Finite Group Databasebeta

← C4×#5730 #10955166

Subgroups — C4×#5730 #10955166

Order 768.

2516 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5730C211yesmaximal, characteristic
2C3×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
3#83230C211yesmaximal, characteristic, complemented
4C4×#946C214yesmaximal, complemented
5#76616C214yesmaximal, complemented
6#76205C212yesmaximal, complemented
7#76203C212yesmaximal
8#76201C212yesmaximal, complemented
9#75989C212yesmaximal, complemented
10#74360C211yesmaximal, characteristic
11#74325C211yesmaximal, characteristic, complemented
12C4×#897C212yesmaximal, complemented
13C4×D3×C4⋊C4C212yesmaximal, complemented
14C4×#890C212yesmaximal, complemented
15C4×#893C212yesmaximal
16C42×Dic6C211yesmaximal, characteristic, complemented
17C42×D12C211yesmaximal, characteristic
18C4×#554—31nomaximal, Sylow
19C2×C3×C4⋊Q8C2211yescharacteristic
20C2×C3×C4×Q8C2212yes—
21C2×#946C2214yes—
22#5730C4116yesdirect product factor
23C2×#897C2212yes—
24C2×#893C2212yes—
25C2×#893C2212yes—
26C2×D3×C4⋊C4C2212yes—
27C2×D3×C4⋊C4C2212yes—
28C2×#890C2212yes—
29C2×C4×D12C2211yescharacteristic
30C2×C4×D12C2211yescharacteristic
31C2×C4×D12C2211yescharacteristic
32C2×C42×D3C2212yes—
33C2×C42×D3C2214yes—
34C2×C4×Dic6C2211yescharacteristic
35C2×C4×Dic6C2211yescharacteristic
36C2×C4×Dic6C2211yescharacteristic
37C3×#391C2212yes—
38C3×#389C2212yes—
39C3×#389C2212yes—
40C3×#384C2211yescharacteristic
41C3×C4×C4⋊C4C2212yes—
42C3×C4×C4⋊C4C2212yes—
43C3×C43C2211yescharacteristic
44#5229C2214yes—
45#4989C2214yes—
46#4989C2214yes—
47#4987C2212yes—
48#4987C2214yes—
49#4984C2212yes—
50#4984C2212yes—
51#4978C2214yes—
52#4978C2214yes—
53#4977C2212yes—
54Dic3×C4⋊C4C2212yes—
55Dic3×C4⋊C4C2212yes—
56Dic3×C4⋊C4C2212yes—
57Dic3×C4⋊C4C2212yes—
58#4973C2212yes—
59#4972C2214yes—
60#4972C2212yes—
61C4×(C2×D3)⋊C4C2214yes—
62C4×(C2×D3)⋊C4C2212yes—
63C4×(C2×D3)⋊C4C2212yes—
64C4×(C2×D3)⋊C4C2212yes—
65C4×C4⋊Dic3C2211yescharacteristic
66C4×C4⋊Dic3C2214yes—
67C4×C4⋊Dic3C2211yescharacteristic
68C4×C4⋊Dic3C2211yescharacteristic
69C4×C4⋊Dic3C2211yescharacteristic
70C4×C4⋊Dic3C2211yescharacteristic
71C4×C4⋊Dic3C2211yescharacteristic
72C4×Dic3⋊C4C2214yes—
73C4×Dic3⋊C4C2212yes—
74C4×Dic3⋊C4C2212yes—
75C4×Dic3⋊C4C2212yes—
76C42×Dic3C2212yes—
77#4668C2214yes—
78#4666C2214yes—
79#4666C2214yes—
80D3×#95C2214yes—
81#4655C2214yes—
82#4654C2214yes—
83#4653C2214yes—
84#4649C2214yes—
85C2×#554—31no—
86#2370—32no—
87#2369—31no—
88#2368—34no—
89#2360—32no—
90#2355—31no—
91#2349—32no—
92D4×C4⋊C4—31no—
93#2345—32no—
94C4×C4⋊Q8D311yescharacteristic, complemented
95C4×#125—32no—
96C4×C22⋊Q8—32no—
