Finite Group Databasebeta

← #11635851

Subgroups — #11635851

Order 768.

3082 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#547C211yesmaximal, characteristic, complemented
2C2×#5831C212yesmaximal, complemented
3C2×D3×C4⋊Q8C211yesmaximal, characteristic, complemented
4#84093C212yesmaximal, complemented
5#83229C211yesmaximal, characteristic, complemented
6#82897C214yesmaximal, complemented
7#82870C214yesmaximal, complemented
8#82758C212yesmaximal, complemented
9#82751C212yesmaximal, complemented
10#82662C212yesmaximal, complemented
11#82641C212yesmaximal, complemented
12C4×#938C211yesmaximal, characteristic, complemented
13C4×#938C211yesmaximal, characteristic, complemented
14#82382C211yesmaximal, characteristic, complemented
15#82379C211yesmaximal, characteristic, complemented
16C4⋊C4×#67C212yesmaximal, complemented
17#82171C212yesmaximal, complemented
18#59125—31nomaximal, Sylow
19C22×C3×#41C2212yes—
20C22×D3×Q8C2212yes—
21C3×#547—28no—
22C2×C3×C4⋊Q8C2211yescharacteristic
23C2×C3×#123C2214yes—
24C2×C3×C22⋊Q8C2212yes—
25C2×C3×#121C2212yes—
26C2×C3×C4×D4C2211yescharacteristic
27C2×C3×C4×D4C2211yescharacteristic
28C22×C3×C4⋊C4C2212yes—
29#5831—216no—
30C2×Q8×Dic3C2212yes—
31C2×#944C2212yes—
32C2×#938C2211yescharacteristic
33C2×#938C2214yes—
34C2×#938C2211yescharacteristic
35C2×#936C2212yes—
36C2×#936C2214yes—
37C2×C4×#67C2212yes—
38C2×C4×#67C2214yes—
39C2×C4×#67C2212yes—
40C2×#924C2212yes—
41C2×#924C2214yes—
42C2×#924C2212yes—
43D3×C4⋊Q8—28no—
44C2×D3×C4⋊C4C2212yes—
45C2×D3×C4⋊C4C2212yes—
46C2×#888C2212yes—
47C2×#888C2212yes—
48C2×C42×D3C2211yescharacteristic
49C2×#869C2211yescharacteristic
50#5229C2212yes—
51#5222C2214yes—
52#5222C2214yes—
53#5221C2211yescharacteristic
54#5221C2212yes—
55#5221C2211yescharacteristic
56#5212C2212yes—
57#5212C2212yes—
58#5210C2214yes—
59#5210C2214yes—
60C4×#217C2212yes—
61C4×#217C2212yes—
62#4989C2214yes—
63#4987C2211yescharacteristic
64#4987C2211yescharacteristic
65#4984C2212yes—
66#4982C2214yes—
67#4980C2214yes—
68#4979C2214yes—
69#4976C2214yes—
70#4975C2212yes—
71Dic3×C4⋊C4C2212yes—
72#4973C2212yes—
73#4972C2211yescharacteristic
74#4972C2211yescharacteristic
75#4956C2214yes—
76#4956C2212yes—
77#4956C2212yes—
78#4953C2214yes—
79#4949C2214yes—
80#4948C2214yes—
81#4947C2214yes—
82#4945C2214yes—
83#4944C2212yes—
84#4944C2212yes—
85C4×C4⋊Dic3C2211yescharacteristic
86C4×C4⋊Dic3C2211yescharacteristic
87C2×#548—32no—
88C2×#547D311yescharacteristic, complemented
89C22×C4⋊Q8—31no—
90#2674—34no—
91#2547—31no—
92#2542—31no—
93#2491—32no—
94#2443—34no—
95#2440—32no—
96#2432—32no—
97#2429—32no—
98#2416—32no—
99#2409—32no—
100#2365—31no—
101D4×C4⋊C4—32no—
102C4×#121—31no—
103C4×#121—31no—
104C2×C3×#41—28no—
105C2×C3×#41—28no—
106C2×C3×#41—44no—
107C22×C3×Q8C2312yes—
108C22×C3×D4C2311yescharacteristic
