Finite Group Databasebeta

← C2×C4×#13063307 #25255031

Subgroups — C2×C4×#13063307 #25255031

Order 11008.

4070 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063307C211yesmaximal, characteristic
2C22×C4×C22⋊D43C211yesmaximal, characteristic
3C22×C42×D43C211yesmaximal, characteristic, complemented
4C4×#13063307C2116yesmaximal, direct product factor
5C2×#14582793C211yesmaximal, characteristic, complemented
6C2×#14582792C211yesmaximal, characteristic, complemented
7C2×#14582782C211yesmaximal, characteristic, complemented
8C2×#14582781C211yesmaximal, characteristic, complemented
9C2×#14582775C211yesmaximal, characteristic
10C2×#14582773C211yesmaximal, characteristic, complemented
11C2×#14582761C211yesmaximal, characteristic, complemented
12C2×C4×Dic43⋊C4C211yesmaximal, characteristic, complemented
13C2×C4×C4⋊Dic43C211yesmaximal, characteristic, complemented
14C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic43C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
17C23×C22⋊D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C2×#13063307C4116yesdirect product factor
22C2×#13063307C2218yes—
23C2×C4×C22⋊D43—28no—
24C2×C4×C22⋊D43C2218yes—
25C22×C4⋊Dic43C2211yescharacteristic
26C22×C4⋊Dic43C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×C22⋊Dic43C2211yescharacteristic
31C22×C22⋊Dic43C2211yescharacteristic
32C22×C22⋊Dic43C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×C4×Dic43C2211yescharacteristic
37C22×C4×Dic43C2211yescharacteristic
38C22×C4×Dic43C2211yescharacteristic
39C22×C4×Dic43C2211yescharacteristic
40C22×C4×Dic43C2211yescharacteristic
41C2×C42×D43—28no—
42C2×C42×D43C2218yescomplemented
43#14582793C2218yescomplemented
44#14582792C2218yescomplemented
45#14582782C2218yescomplemented
46#14582781C2218yescomplemented
47#14582775C2218yes—
48#14582773C2218yescomplemented
49#14582761C2218yescomplemented
50C4×Dic43⋊C4C2218yescomplemented
51C4×C4⋊Dic43C2218yescomplemented
52C4×(C2×D43)⋊C4C2218yescomplemented
53C4×C22⋊Dic43C2218yescomplemented
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2211yescharacteristic
61C2×C43⋊#95C2211yescharacteristic
62C24×C4×C43C2211yescharacteristic
63C22×C22⋊C4×C43C2211yescharacteristic
64C22×C22⋊C4×C43C2211yescharacteristic
65C22×C42×C43C2211yescharacteristic
66C22×C42×C43C2211yescharacteristic
67C4×C22⋊C4×C43C2218yescomplemented
68C2×#95×C43C2211yescharacteristic
69C2×#95×C43C2211yescharacteristic
70C24×D43C2311yescharacteristic
71C22×C22⋊D43—24no—
72C22×C22⋊D43—24no—
73C22×C22⋊D43C2×C418yes—
74C22×C22⋊D43C2314yes—
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C22×C4×D43—24no—
83C22×C4×D43—24no—
84C22×C4×D43—24no—
85C22×C4×D43—24no—
