Finite Group Databasebeta

← C2×#19145451 #25967254

Subgroups — C2×#19145451 #25967254

Order 11008.

2378 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583479C211yesmaximal, characteristic, complemented
2C2×#14583466C211yesmaximal, characteristic, complemented
3#19145451C2116yesmaximal, direct product factor
4C2×#14583216C211yesmaximal, characteristic, complemented
5C2×#14583237C211yesmaximal, characteristic, complemented
6C2×#14583224C211yesmaximal, characteristic, complemented
7C2×#14583211C211yesmaximal, characteristic, complemented
8C2×#14583151C211yesmaximal, characteristic, complemented
9C2×#14583142C211yesmaximal, characteristic, complemented
10C2×#14583134C211yesmaximal, characteristic, complemented
11C2×#14583125C211yesmaximal, characteristic, complemented
12C2×#14583043C211yesmaximal, characteristic, complemented
13C2×#14583043C211yesmaximal, characteristic, complemented
14C2×#14583033C211yesmaximal, characteristic, complemented
15C2×#14582864C211yesmaximal, characteristic, complemented
16C2×C43×#450C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic, complemented
18C22×#10621898C2211yescharacteristic
19C22×#10621882C2211yescharacteristic
20C22×#10621882C2211yescharacteristic
21C22×#10621872C2211yescharacteristic, complemented
22C22×C8×D43C2211yescharacteristic, complemented
23#14583479—24no—
24#14583479C2218yescomplemented
25#14583466—24no—
26#14583466C2218yescomplemented
27C2×#13063321—21no—
28C2×#13063312—21no—
29C2×#13063303—21no—
30C2×#13063301C2211yescharacteristic, complemented
31C2×#13063300—21no—
32C2×#13063300C2211yescharacteristic, complemented
33C2×#13063299C2211yescharacteristic
34C2×#13063298—21no—
35C2×#13063298—21no—
36C2×#13063296C2211yescharacteristic
37C2×#13063296C2211yescharacteristic
38C2×#13063296C2211yescharacteristic
39C2×#13063296C2211yescharacteristic
40C2×#13063294—21no—
41C2×#13063294—21no—
42C2×#13063284C2211yescharacteristic
43C2×C4⋊C4×D43C2211yescharacteristic, complemented
44#14583237C2218yescomplemented
45#14583224C2218yescomplemented
46#14583216C2218yescomplemented
47#14583211C2218yescomplemented
48#14583151C2218yescomplemented
49#14583142C2218yescomplemented
50#14583134C2218yescomplemented
51#14583125C2218yescomplemented
52#14583043C2218yescomplemented
53#14583043C2218yescomplemented
54#14583033C2218yescomplemented
55C2×#13063259C2211yescharacteristic, complemented
56C2×#13063258C2211yescharacteristic, complemented
57C2×#13063257C2211yescharacteristic, complemented
58C2×#13063256C2211yescharacteristic, complemented
59C2×#13063249C2211yescharacteristic, complemented
60C2×#13063249C2211yescharacteristic, complemented
61C2×#13063247C2211yescharacteristic, complemented
62C2×#13063247C2211yescharacteristic, complemented
63C2×#13063246C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65#14582864C2218yescomplemented
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
69C23×D4×C43C2211yescharacteristic
70C22×SD16×C43C2211yescharacteristic
71C22×SD16×C43C2211yescharacteristic
