Finite Group Databasebeta

← C2×#19138035 #25264408

Subgroups — C2×#19138035 #25264408

Order 11008.

4782 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063299C211yesmaximal, characteristic, complemented
2C22×#13063299C211yesmaximal, characteristic, complemented
3C22×#13063297C212yesmaximal, complemented
4C23×C4⋊Dic43C211yesmaximal, characteristic, complemented
5#19138035C2116yesmaximal, direct product factor
6C2×#14582821C212yesmaximal, complemented
7C2×#14582815C212yesmaximal, complemented
8C2×#14582801C211yesmaximal, characteristic, complemented
9C2×#14582797C211yesmaximal, characteristic, complemented
10C2×#14582776C212yesmaximal, complemented
11C2×#14582759C211yesmaximal, characteristic, complemented
12C22×C4×D4×C43C211yesmaximal, characteristic, complemented
13C23×D172C2211yescharacteristic
14C23×C22⋊D43C2212yes—
15C23×C22⋊D43C2212yes—
16C24×Dic43C2212yes—
17C2×#13063299—28no—
18C2×#13063299—28no—
19C2×#13063299C2218yescomplemented
20C2×#13063299C2218yescomplemented
21C2×#13063297—216no—
22C2×#13063297C22116yescomplemented
23C22×C4⋊Dic43—28no—
24C22×C4⋊Dic43C2212yes—
25C22×C4⋊Dic43C2211yescharacteristic
26C22×C4⋊Dic43C2211yescharacteristic
27C22×C4⋊Dic43C2211yescharacteristic
28C22×C4⋊Dic43C2218yescomplemented
29C22×Dic43⋊C4C2212yes—
30C22×C22⋊Dic43C2212yes—
31C22×(C2×D43)⋊C4C2212yes—
32C22×(C2×D43)⋊C4C2212yes—
33C22×(C2×D43)⋊C4C2212yes—
34C22×(C2×D43)⋊C4C2212yes—
35#14582821C22116yescomplemented
36#14582815C22116yescomplemented
37#14582801C2218yescomplemented
38#14582797C2218yescomplemented
39#14582776C22116yescomplemented
40#14582759C2218yescomplemented
41C2×C43⋊#95C2212yes—
42C2×C43⋊#95C2212yes—
43C23×D4×C43C2211yescharacteristic
44C24×C4×C43C2211yescharacteristic
45C24×C4×C43C2211yescharacteristic
46C2×C4×D4×C43—28no—
47C2×C4×D4×C43C2218yescomplemented
48C22×C4⋊C4×C43C2211yescharacteristic
49C22×C22⋊C4×C43C2211yescharacteristic
50C22×C22⋊C4×C43C2211yescharacteristic
51C22×C42×C43C2211yescharacteristic
52C24×D43C2312yes—
53C22×D172—24no—
54C22×D172—24no—
55C22×D172—24no—
56C22×D172C2314yes—
57C22×C22⋊D43—28no—
58C22×C22⋊D43—28no—
59C22×C22⋊D43—28no—
60C22×C22⋊D43—28no—
61C22×C22⋊D43—28no—
62C22×C22⋊D43—44no—
63C22×C22⋊D43C2318yes—
64C22×C22⋊D43C2318yes—
65C23×Dic43—28no—
66C23×Dic43—28no—
67C23×Dic43—44no—
68C23×Dic43C2312yes—
69C23×Dic43C2312yes—
70C23×Dic43C2318yes—
71C23×Dic43C2312yes—
72#13063299—232no—
73#13063299—232no—
74#13063297—264no—
75C2×C4⋊Dic43—24no—
76C2×C4⋊Dic43—24no—
77C2×C4⋊Dic43—28no—
78C2×C4⋊Dic43—232no—
79C2×C4⋊Dic43D418yescomplemented
80C2×C4⋊Dic43C2314yes—
81C2×C4⋊Dic43C2314yes—
82C2×C4⋊Dic43C2318yes—
83C2×C4⋊Dic43C2314yes—
84C2×Dic43⋊C4—28no—
85C2×Dic43⋊C4C2318yes—
86C2×C22⋊Dic43—28no—
87C2×C22⋊Dic43C2318yes—
88C2×(C2×D43)⋊C4—28no—
89C2×(C2×D43)⋊C4—28no—
90C2×(C2×D43)⋊C4—28no—
91C2×(C2×D43)⋊C4—44no—
92C2×(C2×D43)⋊C4C2318yes—
93C2×(C2×D43)⋊C4C2318yes—
