Finite Group Databasebeta

← #10967669

Subgroups — #10967669

Order 768.

2810 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#41C211yesmaximal, characteristic, complemented
2C2×C4×#235C211yesmaximal, characteristic, complemented
3#84097C212yesmaximal, complemented
4#82500C211yesmaximal, characteristic, complemented
5C4×#946C212yesmaximal, complemented
6#82482C211yesmaximal, characteristic, complemented
7#82417C211yesmaximal, characteristic, complemented
8#82402C212yesmaximal, complemented
9C4×#938C212yesmaximal, complemented
10#82376C211yesmaximal, characteristic, complemented
11#82372C212yesmaximal, complemented
12#82345C214yesmaximal, complemented
13#82285C214yesmaximal, complemented
14#82283C212yesmaximal, complemented
15C4×#924C212yesmaximal, complemented
16C4×#930C212yesmaximal, complemented
17#82062C211yesmaximal, characteristic, complemented
18#34976—31nomaximal, Sylow
19C22×C3×#41C2211yescharacteristic
20C22×#235C2211yescharacteristic
21C3×C4×#41—28no—
22C2×C3×C4×Q8C2211yescharacteristic
23C2×C3×C4×Q8C2211yescharacteristic
24C2×C3×C4×D4C2212yes—
25C2×C3×C4×D4C2212yes—
26C2×C3×C4×D4C2211yescharacteristic
27C2×C3×C4×D4C2211yescharacteristic
28C2×C3×#117C2211yescharacteristic
29C2×C3×#117C2212yes—
30C22×C3×C42C2212yes—
31C22×C3×C42C2211yescharacteristic
32C2×#946C2212yes—
33C2×#938C2212yes—
34C2×#930C2212yes—
35C2×C4×#67C2212yes—
36C2×C4×#67C2212yes—
37C2×C4×#67C2214yes—
38C2×#926C2211yescharacteristic
39C2×#926C2212yes—
40C2×#924C2212yes—
41C4×#235—28no—
42C2×C4×D12C2211yescharacteristic
43C2×C4×D12C2211yescharacteristic
44C2×#872C2212yes—
45C2×C42×D3C2212yes—
46C2×C4×Dic6C2211yescharacteristic
47C2×C4×Dic6C2211yescharacteristic
48#5229C2212yes—
49#5223C2214yes—
50#5222C2214yes—
51#5221C2212yes—
52#5213C2214yes—
53#5212C2212yes—
54#5212C2212yes—
55#5212C2212yes—
56#5212C2212yes—
57#5210C2214yes—
58C4×#217C2214yes—
59#4994C2214yes—
60#4989C2214yes—
61#4987C2212yes—
62#4987C2212yes—
63#4982C2214yes—
64#4978C2214yes—
65#4972C2212yes—
66#4972C2212yes—
67#4961C2214yes—
68#4959C2214yes—
69#4956C2214yes—
70#4952C2214yes—
71#4948C2214yes—
72#4944C2214yes—
73#4940C2214yes—
74#4939C2212yes—
75C4×(C2×D3)⋊C4C2214yes—
76#4936C2212yes—
77#4935C2211yescharacteristic
78#4935C2211yescharacteristic
79C4×C4⋊Dic3C2212yes—
80C4×C4⋊Dic3C2212yes—
81#4933C2214yes—
82C4×Dic3⋊C4C2214yes—
83#4929C2212yes—
84#4928C2212yes—
85#4928C2212yes—
86C2×C4×#41—31no—
87C2×C4×#41D311yescharacteristic, complemented
88#2609—34no—
89#2582—31no—