109C22×C3×D4C2314yes—
110C22×C3×D4C2311yescharacteristic
111C23×C3×C4C2312yes—
112C23×C3×C4C2312yes—
113C23×C3×C4C2314yes—
114C22×#67C2312yes—
115C22×#67C2312yes—
116C2×D3×Q8—28no—
117C2×D3×Q8—28no—
118C2×D3×Q8—44no—
119C22×C4×D3C2311yescharacteristic
120C22×C4×D3C2314yes—
121C22×C4×D3C2311yescharacteristic
122C22×C4×D3C2311yescharacteristic
123C22×Dic6C2312yes—
124C22×Dic6C2314yes—
125C3×C4⋊Q8D418yescomplemented
126C3×#123—216no—
127C3×C22⋊Q8—28no—
128C3×#121—28no—
129C3×C4×D4—24no—
130C3×C4×D4—24no—
131C2×C3×C4⋊C4—28no—
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C4⋊C4C2314yes—
135C2×C3×C4⋊C4C2312yes—
136C2×C3×C4⋊C4C2312yes—
137C2×C3×C22⋊C4C2312yes—
138C2×C3×C22⋊C4C2312yes—
139C2×C3×C22⋊C4C2314yes—
140C2×C3×C42C2311yescharacteristic
141C2×#217C2312yes—
142C2×#217C2312yes—
143C2×#217C2312yes—
144C2×#217C2312yes—
145C2×#217C2314yes—
146C2×#217C2314yes—
147C2×#217C2314yes—
148C2×#217C2312yes—
149C2×#217C2314yes—
150C2×#217C2312yes—
151Q8×Dic3—28no—
152#944—28no—
153#938—216no—
154#938—24no—
155#938D418yescomplemented
156#936—28no—
157#936—216no—
158C4×#67—216no—
159C4×#67—28no—
160C4×#67—28no—
161C2×(C2×D3)⋊C4C2312yes—
162C2×(C2×D3)⋊C4C2312yes—
163C2×C4⋊Dic3C2311yescharacteristic
164C2×C4⋊Dic3C2311yescharacteristic
165C2×C4⋊Dic3C2311yescharacteristic
166C2×C4⋊Dic3C2314yes—
167C2×C4⋊Dic3C2312yes—
168C2×C4⋊Dic3C2312yes—
169C2×C4⋊Dic3C2311yescharacteristic
170#924—216no—
171#924—28no—
172#924—44no—
173C2×Dic3⋊C4C2312yes—
174C2×Dic3⋊C4C2312yes—
175C2×Dic3⋊C4C2314yes—
176C2×Dic3⋊C4C2314yes—
177C2×Dic3⋊C4C2314yes—
178C2×Dic3⋊C4C2314yes—
179C2×C4×Dic3C2312yes—
180C2×C4×Dic3C2312yes—
181C2×C4×Dic3C2311yescharacteristic
182C2×C4×Dic3C2314yes—
183C2×C4×Dic3C2311yescharacteristic
184C2×C4×Dic3C2311yescharacteristic
185D3×C4⋊C4—28no—
186D3×C4⋊C4—28no—
187#888—28no—
188#888—28no—
189C42×D3—24no—
190#869—24no—
191C3⋊#95C2312yes—
192C3⋊#95C2312yes—
193C3⋊#95C2312yes—
194C3⋊#95C2312yes—
195C3⋊#95C2312yes—
196C3⋊#95C2314yes—
197C3⋊#95C2314yes—
198C3⋊#95C2314yes—
199C3⋊#95C2312yes—
200C3⋊#95C2314yes—
201C22×#41C2×D312yes—
202C23×Q8—32no—
203#548—616no—
204#547—28no—
205C2×C4⋊Q8—32no—
206C2×C4⋊Q8—32no—
207C2×C4⋊Q8—32no—
208C2×C4⋊Q8—31no—
209C2×C4⋊Q8—68no—
210C2×C4⋊Q8C2×D311yescharacteristic
211C2×#124—34no—
212C2×#124—32no—
213C2×#123C2×D314yes—
214C2×C22⋊Q8—34no—
215C2×C22⋊Q8—32no—
216C2×C22⋊Q8—32no—
217C2×C22⋊Q8C2×D312yes—
218C2×#121—31no—
219C2×#121—31no—
220C2×#121—34no—
221C2×#121C2×D312yes—
222C2×C4×Q8—32no—
223C2×C4×D4—32no—
224C2×C4×D4—34no—
225C2×C4×D4—32no—
226C2×C4×D4C2×D311yescharacteristic
227C2×C4×D4C2×D311yescharacteristic
228C22×C4⋊C4—32no—
229C22×C4⋊C4—32no—
230C22×C4⋊C4C2×D312yes—
231C22×C42—31no—
232#399—34no—
233#398—34no—
234#397—34no—
235#396—34no—
236#395—34no—
237#394—34no—
238#394—34no—