94C2×(C2×D43)⋊C4C2318yes—
95C2×(C2×D43)⋊C4C2318yes—
96C43⋊#95C2318yes—
97C43⋊#95C2318yes—
98C25×C43C2311yescharacteristic
99C25×C43C2311yescharacteristic
100C22×D4×C43—24no—
101C22×D4×C43—24no—
102C22×D4×C43D418yescomplemented
103C22×D4×C43C2314yes—
104C23×C4×C43—24no—
105C23×C4×C43—24no—
106C23×C4×C43—24no—
107C23×C4×C43—24no—
108C23×C4×C43—24no—
109C23×C4×C43D418yescomplemented
110C23×C4×C43C2311yescharacteristic
111C23×C4×C43C2311yescharacteristic
112C23×C4×C43C2314yes—
113C23×C4×C43C2311yescharacteristic
114C23×C4×C43C2311yescharacteristic
115C23×C4×C43C2314yes—
116C23×C4×C43C2311yescharacteristic
117C4×D4×C43—232no—
118C2×C4⋊C4×C43—24no—
119C2×C4⋊C4×C43C2314yes—
120C2×C22⋊C4×C43—24no—
121C2×C22⋊C4×C43—24no—
122C2×C22⋊C4×C43C2314yes—
123C2×C22⋊C4×C43C2314yes—
124C2×C42×C43—24no—
125C2×C42×C43C2314yes—
126C24×C43—22no—
127C24×C43—22no—
128C24×C43—22no—
129C24×C43—22no—
130C24×C43—22no—
131C24×C43—22no—
132C24×C43—22no—
133C24×C43—22no—
134C24×C43—22no—
135C24×C43—22no—
136C24×C43C2×D414yes—
137C24×C43C2×D414yes—
138C24×C43C2×D414yes—
139C24×C43#4114yes—
140C24×C43C2412yes—
141C24×C43C2412yes—
142C24×C43C2411yescharacteristic
143C23×D43—24no—
144C23×D43—24no—
145C23×D43—24no—
146C23×D43—24no—
147C23×D43—24no—
148C23×D43—24no—
149C23×D43—24no—
150C23×D43C2414yes—
151C2×D4×C43—232no—
152C2×D4×C43—28no—
153C2×D4×C43—28no—
154C2×D4×C43C2×D4116yescomplemented
155C22×C4×C43—232no—
156C22×C4×C43—28no—
157C22×C4×C43—28no—
158C22×C4×C43—28no—
159C22×C4×C43—28no—
160C22×C4×C43—28no—
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—416no—
172C22×C4×C43C2×D414yes—
173C22×C4×C43C2×D414yes—
174C22×C4×C43C2×D414yes—
175C22×C4×C43C2×D414yes—
176C22×C4×C43C2×D4116yescomplemented
177C22×C4×C43#4114yes—
178C22×C4×C43C2412yes—
179C22×C4×C43C2412yes—
180C22×C4×C43C2412yes—
181C22×C4×C43C2412yes—
182C22×C4×C43C2412yes—
183C2×C22⋊D43—216no—
184C2×C22⋊D43—216no—
185C2×C22⋊D43—216no—
186C2×C22⋊D43—216no—
187C2×C22⋊D43—216no—
188C2×C22⋊D43—48no—
189C2×C22⋊D43—432no—
190C2×C22⋊D43—432no—
191C22×Dic43—216no—
192C22×Dic43—24no—
193C22×Dic43—24no—
194C22×Dic43—24no—
195C22×Dic43—24no—
196C22×Dic43—24no—
197C22×Dic43—216no—
198C22×Dic43—24no—
199C22×Dic43—24no—
200C22×Dic43—24no—
201C22×Dic43—48no—
202C22×Dic43—432no—
203C22×Dic43C2×D418yes—
204C22×Dic43C2414yes—
205C22×Dic43C2414yes—
206C22×Dic43C2414yes—
207C2×D172—28no—
208C2×D172—28no—
209C2×D172—28no—
210C2×D172—416no—
211C4⋊C4×C43—28no—
212C22⋊C4×C43—28no—
213C22⋊C4×C43—28no—
214C42×C43—28no—
215C22⋊Dic43—216no—
216(C2×D43)⋊C4—216no—
217(C2×D43)⋊C4—216no—
218(C2×D43)⋊C4—216no—
219(C2×D43)⋊C4—48no—
220C4⋊Dic43—28no—
221C4⋊Dic43—28no—
222C4⋊Dic43—216no—
223C4⋊Dic43C2×D4116yescomplemented
224Dic43⋊C4—216no—
225C23×C43—28no—
226C23×C43—28no—
227C23×C43—28no—
228C23×C43—28no—
229C23×C43—28no—
230C23×C43—28no—
231C23×C43—22no—
232C23×C43—22no—
233C23×C43—22no—
