
632#121—64no—
633#121—64no—
634#120—64no—
635#120—64no—
636C4×D4—64no—
637C4×D4—64no—
638#117—24no—
639C2×C4⋊C4—32no—
640C2×C4⋊C4—32no—
641C2×C4⋊C4—32no—
642C2×C4⋊C4—32no—
643C2×C4⋊C4—32no—
644C2×C4⋊C4—32no—
645C2×C4⋊C4—32no—
646C2×C4⋊C4—32no—
647C2×C4⋊C4—32no—
648C2×C4⋊C4—32no—
649C2×C4⋊C4—31no—
650C2×C4⋊C4—31no—
651C2×C4⋊C4—31no—
652C2×C4⋊C4—31no—
653C2×C4⋊C4—32no—
654C2×C4⋊C4—32no—
655C2×C4⋊C4—32no—
656C2×C4⋊C4—32no—
657C2×C4⋊C4—32no—
658C2×C4⋊C4—32no—
659C2×C4⋊C4—68no—
660C2×C4⋊C4—64no—
661C2×C4⋊C4—64no—
662C2×C4⋊C4—64no—
663C2×C4⋊C4C22×D312yes—
664C2×C4⋊C4C22×D312yes—
665C2×C22⋊C4—24no—
666C2×C22⋊C4—32no—
667C2×C22⋊C4—31no—
668C2×C22⋊C4—32no—
669C2×C22⋊C4—32no—
670C2×C22⋊C4—31no—
671C2×C22⋊C4—31no—
672C2×C22⋊C4—31no—
673C2×C22⋊C4—31no—
674C2×C22⋊C4—32no—
675C2×C22⋊C4—32no—
676C2×C22⋊C4—32no—
677C2×C22⋊C4—31no—
678C2×C22⋊C4—31no—
679C2×C22⋊C4—31no—
680C2×C22⋊C4—32no—
681C2×C22⋊C4—32no—
682C2×C22⋊C4—32no—
683C2×C22⋊C4—32no—
684C2×C22⋊C4—32no—
685C2×C22⋊C4—32no—
686C2×C22⋊C4—32no—
687C2×C22⋊C4—32no—
688C2×C22⋊C4—68no—
689C2×C22⋊C4—64no—
690C2×C22⋊C4—64no—
691C2×C22⋊C4D1218yes—
692C2×C22⋊C4C22×D311yescharacteristic
693C2×C22⋊C4C22×D312yes—
694C2×C22⋊C4C22×D311yescharacteristic
695C2×C22⋊C4C22×D311yescharacteristic
696C2×C22⋊C4C22×D312yes—
697C2×C22⋊C4C22×D312yes—
698C2×C22⋊C4C22×D311yescharacteristic
699C2×C22⋊C4C22×D311yescharacteristic
700C2×C22⋊C4C22×D311yescharacteristic
701C2×C22⋊C4C22×D311yescharacteristic
702C2×C22⋊C4C22×D311yescharacteristic
703C2×C42—31no—
704C2×C42C22×D312yes—
705C2×C42C22×D312yes—
706#95—32no—
707#95—32no—
708#95—32no—
709#95—32no—
710#95—32no—
711#95—32no—
712#95—32no—
713#95—32no—
714#95—32no—
715#95—32no—
716#95C22×D312yes—
717#95C22×D312yes—
718#95C22×D312yes—
719#95C22×D312yes—
720C23×C3—21no—
721C23×C3—21no—
722C23×C3—22no—
723C23×C3—22no—
724C23×C3—22no—
725C23×C3—28no—
726C23×C3—28no—
727C23×C3—21no—
728C23×C3—21no—
729C23×C3—22no—
730C23×C3—22no—
731C23×C3—44no—
732C23×C3—48no—
733C23×C3—48no—
734C23×C3C22×D412yes—
735C23×C3C22×D412yes—
736C23×C3C22×D412yes—
737C23×C3C22×D412yes—
738C23×C3H(5,𝔽2)12yes—
739C23×C32−1+414yes—
740C23×C3C2511yescharacteristic
741C22×D3—21no—
742C22×D3—21no—
743C22×D3—22no—
744C22×D3—22no—
745C22×D3—21no—
746C22×D3—21no—
747C22×D3—21no—
748C22×D3—21no—
749C22×D3—21no—
750C22×D3—21no—
751C22×D3—22no—
752C22×D3—22no—
753C22×D3—22no—
754C22×D3—22no—
755C22×D3—44no—
756C22×D3—48no—
757C22×D3—44no—
758C22×D3—82no—
759C22×D3—84no—
760C22×D3C22×D412yes—
761C2×C3×C4—28no—
762C2×C3×C4—21no—
763C2×C3×C4—21no—
764C2×C3×C4—21no—
765C2×C3×C4—21no—
766C2×C3×C4—22no—
767C2×C3×C4—22no—
768C2×C3×C4—22no—
769C2×C3×C4—22no—
