Finite Group Databasebeta

← C2×C4×#13063239 #25094244

Subgroups — C2×C4×#13063239 #25094244

Order 11008.

2242 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D43C211yesmaximal, characteristic
2C22×#13063239C212yesmaximal
3C2×C4×C22⋊Dic43C211yesmaximal, characteristic, complemented
4C4×#13063239C218yesmaximal, direct product factor
5C2×#14582665C212yesmaximal, complemented
6C2×C4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
7C23×C22⋊D43C2211yescharacteristic
8C23×C4×D43C411yescharacteristic, complemented
9C2×C4×C22⋊D43—21no—
10C2×C4×C22⋊D43—21no—
11C2×C4×C22⋊D43—22no—
12C2×C4×C22⋊D43—21no—
13C2×C4×C22⋊D43—21no—
14C2×C4×C22⋊D43—22no—
15C2×C4×C22⋊D43C414yescomplemented
16C2×C4×C22⋊D43C2214yes—
17C22×Dic43⋊C4C411yescharacteristic, complemented
18C22×C22⋊Dic43C2211yescharacteristic
19C22×C22⋊Dic43C2212yes—
20C22×(C2×D43)⋊C4C411yescharacteristic, complemented
21C22×C4×Dic43—21no—
22C22×C4×Dic43C411yescharacteristic, complemented
23C2×#13063239C4116yesdirect product factor
24C2×#13063239C2218yes—
25C4×C22⋊Dic43—22no—
26C4×C22⋊Dic43C2214yescomplemented
27C2×C43⋊#95—21no—
28#14582665C2218yescomplemented
29C24×C4×C43C2211yescharacteristic
30C22×C22⋊C4×C43C2212yes—
31C22×C42×C43—21no—
32C4×C22⋊C4×C43—22no—
33C4×C22⋊C4×C43C2214yescomplemented
34C2×#95×C43—21no—
35C24×D43C2×C411yescharacteristic
36C22×C22⋊D43—21no—
37C22×C22⋊D43—21no—
38C22×C22⋊D43—21no—
39C22×C22⋊D43—21no—
40C22×C22⋊D43—24no—
41C22×C22⋊D43C2×C418yes—
42C22×C22⋊D43C2×C412yes—
43C22×C22⋊D43C2312yes—
44C23×Dic43—22no—
45C23×Dic43C2×C411yescharacteristic
46C23×Dic43C2×C411yescharacteristic
47C23×Dic43C2×C411yescharacteristic
48C22×C4×D43—21no—
49C22×C4×D43—22no—
50C22×C4×D43—21no—
51C22×C4×D43—44no—
52C22×C4×D43C2×C414yescomplemented
53C4×C22⋊D43—24no—
54C4×C22⋊D43—24no—
55C4×C22⋊D43—24no—
56C4×C22⋊D43—24no—
57C4×C22⋊D43—24no—
58C4×C22⋊D43—24no—
59C4×C22⋊D43—24no—
60C4×C22⋊D43—24no—
61C2×Dic43⋊C4—21no—
62C2×Dic43⋊C4—21no—
63C2×Dic43⋊C4—22no—
64C2×Dic43⋊C4C2×C414yescomplemented
65C2×C22⋊Dic43—21no—
66C2×C22⋊Dic43—21no—
67C2×C22⋊Dic43—21no—
68C2×C22⋊Dic43—21no—
69C2×C22⋊Dic43—22no—
70C2×C22⋊Dic43—24no—
71C2×C22⋊Dic43C2×C412yes—
72C2×C22⋊Dic43C2×C418yescomplemented
73C2×C22⋊Dic43C2312yes—
74C2×C22⋊Dic43C2314yes—
75C2×(C2×D43)⋊C4—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—22no—
78C2×(C2×D43)⋊C4C2×C414yescomplemented
79C2×C4×Dic43—21no—
80C2×C4×Dic43—22no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—24no—
83C2×C4×Dic43—44no—
84C2×C4×Dic43C2×C414yescomplemented
85#13063239C2×C4132yesdirect product factor
86C43⋊#95—24no—
87C25×C43C2311yescharacteristic
88C23×C4×C43—22no—
89C23×C4×C43—44no—
90C23×C4×C43C2×C411yescharacteristic
91C23×C4×C43C2×C411yescharacteristic
92C23×C4×C43C2×C412yes—
93C23×C4×C43D411yescharacteristic
94C23×C4×C43D411yescharacteristic
