Finite Group Databasebeta

← C2×#19138017 #25265004

Subgroups — C2×#19138017 #25265004

Order 11008.

3526 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×#13063302C211yesmaximal, characteristic, complemented
2C22×#13063302C211yesmaximal, characteristic, complemented
3C22×D4×Dic43C211yesmaximal, characteristic
4C22×#13063281C211yesmaximal, characteristic, complemented
5#19138017C2116yesmaximal, direct product factor
6C2×#14582827C211yesmaximal, characteristic, complemented
7C2×#14582824C211yesmaximal, characteristic, complemented
8C2×#14582813C211yesmaximal, characteristic
9C2×#14582803C211yesmaximal, characteristic, complemented
10C2×#14582798C211yesmaximal, characteristic, complemented
11C2×#14582796C211yesmaximal, characteristic, complemented
12C2×#14582794C211yesmaximal, characteristic, complemented
13C2×#14582792C211yesmaximal, characteristic, complemented
14C2×#14582787C211yesmaximal, characteristic, complemented
15C2×#14582757C211yesmaximal, characteristic, complemented
16C2×C43×#394C211yesmaximal, characteristic
17C23×Dic86C2211yescharacteristic
18C24×Dic43C2211yescharacteristic
19C24×Dic43C2211yescharacteristic
20C2×#13063302—28no—
21C2×#13063302—28no—
22C2×#13063302C2218yescomplemented
23C2×#13063302C2218yescomplemented
24C2×D4×Dic43—28no—
25C2×D4×Dic43C2218yes—
26C2×#13063281—28no—
27C2×#13063281C2218yescomplemented
28C22×C4⋊Dic43C2211yescharacteristic
29C22×C4⋊Dic43C2211yescharacteristic
30C22×C4⋊Dic43C2211yescharacteristic
31C22×Dic43⋊C4C2211yescharacteristic
32C22×Dic43⋊C4C2211yescharacteristic
33C22×Dic43⋊C4C2211yescharacteristic
34C22×Dic43⋊C4C2211yescharacteristic
35C22×Dic43⋊C4C2211yescharacteristic
36C22×Dic43⋊C4C2211yescharacteristic
37C22×C22⋊Dic43C2211yescharacteristic
38C22×C22⋊Dic43C2211yescharacteristic
39C22×C22⋊Dic43C2211yescharacteristic
40C22×C22⋊Dic43C2211yescharacteristic
41C22×C22⋊Dic43C2211yescharacteristic
42C22×C22⋊Dic43C2211yescharacteristic
43C22×C4×Dic43C2211yescharacteristic
44C22×C4×Dic43C2211yescharacteristic
45C22×C4×Dic43C2211yescharacteristic
46#14582827C2218yescomplemented
47#14582824C2218yescomplemented
48#14582813C2218yes—
49#14582803C2218yescomplemented
50#14582798C2218yescomplemented
51#14582796C2218yescomplemented
52#14582794C2218yescomplemented
53#14582792C2218yescomplemented
54#14582787C2218yescomplemented
55#14582757C2218yescomplemented
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2211yescharacteristic
61C2×C43⋊#95C2211yescharacteristic
62C2×C43⋊#95C2211yescharacteristic
63C23×D4×C43C2211yescharacteristic
64C22×C4⋊C4×C43C2211yescharacteristic
65C22×C22⋊C4×C43C2211yescharacteristic
66C22×C22⋊C4×C43C2211yescharacteristic
67C22×C22⋊C4×C43C2211yescharacteristic
68C22×C22⋊C4×C43C2211yescharacteristic
69C43×#394C2218yes—
70C2×#95×C43C2211yescharacteristic
71C22×Dic86—24no—