72C2×C22⋊Q8×C43C2211yescharacteristic
73C43×#450C2218yescomplemented
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C2×#10621902—22no—
78C2×#10621902—42no—
79C2×#10621902—42no—
80C2×#10621902C2314yescomplemented
81C2×#10621898—42no—
82C2×#10621898—42no—
83C2×#10621898D414yes—
84C2×#10621898C2314yes—
85C22×Dic86D411yescharacteristic
86C22×D172—21no—
87C22×D172—21no—
88C22×D172D411yescharacteristic
89C22×D172C2311yescharacteristic
90C22×C22⋊D43—21no—
91C22×C22⋊D43—21no—
92C22×C22⋊D43—21no—
93C22×C22⋊D43—21no—
94C22×C22⋊D43—21no—
95C22×C22⋊D43D411yescharacteristic
96C22×C22⋊D43D411yescharacteristic
97C22×C4×D43—21no—
98C22×C4×D43—21no—
99C22×C4×D43C2311yescharacteristic
100C22×C4×D43C2311yescharacteristic
101C2×#10621882—42no—
102C2×#10621882—42no—
103C2×#10621882C2314yes—
104C2×#10621882C2314yes—
105C2×#10621872—42no—
106C2×#10621872C2314yescomplemented
107C22×C43⋊C8C2311yescharacteristic
108C22×C43⋊C8C2311yescharacteristic
109C2×C8×D43—42no—
110C2×C8×D43C2314yescomplemented
111#13063321—28no—
112#13063312—28no—
113#13063303—28no—
114#13063301—22no—
115#13063301C2314yescomplemented
116#13063300—28no—
117#13063300—22no—
118#13063300C2314yescomplemented
119#13063299—22no—
120#13063299C2314yes—
121#13063298—28no—
122#13063298—28no—
123#13063296—22no—
124#13063296—22no—
125#13063296—22no—
126#13063296—22no—
127#13063296C2314yes—
128#13063296C2314yes—
129#13063296C2314yes—
130#13063296C2314yes—
131#13063294—28no—
132#13063294—28no—
133#13063284—22no—
134#13063284C2314yes—
135C2×C4⋊Dic43C2311yescharacteristic
136C2×C4⋊Dic43C2311yescharacteristic
137C2×C4⋊Dic43C2311yescharacteristic
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C4⋊C4×D43—22no—
141C4⋊C4×D43C2314yescomplemented
142C2×C22⋊Dic43—21no—
143C2×C22⋊Dic43—21no—
144C2×C22⋊Dic43—21no—
145C2×C22⋊Dic43—21no—
146C2×C22⋊Dic43—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4—21no—
150C2×C4×Dic43—21no—
151#13063259C2314yescomplemented
152#13063258C2314yescomplemented
153#13063257C2314yescomplemented
154#13063256C2314yescomplemented
155#13063249C2314yescomplemented
156#13063249C2314yescomplemented
157#13063247C2314yescomplemented
158#13063247C2314yescomplemented
159#13063246C2314yes—
160#13063246C2314yes—
161C22⋊(C43⋊C8)C2314yes—
162(C2×D43)⋊C8C2314yescomplemented
163(C2×D43)⋊C8C2314yescomplemented
164C25×C43—21no—
165C22×Q8×C43C2311yescharacteristic
166C22×D4×C43—21no—
167C22×D4×C43—22no—
168C22×D4×C43—42no—
169C22×D4×C43—42no—
170C22×D4×C43C2311yescharacteristic
171C22×D4×C43C2311yescharacteristic
172C22×D4×C43C2314yes—
173C23×C4×C43C2311yescharacteristic
174C2×SD16×C43—42no—
175C2×SD16×C43—42no—
176C2×SD16×C43C2314yes—
177C2×SD16×C43C2314yes—
178C22×C8×C43C2311yescharacteristic
179C22×C8×C43C2311yescharacteristic
180C22⋊Q8×C43—22no—
181C22⋊Q8×C43C2314yes—
182C2×C4⋊C4×C43—21no—
183C2×C4⋊C4×C43C2311yescharacteristic
184C2×C22⋊C4×C43—21no—
185#102×C43C2314yes—
186#102×C43C2314yes—
187C22⋊C8×C43C2314yes—
188C24×C43—21no—
189C24×C43—21no—
190C24×C43—24no—
