Finite Group Databasebeta

← C2×#19137588 #25256101

Subgroups — C2×#19137588 #25256101

Order 11008.

3830 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×#13063282C211yesmaximal, characteristic, complemented
4#19137588C2116yesmaximal, direct product factor
5C2×#14582797C211yesmaximal, characteristic, complemented
6C2×#14582792C211yesmaximal, characteristic, complemented
7C2×#14582787C211yesmaximal, characteristic, complemented
8C2×#14582783C211yesmaximal, characteristic, complemented
9C2×#14582782C211yesmaximal, characteristic, complemented
10C2×#14582775C211yesmaximal, characteristic
11C2×#14582773C211yesmaximal, characteristic, complemented
12C2×#14582772C211yesmaximal, characteristic, complemented
13C2×#14582750C211yesmaximal, characteristic, complemented
14C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
15C2×#95×D43C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
17C23×C22⋊D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C2×#13063307C4116yescomplemented
22C2×#13063307C2218yes—
23C2×C4×C22⋊D43—28no—
24C2×C4×C22⋊D43C2218yes—
25C2×#13063282—28no—
26C2×#13063282C2218yescomplemented
27C22×C4⋊Dic43C2211yescharacteristic
28C22×C4⋊Dic43C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×Dic43⋊C4C2211yescharacteristic
31C22×Dic43⋊C4C2211yescharacteristic
32C22×Dic43⋊C4C2211yescharacteristic
33C22×Dic43⋊C4C2211yescharacteristic
34C22×C22⋊Dic43C2211yescharacteristic
35C22×C22⋊Dic43C2211yescharacteristic
36C22×C22⋊Dic43C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C22×(C2×D43)⋊C4C2211yescharacteristic
39C22×(C2×D43)⋊C4C2211yescharacteristic
40C22×C4×Dic43C2211yescharacteristic
41C22×C4×Dic43C2211yescharacteristic
42C22×C4×Dic43C2211yescharacteristic
43#14582797C2218yescomplemented
44#14582792C2218yescomplemented
45#14582787C2218yescomplemented
46#14582783C2218yescomplemented
47#14582782C2218yescomplemented
48#14582775C2218yes—
49#14582773C2218yescomplemented
50#14582772C2218yescomplemented
51#14582750C2218yescomplemented
52C4×(C2×D43)⋊C4C2218yescomplemented
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2211yescharacteristic
61#95×D43C2218yescomplemented
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—42no—
89C22×C4×D43—42no—
90C22×C4×D43C2×C418yescomplemented
91C22×C4×D43C2314yes—
92C22×C4×D43C2314yes—
93C22×C4×D43C2314yes—
94#13063307C2×C4164yescomplemented
95C4×C22⋊D43—232no—
96#13063282—232no—
97C2×C4⋊Dic43—42no—
98C2×C4⋊Dic43C2×C418yescomplemented
99C2×C4⋊Dic43C2314yes—
100C2×C4⋊Dic43C2314yes—
101C2×Dic43⋊C4—24no—
102C2×Dic43⋊C4—24no—
103C2×Dic43⋊C4—24no—
104C2×Dic43⋊C4—24no—
105C2×Dic43⋊C4C2×C418yescomplemented
106C2×Dic43⋊C4C2314yes—
107C2×Dic43⋊C4C2314yes—
108C2×Dic43⋊C4C2314yes—
109C2×Dic43⋊C4C2314yes—
110C2×Dic43⋊C4C2314yes—
111C2×C22⋊Dic43—24no—
112C2×C22⋊Dic43—42no—
113C2×C22⋊Dic43C2×C418yescomplemented
114C2×C22⋊Dic43C2314yes—
115C2×C22⋊Dic43C2314yes—
116C2×C22⋊Dic43C2314yes—
117C2×(C2×D43)⋊C4—24no—
118C2×(C2×D43)⋊C4C2×C418yescomplemented
119C2×(C2×D43)⋊C4D418yes—
120C2×(C2×D43)⋊C4C2314yes—
121C2×(C2×D43)⋊C4C2314yes—
122C2×(C2×D43)⋊C4C2314yes—
123C2×C4×Dic43—24no—
124C2×C4×Dic43—24no—
125C2×C4×Dic43—24no—
126C2×C4×Dic43C2314yes—
127C2×C4×Dic43C2314yes—
128C2×C4×Dic43C2314yes—
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—42no—
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2314yes—
143C23×C4×C43C2311yescharacteristic