72C22×Dic86—24no—
73C22×Dic86—24no—
74C22×Dic86C2314yes—
75C23×Dic43—24no—
76C23×Dic43—24no—
77C23×Dic43—24no—
78C23×Dic43—24no—
79C23×Dic43—24no—
80C23×Dic43D418yes—
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2311yescharacteristic
85C23×Dic43C2311yescharacteristic
86C23×Dic43C2314yes—
87C23×Dic43C2311yescharacteristic
88C23×Dic43C2311yescharacteristic
89C23×Dic43C2314yes—
90C23×Dic43C2311yescharacteristic
91#13063302—232no—
92#13063302—232no—
93D4×Dic43—232no—
94#13063281—232no—
95C2×C4⋊Dic43—24no—
96C2×C4⋊Dic43—24no—
97C2×C4⋊Dic43—24no—
98C2×C4⋊Dic43C2314yes—
99C2×C4⋊Dic43C2314yes—
100C2×C4⋊Dic43C2314yes—
101C2×Dic43⋊C4—24no—
102C2×Dic43⋊C4—24no—
103C2×Dic43⋊C4—24no—
104C2×Dic43⋊C4—24no—
105C2×Dic43⋊C4—24no—
106C2×Dic43⋊C4D418yescomplemented
107C2×Dic43⋊C4C2314yes—
108C2×Dic43⋊C4C2314yes—
109C2×Dic43⋊C4C2314yes—
110C2×Dic43⋊C4C2314yes—
111C2×Dic43⋊C4C2314yes—
112C2×Dic43⋊C4C2314yes—
113C2×C22⋊Dic43—24no—
114C2×C22⋊Dic43—24no—
115C2×C22⋊Dic43—24no—
116C2×C22⋊Dic43—24no—
117C2×C22⋊Dic43—24no—
118C2×C22⋊Dic43—24no—
119C2×C22⋊Dic43C2314yes—
120C2×C22⋊Dic43C2314yes—
121C2×C22⋊Dic43C2314yes—
122C2×C22⋊Dic43C2314yes—
123C2×C22⋊Dic43C2314yes—
124C2×C22⋊Dic43C2314yes—
125C2×C4×Dic43—24no—
126C2×C4×Dic43—24no—
127C2×C4×Dic43—24no—
128C2×C4×Dic43C2314yes—
129C2×C4×Dic43C2314yes—
130C2×C4×Dic43C2314yes—
131C43⋊#95C2314yes—
132C43⋊#95C2314yes—
133C43⋊#95C2314yes—
134C43⋊#95C2314yes—
135C43⋊#95C2314yes—
136C43⋊#95C2314yes—
137C43⋊#95C2314yes—
138C25×C43C2311yescharacteristic
139C25×C43C2311yescharacteristic
140C22×D4×C43—24no—
141C22×D4×C43—24no—
142C22×D4×C43—24no—
143C22×D4×C43C2314yes—
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2311yescharacteristic
149C2×C4⋊C4×C43—24no—
150C2×C4⋊C4×C43C2314yes—
151C2×C22⋊C4×C43—24no—
152C2×C22⋊C4×C43—24no—
153C2×C22⋊C4×C43—24no—
154C2×C22⋊C4×C43—24no—
155C2×C22⋊C4×C43C2314yes—
156C2×C22⋊C4×C43C2314yes—
157C2×C22⋊C4×C43C2314yes—
158C2×C22⋊C4×C43C2314yes—
159#95×C43C2314yes—
160C24×C43—22no—
161C24×C43—22no—
162C24×C43—22no—
163C24×C43—22no—
164C24×C43—22no—
165C24×C43—22no—
166C24×C43—22no—
167C24×C43—22no—
168C24×C43—22no—
169C24×C43—22no—
170C24×C43—22no—
171C24×C43—22no—
172C24×C43C2×D414yes—
173C24×C43#4114yes—
174C24×C43C2412yes—
175C24×C43C2412yes—
176C24×C43C2411yescharacteristic
177C2×D4×C43—232no—
178C2×D4×C43—28no—
179C2×D4×C43—28no—
180C2×D4×C43—28no—
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—22no—
191C22×C4×C43—22no—
192C22×C4×C43—22no—
193C22×C4×C43—22no—
194C22×C4×C43C2×D414yes—
195C22×C4×C43#4114yes—
196C22×C4×C43C2412yes—
197C22×C4×C43C2412yes—
198C22×C4×C43C2412yes—
199C22×C4×C43C2412yes—
200C22×C4×C43C2412yes—
201C22×Dic43—232no—
202C22×Dic43—28no—
203C22×Dic43—28no—
204C22×Dic43—28no—
205C22×Dic43—28no—
206C22×Dic43—28no—