90#2538—31no—
91#2538—31no—
92#2537—31no—
93#2485—32no—
94#2485—32no—
95#2407—32no—
96#2407—32no—
97#2392—34no—
98C4×C22⋊Q8—32no—
99C4×C22⋊Q8—32no—
100C4×#121—32no—
101C4×#121—32no—
102#2285—31no—
103C2×C3×#41—24no—
104C2×C3×#41—24no—
105C2×C3×#41—24no—
106C22×C3×Q8C2311yescharacteristic
107C22×C3×D4C2312yes—
108C22×C3×D4C2311yescharacteristic
109C23×C3×C4C2312yes—
110C23×C3×C4C2312yes—
111C23×C3×C4C2312yes—
112C23×C3×C4C2311yescharacteristic
113C23×C3×C4C2311yescharacteristic
114C23×C3×C4C2311yescharacteristic
115C22×#67C2312yes—
116C22×#67C2314yes—
117C2×#235—24no—
118C2×#235—24no—
119C2×#235—24no—
120C22×D12C2311yescharacteristic
121C22×C4×D3C2312yes—
122C22×C4×D3C2312yes—
123C22×C4×D3C2312yes—
124C22×Dic6C2311yescharacteristic
125C3×C4×Q8—24no—
126C3×C4×Q8—24no—
127C3×C4×D4—28no—
128C3×C4×D4—28no—
129C3×C4×D4—24no—
130C3×C4×D4—24no—
131C3×#117—24no—
132C3×#117—28no—
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C4⋊C4C2312yes—
136C2×C3×C4⋊C4C2312yes—
137C2×C3×C22⋊C4C2312yes—
138C2×C3×C22⋊C4C2312yes—
139C2×C3×C22⋊C4C2312yes—
140C2×C3×C42—28no—
141C2×C3×C42D418yescomplemented
142C2×C3×C42C2312yes—
143C2×C3×C42C2312yes—
144C2×C3×C42C2312yes—
145C2×C3×C42C2311yescharacteristic
146C2×C3×C42C2311yescharacteristic
147C2×C3×C42C2311yescharacteristic
148C2×C3×C42C2311yescharacteristic
149C2×#217C2314yes—
150C2×#217C2314yes—
151C2×#217C2312yes—
152C2×#217C2314yes—
153C2×#217C2314yes—
154#946—28no—
155#938—28no—
156#930—28no—
157C4×#67—28no—
158C4×#67—28no—
159C4×#67—48no—
160C2×(C2×D3)⋊C4C2314yes—
161C2×(C2×D3)⋊C4C2314yes—
162C2×(C2×D3)⋊C4C2312yes—
163C2×(C2×D3)⋊C4C2312yes—
164C2×(C2×D3)⋊C4C2314yes—
165#926—24no—
166#926—44no—
167C2×C4⋊Dic3C2311yescharacteristic
168C2×C4⋊Dic3C2311yescharacteristic
169C2×C4⋊Dic3C2312yes—
170C2×C4⋊Dic3C2312yes—
171C2×C4⋊Dic3C2312yes—
172C2×C4⋊Dic3C2312yes—
173C2×C4⋊Dic3C2312yes—
174C2×C4⋊Dic3C2312yes—
175#924—28no—
176C2×Dic3⋊C4C2314yes—
177C2×Dic3⋊C4C2314yes—
178C2×Dic3⋊C4C2312yes—
179C2×Dic3⋊C4C2312yes—
180C2×Dic3⋊C4C2314yes—
181C2×C4×Dic3C2312yes—
182C2×C4×Dic3C2314yes—
183C2×C4×Dic3C2312yes—
184C2×C4×Dic3C2312yes—
185C4×D12—24no—
186C4×D12—24no—
187#872—28no—
188C42×D3—28no—
189C4×Dic6—24no—
190C4×Dic6—24no—
191C3⋊#95C2314yes—
192C3⋊#95C2314yes—
193C3⋊#95C2314yes—
194C3⋊#95C2314yes—
195C3⋊#95C2314yes—
196C3⋊#95C2314yes—
197C3⋊#95C2314yes—
198C3⋊#95C2314yes—
199C22×#41—31no—
200C22×#41C2×D311yescharacteristic
201C2×C22⋊Q8—32no—
202C2×C22⋊Q8—32no—
203C2×#121—32no—
204C2×#121—32no—
205C4×#41—28no—
