Finite Group Databasebeta

← #25149688

Subgroups — #25149688

Order 11008.

1178 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583223C211yesmaximal, characteristic, complemented
2C2×#14583147C211yesmaximal, characteristic, complemented
3#19138035C211yesmaximal, characteristic
4#19135930C211yesmaximal, characteristic, complemented
5#19135788C211yesmaximal, characteristic, complemented
6#19135738C211yesmaximal, characteristic, complemented
7#19135596C211yesmaximal, characteristic, complemented
8#19134950C211yesmaximal, characteristic, complemented
9#19134912C211yesmaximal, characteristic, complemented
10#19134903C211yesmaximal, characteristic, complemented
11#19134893C211yesmaximal, characteristic, complemented
12#19134849C211yesmaximal, characteristic, complemented
13#19134783C211yesmaximal, characteristic, complemented
14#19134316C211yesmaximal, characteristic, complemented
15C2×C43×#552C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20C2×#13063297—21no—
21C22×C4⋊Dic43C2211yescharacteristic
22#14583223—24no—
23#14583147—24no—
24C2×#13063258C2211yescharacteristic
25C2×#13063258C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36#14582821—21no—
37#14582815—21no—
38#14582801C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582776—21no—
41#14582759C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C43×#552—24no—
51C43×#552—24no—
52C2×#126×C43—21no—
53C2×#125×C43—21no—
54C2×#125×C43C2211yescharacteristic
55C2×#123×C43—21no—
56C2×C22⋊Q8×C43C2211yescharacteristic
57C2×C22⋊Q8×C43C2211yescharacteristic
58C2×C4×Q8×C43C2211yescharacteristic
59C2×C4×D4×C43C2211yescharacteristic
60C2×#117×C43—21no—
61C2×#117×C43C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C22×C22⋊D43—21no—
66C23×Dic43—21no—
67C2×#10621884—22no—
68C2×#10621884—22no—
69C2×#10621884—41no—
70C2×#10621877—22no—
71C2×#10621877—22no—
72C2×#10621877—41no—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77#13063299—22no—
78#13063299—22no—
79#13063299—22no—
80#13063299—41no—
81#13063297—44no—
82C2×C4⋊Dic43—22no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43—41no—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×C22⋊Dic43—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94#13063258—22no—
95#13063258—22no—
96#13063256—22no—
97#13063249—22no—
98#13063249—22no—
99#13063249—41no—
100#13063245—22no—
101#13063245—22no—
102#13063245—22no—
103C22⋊(C43⋊C8)—22no—
104C22⋊(C43⋊C8)—22no—
105C22⋊(C43⋊C8)—41no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C22×Q8×C43C2311yescharacteristic
109C22×D4×C43D411yescharacteristic
110C23×C4×C43—21no—
111C23×C4×C43C2311yescharacteristic
112C23×C4×C43C2311yescharacteristic
113#126×C43—28no—
114#125×C43—28no—
115#125×C43—22no—
116#125×C43—22no—
117#123×C43—28no—
118C22⋊Q8×C43—22no—
119C22⋊Q8×C43—22no—
120C22⋊Q8×C43—22no—
121C22⋊Q8×C43D414yescomplemented
122C4×Q8×C43—22no—
123C4×Q8×C43—22no—
124C4×D4×C43—22no—
125C4×D4×C43—22no—
126#117×C43—28no—
127#117×C43—22no—
128#117×C43D414yescomplemented
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43—22no—
136C2×C4⋊C4×C43—22no—
137C2×C4⋊C4×C43D411yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43D411yescharacteristic
145C2×C22⋊C4×C43D411yescharacteristic
146C2×C42×C43—21no—
147C2×C42×C43—21no—
148C2×C42×C43C2311yescharacteristic
149C24×C43C2×D411yescharacteristic
150C24×C43C2×D411yescharacteristic
151C23×D43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43C2×D412yes—
158C2×D4×C43—22no—
159C2×D4×C43—22no—
160C2×D4×C43—41no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—24no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—42no—
