Finite Group Databasebeta

← C2×#19137523 #25255923

Subgroups — C2×#19137523 #25255923

Order 11008.

3894 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×(C22⋊D43)⋊C4C211yesmaximal, characteristic
2C22×#13063281C211yesmaximal, characteristic, complemented
3C22×C4⋊C4×D43C211yesmaximal, characteristic, complemented
4#19137523C2116yesmaximal, direct product factor
5C2×#14582792C211yesmaximal, characteristic, complemented
6C2×#14582786C211yesmaximal, characteristic, complemented
7C2×#14582780C211yesmaximal, characteristic, complemented
8C2×#14582775C211yesmaximal, characteristic
9C2×#14582775C211yesmaximal, characteristic
10C2×#14582763C211yesmaximal, characteristic, complemented
11C2×#14582758C211yesmaximal, characteristic, complemented
12C2×#14582757C211yesmaximal, characteristic, complemented
13C2×C4×Dic43⋊C4C211yesmaximal, characteristic, complemented
14C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
15C2×#14582746C211yesmaximal, characteristic, complemented
16C2×C43×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D43C2211yescharacteristic
18C24×Dic43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C23×C4×D43C2211yescharacteristic
22C2×(C22⋊D43)⋊C4C4116yescomplemented
23C2×(C22⋊D43)⋊C4C2218yes—
24C2×#13063281—28no—
25C2×#13063281C2218yescomplemented
26C22×C4⋊Dic43C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×Dic43⋊C4C2211yescharacteristic
31C22×Dic43⋊C4C2211yescharacteristic
32C2×C4⋊C4×D43—28no—
33C2×C4⋊C4×D43C2218yescomplemented
34C22×C22⋊Dic43C2211yescharacteristic
35C22×C22⋊Dic43C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C22×(C2×D43)⋊C4C2211yescharacteristic
39C22×C4×Dic43C2211yescharacteristic
40C22×C4×Dic43C2211yescharacteristic
41C22×C4×Dic43C2211yescharacteristic
42C22×C4×Dic43C2211yescharacteristic
43#14582792C2218yescomplemented
44#14582786C2218yescomplemented
45#14582780C2218yescomplemented
46#14582775C2218yes—
47#14582775C2218yes—
48#14582763C2218yescomplemented
49#14582758C2218yescomplemented
50#14582757C2218yescomplemented
51C4×Dic43⋊C4C2218yescomplemented
52C4×(C2×D43)⋊C4C2218yescomplemented
53#14582746C2218yescomplemented
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2211yescharacteristic
61C2×C43⋊#95C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×C22⋊C4×C43C2211yescharacteristic
64C22×C22⋊C4×C43C2211yescharacteristic
65C22×C22⋊C4×C43C2211yescharacteristic
66C22×C42×C43C2211yescharacteristic
67C43×#388C2218yescomplemented
68C2×#95×C43C2211yescharacteristic
69C2×#95×C43C2211yescharacteristic
70C24×D43C2311yescharacteristic
71C22×C22⋊D43—24no—
72C22×C22⋊D43—24no—
73C22×C22⋊D43C2×C418yes—
74C22×C22⋊D43C2314yes—
75C23×Dic43—24no—
76C23×Dic43—24no—
77C23×Dic43C2×C418yescomplemented