191C24×C43—44no—
192C24×C43—82no—
193C24×C43—82no—
194C24×C43C2×D411yescharacteristic
195C23×D43—21no—
196C23×D43C2×D411yescharacteristic
197C23×D43C2×D411yescharacteristic
198C2×Q8×C43—21no—
199C2×Q8×C43—22no—
200C2×Q8×C43—22no—
201C2×Q8×C43C2412yes—
202C2×D4×C43—21no—
203C2×D4×C43—21no—
204C2×D4×C43—24no—
205C2×D4×C43—22no—
206C2×D4×C43—22no—
207C2×D4×C43—22no—
208C2×D4×C43—22no—
209C2×D4×C43—44no—
210C2×D4×C43—44no—
211C2×D4×C43—48no—
212C2×D4×C43—44no—
213C2×D4×C43C2412yes—
214C2×D4×C43C2412yes—
215C22×C4×C43—22no—
216C22×C4×C43—22no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2×D412yes—
221C22×C4×C43C2412yes—
222C22×C4×C43C2411yescharacteristic
223C2×C22⋊D43—24no—
224C2×C22⋊D43—24no—
225C2×C22⋊D43—24no—
226C2×C22⋊D43—24no—
227C2×C22⋊D43—24no—
228C2×C22⋊D43—42no—
229C2×C22⋊D43—42no—
230C2×C22⋊D43—82no—
231C2×C22⋊D43—82no—
232C2×C22⋊D43—82no—
233C2×C22⋊D43—82no—
234C2×C22⋊D43—82no—
235C2×C22⋊D43C2×D414yes—
236C2×C22⋊D43C2×D414yes—
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43—21no—
240C22×Dic43C2×D411yescharacteristic
241C22×Dic43C2×D411yescharacteristic
242#10621902—44no—
243#10621902—44no—
244#10621902—48no—
245#10621898—48no—
246#10621898—44no—
247#10621898—44no—
248C2×D172—21no—
249C2×D172—24no—
250C2×D172—24no—
251C2×D172—22no—
252C2×D172—22no—
253C2×D172—42no—
254C2×D172—44no—
255C2×D172—82no—
256C2×D172C2×D414yes—
257C2×D172C2412yes—
258C2×C4×D43—22no—
259C2×C4×D43—22no—
260C2×C4×D43—22no—
261C2×C4×D43—22no—
262C2×C4×D43—24no—
263C2×C4×D43—24no—
264C2×C4×D43—44no—
265C2×C4×D43—82no—
266C2×C4×D43C2×D412yes—
267C2×C4×D43C2×D412yes—
268C2×C4×D43C2412yes—
269C2×C4×D43C2412yes—
270C2×Dic86—42no—
271C2×Dic86C2×D414yes—
272SD16×C43—44no—
273SD16×C43—44no—
274C2×C8×C43—22no—
275C2×C8×C43—22no—
276C2×C8×C43C2412yes—
277C2×C8×C43C2412yes—
278C4⋊C4×C43—24no—
279C4⋊C4×C43—21no—
280C4⋊C4×C43C2412yes—
281C22⋊C4×C43—24no—
282C22⋊Dic43—24no—
283C22⋊Dic43—24no—
284C22⋊Dic43—24no—
285C22⋊Dic43—24no—
286C22⋊Dic43—24no—
287#10621882—44no—
288#10621882—44no—
289(C2×D43)⋊C4—24no—
290(C2×D43)⋊C4—24no—
291(C2×D43)⋊C4—24no—
292C4⋊Dic43—21no—
293C4⋊Dic43—21no—
294C4⋊Dic43—21no—
295C4⋊Dic43C2412yes—
296C4⋊Dic43C2412yes—
297C4⋊Dic43C2412yes—
298Dic43⋊C4—24no—
299Dic43⋊C4—24no—
300C4×Dic43—24no—
301C2×C43⋊C8—22no—
302C2×C43⋊C8—22no—
303C2×C43⋊C8C2412yes—
304C2×C43⋊C8C2412yes—
305#10621872—44no—
306C8×D43—44no—
307C23×C43—22no—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43—22no—
311C23×C43—22no—
312C23×C43—48no—
313C23×C43—42no—
314C23×C43—42no—
315C23×C43—42no—
316C23×C43—42no—
317C23×C43—42no—
318C23×C43—42no—
319C23×C43—84no—
320C23×C43—84no—
321C23×C43—816no—
322C23×C43C22×D412yes—
323C23×C43C22×D411yescharacteristic
324C22×D43—22no—
325C22×D43—22no—
326C22×D43—22no—
327C22×D43—22no—
328C22×D43—22no—
329C22×D43—22no—
330C22×D43—22no—
331C22×D43—42no—
332C22×D43—42no—
333C22×D43—42no—
334C22×D43C22×D412yes—
335C22×D43C22×D412yes—
336Q8×C43—22no—
337Q8×C43—22no—
338Q8×C43—42no—
339D4×C43—22no—
340D4×C43—22no—