239#393—34no—
240#391—32no—
241#391—32no—
242#390—32no—
243#390—31no—
244#390—31no—
245#389—34no—
246#389—32no—
247#389—31no—
248#389—31no—
249#388—32no—
250#388—32no—
251#388—34no—
252#387—34no—
253#386—34no—
254#386—32no—
255#386—32no—
256#385—34no—
257#385—34no—
258#385—34no—
259#384—32no—
260#380—32no—
261#380—32no—
262#380—31no—
263#380—31no—
264C4×C4⋊C4—32no—
265C4×C4⋊C4—31no—
266C4×C4⋊C4—31no—
267C4×C22⋊C4—32no—
268C4×C22⋊C4—32no—
269C24×C3C2412yes—
270C24×C3C2412yes—
271C23×D3C2411yescharacteristic
272C3×#41—432no—
273C2×C3×Q8—24no—
274C2×C3×Q8—24no—
275C2×C3×Q8C2×D418yes—
276C2×C3×D4—28no—
277C2×C3×D4—22no—
278C2×C3×D4—22no—
279C2×C3×D4—28no—
280C2×C3×D4—22no—
281C2×C3×D4—22no—
282C2×C3×D4—22no—
283C2×C3×D4—44no—
284C2×C3×D4C2×D414yes—
285C22×C3×C4—28no—
286C22×C3×C4—24no—
287C22×C3×C4—24no—
288C22×C3×C4—28no—
289C22×C3×C4—24no—
290C22×C3×C4—24no—
291C22×C3×C4—24no—
292C22×C3×C4—24no—
293C22×C3×C4—44no—
294C22×C3×C4C2412yes—
295C22×C3×C4C2412yes—
296C22×C3×C4C2411yescharacteristic
297C22×C3×C4C2414yes—
298C22×C3×C4C2411yescharacteristic
299C22×C3×C4C2411yescharacteristic
300C2×#67—24no—
301C2×#67—24no—
302C2×#67—24no—
303C2×#67—24no—
304C2×#67—24no—
305C2×#67C2×D418yes—
306C22×Dic3C2412yes—
307C22×Dic3C2412yes—
308C22×Dic3C2412yes—
309C22×Dic3C2414yes—
310C22×Dic3C2412yes—
311C22×Dic3C2411yescharacteristic
312C22×Dic3C2411yescharacteristic
313C22×Dic3C2411yescharacteristic
314D3×Q8—432no—
315C2×C4×D3—22no—
316C2×C4×D3—22no—
317C2×C4×D3—22no—
318C2×C4×D3—22no—
319C2×C4×D3—22no—
320C2×C4×D3—22no—
321C2×C4×D3—22no—
322C2×C4×D3—28no—
323C2×C4×D3—28no—
324C2×C4×D3—44no—
325C2×C4×D3C2×D414yes—
326C2×C4×D3#4114yescomplemented
327C2×Dic6—24no—
328C2×Dic6—28no—
329C2×Dic6—24no—
330C2×Dic6—24no—
331C2×Dic6—28no—
332C2×Dic6—44no—
333C3×C4⋊C4—22no—
334C3×C4⋊C4—28no—
335C3×C4⋊C4—22no—
336C3×C4⋊C4C2×D418yes—
337C3×C4⋊C4C2×D418yes—
338C3×C22⋊C4—24no—
339C3×C22⋊C4—24no—
340C3×C22⋊C4—28no—
341C3×C42C2×D414yes—
342#217—28no—
343#217—28no—
344#217—28no—
345#217—24no—
346#217—24no—
347#217—24no—
348#217—24no—
349#217—24no—
350#217—44no—
351#217C2×D418yes—
352(C2×D3)⋊C4—24no—
353(C2×D3)⋊C4—24no—
354C4⋊Dic3—24no—
355C4⋊Dic3—24no—
356C4⋊Dic3—22no—
357C4⋊Dic3—22no—
358C4⋊Dic3—22no—
359C4⋊Dic3—28no—
360C4⋊Dic3C2×D414yes—
361Dic3⋊C4—28no—
362Dic3⋊C4—28no—
363Dic3⋊C4—24no—
364Dic3⋊C4—28no—
365Dic3⋊C4—24no—
366Dic3⋊C4—44no—
367C4×Dic3—22no—
368C4×Dic3—22no—
369C4×Dic3—22no—
370C4×Dic3—24no—
371C4×Dic3—24no—
372C4×Dic3—28no—
373C2×#41—28no—
374C2×#41—28no—
375C2×#41—44no—
376C22×Q8—32no—
377C22×Q8—34no—
378C22×Q8—68no—
379C22×Q8—68no—
380C22×Q8—124no—
381C22×Q8C22×D312yes—
382C22×D4—32no—
383C22×D4—32no—
384C22×D4C22×D311yescharacteristic
385C22×D4C22×D314yes—
386C22×D4C22×D311yescharacteristic
387C23×C4—31no—
388C23×C4—31no—