95C23×C4×C43D412yes—
96C23×C4×C43D411yescharacteristic
97C23×C4×C43D411yescharacteristic
98C23×C4×C43D412yes—
99C23×C4×C43C2312yes—
100C2×C22⋊C4×C43—22no—
101C2×C22⋊C4×C43—24no—
102C2×C22⋊C4×C43C2×C418yescomplemented
103C2×C22⋊C4×C43C2314yes—
104C2×C42×C43—24no—
105C2×C42×C43—44no—
106#95×C43—24no—
107C24×C43—42no—
108C24×C43—42no—
109C24×C43C22×C411yescharacteristic
110C24×C43C22×C411yescharacteristic
111C24×C43C22×C414yes—
112C24×C43C2×D411yescharacteristic
113C24×C43C2×D411yescharacteristic
114C24×C43C2×D411yescharacteristic
115C24×C43C2×D411yescharacteristic
116C24×C43#4114yes—
117C24×C43C2411yescharacteristic
118C23×D43—21no—
119C23×D43—21no—
120C23×D43—22no—
121C23×D43—42no—
122C23×D43—42no—
123C23×D43C4214yescomplemented
124C23×D43C22×C412yes—
125C22×C4×C43—24no—
126C22×C4×C43—24no—
127C22×C4×C43—24no—
128C22×C4×C43—28no—
129C22×C4×C43—24no—
130C22×C4×C43—42no—
131C22×C4×C43—42no—
132C22×C4×C43—42no—
133C22×C4×C43—44no—
134C22×C4×C43—44no—
135C22×C4×C43—44no—
136C22×C4×C43—44no—
137C22×C4×C43—44no—
138C22×C4×C43—44no—
139C22×C4×C43C22⋊C412yes—
140C22×C4×C43C22⋊C411yescharacteristic
141C22×C4×C43C22⋊C411yescharacteristic
142C22×C4×C43C22⋊C411yescharacteristic
143C22×C4×C43C22⋊C412yes—
144C22×C4×C43C22⋊C412yes—
145C22×C4×C43C22⋊C412yes—
146C22×C4×C43C22⋊C412yes—
147C22×C4×C43C22⋊C412yes—
148C22×C4×C43C22⋊C411yescharacteristic
149C22×C4×C43C22×C412yes—
150C22×C4×C43C22×C412yes—
151C22×C4×C43C2×D412yes—
152C22×C4×C43C2×D412yes—
153C22×C4×C43C2×D412yes—
154C22×C4×C43C2×D412yes—
155C2×C22⋊D43—22no—
156C2×C22⋊D43—22no—
157C2×C22⋊D43—24no—
158C2×C22⋊D43—28no—
159C2×C22⋊D43—28no—
160C2×C22⋊D43—28no—
161C2×C22⋊D43—28no—
162C2×C22⋊D43—22no—
163C2×C22⋊D43—22no—
164C2×C22⋊D43—24no—
165C2×C22⋊D43C4218yescomplemented
166C2×C22⋊D43C22×C418yes—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—22no—
174C22×Dic43—28no—
175C22×Dic43—24no—
176C22×Dic43—42no—
177C22×Dic43—42no—
178C22×Dic43—44no—
179C22×Dic43—44no—
180C22×Dic43C4214yescomplemented
181C22×Dic43C22×C412yes—
182C22×Dic43C22×C412yes—
183C22×Dic43C22×C412yes—
184C2×C4×D43—24no—
185C2×C4×D43—24no—
186C2×C4×D43—48no—
187C2×C4×D43—44no—
188C2×C4×D43—44no—
189C2×C4×D43—48no—
190C22⋊C4×C43—28no—
191C22⋊C4×C43—24no—
192C22⋊C4×C43C22×C418yescomplemented
193C42×C43—48no—
194C22⋊Dic43—22no—
195C22⋊Dic43—22no—
196C22⋊Dic43—28no—
197C22⋊Dic43—22no—
198C22⋊Dic43—22no—
199C22⋊Dic43—24no—
200C22⋊Dic43C22×C418yescomplemented
201(C2×D43)⋊C4—24no—
202(C2×D43)⋊C4—24no—
203Dic43⋊C4—24no—
204Dic43⋊C4—24no—
205C4×Dic43—24no—
206C4×Dic43—24no—
207C4×Dic43—48no—
208C23×C43—22no—
209C23×C43—22no—
210C23×C43—22no—
211C23×C43—22no—
212C23×C43—22no—
213C23×C43—22no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—48no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—48no—