206C4×#41—68no—
207C2×C4×Q8—31no—
208C2×C4×Q8—31no—
209C2×C4×Q8C2×D311yescharacteristic
210C2×C4×Q8C2×D311yescharacteristic
211C2×C4×D4—32no—
212C2×C4×D4—32no—
213C2×C4×D4—34no—
214C2×C4×D4—31no—
215C2×C4×D4—31no—
216C2×C4×D4C2×D312yes—
217C2×C4×D4C2×D312yes—
218C2×C4×D4C2×D311yescharacteristic
219C2×C4×D4C2×D311yescharacteristic
220C2×#117—31no—
221C2×#117—32no—
222C2×#117—32no—
223C2×#117C2×D312yes—
224C2×#117C2×D311yescharacteristic
225C22×C42—32no—
226C22×C42C2×D312yes—
227C22×C42C2×D311yescharacteristic
228#398—34no—
229#397—34no—
230#396—34no—
231#396—34no—
232#394—34no—
233#394—34no—
234#394—34no—
235#392—34no—
236#391—32no—
237#391—32no—
238#390—32no—
239#390—32no—
240#389—32no—
241#389—32no—
242#389—32no—
243#389—32no—
244#388—34no—
245#388—34no—
246#387—34no—
247#387—34no—
248#386—34no—
249#386—34no—
250#385—34no—
251#385—34no—
252#384—31no—
253#384—31no—
254#382—32no—
255#380—32no—
256#380—32no—
257#380—32no—
258#380—32no—
259#380—32no—
260#380—32no—
261C4×C4⋊C4—34no—
262C4×C4⋊C4—32no—
263C4×C4⋊C4—32no—
264C4×C22⋊C4—34no—
265C4×C22⋊C4—34no—
266C24×C3C2411yescharacteristic
267C24×C3C2412yes—
268C23×D3C2412yes—
269C3×#41—232no—
270C2×C3×Q8—22no—
271C2×C3×Q8—22no—
272C2×C3×Q8#4114yescomplemented
273C2×C3×D4—24no—
274C2×C3×D4—24no—
275C2×C3×D4—22no—
276C2×C3×D4—24no—
277C2×C3×D4—22no—
278C2×C3×D4#4114yescomplemented
279C22×C3×C4—24no—
280C22×C3×C4—24no—
281C22×C3×C4—22no—
282C22×C3×C4—22no—
283C22×C3×C4—24no—
284C22×C3×C4—22no—
285C22×C3×C4—22no—
286C22×C3×C4—22no—
287C22×C3×C4—22no—
288C22×C3×C4—24no—
289C22×C3×C4—24no—
290C22×C3×C4—24no—
291C22×C3×C4—24no—
292C22×C3×C4—24no—
293C22×C3×C4—24no—
294C22×C3×C4C2×D414yes—
295C22×C3×C4C2×D414yes—
296C22×C3×C4C2×D414yes—
297C22×C3×C4C2412yes—
298C22×C3×C4C2412yes—
299C22×C3×C4C2411yescharacteristic
300C22×C3×C4C2411yescharacteristic
301C22×C3×C4C2411yescharacteristic
302C22×C3×C4C2412yes—
303C22×C3×C4C2411yescharacteristic
304C22×C3×C4C2411yescharacteristic
305C22×C3×C4C2411yescharacteristic
306C2×#67—24no—
307C2×#67—24no—
308C2×#67—28no—
309C2×#67—28no—
310C2×#67—24no—
311C2×#67—44no—
312C22×Dic3C2414yes—
313C22×Dic3C2412yes—
314C22×Dic3C2412yes—
315C22×Dic3C2414yes—
316C22×Dic3C2412yes—
317#235—232no—
318C2×D12—22no—
319C2×D12—22no—
320C2×D12#4114yescomplemented
321C2×C4×D3—24no—
322C2×C4×D3—24no—
323C2×C4×D3—24no—
324C2×C4×D3—24no—
325C2×C4×D3—24no—
326C2×C4×D3—24no—
327C2×C4×D3—24no—
328C2×C4×D3—24no—
329C2×C4×D3—24no—
330C2×Dic6—22no—
331C2×Dic6—22no—
