Finite Group Databasebeta

← C2×#19139012 #25265709

Subgroups — C2×#19139012 #25265709

Order 11008.

2574 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063320C211yesmaximal, characteristic
2C22×#13063320C211yesmaximal, characteristic
3#19139012C2116yesmaximal, direct product factor
4C2×#14582839C211yesmaximal, characteristic, complemented
5C2×#14582828C211yesmaximal, characteristic
6C2×#14582828C211yesmaximal, characteristic
7C2×#14582796C211yesmaximal, characteristic, complemented
8C2×#14582794C211yesmaximal, characteristic, complemented
9C2×#14582786C211yesmaximal, characteristic, complemented
10C2×#14582781C211yesmaximal, characteristic, complemented
11C2×#14582768C211yesmaximal, characteristic, complemented
12C2×#14582758C211yesmaximal, characteristic
13C2×#14582758C211yesmaximal, characteristic
14C2×#14582750C211yesmaximal, characteristic, complemented
15C2×#14582746C211yesmaximal, characteristic
16C2×C43×#400C211yesmaximal, characteristic, complemented
17C23×C4×D43C2211yescharacteristic
18C2×#13063320—28no—
19C2×#13063320—28no—
20C2×#13063320C2218yes—
21C2×#13063320C2218yes—
22C22×C4⋊Dic43C2211yescharacteristic
23C22×C4⋊Dic43C2211yescharacteristic
24C22×Dic43⋊C4C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×Dic43⋊C4C2211yescharacteristic
31C22×Dic43⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C22×C4×Dic43C2211yescharacteristic
39C22×C4×Dic43C2211yescharacteristic
40C22×C4×Dic43C2211yescharacteristic
41C22×C4×Dic43C2211yescharacteristic
42#14582839C2218yescomplemented
43#14582828C2218yes—
44#14582828C2218yes—
45#14582796C2218yescomplemented
46#14582794C2218yescomplemented
47#14582786C2218yescomplemented
48#14582781C2218yescomplemented
49#14582768C2218yescomplemented
50#14582758C2218yes—
51#14582758C2218yes—
52#14582750C2218yescomplemented
53#14582746C2218yes—
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2211yescharacteristic
61C22×C4⋊C4×C43C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C43×#400C2218yescomplemented
64C2×#95×C43C2211yescharacteristic
65C2×#95×C43C2211yescharacteristic
66C2×#95×C43C2211yescharacteristic
67C2×#95×C43C2211yescharacteristic
68C2×#95×C43C2211yescharacteristic
69C24×D43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C22×C4×D43—24no—
78C22×C4×D43—24no—
79C22×C4×D43—24no—
80C22×C4×D43C2314yes—
81#13063320—232no—
82#13063320—232no—
83C2×C4⋊Dic43—24no—
84C2×C4⋊Dic43—24no—
85C2×C4⋊Dic43C2314yes—
86C2×C4⋊Dic43C2314yes—
87C2×Dic43⋊C4—24no—
88C2×Dic43⋊C4—24no—
89C2×Dic43⋊C4—24no—
90C2×Dic43⋊C4—24no—
91C2×Dic43⋊C4—24no—
92C2×Dic43⋊C4—24no—
93C2×Dic43⋊C4—24no—
94C2×Dic43⋊C4—24no—
95C2×Dic43⋊C4C2314yes—
96C2×Dic43⋊C4C2314yes—
97C2×Dic43⋊C4C2314yes—
98C2×Dic43⋊C4C2314yes—
99C2×Dic43⋊C4C2314yes—
100C2×Dic43⋊C4C2314yes—
101C2×Dic43⋊C4C2314yes—
102C2×Dic43⋊C4C2314yes—
103C2×(C2×D43)⋊C4—24no—
104C2×(C2×D43)⋊C4—24no—
105C2×(C2×D43)⋊C4—24no—
106C2×(C2×D43)⋊C4—24no—
107C2×(C2×D43)⋊C4—24no—
108C2×(C2×D43)⋊C4D418yes—
109C2×(C2×D43)⋊C4C2314yes—
110C2×(C2×D43)⋊C4C2314yes—