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2314yes—
84C23×Dic43C2311yescharacteristic
85C23×Dic43C2311yescharacteristic
86C22×C4×D43—24no—
87C22×C4×D43—24no—
88C22×C4×D43—24no—
89C22×C4×D43—24no—
90C22×C4×D43—24no—
91C22×C4×D43—24no—
92C22×C4×D43—42no—
93C22×C4×D43—42no—
94C22×C4×D43C2×C418yes—
95C22×C4×D43C2314yes—
96C22×C4×D43C2314yes—
97C22×C4×D43C2314yes—
98(C22⋊D43)⋊C4C2×C4164yescomplemented
99#13063281—232no—
100C2×C4⋊Dic43—24no—
101C2×C4⋊Dic43C2314yes—
102C2×Dic43⋊C4—24no—
103C2×Dic43⋊C4—24no—
104C2×Dic43⋊C4—24no—
105C2×Dic43⋊C4C2×C418yescomplemented
106C2×Dic43⋊C4D418yescomplemented
107C2×Dic43⋊C4C2314yes—
108C2×Dic43⋊C4C2314yes—
109C2×Dic43⋊C4C2314yes—
110C2×Dic43⋊C4C2314yes—
111C2×Dic43⋊C4C2314yes—
112C4⋊C4×D43—232no—
113C2×C22⋊Dic43—24no—
114C2×C22⋊Dic43—42no—
115C2×C22⋊Dic43C2314yes—
116C2×C22⋊Dic43C2314yes—
117C2×(C2×D43)⋊C4—24no—
118C2×(C2×D43)⋊C4—24no—
119C2×(C2×D43)⋊C4C2×C418yes—
120C2×(C2×D43)⋊C4C2314yes—
121C2×(C2×D43)⋊C4C2314yes—
122C2×(C2×D43)⋊C4C2314yes—
123C2×C4×Dic43—24no—
124C2×C4×Dic43—24no—
125C2×C4×Dic43—42no—
126C2×C4×Dic43C2×C418yescomplemented
127C2×C4×Dic43C2314yes—
128C2×C4×Dic43C2314yes—
129C2×C4×Dic43C2314yes—
130C2×C4×Dic43C2314yes—
131C43⋊#95C2314yes—
132C43⋊#95C2314yes—
133C43⋊#95C2314yes—
134C43⋊#95C2314yes—
135C43⋊#95C2314yes—
136C43⋊#95C2314yes—
137C43⋊#95C2314yes—
138C43⋊#95C2314yes—
139C25×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C2×C4⋊C4×C43—24no—
147C2×C4⋊C4×C43C2314yes—
148C2×C22⋊C4×C43—24no—
149C2×C22⋊C4×C43—42no—
150C2×C22⋊C4×C43C2×C418yescomplemented
151C2×C22⋊C4×C43C2314yes—
152C2×C22⋊C4×C43C2314yes—
153C2×C22⋊C4×C43C2314yes—
154C2×C42×C43—42no—
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×D43#4114yes—
173C23×D43#4114yes—
174C23×D43C2412yes—
175C22×C4×C43—22no—
176C22×C4×C43—22no—
177C22×C4×C43—22no—
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×C43C22×C414yes—
191C22×C4×C43C22×C414yes—
192C22×C4×C43C2×D414yes—
193C22×C4×C43C2412yes—
194C22×C4×C43C2412yes—
195C22×C4×C43C2412yes—
196C22×C4×C43C2412yes—
197C22×C4×C43C2412yes—
198C22×C4×C43C2412yes—
199C2×C22⋊D43—232no—
200C2×C22⋊D43—28no—
201C2×C22⋊D43—28no—
202C2×C22⋊D43C22×C4116yes—
203C22×Dic43—232no—
204C22×Dic43—28no—
205C22×Dic43—28no—
206C22×Dic43—22no—
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×Dic43C22×C414yes—
222C22×Dic43C22×C414yes—
223C22×Dic43C22×C414yes—
224C22×Dic43C22×C4116yescomplemented
225C22×Dic43C2×D414yes—
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—28no—
237C2×C4×D43—28no—
238C2×C4×D43—28no—
239C2×C4×D43—28no—
240C2×C4×D43—28no—
241C2×C4×D43—28no—
242C2×C4×D43—44no—
243C2×C4×D43—44no—
244C2×C4×D43—416no—
245C2×C4×D43—416no—
246C2×C4×D43C22×C4116yes—