97C4×C22⋊Q8—34no—
98C42×Q8—31no—
99C42×D4—32no—
100C42×D4—31no—
101C2×C4×C4⋊C4—32no—
102C22×C3×Q8C2312yes—
103C22×D12C2311yescharacteristic
104C22×C4×D3C2312yes—
105C22×C4×D3C2314yes—
106C22×C4×D3C2312yes—
107C22×C4×D3C2312yes—
108C22×C4×D3C2314yes—
109C22×Dic6C2311yescharacteristic
110C3×C4⋊Q8C2×C418yescomplemented
111C3×C4×Q8—44no—
112C2×C3×C4⋊C4C2312yes—
113C2×C3×C4⋊C4C2312yes—
114C2×C3×C4⋊C4C2314yes—
115C2×C3×C4⋊C4C2312yes—
116C2×C3×C4⋊C4C2312yes—
117C2×C3×C4⋊C4C2312yes—
118C2×C3×C42C2311yescharacteristic
119C2×C3×C42C2311yescharacteristic
120C2×C3×C42C2314yes—
121C2×C3×C42C2311yescharacteristic
122C2×C3×C42C2311yescharacteristic
123C2×C3×C42C2311yescharacteristic
124C2×C3×C42C2311yescharacteristic
125C2×C3×C42C2311yescharacteristic
126#946C2×C4132yescomplemented
127C2×(C2×D3)⋊C4C2314yes—
128C2×(C2×D3)⋊C4C2312yes—
129C2×(C2×D3)⋊C4C2314yes—
130C2×(C2×D3)⋊C4C2312yes—
131C2×(C2×D3)⋊C4C2312yes—
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134C2×C4⋊Dic3C2314yes—
135C2×C4⋊Dic3C2314yes—
136C2×C4⋊Dic3C2311yescharacteristic
137C2×C4⋊Dic3C2311yescharacteristic
138C2×C4⋊Dic3C2311yescharacteristic
139C2×C4⋊Dic3C2311yescharacteristic
140C2×Dic3⋊C4C2314yes—
141C2×Dic3⋊C4C2312yes—
142C2×Dic3⋊C4C2312yes—
143C2×Dic3⋊C4C2314yes—
144C2×Dic3⋊C4C2312yes—
145C2×C4×Dic3C2312yes—
146C2×C4×Dic3C2312yes—
147C2×C4×Dic3C2312yes—
148C2×C4×Dic3C2312yes—
149C2×C4×Dic3C2312yes—
150C2×C4×Dic3C2312yes—
151C2×C4×Dic3C2312yes—
152C2×C4×Dic3C2314yes—
153C2×C4×Dic3C2314yes—
154C2×C4×Dic3C2312yes—
155C2×C4×Dic3C2312yes—
156#897C2×C4116yescomplemented
157#893—28no—
158#893C2×C4116yes—
159D3×C4⋊C4—28no—
160D3×C4⋊C4C2×C4116yescomplemented
161#890C2×C4116yescomplemented
162C4×D12—24no—
163C4×D12C2×C418yes—
164C4×D12Q818yescomplemented
165C42×D3—28no—
166C42×D3—48no—
167C4×Dic6—24no—
168C4×Dic6—24no—
169C4×Dic6C2×C418yescomplemented
170C3×#95C2314yes—
171C3×#95C2314yes—
172C3⋊#95C2312yes—
173C3⋊#95C2314yes—
174C3⋊#95C2314yes—
175C3⋊#95C2314yes—
176C3⋊#95C2312yes—
177C3⋊#95C2314yes—
178C3⋊#95C2314yes—
179C3⋊#95C2314yes—
180C3⋊#95C2312yes—
181C3⋊#95C2312yes—
182C3⋊#95C2312yes—
183C3⋊#95C2312yes—
184#554—316no—
185C2×C4⋊Q8C2×D311yescharacteristic
186C2×#125—32no—
187C2×C22⋊Q8—34no—
188C2×C22⋊Q8—32no—
189C2×C4×Q8—31no—
190C2×C4×Q8—31no—
191C2×C4×Q8—31no—
192C2×C4×Q8C2×D312yes—
193C2×C4×D4—32no—
194C2×C4×D4—32no—
195C2×C4×D4—31no—
196C2×C4×D4—31no—
197C2×C4×D4—31no—
198C22×C4⋊C4—32no—
199C22×C4⋊C4—32no—
200C22×C42—32no—
201C22×C42—34no—
202#391—34no—
203#391—32no—
204#391C2×D312yes—
205#389—32no—
206#389—32no—
207#389—32no—
208#389—34no—
209#389C2×D312yes—
210#389C2×D312yes—
211#387—34no—
212#387—34no—
213#387—34no—