111C2×(C2×D43)⋊C4C2314yes—
112C2×(C2×D43)⋊C4C2314yes—
113C2×(C2×D43)⋊C4C2314yes—
114C2×(C2×D43)⋊C4C2314yes—
115C2×C4×Dic43—24no—
116C2×C4×Dic43—24no—
117C2×C4×Dic43—24no—
118C2×C4×Dic43—24no—
119C2×C4×Dic43C2314yes—
120C2×C4×Dic43C2314yes—
121C2×C4×Dic43C2314yes—
122C2×C4×Dic43C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C43⋊#95C2314yes—
127C43⋊#95C2314yes—
128C43⋊#95C2314yes—
129C43⋊#95C2314yes—
130C23×C4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43—24no—
138C2×C4⋊C4×C43—24no—
139C2×C4⋊C4×C43C2314yes—
140C2×C4⋊C4×C43C2314yes—
141#95×C43C2314yes—
142#95×C43C2314yes—
143#95×C43C2314yes—
144#95×C43C2314yes—
145#95×C43C2314yes—
146C24×C43C2411yescharacteristic
147C23×D43—22no—
148C23×D43—22no—
149C23×D43—22no—
150C23×D43—22no—
151C23×D43—22no—
152C23×D43—22no—
153C23×D43C2×D414yes—
154C23×D43C2412yes—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43—22no—
160C22×C4×C43—22no—
161C22×C4×C43—22no—
162C22×C4×C43—22no—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43—22no—
166C22×C4×C43—22no—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—22no—
170C22×C4×C43—22no—
171C22×C4×C43—22no—
172C22×C4×C43—22no—
173C22×C4×C43—22no—
174C22×C4×C43—22no—
175C22×C4×C43C2×D414yes—
176C22×C4×C43C2412yes—
177C22×C4×C43C2412yes—
178C22×C4×C43C2412yes—
179C22×C4×C43C2412yes—
180C22×C4×C43C2412yes—
181C22×C4×C43C2412yes—
182C22×C4×C43C2412yes—
183C22×Dic43—22no—
184C22×Dic43—22no—
185C22×Dic43—22no—
186C22×Dic43—22no—
187C22×Dic43—22no—
188C22×Dic43—22no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192C22×Dic43—22no—
193C22×Dic43—22no—
194C22×Dic43—22no—
195C22×Dic43—22no—
196C22×Dic43—22no—
197C22×Dic43—22no—
198C22×Dic43—22no—
199C22×Dic43C2×D414yes—
200C22×Dic43#4114yes—
201C22×Dic43#4114yes—
202C22×Dic43#4114yes—
203C22×Dic43#4114yes—
204C22×Dic43C2412yes—
205C22×Dic43C2412yes—
206C22×Dic43C2412yes—
207C22×Dic43C2412yes—
208C22×Dic43C2412yes—
209C22×Dic43C2412yes—
210C22×Dic43C2412yes—
211C2×C4×D43—28no—
212C2×C4×D43—28no—
213C2×C4×D43—28no—
214C2×C4×D43—416no—
215C4⋊C4×C43—28no—
216C4⋊C4×C43—28no—
217(C2×D43)⋊C4—28no—
218(C2×D43)⋊C4—28no—
219(C2×D43)⋊C4—28no—
220(C2×D43)⋊C4—28no—
221(C2×D43)⋊C4—28no—
222(C2×D43)⋊C4C2×D4116yes—
223C4⋊Dic43—28no—
224C4⋊Dic43—28no—
225Dic43⋊C4—28no—
226Dic43⋊C4—28no—
227Dic43⋊C4—28no—
228Dic43⋊C4—28no—
229Dic43⋊C4—28no—
230Dic43⋊C4—28no—
231Dic43⋊C4—28no—
232Dic43⋊C4—28no—
233C4×Dic43—28no—
234C4×Dic43—28no—
235C4×Dic43—28no—
236C4×Dic43—28no—
237C23×C43C22×D412yes—
238C23×C43C2×#4112yes—
239C23×C43C2×#4112yes—
240C23×C43C2×#4112yes—
241C23×C43C2×#4112yes—
242C23×C432−1+412yes—
243C23×C432−1+412yes—
244C23×C43C2511yescharacteristic
245C22×D43—28no—
246C22×D43—28no—
247C22×D43—28no—
248C22×D43—22no—
249C22×D43—22no—
250C22×D43—22no—
251C22×D43—22no—
252C22×D43—22no—
253C22×D43—22no—
254C22×D43—44no—
255C22×D43—44no—
256C22×D43—44no—
257C22×D43—44no—
258C22×D43C22×D414yes—
259C2×C4×C43—28no—
260C2×C4×C43—22no—
261C2×C4×C43—22no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—44no—
281C2×C4×C43—44no—