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×Dic43—22no—
225C22×Dic43—22no—
226C22×Dic43—416no—
227C22×Dic43C2×D414yes—
228C22×Dic43C2×D414yes—
229C22×Dic43C2×D4116yes—
230C22×Dic43C2×D414yes—
231C22×Dic43C2×D414yes—
232C22×Dic43#4114yes—
233C22×Dic43C2412yes—
234C22×Dic43C2412yes—
235C22×Dic43C2412yes—
236C22×Dic43C2412yes—
237C22×Dic43C2412yes—
238C22×Dic43C2412yes—
239C22×Dic43C2412yes—
240C22×Dic43C2412yes—
241C2×Dic86—28no—
242C2×Dic86—28no—
243C2×Dic86—28no—
244C2×Dic86—416no—
245C4⋊C4×C43—28no—
246C22⋊C4×C43—28no—
247C22⋊C4×C43—28no—
248C22⋊C4×C43—28no—
249C22⋊C4×C43—28no—
250C22⋊Dic43—28no—
251C22⋊Dic43—28no—
252C22⋊Dic43—28no—
253C22⋊Dic43—28no—
254C22⋊Dic43—28no—
255C22⋊Dic43—28no—
256C4⋊Dic43—28no—
257C4⋊Dic43—28no—
258C4⋊Dic43—28no—
259Dic43⋊C4—28no—
260Dic43⋊C4—28no—
261Dic43⋊C4—28no—
262Dic43⋊C4—28no—
263Dic43⋊C4—28no—
264Dic43⋊C4C2×D4116yescomplemented
265C4×Dic43—28no—
266C4×Dic43—28no—
267C4×Dic43—28no—
268C23×C43—28no—
269C23×C43—28no—
270C23×C43—28no—
271C23×C43—28no—
272C23×C43—28no—
273C23×C43—28no—
274C23×C43—22no—
275C23×C43—22no—
276C23×C43—22no—
277C23×C43—22no—
278C23×C43—22no—
279C23×C43—22no—
280C23×C43—22no—
281C23×C43—22no—
282C23×C43—22no—
283C23×C43—22no—
284C23×C43—22no—
285C23×C43—22no—
286C23×C43—44no—
287C23×C43—44no—
288C23×C43—44no—
289C23×C43—44no—
290C23×C43—44no—
291C23×C43—44no—
292C23×C43—44no—
293C23×C43—44no—
294C23×C43C22×D414yes—
295C23×C43C22×D412yes—
296C23×C43C22×D412yes—
297C23×C43C2×#4112yes—
298C23×C43C2×#4114yes—
299C23×C43C2×#4112yes—
300C23×C43C2×#4112yes—
301C23×C432−1+412yes—
302C23×C432−1+412yes—
303C23×C43C2511yescharacteristic
304D4×C43—232no—
305C2×C4×C43—28no—
306C2×C4×C43—28no—
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—44no—
321C2×C4×C43—44no—
322C2×C4×C43—44no—
323C2×C4×C43C22×D414yes—
324C2×C4×C43C2×#4114yes—
325C2×Dic43—28no—
326C2×Dic43—28no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—232no—
332C2×Dic43—22no—
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—44no—
348C2×Dic43—44no—
349C2×Dic43—44no—
350C2×Dic43—44no—
351C2×Dic43—44no—
352C2×Dic43—416no—
353C2×Dic43#121116yes—
354C2×Dic43C22×D414yes—
355C2×Dic43C22×D414yes—
356C2×Dic43C22×D414yes—
357C2×Dic43C22×D414yes—
358C2×Dic43C2×#4114yes—
359Dic86—416no—
360C2×#2415—431nomaximal, Sylow
361C22×C43—24no—
362C22×C43—24no—
363C22×C43—24no—
364C22×C43—24no—
365C22×C43—24no—
366C22×C43—24no—
367C22×C43—42no—
368C22×C43—416no—
369C22×C43—416no—
370C22×C43—42no—
371C22×C43—42no—
372C22×C43—42no—
373C22×C43—42no—
374C22×C43—42no—
375C22×C43—42no—
376C22×C43—42no—
377C22×C43C2×#12114yes—
378C22×C43#52514yes—
379C22×C43#53614yes—
380C22×C43#54714yes—
381C22×C43#54814yes—
382C22×C43#55214yes—
383C22×C43#55614yes—
384C22×C43C23×D411yescharacteristic
385C22×C43C23×D411yescharacteristic
386C22×C43C22×#4111yescharacteristic