389C23×C4—31no—
390C23×C4—34no—
391C23×C4C22×D312yes—
392C23×C4C22×D312yes—
393C23×C4C22×D314yes—
394C4⋊Q8—68no—
395C4⋊Q8—68no—
396C4⋊Q8—68no—
397C4⋊Q8—64no—
398C4⋊Q8#6718yescomplemented
399#124—616no—
400#124—68no—
401#123—216no—
402C22⋊Q8—28no—
403C22⋊Q8—616no—
404C22⋊Q8—68no—
405C22⋊Q8—124no—
406#121—28no—
407#121—38no—
408#121—64no—
409#121—616no—
410C4×Q8—68no—
411C4×D4—24no—
412C4×D4—24no—
413C4×D4—68no—
414C4×D4—68no—
415C4×D4—616no—
416C2×C4⋊C4—28no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—32no—
419C2×C4⋊C4—34no—
420C2×C4⋊C4—34no—
421C2×C4⋊C4—32no—
422C2×C4⋊C4—34no—
423C2×C4⋊C4—32no—
424C2×C4⋊C4—32no—
425C2×C4⋊C4—34no—
426C2×C4⋊C4—31no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—34no—
430C2×C4⋊C4—68no—
431C2×C4⋊C4—68no—
432C2×C4⋊C4C22×D311yescharacteristic
433C2×C4⋊C4C22×D314yes—
434C2×C4⋊C4C22×D311yescharacteristic
435C2×C4⋊C4C22×D312yes—
436C2×C4⋊C4C22×D312yes—
437C2×C22⋊C4—32no—
438C2×C22⋊C4—34no—
439C2×C22⋊C4—32no—
440C2×C22⋊C4—32no—
441C2×C22⋊C4—34no—
442C2×C22⋊C4—34no—
443C2×C22⋊C4—32no—
444C2×C22⋊C4—32no—
445C2×C22⋊C4—32no—
446C2×C22⋊C4—32no—
447C2×C22⋊C4—32no—
448C2×C22⋊C4—34no—
449C2×C22⋊C4C22×D312yes—
450C2×C22⋊C4C22×D312yes—
451C2×C22⋊C4C22×D314yes—
452C2×C42—32no—
453C2×C42—34no—
454C2×C42—32no—
455C2×C42—31no—
456C2×C42—31no—
457C2×C42—31no—
458C2×C42—64no—
459C2×C42C22×D311yescharacteristic
460#95—32no—
461#95—32no—
462#95—32no—
463#95—32no—
464#95—34no—
465#95—32no—
466#95—32no—
467#95—34no—
468#95—34no—
469#95—34no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—22no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3C22×D414yes—
484C23×C3C2511yescharacteristic
485C22×D3—21no—
486C22×D3—21no—
487C22×D3—21no—
488C22×D3—21no—
489C22×D3C22×D412yes—
490C22×D3C2×#4112yes—
491C22×D32−1+412yes—
492C3×Q8—216no—
493C3×D4—28no—
494C3×D4—416no—
495C3×D4—44no—
496C2×C3×C4—24no—
497C2×C3×C4—24no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—416no—
507C2×C3×C4—48no—
508C2×C3×C4—48no—
509C2×C3×C4C22×D412yes—
510C2×C3×C4C22×D412yes—
511C2×C3×C4C22×D418yes—
512C2×C3×C4C22×D412yes—
513C2×C3×C4C22×D412yes—
514C2×C3×C4C2×#4112yes—
515C2×C3×C4H(5,𝔽2)12yes—
516C2×C3×C42−1+412yes—
517#67—216no—
518#67—48no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—22no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—22no—
527C2×Dic3—22no—
528C2×Dic3—22no—
529C2×Dic3—24no—
530C2×Dic3—24no—
531C2×Dic3—22no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—24no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3C22×D414yes—
540C2×Dic3C22×D412yes—
541C2×Dic3C2×#4112yes—
542C2×Dic32−1+412yes—
543C4×D3—28no—
544C4×D3—28no—
545C4×D3—28no—
546C4×D3—416no—
547Dic6—416no—
548Dic6—48no—
549C24—31no—
550C24C23×D312yes—
551C24C23×D312yes—
552#41—432no—
553C2×Q8—24no—
554C2×Q8—24no—