247C4⋊C4×C43—28no—
248C22⋊C4×C43—28no—
249C22⋊C4×C43—44no—
250C22⋊C4×C43C22×C4116yescomplemented
251C42×C43—44no—
252C22⋊Dic43—28no—
253C22⋊Dic43—44no—
254(C2×D43)⋊C4—28no—
255(C2×D43)⋊C4—28no—
256(C2×D43)⋊C4C22×C4116yes—
257C4⋊Dic43—28no—
258Dic43⋊C4—28no—
259Dic43⋊C4—28no—
260Dic43⋊C4—28no—
261Dic43⋊C4C22×C4116yescomplemented
262Dic43⋊C4C2×D4116yescomplemented
263C4×Dic43—28no—
264C4×Dic43—28no—
265C4×Dic43—44no—
266C4×Dic43C22×C4116yescomplemented
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×C43H(5,𝔽2)12yes—
287C23×C432−1+412yes—
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×D43#117116yescomplemented
300C22×D43C23×C414yes—
301C22×D43C2×#4114yes—
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—22no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—44no—
322C2×C4×C43—44no—
323C2×C4×C43—44no—
324C2×C4×C43C23×C414yes—
325C2×C4×C43C23×C414yes—
326C2×C4×C43C22×D414yes—
327C22⋊D43—232no—
328C2×Dic43—28no—
329C2×Dic43—28no—
330C2×Dic43—28no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—232no—
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—44no—
348C2×Dic43—44no—
349C2×Dic43—44no—
350C2×Dic43C4×D4116yes—
351C2×Dic43C23×C414yes—
352C2×Dic43C23×C414yes—
353C2×Dic43C23×C414yes—
354C2×Dic43C22×D414yes—
355C2×Dic43C22×D414yes—
356C2×Dic43C2×#4114yes—
357C4×D43—232no—
358C4×D43—416no—
359C4×D43—416no—
360C2×#2352—431nomaximal, Sylow
361C22×C43—24no—
362C22×C43—24no—
363C22×C43—24no—
364C22×C43—416no—
365C22×C43—42no—
366C22×C43—42no—
367C22×C43—42no—
368C22×C43—42no—
369C22×C43C2×#11714yes—
370C22×C43C2×C4×D414yes—
371C22×C43#52014yes—
372C22×C43#54614yes—
373C22×C43#54814yes—
374C22×C43#55214yes—
375C22×C43#55314yes—
376C22×C43C24×C411yescharacteristic
377C22×C43C23×D411yescharacteristic
378C22×C43C22×#4111yescharacteristic
379C22×C43C22×#4111yescharacteristic
380C22×C43C22×#4111yescharacteristic
381C22×C43C2×H(5,𝔽2)11yescharacteristic
382C22×C43C2×2−1+411yescharacteristic
383C2×D43—232no—
384C2×D43—24no—
385C2×D43—24no—
386C2×D43—24no—
387C2×D43—24no—
388C2×D43—24no—
389C2×D43—24no—
390C2×D43C2×#11718yescomplemented
391C4×C43—24no—
392C4×C43—24no—
393C4×C43—24no—
394C4×C43—42no—
395C4×C43—42no—
396C4×C43—42no—
397Dic43—24no—
398Dic43—24no—
399Dic43—24no—
400Dic43—42no—
401Dic43—42no—
402Dic43—42no—
403Dic43C2×C4×D418yes—
404C22×C4×D4—431no—
405C22×#117—431no—
406C23×C4⋊C4—431no—
407#2352—4316no—
408C2×#388—431no—
409C2×#388D4311yescharacteristic, complemented
410C2×#387—431no—
411C2×#387—431no—
412C2×#386—431no—
413C2×#386—431no—
414C2×#382—431no—
415C2×#380—431no—
416C2×#380—431no—
417C2×C4×C4⋊C4—431no—
418C2×C4×C22⋊C4—431no—
419C2×C4×C22⋊C4—431no—
420C2×C43—44no—
421C2×C43#235218yescomplemented