282C2×C4×C43—44no—
283C2×C4×C43—44no—
284C2×C4×C43—44no—
285C2×C4×C43—44no—
286C2×C4×C43C22×D414yes—
287C2×Dic43—28no—
288C2×Dic43—28no—
289C2×Dic43—22no—
290C2×Dic43—22no—
291C2×Dic43—22no—
292C2×Dic43—22no—
293C2×Dic43—22no—
294C2×Dic43—22no—
295C2×Dic43—22no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—44no—
306C2×Dic43—44no—
307C2×Dic43—44no—
308C2×Dic43—44no—
309C2×Dic43#126116yescomplemented
310C2×Dic43C22×D414yes—
311C2×Dic43C2×#4114yes—
312C2×Dic43C2×#4114yes—
313C2×Dic43C2×#4114yes—
314C2×Dic43C2×#4114yes—
315C4×D43—416no—
316C2×#2496—431nomaximal, Sylow
317C22×C43C2×#12614yes—
318C22×C43#53214yes—
319C22×C43#54114yes—
320C22×C43#54714yes—
321C22×C43#54714yes—
322C22×C43#55214yes—
323C22×C43#55614yes—
324C22×C43C23×D411yescharacteristic
325C22×C43C22×#4111yescharacteristic
326C22×C43C22×#4111yescharacteristic
327C22×C43C22×#4111yescharacteristic
328C22×C43C22×#4111yescharacteristic
329C22×C43C2×2−1+411yescharacteristic
330C22×C43C2×2−1+411yescharacteristic
331C2×D43—24no—
332C2×D43—24no—
333C2×D43—24no—
334C2×D43—42no—
335C2×D43—42no—
336C2×D43—42no—
337C2×D43—42no—
338C2×D43—416no—
339C4×C43—24no—
340C4×C43—42no—
341C4×C43—42no—
342C4×C43—42no—
343C4×C43—42no—
344C4×C43—42no—
345C4×C43—42no—
346Dic43—24no—
347Dic43—24no—
348Dic43—42no—
349Dic43—42no—
350Dic43—42no—
351Dic43—42no—
352Dic43C2×#12618yescomplemented
353C22×#126—431no—
354C22×#126—431no—
355#2496—4316no—
356C2×#400—431no—
357C2×#400D4311yescharacteristic, complemented
358C2×#397—431no—
359C2×#397—431no—
360C2×#389—431no—
361C2×#389—431no—
362C2×#387—431no—
363C2×#387—431no—
364C2×#384—431no—
365C2×#380—431no—
366C2×#380—431no—
367C2×C4×C4⋊C4—431no—
368C2×C4×C22⋊C4—431no—
369C2×C43#249618yescomplemented
370C2×C43C22×#12611yescharacteristic
371C2×C43C2×#53211yescharacteristic
372C2×C43C2×#54111yescharacteristic
373C2×C43C2×#54711yescharacteristic
374C2×C43C2×#54711yescharacteristic
375C2×C43C2×#55211yescharacteristic
376C2×C43C2×#55611yescharacteristic
377D43—44no—
378C24×C4—431no—
379C2×#126—438no—
380C2×#126—438no—
381C2×#126—868no—
382C2×#126—868no—
383C22×C4⋊C4—431no—
384C22×C4⋊C4—431no—
385C22×C4⋊C4—431no—
386C22×C4⋊C4—431no—
387C22×C4⋊C4—431no—
388C22×C4⋊C4—431no—
389C22×C4⋊C4—431no—
390C22×C4⋊C4—431no—
391C22×C4⋊C4—431no—
392C22×C4⋊C4—431no—
393C22×C4⋊C4C2×D4311yescharacteristic
394C22×C4⋊C4C2×D4311yescharacteristic
395C22×C22⋊C4—431no—
396C22×C22⋊C4—431no—
397C22×C22⋊C4—431no—
398C22×C22⋊C4—431no—
399C22×C22⋊C4—431no—
400C22×C22⋊C4—431no—
401C22×C42—431no—
402C22×C42—431no—
403C22×C42—431no—
404C22×C42—431no—
405#400—438no—
406#400C2×D4318yescomplemented
407#397—438no—
408#397—438no—
409#389—438no—
410#389—438no—
411#387—438no—
412#387—438no—
413#384—438no—
414#380—438no—
415#380—438no—
416C4×C4⋊C4—438no—
417C4×C22⋊C4—438no—
418C2×#95—431no—
419C2×#95—431no—
420C2×#95—431no—
421C2×#95—431no—
422C2×#95—431no—
423C2×#95—431no—
424C2×#95—431no—
425C2×#95C2×D4311yescharacteristic
426C2×#95C2×D4311yescharacteristic
427C2×#95C2×D4311yescharacteristic