555C2×Q8—68no—
556C2×Q8—64no—
557C2×Q8—64no—
558C2×Q8—68no—
559C2×Q8—64no—
560C2×Q8—124no—
561C2×Q8—1232no—
562C2×Q8C2×#6718yes—
563C2×D4—28no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—28no—
570C2×D4—38no—
571C2×D4—44no—
572C2×D4—64no—
573C2×D4—64no—
574C2×D4—64no—
575C2×D4—64no—
576C2×D4—64no—
577C2×D4D3×D414yes—
578C22×C4—28no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—28no—
585C22×C4—24no—
586C22×C4—31no—
587C22×C4—32no—
588C22×C4—31no—
589C22×C4—31no—
590C22×C4—34no—
591C22×C4—34no—
592C22×C4—32no—
593C22×C4—32no—
594C22×C4—32no—
595C22×C4—34no—
596C22×C4—44no—
597C22×C4—62no—
598C22×C4—62no—
599C22×C4—68no—
600C22×C4—62no—
601C22×C4—62no—
602C22×C4—62no—
603C22×C4—62no—
604C22×C4—62no—
605C22×C4—68no—
606C22×C4—124no—
607C22×C4C23×D312yes—
608C22×C4C23×D312yes—
609C22×C4C23×D311yescharacteristic
610C22×C4C23×D314yes—
611C22×C4C23×D311yescharacteristic
612C22×C4C23×D311yescharacteristic
613C4⋊C4—22no—
614C4⋊C4—28no—
615C4⋊C4—22no—
616C4⋊C4—34no—
617C4⋊C4—68no—
618C4⋊C4—64no—
619C4⋊C4—64no—
620C4⋊C4—68no—
621C4⋊C4—62no—
622C4⋊C4—62no—
623C4⋊C4—62no—
624C4⋊C4—68no—
625C4⋊C4—68no—
626C4⋊C4—64no—
627C4⋊C4—64no—
628C4⋊C4—124no—
629C4⋊C4C2×#6718yes—
630C4⋊C4C2×#6718yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—28no—
634C22⋊C4—38no—
635C22⋊C4—64no—
636C22⋊C4—64no—
637C22⋊C4—64no—
638C22⋊C4—64no—
639C22⋊C4—68no—
640C22⋊C4—64no—
641C22⋊C4—64no—
642C22⋊C4—64no—
643C22⋊C4—68no—
644C22⋊C4—68no—
645C22⋊C4—124no—
646C42—68no—
647C42—64no—
648C42—64no—
649C42—62no—
650C42—62no—
651C42—62no—
652C42C2×#6714yes—
653C22×C3—24no—
654C22×C3—24no—
655C22×C3—24no—
656C22×C3—42no—
657C22×C3—42no—
658C22×C3—42no—
659C22×C3—42no—
660C22×C3—42no—
661C22×C3—42no—
662C22×C3—42no—
663C22×C3—42no—
664C22×C3—42no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3C23×D411yescharacteristic
668C22×C3C23×D411yescharacteristic
669C22×C3C22×#4111yescharacteristic
670C22×C3C2×H(5,𝔽2)11yescharacteristic
671C22×C3C2×2−1+411yescharacteristic
672C22×C3C2×2−1+411yescharacteristic
673C22×C3C2×2−1+411yescharacteristic
674C2×D3—22no—
675C2×D3—22no—
676C2×D3—22no—
677C2×D3—22no—
678C2×D3—22no—
679C2×D3—22no—
680C2×D3#54714yescomplemented
681C3×C4—28no—
682C3×C4—22no—
683C3×C4—42no—
684C3×C4—42no—
685C3×C4D4214yes—
686C3×C4#54814yescomplemented
687Dic3—22no—
688Dic3—24no—
689Dic3—22no—
690Dic3—22no—
691Dic3—44no—
692Dic3—42no—
693Dic3—42no—
694Dic3—42no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—32no—
709C23—32no—
710C23—32no—
711C23—61no—
712C23—61no—
713C23—61no—
714C23—61no—
715C23C2×D3×D414yes—
716C23C24×D311yescharacteristic
717Q8—216no—
718Q8—1216no—
719Q8—128no—
720D4—28no—
721D4—416no—
722D4—44no—
723D4—616no—
724D4—128no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—34no—
736C2×C4—32no—
737C2×C4—32no—