234C23×C43—22no—
235C23×C43—28no—
236C23×C43—28no—
237C23×C43—28no—
238C23×C43—22no—
239C23×C43—22no—
240C23×C43—22no—
241C23×C43—22no—
242C23×C43—22no—
243C23×C43—22no—
244C23×C43—44no—
245C23×C43—44no—
246C23×C43—44no—
247C23×C43—44no—
248C23×C43#121116yescomplemented
249C23×C43C22×D412yes—
250C23×C43C22×D414yes—
251C23×C43C22×D412yes—
252C23×C43C22×D414yes—
253C23×C43C22×D414yes—
254C23×C43C22×D412yes—
255C23×C43C2×#4112yes—
256C23×C43C2×#4114yes—
257C23×C43C2×#4112yes—
258C23×C43H(5,𝔽2)12yes—
259C23×C432−1+412yes—
260C23×C43C2511yescharacteristic
261C22×D43—24no—
262C22×D43—24no—
263C22×D43—24no—
264C22×D43—24no—
265C22×D43—24no—
266C22×D43—24no—
267C22×D43—24no—
268C22×D43—48no—
269C22×D43—48no—
270C22×D43—48no—
271C22×D43—48no—
272C22×D43—48no—
273C22×D43—48no—
274C22×D43—48no—
275D4×C43—232no—
276C2×C4×C43—28no—
277C2×C4×C43—28no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—232no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—44no—
290C2×C4×C43—44no—
291C2×C4×C43—416no—
292C2×C4×C43#121116yescomplemented
293C2×C4×C43C22×D414yes—
294C2×C4×C43C22×D414yes—
295C2×C4×C43C22×D414yes—
296C2×C4×C43C22×D414yes—
297C2×C4×C43C2×#4114yes—
298C22⋊D43—432no—
299C22⋊D43—432no—
300C2×Dic43—216no—
301C2×Dic43—24no—
302C2×Dic43—24no—
303C2×Dic43—24no—
304C2×Dic43—24no—
305C2×Dic43—24no—
306C2×Dic43—24no—
307C2×Dic43—24no—
308C2×Dic43—24no—
309C2×Dic43—432no—
310C2×Dic43—48no—
311C2×Dic43—48no—
312C2×Dic43C22×D418yes—
313D172—416no—
314C2×#2416—431nomaximal, Sylow
315C22×C43—24no—
316C22×C43—232no—
317C22×C43—24no—
318C22×C43—24no—
319C22×C43—24no—
320C22×C43—24no—
321C22×C43—24no—
322C22×C43—24no—
323C22×C43—24no—
324C22×C43—24no—
325C22×C43—42no—
326C22×C43—416no—
327C22×C43—42no—
328C22×C43—42no—
329C22×C43—42no—
330C22×C43C2×#12114yes—
331C22×C43C2×#12114yes—
332C22×C43C2×#12118yescomplemented
333C22×C43#53714yes—
334C22×C43D4214yes—
335C22×C43#54714yes—
336C22×C43#54814yes—
337C22×C43#55314yes—
338C22×C43C23×D411yescharacteristic
339C22×C43C23×D411yescharacteristic
340C22×C43C23×D411yescharacteristic
341C22×C43C22×#4111yescharacteristic
342C22×C43C22×#4111yescharacteristic
343C22×C43C2×H(5,𝔽2)11yescharacteristic
344C22×C43C2×2−1+411yescharacteristic
345C2×D43—44no—
346C2×D43—44no—
347C2×D43—44no—
348C2×D43—44no—
349C2×D43—44no—
350C2×D43—44no—
351C2×D43—44no—
352C2×D43—816no—
353C4×C43—24no—
354C4×C43—24no—
355C4×C43—42no—
356C4×C43—42no—
357C4×C43C2×#12118yescomplemented
358Dic43—28no—
359Dic43—44no—
360Dic43—44no—
361C22×#121—432no—
362C22×#121—431no—
363C22×#121—431no—
364C22×C4×D4D4311yescharacteristic, complemented
365C23×C4⋊C4—431no—
366#2416—4316no—
367C2×#396—432no—
368C2×#394—432no—
369C2×#390—431no—
370C2×#389—431no—
371C2×#386—432no—
372C2×#380—431no—
373C2×C43—28no—
374C2×C43—44no—
375C2×C43#241618yescomplemented
376C2×C43C22×#12111yescharacteristic