86C22×C4×D43—24no—
87C22×C4×D43—24no—
88C22×C4×D43—24no—
89C22×C4×D43C2×C418yescomplemented
90C22×C4×D43D418yes—
91C22×C4×D43C2314yes—
92C22×C4×D43C2314yes—
93C22×C4×D43C2314yes—
94#13063307C2×C4164yesdirect product factor
95C4×C22⋊D43—232no—
96C2×C4⋊Dic43—24no—
97C2×C4⋊Dic43C2×C418yescomplemented
98C2×C4⋊Dic43C2314yes—
99C2×C4⋊Dic43C2314yes—
100C2×Dic43⋊C4—24no—
101C2×Dic43⋊C4—24no—
102C2×Dic43⋊C4C2×C418yescomplemented
103C2×Dic43⋊C4C2314yes—
104C2×Dic43⋊C4C2314yes—
105C2×Dic43⋊C4C2314yes—
106C2×C22⋊Dic43—24no—
107C2×C22⋊Dic43—24no—
108C2×C22⋊Dic43C2×C418yescomplemented
109C2×C22⋊Dic43C2314yes—
110C2×C22⋊Dic43C2314yes—
111C2×C22⋊Dic43C2314yes—
112C2×(C2×D43)⋊C4—24no—
113C2×(C2×D43)⋊C4—24no—
114C2×(C2×D43)⋊C4C2×C418yescomplemented
115C2×(C2×D43)⋊C4C2314yes—
116C2×(C2×D43)⋊C4C2314yes—
117C2×(C2×D43)⋊C4C2314yes—
118C2×C4×Dic43—24no—
119C2×C4×Dic43—24no—
120C2×C4×Dic43—24no—
121C2×C4×Dic43—24no—
122C2×C4×Dic43—24no—
123C2×C4×Dic43C2314yes—
124C2×C4×Dic43C2314yes—
125C2×C4×Dic43C2314yes—
126C2×C4×Dic43C2314yes—
127C2×C4×Dic43C2314yes—
128C42×D43—232no—
129C43⋊#95C2314yes—
130C43⋊#95C2314yes—
131C43⋊#95C2314yes—
132C43⋊#95C2314yes—
133C43⋊#95C2314yes—
134C43⋊#95C2314yes—
135C43⋊#95C2314yes—
136C43⋊#95C2314yes—
137C25×C43C2311yescharacteristic
138C23×C4×C43—24no—
139C23×C4×C43—24no—
140C23×C4×C43—24no—
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2314yes—
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C2×C22⋊C4×C43—24no—
149C2×C22⋊C4×C43C2×C418yescomplemented
150C2×C22⋊C4×C43C2314yes—
151C2×C22⋊C4×C43C2314yes—
152C2×C42×C43—24no—
153C2×C42×C43—24no—
154C2×C42×C43C2314yes—
155C2×C42×C43C2314yes—
156#95×C43C2314yes—
157#95×C43C2314yes—
158C24×C43—22no—
159C24×C43—22no—
160C24×C43—22no—
161C24×C43—22no—
162C24×C43—22no—
163C24×C43—22no—
164C24×C43C22×C414yes—
165C24×C43C2412yes—
166C24×C43C2411yescharacteristic
167C23×D43—22no—
168C23×D43—22no—
169C23×D43—22no—
170C23×D43—22no—
171C23×D43C22×C414yes—
172C23×D43C2×D414yes—
173C23×D43#4114yes—
174C23×D43C2412yes—
175C22×C4×C43—28no—
176C22×C4×C43—28no—
177C22×C4×C43—28no—
178C22×C4×C43—22no—
179C22×C4×C43—22no—
180C22×C4×C43—22no—
181C22×C4×C43—22no—
182C22×C4×C43—22no—
183C22×C4×C43—22no—
184C22×C4×C43—22no—
185C22×C4×C43—22no—
186C22×C4×C43—22no—
187C22×C4×C43—22no—
188C22×C4×C43—22no—
189C22×C4×C43—22no—
190C22×C4×C43—416no—
191C22×C4×C43C22×C414yes—
192C22×C4×C43C22×C414yes—
193C22×C4×C43C2×D414yes—
194C22×C4×C43#4114yes—
195C22×C4×C43#4114yes—
196C22×C4×C43#4114yes—
197C22×C4×C43C2412yes—
198C22×C4×C43C2412yes—
199C22×C4×C43C2412yes—
200C22×C4×C43C2412yes—
201C22×C4×C43C2412yes—
202C22×C4×C43C2412yes—
203C2×C22⋊D43—232no—
204C2×C22⋊D43—28no—