332C2×Dic6#4114yescomplemented
333C3×C4⋊C4—24no—
334C3×C4⋊C4—24no—
335C3×C4⋊C4—22no—
336C3×C4⋊C4—22no—
337C3×C22⋊C4—24no—
338C3×C22⋊C4—24no—
339C3×C22⋊C4—24no—
340C3×C42—24no—
341C3×C42—24no—
342C3×C42—24no—
343C3×C42C2×D414yes—
344C3×C42C2×D414yes—
345C3×C42C2×D414yes—
346C3×C42C2×D414yes—
347#217—24no—
348#217—28no—
349#217—28no—
350#217—44no—
351#217—44no—
352(C2×D3)⋊C4—28no—
353(C2×D3)⋊C4—24no—
354(C2×D3)⋊C4—24no—
355(C2×D3)⋊C4—28no—
356(C2×D3)⋊C4—44no—
357C4⋊Dic3—22no—
358C4⋊Dic3—22no—
359C4⋊Dic3—24no—
360C4⋊Dic3—24no—
361C4⋊Dic3—24no—
362C4⋊Dic3—24no—
363C4⋊Dic3—42no—
364C4⋊Dic3—42no—
365Dic3⋊C4—24no—
366Dic3⋊C4—24no—
367Dic3⋊C4—28no—
368Dic3⋊C4—28no—
369Dic3⋊C4—44no—
370C4×Dic3—24no—
371C4×Dic3—24no—
372C4×Dic3—24no—
373C4×Dic3—28no—
374C2×#41—24no—
375C2×#41—24no—
376C2×#41—24no—
377C2×#41—64no—
378C2×#41—64no—
379C2×#41—64no—
380C22×Q8—31no—
381C22×Q8C22×D311yescharacteristic
382C22×D4—32no—
383C22×D4—34no—
384C22×D4—31no—
385C22×D4C22×D312yes—
386C22×D4C22×D311yescharacteristic
387C23×C4—32no—
388C23×C4—32no—
389C23×C4—32no—
390C23×C4C22×D312yes—
391C23×C4C22×D312yes—
392C23×C4C22×D312yes—
393C23×C4C22×D311yescharacteristic
394C23×C4C22×D311yescharacteristic
395C23×C4C22×D311yescharacteristic
396C22⋊Q8—68no—
397C22⋊Q8—68no—
398#121—68no—
399#121—68no—
400C4×Q8—24no—
401C4×Q8—24no—
402C4×Q8—64no—
403C4×Q8—64no—
404C4×D4—28no—
405C4×D4—28no—
406C4×D4—24no—
407C4×D4—24no—
408C4×D4—68no—
409C4×D4—68no—
410C4×D4—64no—
411C4×D4—64no—
412C4×D4—128no—
413#117—24no—
414#117—28no—
415#117—64no—
416#117—68no—
417#117—124no—
418C2×C4⋊C4—31no—
419C2×C4⋊C4—31no—
420C2×C4⋊C4—32no—
421C2×C4⋊C4—32no—
422C2×C4⋊C4—32no—
423C2×C4⋊C4—32no—
424C2×C4⋊C4—32no—
425C2×C4⋊C4—32no—
426C2×C4⋊C4—34no—
427C2×C4⋊C4—34no—
428C2×C4⋊C4—32no—
429C2×C4⋊C4—32no—
430C2×C4⋊C4—34no—
431C2×C4⋊C4C22×D311yescharacteristic
432C2×C4⋊C4C22×D311yescharacteristic
433C2×C4⋊C4C22×D312yes—
434C2×C4⋊C4C22×D312yes—
435C2×C22⋊C4—32no—
436C2×C22⋊C4—34no—
437C2×C22⋊C4—34no—
438C2×C22⋊C4—32no—
439C2×C22⋊C4—32no—
440C2×C22⋊C4—34no—
441C2×C22⋊C4—34no—
442C2×C22⋊C4—34no—
443C2×C22⋊C4—34no—
444C2×C22⋊C4—34no—
445C2×C22⋊C4C22×D312yes—
446C2×C22⋊C4C22×D312yes—
447C2×C22⋊C4C22×D312yes—
448C2×C42—28no—
449C2×C42—32no—
450C2×C42—32no—
451C2×C42—34no—
452C2×C42—32no—
453C2×C42—68no—
454C2×C42#6718yescomplemented
455C2×C42C22×D312yes—
456C2×C42C22×D312yes—
457C2×C42C22×D312yes—
458C2×C42C22×D311yescharacteristic
459C2×C42C22×D311yescharacteristic
460C2×C42C22×D311yescharacteristic