377C2×C43C22×#12111yescharacteristic
378C2×C43C2×#53711yescharacteristic
379C2×C43C2×D4211yescharacteristic
380C2×C43C2×#54711yescharacteristic
381C2×C43C2×#54811yescharacteristic
382C2×C43C2×#55311yescharacteristic
383D43—84no—
384C23×D4—432no—
385C23×D4—432no—
386C23×D4—431no—
387C23×D4C2×D4311yescharacteristic
388C24×C4—432no—
389C24×C4C2×D4311yescharacteristic
390C24×C4C2×D4311yescharacteristic
391C2×#121—4316no—
392C2×#121—438no—
393C2×#121—438no—
394C2×#121—868no—
395C2×#121—8616no—
396C2×#121—868no—
397C2×C4×D4—28no—
398C2×C4×D4C2×D4318yescomplemented
399C22×C4⋊C4—431no—
400C22×C4⋊C4—432no—
401C22×C4⋊C4—432no—
402C22×C4⋊C4—431no—
403C22×C4⋊C4—431no—
404C22×C4⋊C4—438no—
405C22×C4⋊C4—868no—
406C22×C4⋊C4C2×D4311yescharacteristic
407C22×C22⋊C4—432no—
408C22×C22⋊C4—432no—
409C22×C22⋊C4—432no—
410C22×C22⋊C4—432no—
411C22×C22⋊C4—432no—
412C22×C22⋊C4C2×D4311yescharacteristic
413C22×C22⋊C4C2×D4311yescharacteristic
414C22×C42C2×D4311yescharacteristic
415#396—4316no—
416#394—4316no—
417#390—438no—
418#389—438no—
419#386—4316no—
420#380—438no—
421C2×#95—432no—
422C2×#95—432no—
423C43C2×#241611yescharacteristic, complemented, Sylow
424C25—432no—
425C25C22×D4311yescharacteristic
426C25C22×D4311yescharacteristic
427C22×D4—24no—
428C22×D4—24no—
429C22×D4—438no—
430C22×D4—438no—
431C22×D4—434no—
432C22×D4—868no—
433C22×D4—868no—
434C22×D4—868no—
435C22×D4—868no—
436C22×D4—868no—
437C22×D4—864no—
438C22×D4—864no—
439C22×D4—864no—
440C22×D4—1724no—
441C22×D4D17218yescomplemented
442C22×D4C22×D4314yes—
443C23×C4—24no—
444C23×C4—24no—
445C23×C4—24no—
446C23×C4—24no—
447C23×C4—24no—
448C23×C4—432no—
449C23×C4—432no—
450C23×C4—432no—
451C23×C4—438no—
452C23×C4—868no—
453C23×C4—868no—
454C23×C4—1724no—
455C23×C4C22⋊D4318yescomplemented
456C23×C4C22×D4314yes—
457C23×C4C22×D4311yescharacteristic
458C23×C4C22×D4311yescharacteristic
459C23×C4C22×D4311yescharacteristic
460C23×C4C22×D4311yescharacteristic
461C23×C4C22×D4314yes—
462C23×C4C22×D4311yescharacteristic
463#121—8632no—
464#121—8664no—
465#121—8632no—
466C4×D4—232no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—438no—
469C2×C4⋊C4—434no—
470C2×C4⋊C4—434no—
471C2×C4⋊C4—438no—
472C2×C4⋊C4—438no—
473C2×C4⋊C4—434no—
474C2×C4⋊C4—8632no—
475C2×C4⋊C4—868no—
476C2×C4⋊C4—868no—
477C2×C4⋊C4—864no—
478C2×C4⋊C4—864no—
479C2×C4⋊C4C22×D4314yes—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—438no—
483C2×C22⋊C4—438no—
484C2×C22⋊C4—438no—
485C2×C22⋊C4—438no—
486C2×C22⋊C4—438no—
487C2×C22⋊C4—868no—
488C2×C22⋊C4—868no—
489C2×C22⋊C4—868no—
490C2×C22⋊C4—868no—
491C2×C22⋊C4—1724no—
492C2×C22⋊C4C22×D4314yes—
493C2×C22⋊C4C22×D4314yes—
494C2×C42—24no—
495C2×C42C22×D4314yes—
496#95—438no—
497#95—438no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—434no—
509C24—864no—
510C24—864no—
511C24—864no—
512C24—864no—
513C24—864no—
514C24—864no—
515C24—864no—
516C24C2×D17214yes—