223C23×C43—41no—
224C23×C43C2×C4212yes—
225C23×C43C2×C4212yes—
226C23×C43C2×C22⋊C411yescharacteristic
227C23×C43C2×C22⋊C411yescharacteristic
228C23×C43C2×C22⋊C411yescharacteristic
229C23×C43C2×C22⋊C411yescharacteristic
230C23×C43#11712yes—
231C23×C43#11712yes—
232C23×C43C4×D414yes—
233C23×C43C4×D414yes—
234C23×C43C4×D414yes—
235C23×C43C4×D414yes—
236C23×C43C23×C411yescharacteristic
237C23×C43C23×C412yes—
238C23×C43C22×D411yescharacteristic
239C23×C43C22×D411yescharacteristic
240C23×C43C2×#4112yes—
241C22×D43—22no—
242C22×D43—22no—
243C22×D43—24no—
244C22×D43—24no—
245C22×D43—42no—
246C22×D43—42no—
247C22×D43—48no—
248C22×D43—42no—
249C22×D43—42no—
250C22×D43—42no—
251C22×D43—48no—
252C22×D43—42no—
253C22×D43C2×C4214yescomplemented
254C2×C4×C43—22no—
255C2×C4×C43—22no—
256C2×C4×C43—22no—
257C2×C4×C43—24no—
258C2×C4×C43—24no—
259C2×C4×C43—24no—
260C2×C4×C43—24no—
261C2×C4×C43—24no—
262C2×C4×C43—24no—
263C2×C4×C43—28no—
264C2×C4×C43—42no—
265C2×C4×C43—42no—
266C2×C4×C43—42no—
267C2×C4×C43—42no—
268C2×C4×C43—42no—
269C2×C4×C43—42no—
270C2×C4×C43—44no—
271C2×C4×C43—44no—
272C2×C4×C43—416no—
273C2×C4×C43#9914yescomplemented
274C2×C4×C43C2×C22⋊C412yes—
275C2×C4×C43C2×C22⋊C412yes—
276C2×C4×C43C2×C22⋊C412yes—
277C2×C4×C43C2×C22⋊C412yes—
278C22⋊D43—28no—
279C22⋊D43—28no—
280C22⋊D43—28no—
281C22⋊D43—28no—
282C2×Dic43—22no—
283C2×Dic43—22no—
284C2×Dic43—24no—
285C2×Dic43—24no—
286C2×Dic43—22no—
287C2×Dic43—22no—
288C2×Dic43—28no—
289C2×Dic43—44no—
290C2×Dic43—42no—
291C2×Dic43—44no—
292C2×Dic43—416no—
293C2×Dic43—42no—
294C2×Dic43—42no—
295C2×Dic43—42no—
296C2×Dic43—42no—
297C2×Dic43—42no—
298C2×Dic43C2×C4214yescomplemented
299C4×D43—48no—
300C4×D43—48no—
301C2×C4×#99—431nomaximal, Sylow
302C22×C43—21no—
303C22×C43—21no—
304C22×C43—21no—
305C22×C43—21no—
306C22×C43—21no—
307C22×C43—21no—
308C22×C43—21no—
309C22×C43—21no—
310C22×C43—21no—
311C22×C43—21no—
312C22×C43—21no—
313C22×C43—21no—
314C22×C43—24no—
315C22×C43—24no—
316C22×C43—28no—
317C22×C43—28no—
318C22×C43—42no—
319C22×C43—42no—
320C22×C43—44no—
321C22×C43—44no—
322C22×C43—42no—
323C22×C43—42no—
324C22×C43C4×C22⋊C412yes—
325C22×C43C4×C22⋊C412yes—
326C22×C43C4×C22⋊C412yes—
327C22×C43C4×C22⋊C412yes—
328C22×C43C2×#9912yes—
329C22×C43#41012yes—
330C22×C43C22×C4211yescharacteristic
331C22×C43C22×C22⋊C411yescharacteristic
332C22×C43C2×#11711yescharacteristic
333C22×C43C2×C4×D412yes—
334C22×C43C2×C4×D412yes—
335C2×D43—24no—
336C2×D43—44no—
337C2×D43—48no—
338C2×D43—42no—
339C2×D43—42no—
340C2×D43—48no—
341C2×D43—44no—
342C4×C43—22no—
343C4×C43—22no—
344C4×C43—22no—
345C4×C43—48no—
346C4×C43C2×#9914yescomplemented
347Dic43—24no—
348Dic43—48no—
349Dic43—42no—
350Dic43—42no—
351C22×C4×D4—431no—
352C22×#99—432no—
353C2×C4×C22⋊C4—431no—
354C2×C4×C22⋊C4D4311yescharacteristic, complemented