177C22×C4×C43—42no—
178C22×C4×C43C2×D412yes—
179C22×C4×C43C2×D412yes—
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2411yescharacteristic
185C2×C22⋊D43—42no—
186C2×C22⋊D43—42no—
187C2×C22⋊D43—42no—
188C2×C22⋊D43—42no—
189C2×C22⋊D43—42no—
190C2×C22⋊D43—81no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—42no—
195C22×Dic43—42no—
196C22×Dic43—81no—
197C2×D172—21no—
198C2×D172—21no—
199C2×D172—21no—
200C2×D172—21no—
201C2×D172—21no—
202C2×D172—21no—
203C4⋊C4×C43—24no—
204C4⋊C4×C43—24no—
205C4⋊C4×C43—24no—
206C4⋊C4×C43—24no—
207C4⋊C4×C43—24no—
208C4⋊C4×C43—24no—
209C4⋊C4×C43—22no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43C2×D412yes—
214C4⋊C4×C43C2×D412yes—
215C4⋊C4×C43C2×D412yes—
216C22⋊C4×C43—24no—
217C22⋊C4×C43—22no—
218C22⋊C4×C43—24no—
219C22⋊C4×C43—24no—
220C22⋊C4×C43—22no—
221C42×C43—24no—
222C42×C43—24no—
223C42×C43—21no—
224C42×C43—21no—
225C22⋊Dic43—42no—
226#10621884—44no—
227(C2×D43)⋊C4—42no—
228(C2×D43)⋊C4—42no—
229(C2×D43)⋊C4—42no—
230(C2×D43)⋊C4—81no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—42no—
237C4⋊Dic43#4112yes—
238Dic43⋊C4—42no—
239#10621877—44no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8#4112yes—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43#12012yes—
265C23×C43AGL(1,ℤ/8)12yes—
266C23×C43C22×D411yescharacteristic
267C22×D43—41no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43—41no—
272C22×D43—41no—
273C22×D43—41no—
274Q8×C43—22no—
275Q8×C43—22no—
276Q8×C43—41no—
277Q8×C43—41no—
278D4×C43—44no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—21no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—22no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—48no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43#12012yes—
312C2×C4×C43C22×D411yescharacteristic
313C2×C4×C43C22×D411yescharacteristic
314C2×C4×C43C2×#4111yescharacteristic
315C2×C4×C43C2×#4111yescharacteristic
316C2×C4×C43H(5,𝔽2)11yescharacteristic
317C2×C4×C432−1+411yescharacteristic
318C22⋊D43—84no—
319C22⋊D43—84no—
320C2×Dic43—22no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—84no—
330D172—41no—
331D172—41no—
332D172—41no—
333D172—41no—
334C43⋊C8—22no—
335C43⋊C8—41no—
336C43⋊C8—41no—
337C43⋊C8—41no—
338#25560—431nomaximal, Sylow
339C22×C43—22no—
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—22no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—41no—
350C22×C43—41no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43C2×#12011yescharacteristic
354C22×C43#54611yescharacteristic
355C22×C43#54711yescharacteristic
356C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
357C22×C43#57511yescharacteristic
358C22×C43#57711yescharacteristic
359C22×C43#57811yescharacteristic
360C2×D43—81no—
361C2×D43—81no—
362C2×D43—81no—
363C2×D43—81no—
364C2×D43—81no—
365C2×D43—81no—
366C2×D43—81no—
367C4×C43—22no—
368C4×C43—41no—
369C4×C43—42no—
370C4×C43—41no—
371C4×C43—42no—
372C4×C43—42no—
373C4×C43—41no—
374C4×C43—42no—
375C4×C43#53211yescharacteristic
376C4×C43#53711yescharacteristic
377C4×C43#54611yescharacteristic
378C4×C43#54711yescharacteristic
379Dic43—42no—
380Dic43—81no—
381Dic43—81no—
382C2×#552D4311yescharacteristic, complemented
383C2×#482—431no—
384C2×#468—431no—
385#2416—431no—
386#2059—431no—
387#2035—431no—
388#2025—431no—
389#2000—431no—
390#1880—431no—
391#1874—431no—
392#1872—431no—
393#1870—431no—
394#1863—431no—
395#1852—431no—
396#1736—431no—
397C2×C43—42no—
398C2×C43—42no—
399C2×C43#243011yescharacteristic
400C2×C43#300611yescharacteristic