205C2×C22⋊D43—28no—
206C2×C22⋊D43C22×C4116yes—
207C22×Dic43—22no—
208C22×Dic43—22no—
209C22×Dic43—22no—
210C22×Dic43—22no—
211C22×Dic43—22no—
212C22×Dic43—22no—
213C22×Dic43—22no—
214C22×Dic43—22no—
215C22×Dic43—22no—
216C22×Dic43—22no—
217C22×Dic43—22no—
218C22×Dic43—22no—
219C22×Dic43—22no—
220C22×Dic43—22no—
221C22×Dic43—22no—
222C22×Dic43—22no—
223C22×Dic43C22×C414yes—
224C22×Dic43C22×C414yes—
225C22×Dic43C22×C414yes—
226C22×Dic43C2×D414yes—
227C22×Dic43#4114yes—
228C22×Dic43C2412yes—
229C22×Dic43C2412yes—
230C22×Dic43C2412yes—
231C22×Dic43C2412yes—
232C22×Dic43C2412yes—
233C22×Dic43C2412yes—
234C22×Dic43C2412yes—
235C2×C4×D43—232no—
236C2×C4×D43—232no—
237C2×C4×D43—28no—
238C2×C4×D43—28no—
239C2×C4×D43—28no—
240C2×C4×D43—28no—
241C2×C4×D43—232no—
242C2×C4×D43—28no—
243C2×C4×D43—28no—
244C2×C4×D43—28no—
245C2×C4×D43C22×C4116yescomplemented
246C2×C4×D43C2×D4116yes—
247C22⋊C4×C43—28no—
248C22⋊C4×C43C22×C4116yescomplemented
249C42×C43—28no—
250C42×C43—28no—
251C22⋊Dic43—28no—
252C22⋊Dic43—28no—
253C22⋊Dic43C22×C4116yescomplemented
254(C2×D43)⋊C4—28no—
255(C2×D43)⋊C4—28no—
256(C2×D43)⋊C4C22×C4116yescomplemented
257C4⋊Dic43—28no—
258C4⋊Dic43C22×C4116yescomplemented
259Dic43⋊C4—28no—
260Dic43⋊C4—28no—
261Dic43⋊C4C22×C4116yescomplemented
262C4×Dic43—28no—
263C4×Dic43—28no—
264C4×Dic43—28no—
265C4×Dic43—28no—
266C4×Dic43—28no—
267C23×C43—28no—
268C23×C43—28no—
269C23×C43—28no—
270C23×C43—22no—
271C23×C43—22no—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—22no—
276C23×C43—44no—
277C23×C43—44no—
278C23×C43—44no—
279C23×C43—44no—
280C23×C43C23×C414yes—
281C23×C43C23×C412yes—
282C23×C43C22×D412yes—
283C23×C43C2×#4112yes—
284C23×C43C2×#4112yes—
285C23×C43C2×#4112yes—
286C23×C43C2×#4112yes—
287C23×C43C2×#4112yes—
288C23×C43C2511yescharacteristic
289C22×D43—28no—
290C22×D43—28no—
291C22×D43—28no—
292C22×D43—28no—
293C22×D43—28no—
294C22×D43—28no—
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—22no—
299C22×D43C4×D4116yes—
300C22×D43C23×C414yes—
301C22×D43C22×D414yes—
302C22×D43C2×#4114yes—
303C2×C4×C43—28no—
304C2×C4×C43—28no—
305C2×C4×C43—28no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—44no—
319C2×C4×C43—44no—
320C2×C4×C43—416no—
321C2×C4×C43#123116yescomplemented
322C2×C4×C43C23×C414yes—
323C2×C4×C43C23×C414yes—
324C2×C4×C43C22×D414yes—
325C2×C4×C43C2×#4114yes—
326C2×C4×C43C2×#4114yes—
327C2×C4×C43C2×#4114yes—
328C22⋊D43—232no—
329C2×Dic43—28no—
330C2×Dic43—28no—
331C2×Dic43—28no—
332C2×Dic43—28no—
333C2×Dic43—28no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—22no—
350C2×Dic43—44no—
351C2×Dic43—44no—
352C2×Dic43C23×C414yes—
353C2×Dic43C23×C414yes—
354C2×Dic43C23×C414yes—