355C4×#99—438no—
356C2×#342—432no—
357C2×C43—22no—
358C2×C43—22no—
359C2×C43—21no—
360C2×C43—22no—
361C2×C43—21no—
362C2×C43—22no—
363C2×C43—22no—
364C2×C43C4×#9914yescomplemented
365C2×C43C2×C4×C22⋊C411yescharacteristic
366C2×C43C22×#9911yescharacteristic
367C2×C43C2×#41011yescharacteristic
368D43—44no—
369C23×D4—431no—
370C24×C4—431no—
371C24×C4C2×D4311yescharacteristic
372C2×C4×D4—434no—
373C2×C4×D4—434no—
374C2×C4×D4—861no—
375C2×C4×D4—862no—
376C2×C4×D4—861no—
377C2×C4×D4—861no—
378C2×C4×D4—862no—
379C2×C4×D4—861no—
380C22×C4⋊C4—431no—
381C22×C22⋊C4—432no—
382C22×C22⋊C4—431no—
383C22×C22⋊C4—431no—
384C22×C22⋊C4C2×D4312yes—
385C22×C42—21no—
386C22×C42—431no—
387C22×C42—861no—
388C2×#99—438no—
389C2×#99—4316no—
390C4×C22⋊C4—22no—
391C4×C22⋊C4—434no—
392C4×C22⋊C4—862no—
393C4×C22⋊C4C2×D4314yescomplemented
394C2×#95—21no—
395C2×#95—861no—
396#342—438no—
397C43C2×C4×#9911yescharacteristic, complemented, Sylow
398C25—431no—
399C25C22×D4311yescharacteristic
400C22×D4—432no—
401C22×D4—438no—
402C22×D4—432no—
403C22×D4—861no—
404C22×D4—861no—
405C22×D4—864no—
406C22×D4—861no—
407C22×D4—861no—
408C23×C4—22no—
409C23×C4—44no—
410C23×C4—431no—
411C23×C4—431no—
412C23×C4—431no—
413C23×C4—434no—
414C23×C4—862no—
415C23×C4—862no—
416C23×C4—861no—
417C23×C4—861no—
418C23×C4—1724no—
419C23×C4C4×D4311yescharacteristic
420C23×C4C4×D4311yescharacteristic
421C23×C4C4×D4312yes—
422C23×C4D17211yescharacteristic
423C23×C4D17211yescharacteristic
424C23×C4D17212yes—
425C23×C4C22⋊D4311yescharacteristic
426C23×C4C22⋊D4311yescharacteristic
427C23×C4C22⋊D4312yes—
428C23×C4C22×D4312yes—
429C4×D4—864no—
430C4×D4—864no—
431C4×D4—864no—
432C4×D4—864no—
433C4×D4—864no—
434C4×D4—864no—
435C4×D4—864no—
436C4×D4—864no—
437C2×C4⋊C4—434no—
438C2×C4⋊C4—861no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4—862no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—438no—
444C2×C22⋊C4—434no—
445C2×C22⋊C4—432no—
446C2×C22⋊C4—432no—
447C2×C22⋊C4—434no—
448C2×C22⋊C4—861no—
449C2×C22⋊C4—861no—
450C2×C22⋊C4—862no—
451C2×C22⋊C4—864no—
452C2×C22⋊C4—861no—
453C2×C22⋊C4—861no—
454C2×C22⋊C4—861no—
455C2×C22⋊C4—861no—
456C2×C22⋊C4—862no—
457C2×C22⋊C4C4×D4318yescomplemented
458C2×C22⋊C4C22×D4314yes—
459C2×C42—24no—
460C2×C42—44no—
461C2×C42—434no—
462C2×C42—861no—
463C2×C42—862no—
464C2×C42—861no—
465C2×C42—864no—
466C2×C42—1724no—
467#99—4332no—
468#95—24no—
469#95—864no—
470C24—42no—
471C24—42no—
472C24—434no—
473C24—432no—
474C24—861no—
475C24—861no—
476C24—862no—
477C24—1722no—
478C24—1722no—
479C24C2×C4×D4311yescharacteristic
480C24C2×C4×D4311yescharacteristic
481C24C2×C4×D4314yes—
482C24C2×D17211yescharacteristic
483C24C2×D17211yescharacteristic
484C24#1062189814yes—
485C24C2×C22⋊D4311yescharacteristic
486C24C2×C22⋊D4311yescharacteristic