461C2×C42C22×D311yescharacteristic
462#95—34no—
463#95—34no—
464#95—34no—
465#95—34no—
466#95—34no—
467#95—34no—
468#95—34no—
469#95—34no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—22no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—22no—
478C23×C3—21no—
479C23×C3—22no—
480C23×C3—21no—
481C23×C3—22no—
482C23×C3C22×D412yes—
483C23×C3C2×#4114yes—
484C23×C3C2511yescharacteristic
485C22×D3—22no—
486C22×D3—22no—
487C22×D3—22no—
488C22×D3—22no—
489C22×D3—22no—
490C22×D3—22no—
491C22×D3C2×#4114yes—
492C3×Q8—28no—
493C3×D4—216no—
494C3×D4—28no—
495C2×C3×C4—216no—
496C2×C3×C4—22no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—22no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—28no—
505C2×C3×C4—28no—
506C2×C3×C4—28no—
507C2×C3×C4—22no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—48no—
514C2×C3×C4—48no—
515C2×C3×C4C22×D412yes—
516C2×C3×C4C22×D412yes—
517C2×C3×C4C22×D412yes—
518C2×C3×C4C22×D412yes—
519C2×C3×C4C22×D412yes—
520C2×C3×C4C22×D412yes—
521C2×C3×C4C2×#4114yes—
522C2×C3×C4C2×#4112yes—
523C2×C3×C4C2×#4112yes—
524C2×C3×C4C2×#4112yes—
525C2×C3×C4C2×#4112yes—
526C2×C3×C4H(5,𝔽2)12yes—
527C2×C3×C42−1+412yes—
528#67—216no—
529#67—416no—
530C2×Dic3—22no—
531C2×Dic3—22no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—22no—
535C2×Dic3—24no—
536C2×Dic3—24no—
537C2×Dic3—24no—
538C2×Dic3—24no—
539C2×Dic3—22no—
540C2×Dic3—24no—
541C2×Dic3—24no—
542C2×Dic3—22no—
543C2×Dic3—22no—
544C2×Dic3C2×#4114yes—
545D12—28no—
546C4×D3—216no—
547C4×D3—48no—
548C4×D3—48no—
549Dic6—28no—
550C24—32no—
551C24C23×D312yes—
552C24C23×D311yescharacteristic
553#41—232no—
554#41—632no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—34no—
558C2×Q8—62no—
559C2×Q8—62no—
560C2×Q8#23514yescomplemented
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—34no—
567C2×D4—64no—
568C2×D4—64no—
569C2×D4—64no—
570C2×D4—68no—
571C2×D4—68no—
572C2×D4—62no—
573C2×D4—62no—
574C2×D4—124no—
575C2×D4#23514yescomplemented
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—32no—
592C22×C4—34no—
593C22×C4—32no—
594C22×C4—32no—
595C22×C4—34no—
596C22×C4—64no—
597C22×C4—64no—
598C22×C4—64no—
599C22×C4—64no—
600C22×C4—64no—
601C22×C4—64no—
602C22×C4—64no—
603C22×C4—64no—
604C22×C4—64no—
605C22×C4C2×#6714yes—
606C22×C4C2×#6714yes—
607C22×C4C2×#6714yes—
608C22×C4C23×D312yes—
609C22×C4C23×D312yes—
610C22×C4C23×D312yes—
611C22×C4C23×D311yescharacteristic
612C22×C4C23×D311yescharacteristic
613C22×C4C23×D311yescharacteristic
614C22×C4C23×D311yescharacteristic