355C2×Dic43C22×D414yes—
356C2×Dic43C2×#4114yes—
357C4×D43—232no—
358C4×D43—232no—
359C4×D43—232no—
360C2×C4×#123—431nomaximal, Sylow
361C22×C43—24no—
362C22×C43—24no—
363C22×C43—24no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—42no—
367C22×C43—42no—
368C22×C43—416no—
369C22×C43C2×C4×D414yes—
370C22×C43C4×#4114yes—
371C22×C43C4×#4114yes—
372C22×C43C2×#12314yes—
373C22×C43#52514yes—
374C22×C43#52914yes—
375C22×C43#52914yes—
376C22×C43C24×C411yescharacteristic
377C22×C43C23×D411yescharacteristic
378C22×C43C22×#4111yescharacteristic
379C22×C43C22×#4111yescharacteristic
380C22×C43C22×#4111yescharacteristic
381C22×C43C22×#4111yescharacteristic
382C22×C43C22×#4111yescharacteristic
383C2×D43—24no—
384C2×D43—24no—
385C2×D43—24no—
386C2×D43—24no—
387C2×D43—24no—
388C2×D43—24no—
389C2×D43—232no—
390C2×D43C2×C4×D418yes—
391C4×C43—24no—
392C4×C43—24no—
393C4×C43—24no—
394C4×C43—42no—
395C4×C43—42no—
396C4×C43C2×#12318yescomplemented
397Dic43—24no—
398Dic43—24no—
399Dic43—24no—
400Dic43—24no—
401Dic43—24no—
402Dic43—42no—
403Dic43—42no—
404C22×#123—431no—
405C22×C4×D4—431no—
406C23×C42—431no—
407C4×#123—4316no—
408C2×#388—431no—
409C2×#388—431no—
410C2×#387—431no—
411C2×#387—431no—
412C2×#386—431no—
413C2×#385—431no—
414C2×#381—431no—
415C2×C4×C4⋊C4—431no—
416C2×C4×C4⋊C4—431no—
417C2×C4×C22⋊C4—431no—
418C2×C4×C22⋊C4—431no—
419C2×C4×C22⋊C4D4311yescharacteristic, complemented
420C2×C43—44no—
421C2×C43C4×#12318yescomplemented
422C2×C43C22×C4×D411yescharacteristic
423C2×C43C2×C4×#4111yescharacteristic
424C2×C43C2×C4×#4111yescharacteristic
425C2×C43C22×#12311yescharacteristic
426C2×C43C2×#52511yescharacteristic
427C2×C43C2×#52911yescharacteristic
428C2×C43C2×#52911yescharacteristic
429D43—28no—
430C23×D4—431no—
431C24×C4—431no—
432C24×C4—431no—
433C24×C4—431no—
434C24×C4C2×D4311yescharacteristic
435C2×#123—438no—
436C2×#123—4316no—
437C2×C4×D4—438no—
438C2×C4×D4—868no—
439C22×C4⋊C4—431no—
440C22×C4⋊C4—431no—
441C22×C4⋊C4—431no—
442C22×C4⋊C4—431no—
443C22×C4⋊C4—431no—
444C22×C22⋊C4—431no—
445C22×C22⋊C4—431no—
446C22×C22⋊C4—431no—
447C22×C22⋊C4—431no—
448C22×C22⋊C4—431no—
449C22×C22⋊C4—431no—
450C22×C22⋊C4C2×D4311yescharacteristic
451C22×C22⋊C4C2×D4311yescharacteristic
452C22×C42—431no—
453C22×C42—431no—
454C22×C42—431no—
455C22×C42—431no—
456C22×C42—431no—
457C22×C42—438no—
458C22×C42—868no—
459C22×C42C2×D4311yescharacteristic
460C22×C42C2×D4311yescharacteristic
461#388—438no—
462#388—438no—
463#387—438no—
464#387—438no—
465#386—438no—
466#385—438no—
467#381—438no—
468C4×C4⋊C4—438no—
469C4×C4⋊C4—438no—
470C4×C22⋊C4—438no—
471C4×C22⋊C4—438no—
472C4×C22⋊C4C2×D4318yescomplemented
473C2×#95—431no—
474C2×#95—431no—