387C22×C43C22×#4111yescharacteristic
388C22×C43C22×#4111yescharacteristic
389C22×C43C2×2−1+411yescharacteristic
390C22×C43C2×2−1+411yescharacteristic
391C4×C43—24no—
392C4×C43—24no—
393C4×C43—42no—
394C4×C43—42no—
395C4×C43—42no—
396Dic43—24no—
397Dic43—24no—
398Dic43—42no—
399Dic43—42no—
400Dic43—42no—
401Dic43—42no—
402Dic43—42no—
403Dic43C2×#12118yes—
404C22×C22⋊Q8—431no—
405C22×C22⋊Q8—431no—
406C22×C4×D4—431no—
407C22×#117—431no—
408#2415—4316no—
409C2×#397—431no—
410C2×#397—431no—
411C2×#394—431no—
412C2×#394D4311yescharacteristic
413C2×#391—431no—
414C2×#389—431no—
415C2×#389—431no—
416C2×#389—431no—
417C2×#388—431no—
418C2×#388—431no—
419C2×#380—431no—
420C2×C43—44no—
421C2×C43—44no—
422C2×C43#241518yescomplemented
423C2×C43C22×#12111yescharacteristic
424C2×C43C2×#52511yescharacteristic
425C2×C43C2×#53611yescharacteristic
426C2×C43C2×#54711yescharacteristic
427C2×C43C2×#54811yescharacteristic
428C2×C43C2×#55211yescharacteristic
429C2×C43C2×#55611yescharacteristic
430C23×Q8—431no—
431C23×D4C2×D4311yescharacteristic
432C24×C4—431no—
433C24×C4—431no—
434C2×C22⋊Q8—438no—
435C2×C22⋊Q8—438no—
436C2×C22⋊Q8—868no—
437C2×C22⋊Q8—868no—
438C2×C4×D4—438no—
439C2×C4×D4—868no—
440C2×#117—438no—
441C2×#117—868no—
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×C4⋊C4—431no—
449C22×C4⋊C4—431no—
450C22×C4⋊C4—431no—
451C22×C4⋊C4C2×D4311yescharacteristic
452C22×C22⋊C4—431no—
453C22×C22⋊C4—431no—
454C22×C22⋊C4—431no—
455C22×C22⋊C4—431no—
456C22×C22⋊C4—431no—
457C22×C22⋊C4—431no—
458C22×C22⋊C4C2×D4311yescharacteristic
459C22×C22⋊C4C2×D4311yescharacteristic
460C22×C22⋊C4C2×D4311yescharacteristic
461C22×C22⋊C4C2×D4311yescharacteristic
462C22×C42—431no—
463C22×C42—431no—
464C22×C42—431no—
465#397—438no—
466#397—438no—
467#394—438no—
468#394C2×D4318yes—
469#391—438no—
470#389—438no—
471#389—438no—
472#389—438no—
473#388—438no—
474#388—438no—
475#380—438no—
476C2×#95—431no—
477C2×#95—431no—
478C2×#95—431no—
479C2×#95—431no—
480C2×#95—431no—
481C2×#95—431no—
482C2×#95—431no—
483C2×#95C2×D4311yescharacteristic
484C43C2×#241511yescharacteristic, complemented, Sylow
485C25C22×D4311yescharacteristic
486C25C22×D4311yescharacteristic
487C22×Q8—434no—
488C22×Q8—864no—
489C22×Q8—864no—
490C22×Q8—864no—
491C22×D4—24no—
492C22×D4—24no—
493C22×D4—24no—
494C22×D4C22×D4314yes—
495C23×C4—431no—
496C23×C4—438no—
497C23×C4—434no—
498C23×C4—431no—
499C23×C4—431no—
500C23×C4—434no—
501C23×C4—431no—
502C23×C4—431no—
503C23×C4—431no—
504C23×C4—431no—
505C23×C4—431no—
506C23×C4—864no—
507C23×C4—864no—
508C23×C4—864no—
509C23×C4—864no—
510C23×C4—864no—
511C23×C4C22×D4311yescharacteristic
512C23×C4C22×D4311yescharacteristic
513C23×C4C22×D4311yescharacteristic
514C23×C4C22×D4311yescharacteristic
515C23×C4C22×D4311yescharacteristic
516C22⋊Q8—8632no—