770C2×C3×C4—22no—
771C2×C3×C4—22no—
772C2×C3×C4—22no—
773C2×C3×C4—22no—
774C2×C3×C4—22no—
775C2×C3×C4—22no—
776C2×C3×C4—22no—
777C2×C3×C4—22no—
778C2×C3×C4—22no—
779C2×C3×C4—44no—
780C2×C3×C4—48no—
781C2×C3×C4C22×D412yes—
782C2×C3×C4C22×D412yes—
783C2×C3×C4C22×D412yes—
784C2×C3×C4C22×D412yes—
785C2×C3×C4C22×D414yes—
786#67—28no—
787#67—44no—
788#67—44no—
789#67—44no—
790#67—44no—
791#67—44no—
792#67—82no—
793C2×Dic3—28no—
794C2×Dic3—21no—
795C2×Dic3—22no—
796C2×Dic3—22no—
797C2×Dic3—21no—
798C2×Dic3—21no—
799C2×Dic3—22no—
800C2×Dic3—22no—
801C2×Dic3—21no—
802C2×Dic3—21no—
803C2×Dic3—21no—
804C2×Dic3—21no—
805C2×Dic3—22no—
806C2×Dic3—22no—
807C2×Dic3—22no—
808C2×Dic3—21no—
809C2×Dic3—21no—
810C2×Dic3—21no—
811C2×Dic3—22no—
812C2×Dic3—22no—
813C2×Dic3—22no—
814C2×Dic3—22no—
815C2×Dic3—22no—
816C2×Dic3—22no—
817C2×Dic3—48no—
818C2×Dic3—48no—
819C2×Dic3—44no—
820C2×Dic3—44no—
821C2×Dic3—44no—
822C2×Dic3—44no—
823C2×Dic3C22×D412yes—
824C2×Dic3C22×D414yes—
825D12—44no—
826D12—82no—
827C4×D3—44no—
828C4×D3—44no—
829C4×D3—82no—
830Dic6—48no—
831Dic6—48no—
832Dic6—44no—
833C24—22no—
834C24—22no—
835C24—24no—
836C24—31no—
837C24—31no—
838C24—31no—
839C24—42no—
840C24—62no—
841C24—62no—
842C24—64no—
843C24—121no—
844C24—122no—
845C24C2×D1214yes—
846C24C23×D311yescharacteristic
847C24C23×D311yescharacteristic
848C24C23×D311yescharacteristic
849#41—1216no—
850C2×Q8—64no—
851C2×Q8—64no—
852C2×Q8—62no—
853C2×Q8—64no—
854C2×Q8—64no—
855C2×Q8—62no—
856C2×Q8—122no—
857C2×Q8—122no—
858C2×Q8—121no—
859C2×Q8—1216no—
860C2×D4—34no—
861C2×D4—62no—
862C2×D4—62no—
863C2×D4—62no—
864C2×D4—62no—
865C2×D4—62no—
866C2×D4—62no—
867C2×D4—62no—
868C2×D4—62no—
869C2×D4—62no—
870C2×D4—62no—
871C2×D4—62no—
872C2×D4—62no—
873C2×D4—62no—
874C2×D4—62no—
875C2×D4—64no—
876C2×D4—62no—
877C2×D4—62no—
878C2×D4—62no—
879C2×D4—121no—
880C2×D4—122no—
881C2×D4—121no—
882C2×D4—121no—
883C2×D4—122no—
884C2×D4—1216no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—24no—
888C22×C4—24no—
889C22×C4—34no—
890C22×C4—31no—
891C22×C4—32no—
892C22×C4—31no—
893C22×C4—31no—
894C22×C4—32no—
895C22×C4—32no—
896C22×C4—32no—
897C22×C4—31no—
898C22×C4—31no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—62no—
902C22×C4—62no—
903C22×C4—64no—
904C22×C4—62no—
905C22×C4—64no—
906C22×C4—62no—
907C22×C4—62no—
908C22×C4—62no—
909C22×C4—62no—
910C22×C4—62no—
911C22×C4—62no—
912C22×C4—64no—
913C22×C4—64no—
914C22×C4—62no—
915C22×C4—62no—
916C22×C4—62no—
917C22×C4—62no—
918C22×C4—62no—
919C22×C4—62no—
920C22×C4—62no—
921C22×C4—121no—
922C22×C4—121no—
923C22×C4—122no—
924C22×C4—122no—
925C22×C4—122no—
926C22×C4—121no—
927C22×C4—122no—
928C22×C4—1216no—