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—42no—
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—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×C43—44no—
191C22×C4×C43—416no—
192C22×C4×C43C22×C414yes—
193C22×C4×C43C22×C414yes—
194C22×C4×C43C2×D414yes—
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×Dic43—22no—
224C22×Dic43C22×C414yes—
225C22×Dic43C22×C414yes—
226C22×Dic43C22×C414yes—
227C22×Dic43C2×D414yes—
228C22×Dic43C2412yes—
229C22×Dic43C2412yes—
230C22×Dic43C2412yes—
231C22×Dic43C2412yes—
232C22×Dic43C2412yes—
233C22×Dic43C2412yes—
234C22×Dic43C2412yes—
235C2×C4×D43—28no—
236C2×C4×D43—28no—
237C2×C4×D43—232no—
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×C4116yescomplemented
247C22⋊C4×C43—28no—
248C22⋊C4×C43C22×C4116yescomplemented
249C42×C43—28no—
250C42×C43—44no—
251C22⋊Dic43—28no—
252C22⋊Dic43—44no—
253C22⋊Dic43C22×C4116yescomplemented
254(C2×D43)⋊C4—28no—
255(C2×D43)⋊C4C22×C4116yescomplemented
256(C2×D43)⋊C4C2×D4116yes—
257C4⋊Dic43—44no—
258C4⋊Dic43C22×C4116yescomplemented
259Dic43⋊C4—28no—
260Dic43⋊C4—28no—
261Dic43⋊C4—28no—
262Dic43⋊C4—28no—
263Dic43⋊C4C22×C4116yescomplemented
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×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×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—28no—
307C2×C4×C43—28no—
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—416no—
322C2×C4×C43—44no—
323C2×C4×C43C23×C414yes—
324C2×C4×C43C23×C414yes—
325C2×C4×C43C22×D414yes—
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—22no—
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×Dic43—44no—
353C2×Dic43C23×C414yes—
354C2×Dic43C23×C414yes—
355C2×Dic43C23×C414yes—
356C2×Dic43C22×D414yes—
357C4×D43—232no—
358C4×D43—416no—
359C4×D43—416no—
360C2×#2359—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×C4×D414yes—
370C22×C43C4×#4114yes—
371C22×C43#52014yes—
372C22×C43#54614yes—
373C22×C43#54714yes—
374C22×C43#55114yes—
375C22×C43#55214yes—
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×C4×D418yes—
391C4×C43—24no—
392C4×C43—24no—
393C4×C43—24no—
394C4×C43—24no—
395C4×C43—24no—
396C4×C43—42no—
397Dic43—24no—
398Dic43—24no—
399Dic43—24no—
400Dic43—24no—
401Dic43—42no—
402Dic43—42no—
403Dic43—42no—
404C22×#123—431no—
405C22×C4×D4—431no—
406C22×#117—431no—
407#2359—4316no—
408C2×#389—431no—
409C2×#388—431no—
410C2×#388—431no—
411C2×#387—431no—
412C2×#387—431no—
413C2×#386—431no—
414C2×#385—431no—
415C2×#385—431no—
416C2×C4×C4⋊C4—431no—
417C2×C4×C22⋊C4—431no—
418C2×C4×C22⋊C4D4311yescharacteristic, complemented
419C22×#95—431no—
420C2×C43—44no—
421C2×C43#235918yescomplemented
422C2×C43C22×C4×D411yescharacteristic
423C2×C43C2×C4×#4111yescharacteristic
424C2×C43C2×#52011yescharacteristic
425C2×C43C2×#54611yescharacteristic
426C2×C43C2×#54711yescharacteristic
427C2×C43C2×#55111yescharacteristic
428C2×C43C2×#55211yescharacteristic
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—
439C2×#117—438no—
440C2×#117—868no—
441C22×C4⋊C4—431no—
442C22×C4⋊C4—431no—
443C22×C4⋊C4—431no—
444C22×C4⋊C4—431no—
445C22×C4⋊C4—431no—
446C22×C4⋊C4—431no—
447C22×C4⋊C4—431no—
448C22×C22⋊C4—431no—
449C22×C22⋊C4—431no—
450C22×C22⋊C4—431no—
451C22×C22⋊C4—431no—
452C22×C22⋊C4—431no—
453C22×C22⋊C4—431no—
454C22×C22⋊C4C2×D4311yescharacteristic
455C22×C22⋊C4C2×D4311yescharacteristic
456C22×C42—431no—
457C22×C42—431no—