475C2×#95—431no—
476C2×#95—431no—
477C2×#95—431no—
478C2×#95—431no—
479C2×#95—431no—
480C2×#95—431no—
481C2×#95C2×D4311yescharacteristic
482C2×#95C2×D4311yescharacteristic
483C43C2×C4×#12311yescharacteristic, complemented, Sylow
484C25—431no—
485C25C22×D4311yescharacteristic
486C22×D4—438no—
487C22×D4—434no—
488C22×D4—864no—
489C22×D4—864no—
490C23×C4—24no—
491C23×C4—24no—
492C23×C4—24no—
493C23×C4—431no—
494C23×C4—431no—
495C23×C4—431no—
496C23×C4—431no—
497C23×C4—431no—
498C23×C4—438no—
499C23×C4—438no—
500C23×C4—434no—
501C23×C4—434no—
502C23×C4—431no—
503C23×C4—431no—
504C23×C4—434no—
505C23×C4—864no—
506C23×C4—864no—
507C23×C4—864no—
508C23×C4—864no—
509C23×C4—864no—
510C23×C4—864no—
511C23×C4—864no—
512C23×C4C22×D4311yescharacteristic
513C23×C4C22×D4311yescharacteristic
514C23×C4C22×D4314yes—
515C23×C4C22×D4311yescharacteristic
516C23×C4C22×D4311yescharacteristic
517C23×C4C22×D4311yescharacteristic
518C23×C4C22×D4311yescharacteristic
519#123—4364no—
520C4×D4—8632no—
521C2×C4⋊C4—438no—
522C2×C4⋊C4—438no—
523C2×C4⋊C4—434no—
524C2×C4⋊C4—434no—
525C2×C4⋊C4—434no—
526C2×C4⋊C4—434no—
527C2×C4⋊C4—434no—
528C2×C4⋊C4—864no—
529C2×C4⋊C4—864no—
530C2×C4⋊C4—864no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—438no—
533C2×C22⋊C4—434no—
534C2×C22⋊C4—438no—
535C2×C22⋊C4—434no—
536C2×C22⋊C4—434no—
537C2×C22⋊C4—434no—
538C2×C22⋊C4—434no—
539C2×C22⋊C4—434no—
540C2×C22⋊C4—864no—
541C2×C22⋊C4—864no—
542C2×C22⋊C4—864no—
543C2×C22⋊C4—864no—
544C2×C22⋊C4C4×D4318yescomplemented
545C2×C22⋊C4C22×D4314yes—
546C2×C22⋊C4C22×D4314yes—
547C2×C42—24no—
548C2×C42—24no—
549C2×C42—434no—
550C2×C42—434no—
551C2×C42—434no—
552C2×C42—434no—
553C2×C42—434no—
554C2×C42—8632no—
555C2×C42—864no—
556C2×C42—864no—
557C2×C42—864no—
558C2×C42—864no—
559C2×C42—864no—
560C2×C42C22×D4314yes—
561C2×C42C22×D4314yes—
562#95—434no—
563#95—434no—
564#95—434no—
565#95—434no—
566#95—434no—
567#95—434no—
568#95—434no—
569#95—434no—
570#95C22×D4314yes—
571#95C22×D4314yes—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—434no—
579C24—434no—
580C24—434no—
581C24—432no—
582C24—862no—
583C24—862no—
584C24—862no—
585C24—862no—
586C24C2×C4×D4314yes—
587C24C23×D4312yes—
588C24C23×D4311yescharacteristic
589C2×D4—4316no—
590C2×D4—868no—
591C2×D4—8632no—
592C2×D4—868no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—28no—
606C22×C4—28no—
607C22×C4—28no—
608C22×C4—416no—
609C22×C4—434no—
610C22×C4—434no—
611C22×C4—434no—
612C22×C4—434no—
613C22×C4—434no—
614C22×C4—432no—
615C22×C4—432no—
616C22×C4—432no—
617C22×C4—432no—
618C22×C4—432no—
619C22×C4—4316no—
620C22×C4—4316no—
621C22×C4—432no—
622C22×C4—432no—
623C22×C4—868no—
624C22×C4—868no—