929C22×C4C2×D1214yes—
930C22×C4C2×D1214yes—
931C22×C4C23×D312yes—
932C22×C4C23×D312yes—
933C22×C4C23×D312yes—
934C22×C4C23×D311yescharacteristic
935C22×C4C23×D311yescharacteristic
936C22×C4C23×D311yescharacteristic
937C22×C4C23×D311yescharacteristic
938C22×C4C23×D312yes—
939C4⋊C4—24no—
940C4⋊C4—38no—
941C4⋊C4—42no—
942C4⋊C4—64no—
943C4⋊C4—64no—
944C4⋊C4—64no—
945C4⋊C4—64no—
946C4⋊C4—64no—
947C4⋊C4—64no—
948C4⋊C4—64no—
949C4⋊C4—64no—
950C4⋊C4—64no—
951C4⋊C4—64no—
952C4⋊C4—62no—
953C4⋊C4—62no—
954C4⋊C4—62no—
955C4⋊C4—62no—
956C4⋊C4—64no—
957C4⋊C4—64no—
958C4⋊C4—122no—
959C4⋊C4—122no—
960C4⋊C4—122no—
961C22⋊C4—22no—
962C22⋊C4—22no—
963C22⋊C4—22no—
964C22⋊C4—24no—
965C22⋊C4—24no—
966C22⋊C4—38no—
967C22⋊C4—42no—
968C22⋊C4—64no—
969C22⋊C4—64no—
970C22⋊C4—64no—
971C22⋊C4—64no—
972C22⋊C4—62no—
973C22⋊C4—64no—
974C22⋊C4—64no—
975C22⋊C4—62no—
976C22⋊C4—62no—
977C22⋊C4—62no—
978C22⋊C4—62no—
979C22⋊C4—62no—
980C22⋊C4—62no—
981C22⋊C4—62no—
982C22⋊C4—64no—
983C22⋊C4—64no—
984C22⋊C4—122no—
985C22⋊C4—122no—
986C22⋊C4—122no—
987C22⋊C4—122no—
988C22⋊C4—122no—
989C22⋊C4C2×D1214yes—
990C22⋊C4C2×D1214yes—
991C22⋊C4C2×D1214yes—
992C22⋊C4C2×D1214yes—
993C22⋊C4D3×D414yes—
994C42—24no—
995C42—42no—
996C42—62no—
997C22×C3—22no—
998C22×C3—22no—
999C22×C3—22no—
1000C22×C3—22no—
1001C22×C3—24no—
1002C22×C3—24no—
1003C22×C3—24no—
1004C22×C3—24no—
1005C22×C3—22no—
1006C22×C3—22no—
1007C22×C3—22no—
1008C22×C3—416no—
1009C22×C3—42no—
1010C22×C3—42no—
1011C22×C3#53614yescomplemented
1012C22×C3D4214yes—
1013C22×C3C23×D411yescharacteristic
1014C22×C3C23×D411yescharacteristic
1015C22×C3C2×H(5,𝔽2)11yescharacteristic
1016C22×C3C2×2−1+412yes—
1017C22×C3#58512yes—
1018C2×D3—22no—
1019C2×D3—24no—
1020C2×D3—41no—
1021C2×D3—41no—
1022C2×D3—42no—
1023C2×D3—41no—
1024C2×D3—41no—
1025C2×D3—41no—
1026C2×D3—41no—
1027C2×D3—41no—
1028C2×D3—41no—
1029C2×D3—42no—
1030C2×D3—42no—
1031C2×D3—42no—
1032C2×D3—42no—
1033C2×D3—88no—
1034C3×C4—22no—
1035C3×C4—22no—
1036C3×C4—22no—
1037C3×C4—22no—
1038C3×C4—24no—
1039C3×C4—42no—
1040C3×C4—42no—
1041C3×C4—42no—
1042Dic3—24no—
1043Dic3—22no—
1044Dic3—41no—
1045Dic3—42no—
1046Dic3—41no—
1047Dic3—42no—
1048Dic3—41no—
1049Dic3—41no—
1050Dic3—42no—
1051C23—21no—
1052C23—21no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—21no—
1057C23—21no—
1058C23—22no—
1059C23—22no—
1060C23—28no—
1061C23—28no—
1062C23—32no—
1063C23—44no—
1064C23—48no—
1065C23—48no—
1066C23—61no—
1067C23—61no—
1068C23—62no—
1069C23—62no—
1070C23—61no—
1071C23—61no—
1072C23—61no—
1073C23—61no—
1074C23—61no—
1075C23—61no—
1076C23—62no—
1077C23—62no—
1078C23—62no—
1079C23—62no—
1080C23—124no—
1081C23—128no—
1082C23—124no—