487C24C23×D4311yescharacteristic
488C2×D4—438no—
489C2×D4—438no—
490C2×D4—862no—
491C2×D4—862no—
492C2×D4—864no—
493C2×D4—868no—
494C2×D4—868no—
495C2×D4—868no—
496C2×D4—868no—
497C2×D4—862no—
498C2×D4—862no—
499C2×D4—864no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—28no—
504C22×C4—24no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—434no—
515C22×C4—432no—
516C22×C4—432no—
517C22×C4—432no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—862no—
521C22×C4—861no—
522C22×C4—861no—
523C22×C4—861no—
524C22×C4—861no—
525C22×C4—868no—
526C22×C4—864no—
527C22×C4—864no—
528C22×C4—864no—
529C22×C4—1724no—
530C22×C4—1728no—
531C22×C4—1728no—
532C22×C4—1724no—
533C22×C4—1724no—
534C22×C4—1724no—
535C22×C4—1722no—
536C22×C4—1722no—
537C22×C4(C2×D43)⋊C411yescharacteristic
538C22×C4(C2×D43)⋊C412yes—
539C22×C4(C2×D43)⋊C411yescharacteristic
540C22×C4(C2×D43)⋊C411yescharacteristic
541C22×C4(C2×D43)⋊C412yes—
542C22×C4(C2×D43)⋊C412yes—
543C22×C4(C2×D43)⋊C412yes—
544C22×C4(C2×D43)⋊C412yes—
545C22×C4(C2×D43)⋊C412yes—
546C22×C4(C2×D43)⋊C411yescharacteristic
547C22×C4C2×C4×D4312yes—
548C22×C4C2×C4×D4312yes—
549C22×C4C2×D17212yes—
550C22×C4C2×D17212yes—
551C22×C4C2×C22⋊D4312yes—
552C22×C4C2×C22⋊D4312yes—
553C4⋊C4—864no—
554C4⋊C4—864no—
555C22⋊C4—28no—
556C22⋊C4—24no—
557C22⋊C4—438no—
558C22⋊C4—862no—
559C22⋊C4—862no—
560C22⋊C4—868no—
561C22⋊C4—862no—
562C22⋊C4—862no—
563C22⋊C4—864no—
564C22⋊C4—864no—
565C22⋊C4—864no—
566C22⋊C4C2×C4×D4318yescomplemented
567C42—48no—
568C42—864no—
569C42—864no—
570C42—1728no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—48no—
583C23—41no—
584C23—48no—
585C23—41no—
586C23—41no—
587C23—434no—
588C23—862no—
589C23—862no—
590C23—864no—
591C23—864no—
592C23—1722no—
593C23—1722no—
594C23—1728no—
595C23—1722no—
596C23—1722no—
597C23—1728no—
598C23—1722no—
599C23—1722no—
600C23C42×D4312yes—
601C23C42×D4312yes—
602C23C2×(C2×D43)⋊C411yescharacteristic
603C23C2×(C2×D43)⋊C411yescharacteristic
604C23C2×(C2×D43)⋊C411yescharacteristic
605C23C2×(C2×D43)⋊C411yescharacteristic
606C23#1306328212yes—
607C23#1306328212yes—
608C23C4×C22⋊D4314yes—
609C23C4×C22⋊D4314yes—
610C23C4×D17214yes—
611C23C4×D17214yes—
612C23C22×C4×D4311yescharacteristic
613C23C22×C4×D4312yes—
614C23C22×C22⋊D4311yescharacteristic
615C23C22×D17211yescharacteristic
616C23C2×#1062189812yes—
617D4—868no—
618D4—868no—
619D4—868no—
620D4—868no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—28no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—416no—
640C2×C4—434no—
641C2×C4—862no—
642C2×C4—862no—
643C2×C4—864no—
644C2×C4—864no—
645C2×C4—862no—
646C2×C4—862no—
647C2×C4—868no—
648C2×C4—1728no—
649C2×C4—1724no—
650C2×C4—1722no—
651C2×C4—1724no—
652C2×C4—17216no—
653C2×C4—1722no—
654C2×C4—1722no—
655C2×C4—1722no—
656C2×C4—1728no—