615C22×C4C23×D311yescharacteristic
616C22×C4C23×D311yescharacteristic
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—68no—
622C4⋊C4—64no—
623C4⋊C4—68no—
624C4⋊C4—64no—
625C4⋊C4—64no—
626C4⋊C4—64no—
627C4⋊C4—64no—
628C4⋊C4—64no—
629C4⋊C4—62no—
630C4⋊C4—62no—
631C4⋊C4—122no—
632C4⋊C4—122no—
633C4⋊C4—124no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—68no—
638C22⋊C4—68no—
639C22⋊C4—68no—
640C22⋊C4—64no—
641C22⋊C4—68no—
642C22⋊C4—64no—
643C22⋊C4—64no—
644C22⋊C4—124no—
645C22⋊C4—124no—
646C22⋊C4—124no—
647C42—24no—
648C42—24no—
649C42—24no—
650C42—68no—
651C42—64no—
652C42—64no—
653C42—64no—
654C42C2×#6714yes—
655C42C2×#6714yes—
656C42C2×#6714yes—
657C42C2×#6714yes—
658C22×C3—22no—
659C22×C3—22no—
660C22×C3—24no—
661C22×C3—22no—
662C22×C3—24no—
663C22×C3—24no—
664C22×C3—42no—
665C22×C3—42no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—42no—
670C22×C3—42no—
671C22×C3—41no—
672C22×C3C23×D411yescharacteristic
673C22×C3C22×#4111yescharacteristic
674C22×C3C22×#4111yescharacteristic
675C22×C3C22×#4111yescharacteristic
676C22×C3C22×#4111yescharacteristic
677C22×C3C2×H(5,𝔽2)11yescharacteristic
678C22×C3C2×2−1+411yescharacteristic
679C2×D3—24no—
680C2×D3—24no—
681C2×D3—24no—
682C2×D3—42no—
683C2×D3—42no—
684C2×D3—42no—
685C2×D3—42no—
686C3×C4—22no—
687C3×C4—22no—
688C3×C4—24no—
689C3×C4—22no—
690C3×C4—42no—
691C3×C4—42no—
692C3×C4#52514yes—
693C3×C4#52514yes—
694C3×C4#53714yes—
695Dic3—24no—
696Dic3—42no—
697Dic3—42no—
698Dic3—44no—
699Dic3—44no—
700C23—22no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—22no—
709C23—22no—
710C23—21no—
711C23—22no—
712C23—34no—
713C23—62no—
714C23—62no—
715C23—62no—
716C23—62no—
717C23—62no—
718C23—62no—
719C23C2×#23514yes—
720C23C22×#6712yes—
721C23C24×D311yescharacteristic
722Q8—28no—
723Q8—68no—
724D4—216no—
725D4—28no—
726D4—616no—
727D4—68no—
728D4—1216no—
729C2×C4—216no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—28no—
739C2×C4—28no—
740C2×C4—28no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—34no—
748C2×C4—48no—
749C2×C4—48no—
750C2×C4—616no—
751C2×C4—62no—
752C2×C4—62no—
753C2×C4—62no—
754C2×C4—64no—
755C2×C4—64no—
756C2×C4—62no—
757C2×C4—64no—
758C2×C4—64no—
759C2×C4—64no—
760C2×C4—64no—
761C2×C4—62no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—62no—
765C2×C4—128no—
766C2×C4—128no—
767C2×C4C2×#23514yes—
768C2×C4C2×#23512yes—
769C2×C4C2×#23512yes—
770C2×C4D3×#4112yes—
771C2×C4D3×#4112yes—
772C2×C4#100912yes—
773C2×C4#101012yes—