1083C23—244no—
1084C23—242no—
1085C23C22×D1212yes—
1086C23C22×D1212yes—
1087C23C22×D1212yes—
1088C23C2×D3×D412yes—
1089C23#100912yes—
1090C23#101014yes—
1091C23C24×D311yescharacteristic
1092Q8—128no—
1093Q8—128no—
1094Q8—124no—
1095D4—68no—
1096D4—124no—
1097D4—124no—
1098D4—124no—
1099D4—124no—
1100D4—124no—
1101D4—124no—
1102D4—242no—
1103D4—242no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—28no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—34no—
1123C2×C4—32no—
1124C2×C4—44no—
1125C2×C4—48no—
1126C2×C4—61no—
1127C2×C4—62no—
1128C2×C4—62no—
1129C2×C4—61no—
1130C2×C4—68no—
1131C2×C4—61no—
1132C2×C4—61no—
1133C2×C4—61no—
1134C2×C4—62no—
1135C2×C4—62no—
1136C2×C4—61no—
1137C2×C4—62no—
1138C2×C4—62no—
1139C2×C4—62no—
1140C2×C4—61no—
1141C2×C4—61no—
1142C2×C4—62no—
1143C2×C4—62no—
1144C2×C4—61no—
1145C2×C4—61no—
1146C2×C4—62no—
1147C2×C4—62no—
1148C2×C4—62no—
1149C2×C4—62no—
1150C2×C4—124no—
1151C2×C4—124no—
1152C2×C4—128no—
1153C2×C4—128no—
1154C2×C4—124no—
1155C2×C4—124no—
1156C2×C4—124no—
1157C2×C4—124no—
1158C2×C4—242no—
1159C2×C4C22×D1212yes—
1160C2×C4C22×D1212yes—
1161C2×C4C22×D1212yes—
1162C2×C4C22×D1212yes—
1163C2×C4C2×D3×D414yes—
1164C2×C3—24no—
1165C2×C3—24no—
1166C2×C3—42no—
1167C2×C3C2×#53611yescharacteristic
1168C2×C3C2×D4211yescharacteristic
1169C2×C3#348511yescharacteristic
1170C2×C3#348912yes—
1171C2×C3#353512yes—
1172D3—42no—
1173D3—81no—
1174D3—81no—
1175C22—22no—
1176C22—24no—
1177C22—24no—
1178C22—22no—
1179C22—22no—
1180C22—24no—
1181C22—24no—
1182C22—22no—
1183C22—22no—
1184C22—22no—
1185C22—22no—
1186C22—416no—
1187C22—42no—
1188C22—42no—
1189C22—62no—
1190C22—64no—
1191C22—122no—
1192C22—121no—
1193C22—121no—
1194C22—121no—
1195C22—121no—
1196C22—122no—
1197C22—122no—
1198C22—121no—
1199C22—121no—
1200C22—122no—
1201C22—122no—
1202C22—121no—
1203C22—121no—
1204C22—248no—
1205C22#552614yescomplemented
1206C22D4×D1214yes—
1207C22C23×D1211yescharacteristic
1208C22C22×D3×D411yescharacteristic
1209C22C2×#100911yescharacteristic
1210C22C2×#101012yes—
1211C22#596612yes—
1212C4—22no—
1213C4—22no—
1214C4—22no—
1215C4—22no—
1216C4—24no—
1217C4—42no—
1218C4—42no—
1219C4—42no—
1220C4—64no—
1221C4—62no—
1222C4—122no—
1223C4—121no—
1224C4—121no—
1225C4—122no—
1226C4—122no—
1227C4—121no—
1228C4—121no—
1229C3#3764711yescharacteristic, complemented, Sylow
1230C2—24no—
1231C2—24no—
1232C2—42no—
1233C2—122no—
1234C2—241no—
1235C2—241no—
1236C2C2×#552611yescharacteristic
1237C2C2×D4×D1211yescharacteristic
1238C2#8585811yescharacteristic
1239C2#8663012yes—
1240C2#8680212yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2342C2
prime radicalC2×#5490C2