422C2×C43C22×#11711yescharacteristic
423C2×C43C22×C4×D411yescharacteristic
424C2×C43C2×#52011yescharacteristic
425C2×C43C2×#54611yescharacteristic
426C2×C43C2×#54811yescharacteristic
427C2×C43C2×#55211yescharacteristic
428C2×C43C2×#55311yescharacteristic
429D43—28no—
430C23×D4—431no—
431C24×C4—431no—
432C24×C4—431no—
433C24×C4—431no—
434C24×C4—431no—
435C2×C4×D4—438no—
436C2×C4×D4—4316no—
437C2×#117—438no—
438C2×#117—868no—
439C22×C4⋊C4—431no—
440C22×C4⋊C4—431no—
441C22×C4⋊C4—431no—
442C22×C4⋊C4—431no—
443C22×C4⋊C4—431no—
444C22×C4⋊C4—431no—
445C22×C4⋊C4—438no—
446C22×C4⋊C4—868no—
447C22×C4⋊C4C2×D4311yescharacteristic
448C22×C22⋊C4—431no—
449C22×C22⋊C4—431no—
450C22×C22⋊C4—431no—
451C22×C22⋊C4—431no—
452C22×C22⋊C4—431no—
453C22×C22⋊C4C2×D4311yescharacteristic
454C22×C22⋊C4C2×D4311yescharacteristic
455C22×C22⋊C4C2×D4311yescharacteristic
456C22×C42—431no—
457C22×C42—431no—
458C22×C42—431no—
459C22×C42—431no—
460C22×C42C2×D4311yescharacteristic
461#388—438no—
462#388C2×D4318yescomplemented
463#387—438no—
464#387—438no—
465#386—438no—
466#386—438no—
467#382—438no—
468#380—438no—
469#380—438no—
470C4×C4⋊C4—438no—
471C4×C22⋊C4—438no—
472C4×C22⋊C4—438no—
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×#235211yescharacteristic, complemented, Sylow
484C25—431no—
485C25C22×D4311yescharacteristic
486C22×D4—438no—
487C22×D4—434no—
488C22×D4—864no—
489C22×D4—864no—
490C23×C4—431no—
491C23×C4—438no—
492C23×C4—434no—
493C23×C4—431no—
494C23×C4—431no—
495C23×C4—431no—
496C23×C4—438no—
497C23×C4—434no—
498C23×C4—431no—
499C23×C4—431no—
500C23×C4—431no—
501C23×C4—434no—
502C23×C4—434no—
503C23×C4—864no—
504C23×C4—864no—
505C23×C4—864no—
506C23×C4—864no—
507C23×C4—864no—
508C23×C4—864no—
509C23×C4—864no—
510C23×C4—864no—
511C23×C4—1722no—
512C23×C4—1722no—
513C23×C4C22×D4311yescharacteristic
514C23×C4C22×D4311yescharacteristic
515C23×C4C22×D4311yescharacteristic
516C23×C4C22×D4311yescharacteristic
517C23×C4C22×D4311yescharacteristic
518C23×C4C22×D4311yescharacteristic
519C4×D4—4364no—
520#117—8632no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—438no—
523C2×C4⋊C4—438no—
524C2×C4⋊C4—434no—
525C2×C4⋊C4—434no—
526C2×C4⋊C4—434no—
527C2×C4⋊C4—434no—
528C2×C4⋊C4—434no—
529C2×C4⋊C4—434no—
530C2×C4⋊C4—8632no—
531C2×C4⋊C4—864no—
532C2×C4⋊C4—864no—
533C2×C4⋊C4—864no—
534C2×C4⋊C4—864no—
535C2×C4⋊C4C22×D4314yes—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—438no—
539C2×C22⋊C4—434no—
540C2×C22⋊C4—434no—
541C2×C22⋊C4—434no—
542C2×C22⋊C4—434no—
543C2×C22⋊C4—434no—
544C2×C22⋊C4—864no—
545C2×C22⋊C4—864no—
546C2×C22⋊C4—864no—
547C2×C22⋊C4—1722no—
548C2×C22⋊C4C4×D4318yescomplemented
549C2×C22⋊C4C22×D4314yes—
550C2×C22⋊C4C22×D4314yes—