214#387—34no—
215#387—34no—
216#385—34no—
217#385—34no—
218#385—34no—
219#384C2×D311yescharacteristic
220#382—32no—
221#380—32no—
222#380—34no—
223C4×C4⋊C4—32no—
224C4×C4⋊C4—32no—
225C4×C4⋊C4—32no—
226C4×C4⋊C4—32no—
227C4×C4⋊C4—31no—
228C4×C4⋊C4—34no—
229C4×C4⋊C4—34no—
230C4×C4⋊C4—31no—
231C4×C4⋊C4—31no—
232C4×C4⋊C4—32no—
233C4×C4⋊C4—31no—
234C4×C4⋊C4—32no—
235C4×C4⋊C4—31no—
236C4×C4⋊C4—32no—
237C4×C4⋊C4—31no—
238C4×C4⋊C4—34no—
239C4×C4⋊C4C2×D312yes—
240C4×C4⋊C4C2×D312yes—
241C4×C22⋊C4—32no—
242C4×C22⋊C4—32no—
243C4×C22⋊C4—32no—
244C4×C22⋊C4—34no—
245C4×C22⋊C4—34no—
246C4×C22⋊C4—34no—
247C2×#95—34no—
248C43—32no—
249C43C2×D311yescharacteristic
250C23×D3C2412yes—
251C2×C3×Q8—42no—
252C2×C3×Q8—42no—
253C2×C3×Q8C22×C418yes—
254C22×C3×C4C2414yes—
255C22×C3×C4C2411yescharacteristic
256C22×C3×C4C2411yescharacteristic
257C22×C3×C4C2414yes—
258C22×C3×C4C2411yescharacteristic
259C22×C3×C4C2411yescharacteristic
260C22×C3×C4C2411yescharacteristic
261C22×C3×C4C2411yescharacteristic
262C22×C3×C4C2411yescharacteristic
263C22×Dic3C2412yes—
264C22×Dic3C2412yes—
265C22×Dic3C2412yes—
266C22×Dic3C2412yes—
267C22×Dic3C2412yes—
268C22×Dic3C2412yes—
269C22×Dic3C2412yes—
270C2×D12C22×C414yes—
271C2×D12C2×Q814yes—
272C2×D12#4114yes—
273C2×C4×D3—24no—
274C2×C4×D3—24no—
275C2×C4×D3—24no—
276C2×C4×D3—24no—
277C2×C4×D3—24no—
278C2×C4×D3—28no—
279C2×C4×D3—24no—
280C2×C4×D3—28no—
281C2×C4×D3—44no—
282C2×C4×D3—44no—
283C2×C4×D3—44no—
284C2×C4×D3—42no—
285C2×C4×D3C22×C418yes—
286C2×C4×D3C22×C4116yes—
287C2×C4×D3C2×Q818yes—
288C2×Dic6—22no—
289C2×Dic6—22no—
290C2×Dic6C22×C414yes—
291C3×C4⋊C4—24no—
292C3×C4⋊C4—24no—
293C3×C4⋊C4—44no—
294C3×C4⋊C4—42no—
295C3×C4⋊C4C22×C418yes—
296C3×C4⋊C4C22×C418yes—
297C3×C42—22no—
298C3×C42—22no—
299C3×C42—28no—
300C3×C42—22no—
301C3×C42—41no—
302C3×C42C22×C414yes—
303C3×C42C2×Q814yes—
304C3×C42#4114yes—
305(C2×D3)⋊C4—24no—
306(C2×D3)⋊C4—28no—
307(C2×D3)⋊C4C22×C418yes—
308(C2×D3)⋊C4C22×C4116yes—
309(C2×D3)⋊C4C2×Q818yes—
310C4⋊Dic3—22no—
311C4⋊Dic3—22no—
312C4⋊Dic3—44no—
313C4⋊Dic3C22×C414yes—
314C4⋊Dic3C22×C414yes—
315C4⋊Dic3C22×C4116yes—
316C4⋊Dic3C2×Q814yes—
317C4⋊Dic3#4114yes—
318Dic3⋊C4—24no—
319Dic3⋊C4—24no—
320Dic3⋊C4—28no—
321Dic3⋊C4C22×C418yes—
322Dic3⋊C4C22×C4116yes—
323C4×Dic3—24no—
324C4×Dic3—24no—
325C4×Dic3—24no—
326C4×Dic3—24no—
327C4×Dic3—24no—
328C4×Dic3—24no—
329C4×Dic3—24no—
330C4×Dic3—44no—
331C4×Dic3—44no—
332C4×Dic3—42no—
333C4×Dic3C22×C418yes—
334C22×Q8—31no—
335C22×Q8C22×D312yes—
336C22×D4—31no—
337C23×C4—32no—
338C23×C4—32no—
339C23×C4—34no—
340C23×C4—34no—
341C23×C4—32no—
342C4⋊Q8C4×D318yescomplemented
343#125—316no—
344C22⋊Q8—332no—