341D4×C43—22no—
342D4×C43—22no—
343D4×C43—48no—
344D4×C43—42no—
345D4×C43—42no—
346C2×C4×C43—22no—
347C2×C4×C43—24no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—42no—
353C2×C4×C43—42no—
354C2×C4×C43C22×D412yes—
355C2×C4×C43C22×D411yescharacteristic
356C2×C4×C43H(5,𝔽2)12yes—
357C2×C4×C43H(5,𝔽2)12yes—
358C2×C4×C43C2511yescharacteristic
359C22⋊D43—44no—
360C22⋊D43—44no—
361C22⋊D43—84no—
362C22⋊D43—84no—
363C22⋊D43—84no—
364C22⋊D43—84no—
365C22⋊D43—84no—
366C2×Dic43—22no—
367C2×Dic43—22no—
368C2×Dic43—22no—
369C2×Dic43—22no—
370C2×Dic43—22no—
371C2×Dic43—42no—
372C2×Dic43—42no—
373C2×Dic43—42no—
374C2×Dic43C22×D412yes—
375C2×Dic43C22×D412yes—
376D172—22no—
377D172—22no—
378D172—44no—
379D172—48no—
380D172—42no—
381D172—84no—
382C4×D43—24no—
383C4×D43—24no—
384C4×D43—22no—
385C4×D43—22no—
386C4×D43—22no—
387C4×D43—22no—
388C4×D43—48no—
389C4×D43—84no—
390Dic86—44no—
391C8×C43—22no—
392C8×C43—22no—
393C43⋊C8—22no—
394C43⋊C8—22no—
395C2×#3198—431nomaximal, Sylow
396C22×C43—22no—
397C22×C43—22no—
398C22×C43—22no—
399C22×C43—44no—
400C22×C43—42no—
401C22×C43—42no—
402C22×C43—42no—
403C22×C43—42no—
404C22×C43—42no—
405C22×C43—42no—
406C22×C43—816no—
407C22×C43—84no—
408C22×C43—84no—
409C22×C43#53412yes—
410C22×C43#57612yes—
411C22×C43#57712yes—
412C22×C43C23×D411yescharacteristic
413C2×D43—22no—
414C2×D43—22no—
415C2×D43—22no—
416C2×D43—22no—
417C2×D43—22no—
418C2×D43—22no—
419C2×D43—44no—
420C2×D43—44no—
421C2×D43—42no—
422C2×D43—42no—
423C2×D43—42no—
424C2×D43—84no—
425C4×C43—22no—
426C4×C43—42no—
427C4×C43—42no—
428C4×C43#53412yes—
429C4×C43C2×H(5,𝔽2)11yescharacteristic
430C4×C43C2×H(5,𝔽2)11yescharacteristic
431Dic43—22no—
432Dic43—22no—
433Dic43—42no—
434Dic43—42no—
435Dic43—42no—
436C2×#537—431no—
437C2×#535—431no—
438#3198—4316no—
439C2×#481—431no—
440C2×#485—431no—
441C2×#482—431no—
442C2×#480—431no—
443C2×#469—431no—
444C2×#468—431no—
445C2×#466—431no—
446C2×#465—431no—
447C2×#449—431no—
448C2×#449—431no—
449C2×#450D4311yescharacteristic, complemented
450C2×#447—431no—
451C2×#408—431no—
452C2×C43—42no—
453C2×C43—82no—
454C2×C43—82no—
455C2×C43#319814yescomplemented
456C2×C43C2×#53411yescharacteristic
457C2×C43C2×#57611yescharacteristic
458C2×C43C2×#57711yescharacteristic
459D43—42no—
460D43—42no—
461D43—82no—
462C22×#41—431no—
463C22×#41—431no—
464C23×D4C2×D4311yescharacteristic
465C22×SD16C2×D4311yescharacteristic
466C22×SD16C2×D4311yescharacteristic
467C22×D8—431no—
468C22×D8—431no—
469C22×M16—431no—
470C23×C8—431no—
471#537—438no—
472#537—864no—
473#535—438no—
474#535—864no—
475C2×#127—861no—
476C2×#124—861no—
477C2×C22⋊Q8—431no—
478C2×C22⋊Q8—861no—
479C2×C22⋊Q8C2×D4311yescharacteristic
480C2×#121—431no—
481C2×#121—431no—
482C2×#121—431no—
483C2×#121—431no—
484C2×#121—431no—
485C2×#121—431no—
486C2×#121—861no—
487C2×#121—861no—
488C2×#121—861no—
489C2×#120—861no—
490C2×#120—861no—
491C2×#117—431no—
492C22×C4⋊C4—431no—
493#485—438no—
494#482—438no—
495#481—438no—
496#480—438no—
497#469—438no—
498#468—438no—
499#466—438no—