657C2×C4—1722no—
658C2×C4—1722no—
659C2×C4#1306323914yesdirect product factor
660C2×C4C2×(C2×D43)⋊C412yes—
661C2×C4C2×(C2×D43)⋊C412yes—
662C2×C4C2×(C2×D43)⋊C412yes—
663C2×C4C2×(C2×D43)⋊C412yes—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—28no—
677C22—28no—
678C22—24no—
679C22—24no—
680C22—42no—
681C22—42no—
682C22—44no—
683C22—44no—
684C22—42no—
685C22—42no—
686C22—864no—
687C22—1724no—
688C22—1724no—
689C22—1728no—
690C22—1722no—
691C22—1722no—
692C22—1728no—
693C22C4×(C2×D43)⋊C412yes—
694C22C4×(C2×D43)⋊C412yes—
695C22C4×(C2×D43)⋊C412yes—
696C22C4×(C2×D43)⋊C412yes—
697C22C2×#1306323912yes—
698C22#1458287212yes—
699C22C2×C42×D4311yescharacteristic
700C22C22×(C2×D43)⋊C411yescharacteristic
701C22C2×#1306328211yescharacteristic
702C22C2×C4×C22⋊D4312yes—
703C22C2×C4×D17212yes—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—48no—
708C4—864no—
709C4—1728no—
710C4—1722no—
711C4—1722no—
712C4C2×#1306323914yesdirect product factor
713C2—22no—
714C2—22no—
715C2—21no—
716C2—21no—
717C2—22no—
718C2—22no—
719C2—22no—
720C2—1724no—
721C2C4×#1306323914yesdirect product factor
722C2C2×C4×(C2×D43)⋊C411yescharacteristic
723C2C22×#1306323911yescharacteristic
724C2C2×#1458287211yescharacteristic
subgroupG/H
centerC22×C4(C2×D43)⋊C4
commutatorC22×C43C22×C42
FrattiniC24C23×D43
FittingC2×C4×C22⋊C4×C43C2
socleC23×C43C2×C22⋊C4
prime radicalC23×C22⋊D43C22
cosocleC24×C43C24
hypercenterC2×C4×C22⋊C4D43
hypocenterC43C2×C4×#99
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×C22⋊Dic43C2semidirect
4. C4×#13063239C2direct (N × H)
5. C2×#14582665C2semidirect
6. C2×C4×C22⋊C4×C43C2semidirect
8. C23×C4×D43C4semidirect
15. C2×C4×C22⋊D43C4semidirect
17. C22×Dic43⋊C4C4semidirect
20. C22×(C2×D43)⋊C4C4semidirect
22. C22×C4×Dic43C4semidirect
23. C2×#13063239C4direct (N × H)
26. C4×C22⋊Dic43C22semidirect
28. #14582665C22semidirect
33. C4×C22⋊C4×C43C22semidirect
52. C22×C4×D43C2×C4semidirect
64. C2×Dic43⋊C4C2×C4semidirect
72. C2×C22⋊Dic43C2×C4semidirect
78. C2×(C2×D43)⋊C4C2×C4semidirect
84. C2×C4×Dic43C2×C4semidirect
85. #13063239C2×C4direct (N × H)
102. C2×C22⋊C4×C43C2×C4semidirect
123. C23×D43C42semidirect
165. C2×C22⋊D43C42semidirect
180. C22×Dic43C42semidirect
192. C22⋊C4×C43C22×C4semidirect
200. C22⋊Dic43C22×C4semidirect
253. C22×D43C2×C42semidirect
273. C2×C4×C43#99semidirect
298. C2×Dic43C2×C42semidirect
346. C4×C43C2×#99semidirect
354. C2×C4×C22⋊C4D43semidirect
364. C2×C43C4×#99semidirect
393. C4×C22⋊C4C2×D43semidirect
397. C43C2×C4×#99semidirect
457. C2×C22⋊C4C4×D43semidirect
566. C22⋊C4C2×C4×D43semidirect
659. C2×C4#13063239direct (N × H)
712. C4C2×#13063239direct (N × H)
721. C2C4×#13063239direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D432
C22×#130632392
C2×C4×C22⋊Dic432
C4×#130632392
C2×#145826652
C2×C4×C22⋊C4×C432
C2×C4×#9943