345C22⋊Q8—316no—
346C4×Q8—38no—
347C4×Q8—44no—
348C4×Q8—64no—
349C4×Q8—64no—
350C4×D4—316no—
351C4×D4—38no—
352C4×D4—38no—
353C4×D4—64no—
354C4×D4—68no—
355C2×C4⋊C4—31no—
356C2×C4⋊C4—31no—
357C2×C4⋊C4—34no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—32no—
361C2×C4⋊C4—34no—
362C2×C4⋊C4—316no—
363C2×C4⋊C4—34no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—32no—
367C2×C4⋊C4—32no—
368C2×C4⋊C4—34no—
369C2×C4⋊C4—68no—
370C2×C4⋊C4C22×D312yes—
371C2×C4⋊C4C22×D312yes—
372C2×C4⋊C4C22×D314yes—
373C2×C4⋊C4C22×D312yes—
374C2×C4⋊C4C22×D312yes—
375C2×C4⋊C4C22×D312yes—
376C2×C22⋊C4—34no—
377C2×C22⋊C4—32no—
378C2×C22⋊C4—32no—
379C2×C22⋊C4—32no—
380C2×C22⋊C4—34no—
381C2×C42—32no—
382C2×C42—32no—
383C2×C42—32no—
384C2×C42—32no—
385C2×C42—32no—
386C2×C42—32no—
387C2×C42—32no—
388C2×C42—32no—
389C2×C42—32no—
390C2×C42—34no—
391C2×C42—34no—
392C2×C42—68no—
393C2×C42—128no—
394C2×C42C22×D311yescharacteristic
395C2×C42C22×D311yescharacteristic
396C2×C42C22×D311yescharacteristic
397C2×C42C22×D314yes—
398C2×C42C22×D311yescharacteristic
399C2×C42C22×D311yescharacteristic
400C2×C42C22×D311yescharacteristic
401C2×C42C22×D311yescharacteristic
402#95—32no—
403#95—34no—
404#95—34no—
405#95—32no—
406#95—32no—
407#95—34no—
408#95—34no—
409#95—32no—
410#95—32no—
411#95—32no—
412#95—34no—
413#95—34no—
414#95C22×D314yes—
415#95C22×D314yes—
416C23×C3C2511yescharacteristic
417C22×D3—22no—
418C22×D3—22no—
419C22×D3—22no—
420C22×D3—22no—
421C22×D3C23×C414yes—
422C22×D3C22×Q814yes—
423C22×D3C2×#4114yes—
424C3×Q8—48no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—24no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—24no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—24no—
435C2×C3×C4—21no—
436C2×C3×C4—24no—
437C2×C3×C4—24no—
438C2×C3×C4—21no—
439C2×C3×C4C23×C412yes—
440C2×C3×C4C23×C418yes—
441C2×C3×C4C23×C412yes—
442C2×C3×C4C23×C412yes—
443C2×C3×C4C22×Q812yes—
444C2×C3×C4C22×Q812yes—
445C2×C3×C4C22×Q812yes—
446C2×C3×C4C2×#4112yes—
447C2×C3×C4C2×#4112yes—
448C2×C3×C4C2×#4112yes—
449C2×C3×C4C2×#4112yes—
450C2×C3×C4C2×#4112yes—
451C2×C3×C4H(5,𝔽2)12yes—
452C2×Dic3—22no—
453C2×Dic3—22no—
454C2×Dic3—22no—
455C2×Dic3—22no—
456C2×Dic3—22no—
457C2×Dic3—22no—
458C2×Dic3—22no—
459C2×Dic3—22no—
460C2×Dic3—22no—
461C2×Dic3—22no—
462C2×Dic3—22no—
463C2×Dic3—22no—
464C2×Dic3—22no—
465C2×Dic3—22no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3C23×C414yes—
469C2×Dic3C23×C414yes—
470C2×Dic3C23×C414yes—
471C2×Dic3C22×Q814yes—
472C2×Dic3C2×#4114yes—
473D12C4×Q8116yescomplemented
474C4×D3—216no—
475C4×D3—216no—
476C4×D3—416no—
477C4×D3—416no—
478C4×D3—48no—
479Dic6—28no—
480C24—32no—