517C22⋊Q8—8632no—
518C4×D4—8632no—
519#117—8632no—
520C2×C4⋊C4—24no—
521C2×C4⋊C4—438no—
522C2×C4⋊C4—434no—
523C2×C4⋊C4—434no—
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—864no—
536C2×C4⋊C4—864no—
537C2×C4⋊C4—864no—
538C2×C4⋊C4—864no—
539C2×C4⋊C4C22×D4314yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—434no—
545C2×C22⋊C4—434no—
546C2×C22⋊C4—434no—
547C2×C22⋊C4—434no—
548C2×C22⋊C4—434no—
549C2×C22⋊C4—434no—
550C2×C22⋊C4—864no—
551C2×C22⋊C4—864no—
552C2×C22⋊C4—864no—
553C2×C22⋊C4—864no—
554C2×C22⋊C4—864no—
555C2×C22⋊C4—864no—
556C2×C22⋊C4C22×D4314yes—
557C2×C22⋊C4C22×D4314yes—
558C2×C22⋊C4C22×D4314yes—
559C2×C22⋊C4C22×D4314yes—
560C2×C42—434no—
561C2×C42—434no—
562C2×C42—434no—
563C2×C42—864no—
564C2×C42—864no—
565C2×C42—864no—
566#95—434no—
567#95—434no—
568#95—434no—
569#95—434no—
570#95—434no—
571#95—434no—
572#95—434no—
573#95C22×D4314yes—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24D4×D4314yes—
587C24#1062190014yes—
588C24C23×D4312yes—
589C24C23×D4312yes—
590C24C23×D4311yescharacteristic
591C2×Q8—868no—
592C2×Q8—868no—
593C2×Q8—868no—
594C2×Q8—17216no—
595C2×D4—232no—
596C2×D4—28no—
597C2×D4—28no—
598C2×D4—28no—
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—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—434no—
613C22×C4—434no—
614C22×C4—434no—
615C22×C4—432no—
616C22×C4—434no—
617C22×C4—434no—
618C22×C4—4316no—
619C22×C4—432no—
620C22×C4—432no—
621C22×C4—432no—
622C22×C4—432no—
623C22×C4—432no—
624C22×C4—432no—
625C22×C4—432no—
626C22×C4—868no—
627C22×C4—8632no—
628C22×C4—868no—
629C22×C4—868no—
630C22×C4—868no—
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—862no—
648C22×C4—862no—
649C22×C4—862no—
650C22×C4—862no—
651C22×C4—17216no—
652C22×C4D4×D4314yes—
653C22×C4#1062190014yes—
654C22×C4C23×D4312yes—
655C22×C4C23×D4312yes—
656C22×C4C23×D4312yes—
657C22×C4C23×D4312yes—
658C22×C4C23×D4312yes—
659C4⋊C4—28no—
660C4⋊C4—4316no—
661C4⋊C4—868no—
662C4⋊C4—868no—
663C4⋊C4—868no—
664C4⋊C4—868no—
665C4⋊C4—868no—
666C4⋊C4—868no—
667C4⋊C4—868no—
668C4⋊C4—868no—
669C22⋊C4—28no—
670C22⋊C4—28no—
671C22⋊C4—28no—
672C22⋊C4—28no—
673C22⋊C4—868no—
674C22⋊C4—868no—
675C22⋊C4—868no—
676C22⋊C4—868no—
677C22⋊C4—868no—
678C22⋊C4—868no—
679C42—868no—
680C42—868no—
681C42—868no—
682C23—28no—
683C23—28no—
684C23—28no—
685C23—28no—
686C23—28no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—28no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23C2×D4×D4314yes—
709C23C2×D4×D4312yes—
710C23C2×D4×D4312yes—
711C23#41×D4312yes—
712C23C2×#1062190014yes—
713C23C2×#1062190012yes—
714C23C2×#1062190012yes—
715C23#1306337212yes—
716C23#1306337212yes—
717C23C24×D4311yescharacteristic
718Q8—17216no—
719D4—232no—
720C2×C4—28no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—28no—
726C2×C4—22no—