458C22×C42—431no—
459C22×C42C2×D4311yescharacteristic
460C22×C42C2×D4311yescharacteristic
461#389—438no—
462#388—438no—
463#388—438no—
464#387—438no—
465#387—438no—
466#386—438no—
467#385—438no—
468#385—438no—
469C4×C4⋊C4—438no—
470C4×C22⋊C4—438no—
471C4×C22⋊C4C2×D4318yescomplemented
472C2×#95—431no—
473C2×#95—431no—
474C2×#95—431no—
475C2×#95—431no—
476C2×#95—431no—
477C2×#95—431no—
478C2×#95—431no—
479C2×#95—431no—
480C2×#95—438no—
481C2×#95C2×D4311yescharacteristic
482C2×#95C2×D4311yescharacteristic
483C43C2×#235911yescharacteristic, 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—42no—
493C23×C4—431no—
494C23×C4—431no—
495C23×C4—431no—
496C23×C4—431no—
497C23×C4—438no—
498C23×C4—434no—
499C23×C4—431no—
500C23×C4—431no—
501C23×C4—431no—
502C23×C4—434no—
503C23×C4—434no—
504C23×C4—864no—
505C23×C4—864no—
506C23×C4—864no—
507C23×C4—864no—
508C23×C4—864no—
509C23×C4—864no—
510C23×C4—1722no—
511C23×C4—1722no—
512C23×C4C22×D4311yescharacteristic
513C23×C4C22×D4314yes—
514C23×C4C22×D4311yescharacteristic
515C23×C4C22×D4311yescharacteristic
516C23×C4C22×D4311yescharacteristic
517C23×C4C22×D4311yescharacteristic
518C23×C4C22×D4311yescharacteristic
519#123—4364no—
520C4×D4—8632no—
521#117—8632no—
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—434no—
531C2×C4⋊C4—864no—
532C2×C4⋊C4—864no—
533C2×C4⋊C4—864no—
534C2×C4⋊C4—864no—
535C2×C4⋊C4—1722no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—438no—
538C2×C22⋊C4—434no—
539C2×C22⋊C4—438no—
540C2×C22⋊C4—438no—
541C2×C22⋊C4—434no—
542C2×C22⋊C4—434no—
543C2×C22⋊C4—434no—
544C2×C22⋊C4—434no—
545C2×C22⋊C4—434no—
546C2×C22⋊C4—864no—
547C2×C22⋊C4—864no—
548C2×C22⋊C4—1722no—
549C2×C22⋊C4C4×D4318yescomplemented
550C2×C22⋊C4C22×D4314yes—
551C2×C22⋊C4C22×D4314yes—
552C2×C42—24no—
553C2×C42—42no—
554C2×C42—434no—
555C2×C42—434no—
556C2×C42—434no—
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—22no—
606C22×C4—28no—
607C22×C4—28no—
608C22×C4—44no—
609C22×C4—416no—
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—4316no—
619C22×C4—432no—
620C22×C4—432no—
621C22×C4—432no—
622C22×C4—868no—
623C22×C4—8632no—
624C22×C4—868no—
625C22×C4—868no—
626C22×C4—868no—
627C22×C4—862no—
628C22×C4—862no—
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—862no—
640C22×C4—862no—
641C22×C4—862no—
642C22×C4—862no—
643C22×C4—862no—
644C22×C4—868no—
645C22×C4—868no—
646C22×C4—1724no—
647C22×C4—1724no—
648C22×C4—17216no—
649C22×C4—17216no—
650C22×C4C2×C4×D4314yes—
651C22×C4C2×C4×D4314yes—
652C22×C4#1062189814yes—
653C22×C4#1062189814yes—
654C22×C4D4×D4314yes—
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—
666C4⋊C4—868no—
667C4⋊C4—1724no—
668C22⋊C4—28no—
669C22⋊C4—4316no—
670C22⋊C4—4316no—
671C22⋊C4—4316no—
672C22⋊C4—868no—
673C22⋊C4—868no—
674C22⋊C4—1724no—
675C22⋊C4C2×C4×D43116yescomplemented
676C42—28no—
677C42—44no—
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—862no—
704C23—862no—
705C23—862no—
706C23—862no—
707C23—868no—
708C23C22×C4×D4314yes—
709C23C22×C4×D4312yes—
710C23C2×D4×D4312yes—
711C23#41×D4312yes—
712C23C2×#1062189812yes—
713C23C2×#1062189812yes—
714C23#1306337012yes—
715C23#1306337212yes—
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—28no—
732C2×C4—28no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—416no—
737C2×C4—44no—
738C2×C4—434no—
739C2×C4—434no—
740C2×C4—434no—
741C2×C4—434no—
742C2×C4—8632no—
743C2×C4—868no—