500#465—438no—
501#450C2×D4318yescomplemented
502#449—438no—
503#449—438no—
504#447—438no—
505C2×#107—431no—
506C2×#107—431no—
507C2×#106—431no—
508C2×#106—431no—
509C2×#103—431no—
510C2×#103—431no—
511C2×#102—431no—
512C2×#102—431no—
513C2×#102—431no—
514C2×#102—431no—
515C2×#102C2×D4311yescharacteristic
516C2×#102C2×D4311yescharacteristic
517#408—438no—
518C2×C22⋊C8—431no—
519C2×C22⋊C8—431no—
520C2×C22⋊C8—431no—
521C2×C22⋊C8C2×D4311yescharacteristic
522C43C2×#319811yescharacteristic, complemented, Sylow
523C25—21no—
524C2×#41—434no—
525C2×#41—434no—
526C2×#41—434no—
527C2×#41—862no—
528C2×#41—1722no—
529C2×#41—1722no—
530C2×#41—1722no—
531C2×#41—1722no—
532C22×Q8—431no—
533C22×Q8C22×D4311yescharacteristic
534C22×D4—21no—
535C22×D4—22no—
536C22×D4—42no—
537C22×D4—42no—
538C22×D4—431no—
539C22×D4—431no—
540C22×D4—431no—
541C22×D4—431no—
542C22×D4—861no—
543C22×D4—861no—
544C22×D4—861no—
545C22×D4—861no—
546C22×D4—861no—
547C22×D4—861no—
548C22×D4—861no—
549C22×D4C22×D4311yescharacteristic
550C22×D4C22×D4311yescharacteristic
551C22×D4C22×D4314yes—
552C23×C4—431no—
553C23×C4—431no—
554C23×C4—861no—
555C23×C4—861no—
556C23×C4C22×D4311yescharacteristic
557C2×SD16—42no—
558C2×SD16—42no—
559C2×SD16C22×D4314yes—
560C2×SD16C22×D4314yes—
561C2×D8—434no—
562C2×D8—434no—
563C2×D8—1722no—
564C2×D8—1722no—
565C2×M16—434no—
566C2×M16—1722no—
567C22×C8—431no—
568C22×C8—431no—
569C22×C8—434no—
570C22×C8—1722no—
571C22×C8C22×D4311yescharacteristic
572C22×C8C22×D4311yescharacteristic
573#127—868no—
574#124—868no—
575C22⋊Q8—22no—
576C22⋊Q8—434no—
577C22⋊Q8—868no—
578C22⋊Q8—862no—
579C22⋊Q8C22×D4314yes—
580#121—434no—
581#121—434no—
582#121—434no—
583#121—434no—
584#121—434no—
585#121—434no—
586#121—868no—
587#121—868no—
588#121—862no—
589#121—868no—
590#121—862no—
591#121—862no—
592#121—862no—
593#121—862no—
594#121—862no—
595#120—868no—
596#120—868no—
597#117—434no—
598#117—862no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—431no—
601C2×C4⋊C4—431no—
602C2×C4⋊C4—431no—
603C2×C4⋊C4—434no—
604C2×C4⋊C4—862no—
605C2×C4⋊C4—861no—
606C2×C4⋊C4—861no—
607C2×C4⋊C4C22×D4311yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—861no—
610C2×C22⋊C4—861no—
611C2×C22⋊C4—861no—
612C2×C22⋊C4—861no—
613C2×C22⋊C4—861no—
614C2×C22⋊C4—861no—
615C2×C22⋊C4—861no—
616C2×C22⋊C4—861no—
617C2×C42—861no—
618#107—434no—
619#107—434no—
620#106—434no—
621#106—434no—
622#103—434no—
623#103—434no—
624#102—434no—
625#102—434no—
626#102—434no—
627#102—434no—
628#102C22×D4314yes—
629#102C22×D4314yes—
630C22⋊C8—434no—
631C22⋊C8—434no—
632C22⋊C8—434no—
633C22⋊C8C22×D4314yes—
634C24—21no—
635C24—21no—
636C24—24no—
637C24—44no—
638C24—82no—
639C24—82no—
640C24—431no—
641C24—431no—
642C24—861no—
643C24D4×D4311yescharacteristic
644#41—1728no—
645#41—1724no—
646#41—1724no—
647#41—1724no—
648#41—1724no—
649#41—1728no—
650C2×Q8—21no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—434no—
654C2×Q8—1722no—