401C2×C43#301311yescharacteristic
402C2×C43#331011yescharacteristic
403C2×C43#332711yescharacteristic
404C2×C43#334311yescharacteristic
405C2×C43#335111yescharacteristic
406D43—161no—
407C22×SD16—431no—
408C22×M16—431no—
409#552—24no—
410#552—24no—
411C2×#126—21no—
412C2×#125—21no—
413C2×#125C2×D4311yescharacteristic
414C2×#123—21no—
415C2×C22⋊Q8C2×D4311yescharacteristic
416C2×C22⋊Q8C2×D4311yescharacteristic
417C2×#121—431no—
418C2×#121—431no—
419C2×#121—861no—
420C2×C4×Q8C2×D4311yescharacteristic
421C2×C4×D4C2×D4311yescharacteristic
422C2×#117—21no—
423C2×#117C2×D4311yescharacteristic
424C22×C4⋊C4—431no—
425C22×C4⋊C4C2×D4311yescharacteristic
426#482—864no—
427#468—864no—
428C2×#107—431no—
429C2×#107—431no—
430C2×#106—431no—
431C2×#103—431no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#102—431no—
435C2×#102—431no—
436C2×#102—431no—
437C2×C22⋊C8—431no—
438C2×C22⋊C8—431no—
439C2×C22⋊C8—431no—
440#396—861no—
441#394—861no—
442#390—431no—
443#389—431no—
444#386—861no—
445#380—431no—
446#340—431no—
447#340—431no—
448#340—431no—
449#340—431no—
450#340—431no—
451#340—431no—
452#336—431no—
453#336—431no—
454C43#2556011yescharacteristic, complemented, Sylow
455C22×Q8C22×D4311yescharacteristic
456C22×D4—431no—
457C22×D4—861no—
458C22×D4—861no—
459C22×D4C22⋊D4311yescharacteristic
460C23×C4—21no—
461C23×C4—861no—
462C23×C4C22×D4311yescharacteristic
463C23×C4C22×D4311yescharacteristic
464C2×SD16—862no—
465C2×SD16—862no—
466C2×SD16—1721no—
467C2×M16—862no—
468C2×M16—862no—
469C2×M16—1721no—
470C22×C8—431no—
471C22×C8—431no—
472C22×C8—431no—
473C22×C8—431no—
474#126—28no—
475#125—28no—
476#125—22no—
477#125—22no—
478#123—28no—
479C22⋊Q8—22no—
480C22⋊Q8—22no—
481C22⋊Q8—22no—
482C22⋊Q8C22⋊D4314yescomplemented
483#121—862no—
484#121—862no—
485#121—862no—
486#121—1721no—
487#121—1724no—
488C4×Q8—22no—
489C4×Q8—22no—
490C4×D4—22no—
491C4×D4—22no—
492#117—28no—
493#117—22no—
494#117C22⋊D4314yescomplemented
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4—862no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—1721no—
510C2×C4⋊C4C22⋊D4311yescharacteristic
511C2×C4⋊C4C22×D4311yescharacteristic
512C2×C4⋊C4C22×D4311yescharacteristic
513C2×C4⋊C4C22×D4311yescharacteristic
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—861no—
518C2×C22⋊C4—861no—
519C2×C22⋊C4—861no—
520C2×C22⋊C4—861no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4C22⋊D4311yescharacteristic
523C2×C22⋊C4C22⋊D4311yescharacteristic
524C2×C42—21no—
525C2×C42—21no—
526C2×C42C22×D4311yescharacteristic
527#107—862no—
528#107—862no—
529#106—862no—
530#103—862no—
531#103—862no—
532#103—1721no—
533#102—862no—
534#102—862no—
535#102—862no—
536C22⋊C8—862no—
537C22⋊C8—862no—
538C22⋊C8—1721no—
539#95—861no—
540#95—861no—
541C24—861no—
542C24C2×C22⋊D4311yescharacteristic
543C24C2×C22⋊D4311yescharacteristic
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8C2×C22⋊D4312yes—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—41no—
553C2×D4—861no—
554C2×D4—861no—
555C2×D4—861no—
556C2×D4—861no—
557C2×D4—861no—
558C2×D4—861no—
559C2×D4—3441no—
560C2×D4—1722no—
561C2×D4—1722no—
562C2×D4—1722no—
563C2×D4—1722no—
564C2×D4—1722no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—24no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—3441no—
586C22×C4—1722no—
587C22×C4—1722no—
588C22×C4C2×C22⋊D4311yescharacteristic
589C22×C4C2×C22⋊D4311yescharacteristic
590C22×C4C2×C22⋊D4311yescharacteristic
591C22×C4C2×C22⋊D4311yescharacteristic
592C22×C4C2×C22⋊D4312yes—
593C22×C4C2×C22⋊D4312yes—