744C2×C4—868no—
745C2×C4—868no—
746C2×C4—868no—
747C2×C4—862no—
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—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—17216no—
765C2×C4—17216no—
766C2×C4—1724no—
767C2×C4—1724no—
768C2×C4—1724no—
769C2×C4C22×C4×D4314yes—
770C2×C4C22×C4×D4314yes—
771C2×C4C2×D4×D4314yes—
772C2×C4C2×#1062189814yes—
773C2×C4C2×#1062189814yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—42no—
778C22—42no—
779C22—416no—
780C22—42no—
781C22—42no—
782C22—438no—
783C22—864no—
784C22—864no—
785C22—864no—
786C22—8632no—
787C22—864no—
788C22—864no—
789C22—864no—
790C22C4×D4×D4314yes—
791C22C4×#1062189814yes—
792C22#1458337814yes—
793C22#1458353914yes—
794C22#1458355414yes—
795C22#1458357814yes—
796C22#1458358814yes—
797C22C23×C4×D4311yescharacteristic
798C22C22×D4×D4311yescharacteristic
799C22C2×#41×D4311yescharacteristic
800C22C22×#1062189811yescharacteristic
801C22C22×#1062189811yescharacteristic
802C22C2×#1306337011yescharacteristic
803C22C2×#1306337211yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—24no—
808C4—24no—
809C4—42no—
810C4—864no—
811C4—864no—
812C4—864no—
813C4—864no—
814C4—1722no—
815C4—1722no—
816C4—1722no—
817C2—44no—
818C2—868no—
819C2#1913758818yesdirect product factor
820C2C2×C4×D4×D4311yescharacteristic
821C2C2×C4×#1062189811yescharacteristic
822C2C2×#1458337811yescharacteristic
823C2C2×#1458353911yescharacteristic
824C2C2×#1458355411yescharacteristic
825C2C2×#1458357811yescharacteristic
826C2C2×#1458358811yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C4×C22⋊C4×C43C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
cosocleC23×C43C25
hypercenterC2×C4×C22⋊C4D43
hypocenterC43C2×#2359
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×#13063282C2semidirect
4. #19137588C2direct (N × H)
5. C2×#14582797C2semidirect
6. C2×#14582792C2semidirect
7. C2×#14582787C2semidirect
8. C2×#14582783C2semidirect
9. C2×#14582782C2semidirect
11. C2×#14582773C2semidirect
12. C2×#14582772C2semidirect
13. C2×#14582750C2semidirect
14. C2×C4×(C2×D43)⋊C4C2semidirect
15. C2×#95×D43C2semidirect
16. C2×C4×C22⋊C4×C43C2semidirect
21. C2×#13063307C4semidirect
26. C2×#13063282C22semidirect
43. #14582797C22semidirect
44. #14582792C22semidirect
45. #14582787C22semidirect
46. #14582783C22semidirect
47. #14582782C22semidirect
49. #14582773C22semidirect
50. #14582772C22semidirect
51. #14582750C22semidirect
52. C4×(C2×D43)⋊C4C22semidirect
61. #95×D43C22semidirect
67. C4×C22⋊C4×C43C22semidirect
90. C22×C4×D43C2×C4semidirect
94. #13063307C2×C4semidirect
98. C2×C4⋊Dic43C2×C4semidirect
105. C2×Dic43⋊C4C2×C4semidirect
113. C2×C22⋊Dic43C2×C4semidirect
118. C2×(C2×D43)⋊C4C2×C4semidirect
149. C2×C22⋊C4×C43C2×C4semidirect
246. C2×C4×D43C22×C4semidirect
248. C22⋊C4×C43C22×C4semidirect
253. C22⋊Dic43C22×C4semidirect
255. (C2×D43)⋊C4C22×C4semidirect
258. C4⋊Dic43C22×C4semidirect
263. Dic43⋊C4C22×C4semidirect
418. C2×C4×C22⋊C4D43semidirect
421. C2×C43#2359semidirect
471. C4×C22⋊C4C2×D43semidirect
483. C43C2×#2359semidirect
549. C2×C22⋊C4C4×D43semidirect
675. C22⋊C4C2×C4×D43semidirect
819. C2#19137588direct (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×#130632822
#191375882
C2×#145827972
C2×#145827922
C2×#145827872
C2×#145827832
C2×#145827822
C2×#145827752
C2×#145827732
C2×#145827722
C2×#145827502
C2×C4×(C2×D43)⋊C42
C2×#95×D432
C2×C4×C22⋊C4×C432
C2×#235943