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—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—4316no—
739C2×C4—434no—
740C2×C4—434no—
741C2×C4—434no—
742C2×C4—434no—
743C2×C4—434no—
744C2×C4—8632no—
745C2×C4—868no—
746C2×C4—862no—
747C2×C4—862no—
748C2×C4—862no—
749C2×C4—862no—
750C2×C4—868no—
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—862no—
765C2×C4—862no—
766C2×C4—17216no—
767C2×C4—1724no—
768C2×C4—1724no—
769C2×C4—1724no—
770C2×C4—1724no—
771C2×C4—1724no—
772C2×C4C2×D4×D4314yes—
773C2×C4C2×#1062190014yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—416no—
789C22—416no—
790C22#121×D4314yes—
791C22#1458340514yes—
792C22#1458347114yes—
793C22#1458354914yes—
794C22#1458355514yes—
795C22#1458358614yes—
796C22#1458361814yes—
797C22C22×D4×D4311yescharacteristic
798C22C22×D4×D4311yescharacteristic
799C22C2×#41×D4311yescharacteristic
800C22C22×#1062190011yescharacteristic
801C22C22×#1062190011yescharacteristic
802C22C2×#1306337211yescharacteristic
803C22C2×#1306337211yescharacteristic
804C4—24no—
805C4—24no—
806C4—42no—
807C4—42no—
808C4—42no—
809C4—438no—
810C4—864no—
811C4—864no—
812C4—1722no—
813C4—1722no—
814C4—1722no—
815C4—1722no—
816C4—1722no—
817C2—44no—
818C2—44no—
819C2#1913801718yesdirect product factor
820C2C2×#121×D4311yescharacteristic
821C2C2×#1458340511yescharacteristic
822C2C2×#1458347111yescharacteristic
823C2C2×#1458354911yescharacteristic
824C2C2×#1458355511yescharacteristic
825C2C2×#1458358611yescharacteristic
826C2C2×#1458361811yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#394C2
socleC24×C43C24
prime radicalC23×D4×C43C22
hypercenterC2×#394D43
hypocenterC43C2×#2415
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#13063302C2semidirect
2. C22×#13063302C2semidirect
4. C22×#13063281C2semidirect
5. #19138017C2direct (N × H)
6. C2×#14582827C2semidirect
7. C2×#14582824C2semidirect
9. C2×#14582803C2semidirect
10. C2×#14582798C2semidirect
11. C2×#14582796C2semidirect
12. C2×#14582794C2semidirect
13. C2×#14582792C2semidirect
14. C2×#14582787C2semidirect
15. C2×#14582757C2semidirect
22. C2×#13063302C22semidirect
23. C2×#13063302C22semidirect
27. C2×#13063281C22semidirect
46. #14582827C22semidirect
47. #14582824C22semidirect
49. #14582803C22semidirect
50. #14582798C22semidirect
51. #14582796C22semidirect
52. #14582794C22semidirect
53. #14582792C22semidirect
54. #14582787C22semidirect
55. #14582757C22semidirect
106. C2×Dic43⋊C4D4semidirect
264. Dic43⋊C4C2×D4semidirect
422. C2×C43#2415semidirect
484. C43C2×#2415semidirect
819. C2#19138017direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633022
C22×D4×Dic432
C22×#130632812
#191380172
C2×#145828272
C2×#145828242
C2×#145828132
C2×#145828032
C2×#145827982
C2×#145827962
C2×#145827942
C2×#145827922
C2×#145827872
C2×#145827572
C2×C43×#3942
C2×#241543