625C22×C4—868no—
626C22×C4—8632no—
627C22×C4—868no—
628C22×C4—8632no—
629C22×C4—862no—
630C22×C4—862no—
631C22×C4—862no—
632C22×C4—862no—
633C22×C4—862no—
634C22×C4—862no—
635C22×C4—862no—
636C22×C4—862no—
637C22×C4—862no—
638C22×C4—862no—
639C22×C4—8632no—
640C22×C4—868no—
641C22×C4—868no—
642C22×C4—868no—
643C22×C4—862no—
644C22×C4—862no—
645C22×C4—862no—
646C22×C4—862no—
647C22×C4—862no—
648C22×C4—862no—
649C22×C4C2×C4×D4314yes—
650C22×C4C2×C4×D4314yes—
651C22×C4#1062189814yes—
652C22×C4#1062189814yes—
653C22×C4D4×D4314yes—
654C22×C4#1062190014yes—
655C22×C4C23×D4312yes—
656C22×C4C23×D4312yes—
657C22×C4C23×D4312yes—
658C22×C4C23×D4312yes—
659C22×C4C23×D4312yes—
660C22×C4C23×D4312yes—
661C4⋊C4—4316no—
662C4⋊C4—4316no—
663C4⋊C4—868no—
664C4⋊C4—868no—
665C4⋊C4—868no—
666C22⋊C4—28no—
667C22⋊C4—4316no—
668C22⋊C4—4316no—
669C22⋊C4—868no—
670C22⋊C4—868no—
671C22⋊C4—868no—
672C22⋊C4—868no—
673C22⋊C4C2×C4×D43116yescomplemented
674C42—28no—
675C42—28no—
676C42—868no—
677C42—868no—
678C42—868no—
679C42—868no—
680C42—868no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—4316no—
695C23—434no—
696C23—434no—
697C23—434no—
698C23—868no—
699C23—868no—
700C23—868no—
701C23—868no—
702C23—868no—
703C23—868no—
704C23—862no—
705C23—862no—
706C23—862no—
707C23—862no—
708C23C22×C4×D4314yes—
709C23C22×C4×D4312yes—
710C23C2×D4×D4312yes—
711C23#41×D4312yes—
712C23#41×D4312yes—
713C23C2×#1062190012yes—
714C23C2×#1062189812yes—
715C23C2×#1062189812yes—
716C23C24×D4311yescharacteristic
717D4—8632no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—416no—
736C2×C4—434no—
737C2×C4—434no—
738C2×C4—434no—
739C2×C4—434no—
740C2×C4—434no—
741C2×C4—8632no—
742C2×C4—8632no—
743C2×C4—868no—
744C2×C4—868no—
745C2×C4—868no—
746C2×C4—868no—
747C2×C4—868no—
748C2×C4—862no—
749C2×C4—862no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—8632no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—1724no—
766C2×C4—1724no—
767C2×C4#13063307116yesdirect product factor
768C2×C4C22×C4×D4314yes—
769C2×C4C22×C4×D4314yes—
770C2×C4C2×D4×D4314yes—
771C2×C4C2×#1062190014yes—
772C2×C4C2×#1062189814yes—
773C2×C4C2×#1062189814yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—416no—
782C22—438no—
783C22—864no—
784C22—864no—
785C22—864no—
786C22—864no—
787C22—8632no—
788C22—864no—
789C22—864no—
790C22C4×D4×D4314yes—
791C22C4×#1062190014yes—
792C22C4×#1062189814yes—
793C22C2×#1306330714yes—
794C22#1458340814yes—
795C22#1458342714yes—
796C22#1458343114yes—
797C22C23×C4×D4311yescharacteristic
798C22C22×D4×D4311yescharacteristic
799C22C2×#41×D4311yescharacteristic
800C22C2×#41×D4311yescharacteristic
801C22C22×#1062190011yescharacteristic