551C2×C22⋊C4C22×D4314yes—
552C2×C42—42no—
553C2×C42—438no—
554C2×C42—434no—
555C2×C42—434no—
556C2×C42—434no—
557C2×C42—434no—
558C2×C42—864no—
559C2×C42—864no—
560C2×C42—1722no—
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—8632no—
591C2×D4—868no—
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—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—434no—
609C22×C4—434no—
610C22×C4—434no—
611C22×C4—432no—
612C22×C4—434no—
613C22×C4—434no—
614C22×C4—4316no—
615C22×C4—434no—
616C22×C4—432no—
617C22×C4—432no—
618C22×C4—432no—
619C22×C4—4316no—
620C22×C4—432no—
621C22×C4—432no—
622C22×C4—432no—
623C22×C4—868no—
624C22×C4—8632no—
625C22×C4—868no—
626C22×C4—868no—
627C22×C4—868no—
628C22×C4—868no—
629C22×C4—868no—
630C22×C4—8632no—
631C22×C4—868no—
632C22×C4—862no—
633C22×C4—862no—
634C22×C4—862no—
635C22×C4—862no—
636C22×C4—862no—
637C22×C4—862no—
638C22×C4—862no—
639C22×C4—862no—
640C22×C4—862no—
641C22×C4—862no—
642C22×C4—862no—
643C22×C4—862no—
644C22×C4—862no—
645C22×C4—862no—
646C22×C4—862no—
647C22×C4—868no—
648C22×C4—1724no—
649C22×C4—1724no—
650C22×C4—17216no—
651C22×C4—17216no—
652C22×C4C2×C4×D4314yes—
653C22×C4C2×C4×D4314yes—
654C22×C4D4×D4314yes—
655C22×C4C23×D4312yes—
656C22×C4C23×D4312yes—
657C22×C4C23×D4312yes—
658C22×C4C23×D4312yes—
659C22×C4C23×D4312yes—
660C22×C4C23×D4312yes—
661C4⋊C4—28no—
662C4⋊C4—4316no—
663C4⋊C4—4316no—
664C4⋊C4—868no—
665C4⋊C4—868no—
666C4⋊C4—868no—
667C4⋊C4—868no—
668C22⋊C4—28no—
669C22⋊C4—44no—
670C22⋊C4—4316no—
671C22⋊C4—868no—
672C22⋊C4—868no—
673C22⋊C4—868no—
674C22⋊C4—1724no—
675C22⋊C4C2×C4×D43116yescomplemented
676C42—44no—
677C42—4316no—
678C42—868no—
679C42—868no—
680C42—1724no—
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—862no—
704C23—862no—
705C23—862no—
706C23—862no—
707C23—868no—
708C23C22×C4×D4314yes—
709C23C22×C4×D4312yes—
710C23C2×D4×D4312yes—
711C23#41×D4312yes—
712C23#41×D4312yes—
713C23#41×D4312yes—
714C23#1306337012yes—
715C23#1306337212yes—
716C23C24×D4311yescharacteristic
717D4—8632no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—28no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—4316no—
740C2×C4—434no—
741C2×C4—434no—
742C2×C4—434no—
743C2×C4—434no—
744C2×C4—434no—
745C2×C4—434no—
746C2×C4—8632no—
747C2×C4—8632no—
748C2×C4—868no—
749C2×C4—868no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—868no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—862no—
766C2×C4—17216no—
767C2×C4—17216no—
768C2×C4—1724no—
769C2×C4—1724no—
770C2×C4—1724no—
771C2×C4C22×C4×D4314yes—
772C2×C4C22×C4×D4314yes—
773C2×C4C2×D4×D4314yes—
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—864no—
788C22—864no—
789C22—8632no—
790C22#117×D4314yes—
791C22C4×D4×D4314yes—