655C2×Q8C23×D4312yes—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—24no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—22no—
663C2×D4—44no—
664C2×D4—44no—
665C2×D4—44no—
666C2×D4—48no—
667C2×D4—434no—
668C2×D4—434no—
669C2×D4—434no—
670C2×D4—432no—
671C2×D4—864no—
672C2×D4—864no—
673C2×D4—864no—
674C2×D4—864no—
675C2×D4—864no—
676C2×D4—864no—
677C2×D4—864no—
678C2×D4—861no—
679C2×D4—862no—
680C2×D4—862no—
681C2×D4—3442no—
682C2×D4—3442no—
683C2×D4—3442no—
684C2×D4—3442no—
685C2×D4—3442no—
686C2×D4—3442no—
687C2×D4—1722no—
688C2×D4—1724no—
689C2×D4—1722no—
690C2×D4—1722no—
691C2×D4C23×D4312yes—
692C2×D4C23×D4312yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—431no—
698C22×C4—431no—
699C22×C4—432no—
700C22×C4—432no—
701C22×C4—432no—
702C22×C4—432no—
703C22×C4—864no—
704C22×C4—864no—
705C22×C4—862no—
706C22×C4—862no—
707C22×C4—862no—
708C22×C4—862no—
709C22×C4—861no—
710C22×C4—861no—
711C22×C4—861no—
712C22×C4—3442no—
713C22×C4—1724no—
714C22×C4D4×D4312yes—
715C22×C4D4×D4311yescharacteristic
716C22×C4C23×D4312yes—
717C22×C4C23×D4311yescharacteristic
718SD16—44no—
719SD16—44no—
720D8—1724no—
721D8—1724no—
722M16—1724no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—432no—
726C2×C8—432no—
727C2×C8—862no—
728C2×C8—862no—
729C2×C8—1724no—
730C2×C8C23×D4312yes—
731C2×C8C23×D4312yes—
732C4⋊C4—24no—
733C4⋊C4—21no—
734C4⋊C4—432no—
735C4⋊C4—432no—
736C4⋊C4—432no—
737C4⋊C4—864no—
738C4⋊C4—864no—
739C4⋊C4—861no—
740C4⋊C4—861no—
741C4⋊C4—861no—
742C4⋊C4C23×D4312yes—
743C22⋊C4—24no—
744C22⋊C4—864no—
745C22⋊C4—864no—
746C22⋊C4—864no—
747C22⋊C4—864no—
748C22⋊C4—864no—
749C22⋊C4—864no—
750C22⋊C4—864no—
751C22⋊C4—864no—
752C42—864no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—48no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—84no—
766C23—84no—
767C23—816no—
768C23—432no—
769C23—432no—
770C23—862no—
771C23—862no—
772C23—862no—
773C23—862no—
774C23—862no—
775C23—862no—
776C23—862no—
777C23—1722no—
778C23—1722no—
779C23—1722no—
780C23C2×D4×D4312yes—
781C23C2×D4×D4311yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—42no—
785Q8—1724no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—48no—
791D4—42no—
792D4—42no—
793D4—862no—
794D4—862no—
795D4—3444no—
796D4—3444no—
797D4—3444no—
798D4—3444no—
799D4—3444no—
800D4—3444no—
801D4—1724no—
802D4—1728no—
803D4—1724no—
804D4—1724no—
805D4—1722no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—432no—
815C2×C4—432no—
816C2×C4—862no—
817C2×C4—862no—
818C2×C4—864no—
819C2×C4—864no—
820C2×C4—862no—
821C2×C4—862no—
822C2×C4—862no—
823C2×C4—862no—
824C2×C4—862no—
825C2×C4—862no—
826C2×C4—862no—
827C2×C4—3444no—
828C2×C4—1728no—
829C2×C4—1722no—
830C2×C4—1722no—
831C2×C4—1722no—
832C2×C4C2×D4×D4312yes—
833C2×C4C2×D4×D4311yescharacteristic
834C2×C4#1306337012yes—
835C2×C4#1306337012yes—
836C2×C4C24×D4311yescharacteristic
837C8—22no—
838C8—22no—
839C8—862no—
840C8—862no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—816no—
852C22—84no—
853C22—84no—
854C22—862no—
855C22—862no—
856C22—862no—
857C22—862no—
858C22—862no—