802C22C22×#1062189811yescharacteristic
803C22C22×#1062189811yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—864no—
810C4—864no—
811C4—864no—
812C4—864no—
813C4—864no—
814C4—1722no—
815C4—1722no—
816C4C2×#1306330718yesdirect product factor
817C2—44no—
818C2—868no—
819C2C4×#1306330718yesdirect product factor
820C2C2×C4×D4×D4311yescharacteristic
821C2C2×C4×#1062190011yescharacteristic
822C2C2×C4×#1062189811yescharacteristic
823C2C22×#1306330711yescharacteristic
824C2C2×#1458340811yescharacteristic
825C2C2×#1458342711yescharacteristic
826C2C2×#1458343111yescharacteristic
subgroupG/H
centerC23×C4C22×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C4×C22⋊C4×C43C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
cosocleC23×C43C25
hypercenterC2×C4×C22⋊C4D43
hypocenterC43C2×C4×#123
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×C42×D43C2semidirect
4. C4×#13063307C2direct (N × H)
5. C2×#14582793C2semidirect
6. C2×#14582792C2semidirect
7. C2×#14582782C2semidirect
8. C2×#14582781C2semidirect
10. C2×#14582773C2semidirect
11. C2×#14582761C2semidirect
12. C2×C4×Dic43⋊C4C2semidirect
13. C2×C4×C4⋊Dic43C2semidirect
14. C2×C4×(C2×D43)⋊C4C2semidirect
15. C2×C4×C22⋊Dic43C2semidirect
16. C2×C4×C22⋊C4×C43C2semidirect
21. C2×#13063307C4direct (N × H)
42. C2×C42×D43C22semidirect
43. #14582793C22semidirect
44. #14582792C22semidirect
45. #14582782C22semidirect
46. #14582781C22semidirect
48. #14582773C22semidirect
49. #14582761C22semidirect
50. C4×Dic43⋊C4C22semidirect
51. C4×C4⋊Dic43C22semidirect
52. C4×(C2×D43)⋊C4C22semidirect
53. C4×C22⋊Dic43C22semidirect
67. C4×C22⋊C4×C43C22semidirect
89. C22×C4×D43C2×C4semidirect
94. #13063307C2×C4direct (N × H)
97. C2×C4⋊Dic43C2×C4semidirect
102. C2×Dic43⋊C4C2×C4semidirect
108. C2×C22⋊Dic43C2×C4semidirect
114. C2×(C2×D43)⋊C4C2×C4semidirect
149. C2×C22⋊C4×C43C2×C4semidirect
245. C2×C4×D43C22×C4semidirect
248. C22⋊C4×C43C22×C4semidirect
253. C22⋊Dic43C22×C4semidirect
256. (C2×D43)⋊C4C22×C4semidirect
258. C4⋊Dic43C22×C4semidirect
261. Dic43⋊C4C22×C4semidirect
321. C2×C4×C43#123semidirect
396. C4×C43C2×#123semidirect
419. C2×C4×C22⋊C4D43semidirect
421. C2×C43C4×#123semidirect
472. C4×C22⋊C4C2×D43semidirect
483. C43C2×C4×#123semidirect
544. C2×C22⋊C4C4×D43semidirect
673. C22⋊C4C2×C4×D43semidirect
767. C2×C4#13063307direct (N × H)
816. C4C2×#13063307direct (N × H)
819. C2C4×#13063307direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633072
C22×C4×C22⋊D432
C22×C42×D432
C4×#130633072
C2×#145827932
C2×#145827922
C2×#145827822
C2×#145827812
C2×#145827752
C2×#145827732
C2×#145827612
C2×C4×Dic43⋊C42
C2×C4×C4⋊Dic432
C2×C4×(C2×D43)⋊C42
C2×C4×C22⋊Dic432
C2×C4×C22⋊C4×C432
C2×C4×#12343