792C22#1458337814yes—
793C22#1458353814yes—
794C22#1458355714yes—
795C22#1458358514yes—
796C22#1458359414yes—
797C22C23×C4×D4311yescharacteristic
798C22C22×D4×D4311yescharacteristic
799C22C2×#41×D4311yescharacteristic
800C22C2×#41×D4311yescharacteristic
801C22C2×#41×D4311yescharacteristic
802C22C2×#1306337011yescharacteristic
803C22C2×#1306337211yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—438no—
811C4—864no—
812C4—864no—
813C4—864no—
814C4—1722no—
815C4—1722no—
816C4—1722no—
817C2—44no—
818C2—868no—
819C2#1913752318yesdirect product factor
820C2C2×#117×D4311yescharacteristic
821C2C2×C4×D4×D4311yescharacteristic
822C2C2×#1458337811yescharacteristic
823C2C2×#1458353811yescharacteristic
824C2C2×#1458355711yescharacteristic
825C2C2×#1458358511yescharacteristic
826C2C2×#1458359411yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#388C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
cosocleC23×C43C25
hypercenterC2×#388D43
hypocenterC43C2×#2352
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×#13063281C2semidirect
3. C22×C4⋊C4×D43C2semidirect
4. #19137523C2direct (N × H)
5. C2×#14582792C2semidirect
6. C2×#14582786C2semidirect
7. C2×#14582780C2semidirect
10. C2×#14582763C2semidirect
11. C2×#14582758C2semidirect
12. C2×#14582757C2semidirect
13. C2×C4×Dic43⋊C4C2semidirect
14. C2×C4×(C2×D43)⋊C4C2semidirect
15. C2×#14582746C2semidirect
16. C2×C43×#388C2semidirect
22. C2×(C22⋊D43)⋊C4C4semidirect
25. C2×#13063281C22semidirect
33. C2×C4⋊C4×D43C22semidirect
43. #14582792C22semidirect
44. #14582786C22semidirect
45. #14582780C22semidirect
48. #14582763C22semidirect
49. #14582758C22semidirect
50. #14582757C22semidirect
51. C4×Dic43⋊C4C22semidirect
52. C4×(C2×D43)⋊C4C22semidirect
53. #14582746C22semidirect
67. C43×#388C22semidirect
77. C23×Dic43C2×C4semidirect
98. (C22⋊D43)⋊C4C2×C4semidirect
105. C2×Dic43⋊C4C2×C4semidirect
106. C2×Dic43⋊C4D4semidirect
126. C2×C4×Dic43C2×C4semidirect
150. C2×C22⋊C4×C43C2×C4semidirect
224. C22×Dic43C22×C4semidirect
250. C22⋊C4×C43C22×C4semidirect
261. Dic43⋊C4C22×C4semidirect
262. Dic43⋊C4C2×D4semidirect
266. C4×Dic43C22×C4semidirect
299. C22×D43#117semidirect
390. C2×D43C2×#117semidirect
409. C2×#388D43semidirect
421. C2×C43#2352semidirect
462. #388C2×D43semidirect
483. C43C2×#2352semidirect
548. C2×C22⋊C4C4×D43semidirect
675. C22⋊C4C2×C4×D43semidirect
819. C2#19137523direct (N × H)

Maximal subgroups

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

subgroupindex
C22×(C22⋊D43)⋊C42
C22×#130632812
C22×C4⋊C4×D432
#191375232
C2×#145827922
C2×#145827862
C2×#145827802
C2×#145827752
C2×#145827632
C2×#145827582
C2×#145827572
C2×C4×Dic43⋊C42
C2×C4×(C2×D43)⋊C42
C2×#145827462
C2×C43×#3882
C2×#235243