428C2×#95C2×D4311yescharacteristic
429C2×#95C2×D4311yescharacteristic
430C43C2×#249611yescharacteristic, complemented, Sylow
431C25—431no—
432C23×C4—431no—
433C23×C4—431no—
434C23×C4—431no—
435C23×C4—431no—
436C23×C4—431no—
437C23×C4—431no—
438C23×C4—431no—
439C23×C4—434no—
440C23×C4—864no—
441C23×C4—864no—
442C23×C4—864no—
443C23×C4C22×D4311yescharacteristic
444C23×C4C22×D4311yescharacteristic
445C23×C4C22×D4311yescharacteristic
446C23×C4C22×D4311yescharacteristic
447C23×C4C22×D4311yescharacteristic
448C23×C4C22×D4311yescharacteristic
449C23×C4C22×D4311yescharacteristic
450#126—8632no—
451#126—8632no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—434no—
455C2×C4⋊C4—434no—
456C2×C4⋊C4—434no—
457C2×C4⋊C4—434no—
458C2×C4⋊C4—434no—
459C2×C4⋊C4—434no—
460C2×C4⋊C4—434no—
461C2×C4⋊C4—434no—
462C2×C4⋊C4—434no—
463C2×C4⋊C4—434no—
464C2×C4⋊C4—864no—
465C2×C4⋊C4—864no—
466C2×C4⋊C4—864no—
467C2×C4⋊C4—864no—
468C2×C4⋊C4—864no—
469C2×C4⋊C4—864no—
470C2×C4⋊C4—864no—
471C2×C4⋊C4—864no—
472C2×C4⋊C4—864no—
473C2×C4⋊C4—864no—
474C2×C4⋊C4C22×D4314yes—
475C2×C4⋊C4C22×D4314yes—
476C2×C22⋊C4—438no—
477C2×C22⋊C4—434no—
478C2×C22⋊C4—434no—
479C2×C22⋊C4—434no—
480C2×C22⋊C4—434no—
481C2×C22⋊C4—434no—
482C2×C22⋊C4—434no—
483C2×C22⋊C4—864no—
484C2×C22⋊C4—864no—
485C2×C22⋊C4—864no—
486C2×C22⋊C4—864no—
487C2×C22⋊C4—864no—
488C2×C42—434no—
489C2×C42—434no—
490C2×C42—434no—
491C2×C42—434no—
492C2×C42—864no—
493C2×C42—864no—
494C2×C42—864no—
495C2×C42—864no—
496#95—434no—
497#95—434no—
498#95—434no—
499#95—434no—
500#95—434no—
501#95—434no—
502#95—434no—
503#95C22×D4314yes—
504#95C22×D4314yes—
505#95C22×D4314yes—
506#95C22×D4314yes—
507#95C22×D4314yes—
508C24—434no—
509C24—432no—
510C24—862no—
511C24—862no—
512C24—862no—
513C24—862no—
514C24—862no—
515C24—862no—
516C24C23×D4311yescharacteristic
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—434no—
538C22×C4—434no—
539C22×C4—434no—
540C22×C4—432no—
541C22×C4—434no—
542C22×C4—434no—
543C22×C4—432no—
544C22×C4—432no—
545C22×C4—432no—
546C22×C4—432no—
547C22×C4—432no—
548C22×C4—432no—
549C22×C4—868no—
550C22×C4—868no—
551C22×C4—868no—
552C22×C4—862no—
553C22×C4—862no—
554C22×C4—862no—
555C22×C4—862no—
556C22×C4—862no—
557C22×C4—862no—
558C22×C4—862no—
559C22×C4—862no—
560C22×C4—862no—
561C22×C4—862no—
562C22×C4—862no—
563C22×C4—862no—
564C22×C4—862no—
565C22×C4—862no—
566C22×C4—862no—
567C22×C4—862no—
568C22×C4—17216no—
569C22×C4D4×D4314yes—
570C22×C4C23×D4312yes—
571C22×C4C23×D4312yes—
572C22×C4C23×D4312yes—
573C22×C4C23×D4312yes—
574C22×C4C23×D4312yes—
575C22×C4C23×D4312yes—
576C22×C4C23×D4312yes—
577C4⋊C4—28no—
578C4⋊C4—28no—
579C4⋊C4—868no—
580C4⋊C4—868no—
581C4⋊C4—868no—
582C4⋊C4—868no—
583C4⋊C4—868no—
584C4⋊C4—868no—
585C4⋊C4—868no—
586C4⋊C4—868no—
587C4⋊C4—868no—
588C4⋊C4—868no—
589C22⋊C4—4316no—
590C22⋊C4—868no—
591C22⋊C4—868no—
592C22⋊C4—868no—
593C22⋊C4—868no—
594C22⋊C4—868no—
595C42—868no—
596C42—868no—
597C42—868no—
598C42—868no—
599C23—434no—
600C23—868no—
601C23—862no—
602C23—862no—
603C23—862no—