517C24C2×D17214yes—
518C24#1062189814yes—
519C24C2×C22⋊D4314yes—
520C24C23×D4312yes—
521C24C23×D4312yes—
522C24C23×D4311yescharacteristic
523C2×D4—232no—
524C2×D4—28no—
525C2×D4—28no—
526C2×D4—8616no—
527C2×D4—8616no—
528C2×D4—8616no—
529C2×D4—8616no—
530C2×D4—8616no—
531C2×D4—868no—
532C2×D4—868no—
533C2×D4—868no—
534C2×D4—1728no—
535C2×D4—17232no—
536C2×D4—17232no—
537C2×D4—17216no—
538C2×D4C2×D172116yescomplemented
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—232no—
544C22×C4—28no—
545C22×C4—28no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—28no—
553C22×C4—28no—
554C22×C4—28no—
555C22×C4—416no—
556C22×C4—438no—
557C22×C4—434no—
558C22×C4—434no—
559C22×C4—434no—
560C22×C4—8616no—
561C22×C4—864no—
562C22×C4—864no—
563C22×C4—864no—
564C22×C4—864no—
565C22×C4—864no—
566C22×C4—864no—
567C22×C4—8616no—
568C22×C4—864no—
569C22×C4—864no—
570C22×C4—1728no—
571C22×C4—17232no—
572C22×C4C2×D17214yes—
573C22×C4D4×D4314yes—
574C22×C4#1062190014yes—
575C22×C4C2×C22⋊D4314yes—
576C22×C4C2×C22⋊D4314yes—
577C22×C4C2×C22⋊D43116yescomplemented
578C22×C4C23×D4312yes—
579C22×C4C23×D4312yes—
580C22×C4C23×D4312yes—
581C22×C4C23×D4312yes—
582C22×C4C23×D4312yes—
583C4⋊C4—28no—
584C4⋊C4—4316no—
585C4⋊C4—8616no—
586C4⋊C4—868no—
587C4⋊C4—868no—
588C4⋊C4—8616no—
589C22⋊C4—28no—
590C22⋊C4—28no—
591C22⋊C4—8616no—
592C22⋊C4—8616no—
593C22⋊C4—8616no—
594C22⋊C4—8616no—
595C22⋊C4—1728no—
596C42—28no—
597C23—28no—
598C23—28no—
599C23—28no—
600C23—28no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—28no—
606C23—28no—
607C23—28no—
608C23—28no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—28no—
616C23—44no—
617C23—44no—
618C23—44no—
619C23—44no—
620C23—864no—
621C23—864no—
622C23—864no—
623C23—864no—
624C23—864no—
625C23—864no—
626C23—864no—
627C23—1728no—
628C23—1728no—
629C23—1728no—
630C23—1728no—
631C23—1728no—
632C23—1728no—
633C23—1728no—
634C23#13063299116yescomplemented
635C23C2×D4×D4312yes—
636C23C22×C22⋊D4314yes—
637C23C22×C22⋊D4312yes—
638C23C22×D17214yes—
639C23C22×D17214yes—
640C23C22×D17212yes—
641C23C2×#1062190012yes—
642C23C2×#1062189814yes—
643C23C2×#1062189812yes—
644C23#1306337112yes—
645C23#1306337212yes—
646C23C24×D4311yescharacteristic
647D4—232no—
648D4—17232no—
649D4—17232no—
650D4—17216no—
651C2×C4—28no—
652C2×C4—28no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—232no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—416no—
667C2×C4—438no—
668C2×C4—864no—
669C2×C4—864no—
670C2×C4—8616no—
671C2×C4—864no—
672C2×C4—864no—
673C2×C4—864no—
674C2×C4—864no—
675C2×C4—864no—
676C2×C4—864no—
677C2×C4—17232no—
678C2×C4—1728no—
679C2×C4—1728no—
680C2×C4#13063297116yescomplemented
681C2×C4C2×D4×D4314yes—
682C2×C4C22×C22⋊D4314yes—
683C2×C4C22×C22⋊D4314yes—
684C2×C4C22×D17214yes—
685C2×C4C2×#1062190014yes—
686C22—24no—
687C22—24no—
688C22—24no—
689C22—24no—
690C22—24no—
691C22—24no—