774C2×C4C22×#6712yes—
775C2×C4C22×#6712yes—
776C2×C4C22×#6712yes—
777C2×C4C22×#6712yes—
778C2×C4C22×#6712yes—
779C2×C4C22×#6712yes—
780C2×C3—42no—
781C2×C3—44no—
782C2×C3C2×#52511yescharacteristic
783C2×C3C2×#52511yescharacteristic
784C2×C3C2×#53711yescharacteristic
785C2×C3#348111yescharacteristic
786C2×C3#348211yescharacteristic
787C2×C3#348211yescharacteristic
788C2×C3#348311yescharacteristic
789D3—44no—
790C22—24no—
791C22—24no—
792C22—24no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—41no—
797C22—41no—
798C22—42no—
799C22—41no—
800C22—42no—
801C22—41no—
802C22—42no—
803C22—42no—
804C22—64no—
805C22—64no—
806C22—64no—
807C22—122no—
808C22—122no—
809C22—122no—
810C22—122no—
811C22C22×#23511yescharacteristic
812C22C22×#23511yescharacteristic
813C22C2×D3×#4111yescharacteristic
814C22C2×D3×#4111yescharacteristic
815C22C2×#100911yescharacteristic
816C22C2×#101011yescharacteristic
817C22C23×#6711yescharacteristic
818C4—22no—
819C4—24no—
820C4—22no—
821C4—22no—
822C4—42no—
823C4—42no—
824C4—64no—
825C4—124no—
826C4—124no—
827C4—122no—
828C4—122no—
829C4#579114yes—
830C4#582814yes—
831C4#583314yes—
832C3#3497611yescharacteristic, complemented, Sylow
833C2—44no—
834C2—42no—
835C2—124no—
836C2#8582611yescharacteristic
837C2#8584311yescharacteristic
838C2#8584411yescharacteristic
839C2#8584511yescharacteristic
840C2C2×#579111yescharacteristic
841C2C2×#582811yescharacteristic
842C2C2×#583311yescharacteristic
subgroupG/H
centerC22×C4C23×D3
commutator, socle, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×C4×#41C2
hypercenterC2×C4×#41D3
hypocenterC3#34976
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×#41C2semidirect
2. C2×C4×#235C2semidirect
3. #84097C2semidirect
4. #82500C2semidirect
5. C4×#946C2semidirect
6. #82482C2semidirect
7. #82417C2semidirect
8. #82402C2semidirect
9. C4×#938C2semidirect
10. #82376C2semidirect
11. #82372C2semidirect
12. #82345C2semidirect
13. #82285C2semidirect
14. #82283C2semidirect
15. C4×#924C2semidirect
16. C4×#930C2semidirect
17. #82062C2semidirect
87. C2×C4×#41D3semidirect
141. C2×C3×C42D4semidirect
272. C2×C3×Q8#41semidirect
278. C2×C3×D4#41semidirect
320. C2×D12#41semidirect
332. C2×Dic6#41semidirect
454. C2×C42#67semidirect
560. C2×Q8#235semidirect
575. C2×D4#235semidirect
832. C3#34976semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×#412
C2×C4×#2352
#840972
#825002
C4×#9462
#824822
#824172
#824022
C4×#9382
#823762
#823722
#823452
#822852
#822832
C4×#9242
C4×#9302
#820622
#349763