604C23—862no—
605C23—862no—
606C23—862no—
607C23—868no—
608C23—868no—
609C23—1724no—
610C23—1724no—
611C23—1724no—
612C23—1724no—
613C23C2×D4×D4312yes—
614C23#41×D4312yes—
615C23#41×D4312yes—
616C23#41×D4312yes—
617C23#41×D4312yes—
618C23#1306337212yes—
619C23#1306337312yes—
620C23C24×D4311yescharacteristic
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—28no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—44no—
648C2×C4—4316no—
649C2×C4—434no—
650C2×C4—434no—
651C2×C4—434no—
652C2×C4—434no—
653C2×C4—434no—
654C2×C4—868no—
655C2×C4—862no—
656C2×C4—862no—
657C2×C4—862no—
658C2×C4—862no—
659C2×C4—868no—
660C2×C4—862no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—862no—
664C2×C4—862no—
665C2×C4—862no—
666C2×C4—862no—
667C2×C4—862no—
668C2×C4—862no—
669C2×C4—862no—
670C2×C4—862no—
671C2×C4—862no—
672C2×C4—17216no—
673C2×C4—1724no—
674C2×C4—1724no—
675C2×C4—1724no—
676C2×C4—1724no—
677C2×C4C2×D4×D4314yes—
678C22—864no—
679C22—864no—
680C22—864no—
681C22—1722no—
682C22—1722no—
683C22—1722no—
684C22—1722no—
685C22—17216no—
686C22#126×D4314yes—
687C22#1458344814yes—
688C22#1458350814yes—
689C22#1458354714yes—
690C22#1458355114yes—
691C22#1458358114yes—
692C22#1458361614yes—
693C22C22×D4×D4311yescharacteristic
694C22C2×#41×D4311yescharacteristic
695C22C2×#41×D4311yescharacteristic
696C22C2×#41×D4311yescharacteristic
697C22C2×#41×D4311yescharacteristic
698C22C2×#1306337211yescharacteristic
699C22C2×#1306337311yescharacteristic
700C4—24no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—438no—
708C4—864no—
709C4—864no—
710C4—1722no—
711C4—1722no—
712C4—1722no—
713C4—1722no—
714C2—1724no—
715C2#1913901218yesdirect product factor
716C2C2×#126×D4311yescharacteristic
717C2C2×#1458344811yescharacteristic
718C2C2×#1458350811yescharacteristic
719C2C2×#1458354711yescharacteristic
720C2C2×#1458355111yescharacteristic
721C2C2×#1458358111yescharacteristic
722C2C2×#1458361611yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#400C2
socleC24×C43C24
prime radicalC24×D43C23
hypercenterC2×#400D43
hypocenterC43C2×#2496
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
3. #19139012C2direct (N × H)
4. C2×#14582839C2semidirect
7. C2×#14582796C2semidirect
8. C2×#14582794C2semidirect
9. C2×#14582786C2semidirect
10. C2×#14582781C2semidirect
11. C2×#14582768C2semidirect
14. C2×#14582750C2semidirect
16. C2×C43×#400C2semidirect
42. #14582839C22semidirect
45. #14582796C22semidirect
46. #14582794C22semidirect
47. #14582786C22semidirect
48. #14582781C22semidirect
49. #14582768C22semidirect
52. #14582750C22semidirect
63. C43×#400C22semidirect
309. C2×Dic43#126semidirect
352. Dic43C2×#126semidirect
357. C2×#400D43semidirect
369. C2×C43#2496semidirect
406. #400C2×D43semidirect
430. C43C2×#2496semidirect
715. C2#19139012direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633202
#191390122
C2×#145828392
C2×#145828282
C2×#145827962
C2×#145827942
C2×#145827862
C2×#145827812
C2×#145827682
C2×#145827582
C2×#145827502
C2×#145827462
C2×C43×#4002
C2×#249643