594C22×C4C23×D4311yescharacteristic
595SD16—1724no—
596M16—1724no—
597C2×C8—432no—
598C2×C8—861no—
599C2×C8—861no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8—861no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8—861no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—22no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—432no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4—861no—
623C4⋊C4—861no—
624C4⋊C4—861no—
625C4⋊C4—1722no—
626C4⋊C4—1722no—
627C4⋊C4C2×C22⋊D4312yes—
628C4⋊C4C2×C22⋊D4312yes—
629C4⋊C4C2×C22⋊D4312yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—3441no—
636C22⋊C4—1722no—
637C22⋊C4—1722no—
638C22⋊C4—1722no—
639C22⋊C4—1722no—
640C42—24no—
641C42—24no—
642C42—21no—
643C42—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—1721no—
657C23—1721no—
658C23—1721no—
659C23—1721no—
660C23—1721no—
661C23—1721no—
662C23—1721no—
663C23#1306329412yes—
664C23#1306335012yes—
665C23C22×C22⋊D4311yescharacteristic
666Q8—22no—
667Q8—22no—
668Q8—41no—
669Q8—41no—
670D4—44no—
671D4—3444no—
672D4—3444no—
673D4—1721no—
674D4—1721no—
675D4—1721no—
676D4—1721no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—48no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—862no—
710C2×C4—3444no—
711C2×C4—1721no—
712C2×C4—1721no—
713C2×C4—1721no—
714C2×C4—1721no—
715C2×C4—1721no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4#1306329412yes—
720C2×C4C22×C22⋊D4311yescharacteristic
721C2×C4C22×C22⋊D4311yescharacteristic
722C2×C4#41×D4311yescharacteristic
723C2×C4#41×D4311yescharacteristic
724C2×C4#1306337111yescharacteristic
725C2×C4#1306337211yescharacteristic
726C8—862no—
727C8—1721no—
728C8—1721no—
729C8—1721no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—3441no—
745C22—3441no—
746C22—3441no—
747C22—3441no—
748C22—3441no—
749C22—3441no—
750C22—3441no—
751C22C2×#1306329411yescharacteristic
752C22#1458353711yescharacteristic
753C22#1458354811yescharacteristic
754C22C2×#1306335011yescharacteristic
755C22#1458369711yescharacteristic
756C22#1458370711yescharacteristic
757C22#1458371411yescharacteristic
758C4—22no—
759C4—41no—
760C4—42no—
761C4—41no—
762C4—42no—
763C4—42no—
764C4—41no—
765C4—42no—
766C4—3441no—
767C4—3441no—
768C4—1722no—
769C4#1458344511yescharacteristic
770C4#1458347711yescharacteristic
771C4#1458353711yescharacteristic
772C4#1458354811yescharacteristic
773C2—42no—
774C2—42no—
775C2—6881no—
776C2#1913819911yescharacteristic
777C2#1914384711yescharacteristic
778C2#1914391011yescharacteristic
779C2#1914661011yescharacteristic
780C2#1914685711yescharacteristic
781C2#1914703511yescharacteristic
782C2#1914715511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#552C2
socleC23×C43C22×D4
prime radical#19138035C2
hypercenterC2×#552D43
hypocenterC43#25560
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×#14583223C2semidirect
2. C2×#14583147C2semidirect
4. #19135930C2semidirect
5. #19135788C2semidirect
6. #19135738C2semidirect
7. #19135596C2semidirect
8. #19134950C2semidirect
9. #19134912C2semidirect
10. #19134903C2semidirect
11. #19134893C2semidirect
12. #19134849C2semidirect
13. #19134783C2semidirect
14. #19134316C2semidirect
15. C2×C43×#552C2semidirect
121. C22⋊Q8×C43D4semidirect
128. #117×C43D4semidirect
382. C2×#552D43semidirect
454. C43#25560semidirect
482. C22⋊Q8C22⋊D43semidirect
494. #117C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832232
C2×#145831472
#191380352
#191359302
#191357882
#191357382
#191355962
#191349502
#191349122
#191349032
#191348932
#191348492
#191347832
#191343162
C2×C43×#5522
#2556043