859C22—862no—
860C22—3444no—
861C22—1722no—
862C22—1722no—
863C22—1722no—
864C22—1724no—
865C22—1724no—
866C22#1458345912yes—
867C22#1458370312yes—
868C22#1458370512yes—
869C22C22×D4×D4311yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—862no—
874C4—862no—
875C4—1722no—
876C4—1722no—
877C4—1722no—
878C4#1458345912yes—
879C4C2×#1306337011yescharacteristic
880C4C2×#1306337011yescharacteristic
881C2—42no—
882C2—82no—
883C2—82no—
884C2—3442no—
885C2—1722no—
886C2—1722no—
887C2#1914545114yesdirect product factor
888C2C2×#1458345911yescharacteristic
889C2C2×#1458370311yescharacteristic
890C2C2×#1458370511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#450C2
socleC23×C43C22×D4
hypercenterC2×#450D43
hypocenterC43C2×#3198
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. C2×#14583479C2semidirect
2. C2×#14583466C2semidirect
3. #19145451C2direct (N × H)
4. C2×#14583216C2semidirect
5. C2×#14583237C2semidirect
6. C2×#14583224C2semidirect
7. C2×#14583211C2semidirect
8. C2×#14583151C2semidirect
9. C2×#14583142C2semidirect
10. C2×#14583134C2semidirect
11. C2×#14583125C2semidirect
12. C2×#14583043C2semidirect
13. C2×#14583043C2semidirect
14. C2×#14583033C2semidirect
15. C2×#14582864C2semidirect
16. C2×C43×#450C2semidirect
17. C22×#10621902C22semidirect
21. C22×#10621872C22semidirect
22. C22×C8×D43C22semidirect
24. #14583479C22semidirect
26. #14583466C22semidirect
30. C2×#13063301C22semidirect
32. C2×#13063300C22semidirect
43. C2×C4⋊C4×D43C22semidirect
44. #14583237C22semidirect
45. #14583224C22semidirect
46. #14583216C22semidirect
47. #14583211C22semidirect
48. #14583151C22semidirect
49. #14583142C22semidirect
50. #14583134C22semidirect
51. #14583125C22semidirect
52. #14583043C22semidirect
53. #14583043C22semidirect
54. #14583033C22semidirect
55. C2×#13063259C22semidirect
56. C2×#13063258C22semidirect
57. C2×#13063257C22semidirect
58. C2×#13063256C22semidirect
59. C2×#13063249C22semidirect
60. C2×#13063249C22semidirect
61. C2×#13063247C22semidirect
62. C2×#13063247C22semidirect
65. #14582864C22semidirect
67. C2×(C2×D43)⋊C8C22semidirect
68. C2×(C2×D43)⋊C8C22semidirect
73. C43×#450C22semidirect
80. C2×#10621902C23semidirect
106. C2×#10621872C23semidirect
110. C2×C8×D43C23semidirect
115. #13063301C23semidirect
118. #13063300C23semidirect
141. C4⋊C4×D43C23semidirect
151. #13063259C23semidirect
152. #13063258C23semidirect
153. #13063257C23semidirect
154. #13063256C23semidirect
155. #13063249C23semidirect
156. #13063249C23semidirect
157. #13063247C23semidirect
158. #13063247C23semidirect
162. (C2×D43)⋊C8C23semidirect
163. (C2×D43)⋊C8C23semidirect
449. C2×#450D43semidirect
455. C2×C43#3198semidirect
501. #450C2×D43semidirect
522. C43C2×#3198semidirect
887. C2#19145451direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834792
C2×#145834662
#191454512
C2×#145832162
C2×#145832372
C2×#145832242
C2×#145832112
C2×#145831512
C2×#145831422
C2×#145831342
C2×#145831252
C2×#145830432
C2×#145830332
C2×#145828642
C2×C43×#4502
C2×#319843