hypercenter#2342D3
hypocenterC3#37647
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2342

Complements

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

NH ≅ G/Ntype
1. C2×#5526C2semidirect
3. C22×#886C2semidirect
4. C22×#878C2semidirect
5. C3×#2342C2semidirect
6. #82246C2semidirect
7. #82108C2semidirect
8. #75669C2semidirect
9. #75668C2semidirect
10. #75666C2semidirect
11. #75665C2semidirect
12. #74422C2semidirect
13. #74413C2semidirect
14. #74135C2semidirect
15. #74063C2semidirect
16. #74032C2semidirect
17. #74027C2semidirect
18. #73847C2semidirect
19. #73823C2semidirect
20. #73594C2semidirect
21. #73516C2semidirect
22. #73493C2semidirect
23. #73446C2semidirect
28. C23×Dic6C22semidirect
29. C2×C3×#117C22semidirect
39. C22×C4⋊Dic3C22semidirect
40. C22×Dic3⋊C4C22semidirect
41. C22×Dic3⋊C4C22semidirect
43. C2×#897C22semidirect
44. C2×#897C22semidirect
54. C2×#886C22semidirect
55. C2×#886C22semidirect
56. C2×#886C22semidirect
69. C2×#878C22semidirect
70. C2×#878C22semidirect
71. C2×#875C22semidirect
72. C2×#869C22semidirect
73. C3×#388C22semidirect
74. C3×#388C22semidirect
76. C3×#381C22semidirect
77. C3×#380C22semidirect
80. C3×C4×C22⋊C4C22semidirect
83. #4994C22semidirect
84. #4994C22semidirect
85. #4994C22semidirect
86. #4987C22semidirect
87. #4984C22semidirect
88. #4981C22semidirect
91. #4961C22semidirect
95. #4958C22semidirect
96. #4958C22semidirect
98. #4953C22semidirect
101. #4950C22semidirect
102. #4950C22semidirect
103. #4943C22semidirect
104. #4943C22semidirect
105. #4943C22semidirect
106. #4940C22semidirect
107. #4940C22semidirect
108. #4939C22semidirect
109. #4935C22semidirect
110. #4928C22semidirect
111. #4928C22semidirect
112. #4677C22semidirect
113. #4677C22semidirect
114. #4674C22semidirect
115. #4673C22semidirect
116. #4673C22semidirect
117. #4672C22semidirect
118. #4672C22semidirect
119. #4668C22semidirect
120. #4668C22semidirect
121. #4668C22semidirect
122. #4661C22semidirect
123. #4661C22semidirect
124. #4656C22semidirect
125. #4656C22semidirect
126. #4656C22semidirect
127. #4653C22semidirect
149. #2342D3semidirect
273. #886D4semidirect
340. C2×#117C2×D3semidirect
376. #388C2×D3semidirect
377. #388C2×D3semidirect
397. #381C2×D3semidirect
400. #380C2×D3semidirect
404. C4×C22⋊C4C2×D3semidirect
1011. C22×C3#536semidirect
1205. C22#5526semidirect
1229. C3#37647semidirect

Maximal subgroups

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

subgroupindex
C2×#55262
C2×#54902
C22×#8862
C22×#8782
C3×#23422
#822462
#821082
#756692
#756682
#756662
#756652
#744222
#744132
#741352
#740632
#740322
#740272
#738472
#738232
#735942
#735162
#734932
#734462
#376473