481C2×Q8—34no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8—62no—
485C2×Q8—62no—
486C2×Q8C2×C4×D318yes—
487C2×D4—34no—
488C2×D4—34no—
489C2×D4—34no—
490C22×C4—32no—
491C22×C4—32no—
492C22×C4—32no—
493C22×C4—32no—
494C22×C4—32no—
495C22×C4—38no—
496C22×C4—38no—
497C22×C4—316no—
498C22×C4—32no—
499C22×C4—32no—
500C22×C4—68no—
501C22×C4—64no—
502C22×C4—68no—
503C22×C4—64no—
504C22×C4—64no—
505C22×C4—64no—
506C22×C4—64no—
507C22×C4—64no—
508C22×C4—124no—
509C22×C4—124no—
510C22×C4—122no—
511C22×C4—124no—
512C22×C4C23×D314yes—
513C22×C4C23×D311yescharacteristic
514C22×C4C23×D311yescharacteristic
515C22×C4C23×D314yes—
516C22×C4C23×D311yescharacteristic
517C22×C4C23×D311yescharacteristic
518C22×C4C23×D311yescharacteristic
519C22×C4C23×D311yescharacteristic
520C22×C4C23×D311yescharacteristic
521C4⋊C4—24no—
522C4⋊C4—24no—
523C4⋊C4—34no—
524C4⋊C4—316no—
525C4⋊C4—34no—
526C4⋊C4—38no—
527C4⋊C4—316no—
528C4⋊C4—34no—
529C4⋊C4—34no—
530C4⋊C4—44no—
531C4⋊C4—42no—
532C4⋊C4—68no—
533C4⋊C4—64no—
534C4⋊C4—64no—
535C4⋊C4—62no—
536C4⋊C4—62no—
537C4⋊C4—124no—
538C4⋊C4C2×C4×D318yes—
539C4⋊C4C2×C4×D318yes—
540C22⋊C4—316no—
541C22⋊C4—38no—
542C22⋊C4—38no—
543C22⋊C4—64no—
544C22⋊C4—68no—
545C42—28no—
546C42—22no—
547C42—22no—
548C42—22no—
549C42—38no—
550C42—41no—
551C42—64no—
552C42—64no—
553C42—64no—
554C42—64no—
555C42—64no—
556C42—64no—
557C42—64no—
558C42—124no—
559C42—124no—
560C42—122no—
561C42C2×C4×D314yes—
562C42D3×Q814yes—
563C42#23914yes—
564C22×C3C24×C411yescharacteristic
565C22×C3C23×Q811yescharacteristic
566C22×C3C22×#4111yescharacteristic
567C22×C3C22×#4111yescharacteristic
568C22×C3C22×#4111yescharacteristic
569C22×C3C2×H(5,𝔽2)11yescharacteristic
570C22×C3#58511yescharacteristic
571C2×D3—24no—
572C2×D3—24no—
573C2×D3—24no—
574C2×D3—24no—
575C2×D3—24no—
576C2×D3—24no—
577C2×D3C2×C4×Q818yes—
578C3×C4—28no—
579C3×C4—22no—
580C3×C4—22no—
581C3×C4—22no—
582C3×C4—44no—
583C3×C4—41no—
584C3×C4C2×C4×Q814yes—
585C3×C4C4×#4114yes—
586C3×C4#55414yescomplemented
587Dic3—24no—
588Dic3—24no—
589Dic3—24no—
590Dic3—24no—
591Dic3—24no—
592Dic3—42no—
593Dic3—42no—
594C23—34no—
595C23—34no—
596C23—34no—
597C23—62no—
598C23—62no—
599C23—62no—
600C23—62no—
601C23C24×D311yescharacteristic
602Q8—48no—
603Q8—68no—
604D4—316no—
605C2×C4—24no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—34no—
620C2×C4—34no—
621C2×C4—34no—
622C2×C4—34no—
623C2×C4—34no—
624C2×C4—62no—
625C2×C4—62no—
626C2×C4—62no—
627C2×C4—62no—
628C2×C4—62no—
629C2×C4—62no—
630C2×C4—62no—
631C2×C4—62no—
632C2×C4—62no—
633C2×C4—62no—
634C2×C4—616no—
635C2×C4—616no—
636C2×C4—62no—
637C2×C4—62no—
638C2×C4—62no—
639C2×C4—62no—
640C2×C4—62no—