738C2×C4—32no—
739C2×C4—416no—
740C2×C4—48no—
741C2×C4—48no—
742C2×C4—68no—
743C2×C4—61no—
744C2×C4—62no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—62no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—68no—
752C2×C4—68no—
753C2×C4—62no—
754C2×C4—62no—
755C2×C4—64no—
756C2×C4—62no—
757C2×C4—64no—
758C2×C4—62no—
759C2×C4—62no—
760C2×C4—62no—
761C2×C4—62no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—64no—
765C2×C4—1216no—
766C2×C4C2×D3×D412yes—
767C2×C4#100412yes—
768C2×C4D3×#4112yes—
769C2×C4#101012yes—
770C2×C4C22×#6712yes—
771C2×C4C22×#6718yes—
772C2×C4C22×#6712yes—
773C2×C4C22×#6712yes—
774C2×C3—44no—
775C2×C3—82no—
776C2×C3C2×D4211yescharacteristic
777C2×C3C2×#54711yescharacteristic
778C2×C3C2×#54811yescharacteristic
779C2×C3#348611yescharacteristic
780C2×C3#349911yescharacteristic
781C2×C3#351111yescharacteristic
782C2×C3#355211yescharacteristic
783D3—24no—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—34no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—62no—
800C22—62no—
801C22—62no—
802C22—62no—
803C22—62no—
804C22—62no—
805C22C22×D3×D411yescharacteristic
806C22C2×#100411yescharacteristic
807C22C2×D3×#4111yescharacteristic
808C22C2×#101011yescharacteristic
809C22D3×2−1+411yescharacteristic
810C22D3×2−1+411yescharacteristic
811C22C23×#6711yescharacteristic
812C4—28no—
813C4—22no—
814C4—42no—
815C4—42no—
816C4—64no—
817C4—62no—
818C4—62no—
819C4—62no—
820C4—122no—
821C4—122no—
822C4—122no—
823C4—124no—
824C4D4×#6714yes—
825C4#583114yescomplemented
826C3#5912511yescharacteristic, complemented, Sylow
827C2—44no—
828C2—64no—
829C2—82no—
830C2#8667911yescharacteristic
831C2#8668011yescharacteristic
832C2D3×#54711yescharacteristic
833C2#8670911yescharacteristic
834C2C2×D4×#6711yescharacteristic
835C2C2×#583111yescharacteristic
836C2#8729411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×#547C2
hypercenterC2×#547D3
hypocenterC3#59125
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×C3×#547C2semidirect
2. C2×#5831C2semidirect
3. C2×D3×C4⋊Q8C2semidirect
4. #84093C2semidirect
5. #83229C2semidirect
6. #82897C2semidirect
7. #82870C2semidirect
8. #82758C2semidirect
9. #82751C2semidirect
10. #82662C2semidirect
11. #82641C2semidirect
12. C4×#938C2semidirect
13. C4×#938C2semidirect
14. #82382C2semidirect
15. #82379C2semidirect
16. C4⋊C4×#67C2semidirect
17. #82171C2semidirect
88. C2×#547D3semidirect
125. C3×C4⋊Q8D4semidirect
155. #938D4semidirect
326. C2×C4×D3#41semidirect
398. C4⋊Q8#67semidirect
680. C2×D3#547semidirect
686. C3×C4#548semidirect
825. C4#5831semidirect
826. C3#59125semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5472
C2×#58312
C2×D3×C4⋊Q82
#840932
#832292
#828972
#828702
#827582
#827512
#826622
#826412
C4×#9382
#823822
#823792
C4⋊C4×#672
#821712
#591253