692C22—232no—
693C22—24no—
694C22—24no—
695C22—24no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—416no—
701C22—34416no—
702C22—1724no—
703C22—1724no—
704C22—1724no—
705C22—1724no—
706C22—1724no—
707C22—1724no—
708C22—1724no—
709C22C2×#1306329714yes—
710C22C2×#1306329914yes—
711C22C2×#1306329918yescomplemented
712C22#1458347714yes—
713C22D4×D17214yes—
714C22#1458355314yes—
715C22#1458355814yes—
716C22#1458359514yes—
717C22C22×D4×D4311yescharacteristic
718C22C23×C22⋊D4311yescharacteristic
719C22C23×D17211yescharacteristic
720C22C22×#1062190011yescharacteristic
721C22C22×#1062189811yescharacteristic
722C22C2×#1306337111yescharacteristic
723C22C2×#1306337211yescharacteristic
724C4—24no—
725C4—24no—
726C4—42no—
727C4—42no—
728C4—868no—
729C4—1724no—
730C4—1724no—
731C4C2×#1306329718yescomplemented
732C2—28no—
733C2—44no—
734C2—3444no—
735C2#1913803518yesdirect product factor
736C2C22×#1306329711yescharacteristic
737C2C22×#1306329911yescharacteristic
738C2C2×#1458347711yescharacteristic
739C2C2×D4×D17211yescharacteristic
740C2C2×#1458355311yescharacteristic
741C2C2×#1458355811yescharacteristic
742C2C2×#1458359511yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC22×C4×D4×C43C2
socleC24×C43C24
hypercenterC22×C4×D4D43
hypocenterC43C2×#2416
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#13063299C2semidirect
2. C22×#13063299C2semidirect
3. C22×#13063297C2semidirect
4. C23×C4⋊Dic43C2semidirect
5. #19138035C2direct (N × H)
6. C2×#14582821C2semidirect
7. C2×#14582815C2semidirect
8. C2×#14582801C2semidirect
9. C2×#14582797C2semidirect
10. C2×#14582776C2semidirect
11. C2×#14582759C2semidirect
12. C22×C4×D4×C43C2semidirect
19. C2×#13063299C22semidirect
20. C2×#13063299C22semidirect
22. C2×#13063297C22semidirect
28. C22×C4⋊Dic43C22semidirect
35. #14582821C22semidirect
36. #14582815C22semidirect
37. #14582801C22semidirect
38. #14582797C22semidirect
39. #14582776C22semidirect
40. #14582759C22semidirect
47. C2×C4×D4×C43C22semidirect
79. C2×C4⋊Dic43D4semidirect
102. C22×D4×C43D4semidirect
109. C23×C4×C43D4semidirect
154. C2×D4×C43C2×D4semidirect
176. C22×C4×C43C2×D4semidirect
223. C4⋊Dic43C2×D4semidirect
248. C23×C43#121semidirect
292. C2×C4×C43#121semidirect
332. C22×C43C2×#121semidirect
357. C4×C43C2×#121semidirect
364. C22×C4×D4D43semidirect
375. C2×C43#2416semidirect
398. C2×C4×D4C2×D43semidirect
423. C43C2×#2416semidirect
441. C22×D4D172semidirect
455. C23×C4C22⋊D43semidirect
538. C2×D4C2×D172semidirect
577. C22×C4C2×C22⋊D43semidirect
634. C23#13063299semidirect
680. C2×C4#13063297semidirect
711. C22C2×#13063299semidirect
731. C4C2×#13063297semidirect
735. C2#19138035direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130632992
C22×#130632972
C23×C4⋊Dic432
#191380352
C2×#145828212
C2×#145828152
C2×#145828012
C2×#145827972
C2×#145827762
C2×#145827592
C22×C4×D4×C432
C2×#241643