641C2×C4—62no—
642C2×C4—1216no—
643C2×C4—128no—
644C2×C4—1216no—
645C2×C4C22×C4×D312yes—
646C2×C4C22×C4×D318yes—
647C2×C4C22×C4×D312yes—
648C2×C4C22×C4×D312yes—
649C2×C4#100412yes—
650C2×C4C2×D3×Q812yes—
651C2×C4C2×D3×Q812yes—
652C2×C4C2×D3×Q812yes—
653C2×C4C2×#23912yes—
654C2×C4C2×#23912yes—
655C2×C4C2×#23912yes—
656C2×C4D3×#4112yes—
657C2×C4D3×#4112yes—
658C2×C3C22×C4×Q811yescharacteristic
659C2×C3C2×C4×#4111yescharacteristic
660C2×C3C4×H(5,𝔽2)11yescharacteristic
661C2×C3C2×#55411yescharacteristic
662C2×C3#347511yescharacteristic
663C2×C3Q8×#4111yescharacteristic
664C2×C3#348111yescharacteristic
665D3—28no—
666C22—38no—
667C22—64no—
668C22—64no—
669C22—64no—
670C22—64no—
671C22—64no—
672C22—64no—
673C22C23×C4×D311yescharacteristic
674C22C2×#100411yescharacteristic
675C22C22×D3×Q811yescharacteristic
676C22C22×#23911yescharacteristic
677C22C2×D3×#4111yescharacteristic
678C22C2×D3×#4111yescharacteristic
679C22#596411yescharacteristic
680C4—22no—
681C4—22no—
682C4—28no—
683C4—22no—
684C4—44no—
685C4—41no—
686C4—64no—
687C4—64no—
688C4—64no—
689C4—64no—
690C4—64no—
691C4—122no—
692C4—122no—
693C4C4×D3×Q814yes—
694C4C4×#23914yes—
695C4#573014yesdirect product factor
696C3C4×#55411yescharacteristic, complemented, Sylow
697C2—68no—
698C2C4×#100411yescharacteristic
699C2C2×C4×#23911yescharacteristic
700C2C2×C4×D3×Q811yescharacteristic
701C2C2×#573011yescharacteristic
702C2#8623911yescharacteristic
703C2#8627611yescharacteristic
704C2#8627711yescharacteristic
subgroupG/H
centerC22×C4C23×D3
commutatorC22×C3C24×C4
FrattiniC23C24×D3
FittingC3×C4×C4⋊Q8C2
socle, cosocleC23×C3C25
prime radicalC22×D12C23
hypercenterC4×C4⋊Q8D3
hypocenterC3C4×#554
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C3×C4×C4⋊Q8C2semidirect
3. #83230C2semidirect
4. C4×#946C2semidirect
5. #76616C2semidirect
6. #76205C2semidirect
8. #76201C2semidirect
9. #75989C2semidirect
11. #74325C2semidirect
12. C4×#897C2semidirect
13. C4×D3×C4⋊C4C2semidirect
14. C4×#890C2semidirect
16. C42×Dic6C2semidirect
22. #5730C4direct (N × H)
94. C4×C4⋊Q8D3semidirect
110. C3×C4⋊Q8C2×C4semidirect
126. #946C2×C4semidirect
156. #897C2×C4semidirect
160. D3×C4⋊C4C2×C4semidirect
161. #890C2×C4semidirect
164. C4×D12Q8semidirect
169. C4×Dic6C2×C4semidirect
342. C4⋊Q8C4×D3semidirect
473. D12C4×Q8semidirect
586. C3×C4#554semidirect
695. C4#5730direct (N × H)
696. C3C4×#554semidirect

Maximal subgroups

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

subgroupindex
C2×#57302
C3×C4×C4⋊Q82
#832302
C4×#9462
#766162
#762052
#762032
#762012
#759892
#743602
#743252
C4×#8972
C4×D3×C4⋊C42
C4×#8902
C4×#8932
C42×Dic62
C42×D122
C4×#5543